INSPECTION SYSTEM, INSPECTING METHOD, AND PROGRAM

Abstract

 An inspection apparatus (500) gives a measured value of a forward-and-backward-direction force and an actual value of a transformation variable to a Kalman filter, to derive state variables. At this time, a preset fixed value (0 (zero), for example) is used as values to be normally given as measured values of observation variables (accelerations of a vehicle body (11), bogies (12a, 12b), and wheel sets (13a to 13d) in a right and left direction) when performing data assimilation.

Description

TECHNICAL FIELD

[0001] The present invention relates to an inspection system, an inspection method, and a program, and is suitably used for inspecting a track of a railway vehicle, in particular. The present application is based upon and claims the benefit of priority of the prior Japanese Patent Application No. 2018-230834, filed in Japan on December 10, 2018, the entire contents of which are incorporated herein by reference.

BACKGROUND ART

[0002] When a railway vehicle travels on a track, a position of the track changes due to a load from the railway vehicle. When such a change in track occurs, there is a possibility that the railway vehicle exhibits abnormal behavior. Accordingly, Patent Literature 1 discloses a technique in which angular displacements of wheel sets in a yawing direction, state variables derived by a filter that performs data assimilation, and a measured value of a forward-and-backward-direction force being a force in a forward and backward direction that occurs in a member for supporting an axle box are substituted into motion equations that describe yawings of the wheel sets to derive track irregularity (alignment irregularity amount and the like) of a railway vehicle.

CITATION LIST

PATENT LITERATURE

[0003] Patent Literature 1: International Publication Pamphlet No. WO 2017/164133

SUMMARY OF INVENTION

TECHNICAL PROBLEM

[0004] However, in the technique described in Patent Literature 1, the measured value of the forward-and-backward-direction force and measured values of accelerations of the wheel set and a bogie (and a vehicle body in addition to the above, according to need), respectively, in a right and left direction are used when performing the data assimilation.
These measured values can be obtained without using special sensors, but the number of sensors disposed in the railway vehicle is preferably as small as possible.

[0005] The present invention has been made in view of the problems as described above, and an object thereof is to reduce the number of sensors which are used for detecting track irregularity of a railway vehicle.

SOLUTION TO PROBLEM

[0006] An inspection system of the present invention includes: a data acquisition means that acquires data of a measured value of a forward-and-backward-direction force as data of a measured value to be measured by causing a railway vehicle including a vehicle body, a bogie, and a wheel set to travel on a track; a state variable derivation means that derives state variables being variables to be determined in a state equation constituted by using motion equations that describe motions of the railway vehicle, by using the measured value of the forward-and-backward-direction force; and a track state derivation means that derives information reflecting a state of the track, in which the forward-and-backward-direction force is a force in a forward and backward direction that occurs in a member disposed between the wheel set and the bogie on which the wheel set is provided, and is a force to be determined according to a difference between an angular displacement of the wheel set in a yawing direction and an angular displacement of the bogie on which the wheel set is provided in the yawing direction, the member is a member for supporting an axle box, the forward and backward direction is a direction along a traveling direction of the railway vehicle, the yawing direction is a pivoting direction with an up and down direction being a direction vertical to the track set as a pivot axis, the state equation is an equation described by using the state variables, the forward-and-backward-direction force, and a transformation variable, the state variables include a displacement and a velocity of the bogie in a right and left direction, an angular displacement and an angular velocity of the bogie in the yawing direction, an angular displacement and an angular velocity of the bogie in a rolling direction, a displacement and a velocity of the wheel set in the right and left direction, and an angular displacement of an air spring attached to the railway vehicle in the rolling direction, and do not include an angular displacement and an angular velocity of the wheel set in the yawing direction, the rolling direction is a pivoting direction with the forward and backward direction set as a pivot axis, the transformation variable is a variable that performs mutual transformation between the angular displacement of the wheel set in the yawing direction and the angular displacement of the bogie in the yawing direction, the track state derivation means uses the angular displacement of the bogie in the yawing direction, which is one of the state variables derived by the state variable derivation means, and an actual value of the transformation variable to derive an estimated value of the angular displacement of the wheel set in the yawing direction, and uses the derived estimated value of the angular displacement of the wheel set in the yawing direction to derive the information reflecting the state of the track, the actual value of the transformation variable is derived by using the measured value of the forward-and-backward-direction force, and the state variable derivation means derives the state variables without using measured values of accelerations of the bogie, the wheel set, and the vehicle body in the right and left direction during a period in which the measured value of the forward-and-backward-direction force has been obtained.

[0007] An inspection method of the present invention includes: a data acquisition step of acquiring data of a measured value of a forward-and-backward-direction force as data of a measured value to be measured by causing a railway vehicle including a vehicle body, a bogie, and a wheel set to travel on a track; a state variable derivation step of deriving state variables being variables to be determined in a state equation constituted by using motion equations that describe motions of the railway vehicle, by using the measured value of the forward-and-backward-direction force; and a track state derivation step of deriving information reflecting a state of the track, in which the forward-and-backward-direction force is a force in a forward and backward direction that occurs in a member disposed between the wheel set and the bogie on which the wheel set is provided, and is a force to be determined according to a difference between an angular displacement of the wheel set in a yawing direction and an angular displacement of the bogie on which the wheel set is provided in the yawing direction, the member is a member for supporting an axle box, the forward and backward direction is a direction along a traveling direction of the railway vehicle, the yawing direction is a pivoting direction with an up and down direction being a direction vertical to the track set as a pivot axis, the state equation is an equation described by using the state variables, the forward-and-backward-direction force, and a transformation variable, the state variables include a displacement and a velocity of the bogie in a right and left direction, an angular displacement and an angular velocity of the bogie in the yawing direction, an angular displacement and an angular velocity of the bogie in a rolling direction, a displacement and a velocity of the wheel set in the right and left direction, and an angular displacement of an air spring attached to the railway vehicle in the rolling direction, and do not include an angular displacement and an angular velocity of the wheel set in the yawing direction, the rolling direction is a pivoting direction with the forward and backward direction set as a pivot axis, the transformation variable is a variable that performs mutual transformation between the angular displacement of the wheel set in the yawing direction and the angular displacement of the bogie in the yawing direction, the track state derivation step uses the angular displacement of the bogie in the yawing direction, which is one of the state variables derived by the state variable derivation step, and an actual value of the transformation variable to derive an estimated value of the angular displacement of the wheel set in the yawing direction, and uses the derived estimated value of the angular displacement of the wheel set in the yawing direction to derive the information reflecting the state of the track, the actual value of the transformation variable is derived by using the measured value of the forward-and-backward-direction force, and the state variable derivation step derives the state variables without using measured values of accelerations of the bogie, the wheel set, and the vehicle body in the right and left direction during a period in which the measured value of the forward-and-backward-direction force has been obtained.

[0008] A program of the present invention causes a computer to execute: a data acquisition step of acquiring data of a measured value of a forward-and-backward-direction force as data of a measured value to be measured by causing a railway vehicle including a vehicle body, a bogie, and a wheel set to travel on a track; a state variable derivation step of deriving state variables being variables to be determined in a state equation constituted by using motion equations that describe motions of the railway vehicle, by using the measured value of the forward-and-backward-direction force; and a track state derivation step of deriving information reflecting a state of the track, in which the forward-and-backward-direction force is a force in a forward and backward direction that occurs in a member disposed between the wheel set and the bogie on which the wheel set is provided, and is a force to be determined according to a difference between an angular displacement of the wheel set in a yawing direction and an angular displacement of the bogie on which the wheel set is provided in the yawing direction, the member is a member for supporting an axle box, the forward and backward direction is a direction along a traveling direction of the railway vehicle, the yawing direction is a pivoting direction with an up and down direction being a direction vertical to the track set as a pivot axis, the state equation is an equation described by using the state variables, the forward-and-backward-direction force, and a transformation variable, the state variables include a displacement and a velocity of the bogie in a right and left direction, an angular displacement and an angular velocity of the bogie in the yawing direction, an angular displacement and an angular velocity of the bogie in a rolling direction, a displacement and a velocity of the wheel set in the right and left direction, and an angular displacement of an air spring attached to the railway vehicle in the rolling direction, and do not include an angular displacement and an angular velocity of the wheel set in the yawing direction, the rolling direction is a pivoting direction with the forward and backward direction set as a pivot axis, the transformation variable is a variable that performs mutual transformation between the angular displacement of the wheel set in the yawing direction and the angular displacement of the bogie in the yawing direction, the track state derivation step uses the angular displacement of the bogie in the yawing direction, which is one of the state variables derived by the state variable derivation step, and an actual value of the transformation variable to derive an estimated value of the angular displacement of the wheel set in the yawing direction, and uses the derived estimated value of the angular displacement of the wheel set in the yawing direction to derive the information reflecting the state of the track, the actual value of the transformation variable is derived by using the measured value of the forward-and-backward-direction force, and the state variable derivation step derives the state variables without using measured values of accelerations of the bogie, the wheel set, and the vehicle body in the right and left direction during a period in which the measured value of the forward-and-backward-direction force has been obtained.

BRIEF DESCRIPTION OF DRAWINGS

[0009] 

[Fig. 1] Fig. 1 is a view illustrating one example of an outline of a railway vehicle.

[Fig. 2] Fig. 2 is a view conceptually illustrating directions of main motions of components of the railway vehicle.

[Fig. 3] Fig. 3 is a view illustrating a measured value and a calculated value of each of acceleration of a bogie in a right and left direction and accelerations of wheel sets in the right and left direction.

[Fig. 4A] Fig. 4A is a view illustrating one example of an alignment irregularity amount in a linear track.

[Fig. 4B] Fig. 4B is a view illustrating one example of an alignment irregularity amount in a curved track.

[Fig. 5] Fig. 5 is a view illustrating one example of a functional configuration of an inspection apparatus.

[Fig. 6] Fig. 6 is a view illustrating one example of a hardware configuration of the inspection apparatus.

[Fig. 7] Fig. 7 is a flowchart illustrating one example of processing in the inspection apparatus.

[Fig. 8] Fig. 8 is a view illustrating one example of a distribution of eigenvalues of an autocorrelation matrix.

[Fig. 9] Fig. 9 is a view illustrating one example of time-series data of measured values of forward-and-backward-direction forces (measured values) and time-series data of predicted values of the forward-and-backward-direction forces (calculated values).

[Fig. 10] Fig. 10 is a view illustrating one example of time-series data of high-frequency components of the forward-and-backward-direction forces.

[Fig. 11] Fig. 11 is a view illustrating one example of a configuration of an inspection system.

[Fig. 12] Fig. 12 is a view illustrating a calculation example, and is a view illustrating a curvature 1/R of a track being a target of deriving an alignment irregularity amount and a traveling velocity of the railway vehicle.

[Fig. 13A] Fig. 13A is a view illustrating a calculation example, and is a view illustrating a first example of a distribution of eigenvalues of an autocorrelation matrix R.

[Fig. 13B] Fig. 13B is a view illustrating a calculation example, and is a view illustrating a second example of a distribution of eigenvalues of the autocorrelation matrix R.

[Fig. 14] Fig. 14 is a view illustrating a calculation example, and is a view illustrating time-series data of measured values of forward-and-backward-direction forces and time-series data of predicted values of the forward-and-backward-direction forces.

[Fig. 15] Fig. 15 is a view illustrating a calculation example, and is a view illustrating time-series data of high-frequency components of the forward-and-backward-direction forces.

[Fig. 16A] Fig. 16A is a view illustrating a calculation example based on a method of a first embodiment, and is a view illustrating a first example of an alignment irregularity amount y_R.

[Fig. 16B] Fig. 16B is a view illustrating a calculation example based on the method of the first embodiment, and is a view illustrating a second example of the alignment irregularity amount y_R.

[Fig. 17A] Fig. 17A is a view illustrating a calculation example based on a method of a second embodiment, and is a view illustrating a first example of the alignment irregularity amount y_R.

[Fig. 17B] Fig. 17B is a view illustrating a calculation example based on the method of the second embodiment, and is a view illustrating the first example of the alignment irregularity amount y_R.

DESCRIPTION OF EMBODIMENTS

[0010] Hereinafter, embodiments of the present invention will be explained while referring to the drawings.

(Conception)

[0011] First, there will be explained a conception obtained by the present inventors when realizing embodiments of the present invention.

[0012] Fig. 1 is a view illustrating one example of an outline of a railway vehicle. Note that in Fig. 1, the railway vehicle is set to proceed in the positive direction of the x axis (the x axis is an axis along a traveling direction of the railway vehicle). Further, the z axis is set to a direction vertical to a track 16 (the ground) (a height direction of the railway vehicle). The y axis is set to a horizontal direction vertical to the traveling direction of the railway vehicle (a direction vertical to both the traveling direction and the height direction of the railway vehicle). Further, the railway vehicle is set to a commercial vehicle. Note that in the respective drawings, the mark of ● added inside ○ indicates the direction from the far side of the sheet toward the near side, and the mark of × added inside ○ indicates the direction from the near side of the sheet toward the far side.

[0013] As illustrated in Fig. 1, in the present embodiment, the railway vehicle includes a vehicle body 11, bogies 12a, 12b, and wheel sets 13a to 13d. As described above, in the present embodiment, the railway vehicle including the single vehicle body 11 provided with the two bogies 12a, 12b and four sets of the wheel sets 13a to 13d will be explained as an example. The wheel sets 13a to 13d have axles 15a to 15d and wheels 14a to 14d provided on both ends of the axles 15a to 15d respectively. In the present embodiment, a case where each of the bogies 12a, 12b is a bolsterless bogie will be explained as an example. Note that in Fig. 1, for convenience of illustration, only the wheels 14a to 14d on one side of the wheel sets 13a to 13d are illustrated, but wheels are also provided on the other side of the wheel sets 13a to 13d (in the example illustrated in Fig. 1, there are eight wheels in total). Further, the railway vehicle includes components other than the components illustrated in Fig. 1 (components and so on to be explained in later-described motion equations), but for convenience of illustration, illustrations of these components are omitted in Fig. 1. For example, the bogies 12a, 12b have bogie frames, bolster springs, and so on. Further, an axle box is disposed on both sides of each of the wheel sets 13a to 13d in the direction along the y axis. Further, the bogie frame and the axle box are coupled to each other by an axle box suspension. The axle box suspension is a device (suspension) to be disposed between the axle box and the bogie frame. The axle box suspension absorbs vibration to be transmitted to the railway vehicle from the track 16. Further, the axle box suspension supports the axle box in a state where the position of the axle box relative to the bogie frame is restricted, so as to prevent the axle box from moving in a direction along the x axis and a direction along the y axis relative to the bogie frame (so as to prevent these movements from occurring preferably). The axle box suspension is disposed on the both sides of each of the wheel sets 13a to 13d in the direction along the y axis. Note that the railway vehicle itself can be fabricated by a well-known technique, and thus its detailed explanation is omitted here.

[0014] When the railway vehicle travels on the track 16, acting force (creep force) between the wheels 14a to 14d and the track 16 becomes a vibration source and the vibration sequentially propagates to the wheel sets 13a to 13d, the bogies 12a, 12b, and the vehicle body 11. Fig. 2 is a view conceptually illustrating directions of main motions of the components (the wheel sets 13a to 13d, the bogies 12a, 12b, and the vehicle body 11) of the railway vehicle. The x axis, the y axis, and the z axis illustrated in Fig. 2 correspond to the x axis, the y axis, and the z axis illustrated in Fig. 1 respectively.

[0015] As illustrated in Fig. 2, in the present embodiment, a case where the wheel sets 13a to 13d, the bogies 12a, 12b, and the vehicle body 11 perform pivoting motion about the x axis as a pivot axis, pivoting motion about the z axis as a pivot axis, and motion in the direction along the y axis, will be explained as an example. In the following explanation, the pivoting motion about the x axis as a pivot axis is referred to as rolling as necessary, the pivoting direction about the x axis as a pivot axis is referred to as a rolling direction as necessary, and the direction along the x axis is referred to as the forward and backward direction as necessary. Note that the forward and backward direction is the traveling direction of the railway vehicle. In the present embodiment, the direction along the x axis is set to the traveling direction of the railway vehicle. Further, the pivoting motion about the z axis as a pivot axis is referred to as yawing as necessary, the pivoting direction about the z axis as a pivot axis is referred to as a yawing direction as necessary, and the direction along the z axis is referred to as the up and down direction as necessary. Note that the up and down direction is a direction vertical to the track 16. Further, the motion in the direction along the y axis is referred to as a transversal vibration as necessary, and the direction along the y axis is referred to as the right and left direction as necessary. Note that the right and left direction is a direction vertical to both the forward and backward direction (the traveling direction of the railway vehicle) and the up and down direction (the direction vertical to the track 16). Further, the railway vehicle performs motions other than these, but in each of the embodiments, these motions are not considered in order to simplify the explanation. However, these motions may be considered.

(First conception)

[0016] In the technique described in Patent Literature 1, the state variables are derived by performing filtering with a filter (Kalman filter) that performs data assimilation by using, as observation variables, accelerations y_w1 • •, y_w2 • •, y_w3 • •, y_w4 • • of the wheel sets 13a, 13b, 13c, 13d in the right and left direction, accelerations y_t1 • •, y_t2 • • of the bogies 12a, 12b in the right and left direction, and in addition to the above, acceleration y_b • • of the vehicle body 11 in the right and left direction according to need.

[0017] Fig. 3 illustrates a measured value and a calculated value of each of the acceleration y_t1 • • of the bogie 12a in the right and left direction and the accelerations y_w1 • •, y_w2 • • of the wheel sets 13a, 13b in the right and left direction. The calculated value is an estimated value of the observation variable calculated by data assimilation. The horizontal axis in Fig. 3 indicates an elapsed time (second) from a reference time when the reference time is set to 0 (zero). Concretely, the horizontal axis in Fig. 3 indicates a measuring time and a calculating time of the acceleration y_t1 • • of the bogie 12a in the right and left direction and the accelerations y_w1 • •, y_w2 • • of the wheel sets 13a, 13b in the right and left direction. When performing the data assimilation, the estimated value of the state variable is derived so that an error between a value which is normally given as the measured value of the observation variable and the estimated value of the observation variable becomes minimum or an expected value of this error becomes minimum.

[0018] As illustrated in Fig. 3, the measured values of the accelerations y_w1 • •, y_w2• • of the wheel sets 13a, 13b in the right and left direction, and the measured values of the accelerations y_t1 • •, y_t2 • • of the bogie 12a in the right and left direction include a lot of noises. Based on this, the present inventors obtained a finding that, depending on a state of the track 16 (rail), the estimated value does not approximate the measured value and becomes substantially a fixed value even if the data assimilation is performed. The same applies to the accelerations y_w3 • •, y_w4 • • of the wheel sets 13c, 13d in the right and left direction, the acceleration y_t2 • • of the bogie 12b in the right and left direction, and the acceleration y_b • • of the vehicle body 11 in the right and left direction. From the above, the present inventors considered that there may be a chance that, when deriving the state variables, the alignment irregularity amounts y_R1, y_R2, y_R3, y_R4 can be derived without greatly decreasing accuracy, even if the measured values of these accelerations are not used.

[Second conception]

[0019] As described in Patent Literature 1, the present inventors devised a method of calculating an alignment irregularity amount by using a measured value of force in the forward and backward direction that occurs in a member disposed between the wheel sets 13a, 13b (13c, 13d) and the bogie 12a (12b) on which these wheel sets 13a, 13b (13c, 13d) are provided. In the following explanation, the force in the forward and backward direction that occurs in the member is referred to as a forward-and-backward-direction force as necessary.

[0020] The alignment irregularity amount is calculated by using an equation representing a relation between the alignment irregularity amount and the forward-and-backward-direction force, which is an equation based on a motion equation describing motion when the railway vehicle travels on a linear track. The track 16 includes a linear portion and a curved portion. In the following explanation, the linear portion of the track 16 is referred to as a linear track as necessary and the curved portion of the track 16 is referred to as a curved track as necessary.

[0021] When a state equation is constituted by using a motion equation that describes motion of the railway vehicle traveling on the curved track in the case of performing filtering with a filter (Kalman filter) performing data assimilation, state variables may diverge. Therefore, the state equation in the case of performing filtering with the filter (Kalman filter) that performs data assimilation is constituted by using a motion equation that describes motion of the railway vehicle traveling on the linear track.

[0022] It is necessary to consider centrifugal force or the like that the railway vehicle receives when traveling in the motion equation describing the motion of the railway vehicle traveling on the curved track. Accordingly, the motion equation describing the motion of the railway vehicle traveling on the curved track includes a term including a curvature radius of the rail. Therefore, when the state variables are derived by using the filter (Kalman filter) that performs data assimilation constituted by using the motion equation that describes the motion of the railway vehicle traveling on the linear track when the railway vehicle is traveling on the curved track, there is a risk that it becomes impossible to derive the state variables with high accuracy.

[0023] The present inventors focused attention on the fact that the measured value of the forward-and-backward-direction force when the railway vehicle travels on the curved track has a certain bias relative to that when traveling on the linear track. The component itself of the forward-and-backward-direction force due to the alignment irregularity occurs in the same manner even on the curved track or the linear track. Accordingly, the present inventors thought that the alignment irregularity amount itself has nothing to do with the amount of the aforementioned bias, and thought that by reducing a low-frequency component (behavior of the aforementioned bias) from time-series data of the measured value of the forward-and-backward-direction force, the low-frequency component due to the railway vehicle traveling on the curved track can be reduced from an estimated value of the state variable even if the filter (Kalman filter) performing the data assimilation is constituted by using an equation based on the motion equation that describes the motion of the railway vehicle when traveling on the linear track. From this, the present inventors devised calculating the alignment irregularity amount by using the time-series data of the value of the forward-and-backward-direction force from which the low-frequency component has been reduced. The alignment irregularity amount is calculated as above, thereby making it possible to calculate the alignment irregularity amount in the curved track regardless of using the equation based on the motion equation describing the motion of the railway vehicle when traveling on the linear track. Further, the calculating equation of the alignment irregularity amount results in the same calculating equation even on the curved track or the linear track. Note that there is a chance that even a track, which is designed as a linear track, actually has a curvature which may exert an influence on estimation accuracy of the alignment irregularity amount. Therefore, the reduction in the low-frequency component (behavior of the aforementioned bias) from the time-series data of the measured value of the forward-and-backward-direction force contributes to improvement of the estimation accuracy of the alignment irregularity amount on not only the curved track but also the linear track. Hereinafter, explanation will be made by setting that even a track, which is designed as a linear track but actually has a curvature which may exert an influence on estimation accuracy of the alignment irregularity amount, is also regarded as a curved track.

(Motion equation)

[0024] Next, there will be explained one example of a motion equation that describes the motion of the railway vehicle. In the present embodiment, there will be explained, as an example, a case where the railway vehicle has 21 degrees of freedom while taking the motion equations described in Patent Literature 1 as an example. That is, it is set that the wheel sets 13a to 13d perform the motion in the right and left direction (transversal vibration) and the motion in the yawing direction (yawing) (2 × 4 sets = eight degrees of freedom). Further, it is set that the bogies 12a, 12b perform the motion in the right and left direction (transversal vibration), the motion in the yawing direction (yawing), and the motion in the rolling direction (rolling) (3 × 2 sets = six degrees of freedom). Further, it is set that the vehicle body 11 performs the motion in the right and left direction (transversal vibration), the motion in the yawing direction (yawing), and the motion in the rolling direction (rolling) (3 × 1 sets = three degrees of freedom). Further, it is set that air springs (bolster springs) each provided on the bogies 12a, 12b perform the motion in the rolling direction (rolling) (1 × 2 sets = two degrees of freedom). Further, it is set that yaw dampers each provided on the bogies 12a, 12b perform the motion in the yawing direction (yawing) (1 × 2 sets = two degrees of freedom).

[0025] Note that the degree of freedom is not limited to 21 degrees of freedom. When the degree of freedom increases, calculation accuracy improves, but a calculation load becomes high. Further, there is a risk that a later-described Kalman filter no longer operates stably. It is possible to appropriately determine the degree of freedom by taking these points into consideration. Further, the following motion equations can be achieved by representing actions in the respective directions (the right and left direction, the yawing direction, and the rolling direction) of the respective components (the vehicle body 11, the bogies 12a, 12b, and the wheel sets 13a to 13d) based on the descriptions of Non-Patent Literatures 1, 2, for example. Therefore, outlines of the respective motion equations will be explained here, and their detailed explanations are omitted. Note that in each of the following equations, there is no term including the curvature radius (curvature) of the track 16 (rail). That is, each of the following equations is an equation expressing the railway vehicle traveling on the linear track. The equation expressing the railway vehicle traveling on the linear track can be obtained by setting the curvature radius of the track 16 (rail) to be infinite (the curvature to 0 (zero)) in the equation expressing the railway vehicle traveling on the curved track.

[0026] In each of the following equations, each subscript w indicates the wheel sets 13a to 13d. Variables to which (only) the subscript w is added indicate that they are common to the wheel sets 13a to 13d. Subscripts w1, w2, w3, w4 indicate the wheel sets 13a, 13b, 13c, 13d respectively.

[0027] Subscripts t, T indicate the bogies 12a, 12b. Variables to which (only) the subscripts t, T are added indicate that they are common to the bogies 12a, 12b. Subscripts t1, t2 indicate the bogies 12a, 12b respectively.

[0028] Subscripts b, B indicate the vehicle body 11.

[0029] A subscript x indicates the forward and backward direction or the rolling direction, a subscript y indicates the right and left direction, and a subscript z indicates the up and down direction or the yawing direction.

[0030] Further, " • • " and "•" each added above a variable indicate a second-order time differential and a first-order time differential respectively.

[0031] Note that when the following motion equations are explained, explanations of the already-explained variables are omitted as necessary. Further, the motion equations themselves are the same as those described in Patent Literature 1.

[Transversal vibration of wheel set]

[0032] The motion equations that describe the transversal vibrations of the wheel sets 13a to 13d (motion in the right and left direction) are expressed by (1) Equation to (4) Equation below.
[Mathematical equation 1]

[0033] m_w is the mass of the wheel sets 13a to 13d. y_w1 • • is acceleration of the wheel set 13a in the right and left direction (in the equation, • • is added above y_w1 (the same applies to the other variables below)). f₂ is a lateral creep coefficient (note that the lateral creep coefficient f₂ may be given for each of the wheel sets 13a to 13d). v is a traveling velocity of the railway vehicle. y_w1 • is a velocity of the wheel set 13a in the right and left direction (in the equation, • is added above y_w1 (the same applies to the other variables below)). C_wy is a damping constant of the axle box suspension coupling the axle box and the wheel set in the right and left direction. y_t1 • is a velocity of the bogie 12a in the right and left direction. a represents 1/2 of each distance between the wheel sets 13a and 13b and between the wheel sets 13c and 13d in the forward and backward direction, which are provided on the bogies 12a, 12b (the distance between the wheel sets 13a and 13b and the distance between the wheel sets 13c and 13d, which are provided on the bogies 12a, 12b, each become 2a). φ_t1 • is an angular velocity of the bogie 12a in the yawing direction. h₁ is a distance between the center of the axle and the center of gravity of the bogie 12a in the up and down direction. φ_t1 • is an angular velocity of the bogie 12a in the rolling direction. φ_w1 is a pivot amount (angular displacement) of the wheel set 13a in the yawing direction. K_wy is a spring constant of the axle box suspension in the right and left direction. y_w1 is a displacement of the wheel set 13a in the right and left direction. y_t1 is a displacement of the bogie 12a in the right and left direction. φ_t1 is a pivot amount (angular displacement) of the bogie 12a in the yawing direction. φ_t1 is a pivot amount (angular displacement) of the bogie 12a in the rolling direction. Note that respective variables in (2) Equation to (4) Equation are represented by being replaced with the variables in (1) Equation according to the meanings of the subscripts described above.

[Yawing of wheel set]

[0034] The motion equations that describe the yawings of the wheel sets 13a to 13d are expressed by (5) Equation to (8) Equation below.
[Mathematical equation 2]

[0035] I_wz is a moment of inertia of the wheel sets 13a to 13d in the yawing direction. φ_w1 • • is angular acceleration of the wheel set 13a in the yawing direction. f₁ is a longitudinal creep coefficient. b is a distance in the right and left direction between contacts between the two wheels, which are attached to each of the wheel sets 13a to 13d, and the track 16 (rail). φ_w1 • is an angular velocity of the wheel set 13a in the yawing direction. C_wx is a damping constant of the axle box suspension in the forward and backward direction. b₁ represents the length of 1/2 of the interval between the axle box suspensions in the right and left direction (the interval of the two axle box suspensions, which are provided on the right and left sides of the single wheel set, in the right and left direction becomes 2b₁). γ is a tread slope. r is a radius of the wheels 14a to 14d. y_R1 is an alignment irregularity amount at the position of the wheel set 13a. s_a is an offset from the center of the axles 15a to 15d to an axle box suspension spring in the forward and backward direction. y_t1 is a displacement of the bogie 12a in the right and left direction. Kwx is a spring constant of the axle box suspension in the forward and backward direction. Note that respective variables in (6) Equation to (8) Equation are represented by being replaced with the variables in (5) Equation according to the meanings of the subscripts described above. However, y_R2, y_R3, y_R4 are alignment irregularity amounts at the positions of the wheel sets 13b, 13c, 13d respectively.

[0036] Here, the alignment irregularity is a lateral displacement of a rail in a longitudinal direction as described in Japan Industrial Standard (JIS E 1001: 2001). The alignment irregularity amount is an amount of the displacement. Fig. 4A and Fig. 4B each illustrate one example of the alignment irregularity amount y_R1 at the position of the wheel set 13a. In Fig. 4A, the case of the track 16 being the linear track will be explained as an example. In Fig. 4B, the case of the track 16 being the curved track will be explained as an example. In Fig. 4A and Fig. 4B, 16a denotes a rail and 16b denotes a crosstie. In Fig. 4A, it is set that the wheel 14a of the wheel set 13a is in contact with the rail 16a at a position 401. In Fig. 4B, it is set that the wheel 14a of the wheel set 13a is in contact with the rail 16a at a position 402. The alignment irregularity amount y_R1 at the position of the wheel set 13a is a distance in the right and left direction between the contact position between the wheel 14a of the wheel set 13a and the rail 16a and the position of the rail 16a in the case where this position is assumed as a regular state. The position of the wheel set 13a is the contact position between the wheel 14a of the wheel set 13a and the rail 16a. The alignment irregularity amounts y_R2, y_R3, y_R4 at the positions of the wheel sets 13b, 13c, 13d are also defined in the same manner as the alignment irregularity amount y_R1 at the position of the wheel set 13a.

[Transversal vibration of bogie]

[0037] The motion equations that describe the transversal vibrations of the bogies 12a, 12b (motion in the right and left direction) are expressed by (9) Equation and (10) Equation below.
[Mathematical equation 3]

[0038] m_T is the mass of the bogies 12a, 12b. y_t1 • • is acceleration of the bogie 12a in the right and left direction. c'₂ is a damping constant of a lateral movement damper. h₄ is a distance between the center of gravity of the bogie 12a and the lateral movement damper in the up and down direction. y_b • is a velocity of the vehicle body 11 in the right and left direction. L represents 1/2 of the interval between the center of the bogie 12a and the center of the bogie 12b in the forward and backward direction (the interval between the center of the bogie 12a and the center of the bogie 12b in the forward and backward direction becomes 2L). φ_b • is an angular velocity of the vehicle body 11 in the yawing direction. h₅ is a distance between the lateral movement damper and the center of gravity of the vehicle body 11 in the up and down direction. φ_b • is an angular velocity of the vehicle body 11 in the rolling direction. y_w2 • is a velocity of the wheel set 13b in the right and left direction. k'₂ is a spring constant of the air spring (bolster spring) in the right and left direction. h₂ is a distance between the center of gravity of each of the bogies 12a, 12b and the center of the air spring (bolster spring) in the up and down direction. y_b is a displacement of the vehicle body 11 in the right and left direction. φ_b is a pivot amount (angular displacement) of the vehicle body 11 in the yawing direction. h₃ is a distance between the center of the air spring (bolster spring) and the center of gravity of the vehicle body 11 in the up and down direction. φ_b is a pivot amount (angular displacement) of the vehicle body 11 in the rolling direction. Note that respective variables in (10) Equation are represented by being replaced with the variables in (9) Equation according to the meanings of the subscripts described above.

[Yawing of bogie]

[0039] The motion equations that describe the yawings of the bogies 12a, 12b are expressed by (11) Equation and (12) Equation below.
[Mathematical equation 4]

[0040] I_Tz is a moment of inertia of the bogies 12a, 12b in the yawing direction. φ_t1 • • is angular acceleration of the bogie 12a in the yawing direction. φ_w2 • is an angular velocity of the wheel set 13b in the yawing direction. φ_w2 is a pivot amount (angular displacement) of the wheel set 13b in the yawing direction. y_w2 is a displacement of the wheel set 13b in the right and left direction. k'₀ is stiffness of a rubber bush of the yaw damper. b'₀ represents 1/2 of the interval between the two yaw dampers, which are disposed on the right and left sides of each of the bogies 12a, 12b, in the right and left direction (the interval between the two yaw dampers, which are disposed on the right and left sides of each of the bogies 12a, 12b, in the right and left direction becomes 2b'₀). φ_y1 is a pivot amount (angular displacement) of the yaw damper disposed on the bogie 12a in the yawing direction. k"₂ is a spring constant of the air spring (bolster spring) in the forward and backward direction. b₂ represents 1/2 of the interval between the two air springs (bolster springs), which are disposed on the right and left sides of each of the bogies 12a, 12b, in the right and left direction (the interval between the two air springs (bolster springs), which are disposed on the right and left sides of each of the bogies 12a, 12b, in the right and left direction becomes 2b₂). Note that respective variables in (12) Equation are represented by being replaced with the variables in (11) Equation according to the meanings of the subscripts described above.

[Rolling of bogie]

[0041] The motion equations that describe the rollings of the bogies 12a, 12b are expressed by (13) Equation and (14) Equation below.
[Mathematical equation 5]

[0042] I_Tx is a moment of inertia of the bogies 12a, 12b in the rolling direction. φ_t1 • • is angular acceleration of the bogie 12a in the rolling direction. c₁ is a damping constant of an axle damper in the up and down direction. b'₁ represents 1/2 of the interval between the two axle dampers, which are disposed on the right and left sides of each of the bogies 12a, 12b, in the right and left direction (the interval between the two axle dampers, which are disposed on the right and left sides of each of the bogies 12a, 12b, in the right and left direction becomes 2b'₁). c₂ is a damping constant of the air spring (bolster spring) in the up and down direction. φ_a1 • is an angular velocity of the air spring (bolster spring) disposed on the bogie 12a in the rolling direction. k₁ is a spring constant of an axle spring in the up and down direction. λ is a value obtained by dividing the volume of the air spring (bolster spring) main body by the volume of an auxiliary air chamber. k₂ is a spring constant of the air spring (bolster spring) in the up and down direction. φ_a1 is a pivot amount (angular displacement) of the air spring (bolster spring) disposed on the bogie 12a in the rolling direction. k₃ is equivalent stiffness by a change in effective pressure receiving area of the air spring (bolster spring). Note that respective variables in (14) Equation are represented by being replaced with the variables in (13) Equation according to the meanings of the subscripts described above. Note that φ_a2 is a pivot amount (angular displacement) of the air spring (bolster spring) disposed on the bogie 12b in the rolling direction.

[Transversal vibration of vehicle body]

[0043] The motion equation that describes the transversal vibration of the vehicle body 11 (motion in the right and left direction) is expressed by (15) Equation below.
[Mathematical equation 6]

[0044] m_B is the mass of the bogies 12a, 12b. y_b • • is acceleration of the vehicle body 11 in the right and left direction. y_t2 • is a velocity of the bogie 12b in the right and left direction. φ_t2 • is an angular velocity of the bogie 12b in the rolling direction. y_t2 is a displacement of the bogie 12b in the right and left direction. φ_t2 is a pivot amount (angular displacement) of the bogie 12b in the rolling direction.

[Yawing of vehicle body]

[0045] The motion equation that describes the yawing of the vehicle body 11 is expressed by (16) Equation below.
[Mathematical equation 7]

[0046] I_Bz is a moment of inertia of the vehicle body 11 in the yawing direction. φ_b • • is angular acceleration of the vehicle body 11 in the yawing direction. c₀ is a damping constant of the yaw damper in the forward and backward direction. φ_y1 • is an angular velocity of the yaw damper disposed on the bogie 12a in the yawing direction. φ_y2 • is an angular velocity of the yaw damper disposed on the bogie 12b in the yawing direction. φ_t2 is a pivot amount (angular displacement) of the bogie 12b in the yawing direction.

[Rolling of vehicle body]

[0047] The motion equation that describes the rolling of the vehicle body 11 is expressed by (17) Equation below.
[Mathematical equation 8]

[0048] I_Bx is a moment of inertia of the vehicle body 11 in the rolling direction. φ_b • • is angular acceleration of the vehicle body 11 in the rolling direction.

[Yawing of yaw damper]

[0049] The motion equations that describe the yawing of the yaw damper disposed on the bogie 12a and the yawing of the yaw damper disposed on the bogie 12b are expressed by (18) Equation and (19) Equation below respectively.
[Mathematical equation 9]

[0050] φ_y2 is a pivot amount (angular displacement) of the yaw damper disposed on the bogie 12b in the yawing direction.

[Rolling of air spring (bolster spring)]

[0051] The motion equations that describe the rolling of the air spring (bolster spring) disposed on the bogie 12a and the rolling of the air spring (bolster spring) disposed on the bogie 12b are expressed by (20) Equation and (21) Equation below respectively.
[Mathematical equation 10]

[0052] φ_a2 • is an angular velocity of the air spring (bolster spring) disposed on the bogie 12b in the rolling direction.

(Forward-and-backward-direction force)

[0053] Next, the forward-and-backward-direction force will be explained. Note that the forward-and-backward-direction force itself is the same as that described in Patent Literature 1.

[0054] In-phase components of the longitudinal creep force in one wheel of right and left wheels in one wheel set and the longitudinal creep force in the other wheel are components corresponding to a braking force and a driving force. Accordingly, the forward-and-backward-direction force is preferably determined so as to correspond to an opposite-phase component of the longitudinal creep force. The opposite-phase component of the longitudinal creep force is a component to be opposite in phase to each other between the longitudinal creep force in one wheel of the right and left wheels in one wheel set and the longitudinal creep force in the other wheel. That is, the opposite-phase component of the longitudinal creep force is a component, of the longitudinal creep force, in the direction in which the axle is twisted. In this case, the forward-and-backward-direction force becomes a component opposite in phase to each other out of forward-and-backward-direction components of forces that occur in the aforementioned two members attached to both the right and left sides of one wheel set.

[0055] Hereinafter, there will be explained concrete examples of the forward-and-backward-direction force in the case where the forward-and-backward-direction force is determined so as to correspond to the opposite-phase component of the longitudinal creep force.

[0056] In the case of the axle box suspension being a mono-link type axle box suspension, the axle box suspension includes a link, and the axle box and the bogie frame are coupled by the link. A rubber bush is attached to both ends of the link. In this case, the forward-and-backward-direction force becomes, out of forward-and-backward-direction components of loads that two links, which are attached to right and left ends of one wheel set one by one, receive, the component to be opposite in phase to each other. Further, due to arrangement and constitution of the links, the link mainly receives, out of loads in the forward and backward direction, the right and left direction, and the up and down direction, the load in the forward and backward direction. Accordingly, one strain gauge only needs to be attached to each link, for example. By using a measured value of the strain gauge, the forward-and-backward-direction component of the load that this link receives is derived, to thereby obtain a measured value of the forward-and-backward-direction force. Further, in place of applying such a design, a forward-and-backward-direction displacement of the rubber bush attached to the link may be measured by a displacement meter. In this case, the product of a measured displacement and a spring constant of this rubber bush is set as the measured value of the forward-and-backward-direction force. In the case of the axle box suspension being the mono-link type axle box suspension, the previously-described member for supporting the axle box becomes the link or the rubber bush.

[0057] Note that the load measured by the strain gauge attached to the link sometimes includes not only the component in the forward and backward direction, but also at least one component of a component in the right and left direction and a component in the up and down direction. However, even in such a case, due to the structure of the axle box suspension, the load of the component in the right and left direction and the load of the component in the up and down direction that the link receives are sufficiently smaller than the load of the component in the forward and backward direction. Accordingly, only attaching one strain gauge to each link makes it possible to obtain a measured value of the forward-and-backward-direction force, which has accuracy to be required practically. In this manner, the components other than the component in the forward and backward direction are sometimes included in the measured value of the forward-and-backward-direction force. Therefore, three or more strain gauges may be attached to each link so as to cancel the strains in the up and down direction and the right and left direction. This makes it possible to improve the accuracy of the measured value of the forward-and-backward-direction force.

[0058] In the case of the axle box suspension being an axle beam type axle box suspension, the axle box suspension includes an axle beam, and the axle box and the bogie frame are coupled by the axle beam. The axle beam may be formed integrally with the axle box. A rubber bush is attached to a bogie frame-side end of the axle beam. In this case, the forward-and-backward-direction force becomes, out of forward-and-backward-direction components of loads that two axle beams, which are attached to right and left ends of one wheel set one by one, receive, the component to be opposite in phase to each other. Further, due to arrangement and constitution of the axle beams, the axle beam is likely to receive, out of loads in the forward and backward direction, the right and left direction, and the up and down direction, the load in the right and left direction, in addition to the load in the forward and backward direction. Accordingly, two or more strain gauges are attached to each axle beam so as to cancel the strain in the right and left direction, for example. By using measured values of these strain gauges, the forward-and-backward-direction component of the load that the axle beam receives is derived, to thereby obtain a measured value of the forward-and-backward-direction force. Further, in place of applying such a design, a forward-and-backward-direction displacement of the rubber bush attached to the axle beam may be measured by a displacement meter. In this case, the product of a measured displacement and a spring constant of this rubber bush is set as the measured value of the forward-and-backward-direction force. In the case of the axle box suspension being the axle beam type axle box suspension, the previously-described member for supporting the axle box becomes the axle beam or the rubber bush.

[0059] Note that the load measured by the strain gauge attached to the axle beam sometimes includes not only the components in the forward and backward direction and the right and left direction, but also the component in the up and down direction. However, even in such a case, due to the structure of the axle box suspension, the load of the component in the up and down direction that the axle beam receives is sufficiently smaller than the load of the component in the forward and backward direction and the load of the component in the right and left direction. Accordingly, even if the strain gauge is not attached so as to cancel the load of the component in the up and down direction that the axle beam receives, a measured value of the forward-and-backward-direction force, which has accuracy to be required practically, can be obtained. In this manner, the components other than the component in the forward and backward direction are sometimes included in the measured forward-and-backward-direction force, and thus three or more strain gauges may be attached to each axle beam so as to cancel the strain in the up and down direction as well as the strain in the right and left direction. This makes it possible to improve the accuracy of the measured value of the forward-and-backward-direction force.

[0060] In the case of the axle box suspension being a leaf spring type axle box suspension, the axle box suspension includes a leaf spring, and the axle box and the bogie frame are coupled by the leaf spring. A rubber bush is attached to ends of the leaf spring. In this case, the forward-and-backward-direction force becomes, out of forward-and-backward-direction components of loads that two leaf springs, which are attached to right and left ends of one wheel set one by one, receive, the component to be opposite in phase to each other. Further, due to arrangement and constitution of the leaf springs, the leaf spring is likely to receive, out of loads in the forward and backward direction, the right and left direction, and the up and down direction, the load in the right and left direction and the load in the up and down direction, in addition to the load in the forward and backward direction. Accordingly, three or more strain gauges are attached to each leaf spring so as to cancel the strains in the right and left direction and the up and down direction, for example. By using measured values of these strain gauges, the forward-and-backward-direction component of the load that the leaf spring receives is derived, to thereby obtain a measured value of the forward-and-backward-direction force. Further, in place of applying such a design, a forward-and-backward-direction displacement of the rubber bush attached to the leaf spring may be measured by a displacement meter. In this case, the product of a measured displacement and a spring constant of this rubber bush is set as the measured value of the forward-and-backward-direction force. In the case of the axle box suspension being the leaf spring type axle box suspension, the previously-described member for supporting the axle box becomes the leaf spring or the rubber bush.

[0061] Note that as the previously-described displacement meter, a well-known laser displacement meter or eddy current displacement meter can be used.

[0062] Further, the forward-and-backward-direction force has been explained here by taking the case of the system of the axle box suspension being a mono-link type, an axle beam type, and a leaf spring type as an example. However, the system of the axle box suspension is not limited to the mono-link type, the axle beam type, and the leaf spring type. In conformity with the system of the axle box suspension, the forward-and-backward-direction force can be determined in the same manner as in the mono-link type, the axle beam type, and the leaf spring type.

[0063] Further, the case where a measured value of a single forward-and-backward-direction force can be obtained in one wheel set will be explained as an example, in order to simplify the explanation below. That is, the railway vehicle illustrated in Fig. 1 has the four wheel sets 13a to 13d. Accordingly, it is possible to obtain measured values of four forward-and-backward-direction forces T₁ to T₄.

(First embodiment)

[0064] Next, a first embodiment of the present invention will be described.

<Inspection apparatus 500>

[0065] Fig. 5 is a view illustrating one example of a functional configuration of an inspection apparatus 500. Fig. 6 is a view illustrating one example of a hardware configuration of the inspection apparatus 500. Fig. 7 is a flowchart illustrating one example of processing in the inspection apparatus 500. In the present embodiment, as illustrated in Fig. 1, the case where the inspection apparatus 500 is mounted on the railway vehicle will be explained as an example.

[0066] In Fig. 5, the inspection apparatus 500 includes, as its functions, a storage unit 501, a data acquisition unit 502, a first frequency adjustment unit 503, a state variable derivation unit 504, a second frequency adjustment unit 505, a track state derivation unit 506, and an output unit 507.

[0067] In Fig. 6, the inspection apparatus 500 includes a CPU 601, a main memory 602, an auxiliary memory 603, a communication circuit 604, a signal processing circuit 605, an image processing circuit 606, an I/F circuit 607, a user interface 608, a display 609, and a bus 610.

[0068] The CPU 601 overall controls the entire inspection apparatus 500. The CPU 601 uses the main memory 602 as a work area to execute a program stored in the auxiliary memory 603. The main memory 602 stores data temporarily. The auxiliary memory 603 stores various kinds of data, in addition to programs to be executed by the CPU 601. The auxiliary memory 603 stores later-described state equations and observation equations. The storage unit 501 is fabricated by using the CPU 601 and the auxiliary memory 603, for example.

[0069] The communication circuit 604 is a circuit intended for performing communication with the outside of the inspection apparatus 500. The communication circuit 604 receives information of the measured value of the forward-and-backward-direction force, for example. The communication circuit 604 may perform radio communication or wire communication with the outside of the inspection apparatus 500.
The communication circuit 604 is connected to an antenna provided on the railway vehicle in the case of performing radio communication.

[0070] The signal processing circuit 605 performs various kinds of signal processing on signals received by the communication circuit 604 and signals input according to the control made by the CPU 601. The data acquisition unit 502 is fabricated by using the CPU 601, the communication circuit 604, and the signal processing circuit 605, for example. Further, the first frequency adjustment unit 503, the state variable derivation unit 504, the second frequency adjustment unit 505, and the track state derivation unit 506 are fabricated by using the CPU 601 and the signal processing circuit 605, for example.

[0071] The image processing circuit 606 performs various kinds of image processing on signals input according to the control made by the CPU 601. The signal after being subjected to the image processing is output to the display 609.

[0072] The user interface 608 is a part through which an operator gives an instruction to the inspection apparatus 500. The user interface 608 includes buttons, switches, dials, and so on, for example. Further, the user interface 608 may include a graphical user interface using the display 609.

[0073] The display 609 displays an image based on a signal output from the image processing circuit 606. The I/F circuit 607 exchanges data with a device connected to the I/F circuit 607. In Fig. 6, as the device to be connected to the I/F circuit 607, the user interface 608 and the display 609 are illustrated. However, the device to be connected to the I/F circuit 607 is not limited to these. For example, a portable storage medium may be connected to the I/F circuit 607. Further, at least a part of the user interface 608 and the display 609 may be provided outside the inspection apparatus 500.

[0074] The output unit 507 is fabricated by using at least any one of a set including the communication circuit 604, and the signal processing circuit 605, and a set including the image processing circuit 606, the I/F circuit 607, and the display 609, for example.

[0075] Note that the CPU 601, the main memory 602, the auxiliary memory 603, the signal processing circuit 605, the image processing circuit 606, and the I/F circuit 607 are connected to the bus 610. Communication among these components is performed via the bus 610. Further, the hardware of the inspection apparatus 500 is not limited to the one illustrated in Fig. 6 as long as it can realize later-described functions of the inspection apparatus 500.

[Storage unit 501]

[0076] The storage unit 501 stores equations which are used when the later-described state variable derivation unit 504 derives the state variables.

[0077] In the present embodiment, the storage unit 501 stores state equations and observation equations.

[0078] In the present embodiment, the case of using the state equations and the observation equations described in Patent Literature 1 will be explained as an example.

[0079] First, the state equation will be described.

[0080] In the present embodiment, (5) Equation to (8) Equation (the motion equations that describe the yawings of the wheel sets 13a to 13d) are not included in the state equation, and the state equation is constituted as follows.

[0081] First, (9) Equation and (10) Equation (the motion equations that describe the transversal vibrations of the bogies 12a, 12b (motion in the right and left direction)), (13) Equation and (14) Equation (the motion equations that describe the rollings of the bogies 12a, 12b), (15) Equation (the motion equation that describes the transversal vibration of the vehicle body 11 (motion in the right and left direction)), (16) Equation (the motion equation that describes the yawing of the vehicle body 11), (17) Equation (the motion equation that describes the rolling of the vehicle body 11), (18) Equation and (19) Equation (the motion equations that describe the yawings of the yaw damper disposed on the bogie 12a and the yaw damper disposed on the bogie 12b), and (20) Equation and (21) Equation (the motion equations that describe the rollings of the air spring (bolster spring) disposed on the bogie 12a and the air spring (bolster spring) disposed on the bogie 12b) are used as they are to constitute the state equation.

[0082] Meanwhile, in (1) Equation to (4) Equation (the motion equations that describe the transversal vibrations of the wheel sets 13a to 13d (motion in the right and left direction)) and (11) Equation and (12) Equation (the motion equations that describe the yawings of the bogies 12a, 12b), the pivot amounts (angular displacements) φ_w1 to φ_w4 and the angular velocities φ_w1 • to φ_w4 • of the wheel sets 13a to 13d in the yawing direction are included. Results obtained after eliminating these variables from (1) Equation to (4) Equation, (11) Equation, and (12) Equation are used to constitute the state equation.

[0083] First, the forward-and-backward-direction forces T₁ to T₄ of the wheel sets 13a to 13d are expressed by (22) Equation to (25) Equation below.

[0084] In this manner, the forward-and-backward-direction forces T₁ to T₄ are determined according to the differences between the angular displacements φ_w1 to φ_w4 of the wheel sets in the yawing direction and the angular displacements φ_t1 and φ_t2 of the bogies on which these wheel sets are provided in the yawing direction.
[Mathematical equation 11]

[0085] Transformation variables e₁ to e₄ are defined as in (26) Equation to (29) Equation below. As above, the transformation variables e₁ to e₄ are defined by the differences between the angular displacements φ_t1 and φ_t2 of the bogies in the yawing direction and the angular displacements φ_w1 to φ_w4 of the wheel sets in the yawing direction. The transformation variables e₁ to e₄ are variables for performing mutual transformation between the angular displacements φ_t1 and φ_t2 of the bogies in the yawing direction and the angular displacements φ_w1 to φ_w4 of the wheel sets in the yawing direction.
[Mathematical equation 12]

[0086] When (26) Equation to (29) Equation are modified, (30) Equation to (33) Equation below are obtained.
[Mathematical equation 13]

[0087] When (30) Equation to (33) Equation are substituted into the motion equations that describe the transversal vibrations of the wheel sets 13a to 13d (motion in the right and left direction) of (1) Equation to (4) Equation, (34) Equation to (37) Equation below are obtained.
[Mathematical equation 14]

[0088] As above, (1) Equation to (4) Equation (the motion equations that describe the transversal vibrations of the wheel sets 13a to 13d (motion in the right and left direction)) are expressed by using the transformation variables e₁ to e₄, thereby making it possible to eliminate the pivot amounts (angular displacements) φ_w1 to φ_w4 of the wheel sets 13a to 13d in the yawing direction that are included in these motion equations.

[0089] When (22) Equation to (25) Equation are substituted into (11) Equation and (12) Equation (the motion equations that describe the yawings of the bogies 12a, 12b), (38) Equation and (39) Equation below are obtained.
[Mathematical equation 15]

[0090] As above, (11) Equation and (12) Equation (the motion equations that describe the yawings of the bogies 12a, 12b) are expressed by using the forward-and-backward-direction forces T₁ to T₄, thereby making it possible to eliminate the angular displacements φ_w1 to φ_w4 and the angular velocities φ _w1. to φ_w4. of the wheel sets 13a to 13d in the yawing direction that are included in these motion equations.

[0091] Further, when (26) Equation to (29) Equation are substituted into (22) Equation to (25) Equation, (40) Equation to (43) Equation below are obtained.
[Mathematical equation 16]

[0092] As above, in the present embodiment, as in (34) Equation to (37) Equation, the motion equations that describe the transversal vibrations of the wheel sets 13a to 13d (motion in the right and left direction) are expressed, and at the same time, as in (38) Equation and (39) Equation, the motion equations that describe the yawings of the bogies 12a, 12b are expressed. The state equation is constituted by using (34) Equation to (39) Equation. Further, (40) Equation to (43) Equation are ordinary differential equations. Actual values of the transformation variables e₁ to e₄, which are solutions of the ordinary differential equations, can be derived by using the values of the forward-and-backward-direction forces T₁ to T₄ in the wheel sets 13a to 13d. Here, the values of the forward-and-backward-direction forces T₁ to T₄ are obtained by reducing a signal strength of a low-frequency component to be generated due to the railway vehicle traveling on the curved portion of the track from the time-series data of the measured value of the forward-and-backward-direction force, with the use of the later-described first frequency adjustment unit 503.

[0093] The actual values of the transformation variables e₁ to e₄ derived as above are given to (34) Equation to (37) Equation. Further, the values of the forward-and-backward-direction forces T₁ to T₄ in the wheel sets 13a to 13d are given to (38) Equation and (39) Equation. Here, the values of the forward-and-backward-direction forces T₁ to T₄ are obtained by reducing a signal strength of a low-frequency component to be generated due to the railway vehicle traveling on the curved portion of the track from the time-series data of the measured value of the forward-and-backward-direction force, with the use of the later-described first frequency adjustment unit 503.

[0094] In the present embodiment, variables illustrated in (44) Equation below are set as the state variables, and by using the motion equations of (9) Equation, (10) Equation, (13) Equation to (21) Equation, and (34) Equation to (39) Equation, the state equation is constituted.
[Mathematical equation 17]

[0095] The storage unit 501 receives the state equation constituted as above, for example, based on the operation of the user interface 608 made by an operator and stores it.

[0096] Next, the observation equation will be described.

[0097] In the present embodiment, the acceleration of the vehicle body 11 in the right and left direction, the accelerations of the bogies 12a, 12b in the right and left direction, and the accelerations of the wheel sets 13a to 13d in the right and left direction are set to observation variables. These observation variables are observation variables of filtering by a later-described Kalman filter. In the present embodiment, (34) Equation to (37) Equation, (9) Equation, (10) Equation, and (15) Equation (the motion equations that describe the transversal vibrations) are used to constitute an observation equation.

[0098] The storage unit 501 receives the observation equation constituted in this manner, for example, based on the operation of the user interface 608 made by an operator and stores it.

[0099] After the state equation and the observation equation are stored in the inspection apparatus 500 as above, the data acquisition unit 502, the first frequency adjustment unit 503, the state variable derivation unit 504, the second frequency adjustment unit 505, the track state derivation unit 506, and the output unit 507 start. Specifically, the processing according to the flowchart in Fig. 7 starts after the state equation and the observation equation are stored in the inspection apparatus 500.

[Data acquisition unit 502, S701]

[0100] The data acquisition unit 502 acquires time-series data of the measured value of the forward-and-backward-direction force. The method of measuring the forward-and-backward-direction force is as described previously. The data acquisition unit 502 can acquire the time-series data of the measured value of the forward-and-backward-direction force by performing communication with an arithmetic device that calculates the forward-and-backward-direction force by using a measured value of a strain gauge for measuring the forward-and-backward-direction force, for example. Note that the data acquisition unit 502 does not acquire time-series data of a measured value of the acceleration of the vehicle body 11 in the right and left direction, time-series data of measured values of the accelerations of the bogies 12a, 12b in the right and left direction, and time-series data of measured values of the accelerations of the wheel sets 13a to 13d in the right and left direction.

[First frequency adjustment unit 503, S702]

[0101] The first frequency adjustment unit 503 reduces (preferably removes) the signal strength of the low-frequency component included in the time-series data of the measured value of the forward-and-backward-direction force acquired by the data acquisition unit 502. A signal of this low-frequency component is a signal that is not measured when the railway vehicle is traveling on the linear track whose curvature is 0 (zero), but is measured when the railway vehicle is traveling on the curved track. That is, the signal measured when the railway vehicle is traveling on the curved track can be regarded as a signal obtained by superimposing the signal of this low-frequency component on the signal measured when the railway vehicle is traveling on the linear track whose curvature is 0 (zero).

[0102] The present inventors devised a model in which an AR (Auto-regressive) model is corrected. Further, the present inventors came up with an idea of reducing the signal strength of the low-frequency component included in the time-series data of the measured value of the forward-and-backward-direction force by using this model. In the following explanation, the model devised by the present inventors is referred to as a corrected AR model. In contrast to this, the well-known AR model is referred to as an AR model simply. Hereinafter, there will be explained one example of the corrected AR model.

[0103] A value of time-series data of a physical quantity y at a time k (1 ≦ k ≦ M) is set to y_k. M is a number indicating, as the time-series data of the physical quantity y, data until when is contained, and is preset. In the following explanation, the time-series data of the physical quantity will be abbreviated to data y as necessary. The AR model approximating the value y_k of the data y is as in (45) Equation below, for example. The AR model is, as illustrated in (45) Equation, an equation expressing a predicted value y^_k of the physical quantity at the time k (m+1 ≦ k ≦ M) in the data y by using an actual value y_k-l of the physical quantity at a time k-l (1 ≦ l ≦ m) prior to the time k in the data y. Note that y^_k is expressed by adding ^ above y_k in (45) Equation.
[Mathematical equation 18]

[0104] In (45) Equation, α is a coefficient of the AR model. m is a number of the value of the data y to be used for approximating the value y_k of the data y at the time k in the AR model, and is a number among values y_k-1 to y_k-m of the data y at continuous times k-1 to k-m prior to the time k. m is an integer of less than M. As m, for example, 1500 can be used.

[0105] Subsequently, there is derived a conditional expression for approximating the predicted value y^_k of the physical quantity at the time k by the AR model to the value y_k by using a least square method. As the condition for approximating the predicted value y^_k of the physical quantity at the time k by the AR model to the value y_k, it is possible to employ a condition that minimizes a square error between the predicted value y^_k of the physical quantity at the time k by the AR model and the value y_k, for example. That is, the least square method is used in order to approximate the predicted value y^_k of the physical quantity at the time k by the AR model to the value y_k. (46) Equation below is a conditional expression for minimizing the square error between the predicted value y^_k of the physical quantity at the time k by the AR model and the value y_k.
[Mathematical equation 19]

[0106] The relation of (47) Equation below is established by (46) Equation.
[Mathematical equation 20]

[0107] Further, (47) Equation is modified (expressed in matrix notation form), and thereby (48) Equation below is obtained.
[Mathematical equation 21]

[0108] R_jl in (48) Equation is called autocorrelation of the data y, and is a value defined by (49) Equation below. |j-l| at this time is referred to as a time lag.
[Mathematical equation 22]

[0109] Based on (48) Equation, (50) Equation below is considered. (50) Equation is an equation derived from a condition that minimizes the error between the predicted value y^_k of the physical quantity at the time k by the AR model and the value y_k of the physical quantity at the time k corresponding to the predicted value y^_k. (50) Equation is called a Yule-Walker equation. Further, (50) Equation is a linear equation in which a vector composed of coefficients of the AR model is set to a variable vector. A constant vector on the left side in (50) Equation is a vector whose component is the autocorrelation of the data y with a time lag of 1 to m. In the following explanation, the constant vector on the left side in (50) Equation is referred to as an autocorrelation vector as necessary. Further, a coefficient matrix on the right side in (50) Equation is a matrix whose component is the autocorrelation of the data y with a time lag of 0 to m-1. In the following explanation, the coefficient matrix on the right side in (50) Equation is referred to as an autocorrelation matrix as necessary.
[Mathematical equation 23]

[0110] Further, the autocorrelation matrix on the right side in (50) Equation (a matrix of m×m composed of R_jl) is described as an autocorrelation matrix R as in (51) Equation below.
[Mathematical equation 24]

[0111] In general, when deriving the coefficient of the AR model, a method of solving (50) Equation regarding a coefficient α is used. In (50) Equation, the coefficient α is derived so as to make the predicted value y^_k of the physical quantity at the time k derived by the AR model come close to the value y_k of the physical quantity at the time k as much as possible. Therefore, frequency characteristics of the AR model include a large number of frequency components included in the value y_k of the data y at each time.

[0112] Accordingly, the present inventors focused on the autocorrelation matrix R to be multiplied by the coefficient α of the AR model and earnestly examined it. As a result of this, the present inventors found out that it is possible to reduce the influence of a high-frequency component included in the data y by using a part of eigenvalues of the autocorrelation matrix R. That is, the present inventors found out that it is possible to rewrite the autocorrelation matrix R so that the low-frequency component is emphasized.

[0113] There will be explained a concrete example of the above below.

[0114] The autocorrelation matrix R is subjected to singular value decomposition. Elements of the autocorrelation matrix R are symmetric. Therefore, when the autocorrelation matrix R is subjected to singular value decomposition, as in (52) Equation below, the result becomes the product of an orthogonal matrix U, a diagonal matrix Σ, and a transposed matrix of the orthogonal matrix U.
[Mathematical equation 25]

[0115] The diagonal matrix ∑ in (52) Equation is a matrix whose diagonal component is the eigenvalues of the autocorrelation matrix R as illustrated in (53) Equation below. The diagonal component of the diagonal matrix Σ is set to σ₁₁, σ₂₂, · · ·, σmm. Further, the orthogonal matrix U is a matrix in which each column component vector is an eigenvector of the autocorrelation matrix R. The column component vector of the orthogonal matrix U is set to u₁, u₂, ···, u_m. There is a correspondence relation in which the eigenvalue of the autocorrelation matrix R responsive to an eigenvector u_j is σ_jj. The eigenvalue of the autocorrelation matrix R is a variable reflecting the strength of each frequency component included in a time waveform of the predicted value y^_k of the physical quantity at the time k by the AR model.
[Mathematical equation 26]

[0116] The values of σ₁₁, σ₂₂, ···, σ_mm being the diagonal components of the diagonal matrix Σ obtained by the result of the singular value decomposition of the autocorrelation matrix R are set in descending order in order to simplify the illustration of the mathematical equation. A matrix R' is defined as in (54) Equation below by using, out of the eigenvalues of the autocorrelation matrix R illustrated in (53) Equation, s pieces of the eigenvalues, which are chosen from the largest. s is a number that is 1 or more and less than m. In the present embodiment, s is preset. The matrix R' is a matrix resulting from approximating the autocorrelation matrix R by using s pieces of the eigenvalues out of the eigenvalues of the autocorrelation matrix R.
[Mathematical equation 27]

[0117] A matrix U_s in (54) Equation is a matrix of m ×s composed of s pieces of the column component vectors, which are chosen from the left of the orthogonal matrix U of (52) Equation (eigenvectors corresponding to the eigenvalues to be used). That is, the matrix U_s is a submatrix composed of the left elements of m×s cut out from the orthogonal matrix U. Further, U_s^T in (54) Equation is a transposed matrix of U_s. U_s^T is a matrix of s×m composed of s pieces of row component vectors, which are chosen from the top of the matrix U^T in (52) Equation. The matrix Σ_s in (54) Equation is a matrix of s×s composed of s pieces of columns, which are chosen from the left, and s pieces of rows, which are chosen from the top, of the diagonal matrix Σ in (52) Equation. That is, the matrix Σ_s is a submatrix composed of the top and left elements of s×s cut out from the diagonal matrix Σ.

[0118] When the matrix Σ_s and the matrix U_s are expressed by the matrix elements, (55) Equation below is obtained.
[Mathematical equation 28]

[0119] By using the matrix R' in place of the autocorrelation matrix R, the relational expression of (50) Equation is rewritten into (56) Equation below.
[Mathematical equation 29]

[0120] (56) Equation is modified, and thereby (57) Equation below is obtained as the equation for deriving the coefficient α. The model that calculates the predicted value y^_k of the physical quantity at the time k from (45) Equation while using the coefficient α derived by (57) Equation is the "corrected AR model".
[Mathematical equation 30]

[0121] The case where the values of σ₁₁, σ₂₂, ···, σ_mm being the diagonal components of the diagonal matrix Σ are set in descending order has been explained here as an example. However, it is not necessary to set the diagonal components of the diagonal matrix Σ in descending order during a process of calculating the coefficient α. In that case, the matrix U_s is not the submatrix composed of the left elements of m×s cut out from the orthogonal matrix U, but becomes a submatrix composed of the cut out column component vectors corresponding to the eigenvalues to be used (the eigenvectors). Further, the matrix Σ_s is not the submatrix composed of the top and left elements of s×s cut out from the diagonal matrix Σ, but becomes a submatrix to be cut out so as to make the eigenvalues used for determining the coefficient of the corrected AR model become the diagonal components.

[0122] (57) Equation is an equation to be used for determining the coefficient of the corrected AR model. The matrix U_s in (57) Equation is a matrix (a third matrix) in which the eigenvectors corresponding to the eigenvalues used for determining the coefficient of the corrected AR model are set to the column component vectors, which is the submatrix of the orthogonal matrix U obtained by the singular value decomposition of the autocorrelation matrix R. Further, the matrix Σ_s in (57) Equation is a matrix (a second matrix) in which the eigenvalues used for determining the coefficient of the corrected AR model are set to the diagonal components, which is the submatrix of the diagonal matrix obtained by the singular value decomposition of the autocorrelation matrix R. The matrix U_sΣ_sU_s^T in (57) Equation is a matrix (a first matrix) derived from the matrix Σ_s and the matrix U_s.

[0123] The right side of (57) Equation is calculated, and thereby the coefficient α of the corrected AR model is derived. One example of the method of deriving the coefficient α of the corrected AR model has been explained above. Here, as the method of deriving the coefficient of the AR model to be the base of the corrected AR model, the method of using the least square method for the predicted value y^_k of the physical quantity at the time k has been set in order to make the method understandable intuitively. However, there has been known a method of defining the AR model by using the concept of a stochastic process and deriving its coefficient generally. In that case, the autocorrelation is expressed by autocorrelation of the stochastic process (a population). This autocorrelation of the stochastic process is expressed as a function of a time lag. Therefore, the autocorrelation of the data y in the present embodiment may be replaced with a value calculated by another calculating formula as long as it approximates the autocorrelation of the stochastic process. For example, R₂₂ to R_mm are autocorrelation with a time lag of 0 (zero), but they may be replaced with R₁₁.

[0124] The number s of the eigenvalues extracted from the autocorrelation matrix R illustrated in (53) Equation can be determined from a distribution of the eigenvalues of the autocorrelation matrix R, for example.

[0125] As the physical quantity in the explanation of the previously-described corrected AR model, the forward-and-backward-direction force is applied here. The value of the forward-and-backward-direction force varies according to the state and the like of the railway vehicle.

[0126] Accordingly, the railway vehicle is first made to travel on the track 16 to obtain the data y of the measured value of the forward-and-backward-direction force. The autocorrelation matrix R is derived by using (49) Equation and (51) Equation for each of the obtained data y. The autocorrelation matrix R is subjected to singular value decomposition expressed by (52) Equation, to thereby derive the eigenvalues of the autocorrelation matrix R. Fig. 8 is a view illustrating one example of the distribution of the eigenvalues of the autocorrelation matrix R. In Fig. 8, eigenvalues σ₁₁ to σ_mm, which are obtained by the autocorrelation matrix R in each of the time-series data of the measured value y of the forward-and-backward-direction force T₁ in the wheel set 13a being subjected to singular value decomposition, are aligned in ascending order and are plotted. In Fig. 8, the horizontal axis is an index of the eigenvalue and the vertical axis is the value of the eigenvalue.

[0127] In the example illustrated in Fig. 8, there is one eigenvalue having significantly high value when compared to the other values. Further, there are two eigenvalues whose values are not so high when compared to the aforementioned eigenvalue having significantly high value, but are relatively large when compared to the other values and thus cannot be regarded as 0 (zero). Based on this, it is possible to employ two or three, for example, as the number s of eigenvalues to be extracted from the autocorrelation matrix R illustrated in (53) Equation. Even if either of them is employed, there is generated no significant difference in the result. Note that the number of eigenvalue having a value which is significantly higher than the other values may change depending on the configuration of the railway vehicle, the configuration of the track, and so on. Therefore, the number s of eigenvalues to be extracted from the autocorrelation matrix R is not limited to these values as long as it is one or more.

[0128] The first frequency adjustment unit 503 performs the following processing every time the data acquisition unit 502 acquires the value y_k of the time-series data of the measured value y of the forward-and-backward-direction force at the time k at a predetermined sampling period.

[0129] First, the first frequency adjustment unit 503 generates the autocorrelation matrix R by using (49) Equation and (51) Equation based on the time-series data of the measured value y of the forward-and-backward-direction force and preset numbers M, m.

[0130] Next, the first frequency adjustment unit 503 performs singular value decomposition on the autocorrelation matrix R, to thereby derive the orthogonal matrix U and the diagonal matrix Σ of (52) Equation, and derives the eigenvalues σ₁₁ to σ_mm of the autocorrelation matrix R from the diagonal matrix Σ.

[0131] Next, the first frequency adjustment unit 503 chooses s pieces of the eigenvalues σ₁₁ to σ_ss from the largest from among the plural eigenvalues σ₁₁ to σ_mm of the autocorrelation matrix R as the eigenvalues of the autocorrelation matrix R to be used for deriving the coefficient α of the corrected AR model.

[0132] Next, the first frequency adjustment unit 503 determines the coefficient α of the corrected AR model by using (57) Equation based on the time-series data of the measured value y of the forward-and-backward-direction force, the eigenvalues σ₁₁ to σ_ss, and the orthogonal matrix U obtained by the singular value decomposition of the autocorrelation matrix R.

[0133] Subsequently, the first frequency adjustment unit 503 derives the predicted value y^_k of the time-series data of the measured value y of the forward-and-backward-direction force at the time k from (45) Equation based on the coefficient α of the corrected AR model and the time-series data of the measured value y of the forward-and-backward-direction force. Time-series data of the predicted value y^_k of the forward-and-backward-direction force results in the time-series data from which the low-frequency component included in the time-series data of the measured value y of the forward-and-backward-direction force has been extracted.

[0134] Fig. 9 is a view illustrating one example of time-series data of measured values of forward-and-backward-direction forces (measured values) and time-series data of predicted values of the forward-and-backward-direction forces (calculated values). Note that in the present embodiment, the measured values of the four forward-and-backward-direction forces T₁ to T₄ are obtained. That is, four pieces of the data y of the forward-and-backward-direction force are obtained. In Fig. 9, the measured value and the calculated value of each of the four pieces of data y are illustrated. The horizontal axis in Fig. 9 indicates a measuring time and a calculating time of the forward-and-backward-direction forces T₁ to T₄, each of which is an elapsed time (second) from a reference time when the reference time is set to 0 (zero). The vertical axis indicates the forward-and-backward-direction forces T₁ to T₄ (Nm).

[0135] In Fig. 9, the calculated value of the forward-and-backward-direction force T₁ in the wheel set 13a is biased at about 15 seconds to 35 seconds. Specifically, the calculated value of the forward-and-backward-direction force T₁ in the wheel set 13a exhibits, at about 15 seconds to 35 seconds, a value larger than that at another time. This period corresponds to the period when the wheel set 13a passes through the curved track. The calculated value of the forward-and-backward-direction force T₂ in the wheel set 13b, the calculated value of the forward-and-backward-direction force T₃ in the wheel set 13c, and the calculated value of the forward-and-backward-direction force T₄ in the wheel set 13d are also biased during the period when the wheel sets 13b, 13c, 13d pass through the curved track, similarly to the calculated value of the forward-and-backward-direction force T₁ in the wheel set 13a.

[0136] Accordingly, in Fig. 9, removal of the calculated values from the measured values of the forward-and-backward-direction forces T₁ to T₄ in the wheel sets 13a to 13d makes it possible to remove the low-frequency components, which are due to the wheel sets 13a to 13d passing through the curved track, from the signals of the forward-and-backward-direction forces T₁ to T₄. That is, in Fig. 9, when the calculated values are removed from the measured values of the forward-and-backward-direction forces T₁ to T₄ in the wheel sets 13a to 13d, as the forward-and-backward-direction forces T₁ to T₄ when the wheel sets 13a to 13d have passed through the curved track, the forward-and-backward-direction forces equivalent to those when the wheel sets 13a to 13d have passed through the linear track can be obtained.

[0137] Accordingly, the first frequency adjustment unit 503 subtracts the time-series data of the predicted value y^_k of the forward-and-backward-direction force from the time-series data (the data y) of the measured value y_k of the forward-and-backward-direction force. In the following explanation, the time-series data resulting from the subtraction of the time-series data of the predicted value y^_k of the forward-and-backward-direction force from the time-series data (the data y) of the measured value y_k of the forward-and-backward-direction force is referred to as time-series data of a high-frequency component of the forward-and-backward-direction force as necessary. Further, a value of the time-series data of the high-frequency component of the forward-and-backward-direction force at each sampling time is referred to as a value of the high-frequency component of the forward-and-backward-direction force as necessary.

[0138] Fig. 10 is a view illustrating one example of the time-series data of the high-frequency components of the forward-and-backward-direction forces. The vertical axis in Fig. 10 indicates the time-series data of the high-frequency components of the forward-and-backward-direction forces T₁, T₂, T₃, T₄. That is, the high-frequency components of the forward-and-backward-direction forces T₁, T₂, T₃, T₄ illustrated on the vertical axis in Fig. 10 are ones obtained by subtracting the calculated values from the measured values of the forward-and-backward-direction forces T₁, T₂, T₃, T₄ in the wheel sets 13a, 13b, 13c, 13d that are illustrated in Fig. 9 respectively. Further, the horizontal axis in Fig. 10 indicates a measuring time and a calculating time of the forward-and-backward-direction forces T₁ to T₄, each of which is an elapsed time (second) from a reference time when the reference time is set to 0 (zero), similarly to the horizontal axis in Fig. 9.

[0139] The first frequency adjustment unit 503 derives the time-series data of the high-frequency components of the forward-and-backward-direction forces T₁ to T₄ as above.

[State variable derivation unit 504, S703]

[0140] The state variable derivation unit 504 sets the observation equation as the observation equation stored by the storage unit 501, sets the state equation as the state equation stored by the storage unit 501, and determines estimated values of the state variables illustrated in (44) Equation by using the Kalman filter. At this time, the state variable derivation unit 504 uses time-series data of the high-frequency components of the forward-and-backward-direction forces T₁ to T₄ generated by the first frequency adjustment unit 503. In the present embodiment, out of the time-series data of the measured value of the acceleration of the vehicle body 11 in the right and left direction, the time-series data of the measured values of the accelerations of the bogies 12a, 12b in the right and left direction, and the time-series data of the measured values of the accelerations of the wheel sets 13a to 13d in the right and left direction, at least the time-series data during a period in which the measured values of the forward-and-backward-direction forces T₁ to T₄ have been obtained is not used when determining the estimated values of the state variables.

[0141] The Kalman filter is one of the methods of performing data assimilation. That is, the Kalman filter is one example of the method to determine an estimated value of an unobserved variable (state variable) so as to reduce (minimize) the difference between, of an observable variable (observation variable), a measured value and an estimated value. The state variable derivation unit 504 derives a Kalman gain at which the difference between, of the observation variable, the measured value and the estimated value becomes small (minimum) and derives the estimated value of the unobserved variable (state variable) at that time. In the Kalman filter, the following observation equation of (58) Equation and the following state equation of (59) Equation are used.

[0142] In (58) Equation, Y is a vector in which the measured value of the observation variable is stored. H is an observation model. X is a vector in which the state variable is stored. V is observation noise. In (59) Equation, X· indicates a time differentiation of X. Φ is a linear model. W is system noise. Note that the Kalman filter itself can be fabricated by a well-known technique, and thus its detailed explanation is omitted.

[0143] In the technique described in Patent Literature 1, as the values to be given as the measured values of the observation variables, the measured values (the measured value of the acceleration of the vehicle body 11 in the right and left direction, the measured values of the accelerations of the bogies 12a, 12b in the right and left direction, and the measured values of the accelerations of the wheel sets 13a to 13d in the right and left direction) are used as they are. In contrast to this, in the present embodiment, as explained in the term of [first conception], not the measured value but a preset fixed value is given as the value to be normally given as the measured value of the observation variable when performing the data assimilation. In the present embodiment, an average value of the pieces of time-series data of the accelerations is assumed to be 0 (zero), and all of fixed values to be given as the observation variables are set to 0 (zero). Therefore, in the present embodiment, when performing the data assimilation, the state variable derivation unit 504 derives the estimated value of the state variable so as to minimize an error of the estimated value of the observation variable with respect to the fixed value (0 (zero) in this case) or minimize an expected value of the error.

[0144] The state variable derivation unit 504 determines the estimated values of the state variables illustrated in (44) Equation at a predetermined sampling period, to thereby generate time-series data of the estimated values of the state variables illustrated in (44) Equation.

[Second frequency adjustment unit 505, S704]

[0145] When the signal strength of the low-frequency component included in the time-series data of the measured value of the forward-and-backward-direction force is not removed sufficiently by the first frequency adjustment unit 503, the signal of the low-frequency component due to the railway vehicle traveling on the curved track may remain in the time-series data of the estimated values of the state variables generated by the state variable derivation unit 504. Accordingly, the second frequency adjustment unit 505 reduces (preferably removes) the signal strength of the low-frequency component included in the time-series data of the estimated values of the state variables generated by the state variable derivation unit 504. Note that in the case where it is possible to determine the number s of the eigenvalues to be extracted from the autocorrelation matrix R illustrated in (53) Equation so as to sufficiently remove the signal strength of the low-frequency component included in the time-series data of the measured value of the forward-and-backward-direction force by the first frequency adjustment unit 503, the processing of the second frequency adjustment unit 505 is no longer required.

[0146] In the present embodiment, the second frequency adjustment unit 505 uses the corrected AR model to reduce the signal strength of the low-frequency component included in the time-series data of the estimated values of the state variables similarly to the first frequency adjustment unit 503.

[0147] The second frequency adjustment unit 505 performs the following processing for each state variable at a predetermined sampling period.

[0148] As the physical quantity in the explanation of the previously-described corrected AR model, the state variable is applied here. That is, the data y of the state variable results in the time-series data of the estimated values of the state variables generated by the state variable derivation unit 504. Each of the estimated values of the state variables varies according to the state of the railway vehicle.

[0149] First, the second frequency adjustment unit 505 generates the autocorrelation matrix R by using (49) Equation and (51) Equation based on the data y of the estimated values of the state variables and the preset numbers M and m.

[0150] Next, the second frequency adjustment unit 505 performs singular value decomposition on the autocorrelation matrix R, to thereby derive the orthogonal matrix U and the diagonal matrix Σ of (52) Equation, and derives the eigenvalues σ₁₁ to σ_mm of the autocorrelation matrix R from the diagonal matrix Σ.

[0151] Next, the second frequency adjustment unit 505 chooses s pieces of the eigenvalues σ₁₁ to σ_ss from the largest from among the plural eigenvalues σ₁₁ to σ_mm of the autocorrelation matrix R as the eigenvalues of the autocorrelation matrix R to be used for deriving the coefficient α of the corrected AR model. s is preset for each state variable. The data y of the estimated value of each state variable can be obtained in a manner as explained so far in a state of causing the railway vehicle to travel on the track 16, for example. Subsequently, a distribution of the eigenvalues of the autocorrelation matrix R is made by the second frequency adjustment unit 505 individually for each state variable. From the distributions of the eigenvalues of the autocorrelation matrix R, the second frequency adjustment unit 505 determines the number s of the eigenvalues to be extracted from the autocorrelation matrix R illustrated in (53) Equation for each of the state variables.

[0152] Next, the second frequency adjustment unit 505 determines the coefficient α of the corrected AR model by using (57) Equation based on the data y of the estimated value of the state variable, the eigenvalues σ₁₁ to σ_ss, and the orthogonal matrix U obtained by the singular value decomposition of the autocorrelation matrix R.

[0153] Subsequently, the second frequency adjustment unit 505 derives the predicted value y^_k of the data y of the estimated value of the state variable at the time k from (45) Equation based on the coefficient α of the corrected AR model and the data y of the estimated value of the state variable. Time-series data of the predicted value y^_k of the state variable results in the time-series data from which the low-frequency component included in the data y of the estimated value of the state variable has been extracted.

[0154] Subsequently, the second frequency adjustment unit 505 subtracts the time-series data of the predicted value y^_k of the state variable from the data y of the estimated value of the state variable. In the following explanation, a value of time-series data resulting from the subtraction of the time-series data of the predicted value y^_k of the state variable from the data y of the estimated value of the state variable at each sampling time is referred to as a value of a high-frequency component of the state variable as necessary.

[Track state derivation unit 506, S705]

[0155] When (22) Equation to (25) Equation are substituted into the motion equations that describe the yawings of the wheel sets 13a to 13d of (5) Equation to (8) Equation, (60) Equation to (63) Equation below are obtained.
[Mathematical equation 31]

[0156] In the present embodiment, as illustrated in (60) Equation to (63) Equation, relational expressions representing the relations between the forward-and-backward-direction forces T₁ to T₄ and the alignment irregularity amounts y_R1 to y_R4 at the positions of the wheel sets 13a to 13d are set.

[0157] The track state derivation unit 506 calculates estimated values of the pivot amounts (angular displacements) φ_w1 to φ_w4 of the wheel sets 13a to 13d in the yawing direction by (30) Equation to (33) Equation. Subsequently, the track state derivation unit 506 gives the estimated values of the pivot amounts (angular displacements) φ_w1 to φ_w4 of the wheel sets 13a to 13d in the yawing direction, the values of the high-frequency components of the state variables generated by the second frequency adjustment unit 505, and the values of the high-frequency components of the forward-and-backward-direction forces T₁ to T₄ generated by the first frequency adjustment unit 503 to (60) Equation to (63) Equation, to thereby calculate the alignment irregularity amounts y_R1 to y_R4 at the positions of the wheel sets 13a to 13d. The state variables to be used here are the displacements y_t1 and y_t2 of the bogies 12a, 12b in the right and left direction, the velocities y_t1· and y_t2· of the bogies 12a, 12b in the right and left direction, the displacements y_w1 to y_w4 of the wheel sets 13a to 13d in the right and left direction, and the velocities y_w1· to y_w4· of the wheel sets 13a to 13d in the right and left direction. The track state derivation unit 506 performs such a calculation of the alignment irregularity amounts y_R1 to y_R4 as above at a predetermined sampling period, to thereby obtain the time-series data of the alignment irregularity amounts y_R1 to y_R4.

[0158] Subsequently, the track state derivation unit 506 calculates a final alignment irregularity amount y_R from the alignment irregularity amounts y_R1 to y_R4. For example, the track state derivation unit 506 matches phases of the time-series data of the alignment irregularity amounts y_R2 to y_R4 to a phase of the time-series data of the alignment irregularity amount y_R1. That is, the track state derivation unit 506 calculates, from the distance between the wheel set 13a and the wheel sets 13b to 13d in the forward and backward direction and the velocity of the railway vehicle, a delay time between the time when the wheel set 13a passes through a certain position and the time when the wheel sets 13b to 13d pass through the certain position. The track state derivation unit 506 displaces the phases of the time-series data of the alignment irregularity amounts y_R2 to y_R4 by this delay time.

[0159] The track state derivation unit 506 calculates an arithmetic mean value of the sum of the values of the alignment irregularity amounts y_R1 to y_R4 whose phases are matched at the same sampling time as the final alignment irregularity amount y_R at this sampling time. The track state derivation unit 506 performs such a calculation at each sampling time, to thereby obtain time-series data of the final alignment irregularity amount y_R. The phases of the alignment irregularity amounts y_R2 to y_R4 are matched to the phase of the alignment irregularity amount y_R1, thereby making it possible to cancel disturbance factors existing in common in the time-series data of the alignment irregularity amounts y_R1 to y_R4.

[0160] Note that the track state derivation unit 506 may find a moving average of each of the alignment irregularity amounts y_R1 to y_R4 whose phases are matched (namely, pass each of the alignment irregularity amounts y_R1 to y_R4 through a low-pass filter) and calculate the final alignment irregularity amount y_R from the alignment irregularity amounts y_R1 to y_R4 whose moving averages have been found.

[0161] Further, the track state derivation unit 506 may calculate, as the final alignment irregularity amount y_R, an arithmetic mean value of two of the values of the alignment irregularity amounts y_R1 to y_R4 whose phases are matched at the same sampling time from which the maximum value and the minimum value are removed.

[0162] The inspection apparatus 500 uses the time-series data of the measured value of the forward-and-backward-direction force at each sampling time acquired by the data acquisition unit 502 while the railway vehicle is traveling in the traveling section being the target of deriving the alignment irregularity amount, to execute pieces of the processing of the first frequency adjustment unit 503, the state variable derivation unit 504, the second frequency adjustment unit 505, and the track state derivation unit 506.

[0163] In this manner, the track state derivation unit 506 can obtain the alignment irregularity amount y_R at each sampling time while the railway vehicle is traveling in the traveling section being the target of deriving the alignment irregularity amount. The track state derivation unit 506 calculates a traveling position of the railway vehicle at each sampling time based on, for example, a traveling velocity of the railway vehicle and an elapsed time from the time when the railway vehicle starts to travel. The traveling position of the railway vehicle can be set to the position of the wheel set 13a, for example. The track state derivation unit 506 derives the final alignment irregularity amount y_R at each traveling position of the railway vehicle based on the alignment irregularity amount y_R at each sampling time and the traveling position of the railway vehicle at each sampling time.

[0164] Note that the track state derivation unit 506 does not always need to calculate the traveling position of the railway vehicle at each sampling time as described previously. For example, the track state derivation unit 506 may derive the traveling position of the railway vehicle at each sampling time by using a GPS (Global Positioning System).

[Output unit 507, S706]

[0165] The output unit 507 outputs information of the final alignment irregularity amount y_R that is calculated by the track state derivation unit 506. At this time, the output unit 507 may output information indicating that the track 16 is abnormal in the case where the final alignment irregularity amount y_R is larger than a preset value. As a form of output, it is possible to employ at least any one of displaying the information on a computer display, transmitting the information to an external device, and storing the information in an internal or external storage medium, for example.

<Summary>

[0166] As described above, in the present embodiment, the inspection apparatus 500 gives the measured values of the forward-and-backward-direction forces T₁ to T₄ and the actual values of the transformation variables e₁ to e₄ to the Kalman filter, to derive the state variables (y_w1· to y_w4·, y_w1 to y_w4, y_t1· and y_t2·, y_t1 and y_t2, φ_t1· and φ_t2·, φ_t1 and φ_t2, φ_t1· and φ_t2· , φ_t1 and φ_t2, y_b·, y_b, φ_b·, φ_b, φ_b·, φ_b, φ_y1, φ_y2, φ_a1, φ_a2). At this time, the preset fixed value (0 (zero), for example) is used as the values to be normally given as the measured values of the observation variables (the accelerations of the vehicle body 11, the bogies 12a, 12b, and the wheel sets 13a to 13d in the right and left direction) when performing the data assimilation. Next, the inspection apparatus 500 uses the pivot amounts (angular displacements) φ_t1 and φ_t2 of the bogies 12a, 12b in the yawing direction included in the state variables and the actual values of the transformation variables e₁ to e₄, to derive the pivot amounts (angular displacements) φ_w1 to φ_w4 of the wheel sets 13a to 13d in the yawing direction. Next, the inspection apparatus 500 substitutes the pivot amounts (angular displacements) φ_w1 to φ_w4 of the wheel sets 13a to 13d in the yawing direction, the state variables, and the measured values of the forward-and-backward-direction forces T₁ to T₄ into the motion equations that describe the yawings of the wheel sets 13a to 13d, to derive the alignment irregularity amounts y_R1 to y_R4 at the positions of the wheel sets 13a to 13d. Subsequently, the inspection apparatus 500 derives the final alignment irregularity amount y_R from the alignment irregularity amounts y_R1 to y_R4. Therefore, it is possible to derive the alignment irregularity amounts y_R1 to y_R4 (the final alignment irregularity amount y_R) without greatly decreasing accuracy, with no use of the measured values of the accelerations of the vehicle body 11, the bogies 12a, 12b, and the wheel sets 13a to 13d in the right and left direction. Therefore, it is possible to reduce the number of sensors which are used for deriving the alignment irregularity amounts y_R1 to y_R4 (the final alignment irregularity amount y_R).

[0167] Further, in the present embodiment, the inspection apparatus 500 generates the autocorrelation matrix R from the time-series data of the measured value y of the forward-and-backward-direction force, and determines, by using s pieces of the eigenvalues from the largest chosen from the eigenvalues obtained by the singular value decomposition of the autocorrelation matrix R, the coefficient α of the corrected AR model approximating the time-series data of the measured value y of the forward-and-backward-direction force. Therefore, it is possible to determine the coefficient α so as to make the signal of the low-frequency component included in the time-series data of the measured value y of the forward-and-backward-direction force remain and prevent the high-frequency component from remaining. The inspection apparatus 500 calculates the predicted value y^_k of the forward-and-backward-direction force at the time k by giving the time-series data of the measured value y of the forward-and-backward-direction force at the time k-l (1 ≦ 1 ≦ m), which is prior to the time k, to the corrected AR model whose coefficient α is determined in this manner. Therefore, it is possible to reduce the signal of the low-frequency component, which is due to the railway vehicle traveling on the curved track, from the time-series data of the measured value y of the forward-and-backward-direction force without estimating a cutoff frequency beforehand. Subsequently, the inspection apparatus 500 reduces the signal strength of the low-frequency components included in the time-series data of the measured values of the forward-and-backward-direction forces T₁ to T₄ in this manner and generates the time-series data of the high-frequency components of the forward-and-backward-direction forces T₁ to T₄. The inspection apparatus 500 gives the time-series data of the high-frequency components of the forward-and-backward-direction forces T₁ to T₄ to the relational expression between the forward-and-backward-direction forces T₁ to T₄ and the alignment irregularity amounts y_R1 to y_R4 at the positions of the wheel sets 13a to 13d, to thereby calculate the alignment irregularity amounts y_R1 to y_R4 at the positions of the wheel sets 13a to 13d. This relational expression is an expression based on the motion equations that describe the motions of the railway vehicle when traveling on the linear track (namely, the equations not including the curvature radius R of the track 16 (the rail)). Therefore, it is possible to detect the alignment irregularity amounts y_R1 to y_R4 (the final alignment irregularity amount y_R) in the curved track based on the motion equations that describe the motions of the railway vehicle when traveling on the linear track without using a special measuring apparatus.

[Modified example]

[0168] In the present embodiment, the preset fixed value is given as the value to be normally given as the measured value of the observation variable when performing the data assimilation. This fixed value is not limited to 0 (zero). For example, it is also possible that the time-series data of the measured value of the acceleration of the vehicle body 11 in the right and left direction, the time-series data of the measured values of the accelerations of the bogies 12a, 12b in the right and left direction, and the time-series data of the measured values of the accelerations of the wheel sets 13a to 13d in the right and left direction when the railway vehicle having the inspection apparatus 500 mounted thereon or a railway vehicle equivalent to this railway vehicle (a railway vehicle whose structure is the same as that of this railway vehicle) travels on the track 16 being the target of deriving the alignment irregularity amounts y_R1 to y_R4 (the final alignment irregularity amount y_R) are obtained, and an average value of the respective pieces of time-series data is used as the fixed value. Further, by using these measured values, time-series data of a predicted value of acceleration y^_k of the vehicle body 11 in the right and left direction, time-series data of predicted values of accelerations y^_k of the bogies 12a, 12b in the right and left direction, and time-series data of predicted values y^_k of accelerations of the wheel sets 13a to 13d in the right and left direction are derived by the above-described corrected AR model. Subsequently, an average value thereof may also be used as the fixed value. When it is designed as above, the measurement of accelerations is performed, but this measurement is only required to be performed once for each of the railway vehicle and the track 16, and measured values of accelerations during a period in which the measured values of the forward-and-backward-direction forces T₁ to T₄ in the wheel sets 13a to 13d have been obtained are not used when deriving the state variables.

[0169] In the present embodiment, the case of using the corrected AR model has been explained as an example. However, it is not always necessary to use the corrected AR model and reduce the signal of the low-frequency component, which is due to the railway vehicle traveling on the curved track, from the time-series data of the measured value y of the forward-and-backward-direction force. For example, in the case where it is possible to specify a frequency band due to the railway vehicle traveling on the curved track, a high-pass filter may be used to reduce the signal of the low-frequency component, which is due to the railway vehicle traveling on the curved track, from the time-series data of the measured value y of the forward-and-backward-direction force. Further, when the track on which the railway vehicle travels is a linear track (being an ideal track whose curvature is 0 (zero)) or a track which is designed as a linear track but has a curvature which is small enough to exert no influence on estimation accuracy of the alignment irregularity amount, the processing of the first frequency adjustment unit 503 and the processing of the second frequency adjustment unit 505 are no longer required.

[0170] Further, in the present embodiment, the case where the wheel set to be a standard when performing the phase matching is the wheel set 13a has been explained as an example. However, the wheel set to be a standard may be the wheel set 13b, 13c, or 13d other than the wheel set 13a.

[0171] Further, in the present embodiment, the case of using the Kalman filter has been explained as an example. However, it is not always necessary to use the Kalman filter as long as a filter that derives the estimated values of the state variables so that the error of the estimated value of the observation variable with respect to the fixed value becomes minimum or the expected value of this error becomes minimum (that is, a filter that performs data assimilation) is used. For example, a particle filter may be used. Note that as the error of the estimated value of the observation variable with respect to the fixed value, for example, a square error between the estimated value of the observation variable and the fixed value is cited.

[0172] Further, in the present embodiment, the case of deriving the alignment irregularity amount has been explained as an example. However, it is not always necessary to derive the alignment irregularity amount as long as information that reflects the track irregularity (appearance failure of the track 16) is derived as information reflecting the state of the track 16. For example, in addition to or in place of the alignment irregularity amount, the following calculations of (64) Equation to (67) Equation may be performed, to thereby derive a lateral force that occurs when the railway vehicle travels on the linear track (stress in the right and left direction between the wheel and the rail). Note that Q₁, Q₂, Q₃, Q₄ are lateral forces in the wheels 14a, 14b, 14c, 14d respectively. f₃ represents a spin creep coefficient.
[Mathematical equation 32]

[0173] Further, in the present embodiment, the case of including the state variables that represent the state of the vehicle body 11 has been explained as an example. However, the vehicle body 11 is a part into which vibrations by acting forces between the wheels 14a to 14d and the track 16 (creep force) propagate finally. Accordingly, it is not necessary to include the state variables representing the state of the vehicle body 11 in the case where the influence by the propagation in the vehicle body 11 is judged to be small, for example. In such a case, out of the motion equations of (1) Equation to (21) Equation, (15) Equation to (17) Equation (the motion equations that describe the transversal vibration, the yawing, and the rolling of the vehicle body 11) and (18) Equation and (19) Equation (the motion equations that describe the yawing of the yaw damper disposed on the bogie 12a and the yawing of the yaw damper disposed on the bogie 12b) are no longer required. Further, in the motion equations of (1) Equation to (21) Equation, the state amount relating to the vehicle body (state amount including the subscript of b) and the value inside {} that includes the state amount relating to the vehicle body (state amount including the subscript of b) (for example, the third term {φ_a2 - φ_b} on the left side of (21) Equation)) are set to 0 (zero) .

[0174] Further, in the present embodiment, the case of the bogies 12a, 12b each being a bolsterless bogie has been explained as an example. However, the bogies 12a, 12b are not limited to the bolsterless bogies. Besides, according to the components of the railway vehicle, forces that the railway vehicle receives, the directions of the motions of the railway vehicle, or the like, the motion equations are rewritten appropriately. That is, the motion equations are not limited to the ones exemplified in the present embodiment. When the motion equation is set to represent that the railway vehicle receives external force which does not depend on the state variables, the state equation includes a term that represents this external force.

(Second embodiment)

[0175] Next, a second embodiment will be described. In the first embodiment, the case where the state variables are derived by using the filter (Kalman filter) that performs the data assimilation by setting the values to be normally given as the measured values of the observation variables (the acceleration of the vehicle body 11 in the right and left direction, the accelerations of the bogies 12a, 12b in the right and left direction, and the accelerations of the wheel sets 13a to 13d in the right and left direction) to the fixed value (0 (zero)), when performing the data assimilation, has been described as an example. In contrast to this, in the present embodiment, a case of deriving the state variables without performing the data assimilation will be described. In this manner, the present embodiment and the first embodiment are different mainly in the method of deriving the state variables (the function of the state variable derivation unit 504). Therefore, in the explanation of the present embodiment, the same reference numerals and symbols as those added to Fig. 1 to Fig. 10 are added to the same parts as those in the first embodiment, or the like, and their detailed explanations are omitted.

[0176] In the present embodiment, the storage unit 501 does not store the state equation ((58) Equation) and the observation equation ((59) Equation), but stores the following motion equation of (68) Equation.

[0177] (68) Equation is one example of equation obtained by changing an equation representing the motion equations of (9) Equation, (10) Equation, (13) Equation to (21) Equation, and (34) Equation to (39) Equation by using the state variables illustrated in (44) Equation (an equation corresponding to (68) Equation in which c is set to 1), so that a temporal change in the state variables becomes smaller than that of this equation. Concretely, (68) Equation is one obtained in a manner that, in an equation representing the motion equations of (9) Equation, (10) Equation, (13) Equation to (21) Equation, and (34) Equation to (39) Equation by using the state variables illustrated in (44) Equation, a term which is connected to a term of first-order time differential (X·) of the state variable by an equal sign is multiplied by a forgetting factor c. Specifically, (68) Equation corresponds to the state equation of (59) Equation in which the forgetting factor c is introduced, to thereby set the system noise W to 0 (zero).

[0178] The forgetting factor c is a preset value, and is (theoretically) a value of greater than 0 and 1 or less (0 < c ≦ 1). The forgetting factor c functions in a manner that the smaller the value thereof, the greater the degree of forgetfulness of a past observation value. In (68) Equation, the smaller the value of the forgetting factor c, the smaller the influence of the measured value of the forward-and-backward-direction force on the estimated value (solution) of the state variable. For this reason, from a viewpoint of correctly obtaining the estimated value (solution) of the state variable, the value of the forgetting factor c is desirably close to 1. On the other hand, when the value of the forgetting factor c is excessively large, there is a high possibility of divergence of the estimated value (solution) of the state variable. In the present embodiment, (68) Equation is directly solved without using the filter that performs the data assimilation. Accordingly, there is a need to suppress the divergence of the estimated value (solution) of the state variable. The value of the forgetting factor c is determined based on the viewpoint as described above. As the forgetting factor c, for example, a value of greater than 0.0 and 1.0 or less (0.0 < c ≦ 1.0), preferably a value of 0.90 or more and 1.0 or less (0.90 ≦ c ≦ 1.0), more preferably a value of 0.95 or more and 1.0 or less (0.95 ≦ c ≦ 1.0), still more preferably a value of 0.99 or more and 1.0 or less (0.99 ≦ c ≦ 1.0), and most preferably 1.0 is selected among them.

[0179] However, it is essential that the forgetting factor c is selected so as to prevent the divergence of the estimated value (solution) of the state variable obtained by solving (68) Equation. If the divergence of the estimated value (solution) of the state variable obtained by solving (68) Equation does not occur, the estimated value (solution) of this state variable when the value of the forgetting factor is 1.0 becomes the most accurate solution. However, when the value of the forgetting factor c is 1.0, it is highly likely that the estimated value (solution) of the state variable obtained by solving (68) Equation diverges (the solution is not determined).

[0180] From such a viewpoint, the forgetting factor c may be selected by setting an upper limit value of the forgetting factor c to less than 1.0. Specifically, the value of the forgetting factor c can be selected from, for example, a value of greater than 0.0 and less than 1.0 (0.0 < c < 1.0), preferably a value of 0.90 or more and less than 1.0 (0.90 ≦ c < 1.0), more preferably a value of 0.95 or more and less than 1.0 (0.95 ≦ c < 1.0), and still more preferably a value of 0.99 or more and less than 1.0 (0.99 ≦ c < 1.0).

[0181] Note that when the value of the forgetting factor c is 1.0, (68) Equation corresponds to the motion equations themselves of (9) Equation, (10) Equation, (13) Equation to (21) Equation, and (34) Equation to (39) Equation (an equation only representing the motion equations by using the state variables).

[0182] The state variable derivation unit 504 uses the time-series data of the high-frequency components of the forward-and-backward-direction forces T₁ to T₄ generated by the first frequency adjustment unit 503 to derive the actual values of the transformation variables e₁ to e₄ and substitutes the actual values into (34) Equation to (37) Equation, and substitutes the time-series data of the high-frequency components of the forward-and-backward-direction forces T₁ to T₄ generated by the first frequency adjustment unit 503 into (38) Equation and (39) Equation as the measured values of the forward-and-backward-direction forces T₁ to T₄ to solve the equation of (68) Equation, thereby determining the estimated values of the state variables illustrated in (44) Equation. The method of solving the equation of (68) Equation can be realized by a well-known numerical solution (Euler method or the like), for example. Therefore, when deriving the estimated values of the state variables, the state variable derivation unit 504 does not use the time-series data of the measured value of the acceleration of the vehicle body 11 in the right and left direction, the time-series data of the measured values of the accelerations of the bogies 12a, 12b in the right and left direction, and the time-series data of the measured values of the accelerations of the wheel sets 13a to 13d in the right and left direction. Besides, the observation equation is also not used.

[0183] As described above, in the present embodiment, the inspection apparatus 500 gives the measured values of the forward-and-backward-direction forces T₁ to T₄ and the actual values of the transformation variables e₁ to e₄ to the equation being the state equation with the system noise W set to 0 (zero) in which the term other than the time differential term X· of the state variable is multiplied by the forgetting factor c, to thereby derive the state variables (y_w1· to y_w4·, y_w1 to y_w4, y_t1· and y_t2·, y_t1 and y_t2, φ_t1· and φ_t2·, φ_t1 and φ_t2, φ_t1· and φ_t2·, φ_t1 and φ_t2, y_b·, y_b, φ_b·, φ_b, φ_b·, φ_b, φ_y1, φ_y2, φ_a1, φ_a2). Therefore, it is possible to derive the alignment irregularity amounts y_R1 to y_R4 (the final alignment irregularity amount y_R) without greatly decreasing accuracy, with no use of the measured values of the accelerations of the vehicle body 11, the bogies 12a, 12b, and the wheel sets 13a to 13d in the right and left direction.

[0184] Also in the present embodiment, it is possible to employ the various modified examples explained in the first embodiment. When the motion equation includes the external force or the like that does not depend on the state equation X, (68) Equation is represented as in the following (69) Equation.

[0185] G is a vector in which the term that does not depend on the state equation is stored. f is a matrix corresponding to the vector G.

(Third embodiment)

[0186] Next, there will be explained a third embodiment.

[0187] In the first and second embodiments, the case where the inspection apparatus 500 mounted on the railway vehicle calculates the final alignment irregularity amount y_R has been explained as an example. In contrast to this, in the present embodiment, a data processing device in which some functions of the inspection apparatus 500 are mounted is disposed in an operation center. The data processing device receives measured data transmitted from the railway vehicle and calculates the final alignment irregularity amount y_R by using the received measured data. In this manner, in the present embodiment, the functions possessed by the inspection apparatus 500 in the first and second embodiments are shared and executed by the railway vehicle and the operation center. Constitutions and processing due to this are mainly different between the present embodiment and the first and second embodiments. Accordingly, in the explanation of the present embodiment, the same reference numerals and symbols as those added to Fig. 1 to Fig. 10 are added to the same parts as those in the first and second embodiments, or the like, and their detailed explanations are omitted. Note that the present embodiment can be applied to any of the first and second embodiments.

[0188] Fig. 11 is a view illustrating one example of a configuration of an inspection system. In Fig. 11, the inspection system includes data collecting devices 1110a, 1110b, and a data processing device 1120. In Fig. 11, one example of functional configurations of the data collecting devices 1110a, 1110b and the data processing device 1120 is also illustrated. Note that each hardware of the data collecting devices 1110a, 1110b and the data processing device 1120 can be fabricated by the one illustrated in Fig. 6, for example. Accordingly, detailed explanations of the hardware configurations of the data collecting devices 1110a, 1110b and the data processing device 1120 are omitted.

[0189] The data collecting devices 1110a, 1110b are mounted on each railway vehicle one by one. The data processing device 1120 is disposed at the operation center. The operation center centrally manages operations of a plurality of railway vehicles, for example.

<Data collecting devices 1110a, 1110b>

[0190] The data collecting devices 1110a, 1110b can be fabricated by the same components. The data collecting devices 1110a, 1110b include data acquisition units 1111a, 1111b and data transmission units 1112a, 1112b.

[Data acquisition units 1111a, 1111b]

[0191] The data acquisition units 1111a, 1111b have the same function as that of the data acquisition unit 502. That is, the data acquisition units 1111a, 1111b acquire the time-series data of the measured values of the forward-and-backward-direction forces, similarly to the data acquisition unit 502. The configuration for obtaining the measured value of the forward-and-backward-direction force is the same as that explained in the first embodiment.

[Data transmission units 1112a, 1112b]

[0192] The data transmission units 1112a, 1112b transmit the time-series data of the measured values of the forward-and-backward-direction forces acquired by the data acquisition units 1111a, 1111b to the data processing device 1120. In the present embodiment, the data transmission units 1112a, 1112b transmit the time-series data of the measured values of the forward-and-backward-direction forces acquired by the data acquisition units 1111a, 1111b to the data processing device 1120 by radio. At this time, the data transmission units 1112a, 1112b add identification numbers of the railway vehicles on which the data collecting devices 1110a, 1110b are mounted to the time-series data of the measured values of the forward-and-backward-direction forces acquired by the data acquisition units 1111a, 1111b. In this manner, the data transmission units 1112a, 1112b transmit the time-series data of the measured values of the forward-and-backward-direction forces with the identification numbers of the railway vehicles added thereto.

<Data processing device 1120>

[Data reception unit 1121]

[0193] A data reception unit 1121 receives the time-series data of the measured values of the forward-and-backward-direction forces transmitted by the data transmission units 1112a, 1112b. To the time-series data of the measured values of the forward-and-backward-direction forces, the identification numbers of the railway vehicles, which are transmission sources of the time-series data of the measured values of the forward-and-backward-direction forces, have been added.

[Data storage unit 1122]

[0194] A data storage unit 1122 stores the time-series data of the measured values of the forward-and-backward-direction forces received by the data reception unit 1121. The data storage unit 1122 stores the time-series data of the measured value of the forward-and-backward-direction force for each identification number of the railway vehicle. The data storage unit 1122 specifies the position of the railway vehicle at the time of receipt of the time-series data of the measured value of the forward-and-backward-direction force based on the current operation situation of the railway vehicle and the time of receipt of the time-series data of the measured value of the forward-and-backward-direction force, and stores information of the specified position and the time-series data of the measured value of the forward-and-backward-direction force in association with each other. Note that the data collecting devices 1110a, 1110b may collect the information of the current positions of the railway vehicles and include the collected information in the time-series data of the measured values of the forward-and-backward-direction forces.

[Data reading unit 1123]

[0195] A data reading unit 1123 reads the time-series data of the measured value of the forward-and-backward-direction force stored in the data storage unit 1122. The data reading unit 1123 can read, out of the time-series data of the measured values of the forward-and-backward-direction forces stored in the data storage unit 1122, data designated by an operator. Further, the data reading unit 1123 can also read the time-series data of the measured value of the forward-and-backward-direction force matching a preset condition at a preset timing. In the present embodiment, the time-series data of the measured value of the forward-and-backward-direction force read by the data reading unit 1123 is determined based on at least any one of the identification number and the position of the railway vehicle, for example.

[0196] A storage unit 501, a first frequency adjustment unit 503, a state variable derivation unit 504, a second frequency adjustment unit 505, a track state derivation unit 506, and an output unit 507 are the same as those explained in the first embodiment. Accordingly, their detailed explanations are omitted here. Note that the first frequency adjustment unit 503 uses the time-series data of the measured value of the forward-and-backward-direction force read by the data reading unit 1123 in place of using the time-series data of the measured value of the forward-and-backward-direction force acquired by the data acquisition unit 502, and generates the time-series data of the high-frequency components of the forward-and-backward-direction forces T₁ to T₄.

<Summary>

[0197] As described above, in the present embodiment, the data collecting devices 1110a, 1110b mounted on the railway vehicles collect the time-series data of the measured values of the forward-and-backward-direction forces to transmit the data to the data processing device 1120. The data processing device 1120 disposed at the operation center stores the time-series data of the measured values of the forward-and-backward-direction forces received from the data collecting devices 1110a, 1110b and uses the stored time-series data of the measured values of the forward-and-backward-direction forces to calculate the final alignment irregularity amount y_R. Accordingly, in addition to the effects explained in the first and second embodiments, for example, the following effects are exhibited. That is, the data processing device 1120 can calculate the final alignment irregularity amount y_R at an arbitrary timing by reading the measured data at an arbitrary timing. Further, the data processing device 1120 can output time-series variation of the final alignment irregularity amount y_R at the same position. Further, the data processing device 1120 can output the final alignment irregularity amounts y_R in a plurality of routes for each route.

<Modified example>

[0198] In the present embodiment, the case where the data collecting devices 1110a, 1110b directly transmit the measured data to the data processing device 1120 has been explained as an example. However, it is not always necessary to design as above. An inspection system may be built by using cloud computing, for example.

[0199] Besides, also in the present embodiment, it is possible to employ the various modified examples explained in the first and second embodiments.

[0200] Further, in the first and second embodiments, the case where the storage unit 501, the data acquisition unit 502, the first frequency adjustment unit 503, the state variable derivation unit 504, the second frequency adjustment unit 505, the track state derivation unit 506, and the output unit 507 are included in one apparatus has been explained as an example. However, it is not always necessary to design as above. Functions of the storage unit 501, the data acquisition unit 502, the first frequency adjustment unit 503, the state variable derivation unit 504, the second frequency adjustment unit 505, the track state derivation unit 506, and the output unit 507 may be fabricated by a plurality of apparatuses. In this case, the inspection system is constituted by using these plural apparatuses.

(Calculation examples)

[0201] Next, calculation examples will be explained. In the present calculation example, derivation of a final alignment irregularity amount y_R based on the method of the first embodiment and derivation of a final alignment irregularity amount y_R based on the method of the second embodiment were performed. In the method of the first embodiment, when performing the data assimilation, the value to be normally given as the measured value of the observation variable (fixed value) was set to 0 (zero). Further, in the method of the second embodiment, the forgetting factor c was set to 0.9987.

[0202] Further, in contrast to the method of the first embodiment, derivation of a final alignment irregularity amount y_R was performed based on a method in which as the values to be given as the measured values of the observation variables (the measured values of the accelerations of the vehicle body 11, the bogies 12a, 12b, and the wheel sets 13a to 13d in the right and left direction), not the preset fixed value but the measured values are given as they are (namely, the method described in Patent Literature 1).

[0203] Fig. 12 illustrates the present calculation example, and is a view illustrating the curvature 1/R of the track 16 being the target of deriving the alignment irregularity amount and the traveling velocity v of the railway vehicle. In Fig. 12, a graph 1201 indicates the traveling velocity of the railway vehicle, and a graph 1202 indicates the curvature 1/R of the track 16. Note that the horizontal axis in Fig. 12 indicates an elapsed time (second) from a reference time when the reference time is set to 0 (zero).

[0204] Each of Fig. 13A and Fig. 13B illustrates the present calculation example, and is a view illustrating a distribution of eigenvalues of an autocorrelation matrix R. Fig. 13A illustrates a distribution of eigenvalues of an autocorrelation matrix R with respect to the forward-and-backward-direction force T₁ in the wheel set 13a, and Fig. 13B illustrates a distribution of eigenvalues of an autocorrelation matrix R with respect to the forward-and-backward-direction force T₂ in the wheel set 13b.

[0205] Fig. 14 illustrates the present calculation example, and is a view illustrating time-series data of the measured values y of the forward-and-backward-direction forces T₁, T₂ and time-series data of predicted values y^_k of the forward-and-backward-direction forces T₁, T₂ (time-series data obtained by extracting low-frequency components included in the time-series data of the measured values y of the forward-and-backward-direction forces). In Fig. 14, the measured value indicates the time-series data of the measured value y of the forward-and-backward-direction force, and bias indicates the time-series data of the predicted value y^_k of the forward-and-backward-direction force. Note that the horizontal axis in Fig. 14 indicates a measuring time and a calculating time of the forward-and-backward-direction forces T₁ to T₄, each of which is an elapsed time (second) from a reference time when the reference time is set to 0 (zero).

[0206] Fig. 15 illustrates the present calculation example, and is a view illustrating the time-series data of the high-frequency components of the forward-and-backward-direction forces T₁, T₂. The time-series data of the high-frequency components of the forward-and-backward-direction forces T₁, T₂ can be obtained by subtracting the time-series data of the predicted values y^_k of the forward-and-backward-direction forces T₁, T₂ from the time-series data of the measured values y of the forward-and-backward-direction forces T₁, T₂ illustrated in Fig. 14. Note that the horizontal axis in Fig. 15 indicates an elapsed time (second) from a reference time when the reference time is set to 0 (zero) and indicates a calculating time of the time-series data of the high-frequency components of the forward-and-backward-direction forces T₁, T₂.

[0207] Fig. 16A and Fig. 16B are views illustrating the alignment irregularity amounts y_R derived by the method of the first embodiment and the method described in Patent Literature 1 by using the time-series data of the high-frequency components of the forward-and-backward-direction forces T₁, T₂ illustrated in Fig. 15. In Fig. 16A, the calculated value indicates the alignment irregularity amount y_R derived by the method described in Patent Literature 1, and the measured value indicates the measured value of the alignment irregularity amount y_R. In Fig. 16B, the calculated value indicates the alignment irregularity amount y_R derived by the method of the first embodiment, and the measured value indicates the measured value of the alignment irregularity amount yR. Here, as the calculated value of the alignment irregularity amount y_R, an average value of the alignment irregularity amount y_R at the position of the wheel set 13a and the alignment irregularity amount y_R2 at the position of the wheel set 13b was used. Further, the measured value illustrated in Fig. 16A and the measured value illustrated in Fig. 16B are the same. Note that the horizontal axis in each of Fig. 16A and Fig. 16B indicates an elapsed time (second) from a reference time when the reference
time is set to 0 (zero) and indicates a time corresponding to the position where the alignment irregularity amount y_R exists. Further, in Fig. 16A, the illustration of data of a part at which a distance from a starting point of the railway vehicle is small is omitted for convenience of illustration.

[0208] Fig. 17A is a view illustrating the alignment irregularity amount y_R derived by the method of the second embodiment by using the time-series data of the high-frequency components of the forward-and-backward-direction forces T₁, T₂ illustrated in Fig. 15. Fig. 17B is a view illustrating the alignment irregularity amount y_R derived by the method described in Patent Literature 1 by using the time-series data of the high-frequency components of the forward-and-backward-direction forces T₁, T₂ illustrated in Fig. 15. In Fig. 17A, the calculated value indicates the alignment irregularity amount y_R derived by the method described in Patent Literature 1, and the measured value indicates the measured value of the alignment irregularity amount y_R. In Fig. 17B, the calculated value indicates the alignment irregularity amount y_R derived by the method of the second embodiment, and the measured value indicates the measured value of the alignment irregularity amount y_R. Here, as the calculated value of the alignment irregularity amount y_R, an average value of the alignment irregularity amount y_R1 at the position of the wheel set 13a and the alignment irregularity amount y_R2 at the position of the wheel set 13b was used. Further, the measured value illustrated in Fig. 17A and the measured value illustrated in Fig. 17B are the same (these measured values are also the same as the measured values illustrated in Fig. 16A and Fig. 16B). Note that the horizontal axis in each of Fig. 17A and Fig. 17B indicates an elapsed time (second) from a reference time when the reference time is set to 0 (zero) and indicates a time corresponding to the position where the alignment irregularity amount y_R exists. Further, in Fig. 17A and Fig. 17B, the illustration of data of a part at which a distance from a starting point of the railway vehicle is small is omitted for convenience of illustration.

[0209] When the calculated value in Fig. 16A and the calculated value in Fig. 16B are compared, it can be understood that the alignment irregularity amount y_R derived by the method of the first embodiment matches the alignment irregularity amount y_R derived by the method described in Patent Literature 1 with good accuracy. Further, it can be understood that the calculated value and the measured value also match with good accuracy. In like manner, when the calculated value in Fig. 17A and the calculated value in Fig. 17B are compared, it can be understood that the alignment irregularity amount y_R derived by the method of the second embodiment matches the alignment irregularity amount y_R derived by the method described in Patent Literature 1 with good accuracy. Further, it can be understood that the calculated value and the measured value also match with good accuracy. Further, when the calculated value in Fig. 16B and the calculated value in Fig. 17B are compared, it can be understood that the both values are almost the same, and thus the equivalent alignment irregularity amount y_R can be derived by both the method of the first embodiment and the method of the second embodiment.

(Another embodiment)

[0210] Note that the embodiments of the present invention explained above can be fabricated by causing a computer to execute a program. Further, a computer-readable recording medium in which the aforementioned program is recorded and a computer program product such as the aforementioned program can also be applied as the embodiment of the present invention. As the recording medium, it is possible to use a flexible disk, a hard disk, an optical disk, a magneto-optic disk, a CD-ROM, a magnetic tape, a nonvolatile memory card, a ROM, or the like, for example.

[0211] Further, the embodiments of the present invention explained above merely illustrate concrete examples of implementing the present invention, and the technical scope of the present invention is not to be construed in a restrictive manner by these embodiments. That is, the present invention may be implemented in various forms without departing from the technical spirit or main features thereof.

[0212] Note that the entire contents of the description and drawings of Patent Literature 1 can be incorporated herein by reference.

INDUSTRIAL APPLICABILITY

[0213] The present invention can be utilized for inspecting railway vehicles, for example.

Claims

1. An inspection system, comprising:

a data acquisition means that acquires data of a measured value of a forward-and-backward-direction force as data of a measured value to be measured by causing a railway vehicle including a vehicle body, a bogie, and a wheel set to travel on a track;

a state variable derivation means that derives state variables being variables to be determined in a state equation constituted by using motion equations that describe motions of the railway vehicle, by using the measured value of the forward-and-backward-direction force; and

a track state derivation means that derives information reflecting a state of the track, wherein

the forward-and-backward-direction force is a force in a forward and backward direction that occurs in a member disposed between the wheel set and the bogie on which the wheel set is provided, and is a force to be determined according to a difference between an angular displacement of the wheel set in a yawing direction and an angular displacement of the bogie on which the wheel set is provided in the yawing direction,

the member is a member for supporting an axle box,

the forward and backward direction is a direction along a traveling direction of the railway vehicle,

the yawing direction is a pivoting direction with an up and down direction being a direction vertical to the track set as a pivot axis,

the state equation is an equation described by using the state variables, the forward-and-backward-direction force, and a transformation variable,

the state variables include a displacement and a velocity of the bogie in a right and left direction, an angular displacement and an angular velocity of the bogie in the yawing direction, an angular displacement and an angular velocity of the bogie in a rolling direction, a displacement and a velocity of the wheel set in the right and left direction, and an angular displacement of an air spring attached to the railway vehicle in the rolling direction, and do not include an angular displacement and an angular velocity of the wheel set in the yawing direction,

the rolling direction is a pivoting direction with the forward and backward direction set as a pivot axis,

the transformation variable is a variable that performs mutual transformation between the angular displacement of the wheel set in the yawing direction and the angular displacement of the bogie in the yawing direction,

the track state derivation means uses the angular displacement of the bogie in the yawing direction, which is one of the state variables derived by the state variable derivation means, and an actual value of the transformation variable to derive an estimated value of the angular displacement of the wheel set in the yawing direction, and uses the derived estimated value of the angular displacement of the wheel set in the yawing direction to derive the information reflecting the state of the track,

the actual value of the transformation variable is derived by using the measured value of the forward-and-backward-direction force, and

the state variable derivation means derives the state variables without using measured values of accelerations of the bogie, the wheel set, and the vehicle body in the right and left direction during a period in which the measured value of the forward-and-backward-direction force has been obtained.

2. The inspection system according to claim 1, wherein

the state variable derivation means performs an operation using a filter performing data assimilation by using the state equation and an observation equation, to derive the state variables,

the observation equation is an equation described by using an observation variable and the transformation variable,

the observation variable includes the accelerations of the bogie and the wheel set in the right and left direction, and

the state variable derivation means uses the state equation into which the measured value of the forward-and-backward-direction force and the actual value of the transformation variable are substituted, and the observation equation into which the actual value of the transformation variable is substituted, by setting a value to be normally given as a measured value of the observation variable to a preset fixed value when performing the data assimilation, and derives the state variables when an error of a calculated value of the observation variable with respect to the fixed value or an expected value of the error becomes minimum.

3. The inspection system according to claim 2, wherein
the fixed value is 0.

4. The inspection system according to claim 2 or 3, wherein

the state equation is constituted by using a motion equation that describes motion of the wheel set in the right and left direction, a motion equation that describes motion of the bogie in the right and left direction, a motion equation that describes motion of the bogie in the yawing direction, a motion equation that describes motion of the bogie in the rolling direction, and a motion equation that describes motion of the air spring in the rolling direction,

the motion equation that describes the motion of the bogie in the yawing direction is a motion equation described by using the forward-and-backward-direction force in place of using the angular displacement and the angular velocity of the wheel set in the yawing direction,

the observation equation is constituted by using the motion equation that describes the motion of the wheel set in the right and left direction and the motion equation that describes the motion of the bogie in the right and left direction,

the motion equation that describes the motion of the wheel set in the right and left direction is a motion equation described by using the transformation variable in place of using the angular displacement of the wheel set in the yawing direction, and

the transformation variable is represented by a difference between the angular displacement of the bogie in the yawing direction and the angular displacement of the wheel set in the yawing direction.

5. The inspection system according to claim 4, wherein

the state equation is constituted by further using a motion equation that describes motion of the vehicle body in the right and left direction, a motion equation that describes motion of the vehicle body in the yawing direction, a motion equation that describes motion of the vehicle body in the rolling direction, and a motion equation that describes motion of a yaw damper attached to the railway vehicle in the yawing direction,

the observation equation is constituted by further using the motion equation that describes the motion of the vehicle body in the right and left direction,

the observation variable further includes the acceleration of the vehicle body in the right and left direction, and

the state variables further include a displacement and a velocity of the vehicle body in the right and left direction, an angular displacement and an angular velocity of the vehicle body in the yawing direction, an angular displacement and an angular velocity of the vehicle body in the rolling direction, and an angular displacement of the yaw damper in the yawing direction.

6. The inspection system according to any one of claims 2 to 5, wherein
the filter is a Kalman filter.

7. The inspection system according to claim 1, wherein
the state variable derivation means does not solve the state equation but solves an equation being an equation representing the motion equations that describe the motions of the railway vehicle by using the state variables, the forward-and-backward-direction force, and the transformation variable, into which the measured value of the forward-and-backward-direction force and the actual value of the transformation variable are substituted, to derive the state variables.

8. The inspection system according to claim 7, wherein
the state variable derivation means does not use the state equation but uses an equation being an equation as a result of changing the equation representing the motion equations that describe the motions of the railway vehicle by using the state variables, the forward-and-backward-direction force, and the transformation variable so that a temporal change in the state variables becomes smaller than that of the equation, into which the measured value of the forward-and-backward-direction force and the actual value of the transformation variable are substituted, to derive the state variables.

9. The inspection system according to claim 8, wherein

the state variable derivation means solves an equation being the equation representing the motion equations that describe the motions of the railway vehicle by using the state variables, the forward-and-backward-direction force, and the transformation variable in which each term which is connected to a term of first-order time differential of the state variable by an equal sign is multiplied by a forgetting factor, to derive the state variables, and

the forgetting factor is a preset value of 0.95 or more and less than 1.

10. The inspection system according to any one of claims 7 to 9, wherein

the motion equations that describe the motions of the railway include a motion equation that describes motion of the wheel set in the right and left direction, a motion equation that describes motion of the bogie in the right and left direction, a motion equation that describes motion of the bogie in the yawing direction, a motion equation that describes motion of the bogie in the rolling direction, and a motion equation that describes motion of the air spring in the rolling direction,

the motion equation that describes the motion of the wheel set in the right and left direction is a motion equation described by using the transformation variable in place of using the angular displacement of the wheel set in the yawing direction,

the motion equation that describes the motion of the bogie in the yawing direction is a motion equation described by using the forward-and-backward-direction force in place of using the angular displacement and the angular velocity of the wheel set in the yawing direction, and

the transformation variable is represented by a difference between the angular displacement of the bogie in the yawing direction and the angular displacement of the wheel set in the yawing direction.

11. The inspection system according to claim 10, wherein

the motion equations that describe the motions of the railway further include a motion equation that describes motion of the vehicle body in the right and left direction, a motion equation that describes motion of the vehicle body in the yawing direction, a motion equation that describes motion of the vehicle body in the rolling direction, and a motion equation that describes motion of a yaw damper attached to the railway vehicle in the yawing direction, and

the state variables further include a displacement and a velocity of the vehicle body in the right and left direction, an angular displacement and an angular velocity of the vehicle body in the yawing direction, an angular displacement and an angular velocity of the vehicle body in the rolling direction, and an angular displacement of the yaw damper in the yawing direction.

12. The inspection system according to any one of claims 1 to 11, wherein

the track state derivation means derives an alignment irregularity amount of the track as information reflecting the state of the track, based on the displacement and the velocity of the bogie in the right and left direction, each of which is one of the state variables derived by the state variable derivation means, the displacement and the velocity of the wheel set in the right and left direction, each of which is one of the state variables derived by the state variable derivation means, the estimated value of the angular displacement of the wheel set in the yawing direction, the measured value of the forward-and-backward-direction force, and the motion equation that describes motion of the wheel set in the yawing direction, and

the motion equation that describes the motion of the wheel set in the yawing direction includes the forward-and-backward-direction force and the alignment irregularity amount of the track as variables.

13. The inspection system according to any one of claims 1 to 11, wherein
the track state derivation means derives a lateral force being a stress in the right and left direction between a wheel provided on the wheel set and the track, as the information reflecting the state of the track, based on the angular displacement of the wheel set in the yawing direction and the velocity of the wheel set in the right and left direction which is one of the state variables.

14. The inspection system according to any one of claims 1 to 13, further comprising

a frequency adjustment means that reduces a signal strength of a low-frequency component to be generated due to the railway vehicle traveling on a curved portion of the track from time-series data of a physical quantity whose value varies according to a state of the railway vehicle, wherein

the frequency adjustment means includes a first frequency adjustment means that reduces a signal strength of a low-frequency component to be generated due to the railway vehicle traveling on a curved portion of the track from time-series data of a measured value of the forward-and-backward-direction force being one of the physical quantity, and

the state variable derivation means uses the value of the forward-and-backward-direction force from which the signal strength of the low-frequency component has been reduced by the first frequency adjustment means to derive the state variables.

15. An inspection method, comprising:

a data acquisition step of acquiring data of a measured value of a forward-and-backward-direction force as data of a measured value to be measured by causing a railway vehicle including a vehicle body, a bogie, and a wheel set to travel on a track;

a state variable derivation step of deriving state variables being variables to be determined in a state equation constituted by using motion equations that describe motions of the railway vehicle, by using the measured value of the forward-and-backward-direction force; and

a track state derivation step of deriving information reflecting a state of the track, wherein

the forward-and-backward-direction force is a force in a forward and backward direction that occurs in a member disposed between the wheel set and the bogie on which the wheel set is provided, and is a force to be determined according to a difference between an angular displacement of the wheel set in a yawing direction and an angular displacement of the bogie on which the wheel set is provided in the yawing direction,

the member is a member for supporting an axle box,

the forward and backward direction is a direction along a traveling direction of the railway vehicle,

the yawing direction is a pivoting direction with an up and down direction being a direction vertical to the track set as a pivot axis,

the state equation is an equation described by using the state variables, the forward-and-backward-direction force, and a transformation variable,

the state variables include a displacement and a velocity of the bogie in a right and left direction, an angular displacement and an angular velocity of the bogie in the yawing direction, an angular displacement and an angular velocity of the bogie in a rolling direction, a displacement and a velocity of the wheel set in the right and left direction, and an angular displacement of an air spring attached to the railway vehicle in the rolling direction, and do not include an angular displacement and an angular velocity of the wheel set in the yawing direction,

the rolling direction is a pivoting direction with the forward and backward direction set as a pivot axis,

the transformation variable is a variable that performs mutual transformation between the angular displacement of the wheel set in the yawing direction and the angular displacement of the bogie in the yawing direction,

the track state derivation step uses the angular displacement of the bogie in the yawing direction, which is one of the state variables derived by the state variable derivation step, and an actual value of the transformation variable to derive an estimated value of the angular displacement of the wheel set in the yawing direction, and uses the derived estimated value of the angular displacement of the wheel set in the yawing direction to derive the information reflecting the state of the track,

the actual value of the transformation variable is derived by using the measured value of the forward-and-backward-direction force, and

the state variable derivation step derives the state variables without using measured values of accelerations of the bogie, the wheel set, and the vehicle body in the right and left direction during a period in which the measured value of the forward-and-backward-direction force has been obtained.

16. A computer program causing a computer to execute:

a data acquisition step of acquiring data of a measured value of a forward-and-backward-direction force as data of a measured value to be measured by causing a railway vehicle including a vehicle body, a bogie, and a wheel set to travel on a track;

a state variable derivation step of deriving state variables being variables to be determined in a state equation constituted by using motion equations that describe motions of the railway vehicle, by using the measured value of the forward-and-backward-direction force; and

a track state derivation step of deriving information reflecting a state of the track, wherein

the forward-and-backward-direction force is a force in a forward and backward direction that occurs in a member disposed between the wheel set and the bogie on which the wheel set is provided, and is a force to be determined according to a difference between an angular displacement of the wheel set in a yawing direction and an angular displacement of the bogie on which the wheel set is provided in the yawing direction,

the member is a member for supporting an axle box,

the forward and backward direction is a direction along a traveling direction of the railway vehicle,

the yawing direction is a pivoting direction with an up and down direction being a direction vertical to the track set as a pivot axis,

the state equation is an equation described by using the state variables, the forward-and-backward-direction force, and a transformation variable,

the state variables include a displacement and a velocity of the bogie in a right and left direction, an angular displacement and an angular velocity of the bogie in the yawing direction, an angular displacement and an angular velocity of the bogie in a rolling direction, a displacement and a velocity of the wheel set in the right and left direction, and an angular displacement of an air spring attached to the railway vehicle in the rolling direction, and do not include an angular displacement and an angular velocity of the wheel set in the yawing direction,

the rolling direction is a pivoting direction with the forward and backward direction set as a pivot axis,

the transformation variable is a variable that performs mutual transformation between the angular displacement of the wheel set in the yawing direction and the angular displacement of the bogie in the yawing direction,

the track state derivation step uses the angular displacement of the bogie in the yawing direction, which is one of the state variables derived by the state variable derivation step, and an actual value of the transformation variable to derive an estimated value of the angular displacement of the wheel set in the yawing direction, and uses the derived estimated value of the angular displacement of the wheel set in the yawing direction to derive the information reflecting the state of the track,

the actual value of the transformation variable is derived by using the measured value of the forward-and-backward-direction force, and

the state variable derivation step derives the state variables without using measured values of accelerations of the bogie, the wheel set, and the vehicle body in the right and left direction during a period in which the measured value of the forward-and-backward-direction force has been obtained.

Drawing