BACKGROUND OF THE INVENTION
[0001] The present invention relates to a method of producing a train running plan which
is effective for realizing a high speed and high density running, or an energy-saving
running of a railway train.
[0002] With respect to a method of producing the optimal train running plan under the conditions
such as line conditions, e.g., a limit speed and a grade, and rolling stock characteristics,
e.g., a running resistance, driving force characteristics, and speed decreasing characteristics,
there are published the following literatures:
Literature 1; 5th National Symposium for Utilization of Cybernetics in a Railway,
June, 1968, pp. 11-16; and
Literature 2; The Transactions of the Institute of Electrical Engineering Engineer's
of Japan, Vol. 106-B, No. 9, September, 1986, pp. 769-776.
[0003] The method in the literature 1 is such that the optimal running method is obtained
in the running of arbitrary form between stations on the basis of the dynamic planning
by treating the running time, the power consumption and the number of notch switching
as the objective factors. This method is obtained in the form of notch sequence. Then,
the running time, the power consumption and the like as the objective factors are
obtained by performing the running simulation of the train to determine the position,
the speed and the like of the train.
[0004] In the literature 2, the discussion is made with respect to the energy-saving running
method in the running of the super-express railway's train stopping every station,
between the stations. In the literature 1, the calculation is made by the simulation
with the time base being divided since the equation of motion of the train cannot
be exactly obtained in the large area. On the other hand, in the literature 2, each
of the strict solutions is obtained on the assumption that the magnitude of the grade
takes a fixed value and the resultant solutions are linked to one another to perform
the calculation of the consumed energy, the necessary time and the like.
[0005] The discussion about the energy-saving running method in the literature 2 is made
in such a way that four patterns near the actual running are prepared, the consumed
energy is calculated every running pattern on the assumption that the magnitude of
the grade is zero over the whole terriotires, and the predetermined comparison is
performed. Out of the four running patterns, the running pattern having the minimum
consumed energy provides the results of the maximum acceleration - the fixed running
at the maximum speed - stopping by the repetition of the coasting and the normal maximum
braking.
[0006] In the above-mentioned running pattern having the minimum consumed energy, only the
maximum speed is changed to obtain the speed in which the necessary time coincides
with the schedule time for realizing the scheduled running in which the necessary
time coincides with the schedule time.
[0007] However, in the prior art method of obtaining the optimal running plan on the basis
of the dynamic planning in the literature 1, there arises a problem in that the calculation
requires much time.
[0008] In the literature 2, as the running pattern of the limit speed between the stations,
only the pattern shown in Fig. 1 is supposed. Thus, the method described therein can
be applied to only this running pattern. Therefore, it cannot be applied to the complicated
pattern as shown in Fig. 2 for example.
[0009] Further, in addition to the literatures 1 and 2, with respect to the method of changing
the train running plan produced in advance in the train in a real-time manner, there
is published the literature 3, i.e., The Transactions of the Institute of Electrical
Engineering Engineer's of Japan, Vol. 107-D, No. 5, May, 1987, pp. 665-672.
[0010] The method described in the literature 3 is about the running plan of the super-express
railway's train stopping every station. In this case, the running pattern as shown
in Fig. 1 is supposed as the running pattern of the limit speed. Then, out of a plurality
of running methods which are supposed in advance, one providing the minimum energy-saving
is determined on the assumption that the magnitude of the grade is zero over the territory
shown in Fig. 1. The resultant energy-saving running method is such that the running
pattern is obtained by combining the maximum acceleration, the fixed speed running,
the coasting and the maximum deceleration with one another.
[0011] In the running method having such a running pattern, the parameters which are to
be determined in advance are the maximum speed and the deceleration starting point
in the running territory. The two parameters are changed so as to provide the maximum
energy-saving running under the condition of the scheduled running (the running time
coincides with the schedule time).
[0012] In the method described in the literature 3, only the running pattern as shown in
Fig. 1 is supposed as the running pattern of the limit speed between the stations,
the method of energy-saving running is determined in advance, and only the determination
of the deceleration starting point is performed in the real-time change in the train.
Therefore, this method cannot cope with the occurrence of change of the limit speed
as shown in Fig. 3A, for example, which is not supposed in advance.
SUMMARY OF THE INVENTION
[0013] It is an object of the present invention to determine the target speed so as to provide
the minimum consumed energy during the running of the train.
[0014] It is another object of the present invention to obtain the subsequent target speed
on the basis of the change ratio of the consumed energy between the running speed
and the target speed of interest when the running speed of the train is changed.
[0015] It is still another object of the present invention to correct the limit speed of
the train to the original one when the limit speed of the train is changed.
[0016] The first feature of the present invention will hereinbelow be described. The general
pattern of the limit speed between the stations is supposed as shown in Fig. 4, and
the running pattern on the basis of that limit speed is assumed here. Then, the limit
speed territories in Fig. 4 are numbered serially (the number of territories is N).
At the same time, it is assumed that the limit speed in the i-th limit speed territory
is V
MAX,i and the running speed to be targeted (hereinafter, referred to as simply "the target
speed", when applicable) is Vi. Then, the relationship of Vi < V
MAX,i is established.
[0017] Under such assumptions, to set the target speed (it is not always possible to reach
this target speed) every limit territory is determined the train running method between
the associated stations. For example, in the running pattern of the maximum acceleration
- the fixed speed running - the deceleration by the normal maximum braking, under
the limit speed of V
MAx,i (i = I, ..., N), if Vi (i = I, ..., N) is established, the train running method between
the associated stations is correspondingly established. Conversely, it is also true
that to establish the train running method between the stations is to establish Vi
(i = I, ..., N).
[0018] By the optimal running method in the train running method as described above, it
means the scheduled running in which the necessary time required for the train to
run between the stations coincides with the schedule time and at this time, the minimum
consumed energy is obtained.
[0019] It is assumed that the necessary time required for the train to run through a predetermined
territory is T and the consumed energy is E. Then, the necessary time T and the consumed
energy E cannot be analytically calculated even if the line conditions and the rolling
stock characteristics as already described are known. However, these factors can be
obtained by making the equation of motion of the train discrete corresponding to the
travel distance and by performing the numerical calculation (i.e., by performing the
simulation).
[0020] At this time, if Vi (i = I, ..., N) is established, the necessary time T and the
consumed energy E are uniquely obtained. Therefore, each of T and E is a function
of Vi (i = I, ..., N). That is, the following relational expressions are established:

Then, to obtain the optimal Vi (i = I, ..., N) is established mathematically in such
a way as to obtain a set of target speed Vi, ..., V
N for minimizing the objective function E(Vi, ..., V
N), under the condition of the necessary time T(V
i, ..., V
N) = the schedule time T
D.
[0021] More specifically, Vi is changed so as to decrease the consumed energy E, and for
example, the partial derivative ∂aE/∂Vi of E with respect to Vi is obtained. Thus,
the direction of decreasing of E is obtained. There is known a non-linear planning
in which the calcualtion for obtaining the direction of decreasing of E is repeated
until the necessary time T approaches the scheduled time T
D within the range of a certain allowable error δT, and when the necessary time T becomes
in the range of the allowable error, the above calculation is finished.
[0022] Or, the following equation may be used as the objective function.

In this case, it is possible to simultaneously evaluate both the consumed energy E
and the necessary time T. At this time, the evaluation by only the consumed energy
E can be performed in the case of a = 0.
[0023] The above description has been given with respect to the specific case where the
train runs through the territory between the two stations, and it is then stopped
at the following station. However, even in the case where both the two stations are
passed stations, the same means can be used by giving the initial speed at the first
station in addition to the above conditions.
[0024] The second feature of the present invention is such that when the running speed of
the train is changed, the subsequent target speed V = (V
1, V
2, ..., V
N) as a vector form is newly obtained on the basis of the change ratio of the consumed
energy between that running speed and the target speed of interest. Therefore, the
component of the gradient vector VE(V) in the direction of decreasing of the consumed
energy E is obtained from the following approximate expression.

[0025] That is, the target speed V(n) is changed in the direction of the gradient vector,
and the target speed V(n) for minimizing the consumed energy E is obtained. According
to the second feature of the present invention, instead of the gradient vector VE(V),
the ratio of the decreasing of the consumed energy E to the increasing of the running
time T when V(n) is changed by AV(n), i.e., the ratio of AE to AT is used. Then, each
of the components of each of the gradient vectors is obtained from the following equation.

[0026] The value of the equation (4) is called p(m). Then, let p(n) be replaced with p as
the form of vector. Then, the target speed V is changed in the direction of p. In
this case, it is assumed that the initial value of the target speed V(n) is expressed
by {the limit speed Vmax(n) - (the marginal speed)}. Then, by the marginal speed it
means the upper limit speed that does not exceed the limit speed during the running
at the fixed speed.
[0027] The third feature of the present invention is such that it is assumed that the optimal
running method is obtained in advance, because of correcting the running time, the
running data which are produced in advance by the simulation and the like are utilized,
and when a predetermined limit speed is changed, the running plan is corrected so
that the running time becauses the previously determined running time.
[0028] In the calculation of the running time, in addition to the running curve on the speed
curve which is expressed by the speed on the axis of ordinate with respect to the
position on the axis of abscissa as shown in Fig. 5, the curve of the inverse number
of the speed is also utilized. Since the single integral of the inverse number of
the speed with respect to the position on the axis of abscissa becomes the running
time of the territory of interest, it is herein referred to as "the running time density",
and is expressed by X.
[0031] Since each of the functions p(x), q(x), f(x), g(x), F(x) and G(x) is a monotonous
function, these functions have respective inverse functions. Moreover, as the functions
necessary for the calculation of the running time, the data of F(f
-1(λ)) with respect to the variable X in the acceleration and the data of G(g
-1(λ)) with respect to the variable λ in the deceleration are produced.
[0032] Although these functions are not always clearly expressed in the form of formula,
they are stored in the computer in the form of discrete numeral data.
[0033] Fig. 9 is a graphical representation showing the running of the train in which the
fixed speed running is performed up to the position x
1 at the speed Vi, the acceleration is started from the position xi, the running speed
reaches the speed V
2 in the position ξ
1, the fixed speed running is performed up to the position x
2 at the speed V
2, the deceleration is started from the position x
2, the running speed reaches the speed V
3 in the position ξ
2, and the fixed speed running is performed up to the position X3. Incidentally, in
this case, it is also assumed that the magnitude of the grade is zero in each of the
running territories.
[0034] Moreover, Fig. 10 is a graphical representation showing the inverse number of the
speed, i.e., the running time density. The running time density is expressed by the
following equation.

[0035] The position ξ
1, where the running is switched over from the accleration to the fixed speed running
can be obtained using the speed curve p(x) in the acceleration of Fig. 7, and the
distance required for the acceleration from V
1 to V
2 can be obtained by the following equation.

[0036] The running time T
A from X
1 to ξ
1, corresponds to the area A shown in Fig. 10. In order to obtain this running time
T
A, the travel territory between X1, and ξ
2 is converted into the characteristics shown in Fig. 7 and the resultant characteristic
curve of Fig. 7 is then integrated. First, the positions y
1, and y
2 shown in Fig. 7 corresponding to λ
1, and X
2 are given by y
1 = f
-1(λ
1) and y
2 = f
-1(λ
2), respectively. Therefore, the running time T
A is given by:

[0037] Moreover, the running time T
B from ξ
1, to x2 corresponds to the area B and is given by λ
2 · (x
2 - ξ
1). As a result, the running time T
AB from X
1 to x
2 is obtained using the following equation.

[0038] The position ξ
2 where the running is switched over from the deceleration to the fixed speed running
is obtained from the following equation, using the speed curve q(x) in the deceleration
of Fig. 8.

In the same manner as in the acceleration, the running time Tc from x
2 to ξ
2 is given by:

[0039] The running time Tα from ξ
2 to
X3 corresponds to the area D and is given by λ
3·(X
3 - ξ
2). As a result, the running time Tαα from x2 to
X3 is obtained using the following equation.

[0040] The reason for performing the calculation on the assumption that the magnitude of
the grade is zero in the above description is that since the magnitude of the grade
depends on the place, taking the actual grades into consideration, it is impossible
to produce the desired data in advance by the simulation. However, the following items
are true:
1. Since the recalculation of the running time in the train is necessary for the territory
where the change of the limit speed occurs locally and the subsequent several territories,
the distance requiring the recalculation is short. Thus, there is a small error between
this case and the case where the magnitude of the grade is taken into consideration.
2. Such a territory where the change of the limit speed occurs is mainly included
in the high speed area, and therefore, there is small influence of some variation
of the speed due to the grade upon the running time.
[0041] For the above reasons, there is the small error between the present case and the
case where the magnitude of the grade is taken into consideration.
[0042] As described above, the necessary data are calculated in advance by the simulation
and the like, and the running time is then calculated using the resultant data, whereby
it is possible to correct the running method which is set in advance, in a real-time
manner.
[0043] According to the correcting method of the third feature of the present invention,
the necessary data is calculated in advance by the simulation and the like, and the
running time is then calculated using the resultant data to correct the running method.
Therefore, even when the necessity of correcting the train running method occurs,
e.g., the change of the limit speed temporarily occurs, it is possible to correct
the running method in the train in a real-time manner.
BRIEF DESCRIPTION OF THE DRAWINGS
[0044]
Fig. 1 is a graphical representation showing a prior art running pattern of a limit
speed between stations;
Fig. 2 is a graphical representation showing an example of a running pattern of a
limit speed between stations;
Fig. 3A is a graphical representation showing an example of the running pattern in
the case where the setting of the limit speed occurs temporarily;
Fig. 3B is a graphical representation showing an example of the running pattern corresponding
to the inverse number of the limit speed illustrated in Fig. 3A;
Fig. 4 is a graphical representation showing an example of the running pattern of
the limit speed between the stations;
Fig. 5 is a graphical representation showing a running pattern used for correcting
the running plan;
Fig. 6 is a graphical representation showing the inverse number of the running pattern
shown in Fig. 5;
Fig. 7 is a graphical representation showing the speed, the inverse number of the
speed and the running time in the acceleration in the case where the magnitude of
the grade of the travel territory is "0";
Fig. 8 is a graphical representation showing the speed, the inverse number of the
speed and the running time in the deceleration in the case where the magnitude of
the grade of the travel territory is "0";
Fig. 9 and Fig. 10 are graphical representations useful in explaining the calculation
of the running time using the inverse number of the speed;
Fig. 11 is a block diagram showing the arrangement of a system for carrying out a
method of producing a train running plan according to the present invention;
Fig. 12 is a flow chart showing the method of producing a train running plan of a
first embodiment according to the present invention;
Fig. 13 is a diagram useful in explaining an example of the running plan which is
displayed on a CRT of a train system;
Fig. 14 is a graphical representation showing an example of the grade data of a limit
speed territory;
Fig. 15 is a graphical representation showing the running pattern of the limit speed
which is used when a train passes a station;
Fig. 16 is a flow chart showing the method of producing a train running plan of a
second embodiment according to the present invention;
Fig. 17 is a flow chart showing the method of producing a train running plan of a
third embodiment according to the present invention;
Fig. 18 and Fig. 19 are graphical representations useful in explaining examples of
correction of the running plan; and
Fig. 20 and Fig. 21 are graphical representations useful in explaining another examples
of correction of the running plan.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0045] Preferred embodiments of the present invention will hereinafter be described in detail
with reference to the accompanying drawings.
[0046] Fig. 11 is a block diagram showing the arrangement of a system for carrying out a
method of producing a train running plan according to the present invention.
[0047] This system arrangement is made up of a train system 200a having a main function
of displaying an optimal train running plan on a CRT 203 provided in a train to perform
the operational support for an engineer, and a ground system 100b having a main function
of producing the optimal train running plan to be displayed by the train system 200a.
[0048] Moreover, for brevity, it is assumed that the traffic route is a line consisting
of two rails, a plurality of stations are included in the traffic route, a running
train is limited in type, and each of the trains is a local train.
[0049] A running plan producing unit 208 serves to refer to the necessary data in a rolling
stock characteristic data file 212 and a line condition data file 213 to produce optimal
train running plan thereby to store the optimal train running plan in a running plan
data file 211. This processing is performed in advance with respect to all the territories,
the type of the train, the up train line and the down train line.
[0050] Then, to determine the train plan is to determine a target speed in each of the limit
speed territories. Incidentally, in addition to the target speed, the curve of the
speed corresponding to the position on the line, which is designated the running curve,
will be also displayed in the train. In the data file 211, the result of the simulation
when the optimal target speed is set will be recorded in the form of the position
and the speed. The details of the method of producing an optimal train running plan
will be described later with reference to Fig. 12.
[0051] Then, by the rolling stock characteristic data it means the drive force characteristic
data and the deceleration characteristic data corresponding to the train speed, the
running resistance which is a function of the second order of the train speed, the
train organization, the train weight and the like all of which are inherent in the
train. These rolling stock characteristic data are stored corresponding to the type
of the running train.
[0052] Moreover, by the line condition data it means the position of the station (stopping
target position), the limit speed information (territory starting position and limit
speed, etc.), the grade information (starting position and magnitude of grade, etc.)
and the like all of which are obtained with the starting point of the traffic route
being treated as a standard. Since it is assumed that the traffic route is a single
line, these data are limited to only two kinds with respect to the up train line and
the down train line.
[0053] Out of the data of the optimal train running plan thus produced, the data corresponding
to the running train and the territory between the stations at which the train is
to be stopped in order need to be transferred to the train system 200a of the running
train. As for the means for transferring such data, there are known various kinds
of ones. However, particularly in the present example, an IC card is used to transfer
the data from the ground system 200b to the train system 200a. The running plan producing
unit 208 serves to search for the necessary data to take out them from the data file
211, thereby to send them to an IC card writer 214. The IC card writer 214 serves
to write the data thus sent thereto in an IC card 215. The IC card 215 having the
data written therein is the same as an IC card 206 in the train system 200a.
[0054] A running support unit 201 serves to read out the running plan from the IC card 206
through an IC card reader 207 prior to the start of the train and to record the running
plan in a running plan data file 204 in a train computer. Further, the running support
unit 201 performs the display of the present position, the target speed at the present
position, the running curve in the running plan, and the like on a CRT 203, corresponding
to the travel position of the train. A keyboard 202 in the train system 200a and the
209 in the ground system 200b are used for the input of the commands and the like
when the respective systems are operated and so forth. An example of the displayed
picture is shown in Fig. 13.
[0055] In Fig. 13, the reference numeral 701 designates the limit speed, the reference numeral
702 designates the optimal target speed, and the reference numeral 703 designates
the running curve which is obtained by performing the simulation of the running at
the optimal target speed. The reference numeral 704 indicates the present position
on the running curve. The target speed, the present speed, the present position and
the running time are numerically displayed in areas 705, 706, 707 and 708, respectively.
[0056] Returning to Fig. 11, the position of the train is calculated in such a way that
a rolling stock position detection unit 205 measures the rotational frequency of the
wheel and the correction is performed in the place where the positions of the station
and the vicinity thereof can be accurately grasped.
[0057] Fig. 12 is a flow chart in accordance with which the running plan producing unit
208 in the ground system 200b shown in Fig. 11 carries out a first embodiment of a
method of producing an optimal train running plan.
[0058] The first embodiment is characterized in that the target speed is determined so as
to provide the minimum consumed energy when the train is running.
[0059] In Step 101, the data inputted from the keyboard 209 is read out. The data which
are inputted from the keyboard 209 are made up of the type of the train, the identifiers
with respect to the individual stations, the starting time, and the estimated time
of arrival.
[0060] In Step 102, on the basis of the data thus inputted, the line condition data with
respect to the stations at which the running train is to be stopped in order (the
line length, the station position, the limit speed information, the grade information
and the like) and the rolling stock characteristic data of the running train (the
drive force characteristics, the deceleration characteristics, the train weight and
the like) which are stored in advance in the files 213 and 212 of the ground system
200b, respectively, are read out. The train weight is calculated on the basis of the
average seat-load factor (it is estimated from the past data and the like).
[0061] In Step 103, on the basis of the above data thus read out, the target speed which
is obtained by subtracting the marginal speed from the limit speed is assigned to
each of the limit speed territories. The marginal speed is set so as not to exceed
the limit speed during the fixed speed running. Thus, for example, if the marginal
speed is set to 3 km/h, when the limit speed is 100 km/h, 97 km/h is set to the target
speed.
[0062] In Step 104, the necessary time T and the consumed energy E in the case where the
train will run between the stations at the target speed thus set are calculated. The
concrete method of calculating the necessary time T and the consumed energy E will
hereinbelow be described.
[0063] The running pattern of the limit speed shown in Fig. 4 is used as that in the present
embodiment. The axis of abscissa designates the distance from the starting station
and will hereinbelow be represented by x. The limit speed territories are numbered
serially (the total number of territories is N). At this time, it is assumed that
the starting position of the i-th territory is x; and the limit speed thereof is V
MAX,
I. That is, if the position of the train satisfies the relationship of x
; < x ≦ X
i+1, the limit speed at that position is V
MAX,i-
[0064] Moreover, as described above, it is assumed that the running pattern takes the combination
of the maximum acceleration - the fixed speed running - the deceleration by the normal
maximum braking.
[0065] Next, it is assumed that the grade of the n-th limit speed territory is as shown
in Fig. 14 and the number of territories each having the grade is Mn. Then, in the
position satisfying the relationship of ξ
n,m-1 ≦ X ≦ ξ
n,m, the grade is
'Yn,
m. Incidentally, the unit of the grade is expressed by o/oo (per mil).
[0066] The running resistance R
R is a function of the second order of the train speed v and is expressed by the following
formula:

where a, b and c are parameters inherent in the kind of the train.
[0067] The grade resistance R
R is a function of the position x. Since the unit of the grade y is given by o/oo,
if the angle corresponding to the grade is given by 0, the following relationship
is established.

Thus, if the train weight is given by M, the following relationship is established.

[0068] Then, if the drive force characteristics and the deceleration characteristics corresponding
to the speed v are expressed by T
Q(v) and T
B(v), respectively, the equation of motion of the train motion are given by:

where F
M(v) is the output of a motor (T
Q(v) in the acceleration and -T
B(v) in the deceleration). Since the limit speed as the constraint condition depends
on the position x, the independent variable of the time t is inconvenient to treat.
Then, the time t is subjected to the change of variables to obtain the independent
variable x. At this time, the equation (14) is rewritten as follows:

[0069] Thereafter, the necessary time T and the consumed energy E can be obtained in such
a way that the distance x is made to be discrete and the equation (20) is solved by
the numerical calculation.
[0070] Incidentally, although it is assumed that with respect to the train running, the
acceleration is performed in accordance with T
Q(v) and the deceleration is performed in accordance with T
B(v), the control is the fixed speed running is performed in the following manner.
[0071] The lower limit ΔVd and the upper limit ΔVu of the error between the present speed
v and the target speed Vn are set. Then, the control in the fixed speed running is
performed in accordance with the following relationship.
v ≦ Vn - AVd : acceleration due to TQ(v)
Vn - ΔVd < v < Vn + ΔVu : coasting (FM(v) = 0)
Vn + ΔVu v : deceleration due to TB(v)
[0072] In order to obtain the partial derivative ∂E/∂Vi of the consumed energy E with respect
to the target speed Vi, the target speed Vi is reduced by the small speed
EV to perform the same calculation. If the consumed energy at this time is given by
E', the following relationship is established.

[0073] Such a calcualtion is repeatedly performed with respect to i(i=I, ..., N).
[0074] After the completion of the above processing, with the target speed being equal to
the initial setting value (i.e., in the first calculation), the schedule time (the
estimated time of arrival - the starting time) is compared with the calculated necessary
time (Step 105). When the schedule time is larger than the necessary time (in the
case where the train is too late for the necessary time at any high speed), it is
judged that the input data are abnormal. Then, this processing is completed (Step
106). The completion of this processing is displayed on the CRT 210.
[0075] On the other hand, when the schedule time is smaller than the necessary time, the
difference between the schedule time and the necessary time is calculated to compare
the magnitude of the difference and the allowable error δT with each other (Step 107).
If the difference therebetween is smaller than the allowable error (formation of end
condition), the target speed and the running curve data at this time are stored in
the running plan data file 204 (Step 108). Thus, the processing for obtaining the
optimal train running method is completed (Step 109).
[0076] If the difference therebetween is more than the allowable error δT, the processing
for changing the target speed is performed (Step 110). There are various methods for
changing the target speed. For exmaple, there is a method in which the grade vector
having ∂E/∂Vi as the i-th component is normalized (making the length thereof 1), the
length along the i-th component, i.e., that of the target speed as the vector is decreased
by 5 km/h. There is another method in which the positive and maximum partial derivative
is selected and the target speed is reduced by 1 km/h. In the present embodiment,
the latter is employed.
[0077] Thereafter, the subsequent target speed is newly set, a series of processings beginning
from Step 104 are repeated.
[0078] As another example in the method of producing a train running plan, it is supposed
that the territory for providing the optimal train running plan exists between the
two passed stations, as shown in Fig. 15. At this time, there is no schedule time
between these stations. However, the difference between the estimated times of passing
with respect to the two stations is regarded as the schedule time, the speed at passing
the station at the left end (the initial speed in the simulation) is added, and the
consumed energy and the necessary time are obtained by the simulation.
[0079] Thus, in the method of producing a train running plan according to the first embodiment,
since the target speed in each of the limit speed territories is obtained on the basis
of the nonlinear planning for obtaining the desired train running plan, the number
of parameters used for determining the target speed can be decreased, and the computation
time becomes less in comparison with the case of the optimal running method for all
the territories by the dynamic planning or the like.
[0080] Moreover, the method of producing a train running plan of the present embodiment
can be applied to the running pattern using the arbitrary limit speed.
[0081] The second embodiment of the present invention will subsequently be described. In
the second embodiment, the subsequent target speed is newly obtained on the basis
of the change ratio of the consumed energy with respect to the change of the running
time when changing the target speed. Incidentally, as the system for carrying out
the method of producing a train running plan of the second embodiment, as shown in
Fig. 11 is used. Therefore, the description of the arrangement of the system is omitted
here for brevity. Then, only the features of the second embodiment will hereinafter
be described with reference to Fig. 16.
[0082] In Step 101 a, the data of the type of the train, the identifiers with respect to
the individual stations, the starting time, the estimated time of arrival, and the
like are inputted from the keyboard 209.
[0083] In Step 102a, on the basis of the data inputted in Step 101 a, the line condition
data with respect to the stations at which the running train is to be stopped (the
line length, the station position, the limit speed information, the grade information
and the like) and the rolling stock characteristic data of the train of interest (the
drive force characteristics, the deceleration characteristics, the train weight, and
the like) which are stored in advance in the files 213 and 212 of the ground system
200b, respectively, are read out. The weight of the passengers in the train weight
is calculated on the basis of the average seat-load factor (it is estimated from the
past data).
[0084] In Step 103a, on the basis of the data thus read out, the initial value of the target
speed of each of the limit speed territories is set by subtracting the marginal speed
from the limit speed Vmax(n). The marginal speed is set so as not to exceed the limit
speed during the fixed speed running at the maximum speed. Thus, for example, if the
marginal speed is set to 3 km/h, when the limit speed is 100 km/h, 97 km/h is set
to the target speed.
[0085] In Step 104a, the processing is performed with respect to the following two items:
(1) The simulation of the train running is performed using the target speed which
is set at present to calculate the running time T and the consumed energy E. At the
same time, the combination data of the target speeds at that time, and the running
curve data which are expressed by the relationship between the running position and
the speed are temporarily stored.
(2) The target speed of the n-th limit speed territory which is set at present is
expressed by V(n). Then, the target speed of that territory is set to V(n) - EV which is obtained by reducing the target speed by the small value EV, to perform the simulation of the train running. Thus, the running time T' and the
consumed energy E' are calculated. Then, the following approximate expression is calculated.

Such a processing is carried out with respect to n (n = 1, ..., N). Incidentally,
as stated in the description of the equation (4), p(n) represents the vector component.
[0086] Now, when the running pattern of the limit speed is that as shown in Fig. 4, the
calculation method of the running time T and the consumed energy E is as follows.
[0087] The running pattern of the train is supposed in such a way that in the acceleration
running, the acceleration by the maximum accelerating force is switched over to the
fixed speed running, and in the deceleration running, the deceleration by the normal
maximum braking is switched over to the fixed speed running. At this time, by determining
the train running plan it means that determining the target speed in each of the limit
speed territories.
[0088] Then, if the drive force characteristics and the deceleration characteristics corresponding
to the speed v are expressed by Tq(v) and Tb(v), respectively, the equation of motion
of the train is given by:

where Fm(v) represents the output of the motor and is expressed by Tq(v) in the acceleration
while being expressed by -Tb(v) in the deceleration. Thereafter, the necessary time
T and the consumed energy E can be obtained in such a way that the time t is made
to be discrete and the above equation is solved by the numerical calculation.
[0089] Incidentally, although it is assumed that with respect to the train running, the
acceleration running is performed in accordance with Tq(v) and the deceleration running
is performed in accordance with Tb(v), the control in the fixed speed running is performed
in the following manner. The lower limit ΔVI and the upper limit ΔVu of the error
between the present speed v and the target speed V(n) are set. Then, the control in
the fixed speed running is performed in accordance with the following relationship.
v < V(n) - ΔVI : accleration due to Tq(v)
V(n) - ΔVI < v < V(n) + AVu : coasting (Fm(v) = 0)
V(n) + ΔVu v : deceleration due to Tb(v)
[0090] After the completion of the above processing, in Step 105a, with the target speed
being equal to the initial setting value which is set in Step 103a (i.e., in the first
calculation), the schedule time (= the estimated time of arrival - the starting time)
is compared with the running time which is calculated by the simulation.
[0091] By the case where the running time is larger than the schedule time, it means that
in the case where the train is too late for the schedule time at any high speed. In
such a case, the input data are abnormal. Then, the processing for obtaining the optimal
target speed is completed (Step 106a). Then, the completion of this processing is
displayed on the CRT 210.
[0092] In the case where the running time is smaller than the schedule time, the calculation
result of "the schedule time - the running time" and the allowable error 6T are compared
with each other (Step 107a). When the difference therebetween is smaller than the
allowable error 6T, the formation of the end condition is established. In this case,
the combination data of the target speeds and the running curve data both of which
are temporarily stored are stored in the running plan data file 204 (Step 108a). Then,
the processing for obtaining the optimal train running method is completed (Step 109a).
[0093] On the other hand, when the difference therebetween is more than the allowable errors
6T, the processing for changing the target speed is performed (Step 110a). Then, the
target speed in the territory having the positive and maximum p(n) is reduced by unit
quantity, e.g., 1 km/h. After the subsequent target speed is newly set, a series of
processing beginning from Step 104a are repeated.
[0094] With respect to the method of changing the target speed in Step 110a, in addition
to the above-mentioned method, there are various ones which will subsequently be listed.
(1) A first method is such that as described on referring to the equation (4), p as
the vector is used, its unit vector ρ/|ρ| is obtained, the target speed is moved along
the direction of that unit vector by unit quantity, and in the territory where the
target velocity exceeds the limit speed, that target speed is not changed.
(2) A second method is such that since in the above method (1), the target speed will
be increased in any territory having the negative p(n), p where p(n) = 0 is set to
that territory is used.
(3) A third method is such that since in the method described in the present embodiment
and the above methods (1) and (2), there is the possibility that the increasing of
the running time corresponding to the change of the target speed per unit quantity
is large and thus it may not be suitably within the range of the allowable error,
when approaching the running time set in advance, the target speed is changed to decrease
the unit quantity.
[0095] Thus, in the method of producing a train running plan according to the second embodiment,
the target speed in each of the limit speed territories is obtained for obtaining
the train running plan, and the combination of the optimal target speeds is obtained
by utilizing the ratio of the decreasing of the consumed energy to the increasing
of the running time in the change of the target speed. Therefore, the number of parameters
used for determining the target speed can be decreased and the computation time becomes
less in comparison with the case of the method of obtaining the optimal running method
over all the territories, such as the dynamic planning. Moreover, the present method
can be applied to the running pattern using the arbitrary limit speed. Further, since
it is unnecessary to search for the minimum target speed within the limited area,
the amount of calculation becomes less in comparison with the solution by the nonlinear
planning.
[0096] The third embodiment of the present invention will be described. The third embodiment
is arranged in such a way that when the limit speed of the train is changed, the running
plan is corrected so that the running time becomes the previously determined running
time. Incidentally, as the system arrangement for carrying out the method of producing
a train running plan of the third embodiment, that shown in Fig. 11 is used. Therefore,
the description of the system arrangement is omitted here for brevity. Then, only
the features of the third embodiment will hereinafter be described with reference
to Fig. 17.
[0097] In Step 101b, the data of the starting position and the ending position of the limit
speed changing territory (the territory 5 in Fig. 3A), and the change value of the
limit speed are inputted.
[0098] In Step 102b, it is judged whether or not the change of the limit speed of the limit
speed changing territory influences upon the target speed of that territory, i.e.,
whether or not that target speed is allowed in the newly set limit speed.
[0099] In the case of no influence thereupon, it is unnecessary to change the target speed,
and thus the processing is completed (Step 103b). In the case where the influence
is more or less present, a series of processing beginning from the Step 104b are carried
out in the following manner.
[0100] Now, the preparation for giving the description of the series of processing from
Step 104b will hereinunder be performed.
[0101] Fig. 18, Fig. 19, Fig. 20 and Fig. 21 are enlarged views of the territories 5 through
7 shown in Fig. 3A and Fig. 3B. Fig. 18 and Fig. 20 relate to the speed and Fig. 19
and Fig. 21 relate to the running time density. Incidentally, it is assumed that the
grade is zero over all the territories. The reason for setting the grade to zero was
already decreased.
[0102] Fig. 18 and Fig. 19 show the running plan before the reduction of the limit speed
of the territory 5, and Fig. 20 and Fig. 21 show the running plan after the reduction
of the limit speed of the territory 5. In these figures, it is assumed that the limit
speed of the territory n is V
MAX,
n, the inverse number of V
MAx,i is X
MAX,
i, the target speed is Vn, the inverse number of Vn is Xn, the starting position of
the territory is x
n, and the position where the switching over to the fixed speed running occurs is ξ
n. In Fig. 20 and Fig. 21, the change value is distinguished from the original value
in Fig. 18 and Fig. 19 by putting "'" to the original value as shown in the form of
ξ'.
[0103] In Step 104b, the target speed Vs' of the territory 5 where the limit speed is reduced
is set to the maximum speed as fast as the train runs through the territory 5. This
setting is performed for the purpose of recovering the delay as soon as possible to
reduce the acceleration in the territory 6. Then, as the margianl speed which is set
so as not to exceed the limit speed in the running is expressed by ov, and then the
target speed is set in accordance with the relationship of Vs' = V
MAX,
5' - ov. If the limit speed is 100 km/h for example, the marginal speed 6v is set to
about 3 km/h.
[0104] In Step 105b, it is judged whether or not the limit speed territory is present between
the target speed changing territory, i.e., in this case, the territory 5 where the
target speed is changed by the change of the limit speed, and the following station.
In the case of absence of such a territory, there is no room for correction, and it
is impossible to carry out the scheduled operation up to the following station (Step
106b).
[0105] In the case of presence of the limit speed territory, the processing proceeds to
Step 107b. In Step 107b, it is judged whether or not the scheduled operation can be
performed as the result of the correction of the target speed of the territory 6.
The detail description will hereinbelow be given with respect to the judgement in
Step 107b.
[0106] The running time T
1 of the territories 5 through 7 shown in Fig. 18 and Fig. 19 is expressed by the following
equation using the equation (14) as already described.

Incidentally, the position ξ
7 in the territory 7 where the switching over to the fixed speed running is carried
out is obtained from the following equation by utilizing the equation (15).

[0107] The calculation of the running time T
2 of the territories 5 through 7 shown in Fig. 20 and Fig. 21 will subsequently be
performed. Now, the target speed V
6' in the territory 6 is uncertain. Then, that target speed is determined so that the
relationship of T
2 = T
1 is established.
[0108] Then, T
2 is calculated while leaving V
6' being an unknown quantity. Therefore, T
2 is a function of V
6'. Then, while ξ
6' and £
7' are also unknown quantities, they are uniquely determined if V
6' is determined. By using the equations (14) and (17), the following expression is
obtained.

Incidentally, with respect to ξ
5', ξ
6' and £
7', the following relationships are established.



[0109] V
6' to be obtained can be calculated as the root of φ(V
i) = T
2(V
6')-T
1 from the numerical calculation by utilizing the Netwon's method or the like.
[0110] In the case where the solution of φ(V
6') = 0 is present, it is judged in Step 107b that it is possible to perform the scheduled
operation. At this time, the target speeds V
5 and V
6 are corrected to Vs' and V
6', respectively, to complete the processing (Step 108b). The resultant target speeds
are displayed on the CRT 210. With the running curve, the data of the territories
(the territories 5 through 7) where the correction occurs are replaced with those
of the running curve (p(x) in Fig. 7 and q(x) in Fig. 8) when the grade is zero.
[0111] In the case of absence of the solution of φ(V
6') = 0, it is judged in Step 107b that it is impossible to perform the scheduled operation
by only the correction of the territories 5 and 6. At this time, in the same manner
as in Vs', V
6' is also set to the maximum speed as fast as the train runs through the territory
6 (Step 109b). Then, the processing is returned to the Step 105b to perform the calculation
for obtaining V
7'.
[0112] In the above-mentioned algorithum, in the case where the correction is necessary
for the fairly foward territories such as the territories 7 and 8, the amount of calculation
is increased so that the calculation requires much time. However, since the target
speed of the nearest territory is set to the maximum speed as fast as the train runs
through that territory, the predetermined calculation may be completed during the
running through that territory. Thus, there is no problem in practical use.
[0113] As described above, according to the method of correcting a train running plan of
the third embodiment, the data which are calculated in advance by the simulation and
the like are used to perform the calculation of the running time, thereby to perform
the correction of the running plan. Therefore, even when the change of the limit speed
occurs temporarily, the running plan can be corrected in a real-time manner.
1. A method of producing a train running plan in which a running plan is produced
so as to make a train run through a predetermined territory of a traffic route of
a railway while maintaining a predetermined limit speed (Vmax) and running time, said
method comprising the steps of:
(a) setting a target speed of the running train every small territory a plurality
of which are obtained by dividing the predetermined territory thereinto and have the
respective fixed limit speeds;
(b) obtaining a consumed energy and a running time of the train so that the train
runs at the fixed speed in accordance with the target speed, every small territory,
after accelerating the train in the acceleration by the maximum accelerating force
or decelerating the train in the deceleration by the maximum decelerating force (Step
104); and
(c) setting the target speeds of all the small territories in the predetermined territory
in such a way that the train runs in a predetermined running time and the consumed
energy becomes minimum, by repeating the Step (a) and Step (b) (Step 110).
2. A method of producing a train running plan according to Claim 1, wherein the running
time (T) and the consumed energy (E) of the train in the predetermined territory are
obtained on the basis of an initial speed when the train enters into the predetermined
territory, predetermined grade information, a running resistance of the train, acceleration
and deceleration characteristics of the train and a weight (M) of the train.
3. A method of producing a train running plan according to Claim 1, wherein the consumed
energy (E) is made to be an objective function (E) which is expressed by an equation
of E = E(Vi, ..., VN) where the individual target speeds are independent variables (Vi, ..., VN), and the target speed (Vn) of the predetermined territory is obtained by solving
the above equation on the basis of a nonlinear planning.
4. A method of producing a train running plan according to Claim 3, wherein the consumed
energy (E) and the running time (T) are made to be objective functions (E) which are
expressed by equations of E = E(Vi, ..., VN) and T = T(Vi, ..., VN) in each of which the individual target speeds (Vn) are independent variables (Vi,
..., VN), and the target speed (Vn) of the predetermined territory is obtained by solving
both the above equations on the basis of a nonlinear planning.
5. A method of producing a train running plan according to Claim 3 or 4, wherein the
nonlinear planning is such that when the consumed energy and the target speed are
expressed by E and V(n), respectively, a differential coefficient is obtained from
an approximate expression of aE/aV(n) ≒ AE/AV(n), and when V(n) is changed in the
range of 0 ≦ V(n) < Vmax(n), V(n) becomes an optimal target speed where E takes a
minimum value.
6. A method of producing a train running plan in which a running plan is produced
so as to make a train run through a predetermined territory of a traffic route of
a railway while maintaining a predetermined limit speed (Vmax) and running time, said
method comprising the steps of:
(a) setting a target speed of the running train every small territory a plurality
of which are obtained by dividing the predetermined territory thereinto and have the
respective fixed limit speeds;
(b) obtaining a consumed energy and a running time of the train so that the train
runs at the fixed speed in accordance with the target speed, every small territory,
after acclerating the train in the acceleration by the maximum accelerating force
or decelerating the train in the deceleration by the maximum decelerating force (Step
104a);
(c) fixing the target speeds of other small territories when the target speed of one
small territory in the predetermined territoty is changed, to obtain a consumed energy
in the target speed of the one small territory obtained in Step (a) (Step 104a);
(d) obtaining the change ratio of the consumed energy obtained in the step (c) and
a consumed energy due to the change of the target speed of the one small territory;
and
(e) setting the target speeds of all the small territories in the predetermined territory
in such a way that the train runs in a predetermined running time on the basis of
the change ratio of the consumed energy, and the consumed energy becomes minimum,
by repeating the Step (a) through the Step
(d) (Step 110a).
7. A method of producing a train running plan according to Claim 6, wherein the Step
(c) comprises:
(Ci) obtaining the change ratio of the consumed energy, every small territory, with
the change ratio of the consumed energy being treated as the positive one, in the
case where the consumed energy is decreased while the running time is increased with
the target speed initially set in the Step (a) being treated as the limit speed (Step
104a);
(C2) reducing the target speed of the territory where the resultant change ratio of the
consumed energy takes the maximum value, by unit quantity (Step 110a); and
(C3) treating the target speed reduced by unit quantity in the Step (C2) as a new target speed (Step 108a), when the running time is in a predetermined error
range (Step 107a).
8. A method of producing a train running plan according to Claim 7, wherein the Step
(C2) includes therein the process of treating the value of the change ratio of the consumed
energy obtained every small territory as a vector quantity to change the target speed
as the vector quantity along the direction of the vector by unit quantity.
9. A method of producing a train running plan according to Claim 7, wherein the Step
(C2) includes therein the process of treating the value of the change ratio of the consumed
energy obtained every small territory as a vector quantity and of changing a component
of the vector quantity of the small territory to "0" if the component of the vector
quantity is negative, thereby to change the target speed as the vector quantity along
the direction of the changed vector by unit quantity.
10. A method of producing a train running plan according to Claim 7, wherein the Step
(C2) includes therein the process of decreasing the unit quantity for changing the target
speed, when the running time of the train in the predetermined small territory approaches
a predetermined running time.
11. A method of producing a train running plan in which a running plan is produced
so as to make a train run through a predetermined territory of a traffic route of
a railway while maintaining a predetermined limit speed and first running time, said
method comprising the steps of:
(a) producing in advance the data of a speed of the train, an inverse number of the
speed and a running time with respect to a travel distance from an acceleration starting
position up to a position at a predetermined travel distance therefrom and the data
of a speed of the train, an inverse number of the speed and a running time with respect
to a travel distance from an deceleration starting position up to a position at a
predetermined travel distance therefrom, under the condition that the grade of the
traffic route is "0" in all the positions;
(b) obtaining a running time of the predetermined territory from the data produced
in advance, when the running plan is corrected (Step 107b); and
(c) correcting the running plan in such a way that the resultant running time in coincidence
with the value of the predetermined first running time (Step 108b).
12. A method of producing a train running plan according to claim 11, wherein the
data produced in the Step (a) in obtained by numerically integrating the equation
of motion of the running train.
13. A method of producing a train running plan according to Claim 11, wherein the
processing in the Step (b) is performed in the individual small territories which
are located in the forward direction from the present position of the train and have
the respective fixed limit speeds (Step 105b, Step 107b).
14. A method of producing a train running plan according to Claim 1, wherein the processing
in the Step (c) comprises:
(c11) setting each of target speeds of the small territories which are located forward
up to the (n-1 )th from the present position of the train and have the respective
fixed limit speeds set thereto, to the limit speed (Step 109b);
(d2) setting a target speed of the n-th small territory having a fixed limit speed
set thereto as an unknown variable; and
(C13) obtaining the unknown variable in such a way that the running time of the predetermined
territory obtained in the Step (b) is in coincidence with a value of a predetermined
running time (Step 107b).
15. A method of producing a train running plan according to Claim 11, wherein the
processing in the Step (c) comprises:
(C21) setting a target speed of the (n + 1)th small territory having a fixed limit
speed set thereto to the limit speed (Step 109b);
(c22) setting a target speed of the n-th small territory having a fixed limit speed set
thereto as an unknown variable; and
(C23) obtaining the unknown variable in such a way that the running time of the predetermined
territory obtained in the Step (b) is in coincidence with a value of a predetermined
running time (Step 107b).
16. A method of producing a train running plan according to Claim 11, wherein the
processing in the Step (c) is performed in such a way that in the case of absence
of the (n + 1)th small territory having a fixed limit speed set thereto, each of the
remaining small territories having respective fixed limit speeds set thereto is set
to a limit speed at which the train may run through the small territory (step 109b).