CN112172838B - Arrangement method for two-way auxiliary parking area of normally-conducting magnetic suspension traffic - Google Patents

Arrangement method for two-way auxiliary parking area of normally-conducting magnetic suspension traffic Download PDF

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CN112172838B
CN112172838B CN202010901260.1A CN202010901260A CN112172838B CN 112172838 B CN112172838 B CN 112172838B CN 202010901260 A CN202010901260 A CN 202010901260A CN 112172838 B CN112172838 B CN 112172838B
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虞翊
楚彭子
董丹阳
林辉
赵华华
袁建军
陈义军
张仿琪
阿力玛斯·伊力夏提
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Tongji University
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Abstract

The invention relates to a method for arranging two-way auxiliary parking areas of normally-conducting magnetic suspension traffic, which is based on 'parking point stepping', a reverse recursion method, a forward recursion method and 'two-way cooperation', and can ensure that each auxiliary parking area obtained by calculation is the auxiliary parking area farthest from a reference parking area at the beginning. Compared with the prior art, the method has the advantages that the construction cost of the normally-conducting magnetic suspension line is saved on the premise of ensuring the running safety of the train, and the scientificity of planning and designing is improved.

Description

Arrangement method for two-way auxiliary parking area of normally-conducting magnetic suspension traffic
Technical Field
The invention relates to the field of single-line bidirectional running magnetic suspension line arrangement and magnetic suspension train running control, in particular to a bidirectional auxiliary parking area arrangement method for normally-conductive magnetic suspension traffic.
Background
The normally-conducting magnetic-levitation train runs by adopting rail-holding operation, and a power supply rail is only arranged in an auxiliary parking area. The auxiliary parking area is arranged between two stations, under the guidance of the idea of 'failure-safety', the operation of the magnetic suspension train takes the current auxiliary parking area as a target parking point, and only when the magnetic suspension train can safely coast to the next auxiliary parking area, the next auxiliary parking area is taken as the target parking point, namely, the 'parking point stepping' operation mode is adopted.
At present, in the construction process of a magnetic suspension line, the arrangement of an auxiliary parking area often refers to the nominal value of an Shanghai magnetic suspension demonstration line, complex working conditions are difficult to deal with, the speed reference range is limited, and the universality is not realized. Based on this, the literature "high-speed maglev auxiliary parking area setting based on protection speed" published in the book of university of coworkers (natural science edition) in 2019 such as corn earassist proposes a method for arranging auxiliary parking areas of one-way operation routes based on a protection speed curve. The method is an arrangement strategy which takes a terminal station as a first reference to assist a parking area and then approaches to a starting station in sequence according to a protection speed curve, and can be used for a magnetic suspension line running in a single direction.
In the field of arrangement of auxiliary parking areas of single-line bidirectional running lines, patent No. CN109050585A, entitled "method for determining auxiliary parking areas for high-speed maglev train line track running", proposes an arrangement mode that uses a starting station as a first reference auxiliary parking area to simulate train running and determine the next auxiliary parking area. And the auxiliary parking area arrangement method of the single-line bidirectional operation line is discussed based on the mode, namely, the auxiliary parking areas are arranged in a single direction at corresponding starting stations, and repeated auxiliary parking areas are combined. The two methods have certain universality, but the complicated working condition is not considered, namely, a section which is not suitable for arranging an auxiliary parking area exists on the line. Meanwhile, the difference between the up-down running speed curve and the running condition of the train causes the difference of the protection curve, and if the arrangement of the auxiliary parking areas is considered separately in both directions, the possibility of repeating the auxiliary parking areas is very low, that is, the number of the auxiliary parking areas cannot be effectively reduced in practice by the method disclosed in the publication number CN 109050585A.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a method for arranging a bidirectional auxiliary parking area of a normally-conductive magnetic suspension traffic.
The purpose of the invention can be realized by the following technical scheme:
a method for arranging a two-way auxiliary parking area of a normally-conducting magnetic suspension traffic comprises the following steps:
step S1: acquiring a starting station and an end station, and selecting one of the stations as a reference parking area;
step S2: on the basis of a reference standard parking area, respectively adopting a reverse recursion method and a forward recursion method to obtain a first-direction temporary parking area and a second-direction temporary parking area;
step S3: selecting one of the first-direction temporary parking area and the second-direction temporary parking area which is farther from the reference parking area as a temporary reference direction parking area, acquiring the reference direction of the temporary reference direction parking area, arranging the temporary parking areas in the direction by adopting the recursion method adopted in the step S2 in the reverse direction of the reference direction until the distance between the temporary parking area in the reverse direction of the reference direction and the reference parking area is larger than the distance between the temporary reference direction parking area and the reference parking area, and recording the temporary parking area in the reverse direction of the reference direction as a temporary parking area p;
step S4: setting a temporary parking area in the opposite direction of the previous reference direction of the temporary parking area p as a bidirectional parking area, canceling the temporary parking area p and the temporary reference direction parking area, and removing the remaining temporary parking areas of the temporary parking area p and the temporary reference direction parking area to be used as auxiliary parking areas;
step S5: setting the bidirectional parking area as a new reference parking area, further obtaining a new first-direction temporary parking area and a new second-direction temporary parking area by adopting a reverse recursion method and a forward recursion method, and returning to the step S3 until the arrangement is completed in one direction of the first direction and the second direction.
Step S6: the other direction completes the arrangement according to the recursion method it adopted in step S2.
The forward recursion method comprises the following steps:
calculating a safety braking speed curve according to the dangerous points of the reference parking area;
determining a maximum speed protection curve according to the safety braking speed curve, and obtaining a first intersection point of the maximum speed protection curve and a train running speed curve;
calculating a minimum speed protection curve according to the first intersection point, and then calculating to obtain a safe suspension speed curve;
obtaining an accessible point of the temporary parking area according to the safe suspension speed curve;
and obtaining the dangerous points of the temporary parking area according to the reachable points and the length of the parking area, and further obtaining the temporary parking area.
The minimum speed protection curve is expressed as:
Figure BDA0002659839480000031
wherein the content of the first and second substances,
Figure BDA0002659839480000032
is the velocity component at the time t of the minimum velocity protection curve,
Figure BDA0002659839480000033
is the mileage component at the t-th moment of the minimum speed protection curve, delta t is the sampling interval, atThe acceleration of the train at the t moment;
the process of obtaining the safe suspension speed curve by utilizing the minimum speed protection curve comprises the following steps:
Figure BDA0002659839480000034
wherein the content of the first and second substances,
Figure BDA0002659839480000035
for the velocity component on the safe levitation velocity profile,
Figure BDA0002659839480000036
for the distance component on the safe suspension speed curve, delta tt is the system delay from the sending of the traction cut-off command to the starting process of the eddy current brake, delta v is the speed measurement error, delta s is the positioning error, aworstThe train is in no-load condition, encounters the maximum upwind speed and has the acceleration under the condition that the friction coefficient between the track surface and the skid of the train reaches the maximum.
The safe braking speed curve is expressed as:
Figure BDA0002659839480000037
wherein the content of the first and second substances,
Figure BDA0002659839480000038
for the speed component at the time t of the safety braking speed profile,
Figure BDA0002659839480000039
is the mileage component at the t-th time, Δ t is the sampling interval, atThe acceleration of the train at the t moment;
the process of calculating the maximum speed protection curve by using the safety braking speed curve comprises the following steps:
Figure BDA00026598394800000310
wherein the content of the first and second substances,
Figure BDA00026598394800000311
for the speed component of the safety braking speed profile,
Figure BDA00026598394800000312
for the mileage component of the safety braking speed curve, delta tt is the system delay from the sending of the traction cut-off command to the completion of the traction cut-off, delta v is the speed measurement error, delta s is the positioning error, aworstThe acceleration of the train under the conditions that the train is unloaded, the train encounters the maximum downwind speed and the friction coefficient of the track surface and the skid of the train reaches the maximum value is achieved.
The reverse recursion method comprises the following steps:
calculating a safe suspension speed curve according to the reachable point of the reference parking area;
determining a minimum speed protection curve according to the safety levitation speed curve, and obtaining a second intersection point of the minimum speed protection curve and the train operation speed curve;
calculating a maximum speed protection curve according to the second intersection point, and then calculating to obtain a safety braking speed curve;
obtaining a dangerous point of the temporary parking area according to the safety braking speed curve;
and obtaining the reachable point of the temporary parking area according to the dangerous point and the length of the parking area, and then obtaining the temporary parking area.
The safe levitation speed curve is represented as:
Figure BDA0002659839480000041
wherein the content of the first and second substances,
Figure BDA0002659839480000042
for the velocity component at time t of the safe levitation velocity profile,
Figure BDA0002659839480000043
is the mileage component of the safe suspension velocity curve at the t-th moment, delta t is the sampling interval, atThe acceleration of the train at the t moment;
the process of calculating the minimum speed protection curve by using the safe suspension speed curve comprises the following steps:
Figure BDA0002659839480000044
wherein
Figure BDA0002659839480000045
Is the velocity component on the minimum velocity profile,
Figure BDA0002659839480000046
for the distance component on the minimum velocity curve, Δ tt is the system delay from the issuance of the traction cut-off command to the activation of the eddy current brake, Δ v is the speed measurement error, Δ s is the positioning error, aworstThe train is in no-load condition, encounters the maximum upwind speed and has the acceleration under the condition that the friction coefficient between the track surface and the skid of the train reaches the maximum.
The maximum speed protection curve is expressed as:
Figure BDA0002659839480000047
wherein the content of the first and second substances,
Figure BDA0002659839480000048
for the velocity component at the time t of the maximum velocity protection curve,
Figure BDA0002659839480000049
is the mileage component at the t-th moment of the maximum speed protection curve, delta t is the sampling interval, atThe acceleration of the train at the t moment;
the process of obtaining the safe braking speed curve by utilizing the maximum speed protection curve comprises the following steps:
Figure BDA00026598394800000410
wherein the content of the first and second substances,
Figure BDA00026598394800000411
for the speed component of the safety braking speed profile,
Figure BDA00026598394800000412
for the mileage component of the safety braking speed curve, delta tt is the system delay from the sending of the traction cut-off command to the completion of the traction cut-off, delta v is the speed measurement error, delta s is the positioning error, aworstThe acceleration of the train under the conditions that the train is unloaded, the train encounters the maximum downwind speed and the friction coefficient of the track surface and the skid of the train reaches the maximum value is achieved.
If the obtained temporary parking area is located at a position where the parking area is not suitable to be set, the position of the temporary parking area is shifted to a reference parking area.
Compared with the prior art, the invention has the following advantages:
for a unidirectional and bidirectional running normal magnetic suspension line, the step S3 uses a bidirectional cooperation arrangement method, so that each calculated auxiliary parking area is the auxiliary parking area farthest from the initial reference parking area, which helps to save the line construction cost and improve the scientificity of the planning and designing on the premise of ensuring the train running safety.
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FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic view of a "stop step" operation mode of a normally conductive magnetic levitation train;
FIG. 3 is a schematic view of an auxiliary parking area arrangement;
FIG. 4 is a schematic diagram of the concept of a "two-way collaboration" arrangement method;
FIG. 5 is a flow chart of an embodiment of the present invention;
fig. 6 is a result of arrangement of auxiliary parking areas according to an embodiment of the present invention;
fig. 7 is a result of a prior art auxiliary parking area arrangement.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
Examples
The embodiment provides a method for arranging a bidirectional auxiliary parking area of a normally-conducting magnetic suspension traffic, and relates to concepts and principles of 'stepping of parking points', a reverse recursion method, a forward recursion method and 'bidirectional cooperation'.
The following principles are "parking spot stepping", reverse recursion and forward recursion, described using the general term "parking area":
as shown in fig. 2, a train running on a normally conductive magnetic levitation train runs in a "stop stepping" mode, which can be described as: in the process of train stepping, the current parking area is always used as a target parking point, and the maximum speed protection curve, the minimum speed protection curve and the interval speed limit are used as safety protection requirements. And only when the speed of the train exceeds the minimum speed protection curve of the next parking area and does not exceed the maximum speed protection curve of the current parking area, stepping is executed, and the next parking area is taken as a target parking point. And so on, and finally reaches the actual operation end point. The parking areas comprise a forward direction parking area, a reverse direction parking area and a bidirectional parking area. The parking areas in the positive direction and the reverse direction only supply the operation in the positive direction or the reverse direction, and the parking areas in the two directions can supply the operation in the two directions. The dangerous point is the tail end position of the parking area according to the running direction of the train, and the reachable point is the head end position of the parking area.
The arrangement of the parking area needs to combine a safe braking speed curve, a safe suspension speed curve, a maximum speed protection curve, a minimum speed protection curve, a train running speed curve and a train 'parking point stepping' running mode. The parking area can be progressively forward recurred by taking the starting station as a reference, and the parking area can be progressively backward recurred by taking the terminal station as a reference.
If the first reference parking area is the starting station in the running direction, a forward recursion mode needs to be adopted, namely:
first, a danger point (H in fig. 3) according to the origin stationi) And calculating a safety braking speed curve, and determining a maximum speed protection curve. And then the intersection point of the maximum speed protection curve and the train running speed curve can be obtained.
Next, a minimum speed protection curve is calculated from the intersection or a point below (when a redundancy margin is considered). And after the minimum speed protection curve is obtained, calculating to obtain a safe suspension speed curve. The mileage component when the velocity component of the safe levitation velocity profile is 0 can be set as the reachable point of the parking area (R in fig. 3)i)。
And moreover, according to the position of the reachable point and the length of the parking area, the dangerous point of the parking area can be determined.
Based on the newly determined danger point, the next parking area can be further determined using the above procedure. If a certain parking area is located at a position where the parking area is not suitable to be set (such as a bridge, a steep slope and a power supply partition boundary), the parking area can be deviated towards the direction of a starting station, and then the parking area is used as a reference parking area to arrange the next parking area.
If the first reference parking area is the terminal station in the running direction, a reverse recursion mode needs to be adopted, namely:
first, based on the accessibility of the terminalDot (R in FIG. 3)i) And calculating a safe suspension speed curve, and determining a minimum speed protection curve. And then the intersection point of the minimum speed protection curve and the train running speed curve can be obtained.
Next, a maximum speed protection curve is calculated from the intersection or a point below (when a redundancy margin is considered). After the maximum speed protection curve is obtained, a safety braking speed curve can be calculated, and the mileage component when the speed component of the safety braking speed curve is 0 can be set as a dangerous point (H in fig. 3) of the parking areai)。
Furthermore, according to the position of the dangerous point and the length of the parking area, the reachable point of the parking area can be determined.
Based on the newly determined reachable point, the next parking area may be further determined using the above process. If a certain parking area is located at a position where the parking area is not suitable to be set (such as a bridge, a steep slope and a power supply partition boundary), the parking area can be deviated towards a terminal station direction, and then the parking area is used as a reference parking area to arrange a next parking area.
In the two recursion processes, for the safe levitation speed curve and the minimum speed protection curve, two situations exist, namely, the safe levitation speed curve is calculated firstly, then the minimum speed protection curve is calculated, and the minimum speed protection curve is calculated firstly, and then the safe levitation speed curve is calculated.
For the first case, the formula for calculating the safe levitation velocity profile is:
Figure BDA0002659839480000061
in the formula (I), the compound is shown in the specification,
Figure BDA0002659839480000062
for the velocity component at time t of the safe levitation velocity profile,
Figure BDA0002659839480000063
is the mileage component of the safe suspension velocity curve at the t-th moment, delta t is the sampling interval, atFor addition of trains at time tSpeed.
Furthermore, according to the safe levitation speed curve, the calculation formula of the minimum speed protection curve is as follows:
Figure BDA0002659839480000071
wherein the content of the first and second substances,
Figure BDA0002659839480000072
is the velocity component on the minimum velocity profile,
Figure BDA0002659839480000073
for distance component, Δ tt is the system delay from the issuance of the traction cut-off command to the activation of the eddy current brake, Δ v is the speed measurement error, Δ s is the positioning error, aworstThe acceleration is the acceleration under the most adverse condition of the train, namely the situation that the train is unloaded, the maximum upwind speed is encountered (the maximum upwind speed is the maximum upwind speed which the train can encounter), and the friction coefficient between the track surface and the skid of the train reaches the maximum.
For the second case, the formula for the minimum speed protection curve is:
Figure BDA0002659839480000074
in the formula (I), the compound is shown in the specification,
Figure BDA0002659839480000075
is the velocity component at the time t of the minimum velocity protection curve,
Figure BDA0002659839480000076
is the mileage component at the t-th moment of the minimum speed protection curve, delta t is the sampling interval, atThe acceleration of the train at the t-th moment.
Furthermore, according to the minimum speed protection curve, the calculation formula of the safe suspension speed curve is as follows:
Figure BDA0002659839480000077
wherein the content of the first and second substances,
Figure BDA0002659839480000078
for the velocity component on the safe levitation velocity profile,
Figure BDA0002659839480000079
for distance component, Δ tt is the system delay from the issuance of the traction cut-off command to the activation of the eddy current brake, Δ v is the speed measurement error, Δ s is the positioning error, aworstThe method is the acceleration under the most unfavorable condition of the train, namely the situation that the train is unloaded, the train encounters the maximum upwind speed and the friction coefficient between the track surface and the skid of the train reaches the maximum.
Meanwhile, for the safety braking speed curve and the maximum speed protection curve, two situations exist, namely the safety braking speed curve is calculated firstly and then the maximum speed protection curve is calculated, and the maximum speed protection curve is calculated firstly and then the safety braking speed curve is calculated.
For the first case, there is a calculation formula for the safe braking speed profile as:
Figure BDA00026598394800000710
wherein the content of the first and second substances,
Figure BDA00026598394800000711
for the speed component at the time t of the safety braking speed profile,
Figure BDA00026598394800000712
is the mileage component at the t-th time, Δ t is the sampling interval, atThe acceleration of the train at the t-th moment.
According to the safety braking speed curve, the calculation formula of the maximum speed protection curve is as follows:
Figure BDA00026598394800000713
wherein the content of the first and second substances,
Figure BDA0002659839480000081
for the purpose of safely braking the velocity component of the velocity profile,
Figure BDA0002659839480000082
mileage component, delta tt is system delay from the sending of a traction cut-off command to the completion of traction cut-off, delta v is speed measurement error, delta s is positioning error, and aworstThe acceleration of the train under the most adverse condition is the situation that the train is fully loaded, the eddy braking force is damaged, the maximum downwind wind speed is encountered (the maximum downwind wind speed is the maximum downwind speed which the train can encounter), and the friction coefficient between the track surface and the skid of the train is minimized.
For the second case, the maximum speed protection curve is calculated as:
Figure BDA0002659839480000083
wherein the content of the first and second substances,
Figure BDA0002659839480000084
for the velocity component at the time t of the maximum velocity protection curve,
Figure BDA0002659839480000085
is the mileage component at the t-th moment of the maximum speed protection curve, delta t is the sampling interval, atThe acceleration of the train at the t-th moment.
According to the maximum speed protection curve, the calculation formula of the safety braking speed curve is as follows:
Figure BDA0002659839480000086
wherein the content of the first and second substances,
Figure BDA0002659839480000087
for the purpose of safely braking the velocity component of the velocity profile,
Figure BDA0002659839480000088
is mileage component, delta tt is system delay from the sending of traction cut-off command to the completion of traction cut-off, delta v is speed measurement error, delta s is positioning error, and aworstThe acceleration of the train under the most adverse condition is the situation that the train is fully loaded, the eddy braking force is damaged, the train encounters the maximum downwind wind speed, and the friction coefficient between the rail surface and the skid of the train is minimized.
The principle of the two-way cooperation is as follows, and the principle is described by using the general word of parking area:
the bidirectional cooperation arrangement method has no difference between the main direction and the secondary direction for the station section, but for distinguishing the types of the parking areas, the parking areas are divided into a forward direction parking area, a reverse direction parking area and a bidirectional parking area. The direction OD in fig. 3 is a forward direction, and the direction DO in fig. 3 is a reverse direction. In fig. 4, no other parking area exists between the reverse direction parking areas 1 and 2 and their reference parking areas (the station D and the parking area 1). To meet the necessity of the train running in the forward direction, the parking areas 1, 2 cannot be set to positions farther from the station. And another parking area exists between the parking area 3 in the forward direction and the reference parking area (station D), so that it can be disposed farther from the station. The positive direction parking area is further determined by setting the parking area 2 as a two-way parking area and setting it as a reference parking area, the result shown in the second row of images in fig. 4 is obtained. At this time, the actually obtained positive direction parking area 4 is the current positive direction auxiliary parking area farthest from the station D and cannot be farther from the station D. When the next reverse direction parking area or the forward direction parking area is arranged, by analogy, each parking area obtained through calculation is the parking area farthest from the station D, namely, the parking areas can be optimally arranged.
Thirdly, the arrangement method of the two-way auxiliary parking area of the normally-conducting magnetic levitation transportation of the embodiment integrates a ' parking point stepping ', a reverse recursion method, a forward recursion method and a two-way cooperation ', as shown in fig. 1, and comprises the following steps:
step S1: acquiring a starting station and an end station, and selecting one of the stations as a reference parking area;
step S2: on the basis of a reference standard parking area, respectively adopting a reverse recursion method and a forward recursion method to obtain a first-direction temporary parking area and a second-direction temporary parking area;
step S3: selecting one of the first-direction temporary parking area and the second-direction temporary parking area which is farther from the reference parking area as a temporary reference direction parking area, acquiring the reference direction of the temporary reference direction parking area, arranging the temporary parking areas in the direction by adopting the recursion method adopted in the step S2 in the reverse direction of the reference direction until the distance between the temporary parking area in the reverse direction of the reference direction and the reference parking area is larger than the distance between the temporary reference direction parking area and the reference parking area, and recording the temporary parking area in the reverse direction of the reference direction as a temporary parking area p;
step S4: setting a temporary parking area in the opposite direction of the previous reference direction of the temporary parking area p as a bidirectional parking area, canceling the temporary parking area p and the temporary reference direction parking area, and removing the remaining temporary parking areas of the temporary parking area p and the temporary reference direction parking area to be used as auxiliary parking areas;
step S5: setting the bidirectional parking area as a new reference parking area, further obtaining a new first-direction temporary parking area and a new second-direction temporary parking area by adopting a reverse recursion method and a forward recursion method, and returning to the step S3 until the arrangement is completed in one direction of the first direction and the second direction.
Step S6: the other direction completes the arrangement according to the recursion method it adopted in step S2.
The forward recursion method is specifically applied to this example:
calculating a safety braking speed curve according to the dangerous points of the reference parking area;
determining a maximum speed protection curve according to the safety braking speed curve, and obtaining a first intersection point of the maximum speed protection curve and a train running speed curve;
calculating a minimum speed protection curve according to the first intersection point, and then calculating to obtain a safe suspension speed curve;
obtaining an accessible point of the temporary parking area according to the safe suspension speed curve;
and obtaining the dangerous points of the temporary parking area according to the reachable points and the length of the parking area, and further obtaining the temporary parking area.
The reverse recursion method is specifically applied to this embodiment:
calculating a safe suspension speed curve according to the reachable point of the reference parking area;
determining a minimum speed protection curve according to the safety levitation speed curve, and obtaining a second intersection point of the minimum speed protection curve and the train operation speed curve;
calculating a maximum speed protection curve according to the second intersection point, and then calculating to obtain a safety braking speed curve;
obtaining a dangerous point of the temporary parking area according to the safety braking speed curve;
and obtaining the reachable point of the temporary parking area according to the dangerous point and the length of the parking area, and then obtaining the temporary parking area.
Fourthly, the following is a specific example:
let the length of parking zone be l and the position of parking zone i be [ S ]i,Si+l]，SOFor the location of the dangerous spot at station O, SDThe specific process is shown in fig. 5 for the reachable point position of the station D:
step 1: and (5) initializing. And taking the terminal D as a reference parking area, and determining a first positive direction temporary parking area by adopting a reverse recursion method, namely i is 1. Meanwhile, a forward recursion method is adopted to arrange a first reverse direction temporary parking area, namely j is equal to 1. And initializes the bidirectional parking lot number k, i.e., k 1.
Step 2: judging whether S existsD-Si＞SD-Sj. If yes, the reverse direction temporary parking area j is closer to the current reference parking area than the forward direction temporary parking area i, the condition that a forward running train safely and continuously steps from the reverse direction temporary parking area j to the reference parking area can be met, the forward direction temporary parking area i serves as the temporary reference direction parking area, and step 3 is executed; otherwise, the vehicle is temporarily stopped in the positive directionThe area i is closer to the reference parking area than the reverse direction temporary parking area j, the condition that the reverse direction running train safely and continuously steps from the reference parking area to the forward direction temporary parking area i can be met, and the step 7 is executed;
and step 3: judging whether S existsD-Si-l＞SD-SO(SOIs the origin station O station boundary position). If so, the condition of stopping calculating the positive direction temporary parking area is achieved, the arrangement of the positive direction temporary parking area is finished, and the step 4 is executed; otherwise, executing step 5;
and 4, step 4: judging whether S existsD-Sj-l＞SD-SO. If so, the condition of stopping calculating the reverse direction temporary parking area is achieved, and the calculation is finished; otherwise, determining the next reverse direction temporary parking area (with the number j +1) by taking the reverse direction temporary parking area j as a temporary reference direction parking area, enabling j to be j +1, and repeating the step 4;
and 5: preliminarily determining the next reverse direction temporary parking area (with the number being j +1) by taking the reverse direction temporary parking area j as a temporary reference direction parking area, and executing the step 6 by enabling j to be j + 1;
step 6: further judging whether S existsD-Si＞SD-Sj. If yes, the reverse direction temporary parking area j is farther from the reference parking area than the reverse direction temporary parking area j-1 and is closer to the reference parking area than the forward direction temporary parking area i, and the condition that the forward running train safely and continuously steps from the reverse direction temporary parking area j to the reference parking area can be met. Based on the above, determining the reverse direction temporary parking area j as a reverse direction auxiliary parking area j, and returning to the step 5; otherwise, the reverse direction temporary parking area j-1 is closer to the reference parking area than the positive direction temporary parking area i and is the reverse direction parking area farthest from the reference parking area. Therefore, the reverse direction temporary parking area j-1 is set as a bidirectional parking area with the number k, and the bidirectional parking area is used as a reference parking area for determining the next forward direction parking area, and the number of the reverse direction temporary parking area j is j-1, that is, j is j-1. Meanwhile, let k equal to k +1, i equal to i +1, return to step 2;
and 7: judging whether S existsD-Sj-l＞SD-SO. If yes, the constraint condition of stopping calculating the reverse direction temporary parking area is reached, and step 8 is executed; otherwise, executing step 9;
and 8: judging whether S existsD-Si-l＞SD-SO. If so, stopping calculating the constraint condition of the temporary parking area, finishing the calculation, performing reverse order adjustment on the numbers of the auxiliary parking area and the bidirectional parking area to obtain an auxiliary parking area arrangement result, and finishing the parking area arrangement; otherwise, taking the temporary parking area i in the positive direction as a reference parking area, further determining the temporary parking area i +1 in the next positive direction, and repeating the step 8 after the step i is changed to i + 1;
and step 9: setting a positive direction temporary parking area i as a reference parking area, preliminarily determining a next positive direction temporary parking area i +1, setting i to be i +1, and executing the step 10;
step 10: further judging whether S existsD-Sj＞SD-Si. If yes, the positive direction temporary parking area i is farther from the temporary reference direction parking area than the positive direction temporary parking area i-1 and is closer to the temporary reference direction parking area than the negative direction temporary parking area j, and the condition that the train running in the reverse direction safely and continuously steps from the temporary reference direction parking area to the positive direction temporary parking area i can be met. Based on the above, determining the positive direction temporary parking area i as a positive direction auxiliary parking area i, and returning to the step 9; otherwise, the positive direction temporary parking area i-1 is closer to the temporary reference direction parking area than the reverse direction temporary parking area j and is the positive direction parking area farthest from the temporary reference direction parking area at present. Therefore, the forward direction temporary parking area i-1 is set as a bidirectional parking area k, the next reverse direction parking area is determined by using the bidirectional parking area as a reference parking area, and the forward direction temporary parking area i is designated as i-1, that is, i is i-1. Meanwhile, let k be k +1 and j be j +1, return to step 2.
Meanwhile, in comparison of the superiority of the method, fig. 6 shows the arrangement obtained by adopting the above-mentioned "bidirectional cooperation" arrangement method flow. For the same scenario of fig. 6, the parking area arrangement result obtained by separately adopting the reverse recursion method in the two directions is shown in fig. 7. As can be seen from comparing fig. 6 and 7, fig. 7 has 18 parking areas and no phenomenon that parking areas in two directions overlap each other, while fig. 6 has only 14 parking areas, that is, the "bidirectional cooperation" arrangement method reduces the number of auxiliary parking areas compared with the two-direction independent arrangement method, thereby greatly improving the economy.
In addition, based on the above thought, the arrangement of the parking area can also be developed by adopting a mode of gradually forwarding in the forward direction and gradually forwarding in the reverse direction.
In conclusion, the bidirectional arrangement process of the parking areas of the normally-conducting magnetic suspension line can be simply applied to engineering practice by means of the calculation method of the maximum speed protection curve, the minimum speed protection curve, the safe braking speed curve and the safe suspension braking speed curve and the setting method of the bidirectional parking areas.

Claims (8)

1. A method for arranging a two-way auxiliary parking area of a normally-conducting magnetic suspension traffic is characterized by comprising the following steps:
step S1: acquiring a starting station and an end station, and selecting one of the stations as a reference parking area;
step S2: on the basis of a reference standard parking area, respectively adopting a reverse recursion method and a forward recursion method to obtain a first-direction temporary parking area and a second-direction temporary parking area;
step S3: selecting one of the first-direction temporary parking area and the second-direction temporary parking area which is farther from the reference parking area as a temporary reference direction parking area, acquiring the reference direction of the temporary reference direction parking area, arranging the temporary parking areas in the direction by adopting the recursion method adopted in the step S2 in the reverse direction of the reference direction until the distance between the temporary parking area in the reverse direction of the reference direction and the reference parking area is larger than the distance between the temporary reference direction parking area and the reference parking area, and recording the temporary parking area in the reverse direction of the reference direction as a temporary parking area p;
step S4: setting a temporary parking area in the opposite direction of the previous reference direction of the temporary parking area p as a bidirectional parking area, canceling the temporary parking area p and the temporary reference direction parking area, and removing the remaining temporary parking areas of the temporary parking area p and the temporary reference direction parking area to be used as auxiliary parking areas;
step S5: setting the bidirectional parking area as a new reference parking area, further obtaining a new first-direction temporary parking area and a new second-direction temporary parking area by adopting a reverse recursion method and a forward recursion method, and returning to the step S3 until the arrangement is finished in one direction of the first direction and the second direction;
step S6: the other direction completes the arrangement according to the recursion method it adopted in step S2.
2. The arrangement method of the two-way auxiliary parking area of the normally-conducting magnetic-levitation transportation according to claim 1, wherein the forward recursion method comprises the following steps:
calculating a safety braking speed curve according to the dangerous points of the reference parking area;
determining a maximum speed protection curve according to the safety braking speed curve, and obtaining a first intersection point of the maximum speed protection curve and a train running speed curve;
calculating a minimum speed protection curve according to the first intersection point, and then calculating to obtain a safe suspension speed curve;
obtaining an accessible point of the temporary parking area according to the safe suspension speed curve;
and obtaining the dangerous points of the temporary parking area according to the reachable points and the length of the parking area, and further obtaining the temporary parking area.
3. The arrangement method of the two-way auxiliary parking area of the normally-conducting magnetic-levitation transportation according to claim 2, wherein the minimum speed protection curve is expressed as:
Figure FDA0002659839470000021
wherein the content of the first and second substances,
Figure FDA0002659839470000022
is the velocity component at the time t of the minimum velocity protection curve,
Figure FDA0002659839470000023
is the mileage component at the t-th moment of the minimum speed protection curve, delta t is the sampling interval, atThe acceleration of the train at the t moment;
the process of obtaining the safe suspension speed curve by utilizing the minimum speed protection curve comprises the following steps:
Figure FDA0002659839470000024
wherein the content of the first and second substances,
Figure FDA0002659839470000025
for the velocity component on the safe levitation velocity profile,
Figure FDA0002659839470000026
for the distance component on the safe suspension speed curve, delta tt is the system delay from the sending of the traction cut-off command to the starting process of the eddy current brake, delta v is the speed measurement error, delta s is the positioning error, aworstThe train is in no-load condition, encounters the maximum upwind speed and has the acceleration under the condition that the friction coefficient between the track surface and the skid of the train reaches the maximum.
4. The arrangement method of the two-way auxiliary parking area of the normally-conducting magnetic-levitation transportation according to claim 2, wherein the safe braking speed curve is expressed as:
Figure FDA0002659839470000027
wherein the content of the first and second substances,
Figure FDA0002659839470000028
for the speed component at the time t of the safety braking speed profile,
Figure FDA0002659839470000029
is the mileage component at the t-th time, Δ t is the sampling interval, atThe acceleration of the train at the t moment;
the process of calculating the maximum speed protection curve by using the safety braking speed curve comprises the following steps:
Figure FDA00026598394700000210
wherein the content of the first and second substances,
Figure FDA00026598394700000211
for the speed component of the safety braking speed profile,
Figure FDA00026598394700000212
for the mileage component of the safety braking speed curve, delta tt is the system delay from the sending of the traction cut-off command to the completion of the traction cut-off, delta v is the speed measurement error, delta s is the positioning error, aworstThe acceleration of the train under the conditions that the train is unloaded, the train encounters the maximum downwind speed and the friction coefficient of the track surface and the skid of the train reaches the maximum value is achieved.
5. The arrangement method of the two-way auxiliary parking area of the normally-conducting magnetic-levitation transportation according to claim 1, wherein the reverse recursion method comprises the following steps:
calculating a safe suspension speed curve according to the reachable point of the reference parking area;
determining a minimum speed protection curve according to the safety levitation speed curve, and obtaining a second intersection point of the minimum speed protection curve and the train operation speed curve;
calculating a maximum speed protection curve according to the second intersection point, and then calculating to obtain a safety braking speed curve;
obtaining a dangerous point of the temporary parking area according to the safety braking speed curve;
and obtaining the reachable point of the temporary parking area according to the dangerous point and the length of the parking area, and then obtaining the temporary parking area.
6. The arrangement method of the two-way auxiliary parking area of the normally-conducting magnetic-levitation transportation according to claim 5, wherein the safe levitation speed curve is represented as:
Figure FDA0002659839470000031
wherein the content of the first and second substances,
Figure FDA0002659839470000032
for the velocity component at time t of the safe levitation velocity profile,
Figure FDA0002659839470000033
is the mileage component of the safe suspension velocity curve at the t-th moment, delta t is the sampling interval, atThe acceleration of the train at the t moment;
the process of calculating the minimum speed protection curve by using the safe suspension speed curve comprises the following steps:
Figure FDA0002659839470000034
wherein the content of the first and second substances,
Figure FDA0002659839470000035
is the velocity component on the minimum velocity profile,
Figure FDA0002659839470000036
for the distance component on the minimum velocity curve, Δ tt is the system delay from the issuance of the traction cut-off command to the activation of the eddy current brake, Δ v is the speed measurement error, Δ s is the positioning error, aworstThe train is in no-load condition, encounters the maximum upwind speed and has the acceleration under the condition that the friction coefficient between the track surface and the skid of the train reaches the maximum.
7. The arrangement method of the two-way auxiliary parking area of the normally-conducting magnetic-levitation transportation according to claim 5, wherein the maximum speed protection curve is expressed as:
Figure FDA0002659839470000037
wherein the content of the first and second substances,
Figure FDA0002659839470000038
for the velocity component at the time t of the maximum velocity protection curve,
Figure FDA0002659839470000039
is the mileage component at the t-th moment of the maximum speed protection curve, delta t is the sampling interval, atThe acceleration of the train at the t moment;
the process of obtaining the safe braking speed curve by utilizing the maximum speed protection curve comprises the following steps:
Figure FDA00026598394700000310
wherein the content of the first and second substances,
Figure FDA00026598394700000311
for the speed component of the safety braking speed profile,
Figure FDA00026598394700000312
for the mileage component of the safety braking speed curve, delta tt is the system delay from the sending of the traction cut-off command to the completion of the traction cut-off, delta v is the speed measurement error, delta s is the positioning error, aworstThe acceleration of the train under the conditions that the train is unloaded, the train encounters the maximum downwind speed and the friction coefficient of the track surface and the skid of the train reaches the maximum value is achieved.
8. The arrangement method of the two-way auxiliary parking area for the normally magnetic and levitation transportation according to claim 2 or 5, wherein if the obtained temporary parking area is located at a position where the parking area is not suitable to be set, the position of the temporary parking area is shifted to the reference parking area.
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