A method for solving the optimal train operation curve based on the maximum principle

Abstract

The present invention provides a method for solving an optimal train running curve based on the maximum principle, and relates to the technical field of train energy-saving optimization control. The method comprises the following steps: obtaining basic data and initialization parameters; determining idling data and full control data by calculation based on the basic data and the initialization parameters; obtaining accompanying variables by calculation based on the initialization parameters, and determining the next train operating condition; calculating the next train running data based on the train running data of the current step and the next train operating condition; performing curve splicing based on the train running data, the idling data and the full control data, and obtaining a complete train running curve and a total running time; and taking the complete train running curve as the final train running curve. The present invention solves the problems of large amount of calculation and low precision in solving the train running curve.

Description

Technical Field

[0001] The present invention relates to the technical field of train energy-saving optimization control, and in particular to a method for solving an optimal train operation curve based on the maximum principle. Background Art

[0002] Since the energy consumption of train operation accounts for a large proportion of the total energy consumption of the railway industry, in order to reduce the energy consumption of train operation, it is necessary to study the energy-saving operation of trains. In the existing calculation of single train operation curves, the adjoint variable differential equation is generally solved numerically, such as the fourth-order Runge-Kutta method, but the adjoint variable is difficult to calculate accurately, and it is necessary to repeatedly iterate to solve the connecting line, and the entire operation curve cannot be obtained at one time; or the non-constant speed section connection method is used to quickly find the suboptimal curve without calculating the adjoint variable, which reduces the difficulty of calculation, but the accuracy is not high, and it is difficult to solve complex operation lines.

[0003] In order to solve the above problems, a method for solving the optimal train operation curve based on the maximum principle is proposed. Summary of the invention

[0004] One or more embodiments of this specification provide a method for solving the optimal train operation curve based on the maximum principle. The method for solving the optimal train operation curve based on the maximum principle includes: S1: obtaining basic data and initialization parameters; the initialization parameters include: optimal constant speed initial value, discrete line step length, number of discrete line sections, train operation data of the first step and train operating value; the train operation data includes train speed, position, running time and the running curve to this step; S2: based on the basic data and the initialization parameters, determine the idling data and full control data by calculation; the idling data includes: idling switching point, idling time and idling curve, and the full control data includes: full control switching point, full control time and full control curve; S3: based on the initialization parameters, from the number of steps Start by calculating the accompanying variable of step i and determine the S4: based on the train operation data of step i and the train operation data of step i The train condition of step 1 is calculated. The train operation data of the step is set Train status; S5: Use the coasting switching point to determine whether the train meets the coasting switching condition at the i-th step. If so, enter S6, otherwise return to S3; S6: Based on the train operation data, coasting data and full system data of the i-th step, perform curve splicing to obtain a complete train operation curve and total operation time; S7: Determine whether the total operation time meets the specified train operation time. If so, use the complete train operation curve as the final train operation curve, otherwise, adjust the optimal constant speed and return to S2.

[0005] In some embodiments of this specification, the processor processes the basic data and initialization parameters based on the maximum principle to obtain the train operation curve. In this way, the operation condition of the entire train can be obtained at one time, which is convenient for practical application and reduces the amount of calculation; using the maximum principle, the accompanying variable value is accurately calculated to determine the train operation curve with the minimum energy consumption, which can improve the accuracy of the obtained curve, so that the method can be applied to complex lines such as continuous ramps, and expand the scope of application. BRIEF DESCRIPTION OF THE DRAWINGS

[0006] This specification will be further described in the form of exemplary embodiments, which will be described in detail by the accompanying drawings. These embodiments are not restrictive, and in these embodiments, the same number represents the same structure, wherein:

[0007] Figure 1 is an exemplary flow chart of a method for solving an optimal train operation curve based on the maximum principle according to some embodiments of this specification;

[0008] Figure 2 is an exemplary flow chart for determining idle data and full control data according to some embodiments of the present specification;

[0009] Figure 3 It is an exemplary flow chart for determining the next train operating condition according to some embodiments of this specification. DETAILED DESCRIPTION

[0010] In order to more clearly illustrate the technical solutions of the embodiments of this specification, the following is a brief introduction to the drawings required for the description of the embodiments. Obviously, the drawings described below are only some examples or embodiments of this specification. For ordinary technicians in this field, this specification can also be applied to other similar scenarios based on these drawings without creative work. Unless it is obvious from the language environment or otherwise explained, the same reference numerals in the figures represent the same structure or operation.

[0011] It should be understood that the "system", "device", "unit" and / or "module" used herein are a method for distinguishing different components, elements, parts, portions or assemblies at different levels. However, if other words can achieve the same purpose, the words can be replaced by other expressions.

[0012] As shown in this specification and claims, unless the context clearly indicates an exception, the words "a", "an", "an" and / or "the" do not refer to the singular and may also include the plural. Generally speaking, the terms "comprise" and "include" only indicate the inclusion of the steps and elements that have been clearly identified, and these steps and elements do not constitute an exclusive list. The method or device may also include other steps or elements.

[0013] Flowcharts are used in this specification to illustrate the operations performed by the system according to the embodiments of this specification. It should be understood that the preceding or following operations are not necessarily performed precisely in order. Instead, the steps may be processed in reverse order or simultaneously. At the same time, other operations may also be added to these processes, or one or more operations may be removed from these processes.

[0014] Figure 1 is an exemplary flow chart of a method for solving an optimal train operation curve based on the maximum principle according to some embodiments of this specification. Figure 1 In some embodiments, the process 100 may be executed by a processor.

[0015] Step 110: The processor obtains basic data and initialization parameters.

[0016] Basic data refers to basic train operation data, such as train weight, train traction and braking characteristics, line speed limit information, line information, train operation time, etc.

[0017] In some embodiments, the processor can obtain basic data by querying the train number on the Internet, uploading data from the railway company, etc.

[0018] Initialization parameters are parameters that need to be set for calculation when the train starts. For example, initialization parameters may include the optimal constant speed initial value, discrete line step length, number of discrete line segments, train operation data and train operating conditions of the first step, etc.; train operation data includes train speed, position, running time and running curve up to this step, etc.

[0019] In some embodiments, the optimal constant speed initial value It can be determined based on the formula:

[0020]

[0021] in, is the train terminal position, is the starting position of the train, The train running time.

[0022] In some embodiments, the line discrete steps It can be determined based on the total distance of the train operation. For example, if the total distance of the train operation is 100 kilometers, then the line discrete length It can be set to 0.1 km, that is, 1 step is set every 0.1 km.

[0023] In some embodiments, the number of discrete line segments It can be determined based on the formula: .

[0024] In some embodiments, the processor may Initialization of train information at time:

[0025]

[0026] in, is the speed of the i-th step, is the position of the i-th step, is the time of the i-th step, is the working condition information of the i-th step, Indicates full traction condition.

[0027] Step 120: The processor determines the idle data and the full control data through calculation based on the basic data and the initialization parameters.

[0028] Coasting data refers to relevant data when the train is in coasting condition, for example, the coasting data may include coasting switching point, coasting time and coasting curve.

[0029] The coasting switching point is the number of steps the train takes to switch to the coasting condition for the last time, the coasting time is the total duration of the train's coasting operation, and the coasting curve is the path curve of the train's coasting operation.

[0030] The full control data is the relevant data when the train is in full control condition. For example, the full control data may include full control switching point, full control time and full control curve.

[0031] The full-control switching point is the number of steps the train takes to switch to the full-control condition for the last time, the full-control time is the total duration of the train's full-control operation, and the full-control curve is the path curve of the train's full-control operation.

[0032] In some embodiments, the processor may determine the coasting switching point and the full control switching point by calculation, and obtain the coasting data and the full control data.

[0033] For more details on getting lazy data and full data, see Figure 2 and its related description.

[0034] Step 130: the processor, based on the initialization parameter, starts from the number of steps Start by calculating the accompanying variable of step i and determine the Step train condition.

[0035] The adjoint variable is a variable generated when constructing the Hamiltonian function based on the maximum principle. For example, the adjoint variable may include the adjoint variable and accompanying variables wait.

[0036] In some embodiments, the accompanying variables can be used to analyze the optimal control conditions of the train.

[0037] The train operating condition is data indicating the running status of the train. For example, the train operating condition may include full traction condition (FP), partial traction condition (PP), coasting condition (C), partial braking condition (PB) and full braking condition (FB).

[0038] In some embodiments, the train operating condition can be determined by comparing the current acceleration with the coasting acceleration. For example, if the current acceleration of the train is greater than the coasting acceleration, the current operating condition is the traction condition; if the current acceleration of the train is equal to the coasting acceleration, the current operating condition is the coasting condition, and so on.

[0039] More details on calculating the accompanying variables to determine the train behavior can be found in Figure 3 and its related description.

[0040] Step 140: The processor calculates the train operation data of step i and step The train condition of step 1 is calculated. The train operation data of the step is set .

[0041] Train operation data is data reflecting the current operation status of the train. For example, the train operation data may include the speed, position, running time of the train at the current step, and the running curve from the first step to the current step.

[0042] In some embodiments, the processor can determine the train operation data of step i by calculation. After the calculation is completed, the train operation data of the first step Steps as the current step number, that is, set .

[0043] In some embodiments, the processor may determine the first The train operation data of the step:

[0044]

[0045]

[0046]

[0047]

[0048] in, is the train running acceleration, is the acceleration due to gravity, and are the i-th step and the The train speed of step and are the i-th step and the The train location of the step, and are the i-th step and the The train running time of step is the traction force utilization factor, is the traction force per unit mass of the train, is the braking force utilization coefficient, is the train braking force per unit mass, Based on the The train operating conditions of the first step are determined. is the basic resistance per unit mass of the train, is the additional resistance per unit mass of the train, Is the distance between the lines.

[0049] In some embodiments, the processor may determine the basic drag and the additional drag experienced by the train based on the kinematic equations:

[0050]

[0051] in, is the train traction force, is the train braking force, is the traction force utilization factor, is the braking force utilization coefficient, is the total basic resistance of the train, is the total additional resistance experienced by the train, is the gyroscopic mass coefficient, is the train mass, is the current train speed.

[0052]

[0053]

[0054] in, is the basic resistance per unit mass, is the Davis coefficient related to the specific train type, is the acceleration due to gravity, Add resistance per unit mass, is the thousandth of the slope, which is numerically equal to the line slope. is the curve radius.

[0055] In some embodiments, the processor calculates the The train operation data of the first step is set as the train operation data of the current step. After the step train operation data calculation is completed, the step number .

[0056] In step 150 , the processor determines whether the train satisfies the coasting switching condition at the i-th step based on the coasting switching point. If the condition is satisfied, the processor proceeds to step 160 , otherwise, the processor returns to step 130 .

[0057] The coasting switching condition is a condition for the train to switch to the coasting state. For example, the coasting switching condition may include the train running time or running distance reaching a threshold, the train reaching a coasting switching point, etc.

[0058] In some embodiments, the processor can determine the current position of the train based on the train operation data and judge whether the train has reached the coasting switching point. If it has reached the coasting switching point, it goes to step 160, otherwise it returns to step 130 to continue calculating the next step of train operation data.

[0059] Step 160: The processor performs curve splicing based on the train operation data, coasting data and full control data of the i-th step to obtain a complete train operation curve and total operation time.

[0060] The complete train operation curve is a curve consisting of the entire running distance of the train from the running start point to the running end point. For example, the train operation curve may include the train operation curve from the first step to the i-th step, the idling curve and the full control curve, as well as the corresponding speed of the train at each position on the curve.

[0061] The total running time is the overall running time of the train from the starting point to the end point.

[0062] In some embodiments, the processor may sum the train's running time, coasting time, and full control time to determine the total train running time. :

[0063]

[0064] in, is the running time of the current number of steps of the train, It is the sum of the train's coasting time and full braking time.

[0065] In some embodiments, the processor can obtain the idling curve and the full control curve of the train based on the idling switching point and the full control switching point; splice the idling curve and the full control curve of the train's running curve to the i-th step to obtain a complete train running curve; and calculate and determine the total running time based on the complete train running curve.

[0066] In some embodiments, the processor may splice the train operation curve, the coasting curve and the full control curve to the i-th step to obtain a complete train operation curve.

[0067] Step 170 , the processor determines whether the total running time meets the specified running time of the train. If so, the complete train running curve is used as the final train running curve. Otherwise, the optimal constant speed is adjusted and the process returns to step 120 .

[0068] In some embodiments, the processor can determine whether the total running time meets the specified running time of the train. If so, the complete train running curve is determined as the final train running curve; otherwise, the optimal constant speed is adjusted based on the formula and returns to step 120.

[0069] In some embodiments, the processor may calculate the total train operation time. Scheduled train running time In contrast, When , the optimal constant speed is adjusted based on the formula: ,Will Return to step 120 to calculate again as the updated optimal constant speed ;when When the train running curve is completed, the complete train running curve at this time is taken as the final train running curve.

[0070] In some embodiments of this specification, the processor processes the basic data and initialization parameters based on the maximum principle to obtain the train operation curve. In this way, the operation condition of the entire train can be obtained through one calculation, reducing the amount of calculation; using the maximum principle, the accompanying variable value is accurately calculated through the analytical method to determine the train operation curve with the minimum energy consumption, which can greatly improve the accuracy of the obtained curve and make the obtained curve more in line with the actual situation; in this way, the operation curve of complex lines such as continuous ramps can be effectively calculated, expanding the scope of application.

[0071] Figure 2 FIG. 1 is an exemplary flow chart for determining idle data and full control data according to some embodiments of the present specification. Figure 2 As shown, process 200 includes the following steps.

[0072] Step 201: The processor classifies the ramp based on the initialization parameters to determine the ramp type of each step.

[0073] The ramp type is data describing the ups and downs and steepness of the ramp. For example, the ramp type may include steep upslope (DSP), steep downslope (DXP), and gentle ramp (HP).

[0074] In some embodiments, the processor may be based on the basic resistance And additional resistance , the ramp type for each step is determined by the formula:

[0075]

[0076]

[0077] in, is the slope in thousandths corresponding to the jth step, is the curve radius of the jth step.

[0078] when When , the slope type of the step is marked as steep uphill; when When , the slope type of the step is marked as steep downhill; when , mark the ramp type of the step as gentle ramp.

[0079] Step 202: The processor obtains the full control step range and the full control data through the train kinematic equation.

[0080] The full control step range is the set of all steps in the full control process of the train.

[0081] In some embodiments, the processor can calculate the current total number of steps N and calculate the last step Initialize parameters; determine whether the train speed at step m is the optimal constant speed. If so, use the step number as the full control switching point position to obtain the full control step number range and the full control data. Otherwise, use the calculation formula to calculate the full control step number range and the full control data. Perform full calculations to determine the train operation data for this number of steps and set .

[0082] In some embodiments, the processor may set the number of steps m to the total step value N, and initialize the train operation data of this step: .

[0083] Determine whether the train speed of the current step is the optimal constant speed. If not, perform a full calculation of the previous step through the train kinematic equation:

[0084]

[0085]

[0086]

[0087]

[0088] After the calculation is completed, the previous step is set as the current step number, that is, ;in, and are the mth and the The train speed of step and are the mth and the The train location of the step, and are the mth and the Step train running time;

[0089] If so, the step position is used as the full control switching point position, the step to the final step is used as the full control step range, and the step data in the range is used as the full control data.

[0090] Step 203: Based on the full control data, the processor uses the midpoint of the previous gentle slope closest to the full control switching point as the coasting switching point, and records the number of steps of the coasting switching point. and train operation data.

[0091] In some embodiments, the processor may obtain the step value of the most recent gentle slope of the full control switching point. , select the midpoint of this step as the coasting switching point. At this time, the number of steps of the coasting switching point .

[0092] In some embodiments, the train operation parameters of the coasting switch point may be determined based on calculations:

[0093]

[0094] in, yes The accompanying variable of the step, yes The speed of the step, yes The location of the step, yes The running time of the step.

[0095] Step 204: the processor The operating parameters of step 1 are used to calculate the Step operation parameters and set .

[0096] In some embodiments, the processor may The operating parameters of the step are calculated from the coasting switching point using the formula Step operating parameters:

[0097]

[0098]

[0099]

[0100]

[0101]

[0102] After the calculation is completed, the position of the next step is set to the current step position, that is, ;in, and They are Step and The train speed of step and They are Step and The train location of the step, and They are Step and steps of train running time, k is an arbitrary real number, and R represents a real number.

[0103] Step 205: The processor uses the The running parameters of the step are used to determine whether the accompanying variable value of the step is 0. If so, the process proceeds to step 206, otherwise, the process returns to step 204.

[0104] In some embodiments, the processor may modify the accompanying variable of the current step Make a judgment, if is not 0, then return to step 204 to continue calculating the next step; if , then the step can be preliminarily identified as the end point of coasting, and the process goes to step 206 .

[0105] In step 206 , the processor uses the operating parameters of the next step to determine whether the train position is within the full control step number range. If so, it proceeds to step 211 , otherwise, it proceeds to step 207 .

[0106] In some embodiments, the processor can determine whether the coasting end position is at a reasonable position based on the full control step range. For example, the processor can determine the position of the current step. If the current step is outside the full control step range, the processor enters step 207 to readjust the coasting switch point; if the previous step is within the full control step range, the processor uses the point as the full control switch point and enters step 211.

[0107] Step 207 : The processor searches for a position with the same speed as the coasting switch point position in the full control data, adjusts the coasting switch point position based on the distance between the two points, and obtains a theoretical coasting switch point position.

[0108] In some embodiments, the processor can select a step that is consistent with the current step number through the full control curve. At the point with the same speed, record its number of steps in M; move the idle curve horizontally Distance, regulations is rightward movement, and vice versa is leftward movement; at this time, the theoretical coasting switching point position Transformed into: .

[0109] In step 208 , the processor uses the theoretical coasting switch point position to determine whether the position is located on a gentle slope. If so, the process proceeds to step 210 , otherwise, the process proceeds to step 209 .

[0110] In some embodiments, the processor may determine whether the theoretical coasting switch point is located on a gentle slope. If not, the processor may proceed to step 209 ; if located on a gentle slope, the processor may proceed to step 210 .

[0111] In step 209 , the processor selects the nearest other gentle ramp as the current coasting switch point position based on the theoretical coasting switch point position, and proceeds to step 203 .

[0112] In some embodiments, the processor may select a gentle slope closest to the theoretical coasting switching point as the position of the current coasting switching point, and return to step 203 to calculate again.

[0113] In step 210 , the processor uses a binary search method to search for the gentle slope where the theoretical coasting switch point is located as the current coasting switch point position, and then proceeds to step 204 .

[0114] In some embodiments, the processor may use a binary search method to search for the gentle slope position where the theoretical coasting switch point is located as the current coasting switch point position, and return to step 204 to calculate again.

[0115] In step 211 , the processor determines the coasting data and the full control data by calculation based on the coasting switch point position and the full control switch point position.

[0116] In some embodiments, the processor determines the position of the coasting switch point based on the And the full switch point position , determine the range of idling steps and the range of full control steps, so as to obtain idling data and full control data.

[0117] In some embodiments, the coasting time It can be determined based on the formula:

[0118]

[0119] Full-time It can be determined based on the formula:

[0120]

[0121] Total coasting and full brake time It can be determined based on the formula:

[0122]

[0123] in, is the running time of the full switching point, is the running time of the coasting switching point, The running time of the end point.

[0124] In some embodiments, the processor may record the speed and position of the coasting switch point: ; Speed ​​and position of the full switching point: ; Record the train speed and position for all steps after the coasting switch point: .

[0125] In some embodiments of the present invention, the processor processes the initialization parameters using the train kinematic equations to obtain the coasting data and the full control data. In this way, the positions of the coasting switching point and the full control switching point can be accurately obtained, and the coasting curve and the full control curve that minimize the energy consumption of the train operation can be determined.

[0126] Figure 3 is an exemplary flow chart for determining the next train operating condition according to some embodiments of this specification. Figure 3 As shown, process 300 includes the following steps.

[0127] Step 310, the processor calculates the accompanying variable based on the formula .

[0128] In some embodiments, the processor may calculate the accompanying variable using the formula :

[0129] .

[0130] Step 320, the processor based on the accompanying variable , calculate and determine the accompanying variable Every step The value of .

[0131] In some embodiments, the processor may be based on the accompanying variable , use the formula to calculate the accompanying variables of each step Values:

[0132]

[0133] in, .

[0134] Step 330, the processor based on the accompanying variable The value of is used to determine the next train condition.

[0135] In some embodiments, the processor may be based on the accompanying variable The value of is used to judge the train working condition. At this time, , the train is in full traction condition; when At this time, , the train is in partial traction condition; when At this time, , the train is in coasting condition; when At this time, , the train is in partial braking condition; when At this time, , the train is in full working condition.

[0136] In some embodiments of this specification, the processor determines the train operating condition by calculating the value range of the accompanying variable. In this way, the value of the accompanying variable can be accurately calculated, making the judgment of the train operating condition more accurate and the result more in line with the actual situation.

[0137] It should be noted that the above descriptions of processes 100, 200 and 300 are only for illustration and description, and do not limit the scope of application of this specification. For those skilled in the art, various modifications and changes can be made to processes 100, 200 and 300 under the guidance of this specification. However, these modifications and changes are still within the scope of this specification.

[0138] The basic concepts have been described above. Obviously, for those skilled in the art, the above detailed disclosure is only for example and does not constitute a limitation of this specification. Although not explicitly stated here, those skilled in the art may make various modifications, improvements and corrections to this specification. Such modifications, improvements and corrections are suggested in this specification, so such modifications, improvements and corrections still belong to the spirit and scope of the exemplary embodiments of this specification.

[0139] At the same time, this specification uses specific words to describe the embodiments of this specification. For example, "one embodiment", "an embodiment", and / or "some embodiments" refer to a certain feature, structure or characteristic related to at least one embodiment of this specification. Therefore, it should be emphasized and noted that "one embodiment" or "an embodiment" or "an alternative embodiment" mentioned twice or more in different positions in this specification does not necessarily refer to the same embodiment. In addition, certain features, structures or characteristics in one or more embodiments of this specification can be appropriately combined.

[0140] In addition, unless explicitly stated in the claims, the order of the processing elements and sequences described in this specification, the use of alphanumeric characters, or the use of other names are not intended to limit the order of the processes and methods of this specification. Although the above disclosure discusses some invention embodiments that are currently considered useful through various examples, it should be understood that such details are only for illustrative purposes, and the attached claims are not limited to the disclosed embodiments. On the contrary, the claims are intended to cover all modifications and equivalent combinations that are consistent with the essence and scope of the embodiments of this specification. For example, although the system components described above can be implemented by hardware devices, they can also be implemented only by software solutions, such as installing the described system on an existing server or mobile device.

[0141] Similarly, it should be noted that in order to simplify the description disclosed in this specification and thus help understand one or more embodiments of the invention, in the above description of the embodiments of this specification, multiple features are sometimes combined into one embodiment, figure or description thereof. However, this disclosure method does not mean that the features required by the subject matter of this specification are more than the features mentioned in the claims. In fact, the features of the embodiments are less than all the features of the single embodiment disclosed above.

[0142] In some embodiments, numbers describing the number of components and attributes are used. It should be understood that such numbers used in the description of the embodiments are modified by the modifiers "about", "approximately" or "substantially" in some examples. Unless otherwise specified, "about", "approximately" or "substantially" indicate that the numbers are allowed to vary by ±20%. Accordingly, in some embodiments, the numerical parameters used in the specification and claims are approximate values, which may change according to the required features of individual embodiments. In some embodiments, the numerical parameters should take into account the specified significant digits and adopt the general method of retaining the digits. Although the numerical domains and parameters used to confirm the breadth of the range in some embodiments of this specification are approximate values, in specific embodiments, the setting of such numerical values ​​is as accurate as possible within the feasible range.

[0143] Each patent, patent application, patent application publication, and other materials, such as articles, books, specifications, publications, documents, etc., cited in this specification is hereby incorporated by reference in its entirety. Except for application history documents that are inconsistent with or conflicting with the contents of this specification, documents that limit the broadest scope of the claims of this specification (currently or later attached to this specification) are also excluded. It should be noted that if the descriptions, definitions, and / or use of terms in the materials attached to this specification are inconsistent or conflicting with the contents described in this specification, the descriptions, definitions, and / or use of terms in this specification shall prevail.

[0144] Finally, it should be understood that the embodiments described in this specification are only used to illustrate the principles of the embodiments of this specification. Other variations may also fall within the scope of this specification. Therefore, as an example and not a limitation, alternative configurations of the embodiments of this specification may be considered consistent with the teachings of this specification. Accordingly, the embodiments of this specification are not limited to the embodiments explicitly introduced and described in this specification.

Claims

1. A method for solving the optimal train operation curve based on the maximum principle, characterized in that: include: S1: Get basic data and initialization parameters; The initialization parameters include: optimal constant speed initial value, discrete line step length, number of discrete line sections, train operation data of the first step and train operating value; the train operation data includes train speed, position, running time and running curve to this step; the basic data includes: train weight, train traction and braking characteristics, line speed limit information, line information, train running time; S2: Based on the basic data and the initialization parameters, the coasting data and the full control data are determined by calculation; the coasting data includes: a coasting switching point, a coasting time, and a coasting curve; the full control data includes: a full control switching point, a full control time, and a full control curve; wherein, step S2 includes: S201: Classifying the ramp based on the initialization parameters to determine the ramp type of each step; the ramp types include: steep uphill, steep downhill and gentle ramp; S202: Obtaining a full control step range and the full control data; wherein the full control step range is a collection of all steps in the full control process of the train, and step S202 includes: S2021: Based on the discrete step lengths of the line and the total length of the line, the number of discrete line segments is calculated as the current total number of steps N, and parameters of the last step m=N are initialized; S2022: Perform full calculation on the m-1th step using the train kinematics equation, determine the train operation data for this step, and set m=m-1; S2203: Determine whether the train speed at the mth step is the optimal constant speed. If so, use the step number as the full control switching point position to obtain the full control step number range and full control data; otherwise, return to S2202; S203: Based on the full control data, the midpoint of the previous gentle slope closest to the full control switching point is used as the coasting switching point, and the number of steps m′=M′ of the coasting switching point and the train operation data are recorded; S204: Based on the operating parameters of the m′th step, starting from the coasting switching point, the operating parameters of the m′th step+1 are calculated using the formula: x(m′+1)=x(m′)+Δs After the calculation is completed, the position of the next step is set to the current step position, that is, m′=m′+1; wherein v(m′) and v(m′+1) are the train speeds of the m′th step and the m′+1th step, respectively, x(m′) and x(m′+1) are the train positions of the m′th step and the m′+1th step, respectively, t(m′) and t(m′+1) are the train running times of the m′th step and the m′+1th step, respectively, k is an arbitrary real number, R represents a real number, λ1 represents an accompanying variable, and θ(m′) represents the value of the accompanying variable θ of the m′th step; S205: using the operating parameters of the m′th step, determine whether the value of the accompanying variable θ(m′) of this step is 0, if so, proceed to S206, otherwise return to S204; S206: using the operating parameters of the m′th step, determining whether the train coasting terminal position is within the full control step number range, if so, proceeding to S211, otherwise, proceeding to S207; S207: by searching the position with the same speed as the coasting switch point position in the full control data, adjusting the coasting switch point position based on the distance between the two points to obtain a theoretical coasting switch point position; S208: using the theoretical coasting switch point position, determining whether the position is located on a gentle slope, if so, proceeding to S210, otherwise proceeding to S209; S209: Based on the theoretical coasting switch point position, select the nearest other gentle ramp as the current coasting switch point position, and proceed to S203; S210: using a binary search method to search for a gentle slope where the theoretical coasting switching point is located, taking the gentle slope as the current coasting switching point, and proceeding to S204; S211: determining the coasting data and the full control data by calculation based on the coasting switching point position and the full control switching point position; S3: Based on the initialization parameters, starting from step number i=1, the accompanying variables of the i-th step are calculated to determine the train operating conditions of the i+1-th step; wherein the accompanying variables are variables generated when the Hamiltonian function is constructed based on the maximum principle, including the accompanying variables λ1 and the accompanying variables θ; step S3 includes: Based on the optimal constant speed, the accompanying variable λ1 is calculated by the formula: Based on the accompanying variable λ1, the value of each step θ(i) of the accompanying variable θ is calculated: in, Based on the value of the accompanying variable θ(i), determining the next train operating condition; Among them, v c is the optimal constant speed, v(i) is the train speed at the i-th step, x(i) is the train position at the i-th step, μ t is the traction force utilization factor, F t is the unit mass train traction, μ b is the braking force utilization factor, F b is the braking force per unit mass of the train, w0 is the basic resistance per unit mass of the train, and w j is the additional resistance per unit mass of the train, k is an arbitrary real number parameter, and R represents a real number; S4: Based on the train operation data of the i-th step and the train operating condition of the i+1-th step, calculate the train operation data of the i+1-th step, and set i=i+1; S5: using the coasting switching point, judging whether the train meets the coasting switching condition at the i-th step, if so, proceeding to S6, otherwise returning to S3; S6: Based on the train operation data, coasting data and full system data of the i-th step, curve splicing is performed to obtain a complete train operation curve and total operation time; wherein, the step S6 includes: Based on the coasting data and the full control data, acquiring a coasting curve and a full control curve of the train; splicing the train running curve, the coasting curve and the full control curve to the i-th step to obtain a complete train running curve; Based on the complete train operation curve, the running time, coasting time and full control time of the train to the i-th step are obtained, and the total running time is calculated and determined; S7: Determine whether the total running time meets the specified running time of the train. If so, take the complete train running curve as the final train running curve. Otherwise, adjust the optimal constant speed and return to S2.

2. The method for solving the optimal train operation curve based on the maximum principle according to claim 1 is characterized in that: The step S4 comprises: Based on the train operation data of step i, the train operation data of step i+1 is determined by calculation: x(i+1)=x(i)+Δs Where a is the train acceleration, g is the acceleration due to gravity, v(i) and v(i+1) are the train velocities at the i-th and i+1-th steps, x(i) and x(i+1) are the train positions at the i-th and i+1-th steps, t(i) and t(i+1) are the train running times at the i-th and i+1-th steps, μ t is the traction force utilization factor, F t is the unit mass train traction, μ b is the braking force utilization factor, F b is the train braking force per unit mass, μ t 、F t , μ b and F b Based on the train working condition determination in step i+1, w0 is the basic resistance per unit mass of the train, w j is the additional resistance per unit mass of the train, Δs is the discrete step length of the line; After the calculation is completed, the next step is used as the current step number, that is, i=i+1.

3. The method for solving the optimal train operation curve based on the maximum principle according to claim 1 is characterized in that: The step S7 comprises: S71: Determine whether the total running time meets the specified running time of the train. If yes, proceed to S73; otherwise, proceed to S72; S72: Adjust the optimal constant speed v based on the following formula c , the adjusted optimal constant speed v′ c Return to S2: Among them, T t is the total running time, T is the specified running time of the train, v c is the original optimal constant speed; S73: Determine the complete train operation curve as the final train operation curve.

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