Train energy-saving distributed robust optimization method and device

Abstract

The invention relates to a train energy-saving distributed robust optimization method and device. An objective function and corresponding constraint conditions are determined. Segmenting the running interval of the train to obtain at least one sub-interval, converting the target function into an energy function sum used for solving consumed energy corresponding to each sub-interval, and determining a constraint condition corresponding to each energy function; historical data distribution of the corresponding operation interval of the train and a corresponding fuzzy set are determined, wherein the historical data distribution comprises at least one candidate data distribution; and converting the sum of the energy function into a distributed robust optimization function according to the distance of the bulldozer, and converting a corresponding constraint condition. And optimizing based on the fuzzy set to obtain a speed curve corresponding to the expected energy consumption. The train energy-saving optimization problem is converted into the distributed robust optimization problem based on the bulldozer distance, the problem is solved according to the fuzzy set corresponding to historical data distribution, and the speed curve corresponding to expected energy consumption is determined based on unfixed data.

Description

Technical Field

[0001] The present disclosure relates to the field of rail transportation, and in particular to a method and device for distributed robust optimization of train energy conservation. Background Art

[0002] Rail transit systems are playing an increasingly important role in public transportation due to their convenience, efficiency, safety, and high capacity. Consequently, they consume increasing amounts of energy, leading to increasing research interest in reducing their energy consumption. However, these train energy-saving optimization methods assume that the train model parameters are known. In reality, however, due to environmental changes during train operation, issues with train equipment, and errors in identifying train model parameters, train energy-saving optimization results based on the assumption of known train model parameters may result in higher energy consumption in actual operation. Summary of the Invention

[0003] In view of this, the present disclosure proposes a distributed robust optimization method and device for train energy saving, which aims to evaluate residents' information perception in a digital twin space.

[0004] According to a first aspect of the present disclosure, a distributed robust optimization method for train energy saving is provided, the method comprising:

[0005] Determine the objective function used to calculate the energy consumption of the train during the entire operation process, as well as the corresponding constraints;

[0006] Dividing the running section of the train to obtain at least one subsection, wherein the traction force / braking force of the train in each subsection is kept constant;

[0007] Based on the subintervals obtained after segmentation, the objective function is converted into an energy function sum for solving the energy consumption corresponding to each of the subintervals, and a constraint condition corresponding to each of the energy functions is determined;

[0008] Determining a historical data distribution of a running section corresponding to the train, and constructing a fuzzy set based on the historical data distribution, wherein the fuzzy set includes at least one candidate data distribution;

[0009] Converting the energy function into a distributed robust optimization function according to the bulldozer distance and converting the corresponding constraints;

[0010] The distributed robust optimization function is optimized based on the fuzzy set to obtain a speed curve corresponding to the expected energy consumption of the train during the entire operation process.

[0011] In a possible implementation, based on the subintervals obtained after segmentation, converting the objective function into an energy function for solving the sum of energy consumption corresponding to each subinterval, and determining the constraint condition corresponding to each energy function, includes:

[0012] Based on the subintervals obtained after segmentation, the objective function is converted into an energy function sum for solving the energy consumption corresponding to each of the subintervals;

[0013] According to the relationship between the traction / braking work, potential energy, kinetic energy and train resistance energy consumption of the train in each subinterval, the constraint condition corresponding to the energy function of each subinterval is determined.

[0014] In one possible implementation, the constraints corresponding to the energy function of each subinterval include a linear problem term consisting of convex terms and a nonlinear problem term including non-convex terms. Based on the subintervals obtained after segmentation, the objective function is converted into an energy function sum for solving the energy consumption corresponding to each subinterval, and the constraints corresponding to each energy function are determined, further comprising:

[0015] The non-convex terms included in the constraint conditions corresponding to the energy function are converted into convex terms, so as to convert all problems in the constraint conditions into linear problems.

[0016] In one possible implementation, determining the historical data distribution of the train corresponding to the running section and constructing a fuzzy set based on the historical data distribution includes:

[0017] Determining the historical data distribution according to the historical data set corresponding to the running section of the train;

[0018] The historical data distribution center is determined according to the bulldozer distance, and the set consisting of candidate data distribution within the radius with the preset adjustment parameter is used as a fuzzy set.

[0019] In one possible implementation, the distributed robust optimization function is N is the number of subintervals in the running interval, v n is the train speed, σ n and ω n is the convex slack auxiliary variable, is a fuzzy set, is the candidate data distribution, ξ is the candidate data that meets the candidate data distribution, u n (ξ) is the traction force / braking force of the train, E n (ξ) is the energy consumed by the train, and n is the sequence number of the subinterval.

[0020] In one possible implementation, the constraints corresponding to the distributed robust optimization function include:

[0021] E n (ξ)≥η b u n (ξ)l n 、

[0022] u n (ξ)≤P t σ n 、

[0023] u n (ξ)≥P b σ n 、

[0024] l n =s n+1 -s n 、v0=0,v N =0,s0=0,s N =S, n∈{0,1,…,N-1}, ξ∈Ξ, where, η t is the effective conversion rate of energy consumption of the train traction system, l n is the length of the subinterval, η b is the regenerative braking energy recovery efficiency, M is the train mass, is the basic resistance of the train, ξ M g n is the resistance caused by the line slope, tr1 and tr2 are the parameters of the constant torque working range of the maximum traction force, br1 and br2 are the parameters of the constant torque working range of the maximum braking force, P t is the power in the constant power working range of maximum traction, P b is the power in the constant power working range of maximum braking force, is the maximum speed of the train in the current sub-interval, T is the running time of the train in the entire running interval, and Used to express the conditions satisfied by the auxiliary variables of convex relaxation, s n is the starting position of the train in the subinterval n, S is the ending position of the trajectory, and Ξ is the range of candidate data distribution.

[0025] In a possible implementation, the method further includes:

[0026] Based on the infinite optimization problem in the distributed robust optimization problem of bulldozer distance, the distributed robust optimization function and the corresponding constraints are simplified.

[0027] In one possible implementation, the simplified distributed robust optimization function is: Constraints include l n =s n+1 -s n 、v0=0,v N =0,s0=0,s N =S、 and n∈{0,1,…,N-1}, where D is the number of historical data, is the extreme value candidate set including the extreme value points of g(ξ), is the candidate data in the extreme value candidate set and, is the random parameter space of the candidate data distribution, Representative historical data The i-th dimension component of , the superscripts + and - indicate the upper and lower bounds, ε is the preset adjustment parameter that controls the size of the fuzzy set, λ and s j is a variable introduced during the transformation of the distributed robust optimization function.

[0028] According to a second aspect of the present disclosure, a train energy-saving distributed robust optimization device is provided, the device comprising:

[0029] The first function module is used to determine the objective function for calculating the energy consumption of the train during the entire operation process, and the corresponding constraints;

[0030] a track segmentation module, configured to segment the train's operating section into at least one subsection, wherein the train's traction force / braking force in each subsection remains constant;

[0031] A second function determination module is configured to convert the objective function into an energy function sum for solving the energy consumption corresponding to each subinterval based on the subintervals obtained after segmentation, and determine a constraint condition corresponding to each energy function;

[0032] a data determination module, configured to determine a historical data distribution of a running section corresponding to the train, and construct a fuzzy set based on the historical data distribution, wherein the fuzzy set includes at least one candidate data distribution;

[0033] a third function determination module, configured to convert the energy function into a distributed robust optimization function according to the bulldozer distance, and convert corresponding constraints;

[0034] A function optimization module is used to optimize the distributed robust optimization function based on the fuzzy set to obtain a speed curve corresponding to the expected energy consumption of the train during the entire operation process.

[0035] In a possible implementation, the second function determination module is further configured to:

[0036] Based on the subintervals obtained after segmentation, the objective function is converted into an energy function sum for solving the energy consumption corresponding to each of the subintervals;

[0037] According to the relationship between the traction / braking work, potential energy, kinetic energy and train resistance energy consumption of the train in each subinterval, the constraint condition corresponding to the energy function of each subinterval is determined.

[0038] In a possible implementation, the constraint corresponding to the energy function of each subinterval includes a linear problem term consisting of convex terms and a nonlinear problem term including non-convex terms, and the second function determination module is further configured to:

[0039] The non-convex terms included in the constraint conditions corresponding to the energy function are converted into convex terms, so as to convert all problems in the constraint conditions into linear problems.

[0040] In a possible implementation, the data determination module is further configured to:

[0041] Determining the historical data distribution according to the historical data set corresponding to the running section of the train;

[0042] The historical data distribution center is determined according to the bulldozer distance, and the set consisting of candidate data distribution within the radius with the preset adjustment parameter is used as a fuzzy set.

[0043] In one possible implementation, the distributed robust optimization function is N is the number of subintervals in the running interval, v n is the train speed, σ n and ω n is the convex slack auxiliary variable, is a fuzzy set, is the candidate data distribution, ξ is the candidate data that meets the candidate data distribution, u n (ξ) is the traction force / braking force of the train, E n (ξ) is the energy consumed by the train, and n is the sequence number of the subinterval.

[0044] In one possible implementation, the constraints corresponding to the distributed robust optimization function include:

[0045] E n (ξ)≥η b u n (ξ)l n 、

[0046] u n (ξ)≤P t σ n 、

[0047] u n (ξ)≥P b σ n 、

[0048] l n =s n+1 -s n 、v0=0,v N =0,s0=0,s N =S, n∈{0,1,…,N-1}, ξ∈Ξ, where, η t is the effective conversion rate of energy consumption of the train traction system, l n is the length of the subinterval, η b is the regenerative braking energy recovery efficiency, M is the train mass, is the basic resistance of the train, ξ M g n is the resistance caused by the line slope, tr1 and tr2 are the parameters of the constant torque working range of the maximum traction force, br1 and br2 are the parameters of the constant torque working range of the maximum braking force, P t is the power in the constant power working range of maximum traction, P b is the power in the constant power working range of maximum braking force, is the maximum speed of the train in the current sub-interval, T is the running time of the train in the entire running interval, and Used to express the conditions satisfied by the auxiliary variables of convex relaxation, s n is the starting position of the train in the subinterval n, S is the ending position of the trajectory, and Ξ is the range of candidate data distribution.

[0049] In a possible implementation, the apparatus further includes:

[0050] The problem simplification module is used for the infinite optimization problem in the distributed robust optimization problem based on the bulldozer distance, and simplifies the distributed robust optimization function and the corresponding constraint conditions.

[0051] In one possible implementation, the simplified distributed robust optimization function is: Constraints include

[0052] l n =s n+1 -s n 、v0=0,v N =0,s0=0,s N =S、 and n∈{0,1,…,N-1}, where D is the number of historical data, is the extreme value candidate set including the extreme value points of g(ξ), is the candidate data in the extreme value candidate set and, is the random parameter space of the candidate data distribution, Representative historical data The i-th dimension component of , the superscripts + and - indicate the upper and lower bounds, ε is the preset adjustment parameter that controls the size of the fuzzy set, λ and s j is a variable introduced during the transformation of the distributed robust optimization function.

[0053] According to a third aspect of the present disclosure, an electronic device is provided, comprising: a processor; and a memory for storing processor-executable instructions; wherein the processor is configured to implement the above method when executing the instructions stored in the memory.

[0054] According to a fourth aspect of the present disclosure, a non-volatile computer-readable storage medium is provided, on which computer program instructions are stored, wherein the computer program instructions implement the above method when executed by a processor.

[0055] According to a fifth aspect of the present disclosure, a computer program product is provided, comprising a computer-readable code, or a non-volatile computer-readable storage medium carrying the computer-readable code. When the computer-readable code runs in a processor of an electronic device, the processor in the electronic device executes the above method.

[0056] In an embodiment of the present disclosure, an objective function and corresponding constraints are determined. The train's operating interval is divided into at least one sub-interval, and the objective function is converted into an energy function sum for solving the energy consumption corresponding to each sub-interval, and the constraints corresponding to each energy function are determined. The historical data distribution of the train's corresponding operating interval and the corresponding fuzzy set are determined, which includes at least one candidate data distribution. According to the bulldozer distance, the energy function sum is converted into a distributed robust optimization function and the corresponding constraints are converted. The speed curve corresponding to the expected energy consumption is obtained by optimization based on the fuzzy set. The present disclosure converts the train energy-saving optimization problem into a distributed robust optimization problem based on the bulldozer distance, and solves the problem based on the fuzzy set corresponding to the historical data distribution, so as to realize the determination of the speed curve corresponding to the expected energy consumption based on non-fixed data.

[0057] Further features and aspects of the present disclosure will become apparent from the following detailed description of exemplary embodiments with reference to the attached drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate exemplary embodiments, features, and aspects of the disclosure and, together with the description, serve to explain the principles of the disclosure.

[0059] Figure 1 A flow chart of a distributed robust optimization method for train energy saving according to an embodiment of the present disclosure is shown;

[0060] Figure 2 A schematic diagram illustrating a train traction feature according to an embodiment of the present disclosure;

[0061] Figure 3 A schematic diagram illustrating a method for dividing a train running section according to an embodiment of the present disclosure is shown;

[0062] Figure 4 A schematic diagram showing a speed curve corresponding to expected energy consumption according to an embodiment of the present disclosure;

[0063] Figure 5 A schematic diagram showing a train energy-saving distributed robust optimization device according to an embodiment of the present disclosure is shown;

[0064] Figure 6 A schematic diagram illustrating an electronic device according to an embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0065] Various exemplary embodiments, features, and aspects of the present disclosure will be described in detail below with reference to the accompanying drawings. The same reference numerals in the accompanying drawings represent elements with the same or similar functions. Although various aspects of the embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless otherwise indicated.

[0066] The word “exemplary” is used exclusively herein to mean “serving as an example, example, or illustration.” Any embodiment described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments.

[0067] In addition, numerous specific details are provided in the following detailed description to better illustrate the present disclosure. Those skilled in the art will appreciate that the present disclosure can be practiced without certain specific details. In some instances, methods, means, components, and circuits well known to those skilled in the art are not described in detail in order to highlight the main points of the present disclosure.

[0068] The distributed robust optimization method for train energy conservation of the embodiment of the present disclosure can be executed by an electronic device such as a terminal device or a server. The terminal device can be any fixed or mobile terminal such as a user equipment (UE), a mobile device, a user terminal, a terminal, a cellular phone, a cordless phone, a personal digital assistant (PDA), a handheld device, a computing device, a vehicle-mounted device, a wearable device, etc. The server can be a single server or a server cluster composed of multiple servers. Any electronic device can implement the distributed robust optimization method for train energy conservation of the embodiment of the present disclosure by calling computer-readable instructions stored in a memory through a processor.

[0069] Figure 1 FIG. 1 is a flow chart showing a method for distributed robust optimization of train energy saving according to an embodiment of the present disclosure. Figure 1 As shown, the train energy-saving distributed robust optimization method of the embodiment of the present disclosure may include the following steps S10-S60.

[0070] Step S10: Determine the objective function for calculating the energy consumed during the entire operation of the train and the corresponding constraints.

[0071] In a possible implementation, when the energy consumption of a train needs to be calculated, the embodiment of the present disclosure can be implemented by using a single particle model. To represent the train, where s is the train position, v is the train speed, t is the time, and M is the train mass. u(s) is the traction or braking force of the train. A+Bv+Cv 2 The basic resistance of the train, A, B, C are the basic resistance coefficients of the train. Mg(s) is the resistance caused by the slope of the running line, and g(s) is a piecewise constant function that describes the acceleration component of the train caused by the slope as the train position s changes. The starting and ending states of the train are x0 = [0, 0] T ,x f =[0,S] T, S is the total length of the line, and the train operation must meet the given running time constraint T, that is,

[0072] The embodiment of the present disclosure determines the objective function for solving the distribution of energy consumption during train operation. When analyzing the energy consumption during train operation, the fixed energy consumption of auxiliary equipment such as air conditioning and ventilation can be ignored, and only the traction energy consumption and regenerative braking energy feedback related to the train driving strategy are considered. The objective function for solving the distribution of energy consumption during train operation is determined as follows: The first of these Used to characterize the train traction energy consumption, the second Used to characterize the energy of train regenerative braking feedback, η t is the effective conversion rate of energy consumption of the train traction system, η b is the regenerative braking energy recovery rate.

[0073] Furthermore, the energy-saving optimization problem of the train operation curve can be described as an optimal control problem based on the single-point model of the train and the objective function. The optimal control problem includes the objective function and the corresponding constraints:

[0074]

[0075] in, Right now is the objective function, and the remaining items are the constraints corresponding to the objective function. The first item is the single-particle model, the second item is the constraint on the train's traction or braking force, and the third constraint is the speed limit on the train's running speed. T is the running time, and s is the running position.

[0076] Figure 2 A schematic diagram showing a train traction feature according to an embodiment of the present disclosure is shown. Figure 2 As shown in the figure, the working range of the train traction system can be divided into two types: constant torque working range and constant power working range. In the constant torque working range, the train speed is in a relatively low range, and the traction torque output by the train traction system is continuously maintained at a fixed value or is linearly related to the train speed; in the constant power working range, the train speed is in a relatively high range, and the traction power output by the train traction system remains constant. Since the train braking system only uses air braking or a mixture of air braking and electric braking when the speed is relatively low, and electric braking is used at other times, the electric braking characteristics can be used to represent the characteristics of the entire braking system of the train. Like the train traction characteristics, the working range of the train braking system using electric braking can also be divided into two types: constant torque working range and constant power working range. Therefore, the second train traction or braking force constraint g(u)≤0 can be expressed as -min{br1+br2v,Pb / v}≤u≤min{tr1+tr2v,P t / v}, tr1 and tr2 are the parameters of the constant torque working range of maximum traction force, br1 and br2 are the parameters of the constant torque working range of maximum braking force, P t is the power in the constant power working range of maximum traction, P b is the power in the constant power working range of maximum braking force, and u is the traction or braking force of the train.

[0077] Step S20: Divide the train's operating section into at least one subsection.

[0078] In one possible implementation, in order to further improve the accuracy of the calculation results and improve the calculation efficiency, the train operation range can be divided into at least one sub-range, so as to further transform the optimal control problem described by the objective function and the corresponding constraints into a nonlinear programming problem. In each sub-range, the train traction or braking force remains constant. That is, when s∈[s n ,s n+1 ],u n is a fixed value, n∈0,1,…,N-1. n ,s n+1 It is the starting and ending point of the n+1th sub-interval.

[0079] Figure 3 A schematic diagram of dividing a train running section according to an embodiment of the present disclosure is shown. Figure 3 As shown, the embodiment of the present disclosure can divide the entire running interval [0, S] of the train according to the speed limit interval and the line gradient interval to obtain N sub-intervals. For example, based on relevant technologies, the intervals with different speed limits or different line gradients can be divided, and l = [l0, l1, ..., l N-1 ] to indicate the length of a subinterval, where Then the above-mentioned train energy-saving optimization control problem can be expressed as a multi-stage optimal control problem.

[0080] Step S30: Based on the subintervals obtained after segmentation, the objective function is converted into an energy function sum for solving the energy consumption corresponding to each subinterval, and the constraint condition corresponding to each energy function is determined.

[0081] In one possible implementation, after determining the segmented subintervals, the disclosed embodiment can, based on the constant traction / braking force characteristics within the subintervals, convert the objective function into an energy function sum for solving the corresponding energy consumption for each subinterval, and determine the constraints corresponding to each energy function. Specifically, based on the segmented subintervals, the objective function can be converted into an energy function sum for solving the corresponding energy consumption for each subinterval. The constraints corresponding to the energy function for each subinterval are then determined based on the relationship between the train's traction / braking force work, potential energy, kinetic energy, and train resistance energy consumption within each subinterval.

[0082] Optionally, based on the law of conservation of energy, within each sub-interval, the relationship between the work done by the traction or braking force, potential energy, kinetic energy, and train resistance energy consumption satisfies n represents the sequence number of the sub-interval. n l n is the gravity component resistance due to the line slope in the sub-interval. The average speed in each sub-interval is The integral term in the objective function can be expressed using The running time of the train in each sub-interval can be approximated using To approximate.

[0083] Based on the energy function E obtained after the above conversion n , and the corresponding constraints consisting of nonlinear programming problems can be expressed as:

[0084]

[0085] The constraints corresponding to the energy function of the subinterval include linear problem items composed of convex items and nonlinear problem items including nonconvex items. The embodiment of the present disclosure can convert all the problems in the constraints into linear problems by converting the nonconvex items included in the constraints corresponding to the energy function into convex items. and The originally non-convex nonlinear programming problem can be relaxed into a convex optimization problem by introducing convex relaxation auxiliary variables. Convex optimization is a fairly mature discipline with many fast and efficient solution methods to solve convex optimization problems. For the convex optimization problem obtained by convex relaxation, a ready-made solution method or solver can be used for rapid solution. In the embodiment of the present disclosure, the constraints corresponding to the energy function of each subinterval include linear problem items composed of convex items and nonlinear problem items including non-convex items. By converting the non-convex items included in the constraints corresponding to the energy function into convex items, all problems in the constraints can be converted into linear problems.

[0086] Specifically, the non-convex term conversion process can be achieved by introducing a convex relaxation auxiliary variable σ n and ω n Achieve. That is, it needs to be satisfied and To replace the non-convex terms in the above nonlinear programming problem and The problem is relaxed and transformed into a convex optimization problem. The conditions that the convex relaxation auxiliary variables introduced satisfy are: and is convex and is a rotated second-order cone. Using the rotated second-order cone form to express the conditions satisfied by the auxiliary variables of the convex relaxation, it can be expressed as and in Represents a rotated second-order cone 2xy≥z 2 ,x,y≥0. Since nonlinear programming problems use σ n and ω n replace and After that, except for the condition that the auxiliary variable of the convex relaxation itself satisfies the rotation of the second-order cone, the rest are linear. Then the problem after the convex relaxation of the nonlinear programming problem is a second-order cone programming problem:

[0087]

[0088] Among them, the newly added constraints Auxiliary variable ω used to make the relaxation convex n The speed limit requirement is also met.

[0089] Step S40: Determine the historical data distribution of the train's corresponding operating section, and construct a fuzzy set based on the historical data distribution.

[0090] In one possible implementation, the disclosed embodiment can obtain historical data from a train's operation within a specific operating range, and then determine a historical data distribution based on the multiple historical data. A fuzzy set can be further constructed based on the historical data distribution, where the fuzzy set includes at least one candidate data distribution. Specifically, the electronic device can first determine the historical data distribution based on the historical data set corresponding to the train's operating range, then determine the center of the historical data distribution based on the bulldozer distance. The set of candidate data distributions within a radius with a preset adjustment parameter as the fuzzy set is then defined. Optionally, the historical data can include the train's mass and the train's basic drag coefficient.

[0091] For example, the train history data includes ξ1, ξ2, ..., ξ D , where D is the number of historical data, we can use these historical data to construct the historical data distribution Furthermore, using the constructed empirical distribution, we can combine the bulldozer distance (Wasserstein distance) to construct the fuzzy set of train parameter distribution Where ε is the adjustment parameter that controls the size of the fuzzy set.

[0092] Step S50: convert the energy function into a distributed robust optimization function according to the bulldozer distance, and convert the corresponding constraint conditions.

[0093] In one possible implementation, the stochastic optimization problem of energy conservation within a train's operating range often assumes that the distribution of the train's random parameters is known. However, in reality, information about the train's random parameters is readily available, but the true distribution of the random parameters is difficult to obtain. When the distribution information used is inconsistent with the train's random parameter distribution information, the results obtained by stochastic optimization are often poor. When the train parameter distribution is unknown, robust optimization can ensure that the train's energy consumption is minimized under the worst-case scenario of different parameter distributions. Although robust optimization can produce robust results for parameter distribution, this result considers the worst-case scenario within the parameter distribution space and fails to effectively utilize the available information about the distribution. Such results are often overly conservative and undesirable. Distributed robust optimization methods lie between stochastic optimization and robust optimization. When the random parameter distribution is unknown, they do not require the true distribution of the random parameters as stochastic optimization does, while effectively utilizing the available information about the distribution, making the results less conservative than robust optimization.

[0094] Since the distributed robust optimization method based on bulldozer distance (Wasserstein distance) has unique advantages over other distributed robust optimization methods, the embodiment of the present disclosure can use this distributed robust optimization method to deal with the energy-saving optimization problem of train operation curve under the condition of random parameter positions of trains. Wasserstein distance is a method for measuring the difference between two probability distributions. This method can effectively measure the difference between two probability distributions. When the two probability distributions are the same, the Wasserstein distance is 0. When the difference between the two probability distributions is greater, the Wasserstein distance is greater. Probability distribution and The Wasserstein distance between where Ξ is the distribution interval of the random variables ξ1 and ξ2, Π is the joint distribution of the random variables ξ1 and ξ2, and the marginal probabilities with respect to the random variables ξ1 and ξ2 are exactly and

[0095] Based on the bulldozer distance, the embodiment of the present disclosure can convert the energy function and into a distributed robust optimization function, and convert the corresponding constraints to convert the second-order cone programming problem into a distributed robust optimization problem based on the bulldozer distance:

[0096]

[0097] Among them, the distributed robust optimization function is N is the number of subintervals in the running interval, v n is the train speed, σ n and ω n is the convex slack auxiliary variable, is a fuzzy set, is the candidate data distribution, ξ is the candidate data that meets the candidate data distribution, u n (ξ) is the traction force / braking force of the train, E n (ξ) is the energy consumed by the train. The constraints corresponding to the distributed robust optimization function include: E n (ξ)≥η b u n (ξ)l n 、 u n (ξ)≤P t σ n 、 u n (ξ)≥P b σ n 、

[0098] l n =s n+1 -s n 、v0=0,v N =0,s0=0,s N =S, n∈{0,1,…,N-1}, ξ∈Ξ, η t is the effective conversion rate of energy consumption of the train traction system, l n is the length of the subinterval, η b is the regenerative braking energy recovery efficiency, M is the train mass,

[0099] is the basic resistance of the train, ξ M g n is the resistance caused by the line slope, tr1 and tr2 are the parameters of the constant torque working range of the maximum traction force, br1 and br2 are the parameters of the constant torque working range of the maximum braking force, P t is the power in the constant power working range of maximum traction, Pb is the power in the constant power working range of maximum braking force, is the maximum speed of the train in the current sub-interval, T is the running time of the train in the entire running interval, and Used to express the conditions satisfied by the auxiliary variables of convex relaxation, s n is the starting position of the train in the subinterval, S is the ending position of the trajectory, and Ξ is the range of candidate data distribution.

[0100] Alternatively, since the spatial distribution of candidate data Ξ of the train has upper and lower bounds, we can use ξ - and ξ + Indicates that Ξ=[ξ - ,ξ + ]. The fourth to seventh constraints in the above distributed robust optimization problem need to be satisfied in the entire distribution space of candidate data. In fact, they only need to be satisfied at the boundary of the distribution space. Then, under the condition that the train candidate data is random, the constraints on the traction or braking force of the train in the distributed robust optimization problem can be simplified as follows:

[0101]

[0102] Furthermore, due to the optimization of the target inner layer There are expectations and extreme values ​​to be sought, so the problem cannot be effectively solved using the existing second-order cone programming solution algorithm. The embodiment of the present disclosure can also change and simplify the problem, that is, the electronic device can simplify the distributed robust optimization function and the corresponding constraints based on the infinite optimization problem in the distributed robust optimization problem of the bulldozer distance.

[0103] Among them, the inner optimization objective of the distributed robust optimization problem is:

[0104]

[0105] This problem involves finding the extreme value and the expectation of infinite-dimensional integral, so it cannot be effectively solved using the existing second-order cone programming algorithm. The inner optimization problem is further simplified. v,σ,ω (ξ) is:

[0106]

[0107] Then the inner optimization problem can be rewritten as Infinite optimization problem of inner layer in distributed robust optimization problem based on bulldozer distance when When it is convex and lower semicontinuous, it can be simplified to a finite convex optimization problem:

[0108]

[0109] Based on the above simplification method, the embodiment of the present disclosure can further simplify the above inner layer optimization problem as follows:

[0110]

[0111] Simplified constraints It is a problem of finding the extreme value, which is still difficult to solve. Next, we can further simplify the problem of finding the extreme value. Among them, V v,σ,ω (ξ) can be written in dual form:

[0112]

[0113] From V v,σ,ω It can be seen from the dual form of (ξ) that when y n >0, When y n <0, When y n = 0, This is consistent with the actual situation: when y n When ≥0, the train is in the traction work state, then the energy consumed by the train is y n / η t , when y n <0, the train is in braking state, then the energy consumed by the train is y n η b , which is in the energy feedback state. v,σ,ω (ξ) dual form is introduced into g(V v,σ,ω (ξ)), we can get the expression for finding the extreme value constraint condition:

[0114]

[0115]

[0116]

[0117] The dimension of the spatial distribution Ξ of train candidate data is m, and the upper and lower bounds of each dimension of candidate data are a i and b i , then the candidate data space Ξ can be represented by a hypercube To express. Since V v,σ,ω (ξ) is a convex function of ξ, and we can determine The extreme point ξ * The i-th dimension It must be One of Represents historical train data The i-th dimension component of . Define the extreme point candidate set Obviously, the extreme point of g(ξ) Therefore, the extreme value constraint can be written as:

[0118]

[0119] From this, we can see that the constraint of finding the extreme value in the continuous space has been transformed into a finite number of convex constraints, which is very easy to solve. The corresponding content optimization objective of the energy-saving distributed robust optimization problem of the train operation curve can be expressed as the formula:

[0120]

[0121] It has been simplified into a convex optimization problem with a finite number of convex constraints, which can be solved stably and quickly.

[0122] In summary, the energy-saving distributed robust optimization problem of the train operation curve based on the bulldozer distance can be simplified into a second-order cone programming problem with a finite number of convex constraints:

[0123]

[0124] That is, the simplified distributed robust optimization function is Constraints include

[0125] u n (ξ + )≤P t σ n 、 u n (ξ - )≥P b σ n 、 l n =s n+1 -s n 、v0=0,v N =0,s0=0,s N =S、 and n∈{0,1,…,N-1}, where D is the number of historical data, is the extreme value candidate set including the extreme value points of g(ξ), is the random parameter space of the candidate data distribution, Representative historical data The i-th dimension component of , the superscripts + and - indicate the upper and lower bounds, ε is the preset adjustment parameter that controls the size of the fuzzy set, λ and s j It is a variable introduced in the convex optimization method, that is, a variable introduced in the conversion process of the distributed robust optimization function. It should be noted that the computational complexity of the energy-saving distributed robust optimization problem of train operation curve based on second-order cone programming is related to the number of constraints in the model, and the number of the first to fourth constraints mainly depends on the extreme value candidate set. Size and number of historical sample data D. And the extreme value candidate set The relationship between the size of and the dimension m of the train candidate data is Here, |·| represents the cardinality of the set, that is, the number of elements in the set. Here, we consider the train random parameter dimension to be 3, and the extreme value candidate set The computational complexity of the distributed robust optimization problem is mainly affected by the number of historical sample data. If the dimension of the candidate data is large, the number of constraints from the first to the fourth in the distributed robust optimization problem will increase dramatically, and the computational complexity will also increase sharply.

[0126] Step S60: Optimize the distributed robust optimization function based on the fuzzy set to obtain a speed curve corresponding to the expected energy consumption of the train during the entire operation process.

[0127] That is, the distributed robust optimization function is optimized with fuzzy sets as constraints, and the optimization goal is to minimize the expected energy consumption.

[0128] In one possible implementation, the embodiment of the present disclosure can optimize the distributed robust optimization problem consisting of the distributed robust optimization function and its corresponding constraints based on fuzzy sets to obtain the speed curve operating range corresponding to the expected energy consumption of the train during the entire operation process.

[0129] Furthermore, for a train schedule including multiple train running sections, the embodiment of the present disclosure can also solve the train schedule energy saving problem through the above-mentioned distributed robust optimization method. It can also be assumed that during a train operation on the line, the basic resistance coefficients A, B and C of the train are constant between different stations, and the train masses between different stations are independent of each other. The train candidate data can be expressed as The historical data corresponding to the train candidate data is Where D is the number of historical data. Then the energy-saving distributed robust optimization problem of train schedule based on Wassersetein distance can be described as follows:

[0130]

[0131] Since the candidate data in the above train timetable energy-saving distributed robust optimization problem The dimension of is very high. Therefore, if we directly apply the above single train distributed robust optimization problem to the train schedule energy-saving distributed robust optimization problem, then the corresponding extreme value candidate set The size of will be very large, and the number of constraints will also be very large, resulting in high computational complexity and difficulty in solving. However, during a train's operation on the line, the basic resistance parameter ξ A ,ξ B and ξ C remains unchanged, while They are independent of each other, so the energy-saving distributed robust optimization problem of train timetable can be decomposed.

[0132] Since the train mass distributions between stations are independent of each other, the inner problem of the energy-saving distributed robust optimization problem of train schedule based on Wasserstein distance can be divided into K independent sub-problems:

[0133]

[0134] For each independent subproblem We can apply the distributed robust optimization problem of a single train, and the candidate data dimensions corresponding to the subproblem are only four dimensions (A, B, C and M k ), the corresponding sub-problem extreme value candidate set Since the random variables A, B and C are common in each subproblem, the candidate set of subproblems is Can be split into and The superscripts - and + represent the lower and upper bounds of the corresponding random variables, respectively. After splitting into K subproblems and transforming the extreme value candidate set By reducing and splitting, the energy-saving distributed robust optimization problem of train schedule based on Wasserstein distance can be simplified to a second-order cone programming problem containing only a finite number of convex constraints:

[0135]

[0136] For the above-mentioned distributed robust optimization method for a single train and the distributed robust optimization method for a train timetable, the disclosed implementation is verified through two groups of experiments. Among them, in the first group of simulation experiments to verify the energy-saving distributed robust optimization of train operation curves based on Wasserstein distance (SEETC-DR), we will compare the energy-saving robust optimization method for train operation curves (SEETC-RO) and the energy-saving random optimization method for train operation curves based on the average sample approximation method (SEETC-SAA). Among them, we use the robust optimization method as the benchmark for the reorganization experiment. Since the results of the distributed robust optimization method based on Wasserstein distance and the random optimization method based on average sample approximation are directly related to the number of samples D in the historical data set of train model parameters, the results of the distributed robust optimization method and the random method based on average sample approximation are verified multiple times under different data sample sizes D. The expected energy consumption results obtained by different optimization results are shown in the following table.

[0137]

[0138] Based on the results in the above table, it can be seen that the energy-saving distributed robust optimization method for train operation curves based on Wasserstein distance in the embodiment of the present disclosure and the random optimization method based on average sample approximation have both improved energy saving compared to the robust optimization method, and the energy-saving improvement effect will also increase with the increase of the data volume D in the historical data. In fact, as the historical data increases, the method using average sample approximation will continue to approach the real train model parameter distribution, and the optimization results will also approach the random optimization results under the known real distribution. Similarly, the results of the energy-saving distributed robust optimization method for train operation curves based on Wasserstein distance in the embodiment of the present disclosure will also approach the random optimization results under the real distribution. But at the same time, when the historical data D is relatively small, the expected energy consumption obtained by the distributed robust optimization method based on Wasserstein distance will be better than the results of the random optimization method based on average sample approximation.

[0139] Figure 4 FIG. 1 is a schematic diagram showing a speed curve corresponding to an expected energy consumption according to an embodiment of the present disclosure. Figure 4 As shown, the energy-saving distributed robust optimization method for train operation curve based on Wasserstein distance in the embodiment of the present disclosure can cover the robust optimization method and the random optimization method of average sample approximation, that is, the robust optimization method and the average sample approximation method are just special cases of the distributed robust optimization method of Wasserstein distance in the present disclosure. The results of the distributed robust optimization method based on Wasserstein distance and the adjustment of fuzzy distribution set in the method The expected energy consumption versus speed curve obtained by the Wasserstein distance-based distributed robust optimization method for train operation curve energy conservation proposed in the present disclosure under different Wasserstein distance parameters ε and different data samples D is as follows: when ε = 0, the result of the random optimization method is approximated by the average sample. As ε increases beyond a certain value, the expected result increases rapidly, and then the result becomes the same as the robust optimization result.

[0140] In the second set of experiments, the performance of the Wasserstein distance-based distributed robust optimization method for train timetables (MSEETC-DR) and other timetable optimization methods were compared across the entire line. Similar to the results of the first set of experiments, the expected energy consumption comparison results obtained by different train timetable optimization methods also show that the Wasserstein distance-based energy-saving distributed robust optimization method for train timetables proposed in the present embodiment can save the most energy. Similarly, the average sample approximate random optimization method and robust optimization are both special cases of the Wasserstein distance-based energy-saving distributed robust optimization method for trains in the present embodiment.

[0141] Based on the above technical features, this paper proposes a distributed robust optimization method for train energy conservation based on the Wasserstein distance. This method can transform the train energy conservation optimization problem or train schedule optimization into a distributed robust optimization problem based on the bulldozer distance. Using the duality principle, the previously difficult infinite-dimensional second-order cone programming problem is simplified to a second-order cone programming problem with a finite number of constraints. Compared to train energy conservation optimization methods that use fixed model parameters, this method solves the problem based on fuzzy sets corresponding to historical data distributions, enabling the determination of the speed curve corresponding to the expected energy consumption based on non-fixed data.

[0142] Figure 5 A schematic diagram of a distributed robust optimization device for train energy saving according to an embodiment of the present disclosure is shown. Figure 5 As shown, the train energy-saving distributed robust optimization device of the embodiment of the present disclosure may include:

[0143] A first function module 50 is used to determine an objective function for calculating the energy consumed during the entire operation of the train, and corresponding constraints;

[0144] a track segmentation module 51 for segmenting the train's operating section into at least one subsection, wherein the train's traction force / braking force in each subsection remains constant;

[0145] A second function determination module 52 is configured to convert the objective function into an energy function sum for solving the energy consumption corresponding to each subinterval based on the subintervals obtained after segmentation, and determine a constraint condition corresponding to each energy function;

[0146] a data determination module 53 for determining a historical data distribution of the train corresponding to the running section, and constructing a fuzzy set based on the historical data distribution, wherein the fuzzy set includes at least one candidate data distribution;

[0147] a third function determination module, configured to convert the energy function into a distributed robust optimization function according to the bulldozer distance, and convert corresponding constraints;

[0148] The function optimization module 54 is configured to optimize the distributed robust optimization function based on the fuzzy set to obtain a speed curve corresponding to the expected energy consumption of the train during the entire operation process.

[0149] In a possible implementation, the second function determination module 52 is further configured to:

[0150] Based on the subintervals obtained after segmentation, the objective function is converted into an energy function sum for solving the energy consumption corresponding to each of the subintervals;

[0151] According to the relationship between the traction / braking work, potential energy, kinetic energy and train resistance energy consumption of the train in each subinterval, the constraint condition corresponding to the energy function of each subinterval is determined.

[0152] In a possible implementation, the constraint corresponding to the energy function of each subinterval includes a linear problem term consisting of convex terms and a nonlinear problem term including non-convex terms, and the second function determination module 52 is further configured to:

[0153] The non-convex terms included in the constraint conditions corresponding to the energy function are converted into convex terms, so as to convert all problems in the constraint conditions into linear problems.

[0154] In a possible implementation, the data determination module 53 is further configured to:

[0155] Determining the historical data distribution according to the historical data set corresponding to the running section of the train;

[0156] The historical data distribution center is determined according to the bulldozer distance, and the set consisting of candidate data distribution within the radius with the preset adjustment parameter is used as a fuzzy set.

[0157] In one possible implementation, the distributed robust optimization function is N is the number of subintervals in the running interval, v n is the train speed, σ n and ω n is the convex slack auxiliary variable, is a fuzzy set, is the candidate data distribution, ξ is the candidate data that meets the candidate data distribution, u n (ξ) is the traction force / braking force of the train, E n (ξ) is the energy consumed by the train, and n is the sequence number of the subinterval.

[0158] In one possible implementation, the constraints corresponding to the distributed robust optimization function include: E n (ξ)≥η b u n (ξ)l n 、 u n (ξ)≤P t σ n 、 u n (ξ)≥P b σ n 、 l n =s n+1 -s n 、v0=0,v N =0,s0=0,s N =S, n∈{0,1,…,N-1}, ξ∈Ξ, where, η t is the effective conversion rate of energy consumption of the train traction system, l n is the length of the subinterval, η b is the regenerative braking energy recovery efficiency, M is the train mass, is the basic resistance of the train, ξ M g n is the resistance caused by the line slope, tr1 and tr2 are the parameters of the constant torque working range of the maximum traction force, br1 and br2 are the parameters of the constant torque working range of the maximum braking force, P t is the power in the constant power working range of maximum traction, P b is the power in the constant power working range of maximum braking force, is the maximum speed of the train in the current sub-interval, T is the running time of the train in the entire running interval, and Used to express the conditions satisfied by the auxiliary variables of convex relaxation, s nis the starting position of the train in the subinterval n, S is the ending position of the trajectory, and Ξ is the range of candidate data distribution.

[0159] In a possible implementation, the apparatus further includes:

[0160] The problem simplification module is used for the infinite optimization problem in the distributed robust optimization problem based on the bulldozer distance, and simplifies the distributed robust optimization function and the corresponding constraint conditions.

[0161] In one possible implementation, the simplified distributed robust optimization function is: Constraints include u n (ξ + )≤P t σ n 、 u n (ξ - )≥P b σ n 、 l n =s n+1 -s n 、v0=0,v N =0,s0=0,s N =S、 and n∈{0,1,…,N-1}, where D is the number of historical data, is the extreme value candidate set including the extreme value points of g(ξ), is the candidate data in the extreme value candidate set and, is the random parameter space of the candidate data distribution, Representative historical data The i-th dimension component of , the superscripts + and - indicate the upper and lower bounds, ε is the preset adjustment parameter that controls the size of the fuzzy set, λ and s j is a variable introduced during the transformation of the distributed robust optimization function.

[0162] In some embodiments, the functions or modules included in the device provided by the embodiments of the present disclosure can be used to execute the method described in the above method embodiments. The specific implementation can refer to the description of the above method embodiments. For the sake of brevity, it will not be repeated here.

[0163] The present disclosure also provides a computer-readable storage medium having computer program instructions stored thereon, wherein the computer program instructions implement the above method when executed by a processor. The computer-readable storage medium may be a volatile or non-volatile computer-readable storage medium.

[0164] An embodiment of the present disclosure further proposes an electronic device, comprising: a processor; and a memory for storing instructions executable by the processor; wherein the processor is configured to implement the above method when executing the instructions stored in the memory.

[0165] An embodiment of the present disclosure also provides a computer program product, including computer-readable code, or a non-volatile computer-readable storage medium carrying computer-readable code. When the computer-readable code runs in a processor of an electronic device, the processor in the electronic device executes the above method.

[0166] Figure 6 1 shows a schematic diagram of an electronic device 1900 according to an embodiment of the present disclosure. For example, the electronic device 1900 can be provided as a server or a terminal device. Figure 6 The electronic device 1900 includes a processing component 1922, which further includes one or more processors, and a memory resource represented by a memory 1932 for storing instructions executable by the processing component 1922, such as an application. The application stored in the memory 1932 may include one or more modules, each corresponding to a set of instructions. In addition, the processing component 1922 is configured to execute the instructions to perform the above-described method.

[0167] The electronic device 1900 may further include a power supply component 1926 configured to perform power management of the electronic device 1900, a wired or wireless network interface 1950 configured to connect the electronic device 1900 to a network, and an input / output interface 1958 (I / O interface). The electronic device 1900 may operate based on an operating system stored in the memory 1932, such as Windows Server 2003. TM , Mac OS X TM , Unix TM ,Linux TM , FreeBSD TM or similar.

[0168] In an exemplary embodiment, a non-volatile computer-readable storage medium is also provided, such as a memory 1932 including computer program instructions that can be executed by the processing component 1922 of the electronic device 1900 to perform the above method.

[0169] The present disclosure may be a system, method and / or computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for causing a processor to implement various aspects of the present disclosure.

[0170] A computer-readable storage medium can be a tangible device that can hold and store instructions for use by an instruction execution device. A computer-readable storage medium can be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanical encoding device, such as a punch card or a raised structure in a groove on which instructions are stored, and any suitable combination thereof. As used herein, a computer-readable storage medium is not to be construed as a transient signal per se, such as a radio wave or other freely propagating electromagnetic wave, an electromagnetic wave propagating through a waveguide or other transmission medium (e.g., a light pulse through a fiber optic cable), or an electrical signal transmitted through an electrical wire.

[0171] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to each computing / processing device, or downloaded to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network, and / or a wireless network. The network can include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. The network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards the computer-readable program instructions to be stored in the computer-readable storage medium in each computing / processing device.

[0172] The computer program instructions for performing the operations of the present disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, and conventional procedural programming languages ​​such as "C" language or similar programming languages. Computer-readable program instructions may be executed entirely on a user's computer, partially on a user's computer, as an independent software package, partially on a user's computer, partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., utilizing an Internet service provider to connect via the Internet). In some embodiments, an electronic circuit, such as a programmable logic circuit, a field programmable gate array (FPGA), or a programmable logic array (PLA), may be personalized by utilizing the state information of the computer-readable program instructions. The electronic circuit may execute the computer-readable program instructions, thereby realizing various aspects of the present disclosure.

[0173] Various aspects of the present disclosure are described herein with reference to flowcharts and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present disclosure. It should be understood that each block of the flowcharts and / or block diagrams, and combinations of blocks in the flowcharts and / or block diagrams, can be implemented by computer-readable program instructions.

[0174] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, thereby producing a machine, so that when these instructions are executed by the processor of the computer or other programmable data processing device, a device is generated that implements the functions / actions specified in one or more blocks in the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium, where these instructions cause the computer, programmable data processing device, and / or other device to operate in a specific manner. Thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing various aspects of the functions / actions specified in one or more blocks in the flowchart and / or block diagram.

[0175] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device so that a series of operational steps are performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to implement the functions / actions specified in one or more blocks in the flowchart and / or block diagram.

[0176] The flow charts and block diagrams in the accompanying drawings show the possible architecture, functions and operations of the systems, methods and computer program products according to multiple embodiments of the present disclosure. In this regard, each box in the flow chart or block diagram can represent a part of a module, program segment or instruction, and the part of the module, program segment or instruction contains one or more executable instructions for realizing the prescribed logical function. In some alternative implementations, the functions marked in the box can also occur in a sequence different from that marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flow chart, and the combination of the boxes in the block diagram and / or flow chart can be implemented by a dedicated hardware-based system that performs the prescribed function or action, or can be implemented by a combination of dedicated hardware and computer instructions.

[0177] While various embodiments of the present disclosure have been described above, the foregoing description is intended to be illustrative, non-exhaustive, and not limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is selected to best explain the principles of the embodiments, their practical applications, or technological improvements in the marketplace, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A distributed robust optimization method for train energy saving, characterized in that: The method comprises: Determine the objective function used to calculate the energy consumption of the train during the entire operation process, as well as the corresponding constraints; Dividing the running section of the train to obtain at least one subsection, wherein the traction force / braking force of the train in each subsection is kept constant; Based on the subintervals obtained after segmentation, the objective function is converted into an energy function sum for solving the energy consumption corresponding to each of the subintervals, and a constraint condition corresponding to each of the energy functions is determined; Determining a historical data distribution of a running section corresponding to the train, and constructing a fuzzy set based on the historical data distribution, wherein the fuzzy set includes at least one candidate data distribution; Converting the energy function into a distributed robust optimization function according to the bulldozer distance and converting the corresponding constraints; The distributed robust optimization function is optimized based on the fuzzy set to obtain a speed curve corresponding to the expected energy consumption of the train during the entire operation process.

2. The method according to claim 1, characterized in that The objective function is converted into an energy function sum for solving the energy consumption corresponding to each subinterval based on the subintervals obtained after segmentation, and the constraint condition corresponding to each energy function is determined, including: Based on the subintervals obtained after segmentation, the objective function is converted into an energy function sum for solving the energy consumption corresponding to each of the subintervals; According to the relationship between the traction / braking work, potential energy, kinetic energy and train resistance energy consumption of the train in each subinterval, the constraint condition corresponding to the energy function of each subinterval is determined.

3. The method according to claim 2, characterized in that The constraints corresponding to the energy function of each subinterval include linear problem terms composed of convex terms and nonlinear problem terms including non-convex terms. Based on the subintervals obtained after segmentation, the objective function is converted into an energy function sum for solving the energy consumption corresponding to each subinterval, and the constraints corresponding to each energy function are determined, further comprising: The non-convex terms included in the constraint conditions corresponding to the energy function are converted into convex terms, so as to convert all problems in the constraint conditions into linear problems.

4. The method according to any one of claims 1 to 3, characterized in that Determining the historical data distribution of the train corresponding to the running section and constructing a fuzzy set based on the historical data distribution includes: Determining the historical data distribution according to the historical data set corresponding to the running section of the train; The historical data distribution center is determined according to the bulldozer distance, and the set consisting of candidate data distribution within the radius with the preset adjustment parameter is used as a fuzzy set.

5. The method according to any one of claims 1 to 4, characterized in that The distributed robust optimization function is N is the number of subintervals in the running interval, v n is the train speed, σ n and ω n is the convex slack auxiliary variable, is a fuzzy set, is the candidate data distribution, ξ is the candidate data that meets the candidate data distribution, u n (ξ) is the traction force / braking force of the train, E n (ξ) is the energy consumed by the train, and n is the sequence number of the subinterval.

6. The method according to claim 5, characterized in that The constraints corresponding to the distributed robust optimization function include: E n (ξ)≥η b u n (ξ)l n 、 u n (ξ)≤P t σ n 、 u n (ξ)≥P b σ n 、 l n =s n+1 -s n 、v0=0,v N =0,s0=0,s N =S, n∈{0,1,…,N-1}, ξ∈Ξ, where, η t is the effective conversion rate of energy consumption of the train traction system, l n is the length of the subinterval, η b is the regenerative braking energy recovery efficiency, M is the train mass, is the basic resistance of the train, ξ M g n is the resistance caused by the line slope, tr1 and tr2 are the parameters of the constant torque working range of the maximum traction force, br1 and br2 are the parameters of the constant torque working range of the maximum braking force, P t is the power in the constant power working range of maximum traction, P b is the power in the constant power working range of maximum braking force, is the maximum speed of the train in the current sub-interval, T is the running time of the train in the entire running interval, and Used to express the conditions satisfied by the auxiliary variables of convex relaxation, s n is the starting position of the train in the subinterval n, S is the ending position of the trajectory, and Ξ is the range of candidate data distribution.

7. The method according to any one of claims 1 to 6, characterized in that The method further comprises: Based on the infinite optimization problem in the distributed robust optimization problem of bulldozer distance, the distributed robust optimization function and the corresponding constraints are simplified.

8. The method according to claim 7, characterized in that The simplified distributed robust optimization function is Constraints include u n (ξ + )≤P t σ n 、 u n (ξ - )≥P b σ n 、 l n =s n+1 -s n 、v0=0,v N =0,s0=0,s N =S、 and n∈{0,1,…,N-1}, where D is the number of historical data, is the extreme value candidate set including the extreme value points of g(ξ), is the candidate data in the extreme value candidate set and, is the random parameter space of the candidate data distribution, Representative historical data The i-th dimension component of , the superscripts + and - indicate the upper and lower bounds, ε is the preset adjustment parameter that controls the size of the fuzzy set, λ and s j is a variable introduced during the transformation of the distributed robust optimization function.

9. A distributed robust optimization device for train energy saving, characterized in that: The device comprises: The first function module is used to determine the objective function for calculating the energy consumption of the train during the entire operation process, and the corresponding constraints; a track segmentation module, configured to segment the train's operating section into at least one subsection, wherein the train's traction force / braking force in each subsection remains constant; A second function determination module is configured to convert the objective function into an energy function sum for solving the energy consumption corresponding to each subinterval based on the subintervals obtained after segmentation, and determine a constraint condition corresponding to each energy function; a data determination module, configured to determine a historical data distribution of a running section corresponding to the train, and construct a fuzzy set based on the historical data distribution, wherein the fuzzy set includes at least one candidate data distribution; a third function determination module, configured to convert the energy function into a distributed robust optimization function according to the bulldozer distance, and convert corresponding constraints; A function optimization module is used to optimize the distributed robust optimization function based on the fuzzy set to obtain a speed curve corresponding to the expected energy consumption of the train during the entire operation process.

10. An electronic device, characterized in that: include: processor; a memory for storing processor-executable instructions; The processor is configured to implement the method according to any one of claims 1 to 8 when executing the instructions stored in the memory.

11. A non-volatile computer-readable storage medium having computer program instructions stored thereon, characterized in that: When the computer program instructions are executed by a processor, the method according to any one of claims 1 to 8 is implemented.

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