Train energy-saving stochastic optimization method and device based on second-order cone programming

Abstract

The invention relates to a train energy-saving stochastic optimization method and device based on second-order cone programming, and the method comprises the steps: constructing a target function and a constraint condition which are used for representing the energy consumed in a train operation process, and enabling the target function and the constraint condition to serve as an energy-saving optimization model; the train parameters in the energy-saving optimization model are set as random parameters meeting preset probability distribution, and a parameter random energy-saving optimization model is obtained; and with minimization of the objective function as an objective, solving the parameter random energy-saving optimization model under the condition that constraint conditions are met to obtain a running speed curve of the train. According to the method, the train parameters are set to be random parameters, the actual running condition of the train can be accurately simulated, in addition, the energy-saving optimization problem under known train model parameter distribution is converted into the random second-order cone programming problem, and compared with traditional train random optimization based on a genetic algorithm or a dynamic programming method, the energy-saving optimization method has the advantages that the energy-saving optimization efficiency is greatly improved. And higher calculation efficiency and global convergence are shown.

Description

Technical Field

[0001] The present disclosure relates to the field of transportation, and in particular to a train energy-saving stochastic optimization method and device based on second-order cone programming, an electronic device, and a storage medium. Background Art

[0002] Rail transit systems play an increasingly important role in public transportation. Their convenience, efficiency, safety, and high capacity make them an increasingly important part of modern society. However, with the widespread use of rail transit systems, their energy consumption has become increasingly prominent. Therefore, reducing the energy consumption of rail transit systems has become a research focus.

[0003] However, due to factors such as changes in the train operating environment, equipment aging, and errors in model parameter identification, this assumption may not be accurate. Therefore, the train energy-saving optimization results obtained based on this assumption may not be ideal in actual operation and may even consume more energy. Summary of the Invention

[0004] In view of this, the present disclosure proposes a train energy-saving stochastic optimization scheme based on second-order cone programming.

[0005] According to one aspect of the present disclosure, a train energy-saving stochastic optimization method based on second-order cone programming is provided, characterized by comprising:

[0006] Construct an objective function and constraints to represent the energy consumed during train operation as an energy-saving optimization model;

[0007] Setting the train parameters in the energy-saving optimization model to random parameters that satisfy a preset probability distribution to obtain a parameter random energy-saving optimization model;

[0008] With the goal of minimizing the objective function and under the condition of satisfying the constraint conditions, the parameter random energy-saving optimization model is solved to obtain the train running speed curve.

[0009] In one possible implementation, constructing an objective function and constraints for representing energy consumed during train operation as an energy-saving optimization model includes:

[0010] Constructing an initial objective function and initial constraints to represent the energy consumed during train operation as an initial energy-saving optimization model;

[0011] Performing discrete approximation processing on the initial energy-saving optimization model to obtain a nonlinear programming model;

[0012] The non-convex terms in the nonlinear programming model are replaced by convex relaxation auxiliary variables to obtain a second-order cone programming model as the energy-saving optimization model.

[0013] In one possible implementation, solving the parameter random energy-saving optimization model to obtain a train running speed curve includes:

[0014] Sampling in the random variable space of the random parameter to obtain a plurality of first random parameters as random parameters in the parameter random energy-saving optimization model;

[0015] Using the first random parameter, converting the operation of continuously integrating the random parameter to calculate energy in the parameter random energy-saving optimization model into an operation of summing the energies calculated under the multiple first random parameters to obtain a finite-dimensional parameter random energy-saving optimization model;

[0016] The finite-dimensional parameter random energy-saving optimization model is solved to obtain a train running speed curve.

[0017] In a possible implementation, the method further includes:

[0018] Using the parameter random energy-saving optimization model, an objective function and constraints for identifying the total energy consumed by a train running between the multiple stations are constructed according to the distances between the multiple stations and the vehicle operating parameters, as a train schedule energy-saving optimization model, wherein the random variables between different stations in the train schedule energy-saving optimization model are different;

[0019] With the goal of minimizing the objective function representing the total energy, the train timetable energy-saving optimization model is solved while satisfying the constraints to obtain the train operation timetable and the operation speed curve between each station.

[0020] In one possible implementation, solving the train timetable energy-saving optimization model to obtain a train operation timetable and an operation speed curve between each station includes:

[0021] Sampling in the random variable space of the random parameter to obtain a plurality of second random parameters as random parameters in the train schedule energy-saving optimization model;

[0022] Using the second random parameter, converting the operation of continuously integrating the random parameter to calculate energy in the train schedule energy-saving optimization model into an operation of summing the energies calculated under the multiple second random parameters, thereby obtaining a finite-dimensional train schedule energy-saving optimization model;

[0023] The finite-dimensional parameter random energy-saving optimization model is solved to obtain a train operation schedule and an operation speed curve between each station.

[0024] In a possible implementation, sampling in the random variable space of the random parameter to obtain a plurality of second random parameters as random parameters in the train schedule energy-saving optimization model includes:

[0025] Maintaining the basic resistance parameters of the train in a single run unchanged between different stations, and maintaining the train masses between different stations independent of each other, sampling the random parameters in the train schedule energy-saving optimization model to obtain multiple second random parameters.

[0026] In a possible implementation, the objective function of the parameter random energy-saving optimization model is: Among them, J sto represents the energy consumed during the train operation, ξ is the train random parameter, p(ξ) is the probability distribution space satisfied by ξ, E n (ξ) is the energy consumed by the train during operation in the nth subinterval, n is a positive integer, and N is the total number of subintervals of the train.

[0027] The constraints of the parameter random energy-saving optimization model include:

[0028]

[0029] E n (ξ)≥η b u n (ξ)l n

[0030]

[0031]

[0032] u n (ξ)≤P t σ n

[0033]

[0034] u n (ξ)≥P b σ n

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041] l n =s n+1 -s n

[0042] v0=0,v N =0

[0043] s0=0,s N =S

[0044] n∈{0,1,…,N-1}

[0045] Among them, u n (ξ) represents the traction or braking force when the train parameter is ξ, η t is the effective conversion rate of energy consumption of the train traction system, l n is the length of the nth subinterval, η b For the regenerative braking energy recovery efficiency, the train random parameters include the basic resistance parameters A, B, C and the train mass M. The train random parameters are expressed as ξ=[ξ A ,ξ B ,ξ C ,ξ M ] T , is the basic resistance of the train, ξ M g n is the resistance caused by the line slope, where tr1 and tr2 are the parameters of the maximum traction force corresponding to the constant torque working range, br1 and br2 are the parameters of the maximum braking force corresponding to the constant torque working range, and P t is the power of the constant power working range corresponding to the maximum traction force, P b is the power of the constant power working range corresponding to the maximum braking force, is the maximum speed of the train in the current sub-interval, is the average velocity of the nth subinterval, v n is the speed of the nth sub-interval, T is the running time of the train in the entire running interval, σ n and ω n is the convex slack auxiliary variable, 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 nth subinterval, S is the total length of the line, and Ξ is the range of candidate data distribution.

[0046] According to another aspect of the present disclosure, a train energy-saving stochastic optimization device based on second-order cone programming is provided, characterized by comprising:

[0047] A first model determination unit is used to construct an objective function and constraint conditions for representing energy consumed during train operation as an energy-saving optimization model;

[0048] A second model determination unit is configured to set the train parameters in the energy-saving optimization model to random parameters that satisfy a preset probability distribution, thereby obtaining a parameter random energy-saving optimization model;

[0049] The solving unit is used to solve the parameter random energy-saving optimization model with the goal of minimizing the objective function and satisfying the constraint conditions to obtain the train running speed curve.

[0050] In a possible implementation manner, the first model determination unit is configured to:

[0051] Constructing an initial objective function and initial constraints to represent the energy consumed during train operation as an initial energy-saving optimization model;

[0052] Performing discrete approximation processing on the initial energy-saving optimization model to obtain a nonlinear programming model;

[0053] The non-convex terms in the nonlinear programming model are replaced by convex relaxation auxiliary variables to obtain a second-order cone programming model as the energy-saving optimization model.

[0054] In a possible implementation, the solving unit is configured to:

[0055] Sampling in the random variable space of the random parameter to obtain a plurality of first random parameters as random parameters in the parameter random energy-saving optimization model;

[0056] Using the first random parameter, converting the operation of continuously integrating the random parameter to calculate energy in the parameter random energy-saving optimization model into an operation of summing the energies calculated under the multiple first random parameters to obtain a finite-dimensional parameter random energy-saving optimization model;

[0057] The finite-dimensional parameter random energy-saving optimization model is solved to obtain a train running speed curve.

[0058] In a possible implementation, the method further includes a train schedule energy-saving optimization unit, configured to:

[0059] Using the parameter random energy-saving optimization model, an objective function and constraints for identifying the total energy consumed by a train running between the multiple stations are constructed according to the distances between the multiple stations and the vehicle operating parameters, as a train schedule energy-saving optimization model, wherein the random variables between different stations in the train schedule energy-saving optimization model are different;

[0060] With the goal of minimizing the objective function representing the total energy, the train timetable energy-saving optimization model is solved while satisfying the constraints to obtain the train operation timetable and the operation speed curve between each station.

[0061] In a possible implementation, the train timetable energy-saving optimization unit is configured to:

[0062] Sampling in the random variable space of the random parameter to obtain a plurality of second random parameters as random parameters in the train schedule energy-saving optimization model;

[0063] Using the second random parameter, converting the operation of continuously integrating the random parameter to calculate energy in the train schedule energy-saving optimization model into an operation of summing the energies calculated under the multiple second random parameters, thereby obtaining a finite-dimensional train schedule energy-saving optimization model;

[0064] The finite-dimensional parameter random energy-saving optimization model is solved to obtain a train operation schedule and an operation speed curve between each station.

[0065] In a possible implementation, the train timetable energy-saving optimization unit is configured to:

[0066] Maintaining the basic resistance parameters of the train in a single run unchanged between different stations, and maintaining the train masses between different stations independent of each other, sampling the random parameters in the train schedule energy-saving optimization model to obtain multiple second random parameters.

[0067] According to another aspect of the present disclosure, a train energy-saving stochastic optimization device based on second-order cone programming is provided, comprising: a processor; 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.

[0068] According to another 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.

[0069] According to another aspect of the present disclosure, a computer program product is provided, including 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.

[0070] By constructing an objective function and constraints, an energy-saving optimization model is established. Random parameters are further introduced to simulate the uncertainty in actual operation. Finally, the model is solved to obtain the optimal train speed curve. Thus, by setting train parameters to random parameters, actual train operation can be accurately simulated. The resulting train speed curve can minimize train energy consumption in actual operation, improve operational efficiency, and reduce operating costs.

[0071] 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

[0072] 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.

[0073] Figure 1 A flowchart of a train energy-saving stochastic optimization method based on second-order cone programming according to an embodiment of the present disclosure is shown.

[0074] Figure 2 A schematic diagram of a train traction force characteristic curve according to an embodiment of the present disclosure is shown.

[0075] Figure 3 A schematic diagram of train running section division according to an embodiment of the present disclosure is shown.

[0076] Figure 4 Schematic diagrams of train speed curves obtained using three methods according to the simulation experiment of the present disclosure are shown.

[0077] Figure 5 The following are train speed curves obtained from four train operation curve optimization methods according to the simulation experiments disclosed herein.

[0078] Figure 6 A block diagram of a train energy-saving stochastic optimization device based on second-order cone programming according to an embodiment of the present disclosure is shown.

[0079] Figure 7 A block diagram of a device for stochastic optimization of train energy saving based on second-order cone programming according to an exemplary embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0080] 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.

[0081] 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.

[0082] 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.

[0083] Figure 1 The flowchart of the train energy saving stochastic optimization method based on second-order cone programming according to an embodiment of the present disclosure is shown. Figure 1 As shown, the method includes:

[0084] In step S11, an objective function and constraints for representing the energy consumed during train operation are constructed as an energy-saving optimization model;

[0085] The objective function is a mathematical expression that describes the goal of an optimization problem. It represents the energy consumed during train operation. Constraints are restrictions on the variables in the optimization problem, defining their feasible range. Constraints are related to train operation, such as speed, time, and safety distance. The energy-saving optimization model is a mathematical model that combines the objective function and constraints. By optimizing this mathematical model, the optimal train operation method is found to minimize energy consumption.

[0086] In step S12, the train parameters in the energy-saving optimization model are set to random parameters that satisfy a preset probability distribution, thereby obtaining a parameter random energy-saving optimization model;

[0087] Train parameters are various parameters related to train operation, such as train mass, drag coefficient, acceleration and deceleration capabilities, etc. The preset probability distribution is the probability distribution of pre-set train parameters, which is used to simulate the uncertainty or changes in actual train operation.

[0088] During train operation, some train parameters are random, such as the mass and resistance coefficient of the train. Taking this randomness into account, on the basis of the energy-saving optimization model, the train parameters can be set as random parameters to simulate the uncertainty in actual operation, that is, the train parameters in the energy-saving optimization model are set to random parameters that meet the preset probability distribution, so that the parameter random energy-saving optimization model is closer to the actual situation.

[0089] For the convenience of description, the energy-saving optimization model after parameter randomization is referred to as the obtained parameter random energy-saving optimization model.

[0090] In step S13, with the goal of minimizing the objective function and under the condition of satisfying the constraint conditions, the parameter random energy-saving optimization model is solved to obtain the running speed curve of the train.

[0091] The operating speed curve represents the curve of the train speed changing with time or distance during operation, and is an important basis for train operation control.

[0092] When solving the parameter random energy-saving optimization model, the parameter random energy-saving optimization model will be solved with the goal of minimizing the objective function under the premise of satisfying the constraints, and the train speed curve that minimizes the objective function (i.e., energy consumption) will be obtained.

[0093] In this disclosed embodiment, an energy-saving optimization model is established by constructing an objective function and constraints. Random parameters are further introduced to simulate the uncertainty in actual operation. Finally, the model is solved to obtain the optimal train speed curve. Thus, by setting train parameters to random parameters, the actual operation of the train can be accurately simulated. The resulting train speed curve can minimize train energy consumption in actual operation, improve operating efficiency, and reduce operating costs.

[0094] In one possible implementation, the objective function and constraints used to represent the energy consumed during the operation of a train are constructed as an energy-saving optimization model, including: constructing an initial objective function and initial constraints used to represent the energy consumed during the operation of a train as an initial energy-saving optimization model; performing discrete approximation processing on the initial energy-saving optimization model to obtain a nonlinear programming model; replacing non-convex terms in the nonlinear programming model with convex relaxation auxiliary variables to obtain a second-order cone programming model as the energy-saving optimization model.

[0095] Most train energy-saving optimization methods use genetic algorithms, dynamic programming, or reinforcement learning. However, these methods suffer from slow convergence, long solution times, and a tendency to fall into local optimal solutions. To overcome these shortcomings, this paper transforms the train energy-saving optimization problem into a second-order cone programming problem.

[0096] In the embodiment of the present disclosure, the train model used is a single-point model, which takes the train position as the independent variable, and its mathematical expression is as follows:

[0097]

[0098] Among them, the train position s is the independent variable, the train speed v and time t are the train state variables, M is the train mass, and u(s) is the train's traction or braking force. 2 is the basic resistance of the train, where A, B, and C are the basic resistance coefficients of the train. Mg(s) is the resistance caused by the line gradient, where g(s) is a piecewise constant function that describes the acceleration component of the train caused by the gradient as the train position s changes. The starting and ending states of the train are x0 = [0, 0] T ,x f =[0,T] T , where T in the upper right corner is the matrix transpose symbol, T is the total running time, and the total time T, the total line length S, the train position s and the speed v(s) satisfy the constraints

[0099] In the disclosed embodiment, when analyzing the energy consumption during train operation, the relatively fixed energy consumption of auxiliary equipment such as air conditioning and ventilation can be ignored, and the traction energy consumption and regenerative braking energy feedback related to the train driving strategy can be mainly considered. Then the energy J consumed during the entire operation of the train can be expressed as:

[0100]

[0101] Among them, the first is the train traction energy consumption, η t The second item is the effective conversion rate of energy consumption of the train traction system; is the energy fed back by the train’s regenerative braking, η b is the regenerative braking energy recovery efficiency.

[0102] The energy-saving optimization problem of train speed curve can be described as an optimal control problem, which is described as formula (3), where u is the abbreviation of the train's traction or braking force u(s). This is the initial objective function constructed to represent the energy consumed during train operation. The initial constraints include 5, among which the first constraint is is the train motion equation, the second constraint g(u)≤0 is the train traction or braking force constraint, the third constraint v≤V max(s) indicates that the train speed must meet the speed limit requirement. The fourth and fifth constraints are described in detail above and are not repeated here. Thus, the initial energy-saving optimization model is constructed.

[0103] Due to the differences in the motion equations in the optimal control problem (3) caused by the different slopes in different sections of the line or the influence of other factors, the train energy-saving optimization problem can be more accurately described as a multi-phase optimal control problem (multi-phase OCP).

[0104]

[0105] The train traction or braking force limitation conditions are related to the characteristics of the train's traction system and braking system. Figure 2 , Figure 2 A schematic diagram of a train traction force characteristic curve according to an embodiment of the present disclosure is shown. Referring to the China High-Speed ​​Train (CRH3), the train traction system operating range can be divided into two types: a constant torque operating range and a constant power operating range. In the constant torque operating range, when the train speed is relatively low, the traction torque output by the train traction system remains constant or linearly proportional to the train speed. In the constant power operating range, when the train speed is relatively high, the traction power output by the train traction system remains constant.

[0106] Since the train's braking system only uses air braking, or a combination of air and electric braking, at relatively low speeds, and electric braking at all other times, the electric braking characteristics can be used to represent the characteristics of the entire train's braking system. Similar to the train's traction characteristics, the operating range of a train's braking system using electric braking can also be divided into two types: constant torque operating range and constant power operating range.

[0107] Based on the characteristics of the train's traction system and braking system, the train traction force or braking force limitation condition in the above formula (3) can be expressed as -min(br1+br2v,P b / v)≤u≤min(tr1+tr2v,P t / v), where tr1, tr2 are the parameters of the maximum traction force corresponding to the constant torque working range, br1, br2 are the parameters of the maximum braking force corresponding to the constant torque working range, P t is the power of the constant power working range corresponding to the maximum traction force, P b The maximum braking force corresponds to the power in the constant power working range.

[0108] By performing discrete approximation on problem (3), a new nonlinear programming problem can be obtained. Figure 3 A schematic diagram of train operation section segmentation according to an embodiment of the present disclosure is shown as follows: Figure 3As shown, the entire interval [0, S] where the train runs is divided into N sub-intervals according to the speed limit interval and the line gradient interval, and l=[l0,l1,…,l N-1 ] to represent the length of each subinterval, where l n is the length of the nth subinterval, l n =s n+1 -s n , Among them, s n is the starting position of the train in the nth subinterval, n is a positive integer, such as Figure 3 As shown, each node s i The corresponding speed is v i , i is a positive integer, then the above train energy-saving optimization control problem can be expressed as a multi-stage optimal control problem, see formula (4) for details, and the speed curve in each sub-interval can be approximated as a straight line.

[0109] Assume that the train traction or braking force remains constant within the sub-interval of the line segmentation, that is, when s∈[s n ,s n+1 ],u n is a fixed value, n∈0,1,…,N-1. Based on the law of conservation of energy, the train does work u by traction or braking force in each subinterval. n l n 、potential energy Mg n l n ,kinetic energy and train resistance The relationship between energy consumption is satisfied:

[0110]

[0111] Among them Mg n l n is the gravity component resistance due to the line slope in the small segmented interval. The average speed in each sub-interval is v n is the speed of the nth subinterval. For the integral term in formula (4), we can use The running time of the train in each sub-interval can be approximated using To approximate.

[0112] Under the above assumptions and approximate processing, the train running curve energy-saving optimization problem (3) is transformed into a nonlinear programming problem through discrete approximate processing, as shown in formula (5). For the convenience of description, the optimization model of formula (5) is called a nonlinear programming model. Nonlinear programming problem is a more general and flexible form of optimization problem. By transforming the train energy-saving optimization problem into a nonlinear programming problem, the actual situation during the train operation process can be more accurately described, including nonlinear processes such as acceleration, deceleration, and braking of the train. In this way, more realistic optimization results can be obtained, improving the efficiency and energy-saving performance of train operation. In addition, nonlinear programming problems can also handle more complex constraints and objective functions. In the train energy-saving optimization problem, there may be multiple constraints, such as the maximum speed, minimum speed, and safety distance of the train. By transforming the problem into a nonlinear programming problem, these constraints can be better handled, ensuring the feasibility and safety of the optimization results in actual operation.

[0113]

[0114] Among them, E n is the energy consumed by the train during operation in the nth sub-interval, specifically: The energy consumed by the train during the entire operation process J nlp . and E n ≥u n l n η b Indicates the energy consumed by the train and the work done by traction or braking force u n l n The relationship that should be satisfied between and For the above -min(br1+br2v,P b / v)≤u≤min(tr1+tr2v,P t / v) is not described here in detail. Indicates that the sum of the distances of all subintervals is S.

[0115] Since the above formula (5) contains non-convex terms and Nonlinear programming problem (5) is also a non-convex optimization problem. A non-convex optimization problem is an optimization problem that does not meet the conditions for a convex optimization problem. A convex optimization problem requires that the variables of the optimization problem belong to a closed convex set and that the objective function is a convex function. If either of these two conditions is not met, then the problem is called a non-convex optimization problem. The non-convex term is the non-convex part of the non-convex optimization problem and can exist in both the objective function and the constraints.

[0116] In formula (5), except for the non-convex terms and All other parts except are linear. We can introduce convex relaxation auxiliary variables to relax the originally nonconvex nonlinear programming problem (5) into a convex optimization problem. Convex relaxation auxiliary variables refer to variables that satisfy the convexity condition. Since convex optimization is a fairly mature discipline, there are many fast and efficient solution methods for solving convex optimization problems. For convex optimization problems obtained by convex relaxation, ready-made solution methods or solvers can be used for rapid solution.

[0117] I can introduce a convex slack auxiliary variable σ n and ω n ,satisfy and To replace the non-convex term in problem (5) and The problem is relaxed and transformed into a convex optimization problem. In fact, the convex relaxation auxiliary variable we introduced satisfies the condition 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.

[0118] Since problem (5) uses 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 convex relaxation of problem (5) is a second-order cone programming problem, which can be expressed as the following formula (6).

[0119]

[0120] The newly added conditions In order to make the convex relaxation auxiliary variable ω n The speed limit requirement is also met. After replacing the non-convex terms in the nonlinear programming model with convex relaxation auxiliary variables, the energy-saving optimization model of the train operation curve based on second-order cone programming (6) is obtained. For the convenience of description, it is referred to as the second-order cone programming model.

[0121] In the disclosed embodiment, an initial objective function and initial constraints representing the energy consumed during train operation are constructed as an initial energy-saving optimization model; the initial energy-saving optimization model is discretized and approximated to obtain a nonlinear programming model; and the non-convex terms in the nonlinear programming model are replaced with convex relaxation auxiliary variables to obtain a second-order cone programming model as the energy-saving optimization model. Thus, by discretizing and approximating the initial energy-saving optimization model, the train operation curve energy-saving optimization problem can be transformed into a nonlinear programming problem. By introducing convex relaxation auxiliary variables, the originally non-convex nonlinear programming problem is successfully transformed into a convex optimization problem. In particular, the convex optimization problem is a second-order cone programming problem. Convex optimization problems have the property of unique and easy global optimal solutions. Therefore, this transformation can greatly simplify the problem-solving difficulty and improve the solution efficiency. Furthermore, as a subclass of convex optimization problems, the second-order cone programming problem has specific structures and properties and can be efficiently solved using specialized solution methods or solvers. This method has fast convergence speed, short solution time, and can obtain a global optimal solution. It can also accurately determine the optimal speed curve under random distribution of train parameters.

[0122] After establishing the parameter random energy-saving optimization model of formula (6), the energy-saving random optimization of the train operation curve between single stations and the energy-saving random optimization of the train schedule between multiple stations can be performed based on this model. The two cases are described in detail below.

[0123] In one possible implementation, the parameter random energy-saving optimization model is solved to obtain a train running speed curve, including: sampling in the random variable space of the random parameters to obtain multiple first random parameters as random parameters in the parameter random energy-saving optimization model; using the first random parameters, converting the operation of continuously integrating and calculating the energy of the random parameters in the parameter random energy-saving optimization model into an operation of summing the energies calculated under the multiple first random parameters to obtain a finite-dimensional parameter random energy-saving optimization model; solving the finite-dimensional parameter random energy-saving optimization model to obtain the train running speed curve.

[0124] Considering the stochastic optimization problem of energy saving of the train running curve between two stations, some parameters in the model can be defined as random, and the actual values ​​of these parameters may change with changes in various conditions.

[0125] Specifically, the train random parameters are defined as ξ={ξ1,ξ2,…,ξ m}, where ξ iis the i-th parameter, and m is the number of parameters. The train operation curve energy-saving stochastic optimization problem is defined as: given a train's random parameter ξ that satisfies a certain probability distribution, solve the train's operation curve so that the train's energy consumption is minimized during operation. This optimization problem can be viewed as a stochastic optimal control problem, as shown in Equation (7).

[0126]

[0127] Among them, the train random parameter ξ satisfies the probability distribution p(ξ), u(s|ξ) represents the traction or braking force at position s when the train parameter is ξ. v(s) is the speed of the train at position s, f(v(s),u(s|ξ)) is the motion equation of the train at position s, g(v(s),u(s|ξ)) represents the constraint condition satisfied by the train traction or braking force at position s, V max (s) is the train speed limit at position s, T is the train's travel time constraint, and S is the train's travel distance. In this problem, the train's operating speed curve does not vary with the train parameter ξ, meaning it is a deterministic curve. However, the train's traction or braking force varies with the train parameter ξ, meaning it is a random variable. In the energy-saving stochastic optimization problem of train operating curves between stations, the train parameters are fixed during a single run. Here, the train's random parameters can vary between different train runs.

[0128] In the embodiment of the present disclosure, the train random parameters include the basic resistance parameters A, B, C and the train mass M. The train random parameters are expressed as ξ=[ξ A ,ξ B ,ξ C ,ξ M ] T Then, based on the obtained second-order cone programming model, the vehicle parameters are replaced with random parameters, and the train operation curve energy-saving stochastic optimization problem (7) is transformed into a stochastic second-order cone programming problem, which can be seen in formula (8).

[0129]

[0130] It should be noted that the random second-order cone programming problem (8) involves continuous integration in the random variable space ξ∈Ξ, so the problem is an infinite-dimensional second-order cone programming problem and is very difficult to solve. To solve this problem, in the embodiment of the present disclosure, a sampling method is used to convert the random second-order cone programming problem (8) into a finite-dimensional second-order cone programming problem, as shown in formula (9). The sampling method can be average sampling or random sampling. For ease of description, the random parameters obtained by sampling are referred to as first random parameters.

[0131] In the disclosed embodiment, the distribution of the train random parameters is known. After using the sampling method, the optimization objective of the continuous integral in the random second-order cone programming problem (8) can be approximated by the finite sum optimization objective, that is, where ξ d is the random parameter of the train sampled for the dth time, p(ξ d ) is the corresponding probability density. Then, after approximation using the sampling method, the parameter random energy-saving optimization model (8) is transformed into a finite-dimensional parameter random energy-saving optimization model (9), and can be solved quickly and effectively using mature second-order cone programming methods such as the interior point method, thereby improving the solution speed of the model.

[0132]

[0133] The above implementation method optimizes the train speed curve between two stations. Based on this, the train speed curve between multiple stations can be optimized. In other words, the train schedule can be optimized while keeping the distance between stations unchanged. The following describes in detail various implementation methods for energy-saving optimization of train schedules.

[0134] In one possible implementation, the method further includes: utilizing the parameter random energy-saving optimization model, and constructing, based on the distances between multiple stations and the vehicle operating parameters, an objective function and constraints for identifying the total energy consumed by a train running between multiple stations, as a train timetable energy-saving optimization model, wherein the random variables between different stations in the train timetable energy-saving optimization model are different; with the goal of minimizing the objective function representing the total energy, while satisfying the constraints, solving the train timetable energy-saving optimization model to obtain the train operation timetable and the operating speed curve between each station.

[0135] Stochastic optimization of train timetables considers how to allocate the train timetable and optimize the running speed curve between each station when the train runs between multiple stations on the line, while the distance between the stations remains unchanged, so as to ensure that the expected value of the total energy consumption of the train can be minimized when there are random changes in the train parameters.

[0136] In the embodiment of the present disclosure, the train random parameters are the basic resistance parameters A, B, C and the train mass M. However, unlike the stochastic optimization of train operation curve energy saving between single stations, the random variables in the train schedule stochastic optimization problem are different between different stations. The random variables in the train schedule energy saving stochastic optimization problem can be expressed as K is the number of stations in the line, and two adjacent stations are one station.

[0137] Based on the obtained parameter random energy-saving optimization model, we can construct a parameter to identify the total energy J consumed by the train running between multiple stations according to the distance between multiple stations and the vehicle operation parameters. sto-timetable The objective function and constraints of are used as the train schedule energy-saving optimization model, and the details are shown in formula (10).

[0138]

[0139] When solving the train schedule energy-saving optimization model, the total energy J is minimized. sto-timetable The train schedule energy-saving optimization model is solved, taking the objective function as the goal and satisfying the constraints, to obtain the train schedule and the operating speed curve between each station. Thus, by setting the train parameters as random parameters, the actual train operation can be accurately simulated. The resulting train schedule can minimize train energy consumption in actual operation, improve operating efficiency, and reduce operating costs.

[0140] In one possible implementation, the train schedule energy-saving optimization model is solved to obtain the train operation schedule and each inter-station operation speed curve, including: sampling in the random variable space of the random parameters to obtain multiple second random parameters as random parameters in the train schedule energy-saving optimization model; using the second random parameters, converting the operation of continuously integrating and calculating the energy of the random parameters in the train schedule energy-saving optimization model into an operation of summing the energies calculated under the multiple second random parameters to obtain a finite-dimensional train schedule energy-saving optimization model; solving the finite-dimensional parameter random energy-saving optimization model to obtain the train operation schedule and each inter-station operation speed curve.

[0141] In this implementation, random parameters in the constructed train schedule energy-saving optimization model can be sampled in the random variable space of the random parameters. For ease of description, the sampled random parameters are referred to as second random parameters. Then, the second random parameters are used as random parameters in the train schedule energy-saving optimization model.

[0142] By using the second random parameter, the operation of continuously integrating the random parameters to calculate the energy in the train schedule energy-saving optimization model can be converted into the operation of summing the energies calculated under multiple second random parameters, thereby obtaining a finite-dimensional train schedule energy-saving optimization model. This realizes the transformation of the infinite-integration second-order cone programming problem into a finite-dimensional second-order cone programming problem, where the optimization objective function can be expressed as formula (11).

[0143]

[0144] Among them, ξd is the random parameter of the train sampled for the dth time, p(ξ d ) is the corresponding probability density. By solving the finite-dimensional parameter random energy-saving optimization model, the optimization speed of the train timetable can be improved.

[0145] In a possible implementation, the random parameters include a basic train resistance and a train mass, and the random parameters in the train schedule energy-saving optimization model are sampled to obtain a plurality of second random parameters, including:

[0146] Maintaining the basic resistance parameters of the train in a single run unchanged between different stations, and maintaining the train masses between different stations independent of each other, sampling the random parameters in the train schedule energy-saving optimization model to obtain multiple second random parameters.

[0147] In the disclosed embodiments, considering the high dimensionality of the train random parameters in the stochastic optimization problem of train schedule energy conservation, the number of samples D required for sampling approximation is very large. Consequently, the finite-dimensional second-order cone programming problem obtained using sampling approximation also has a considerable dimensionality. To further improve optimization speed, reasonable assumptions can be made based on certain relationships between the train random variables, thereby simplifying the problem.

[0148] When a train runs on a line, the basic resistance parameters A, B and C of the train are almost unchanged between different stations. The main reason for the change of train parameters between different stations is the different passenger capacity at different stations, which leads to the change of train mass M. Therefore, we can assume that the basic resistance parameters A, B and C of the train are unchanged between different stations. Then, the random parameters of the train can be expressed as Since the change in train mass between different stations is mainly due to the change in the passenger capacity of the station, and the passenger capacity of different stations has a certain degree of independence, we can further assume that the train mass distribution between different stations is independent of each other.

[0149] Based on the above assumptions, when sampling random parameters, the basic resistance parameters of the train can be kept constant between different stations in a single run, and the train masses between different stations can be kept independent of each other, thereby obtaining multiple second random parameters. Then, the optimization objective function (11) of the finite-dimensional second-order cone programming problem using sampling approximation can be expressed as formula (12). Compared with the approximate optimization objective function (11), the number of samples D required in the objective function (12) is significantly reduced, thereby significantly improving the optimization speed. The corresponding finite-dimensional second-order cone programming problem can be expressed as formula (13).

[0150]

[0151]

[0152] In the disclosed embodiments, the optimization problem is transformed into a second-order cone programming problem, leveraging the favorable properties of convex optimization problems. Convex optimization problems have the characteristic of being unique and easily solvable. This means that during the solution process, the algorithm can quickly converge to the global optimal solution without the need for repeated trial and error between multiple local optimal solutions. Therefore, compared to traditional non-convex optimization methods, the second-order cone programming method can find the global optimal solution to the problem more quickly.

[0153] Furthermore, sampling approximation methods further accelerate convergence. By extracting a portion of random parameters for approximation, the amount of data and computation required for the solution can be significantly reduced. This reduces the amount of information required to be processed during each iteration of the algorithm, thereby accelerating convergence.

[0154] In the embodiments of the present disclosure, the train energy-saving stochastic optimization method based on second-order cone programming provided by the present disclosure is verified through simulation experiments.

[0155] First, we selected data from a specific section of the line, between Stations 11 and 12, to simulate and verify the proposed stochastic energy-saving optimization method for trains based on second-order cone programming (SSEETC). To comprehensively evaluate the performance of SSEETC, we compared it with two existing methods: a train operation curve energy-saving optimization method based on fixed model parameters, which we call the SEETC-nominal model; and a robust energy-saving optimization method for train operation curves, referred to as EETC-RO. For ease of comparison, the results obtained from the fixed model parameter energy-saving optimization method were used as the baseline.

[0156] Figure 4 A schematic diagram of train speed curves obtained by three methods according to the simulation experiment of the present disclosure is shown, and the expected comparison results of energy consumption obtained by different methods are shown in Table 1. Figure 4 In the figure, the horizontal axis is the distance the train runs, the left vertical axis is the speed of the train, and the left vertical axis is the height of the train. Figure 4 In the figure, the top red line represents the train's speed limit, or the train's maximum operating speed, while the blue line represents the altitude at which the train operates. The three lines indicated in the legend represent train speed curves derived using three different methods.

[0157] Table 1 Comparison of energy consumption expectations of different methods

[0158] method Energy consumption expectation (kWh) Energy saving (%) SEETC-nominal model 141.37 -- SSEETC 139.17 1.50 EETC-RO 142.37 -0.7

[0159] According to the experimental results, compared with the traditional method of fixing the train model parameters, the random optimization method proposed in the present disclosure significantly reduces the expected energy consumption, with a specific reduction of 1.50%. In view of the fact that trains run frequently on the line and consume huge energy, this seemingly small reduction in energy consumption actually saves a lot of energy. However, the energy-saving robust optimization method for the train running curve is always calculated based on the most unfavorable situation, so its expected energy consumption is higher than the baseline value. In addition, in the simulation experiment, the random optimization method proposed in the present disclosure only requires 0.98 seconds of CPU running time, which is significantly shortened compared to other energy-saving optimization methods that consider the randomness of train model parameters (such as genetic algorithms and dynamic programming). These methods usually take tens of minutes or even hours. Therefore, the present disclosure not only has a significant energy-saving effect, but also has high computational efficiency and fast solution speed.

[0160] In addition, we also comprehensively compare the performance of the train schedule energy-saving random optimization method proposed in one embodiment of the present disclosure with other optimization methods on the entire line. Figure 5 Figure 2 shows train speed curves for four train operation curve optimization methods derived from simulation experiments based on this disclosure. SMSEETC represents the stochastic energy-saving optimization method for train schedules proposed in this disclosure; EETC-current represents a train operation curve energy-saving optimization method based on the current schedule and using fixed train model parameters (i.e., nominal model values); MSEETC-nominal model represents a train operation curve energy-saving optimization method with nominal model parameters; and MEETC-RO represents a robust energy-saving optimization method for train schedules. For ease of comparison, EETC-current was selected as the benchmark for performance comparison of these optimization methods.

[0161] The energy consumption expectations achieved by different methods under the condition of random distribution of train parameters are listed in detail in Table 2.

[0162] Table 2 Comparison of expected energy consumption results of different train timetable energy-saving optimization methods

[0163] method Expected energy consumption (kWh) Energy saving (%) EETC-current 872.19 - SMSEETC 771.76 11.5 MSEETC-nominal model 786.42 9,40 EETC-RO 796.43 8.60

[0164] According to the data, trains running according to the current schedule have the highest expected energy consumption. Compared to this benchmark, other train schedule energy-saving optimization methods have demonstrated significant energy-saving effects. Among them, the train schedule energy-saving random optimization method proposed in this disclosure has the most significant energy-saving effect, which is about 11.5% higher than the benchmark, making it the optimization scheme with the best energy-saving effect. At the same time, the train schedule energy-saving optimization method based on fixed model parameters also achieved an energy-saving improvement of about 9.4%. However, the energy-saving effect of the train schedule energy-saving robust optimization method is relatively weak, only 8.6%.

[0165] In the embodiment of the present disclosure, in view of the actual situation of random changes in train model parameters, an innovative train energy-saving random optimization method based on second-order cone programming is proposed. Based on the energy-saving optimization of the train operation curve, this method further proposes energy-saving optimization of the train timetable, thereby achieving comprehensive optimization of train energy consumption. By converting the energy-saving optimization problem under the known distribution of train model parameters into a random second-order cone programming problem, it shows higher computational efficiency and global convergence compared to the traditional train random optimization based on genetic algorithms or dynamic programming methods. In simulation experiments based on real line data, compared with the train energy-saving optimization method using fixed model parameters, the train energy-saving random optimization method provided by the present disclosure can achieve an effective reduction in energy consumption expectations under the condition of random distribution of train parameters.

[0166] It should be noted that while the above description of the stochastic optimization method for train energy conservation based on second-order cone programming uses a specific mathematical formula as an example, those skilled in the art will appreciate that the present disclosure is not limited to this. In fact, users can flexibly set the specific formula based on their personal preferences and / or actual application scenarios.

[0167] In addition, the present disclosure also provides a train energy-saving random optimization device based on second-order cone programming, an electronic device, a computer-readable storage medium, and a program. The above can all be used to implement any of the train energy-saving random optimization methods based on second-order cone programming provided by the present disclosure. The corresponding technical solutions and descriptions can be found in the corresponding records in the method section and will not be repeated here.

[0168] Figure 6 A block diagram of a train energy-saving stochastic optimization device based on second-order cone programming according to an embodiment of the present disclosure is shown as follows: Figure 6 As shown, the image processing device 20 includes:

[0169] A first model determination unit 21 is used to construct an objective function and constraints for representing the energy consumed during train operation as an energy-saving optimization model;

[0170] A second model determination unit 22 is configured to set the train parameters in the energy-saving optimization model to random parameters that satisfy a preset probability distribution, thereby obtaining a parameter random energy-saving optimization model;

[0171] The solving unit 23 is used to solve the parameter random energy-saving optimization model with the goal of minimizing the objective function and satisfying the constraint conditions to obtain the train running speed curve.

[0172] In a possible implementation manner, the first model determination unit is configured to:

[0173] Constructing an initial objective function and initial constraints to represent the energy consumed during train operation as an initial energy-saving optimization model;

[0174] Performing discrete approximation processing on the initial energy-saving optimization model to obtain a nonlinear programming model;

[0175] The non-convex terms in the nonlinear programming model are replaced by convex relaxation auxiliary variables to obtain a second-order cone programming model as the energy-saving optimization model.

[0176] In a possible implementation, the solving unit is configured to:

[0177] Sampling in the random variable space of the random parameter to obtain a plurality of first random parameters as random parameters in the parameter random energy-saving optimization model;

[0178] Using the first random parameter, converting the operation of continuously integrating the random parameter to calculate energy in the parameter random energy-saving optimization model into an operation of summing the energies calculated under the multiple first random parameters to obtain a finite-dimensional parameter random energy-saving optimization model;

[0179] The finite-dimensional parameter random energy-saving optimization model is solved to obtain a train running speed curve.

[0180] In a possible implementation, the method further includes a train schedule energy-saving optimization unit, configured to:

[0181] Using the parameter random energy-saving optimization model, an objective function and constraints for identifying the total energy consumed by a train running between the multiple stations are constructed according to the distances between the multiple stations and the vehicle operating parameters, as a train schedule energy-saving optimization model, wherein the random variables between different stations in the train schedule energy-saving optimization model are different;

[0182] With the goal of minimizing the objective function representing the total energy, the train timetable energy-saving optimization model is solved while satisfying the constraints to obtain the train operation timetable and the operation speed curve between each station.

[0183] In a possible implementation, the train timetable energy-saving optimization unit is configured to:

[0184] Sampling in the random variable space of the random parameter to obtain a plurality of second random parameters as random parameters in the train schedule energy-saving optimization model;

[0185] Using the second random parameter, converting the operation of continuously integrating the random parameter to calculate energy in the train schedule energy-saving optimization model into an operation of summing the energies calculated under the multiple second random parameters, thereby obtaining a finite-dimensional train schedule energy-saving optimization model;

[0186] The finite-dimensional parameter random energy-saving optimization model is solved to obtain a train operation schedule and an operation speed curve between each station.

[0187] In a possible implementation, the objective function of the parameter random energy-saving optimization model is: Among them, J sto represents the energy consumed during the train operation, ξ is the train random parameter, p(ξ) is the probability distribution space satisfied by ξ, E n (ξ) is the energy consumed by the train during operation in the nth subinterval, n is a positive integer, and N is the total number of subintervals of the train.

[0188] The constraints of the parameter random energy-saving optimization model include:

[0189]

[0190] E n (ξ)≥η b u n (ξ)l n

[0191]

[0192]

[0193] u n (ξ)≤P t σ n

[0194]

[0195] u n (ξ)≥P b σ n

[0196]

[0197]

[0198]

[0199]

[0200]

[0201]

[0202] l n =s n+1 -s n

[0203] v0=0,v N =0

[0204] s0=0,s N =S

[0205] n∈{0,1,…,N-1}

[0206] Among them, u n (ξ) represents the traction or braking force when the train parameter is ξ, η t is the effective conversion rate of energy consumption of the train traction system, l n is the length of the nth subinterval, η b For the regenerative braking energy recovery efficiency, the train random parameters include the basic resistance parameters A, B, C and the train mass M. The train random parameters are expressed as ξ=[ξ A ,ξ B ,ξ C ,ξ M ] T , is the basic resistance of the train, ξ M g n is the resistance caused by the line slope, where tr1 and tr2 are the parameters of the maximum traction force corresponding to the constant torque working range, br1 and br2 are the parameters of the maximum braking force corresponding to the constant torque working range, and P t is the power of the constant power working range corresponding to the maximum traction force, P b is the power of the constant power working range corresponding to the maximum braking force, is the maximum speed of the train in the current sub-interval, is the average velocity of the nth subinterval, v n is the speed of the nth sub-interval, T is the running time of the train in the entire running interval, σ n and ω n is the convex slack auxiliary variable, 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 nth subinterval, S is the total length of the line, and Ξ is the range of candidate data distribution.

[0207] 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.

[0208] 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.

[0209] 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.

[0210] 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.

[0211] Figure 7 FIG1 shows a block diagram of an apparatus 1900 for stochastic optimization of train energy saving based on second-order cone programming according to an exemplary embodiment of the present disclosure. For example, the apparatus 1900 can be provided as a server or a terminal device. Figure 7 The apparatus 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, such as an application, that can be executed by the processing component 1922. 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.

[0212] The device 1900 may also include a power supply component 1926 configured to perform power management of the device 1900, a wired or wireless network interface 1950 configured to connect the device 1900 to a network, and an input / output interface 1958 (I / O interface). The device 1900 may operate based on an operating system stored in the memory 1932, such as Windows Server 2003. TM , MacOS X TM , Unix TM ,Linux TM , FreeBSD TM or similar.

[0213] 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 apparatus 1900 to perform the above-described method.

[0214] 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.

[0215] 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.

[0216] 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.

[0217] 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.

[0218] 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.

[0219] 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.

[0220] 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.

[0221] 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.

[0222] 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 train energy-saving stochastic optimization method based on second-order cone programming, characterized in that: include: Construct an objective function and constraints to represent the energy consumed during train operation as an energy-saving optimization model; Setting the train parameters in the energy-saving optimization model to random parameters that satisfy a preset probability distribution to obtain a parameter random energy-saving optimization model; With the goal of minimizing the objective function and under the condition of satisfying the constraint conditions, the parameter random energy-saving optimization model is solved to obtain the train running speed curve.

2. The method according to claim 1, characterized in that The objective function and constraints used to represent the energy consumed during train operation are constructed as an energy-saving optimization model, including: Constructing an initial objective function and initial constraints to represent the energy consumed during train operation as an initial energy-saving optimization model; Performing discrete approximation processing on the initial energy-saving optimization model to obtain a nonlinear programming model; The non-convex terms in the nonlinear programming model are replaced by convex relaxation auxiliary variables to obtain a second-order cone programming model as the energy-saving optimization model.

3. The method according to claim 1, characterized in that The parameter random energy-saving optimization model is solved to obtain the train running speed curve, including: Sampling in the random variable space of the random parameter to obtain a plurality of first random parameters as random parameters in the parameter random energy-saving optimization model; Using the first random parameter, converting the operation of continuously integrating the random parameter to calculate energy in the parameter random energy-saving optimization model into an operation of summing the energies calculated under the multiple first random parameters to obtain a finite-dimensional parameter random energy-saving optimization model; The finite-dimensional parameter random energy-saving optimization model is solved to obtain a train running speed curve.

4. The method according to claim 1, wherein The method further comprises: Using the parameter random energy-saving optimization model, an objective function and constraints for identifying the total energy consumed by a train running between the multiple stations are constructed according to the distances between the multiple stations and the vehicle operating parameters, as a train schedule energy-saving optimization model, wherein the random variables between different stations in the train schedule energy-saving optimization model are different; With the goal of minimizing the objective function representing the total energy, the train timetable energy-saving optimization model is solved while satisfying the constraints to obtain the train operation timetable and the operation speed curve between each station.

5. The method according to claim 4, characterized in that Solve the train timetable energy-saving optimization model to obtain the train operation timetable and each station operation speed curve, including: Sampling in the random variable space of the random parameter to obtain a plurality of second random parameters as random parameters in the train schedule energy-saving optimization model; Using the second random parameter, converting the operation of continuously integrating the random parameter to calculate energy in the train schedule energy-saving optimization model into an operation of summing the energies calculated under the multiple second random parameters, thereby obtaining a finite-dimensional train schedule energy-saving optimization model; The finite-dimensional parameter random energy-saving optimization model is solved to obtain a train operation schedule and an operation speed curve between each station.

6. The method according to claim 5, characterized in that The sampling in the random variable space of the random parameter to obtain a plurality of second random parameters as random parameters in the train schedule energy-saving optimization model includes: Maintaining the basic resistance parameters of the train in a single run unchanged between different stations, and maintaining the train masses between different stations independent of each other, sampling the random parameters in the train schedule energy-saving optimization model to obtain multiple second random parameters.

7. The method according to claim 1, characterized in that The objective function of the parameter random energy-saving optimization model is: Among them, J sto represents the energy consumed during the train operation, ξ is the train random parameter, p(ξ) is the probability distribution space satisfied by ξ, E n (ξ) is the energy consumed by the train during operation in the nth subinterval, n is a positive integer, and N is the total number of subintervals of the train. The constraints of the parameter random energy-saving optimization model include: E n (ξ)≥η b you n (ξ)l n you n (ξ)≤P t s n you n (ξ)≥P b s n in n ≤V n max l n =s n+1 -s n v0=0,v N =0 s0=0,s N =S n∈{0,1,…,N-1} Among them, u n (ξ) represents the traction or braking force when the train parameter is ξ, η t is the effective conversion rate of energy consumption of the train traction system, l n is the length of the nth subinterval, η b For the regenerative braking energy recovery efficiency, the train random parameters include the basic resistance parameters A, B, C and the train mass M. The train random parameters are expressed as ξ=[ξ A ,ξ B ,ξ C ,ξ M ] T , is the basic resistance of the train, ξ M g n is the resistance caused by the line slope, where tr1 and tr2 are the parameters of the maximum traction force corresponding to the constant torque working range, br1 and br2 are the parameters of the maximum braking force corresponding to the constant torque working range, and P t is the power of the constant power working range corresponding to the maximum traction force, P b is the power of the maximum braking force corresponding to the constant power working range, V n max is the maximum speed of the train in the current sub-interval, is the average velocity of the nth subinterval, v n is the speed of the nth sub-interval, T is the running time of the train in the entire running interval, σ n and ω n is the convex slack auxiliary variable, 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 nth subinterval, S is the total length of the line, and Ξ is the range of candidate data distribution.

8. A train energy-saving stochastic optimization device based on second-order cone programming, characterized in that: include: A first model determination unit is used to construct an objective function and constraint conditions for representing energy consumed during train operation as an energy-saving optimization model; A second model determination unit is configured to set the train parameters in the energy-saving optimization model to random parameters that satisfy a preset probability distribution, thereby obtaining a parameter random energy-saving optimization model; The solving unit is used to solve the parameter random energy-saving optimization model with the goal of minimizing the objective function and satisfying the constraint conditions to obtain the train running speed curve.

9. A train energy-saving stochastic optimization device based on second-order cone programming, 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 7 when executing the instructions stored in the memory.

10. 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 7 is implemented.

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