Rail train energy-saving optimization method based on intelligent algorithm

Abstract

The invention discloses a rail train energy-saving optimization method based on an intelligent algorithm. The method comprises the following steps: constructing an energy consumption objective function under a continuous condition based on an electric traction force, a mechanical braking force and a traction chain nonlinear loss model; constructing constraint conditions such as electric traction force, mechanical braking force and line speed limitation; performing interval discretization processing on the energy consumption objective function, and uniformly dividing a train operation line into N nodes according to a total distance S in a spatial domain to form a discretization velocity vector so as to obtain discretization representation of the energy consumption objective function; according to the energy consumption objective function and the constraint condition, an improved differential evolution algorithm is adopted to perform adaptive mutation operator optimization on the velocity vector by using at least two mutation strategies to obtain the optimal velocity of each node; and finally outputting the optimal speed of each node as a train energy-saving operation control instruction. According to the method, a collaborative optimization mechanism of the high-precision energy consumption model and the improved differential evolution algorithm is constructed, and the optimization efficiency and the solution quality are remarkably improved on the premise of ensuring engineering constraints.

Description

Technical Field

[0001] This invention relates to the field of traffic management technology, and in particular to an energy-saving optimization method for rail trains based on intelligent algorithms. Background Technology

[0002] With the rapid development of high-speed railways and urban rail transit, energy consumption during train operation has become an increasingly important concern. To improve transportation efficiency and reduce operating costs, existing research mainly focuses on three types of methods: 1) Energy consumption analysis methods based on classical dynamic equations. These methods typically employ idealized relationships between electric traction force, resistance, and speed, simplifying energy consumption to the integral of the product of electric traction force and speed; 2) Trajectory planning methods based on optimal control theory, using Pontryagin's maximum principle, convex optimization, or dynamic programming. However, these methods often employ the assumption of "fixed efficiency" or neglect traction chain losses, resulting in idealized operating modes such as Bang-Coast-Bang; 3) Energy-saving scheduling methods based on intelligent optimization algorithms, such as differential evolution, genetic algorithms, and particle swarm optimization. These methods achieve high-dimensional trajectory optimization through global search, but most still use linear or idealized energy consumption models, failing to reflect the true nonlinear loss characteristics of engineering systems. Furthermore, some studies focus on regenerative braking and energy feedback mechanisms, but the actual feedback amount is limited by the absorption capacity of the motor, inverter, and power grid. Regenerative braking exhibits significant saturation and nonlinear characteristics, which traditional models often fail to fully incorporate.

[0003] Overall, while existing methods have provided valuable insights into energy-efficient train control, they generally rely on overly simplified energy consumption assumptions, making it difficult to accurately reflect the actual energy consumption characteristics of the traction chain and braking system, thus limiting the engineering applicability of the optimization results. Furthermore, existing technologies have the following technical drawbacks in practical engineering applications:

[0004] First, existing models generally adopt the assumption of "fixed efficiency" or "ideal lossless", ignoring the nonlinear losses (such as copper loss, iron loss and mechanical loss) of traction motors, converters, gearboxes and auxiliary equipment in the traction chain. This leads to a systematic underestimation of traction energy consumption and the energy consumption prediction of the optimized trajectory deviates from the true value. In particular, under high traction / high regeneration conditions, it cannot reflect the energy consumption difference caused by nonlinear losses.

[0005] Secondly, many studies have not considered the coupling relationship between regenerative braking and mechanical braking force. They either ignore mechanical braking force or assume that braking is entirely undertaken by electric regeneration, without considering that regenerative braking is limited by the absorption capacity of inverters, motors and power grids, resulting in excess braking force needing to be generated by mechanical braking force and its energy being unrecoverable.

[0006] Third, existing methods often use soft constraints or empirical corrections to handle conditions such as speed, acceleration, and track speed limits, which may lead to the trajectory violating the track speed limit or infeasible acceleration in gradient or curved sections, thus making them unsuitable for direct use in train control systems.

[0007] Fourth, many methods still build models in the time domain, while the infrastructure parameters of high-speed railways, such as resistance, speed limit, and gradient, are defined in the spatial domain. This makes it difficult for time-domain modeling to accurately describe dynamic constraints and train-track coupling characteristics, and it is also easy to introduce numerical errors during variable transformation.

[0008] Finally, traditional optimization algorithms have significant limitations when dealing with high-dimensional, strongly constrained, and nonlinear energy consumption models: optimal control methods struggle to obtain analytical solutions after incorporating complex loss models, while intelligent optimization algorithms, although flexible, lack effective feasibility correction mechanisms, making it difficult to guarantee the continuity and feasibility of velocity trajectories, and are prone to getting trapped in local optima, leading to slow convergence. Furthermore, for the aforementioned high-precision energy consumption models, due to their significant nonlinearity, multiple constraints, and high-dimensionality, traditional differential evolution, genetic algorithms, and particle swarm optimization algorithms are prone to problems such as rapid decline in population diversity, getting trapped in local optima, and slow convergence during the solution process, making it difficult to obtain high-quality solutions that satisfy all constraints within a reasonable time. Therefore, there is an urgent need for an improved intelligent optimization algorithm for this type of complex optimization problem.

[0009] In summary, existing train energy-saving optimization methods suffer from oversimplification of models, inadequate constraint handling, and algorithmic limitations, making it difficult to achieve precise energy consumption control in real-world engineering scenarios. Therefore, there is an urgent need for an optimization method that integrates the nonlinear loss characteristics of the traction chain, rigorously embeds spatial domain constraints, and possesses efficient global search capabilities to improve the feasibility and engineering applicability of train energy-saving trajectories. Summary of the Invention

[0010] The purpose of this invention is to address the technical bottleneck in existing train energy-saving optimization problems, namely the difficulty in effectively solving high-dimensional, strongly constrained, and nonlinear energy consumption models, by providing a collaborative optimization method for rail trains using a model and algorithm. On one hand, a refined energy consumption model considering traction chain nonlinear loss and regenerative braking constraints is constructed. On the other hand, to address the problems caused by this model, such as a highly non-convex search space, complex constraints, and susceptibility to local optima, an improved differential evolution algorithm is proposed. Through multi-strategy adaptive mutation, population diversity determination, and historical trajectory perturbation mechanisms, this algorithm achieves efficient solutions to complex trajectory optimization problems, thereby obtaining the optimal energy-saving operating trajectory that satisfies engineering constraints.

[0011] The technical solution adopted in this invention is:

[0012] An energy-saving optimization method for rail trains based on intelligent algorithms includes the following steps:

[0013] Constructing the energy consumption objective function under continuous conditions: Based on the nonlinear loss model of electric traction force, mechanical braking force, and traction chain, a continuous energy consumption objective function is constructed.

[0014] , ,in, It is the total distance of the route. It is a state variable. , It has already traveled to a certain distance Time, It is the distance traveled speed of time The square of, It is a control variable. , When it is positive, it is traction force; conversely, It is regenerative braking; As a mechanical braking force, it is always positive; To travel to the distance The total loss of all components at that time;

[0015] Establish constraints: Based on the train equipment capacity and track characteristics, establish constraints for train operation. These constraints should include at least electric traction constraints, mechanical braking force constraints, track speed limit constraints, travel time constraints, and traction chain losses.

[0016] The energy consumption objective function under continuous conditions is discretized into intervals: in the spatial domain, the train running line is uniformly divided into N nodes based on the total distance S of the line, and a discretized velocity vector is formed based on the velocity of each node. ;in, This represents the velocity of the k-th node. The energy consumption objective function is expressed in discrete space as follows: ; For the electric traction force of the k-th node, This represents the total specific loss of the k-th node; The distance between two adjacent nodes;

[0017] Based on the energy consumption objective function and constraints, an improved differential evolution algorithm is used to optimize the velocity vector using an adaptive mutation operator with at least two mutation strategies to obtain the optimal velocity for each node. Specifically, the train travel distance *s* is used as the individual code, and new individuals are generated within the feasible space through binomial crossover. Individuals that do not meet the constraints undergo feasibility processing. During the evolutionary stage, the corresponding mutation strategy is dynamically selected to generate a mutation vector for each individual. Based on the individual fitness distribution, the individual with the lowest fitness is selected to obtain the optimal velocity for each node. Specifically, the fitness of each individual is calculated, and the fitness values ​​are sorted in ascending order to obtain the optimal velocity for each node. The velocity vectors based on the velocity of each node are then discretized. As a population, when the population gets stuck in a local optimum, a perturbation mechanism based on historical optimal trajectories is introduced to generate new individuals to replace the stagnant individuals; the improved differential evolution algorithm includes: an adaptive mutation strategy selection mechanism based on population diversity, used to dynamically adjust between global search and local convergence; a population stagnation determination mechanism based on fitness distribution, used to identify evolutionary stagnation states; and a perturbation generation mechanism based on historical optimal trajectories, used to guide individuals out of local optima in stagnation states; thereby improving the global search capability and convergence efficiency in high-dimensional, strongly constrained nonlinear optimization problems;

[0018] Output the optimal speed of each node as the control command for energy-saving train operation.

[0019] Furthermore, ,in, It is the transformer loss. It's the loss from the motor and converter. It is the wear and tear of auxiliary equipment. It's wear and tear on the gearbox.

[0020] Furthermore, the traction chain loss ratio of the k-th node is higher than the power. Based on the corresponding electric traction force and speed The nonlinear relationship calculation shows that the traction chain loss is proportional to the power. The expression is as follows:

[0021] ;

[0022] in, and These are the constant efficiencies for traction and regenerative braking, respectively. and The constant efficiencies for traction and regenerative braking are 0.73, respectively.

[0023] Furthermore, the mutation strategies include the DE / rand / 1 strategy and the DE / best / 1 strategy. Based on this, through extensive experiments, a method for judging population diversity was established: if the fitness value of the offspring population is higher than that of the parent population, the current population is considered stagnant. During evolution, if the number of stagnant generations is greater than 10, the population diversity is considered low; conversely, if it is less than 10, the population diversity is considered high. When the population diversity is high, the DE / rand / 1 strategy is preferentially used to enhance the global search capability; when the population gradually converges, the weight of the DE / best / 1 strategy is increased to accelerate the local convergence speed. The expression for DE / rand / 1 is: The expression for DE / best / 1 is: ,in, It is the first The individual's variation vector, , and These are three distinct individual vectors randomly selected from the population. It is the best individual in the current population; It is the differential scaling factor, also known as the step size.

[0024] Furthermore, new individuals are generated based on a perturbation mechanism using historical optimal trajectories. The expression is:

[0025] ;

[0026] in, For the first Global optimal individual in generational evolution The historical trajectory; , and These are three distinct individual vectors randomly selected from the population. It is the differential scaling factor; For the historical trajectory As an optional implementation method, the weighting coefficients are used. The value is 0.3.

[0027] Furthermore, the constraints include:

[0028] (1) Electric traction force constraint: ,in, This refers to the magnitude of the train's electric traction force; The distance is the route distance. This represents the maximum value of the electric traction force. This is the minimum value of electric traction force. This corresponds to the maximum regenerative braking capacity. When the regenerative braking capacity is insufficient, it is compensated by mechanical braking force. The maximum electric traction force... It is the minimum value among the limits of the traction system, the power limit, and the acceleration constraint; while the minimum value of the electric traction force is... It is determined by taking the maximum value among the braking system limit, regenerative power limit, and comfort constraints.

[0029] (2) Mechanical braking force constraint: ,in, The magnitude of the train's mechanical braking force; This is the maximum mechanical braking force that the brake can provide; the mechanical braking force cannot be negative, and its upper limit is limited by the brake's capacity.

[0030] (3) Speed ​​limit constraints on the line: Or ,in, For train speed; For train speed The square of; It is the upper limit of the line speed, set according to the infrastructure conditions such as the speed limit of the track section, the curve radius, and the gradient.

[0031] (4) Resistance constraints: ,in, This represents the total resistance of the train. It is rolling resistance. It's air resistance. It is the additional resistance of the curve. It is gradient resistance, which is determined by the line parameters and directly affected by acceleration constraints.

[0032] (5) Traction chain wear: ,in, For the wear and tear of the traction chain; These are losses in the motor and converter. It is transformer loss. It is gearbox mechanical wear. It refers to the losses of auxiliary equipment (e.g., constant losses of fans, compressors, etc.).

[0033] (6) Travel time constraints: ,in The total time taken for the train to complete the line. To set an upper limit on the total time taken for a train to reach its destination; that is, the train must reach its destination within a specified running time. .

[0034] (7) Boundary condition constraints: , , The squares of the train's speeds at the starting and ending points satisfy the boundary requirements, where ; Indicates the start time. Starting speed The square of, Speed ​​at the destination The square of.

[0035] Furthermore, a "penalty function" is used to handle individuals that do not meet the constraints. That is, individuals that do not meet the constraints are assigned an infinite value to eliminate them, thus ensuring that the generated individuals meet the scheduling safety requirements.

[0036] The present invention adopts the above technical solution, and compared with the prior art, the present invention has the following beneficial effects:

[0037] 1. This invention explicitly incorporates the nonlinear characteristics of the entire traction chain, including motor copper losses, iron losses, inverter switching losses, gearbox mechanical losses, and auxiliary system losses, to construct an energy consumption model that closely reflects the actual operating state of the equipment. This ensures that the trajectory optimization process is based on the actual characteristics of the equipment, effectively guaranteeing the consistency of energy consumption assessment and control strategies, and significantly improving the engineering feasibility of the optimization results. 2. This invention establishes a distribution model of regenerative electric braking power and non-regenerative mechanical braking force, accurately characterizing the traction chain capacity limitations, regenerative absorption capacity, and regenerative overflow mechanism. This ensures that the generated trajectory strictly meets the physical constraints of actual braking force, avoiding defects in unexecutable braking strategies and guaranteeing the safety and reliability of the train braking process. 3. This invention strictly embeds track constraints such as speed limits, gradients, and curves, as well as equipment and operational constraints such as upper limits for electric braking, upper limits for mechanical braking force, and longitudinal dynamics into the optimization framework. This ensures that the train speed and acceleration meet dynamic feasibility conditions in all spatial positions, allowing the optimized trajectory to be directly sent to the train control system for execution without secondary correction. 4. This invention uses spatial position 's' as the independent variable to construct the model, naturally mapping parameters such as air resistance, gradient, and speed limit curve to the optimization framework. This avoids the complex state transformation process and the resulting numerical instability problems in time-domain modeling, while ensuring the accuracy of energy consumption expression and significantly improving the convergence stability of the optimization process. 5. This invention proposes an efficient algorithm for high-dimensional, strongly constrained nonlinear optimization problems through a continuity repair mechanism for velocity sequences, a feasible region preservation strategy based on constraint projection, and a global search operator with multidimensional adaptive perturbation. It can maintain a high proportion of feasible solutions under strict constraints and quickly converge to near-optimal solutions, effectively overcoming the shortcomings of traditional optimal control methods that are difficult to solve and intelligent algorithms that are prone to getting trapped in local optima. Attached Figure Description

[0038] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments;

[0039] Figure 1This is a flowchart illustrating an energy-saving optimization method for rail trains based on intelligent algorithms according to the present invention.

[0040] Figure 2 This is a flowchart illustrating the improved differential evolution optimization algorithm of this invention. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings.

[0042] To address the problems of existing train energy-saving optimization methods that generally employ assumptions of "fixed efficiency" or "ideal zero loss," failing to reflect the actual nonlinear loss characteristics of converters, motors, gearboxes, and auxiliary equipment in the traction chain, leading to significant deviations between optimization results and actual energy consumption; and the difficulty of traditional models generating executable train trajectories under multiple engineering constraints such as traction and braking capabilities, track speed limits, resistance characteristics, and travel time, this invention aims to establish an energy consumption evaluation model that accurately characterizes the measured loss characteristics of the train traction chain. This model explicitly incorporates the nonlinear coupling relationship between electric traction force, speed, and traction chain losses into the objective function, making energy consumption calculations closer to real-world operating conditions. A spatial domain-based train trajectory optimization method is constructed, which discretizes the trajectory and transforms the energy consumption objective function into a discrete summation form to accurately assess the electrical energy input during train operation along the track. An improved differential evolution optimization scheme suitable for this energy consumption model is proposed. By constructing a feasibility-first individual encoding method, a constraint handling mechanism, a mutation operator based on multi-strategy adaptation, and a historical trajectory perturbation mechanism, it achieves efficient global search of the high-dimensional continuous trajectory space, obtaining energy-saving operation trajectories that satisfy all engineering constraints. This solves the shortcomings of traditional optimization methods, such as numerous infeasible solutions, slow convergence speed, susceptibility to local optima, and disconnect from engineering practice, ultimately achieving a more accurate, implementable, and engineering-deployable train energy-saving operation scheme.

[0043] like Figure 1 As shown in Figure 2, this invention discloses an energy-saving optimization method for rail trains based on intelligent algorithms, comprising the following steps:

[0044] Constructing the energy consumption objective function under continuous conditions: Based on the nonlinear loss model of electric traction force, mechanical braking force, and traction chain, a continuous energy consumption objective function is constructed.

[0045] , ,in, It is the total distance of the route. It is a state variable. , It has already traveled to a certain distance Time, It is the distance traveled speed of time The square of, It is a control variable. , When it is positive, it is traction force; conversely, It is regenerative braking; As a mechanical braking force, it is always positive; To travel to the distance The total loss of all components at that time;

[0046] Establish constraints: Based on the train equipment capacity and track characteristics, establish constraints for train operation. These constraints should include at least electric traction constraints, mechanical braking force constraints, track speed limit constraints, travel time constraints, and traction chain losses.

[0047] The energy consumption objective function under continuous conditions is discretized into intervals: in the spatial domain, the train running line is uniformly divided into N nodes based on the total distance S of the line, and a discretized velocity vector is formed based on the velocity of each node. ;in, This represents the velocity of the k-th node. The energy consumption objective function is expressed in discrete space as follows: ; For the electric traction force of the k-th node, This represents the total specific loss of the k-th node; The distance between two adjacent nodes;

[0048] Based on the energy consumption objective function and constraints, an improved differential evolution algorithm is used to optimize the velocity vector using an adaptive mutation operator with at least two mutation strategies to obtain the optimal velocity for each node. Specifically, the train travel distance *s* is used as the individual code, and new individuals are generated within the feasible space through binomial crossover. Individuals that do not meet the constraints undergo feasibility processing. During the evolutionary stage, the corresponding mutation strategy is dynamically selected to generate a mutation vector for each individual. Based on the individual fitness distribution, the individual with the lowest fitness is selected to obtain the optimal velocity for each node. Specifically, the fitness of each individual is calculated, and the fitness values ​​are sorted in ascending order to obtain the optimal velocity for each node. The velocity vectors based on the velocity of each node are then discretized. As a population, when the population gets stuck in a local optimum, a perturbation mechanism based on historical optimal trajectories is introduced to generate new individuals to replace the stagnant individuals; the improved differential evolution algorithm includes: an adaptive mutation strategy selection mechanism based on population diversity, used to dynamically adjust between global search and local convergence; a population stagnation determination mechanism based on fitness distribution, used to identify evolutionary stagnation states; and a perturbation generation mechanism based on historical optimal trajectories, used to guide individuals out of local optima in stagnation states; thereby improving the global search capability and convergence efficiency in high-dimensional, strongly constrained nonlinear optimization problems;

[0049] Output the optimal speed of each node as the control command for energy-saving train operation.

[0050] Furthermore, ,in, It is the transformer loss. It's the loss from the motor and converter. It is the wear and tear of auxiliary equipment. It's wear and tear on the gearbox.

[0051] Furthermore, the traction chain loss ratio of the k-th node is higher than the power. Based on the corresponding electric traction force and speed The nonlinear relationship calculation shows that the traction chain loss is proportional to the power. The expression is as follows:

[0052] ;

[0053] in, and These are the constant efficiencies for traction and regenerative braking, respectively. and The constant efficiencies for traction and regenerative braking are 0.73, respectively.

[0054] Furthermore, the mutation strategies include the DE / rand / 1 strategy and the DE / best / 1 strategy. Based on this, through extensive experiments, a method for judging population diversity was established: if the fitness value of the offspring population is higher than that of the parent population, the current population is considered stagnant. During evolution, if the number of stagnant generations of a population is greater than 10, its population diversity is considered low; conversely, if it is less than 10, its population diversity is considered high. When the population diversity is high, the DE / rand / 1 strategy is preferentially used to enhance the global search capability; when the population gradually converges, the weight of the DE / best / 1 strategy is increased to accelerate the local convergence speed. The expression for DE / rand / 1 is: The expression for DE / best / 1 is: ,in, It is the first The individual's variation vector, , and These are three distinct individual vectors randomly selected from the population. It is the best individual in the current population; It is the differential scaling factor, also known as the step size.

[0055] Furthermore, new individuals are generated based on a perturbation mechanism using historical optimal trajectories. The expression is:

[0056] ;

[0057] in, For the first Global optimal individual in generational evolution The historical trajectory; , and These are three distinct individual vectors randomly selected from the population. It is the differential scaling factor; For the historical trajectory As an optional implementation method, the weighting coefficients are used. The value is 0.3.

[0058] Furthermore, the constraints include:

[0059] (1) Electric traction force constraint: ,in, This refers to the magnitude of the train's electric traction force; The distance is the route distance. This represents the maximum value of the electric traction force. This is the minimum value of electric traction force. This corresponds to the maximum regenerative braking capacity. When the regenerative braking capacity is insufficient, it is compensated by mechanical braking force. The maximum electric traction force... It is determined by the minimum value among the limits of the traction system, the power limit, and the acceleration constraint; while the minimum value of electric traction force... It is determined by the maximum value among the braking system limits, regenerative power limits, and comfort constraints.

[0060] (2) Mechanical braking force constraint: ,in, The magnitude of the train's mechanical braking force; This is the maximum mechanical braking force that the brake can provide; the mechanical braking force cannot be negative, and its upper limit is limited by the brake's capacity.

[0061] (3) Speed ​​limit constraints on the line: Or ,in, For train speed; For train speed The square of; It is the upper limit of the line speed, set according to the infrastructure conditions such as the speed limit of the track section, the curve radius, and the gradient.

[0062] (4) Resistance constraints: ,in, This represents the total resistance of the train. It is rolling resistance. It's air resistance. It is the additional resistance of the curve. It is gradient resistance, which is determined by the line parameters and directly affected by acceleration constraints.

[0063] (5) Traction chain wear: ,in, For the wear and tear of the traction chain; These are losses in the motor and converter. It is transformer loss. It is gearbox mechanical wear. It refers to the losses of auxiliary equipment (e.g., constant losses of fans, compressors, etc.).

[0064] (6) Travel time constraints: ,in The total time taken for the train to complete the line. To set an upper limit on the total time taken for a train to reach its destination; that is, the train must reach its destination within a specified running time. .

[0065] (7) Boundary condition constraints: , , The squares of the train's speeds at the starting and ending points satisfy the boundary requirements, where ; Indicates the start time. Starting speed The square of, Speed ​​at the destination The square of.

[0066] Furthermore, a "penalty function" is used to handle individuals that do not meet the constraints. That is, individuals that do not meet the constraints are assigned an infinite value to eliminate them, thus ensuring that the generated individuals meet the scheduling safety requirements.

[0067] The specific principles of this invention will be explained in detail below:

[0068] To solve the energy-saving problem of trains, the ultimate optimization objective of this invention is to minimize the energy consumption of the power grid infrastructure, and to optimize this problem under given physical and operational constraints. Traditional models generally adopt the assumptions of "fixed efficiency" or "ideal lossless" and ignore the nonlinear losses of converters, traction motors, gearboxes, and auxiliary equipment, resulting in significant deviations between the optimization results and actual energy consumption. To obtain an energy consumption evaluation that more closely approximates actual operating conditions, it is necessary to establish an energy consumption objective function that reflects the measured loss characteristics of the train traction chain, and to explicitly incorporate the nonlinear coupling relationship between electric traction force, speed, and losses into the optimization model.

[0069] This invention uses spatial coordinates The trajectory optimization method (based on the track distance variable) constructs an objective function, which accurately characterizes the train's electrical energy input during operation through integral form, thereby achieving more accurate and engineered energy consumption optimization. The specific expression of the objective function in the continuous case is:

[0070] , ,

[0071] in, It is the total distance of the route. It is a state variable, specifically expressed as , It has already traveled to a certain distance Time, It is the square of the speed. It is a control variable, specifically expressed as , When the time is positive, it is electric traction; otherwise, it is regenerative braking.

[0072] because It is the only positive source of energy that the train absorbs from the power grid. The regenerative braking system allows energy to be fed back to the power grid and directly determines the power distribution of the traction chain, so it must be used as a core control variable. The mechanical braking force is always positive. Regenerative braking is limited by the capacity of the motor and inverter and cannot meet all braking demands. Therefore, excess braking must be provided by the mechanical braking force, and all the energy of the mechanical braking force is dissipated as heat loss. Therefore, it must be explicitly modeled in the optimization process; otherwise, solutions that do not conform to engineering reality will be produced. Total power loss. This is achieved by adding up the losses of all components, that is: ,in, It is the transformer loss. It's the loss from the motor and converter. It is the wear and tear of auxiliary equipment. This refers to the losses in the gearbox. In practical scenarios, all losses must be positive. In the specific formula, the part to be integrated is the sum of the electric traction force and the loss term. Real losses are highly nonlinear and therefore must be included in the optimization; otherwise, a completely different optimal trajectory will occur.

[0073] To ensure that train operations do not exceed equipment capacity, the following constraints are stipulated:

[0074] (1) Electric traction force: ,in, It is determined by the converter, motor, and voltage capability. This indicates the maximum regenerative braking capacity. When the regenerative braking capacity is insufficient, it is compensated by mechanical braking force.

[0075] (2) Mechanical braking force: Mechanical braking force cannot be negative, and its upper limit is limited by the braking capacity.

[0076] (3) Train speed is subject to the line speed limit: Or Line speed limit These conditions come from infrastructure factors such as speed limits, curve radii, and gradients within the track section.

[0077] (4) Resistance constraints: ,in It is rolling resistance. It's air resistance. It is the additional resistance of the curve and It is gradient resistance, which is determined by the line parameters and directly affected by acceleration constraints.

[0078] (5) Traction chain loss constraints: , These are losses in the motor and converter. It is transformer loss. It is gearbox mechanical wear. It refers to the losses of auxiliary equipment (e.g., constant losses of fans, compressors, etc.).

[0079] (6) Travel time constraints: The train must arrive at its destination within the prescribed travel time. ,therefore, .

[0080] (7) Boundary condition constraints: , , The squares of the train's speeds at the starting and ending points satisfy the boundary requirements, where ; Indicates the start time. Starting speed The square of, Speed ​​at the destination The square of.

[0081] This invention discretizes the continuous train trajectory and constructs the individual encoding method, mutation strategy, and constraint handling method from the Differential Evolution (DE) algorithm, enabling DE to be directly applied to train trajectory optimization. The trajectory is spatially... As the independent variable, the interval is evenly divided into... There are several nodes. A mapping is performed between the objective and variables, and the objective function is approximately discretized into... All individuals violating the constraints are dealt with according to the penalty strategy to ensure scheduling safety and engineering feasibility. In this embodiment, the population size is initially set to 100, the scaling factor ranges from [0.45, 0.8], the crossover probability ranges from [0, 1], and the evolution terminates when the number of iterations reaches 10,000. The specific steps include:

[0082] Step 1: Divide the interval Average score Each node, index ,Location The discrete variable is the velocity vector: The population is initialized using random uniformity. Each individual must pass a constraint check, and illegal solutions are eliminated. If an individual satisfies all constraints, it is retained; otherwise, a simple projection / repair is attempted (e.g., truncating the out-of-bounds velocity to...). Alternatively, local linear interpolation can be performed to repair the violated acceleration points; if repair fails, the individual is discarded and randomly regenerated until the population is full or the retry limit is reached. That is, when a local constraint is violated in an individual's velocity sequence, the violating segment is reconstructed through linear interpolation between the nearest feasible nodes, combined with velocity limits and acceleration checks, to achieve local repair of the velocity trajectory, ensuring dynamic feasibility while avoiding overall individual failure. Adopting a feasibility-first strategy can improve subsequent computational efficiency (when using a preference-penalty approach, it is also possible to directly assign...). ).

[0083] Step 2: Construct an evaluation function for an individual, given a certain velocity trajectory. Precise calculation of the target and detection constraints is required. For each interval k, the squared velocity is represented as: Approximate spatial derivative Using finite differences within an interval: The acceleration is The required power is broken down into and ,when hour, , ;when At that time, try to use regenerative braking force (motor) feedback. Assume ideal electric braking force. (Negative value), but must meet the lower limit of electrical regeneration capability. (Negative number). When Exceeding Then it is determined to be infeasible. Calculate the specific power and losses on the grid side. ,in, It's the power ratio at the wheels, and the power ratio due to traction chain losses. Therefore, the objective function value per meter is The cumulative target total is .

[0084] Step 3: For the high-dimensional, strongly constrained, and non-convex optimization problem formed by the above energy consumption model, traditional differential evolution algorithms are prone to premature convergence and a low proportion of feasible solutions during the search process. Therefore, this invention makes targeted improvements to the differential evolution algorithm to adapt it to the characteristics of the train trajectory optimization problem. In the mutation phase, an adaptive multi-strategy mutation mechanism based on population diversity is introduced. By evaluating the population fitness distribution in real time, the DE / rand / 1 strategy is adopted to enhance the global search capability when the population is in a high-diversity stage; when the population tends to converge, the weight of the DE / best / 1 strategy is increased to accelerate the convergence speed. This adaptive multi-strategy mutation operator achieves a dynamic balance between exploration and development, effectively suppressing premature convergence and improving the algorithm's global optimization capability. The expression for DE / rand / 1 is: The expression for DE / best / 1 is: ,in, It is the first The individual's variation vector, , and These are three distinct individual vectors randomly selected from the population. It is the best individual in the current population and It is the differential scaling factor, also known as the step size.

[0085] Step 4: Record historical excellent solution paths to guide individual searches; introduce perturbations for individuals trapped in local optima to increase the probability of escaping local optima. In the... In generational evolution, record the globally optimal individual. Historical trajectory ,in When the number of stagnant individuals reaches 10, the population is considered to be trapped in a local optimum, and as an optional implementation method, the following approach is used: New individuals are generated to replace stagnant individuals. This mechanism increases the diversity of local searches when the algorithm stagnates, significantly improving the probability of escaping local optima.

[0086] Step 5: Use binomial crossover to ensure that new individuals are generated within the feasible space, applying crossover probabilities to each dimension of the individual. Inherited from the mutation vector, otherwise the value of the corresponding dimension of the original individual is retained. This mechanism effectively ensures that new individuals fall within the feasible space while maintaining population diversity, avoiding constraint violations, and selectively retains the best individuals based on the objective function value.

[0087] Step 6: Use a "penalty function" to handle constraint conflicts, ensuring that generated individuals meet scheduling safety. When an individual does not meet the constraints, assign a value to its solution. .

[0088] This invention constructs an objective function using trajectory optimization along spatial coordinates s (track distance variable), and accurately characterizes the electrical energy input of the train during operation through integral form, thereby achieving more accurate and engineered energy consumption optimization.

[0089] The present invention adopts the above technical solution, and compared with the prior art, the present invention has the following beneficial effects:

[0090] 1. This invention explicitly incorporates the nonlinear characteristics of the entire traction chain, including motor copper losses, iron losses, inverter switching losses, gearbox mechanical losses, and auxiliary system losses, to construct an energy consumption model that closely reflects the actual operating state of the equipment. This ensures that the trajectory optimization process is based on the actual characteristics of the equipment, effectively guaranteeing the consistency of energy consumption assessment and control strategies, and significantly improving the engineering feasibility of the optimization results. 2. This invention establishes a distribution model of regenerative electric braking power and non-regenerative mechanical braking force, accurately characterizing the traction chain capacity limitations, regenerative absorption capacity, and regenerative overflow mechanism. This ensures that the generated trajectory strictly meets the physical constraints of actual braking force, avoiding defects in unexecutable braking strategies and guaranteeing the safety and reliability of the train braking process. 3. This invention strictly embeds track constraints such as speed limits, gradients, and curves, as well as equipment and operational constraints such as upper limits for electric braking, upper limits for mechanical braking force, and longitudinal dynamics into the optimization framework. This ensures that the train speed and acceleration meet dynamic feasibility conditions in all spatial positions, allowing the optimized trajectory to be directly sent to the train control system for execution without secondary correction. 4. This invention uses spatial position 's' as the independent variable to construct the model, naturally mapping parameters such as air resistance, slope, and speed limit curve to the optimization framework. This avoids the complex state transformation process and numerical instability issues caused by time-domain modeling, while ensuring the accuracy of energy consumption expression and significantly improving the convergence stability of the optimization process. 5. The improved differential evolution algorithm proposed in this invention significantly improves the algorithm's performance in high-dimensional, strongly constrained nonlinear optimization problems by introducing a multi-strategy adaptive mutation mechanism, a population diversity determination mechanism, and a historical trajectory-guided perturbation mechanism. Compared with the traditional differential evolution algorithm, this method effectively avoids premature convergence, increases the proportion of feasible solutions, and accelerates the convergence speed, thereby obtaining a better energy-saving trajectory under complex energy consumption models and enhancing the method's engineering practicality and robustness. Comparative experiments verify that the method of this invention significantly improves the convergence speed and energy consumption optimization results compared to the standard differential evolution algorithm under the same conditions.

[0091] Obviously, the described embodiments are only a part of the embodiments of this application, not all of them. Without conflict, the embodiments and features in the embodiments of this application can be combined with each other. The components of the embodiments of this application described and illustrated herein can generally be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of this application is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

Claims

1. A method for energy-saving optimization of rail trains based on intelligent algorithms, characterized in that: It includes the following steps: Constructing the energy consumption objective function under continuous conditions: Based on the nonlinear loss model of electric traction force, mechanical braking force, and traction chain, a continuous energy consumption objective function is constructed. , ,in, It is the total distance of the route. It is a state variable. , It has already traveled to a certain distance Time, It is the distance traveled speed of time The square of, It is a control variable. , When it is positive, it is traction force; conversely, It is regenerative braking; As a mechanical braking force, it is always positive; To travel to the distance The total loss of all components at that time; Establish constraints: Based on the train equipment capacity and track characteristics, establish constraints for train operation. These constraints should include at least electric traction constraints, mechanical braking force constraints, track speed limit constraints, travel time constraints, and traction chain losses. The energy consumption objective function under continuous conditions is discretized into intervals: in the spatial domain, the train running line is uniformly divided into N nodes based on the total distance S of the line, and a discretized velocity vector is formed based on the velocity of each node. ;in, This represents the velocity of the k-th node. The energy consumption objective function is expressed in discrete space as follows: ; For the electric traction force of the k-th node, This represents the total specific loss of the k-th node; The distance between two adjacent nodes; Based on the energy consumption objective function and constraints, an improved differential evolution algorithm is used to optimize the velocity vector using an adaptive mutation operator with at least two mutation strategies to obtain the optimal velocity for each node. Specifically, the train travel distance *s* is used as the individual code, and new individuals are generated within the feasible space through binomial crossover. Individuals that do not meet the constraints undergo feasibility processing. During the evolutionary stage, the corresponding mutation strategy is dynamically selected to generate a mutation vector for each individual, and the optimal velocity for each node is obtained by optimizing based on the individual fitness distribution. The velocity vectors based on each node are then discretized. As a population, when the population gets stuck in a local optimum, a perturbation mechanism based on the historical optimal trajectory is introduced to generate new individuals to replace the stagnant individuals; Output the optimal speed of each node as the control command for energy-saving train operation.

2. The energy-saving optimization method for rail trains based on intelligent algorithms according to claim 1, characterized in that: The formula for calculating the total loss of all components is as follows: ,in, It is the transformer loss. It is the loss of the motor and converter. It is the wear and tear of auxiliary equipment. It's wear and tear on the gearbox.

3. The energy-saving optimization method for rail trains based on intelligent algorithms according to claim 1, characterized in that: The total specific loss of the kth node is The total specific loss is based on the corresponding regenerative braking. and speed The calculation of nonlinear relationships, total specific loss The expression is as follows: ； in, and These are the constant efficiencies for traction and regenerative braking, respectively.

4. The energy-saving optimization method for rail trains based on intelligent algorithms according to claim 3, characterized in that: and The value is 0.

73.

5. The energy-saving optimization method for rail trains based on intelligent algorithms according to claim 1, characterized in that: Mutation strategies include the DE / rand / 1 strategy and the DE / best / 1 strategy; The method for determining population diversity is as follows: when the fitness value of the offspring population is greater than that of the parent population, the current population is considered to be stagnant; if the number of stagnant generations of the population is greater than 10 during the evolutionary process, the population diversity is considered to be low, and vice versa; when the population diversity is high, the DE / rand / 1 strategy is adopted to enhance the global search capability; when the population gradually converges, the weight of the DE / best / 1 strategy is increased to accelerate the local convergence speed.

6. The energy-saving optimization method for rail trains based on intelligent algorithms according to claim 5, characterized in that: The expression for DE / rand / 1 is: ; The expression for DE / best / 1 is: , in, It is the first The individual's variation vector, , and These are three distinct individual vectors randomly selected from the population. It is the best individual in the current population; It is the differential scaling factor.

7. The energy-saving optimization method for rail trains based on intelligent algorithms according to claim 1, characterized in that: New individuals are generated based on a perturbation mechanism using historical best trajectories. The expression is: ； in, For the first Global optimal individual in generational evolution The historical trajectory; , and These are three distinct individual vectors randomly selected from the population. It is the differential scaling factor. For the historical trajectory The weighting coefficients.

8. The energy-saving optimization method for rail trains based on intelligent algorithms according to claim 1, characterized in that: The constraints include: (1) Electric traction force constraint: ,in, This refers to the magnitude of the train's electric traction force; The distance is the route distance. The maximum value of the electric traction force is determined by the minimum value among the limits of the traction system, the power limit, and the acceleration constraint. The minimum electric traction force is determined by the maximum value among the braking system limits, regenerative power limits, and comfort constraints. (2) Mechanical braking force constraint: ,in, The magnitude of the train's mechanical braking force; The maximum mechanical braking force that the brake can provide; (3) Speed ​​limit constraints on the line: Or ,in, For train speed; For train speed The square of; The upper limit of the line speed is set according to the infrastructure conditions such as the speed limit of the track section, the curve radius, and the gradient; (4) Resistance constraints: ,in, This represents the total resistance of the train. It is rolling resistance. It's air resistance. It is the additional resistance of the curve. It is slope resistance; (5) Traction chain wear: ,in, For the wear and tear of the traction chain; These are losses in the motor and converter. It is transformer loss. It is gearbox mechanical wear. It is the wear and tear of auxiliary equipment; (6) Travel time constraints: ,in, The total time taken for the train to complete the line. To set an upper limit on the total time taken for the train to reach its destination; (7) Boundary condition constraints: , , The squares of the train's speeds at the starting and ending points satisfy the boundary requirements, where ; Indicates the start time. Starting speed The square of, Speed ​​at the destination The square of.

9. The energy-saving optimization method for rail trains based on intelligent algorithms according to claim 1, characterized in that: Individuals that do not meet the constraints are handled using a "penalty function," which assigns an infinite value to individuals that do not meet the constraints in order to mark them for elimination.

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