Magnetic latching relay optimization method based on prison-trapping dilemma cracking game theory

Abstract

The invention relates to the technical field of magnetic latching relay parameter optimization design analysis, and discloses a magnetic latching relay optimization method based on the game theory of'cracking prisoner dilemma ', and the method comprises the steps: selecting the width of a biased magnetic steel, the width of an iron core pole face, the diameter of an iron core and the width of an armature as optimization variables; establishing an optimization model aiming at increasing the positioning torque and reducing the anti-position torque based on NSGA-II; then, a variable coefficient method and a CRITIC method are fused, and a positioning torque and reverse torque dual-index weight model is established; then setting a positioning torque and anti-position torque double-index weight model occupancy rate, introducing a third-party penalty mechanism to crack'capturer dilemma ', and establishing a multi-target weight loss model of a Pareto optimal solution set of the magnetic latching relay; and finally, the difference between the weighted torque sample and the ideal weighted torque sample is calculated based on TOPSIS, the weighted torque sample with the minimum difference with the ideal weighted torque sample is used as a multi-target optimal solution, and the optimal cooperation of the positioning torque and the anti-position torque is obtained.

Description

Technical Field

[0001] The invention relates to the technical field of magnetic latching relay parameter optimization design and analysis, in particular to a magnetic latching relay optimization method based on "breaking the prisoner's dilemma" game theory. Background Art

[0002] The magnetic latching relay with multi-reed structure is widely used in railway systems, responsible for signal transmission and logic control in rail transit. Especially in high-speed rail systems, it controls the working mode of signal machines and reflects the driving status of trains, and its performance directly affects the safety of high-speed rail system operation.

[0003] Traditional electrical appliance optimization design uses experimental design methods represented by orthogonal experiments, which are suitable for single-objective optimization and have a limited optimization range. Modern electrical appliance optimization design is a multi-objective optimization problem with multiple constraints, nonlinearity, non-convexity and non-differentiability, and traditional experimental design methods are limited. Therefore, it is necessary to start from the topological structure of the magnetic latching relay and carry out optimization design of the characteristic parameters such as the armature torque, pull-in time and bounce time of the magnetic latching relay. Summary of the invention

[0004] The purpose of the present invention is to solve the above problems and to design a magnetic latching relay optimization method based on the game theory of "breaking the prisoner's dilemma".

[0005] To achieve the above-mentioned purpose, the technical solution of the present invention is a magnetic latching relay optimization method based on the game theory of "breaking the prisoner's dilemma", which comprises the following steps:

[0006] Step 1: Select the polarized magnetic steel width, core pole face width, core diameter, and armature width as optimization variables, and establish an optimization model based on NSGA-II to increase the detent torque and reduce the reverse torque;

[0007] Step 2: The coefficient of variation method and CRITIC method are integrated to establish a dual-index weight model of positioning torque and anti-position torque;

[0008] Step 3: Set the occupancy rate of the dual-index weight model of positioning torque and anti-position torque, introduce a third-party penalty mechanism to solve the "prisoner's dilemma", and establish a multi-objective weight loss model of the Pareto optimal solution set of the magnetic latching relay;

[0009] Step 4: Calculate the gap between the weighted torque sample and the ideal weighted torque sample based on TOPSIS, and take the weighted torque sample with the smallest gap with the ideal weighted torque sample as the multi-objective optimal solution to obtain the best match between the positioning torque and the anti-positioning torque.

[0010] The specific steps of NSGA-II in step 1 are:

[0011] 1) Randomly generate optimization variables and objective functions of parent magnetic latching relays as parent populations;

[0012] 2) Calculate the fast non-dominated level and congestion degree of the optimization variables and objective function of the parent generation magnetic latching relay;

[0013] 3) Perform tournament selection, crossover, and mutation operations on the optimization variables and objective functions of the parent generation magnetic latching relay to generate a descendant population;

[0014] 4) Merge the optimization variables and objective functions of the parent and child magnetic latching relays as a new population;

[0015] 5) Perform fast non-dominated sorting and congestion sorting on the newly generated optimization variables and objective functions;

[0016] 6) Keep the top-ranked optimization variables and objective functions to form the next generation parent population;

[0017] 7) If the number of iterations is not greater than the maximum value, go to step 2 to continue iterating; otherwise, output the optimal solution set.

[0018] In the step 1, increasing the detent torque and reducing the counter-torque can effectively reduce the closing speed and closing time of the magnetic latching relay with a multi-reed structure. To this end, increasing the detent torque and reducing the counter-torque are set as optimization goals, and the optimization is performed 500 times to obtain a stable Pareto optimal solution set.

[0019] The increase of positioning torque will cause the increase of anti-position torque, and the two cannot obtain the optimal value at the same time during the optimization process. Considering the non-dominance characteristics of the Pareto optimal solution set, the coefficient of variation method and CRITIC method are introduced to analyze the weights of the positioning torque and anti-position torque in the Pareto optimal solution, and the Pareto optimal solution set after comprehensive decision-making multi-objective optimization is determined.

[0020] The specific process of the coefficient of variation method in step 2 is as follows:

[0021] 1) Calculate the mean of indicator data:

[0022]

[0023] In the formula, μ″ j is the mean of indicator j, n is the number of sample data for each indicator, x″ ij It is the preprocessed indicator data.

[0024] 2) Calculate the standard deviation of indicator data:

[0025]

[0026] In the formula, σ″ j is the standard deviation of indicator j.

[0027] 3) Calculate the coefficient of variation of the indicator:

[0028]

[0029] In the formula, CV″ j is the coefficient of variation of indicator j.

[0030] 4) Calculate the weight of the index coefficient of variation method:

[0031]

[0032] The specific process of the CRITIC method in step 2 is as follows:

[0033] 1) Calculate the mean and standard deviation of the indicator data:

[0034]

[0035] In the formula, μ″ j is the mean value of index j; σ″ j is the standard deviation of indicator j.

[0036] 2) Conflict of calculation indicator data:

[0037]

[0038] In the formula, R″ ij is the conflict between indicators i and j; r″ ij is the correlation coefficient between indicators i and j.

[0039] 3) The product of contrast intensity and conflict is the amount of information in the indicator data:

[0040] C″ j =σ″ j ×R″ j (7)

[0041] In the formula, C″ j is the information content of index j, C″ j The larger it is, the greater the weight of indicator j is.

[0042] 4) Calculate the weight of the CRITIC method:

[0043]

[0044] The Nash equilibrium point of the prisoner's dilemma in game theory in step 3 is not the collective optimal solution. The third-party punishment mechanism is introduced to crack the prisoner's dilemma and make the Nash equilibrium point the collective optimal solution. Based on the game theory of "cracking the prisoner's dilemma", considering the behavior of the prisoner to maximize profit, the loss must be minimized, and the multi-objective weight loss model of the Pareto optimal solution set of the magnetic latching relay is established as follows:

[0045]

[0046] Where Loss(α) is the total weight loss; α=[α1,α2,…,α g ,…,α (l-1) ,α l ] is the weight model occupancy; u=[u1,u2,…,u (l-1) ,u l ] is the basic weight; l and m are the number of weight models and the number of optimization targets. Let x = [x1, x2, …, x (n-1) ,x n ],y=[y1,y2,…,y (n-1) ,y n ],definition Get the combined weight ω=[ω1,ω2,…,ω (l-1) ,ω l ]=αu.

[0047] In step 3, the psychological tolerance of prisoners is considered, and the result must be balanced. Based on the equal division method, the weight model occupancy is evenly divided, and the balance occupancy is introduced to avoid extreme phenomena. The occupancy is expressed as:

[0048]

[0049] In the formula, α av is the average occupancy rate; τ=[τ1,τ2,…,τ l-1 ,τ l ] is the balance degree. Assuming that the prisoners have the same psychological tolerance, the balance degree of the weight model is 0.5; α min , α max is the minimum and maximum occupancy rate within the equilibrium degree; It is Hadamard.

[0050] The specific steps of the TOPSIS method in step 4 are:

[0051] 1) Perform weighted processing on the torque sample matrix in equation (11) so that it satisfies equation (12).

[0052] 2) Determine the positive and negative ideal weighted torques. The positive and negative ideal weighted torques are the ideal optimal value and ideal worst value that the indicator in the sample can achieve.

[0053]

[0054] In the formula, is the weighting matrix.

[0055] 3) Calculate the distance between the weighted torque sample and the positive and negative ideal weighted torque samples, expressed as:

[0056]

[0057] Where D + , D - is the distance between the weighted torque sample and the positive and negative ideal weighted torque samples; They are the ideal optimal value and ideal worst value of weighted positioning torque and weighted anti-positioning torque respectively.

[0058] 4) Calculate the proximity index between the weighted torque sample solution and the ideal optimal solution, expressed as:

[0059]

[0060] In the formula, CL i is the proximity index of weighted torque sample solution i.

[0061] The weighted torque sample solution close to the maximum index is taken as the optimal solution.

[0062] Beneficial Effects

[0063] The magnetic latching relay optimization method based on the game theory of "breaking the prisoner's dilemma" produced by the technical solution of the present invention has the following advantages:

[0064] Traditional electrical appliance optimization design uses experimental design methods represented by orthogonal experiments, which are suitable for single-objective optimization and have a limited optimization range. Modern electrical appliance optimization design is a multi-constrained, nonlinear, non-convex and non-differentiable multi-objective optimization problem, and traditional experimental design methods are limited. Electrical appliances with multiple magnetic steels and multiple reed structures have complex topologies, and the number of optimization factors and levels increases; at the same time, in order to fully represent the sample space, the number of experimental sample points increases dramatically, and the number of experiments increases, which increases the difficulty of optimization and reduces the matching degree of traditional design methods.

[0065] Intelligent optimization algorithms such as genetic algorithms and particle swarm algorithms are prone to fall into local optimal solutions during the optimization process, reducing the convergence speed and optimization accuracy.

[0066] At present, when making multi-objective optimization decisions for electrical appliances, the linear weighted method is mostly used to transform the multi-objective optimization into a single objective, and the weight of the objective function is determined based on the empirical method or the subjective and objective weighting method, which is highly subjective.

[0067] When optimizing the design of electrical appliances with multiple magnetic steels and multiple reed structures, this method takes into account the characteristics and performance of complex structures such as multiple reeds, ensuring that the optimization method can obtain the global optimal solution when the number of iterations is small; introduces the Pareto optimal solution set, converges multiple optimization objectives to the Pareto optimal frontier, gets rid of the shortcoming of relying on subjective experience to transform multiple objectives into a single objective, effectively solves the problem of poor representativeness of the optimal solution of multi-objective optimization design, and meets the goal of electrical appliance optimization design; combines the Pareto solution set with the weighting method to obtain the multi-objective optimal solution and improve the optimization effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 It is a structural schematic diagram of the magnetic latching relay optimization method based on the "breaking the prisoner's dilemma" game theory of the present invention. DETAILED DESCRIPTION

[0069] The present invention will be described in detail below in conjunction with the accompanying drawings. Figure 1 As shown;

[0070] A method for optimizing the parameters of a magnetic latching relay based on the game theory of "breaking the prisoner's dilemma" is described. The specific steps are as follows:

[0071] (1) Firstly, the width of the polarized magnet, the width of the core pole surface, the core diameter and the armature width are selected as optimization variables, and an optimization model is established based on NSGA-II with the goal of increasing the detent torque and reducing the reverse torque.

[0072] NSGA-Ⅱ schematic diagram Figure 1 As shown, the specific steps are:

[0073] 1) Randomly generate optimization variables and objective functions of parent magnetic latching relays as parent populations;

[0074] 2) Calculate the fast non-dominated level and congestion degree of the optimization variables and objective function of the parent generation magnetic latching relay;

[0075] 3) Perform tournament selection, crossover, and mutation operations on the optimization variables and objective functions of the parent generation magnetic latching relay to generate a descendant population;

[0076] 4) Merge the optimization variables and objective functions of the parent and child magnetic latching relays as a new population;

[0077] 5) Perform fast non-dominated sorting and congestion sorting on the newly generated optimization variables and objective functions;

[0078] 6) Keep the top-ranked optimization variables and objective functions to form the next generation parent population;

[0079] 7) If the number of iterations is not greater than the maximum value, go to step 2 to continue iterating; otherwise, output the optimal solution set.

[0080] Increasing the positioning torque and reducing the anti-positioning torque were set as the optimization objectives, and after 500 iterations, a stable Pareto optimal solution set was obtained.

[0081] (2) The coefficient of variation method and CRITIC method were integrated to establish a weight model.

[0082] The coefficient of variation method and CRITIC method are introduced to analyze the weights of the dual indicators of positioning torque and anti-positioning torque in the Pareto optimal solution, and the Pareto optimal solution set after comprehensive decision-making multi-objective optimization is determined.

[0083] The specific process of the coefficient of variation method is:

[0084] 1) Calculate the mean of indicator data:

[0085]

[0086] In the formula, μ″ j is the mean value of indicator j.

[0087] 2) Calculate the standard deviation of indicator data:

[0088]

[0089] In the formula, σ″ j is the standard deviation of indicator j.

[0090] 3) Calculate the coefficient of variation of the indicator:

[0091]

[0092] In the formula, CV″ j is the coefficient of variation of indicator j.

[0093] 4) Calculate the weight of the index coefficient of variation method:

[0094]

[0095] The specific process of CRITIC method is as follows:

[0096] 1) Calculate the mean and standard deviation of the indicator data:

[0097]

[0098] In the formula, μ″ j is the mean value of index j; σ″ j is the standard deviation of indicator j.

[0099] 2) Conflict of calculation indicator data:

[0100]

[0101] In the formula, R″ij is the conflict between indicators i and j; r″ ij is the correlation coefficient between indicators i and j.

[0102] 3) The product of contrast intensity and conflict is the amount of information in the indicator data:

[0103] C″ j =σ″ j ×R″ j (7)

[0104] In the formula, C″ j is the information content of index j, C″ j The larger it is, the greater the weight of indicator j is.

[0105] 4) Calculate the weight of the CRITIC method:

[0106]

[0107] (3) Set the weight model occupancy rate, introduce a third-party penalty mechanism to solve the "prisoner's dilemma", and establish a weight loss model.

[0108] Based on the game theory of "breaking the prisoner's dilemma", a multi-objective weight loss model of the Pareto optimal solution set of the magnetic latching relay is established as follows:

[0109]

[0110] Where Loss(α) is the total weight loss; α=[α1,α2,…,α g ,…,α (l-1) ,α l ] is the weight model occupancy; u=[u1,u2,…,u (l-1) ,u l ] is the basic weight; l and m are the number of weight models and the number of optimization targets. Let x = [x1, x2, …, x (n-1) ,x n ],y=[y1,y2,…,y (n-1) ,y n ],definition Get the combined weight ω=[ω1,ω2,…,ω (l-1) ,ω l ]=αu.

[0111] Based on the equal division method, the weight model occupancy is evenly divided, and the balance occupancy is introduced. The occupancy is expressed as:

[0112]

[0113] In the formula, α av is the average occupancy rate; τ=[τ1,τ2,…,τl-1 ,τ l ] is the balance degree. Assuming that the prisoners have the same psychological tolerance, the balance degree of the weight model is 0.5; α min , α max is the minimum and maximum occupancy rate within the equilibrium degree; It is Hadamard.

[0114] (4) Based on TOPSIS, the gap between the weighted torque sample and the ideal weighted torque sample is calculated. The weighted torque sample with the smallest gap with the ideal weighted torque sample is taken as the multi-objective optimal solution to obtain the best match between the positioning torque and the anti-positioning torque.

[0115] The specific steps of TOPSIS method are:

[0116] 1) Perform weighted processing on the torque sample matrix in equation (11) so that it satisfies equation (12).

[0117] 2) Determine the positive and negative ideal weighted torques, which are the ideal optimal value and ideal worst value that the indicator in the sample can achieve.

[0118]

[0119] In the formula, is the weighting matrix.

[0120] 3) Calculate the distance between the weighted torque sample and the positive and negative ideal weighted torque samples. It can be expressed as:

[0121]

[0122] Where D + , D - is the distance between the weighted torque sample and the positive and negative ideal weighted torque samples; They are the ideal optimal value and ideal worst value of weighted positioning torque and weighted anti-positioning torque respectively.

[0123] 4) Calculate the proximity index between the weighted torque sample solution and the ideal optimal solution, expressed as:

[0124]

[0125] In the formula, CL i is the proximity index of weighted torque sample solution i.

[0126] The weighted torque sample solution close to the maximum index is taken as the optimal solution.

[0127] In view of the limited optimization range and reduced matching degree of the traditional design method of magnetic latching relay, the present invention proposes a magnetic latching relay parameter optimization method based on the game theory of "breaking the prisoner's dilemma". The present invention can effectively reduce contact bounce, reduce contact wear, extend the electrical life of the contact, and improve the reliability of the magnetic latching relay with a multi-reed structure.

[0128] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions. The sentence "includes an element defined by..." does not exclude the existence of other identical elements in the process, method, article or device including the element. The above technical solution only embodies the preferred technical solution of the technical solution of the present invention. Some changes that may be made to some parts by technicians in this technical field all embody the principles of the present invention and belong to the protection scope of the present invention.

Claims

1. A magnetic latching relay optimization method based on the game theory of "breaking the prisoner's dilemma", characterized in that: The method includes the following steps: Select optimization variables and establish an optimization model based on NSGA-II; A dual-index weight model of positioning torque and counter-positioning torque is established; Set the occupancy rate of the dual-index weight model, introduce a third-party penalty mechanism to solve the "prisoner's dilemma", and establish a multi-objective weight loss model for the Pareto optimal solution set of the magnetic latching relay; The gap between the weighted torque sample and the ideal weighted torque sample is calculated based on TOPSIS, and the weighted torque sample with the smallest gap with the ideal weighted torque sample is taken as the multi-objective optimal solution to obtain the best coordination of positioning torque and anti-positioning torque.

2. The magnetic latching relay optimization method based on the "breaking the prisoner's dilemma" game theory according to claim 1 is characterized in that: The optimization variables include but are not limited to: polarized magnetic steel width, core pole face width, core diameter and armature width. The optimization model established based on NSGA-II aims to increase the positioning torque and reduce the reverse torque.

3. The magnetic latching relay optimization method based on the "breaking the prisoner's dilemma" game theory according to claim 1 is characterized in that: The process of establishing the optimization model based on NSGA-II includes: 1) Randomly generate optimization variables and objective functions of parent magnetic latching relays as parent populations; 2) Calculate the fast non-dominated level and congestion degree of the optimization variables and objective function of the parent generation magnetic latching relay; 3) Perform tournament selection, crossover, and mutation operations on the optimization variables and objective functions of the parent generation magnetic latching relay to generate a descendant population; 4) Merge the optimization variables and objective functions of the parent and child magnetic latching relays as a new population; 5) Perform fast non-dominated sorting and congestion sorting on the newly generated optimization variables and objective functions; 6) Keep the top-ranked optimization variables and objective functions to form the next generation parent population; 7) If the number of iterations is not greater than the maximum value, go to step 2 to continue iterating; otherwise, output the optimal solution set.

4. The magnetic latching relay optimization method based on the "breaking the prisoner's dilemma" game theory according to claim 1 is characterized in that: The dual index weight model is established by introducing the coefficient of variation method and the CRITIC method to calculate the dual index weights of the positioning torque and the counter-positioning torque.

5. The magnetic latching relay optimization method based on the "breaking the prisoner's dilemma" game theory according to claim 4 is characterized in that: The specific process of calculating the weights of the dual indicators using the coefficient of variation method is as follows: 1) Calculate the mean of indicator data: In the formula, μ″ j is the mean of indicator j, n is the number of sample data for each indicator, x″ ij is the preprocessed indicator data; 2) Calculate the standard deviation of indicator data: In the formula, σ″ j is the standard deviation of indicator j; 3) Calculate the coefficient of variation of the indicator: In the formula, CV″ j is the coefficient of variation of indicator j; 4) Calculate the weight of the index coefficient of variation method:

6. The magnetic latching relay optimization method based on the "breaking the prisoner's dilemma" game theory according to claim 4 is characterized in that: The specific process of calculating the weights of the dual indicators by the CRITIC method is as follows: 1) Calculate the mean and standard deviation of the indicator data: In the formula, μ″ j is the mean value of index j; σ″ j is the standard deviation of indicator j; 2) Conflict of calculation indicator data: In the formula, R″ ij is the conflict between indicators i and j; r″ ij is the correlation coefficient between indicators i and j; 3) The product of contrast intensity and conflict is the amount of information in the indicator data: C″ j =s″ j ×R″ j (7) In the formula, C″ j is the information content of index j, C″ j The larger it is, the greater the weight of indicator j; 4) Calculate the weight of the CRITIC method:

7. The magnetic latching relay optimization method based on the "breaking the prisoner's dilemma" game theory according to claim 1 is characterized in that: The multi-objective weight loss model is as follows: Where Loss(α) is the total weight loss; α=[α1,α2,…,α g ,…,α (l-1) ,α l ] is the weight model occupancy; u=[u1,u2,…,u (l-1) ,u l ] is the basic weight; l and m are the number of weight models and the number of optimization targets respectively; let x = [x1, x2, …, x (n-1) ,x n ],y=[y1,y2,…,y (n-1) ,y n ],definition Get the combined weight ω=[ω1,ω2,…,ω (l-1) ,ω l ]=αu.

8. The magnetic latching relay optimization method based on the "breaking the prisoner's dilemma" game theory according to claim 1 is characterized in that: The dual-index weight model occupancy rate is expressed as: In the formula, α av is the average occupancy rate; τ=[τ1,τ2,…,τ l-1 ,τ l ] is the balance degree. Assuming that the prisoners have the same psychological tolerance, the balance degree of the weight model is 0.5; α min and α max is the minimum and maximum value of the occupancy rate within the equilibrium degree; It is Hadamard.

9. The magnetic latching relay optimization method based on the "breaking the prisoner's dilemma" game theory according to claim 1 is characterized in that: The steps of calculating the gap between the weighted torque sample and the ideal weighted torque sample by the TOPSIS method are as follows: 1) Weighting the torque sample matrix in equation (11) to satisfy equation (12); 2) Determine the positive and negative ideal weighted torques, which are the ideal optimal value and ideal worst value that the indicator can achieve in the sample; In the formula, is the weighting matrix; 3) Calculate the distance between the weighted torque sample and the positive and negative ideal weighted torque samples, expressed as: Where D + , D - is the distance between the weighted torque sample and the positive and negative ideal weighted torque samples; They are the ideal optimal value and the ideal worst value of the weighted positioning torque and the weighted counter-positioning torque respectively; 4) Calculate the proximity index between the weighted torque sample solution and the ideal optimal solution, expressed as: In the formula, CL i is the proximity index of weighted torque sample solution i; The weighted torque sample solution close to the maximum index is taken as the optimal solution.

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