Magnetic track brake design method based on radial basis function neural network

Abstract

The invention relates to the technical field of magnetic track brake design, and discloses a magnetic track brake design method based on a radial basis function neural network. Basic data of the magnetic track brake to be optimized are measured and obtained, and a finite element model is constructed; obtaining design factors of the finite element model, screening the factors in combination with principal component analysis to obtain key factors, and obtaining a value range of the key factors according to an orthogonal test; latin hypercube sampling is carried out in the value range; simulating a performance response value of the magnetic track brake according to a sampling result, constructing a sample set according to the key factors and the performance response value, and constructing a magnetic track brake prediction model based on the sample set in combination with a radial basis function neural network; a multi-target genetic algorithm framework is embedded according to the magnetic track brake prediction model, the maximum suction force and the minimum brake mass serve as target functions to solve and obtain a Pareto target solution set, and the magnetic track brake is designed based on the Pareto target solution set. The problem that only a single factor is considered in the design process of an existing magnetic track brake is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetic rail brake design, and in particular to a magnetic rail brake design method based on radial basis function neural network. Background Art

[0002] With the rapid development of permanent magnet materials, the magnetic properties of NdFeB have been gradually developed. Existing NdFeB has extremely high magnetic energy product and coercive force, as well as the advantages of high energy density. The maximum operating temperature can reach 200°C, providing a solid foundation for the realization of permanent magnet rail brakes.

[0003] Permanent magnet rail brakes are widely used in various engineering machinery fields due to their strong suction force, simple structure and high reliability. The essential difference between permanent magnet rail brakes and electromagnetic rail brakes is that, except for the driving force required to drive the permanent magnet to flip in the initial stage of braking, permanent magnet rail brakes no longer require an external power source once braking. Therefore, during emergency braking, permanent magnet rail brakes have fast response, high reliability and do not require batteries to provide energy. When the train is parked on a slope, the brake can still be in working condition and can be maintained for a long time without external energy supply, so it can be used for anti-skid braking when the train is parked. For example, the patent document with publication number CN101708728B provides a component structure of a permanent magnet rail brake, but the most important design point of the permanent magnet brake is how to ensure that the working suction force is maximized under a certain weight, or to minimize the structural weight while meeting the suction force requirements. The weight and working suction of a permanent magnet brake have a strongly nonlinear relationship with its structural parameters, and increasing each parameter individually cannot improve brake performance. For example, increasing the volume of the permanent magnet does not necessarily increase its working suction. Finding an effective design method is the only way to achieve engineering success for permanent magnet brakes.

[0004] However, current research on permanent magnet brake design at home and abroad mainly focuses on: conducting single-factor analysis on the parameters of permanent magnet brakes to obtain the impact of each parameter on performance indicators, without considering the interaction between the parameters, which makes the results limited. Summary of the Invention

[0005] The present invention provides a magnetic rail brake design method based on radial basis function neural network to solve the problem that only a single factor is considered in the design process of the existing magnetic rail brake.

[0006] In order to achieve the above object, the present invention is implemented through the following technical solutions: The present invention provides a magnetic rail brake design method based on radial basis function neural network, comprising the following steps: Step 1: Measure and obtain the basic data of the magnetic rail brake to be optimized, and build a finite element model based on the basic data; Step 2: Obtain the design factors of the finite element model, and screen the design factors to obtain key factors based on principal component analysis. The value range of the key factors is obtained based on orthogonal experiments. Step 3: Latin hypercube sampling is performed based on the value range of the key factors to obtain sampling results, and the performance response value of the magnetic rail brake is simulated based on the sampling results. A sample set is constructed based on the key factors and the performance response values, and a magnetic rail brake prediction model is constructed based on the sample set and combined with a radial basis function neural network; Step 4: Embed a multi-objective genetic algorithm framework based on the magnetic rail brake prediction model, and use maximum suction force and minimized brake mass as objective functions to obtain the Pareto target solution set, and design the magnetic rail brake based on the Pareto target solution set.

[0007] Among them, when executing step 2, the design factors are preliminarily screened in combination with domain knowledge, and the design factors that theoretically have almost no effect on the system target response are excluded, and then the principal component analysis of the design factors is further performed.

[0008] Furthermore, the basic data includes: box length, box width, box height, chamfer size, permanent magnet length, permanent magnet width, permanent magnet height, magnet gap, magnetic box gap, magnetic isolation position, wear plate thickness, shape, maximum suction force and brake quality.

[0009] Furthermore, step 1 also includes: constructing a physical prototype model based on the braking principle of the magnetic rail brake, and measuring the maximum suction and prototype mass of the physical prototype model, and adjusting the parameters of the finite element model based on the maximum suction and prototype mass, so that the errors between the maximum suction and model mass simulated by the finite element model and the maximum suction and prototype mass measured by the physical prototype model are less than a predetermined threshold.

[0010] Through the above design, the consistent matching between the finite element model and the actual prototype performance can be achieved, effectively improving the simulation accuracy and modeling reliability.

[0011] Furthermore, the screening of design factors in combination with principal component analysis includes: standardizing the design factors to construct a factor matrix, calculating the covariance matrix based on the factor matrix, calculating the eigenvalues ​​of the eigenvectors in the covariance matrix, and sorting and calculating the contribution, and performing factor elimination and screening according to the size of the contribution.

[0012] Through the above design, the complexity of the optimization problem can be effectively reduced, the modeling efficiency and the algorithm convergence speed can be improved; at the same time, the interference of redundant factors on the optimization process can be avoided, and the generalization ability and engineering practicality of the model can be improved.

[0013] Furthermore, the value range of the key factors obtained according to the orthogonal experiment includes: constructing an orthogonal test table for the key factors, and performing data simulation of the finite element model based on the orthogonal test table, recording the suction and quality in each case, obtaining the optimal level combination based on the recorded suction and quality combined with the range analysis, and determining the value range of the key factors based on the optimal level combination.

[0014] Through the above design, it is possible to systematically and efficiently explore the influence of multi-factor interactions on brake performance, obtain representative parameter combinations while reducing the number of experiments, and significantly improve optimization efficiency and modeling accuracy.

[0015] Furthermore, obtaining the optimal level combination based on the suction and quality combined with the range analysis includes: calculating the influence values ​​of various key factors on the suction and quality based on the recorded suction and quality combined with the range analysis, and determining the group with the largest mean of the influence values ​​of the suction and quality as the optimal level combination; The impact value is expressed by the following formula: ; ; ; in, K ji It represents the sum of the response values ​​corresponding to all levels of the j-th key factor in the orthogonal test table; Represents the average response value of the jth key factor in the orthogonal test table; Indicates the range value of the key factor of column j; n is the horizontal number.

[0016] Furthermore, the method of constructing a magnetic rail brake prediction model based on a sample set in combination with a radial basis function neural network includes: constructing a prediction model based on a sample set in combination with a radial basis function neural network, minimizing a prediction error by adjusting a network weight of the prediction model, calculating a judgment coefficient of an approximate model by a cross-validation method, and selecting a corresponding approximate model as the magnetic rail brake prediction model based on the judgment coefficient; The method of selecting a corresponding approximate model as a magnetic rail brake prediction model based on the judgment coefficient includes: based on whether the judgment coefficient exceeds a predetermined threshold, if so, selecting the approximate model as the magnetic rail brake prediction model; if not, retraining and / or adjusting the model parameters of the approximate model until the judgment coefficient of the approximate model exceeds the predetermined threshold.

[0017] This design effectively improves the model's predictive accuracy and generalization capabilities, ensuring the stability and practicality of the constructed radial basis function neural network model in subsequent multi-objective optimization. This method not only reduces the computational overhead of traditional finite element simulation but also provides reliable technical support for achieving efficient and high-precision performance prediction of magnetic rail brakes, demonstrating its strong potential for engineering applications.

[0018] Furthermore, the method of obtaining the Pareto target solution set by using the maximum suction force and the minimum brake mass as the objective function includes: based on the magnetic rail brake prediction model, introducing the minimum suction force constraint and the maximum mass constraint, and gradually searching the Pareto target solution set through the non-dominated sorting genetic algorithm.

[0019] Through the above design, it is possible to effectively balance the contradiction between performance and lightweight in complex multi-objective optimization problems, avoiding the one-sidedness and limitations brought by traditional single-objective optimization methods; at the same time, with the help of the powerful global search capabilities of the intelligent optimization algorithm, design efficiency can be improved.

[0020] Beneficial effects: The present invention provides a magnetic rail brake design method based on a radial basis function neural network. By constructing a radial basis function neural network, the method successfully predicts the performance of permanent magnet brakes of different design sizes, effectively reducing the cost and time overhead associated with the reliance on extensive finite element simulations or physical experiments in traditional designs. The method also uses a trained neural network to replace parts of the numerical simulation process, significantly shortening the design cycle and improving design efficiency. Under the guidance of a multi-objective genetic algorithm, a Pareto optimal solution set was obtained that takes into account multiple design objectives (such as maximum suction and minimum mass). This provides engineers with flexible choices based on different needs in practical applications and provides a reference for the engineering of permanent magnet brakes. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 This is a flow chart of a magnetic rail brake design method based on radial basis function neural network according to embodiment 1 of the present invention; DETAILED DESCRIPTION The following is a clear and complete description of the technical solutions of the present invention. It should be understood that the embodiments described are only a portion of the embodiments of the present invention, not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are intended to fall within the scope of protection of the present invention.

[0022] Unless otherwise defined, the technical or scientific terms used in the present invention shall have the usual meanings understood by persons of ordinary skill in the field to which the present invention belongs. The words "first", "second" and similar terms used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Similarly, words such as "one" or "a" do not indicate a quantity limitation, but rather indicate the existence of at least one. Words such as "connected" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the object being described changes, the relative positional relationship also changes accordingly.

[0023] Example 1 See Figure 1 The embodiment of the present application provides a magnetic rail brake design method based on a radial basis function neural network, comprising the following steps: Step 1: Measure and obtain the basic data of the magnetic rail brake to be optimized, and build a finite element model based on the basic data; Among them, the basic data include: box length, box width, box height, chamfer size, permanent magnet length, permanent magnet width, permanent magnet height, magnet gap, wear plate thickness, shape, maximum suction force and brake mass. Regarding the quantification of the magnetic isolation position and shape, the magnetic isolation position is the relative position of the two magnetic isolation plates, and the shape is defined as 1, 2, and 3 for different types of conventional design shapes.

[0024] In this embodiment, a physical prototype model is also constructed based on the braking principle of the magnetic rail brake, and the maximum suction force and prototype mass of the physical prototype model are measured. Based on the maximum suction force and prototype mass, the grid size and material parameters of the finite element model are adjusted so that the errors between the maximum suction force and model mass simulated by the finite element model and the maximum suction force and prototype mass measured by the physical prototype model are less than 5%.

[0025] The error here is calculated using the following formula: ; in, Indicates error; Indicates the maximum suction force or model mass of the finite element model simulation; Indicates the maximum suction force or prototype mass measured by the physical performance model.

[0026] Step 2: Obtain the design factors of the finite element model, and screen the factors to obtain key factors based on principal component analysis. The value range of the key factors is obtained based on orthogonal experiments. Specifically, after eliminating the design factors that have almost no effect on the target response of the system, the design factors are first standardized to eliminate the influence of different dimensions on the analysis results, and then the factor matrix is ​​constructed. The covariance matrix is ​​calculated based on the factor matrix, the eigenvalues ​​of the eigenvectors in the covariance matrix are calculated, and the contribution is calculated by sorting. Factors are eliminated and screened according to the contribution to obtain key factors, and then an orthogonal test table is constructed for the key factors. The data simulation of the finite element model is performed based on the orthogonal test table, that is, the key factors in the orthogonal test table are combined, involving multiple groups of parameter combinations, and the maximum suction and mass simulated in the finite element model for each parameter combination are recorded. The optimal level combination is obtained based on the recorded maximum suction and mass combined with the range analysis, and the value range of the key factors is determined based on the optimal level combination.

[0027] Regarding the determination of the optimal level combination, the influence values ​​of each key factor on suction and quality are calculated based on the recorded suction and quality combined with range analysis, and the group with the largest mean of the influence values ​​of suction and quality is determined as the optimal level combination; The impact value is expressed by the following formula: ; ; ; in, K ji It represents the sum of the response values ​​corresponding to all levels of the j-th key factor in the orthogonal test table; Represents the average response value of the jth key factor in the orthogonal test table; Indicates the range value of the key factor of column j; n is the horizontal number.

[0028] Step 3: Latin hypercube sampling is performed based on the value range of the key factors to obtain sampling results, and the performance response value of the magnetic rail brake is simulated based on the sampling results. A sample set is constructed based on the key factors and the performance response values, and a magnetic rail brake prediction model is constructed based on the sample set and combined with a radial basis function neural network; A prediction model is constructed based on the sample set combined with a radial neural network. The prediction error is minimized by adjusting the network weights of the prediction model. The judgment coefficient of the approximate model is calculated through a cross-validation method. Based on the judgment coefficient, the corresponding approximate model is selected as the magnetic rail brake prediction model. Regarding the selection of the magnetic rail brake prediction model based on the judgment coefficient, whether the judgment coefficient exceeds a predetermined threshold value, if it exceeds, the approximate model is selected as the magnetic rail brake prediction model, if it does not exceed, the model parameters of the approximate model (such as kernel function type, expansion constant, number of hidden layer nodes, etc.) are retrained and / or adjusted until the judgment coefficient of the approximate model exceeds the predetermined threshold value, and the warning model is determined as the magnetic rail brake prediction model. In this embodiment, the predetermined threshold value of the judgment coefficient Set to 0.95.

[0029] The formula for the coefficient of determination is: ; ; ; in, is the residual sum of squares, is the actual observed value, is the model prediction value; is the total sum of squares, is the mean of the observations. The value of ranges from 0 to 1, and the closer the value is to 1, the better the model fits the data.

[0030] Step 4: Embed a multi-objective genetic algorithm framework based on the magnetic rail brake prediction model, and use maximum suction force and minimized brake mass as objective functions to obtain the Pareto target solution set, and design the magnetic rail brake based on the Pareto target solution set.

[0031] Specifically, based on the magnetic rail brake prediction model, the minimum suction force constraint and the maximum mass constraint are introduced, and the Pareto target solution set is gradually searched through the non-dominated sorting genetic algorithm. Then, the design parameters are obtained based on the Pareto target solution set, and the magnetic rail brake is designed based on the design parameters.

[0032] In this embodiment, during the design process of the magnetic rail brake, the physical prototype model is also adjusted based on the design parameters, and the actual performance of the physical prototype model is verified through experiments, and its quality and suction force are tested. After verification, the design of the magnetic rail brake is actually carried out.

[0033] Example 2 In this implementation case, the relevant factors are selected: box width A (84, 88, 92), permanent magnet width B (12, 13, 14), upper and lower permanent magnet gap C (4, 5, 6), wear plate thickness D (8, 10, 12) to establish L9(3 4 ) orthogonal table (see Table 1) and perform finite element simulation based on the orthogonal table, and calculate the range value based on the simulation results (see Table 2).

[0034] Table 1: L9(3 4 )Orthogonal test plan and results

[0035] Table 2: Orthogonal test range table

[0036] Note: Levels 1, 2, and 3 are the values ​​of the factors. For example, for factor A, level 1 is 84, level 2 is 88, and level 3 is 92.

[0037] According to the horizontal average value, the optimal horizontal box width is 84mm, the permanent magnet width is 14mm, the gap between the upper and lower permanent magnets is 4mm, and the wear plate thickness is 12mm. Based on the optimal horizontal combination, the value range of each factor is determined as follows: box width [80, 88], permanent magnet width [12, 16], gap between the upper and lower permanent magnets [2, 6], and wear plate thickness [10, 14].

[0038] According to the value range, Latin hypercube sampling is performed and finite element simulation is completed. Some samples are shown in Table 3.

[0039] Table 3: Results of some samples of Latin hypercube sampling finite element simulation

[0040] A radial basis function neural network was constructed based on the sample set, and the minimum prediction error of the radial basis function neural network was adjusted. A non-dominated sorting genetic algorithm was used to determine the critical design dimensions of the magnetic rail brake structure for maximum suction and minimum mass. The algorithm's initial sample number was set to 100, the maximum number of iterations was set to 500, and the maximum allowable Patopancreas percentage was set to 30. The optimal solution, determined by iterative multi-objective genetic algorithm, was a box width of 86.2, a permanent magnet width of 14.2, a gap between the upper and lower permanent magnets of 5.6, and a wear plate thickness of 12.1.

[0041] Experimental results demonstrate that this method can effectively reduce the overall mass of the magnetic rail brake while ensuring a maximum suction force of 90kN, achieving an optimal balance between performance and lightweighting. Compared to traditional design methods that only consider a single factor, this method comprehensively considers multi-objective collaborative optimization, significantly improving the overall performance and engineering practicality of the magnetic rail brake, and resolving the difficulty of balancing multiple key indicators in existing designs.

[0042] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A magnetic rail brake design method based on radial basis function neural network, characterized in that: The steps include: Step 1: Measure and obtain the basic data of the magnetic rail brake to be optimized, and build a finite element model based on the basic data; Step 2: Obtain the design factors of the finite element model, and screen the design factors to obtain key factors based on principal component analysis. The value range of the key factors is obtained based on orthogonal experiments. Step 3: Latin hypercube sampling is performed based on the value range of the key factors to obtain sampling results, and the performance response value of the magnetic rail brake is simulated based on the sampling results. A sample set is constructed based on the key factors and the performance response values, and a magnetic rail brake prediction model is constructed based on the sample set and combined with a radial basis function neural network; Step 4: Embed a multi-objective genetic algorithm framework based on the magnetic rail brake prediction model, and use maximum suction force and minimized brake mass as objective functions to obtain the Pareto target solution set, and design the magnetic rail brake based on the Pareto target solution set.

2. The magnetic rail brake design method based on radial basis function neural network according to claim 1 is characterized in that: The basic data include: box length, box width, box height, chamfer size, permanent magnet length, permanent magnet width, permanent magnet height, magnet gap, wear plate thickness, shape, maximum suction force and brake mass.

3. The magnetic rail brake design method based on radial basis function neural network according to claim 1 is characterized in that: Step 1 also includes: constructing a physical prototype model based on the braking principle of the magnetic rail brake, measuring the maximum suction force and prototype mass of the physical prototype model, and adjusting the parameters of the finite element model based on the maximum suction force and prototype mass, so that the errors between the maximum suction force and model mass simulated by the finite element model and the maximum suction force and prototype mass measured by the physical prototype model are all less than a predetermined threshold.

4. The magnetic rail brake design method based on radial basis function neural network according to claim 1, characterized in that: The screening of design factors in combination with principal component analysis includes: standardizing the design factors to construct a factor matrix, calculating the covariance matrix based on the factor matrix, calculating the eigenvalues ​​of the eigenvectors in the covariance matrix, sorting and calculating the contribution, and screening the factors according to the contribution.

5. The magnetic rail brake design method based on radial basis function neural network according to claim 1 is characterized in that: The method of obtaining the value range of the key factors based on the orthogonal test includes: constructing an orthogonal test table for the key factors, and performing data simulation of the finite element model based on the orthogonal test table, recording the maximum suction and mass in each case, obtaining the optimal level combination based on the recorded suction and mass combined with range analysis, and determining the value range of the key factors based on the optimal level combination.

6. The magnetic rail brake design method based on radial basis function neural network according to claim 5, characterized in that: The obtaining of the optimal level combination based on the suction and quality combined with the range analysis includes: calculating the influence values ​​of various key factors on the suction and quality based on the recorded suction and quality combined with the range analysis, and determining the group with the largest mean of the influence values ​​of the suction and quality as the optimal level combination; The impact value is expressed by the following formula: ； ； ； in, K ji Indicates the first j The sum of the response values ​​corresponding to all levels of the key factors; Represents the average response value of the jth key factor in the orthogonal test table; express j The range values ​​of the key factors of the columns; n is the horizontal number.

7. The magnetic rail brake design method based on radial basis function neural network according to claim 1, characterized in that: The method of constructing a magnetic rail brake prediction model based on a sample set combined with a radial basis function neural network includes: constructing a prediction model based on a sample set combined with a radial basis function neural network, minimizing a prediction error by adjusting a network weight of the prediction model, calculating a judgment coefficient of an approximate model by a cross-validation method, and selecting a corresponding approximate model as the magnetic rail brake prediction model based on the judgment coefficient; The method of selecting a corresponding approximate model as a magnetic rail brake prediction model based on the judgment coefficient includes: based on whether the judgment coefficient exceeds a predetermined threshold, if so, selecting the approximate model as the magnetic rail brake prediction model; if not, retraining and / or adjusting the model parameters of the approximate model until the judgment coefficient of the approximate model exceeds the predetermined threshold.

8. The magnetic rail brake design method based on radial basis function neural network according to claim 1 is characterized in that: The method of obtaining the Pareto target solution set by taking the maximum suction force and the minimum brake mass as the objective function includes: introducing the minimum suction force constraint and the maximum mass constraint based on the magnetic rail brake prediction model, and gradually searching the Pareto target solution set through the non-dominated sorting genetic algorithm.

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