CN115310364A - Multi-objective optimization method for electromagnetic actuator containing permanent magnet - Google Patents

Multi-objective optimization method for electromagnetic actuator containing permanent magnet Download PDF

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CN115310364A
CN115310364A CN202211011529.4A CN202211011529A CN115310364A CN 115310364 A CN115310364 A CN 115310364A CN 202211011529 A CN202211011529 A CN 202211011529A CN 115310364 A CN115310364 A CN 115310364A
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electromagnetic actuator
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郑昕
柯丹阳
赵福民
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Fuzhou University
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Abstract

The invention discloses a multi-objective optimization method for an electromagnetic actuator containing a permanent magnet, which is characterized in that the relation between performance indexes and parameters of the electromagnetic actuator is fitted through an improved OLS-RBF neural network rapid algorithm, and the relation is combined with an improved NSGA-II algorithm to obtain a Pareto solution set of the performance of the electromagnetic actuator; because of the mutual influence among the optimization targets, one is increased, the other is also increased, and when the optimization size directions of a plurality of optimization targets are different, an optimal solution does not exist; and (3) finding a compromise solution in a Pareto solution set by adopting a fuzzy membership method, and then selecting a compromise optimal solution by using a membership function to obtain an optimal structure parameter. The electromagnetic actuating mechanism containing the permanent magnet is optimally designed.

Description

Multi-objective optimization method for electromagnetic actuator containing permanent magnet
Technical Field
The invention relates to the technical field of electromagnetic actuators containing permanent magnets, in particular to a multi-objective optimization method of an electromagnetic actuator containing permanent magnets.
Background
The reduction of manufacturing cost and the optimization of performance of electromagnetic actuators have been important research directions for the improvement of electromagnetic actuators. With the exploitation and processing of a large amount of high-performance rare earth permanent magnet materials such as neodymium iron boron and the like, the permanent magnet materials are widely used in electromagnetic execution mechanisms, the permanent magnet electromagnetic execution mechanisms utilize the characteristics of high coercivity, high magnetic energy accumulation and high remanence of the rare earth permanent magnet materials, provide electromagnetic attraction force under a closing state often, replace traditional coil excitation, and have the advantages of low energy consumption, high safety and no temperature rise. However, there are major difficulties in practical research: 1. the cost of the electromagnetic actuator containing the permanent magnet is high; 2. the working efficiency of the electromagnetic actuator is improved. The multi-objective optimization of the electromagnetic actuator containing the permanent magnet is the key for solving the problems of manufacturing cost reduction and performance optimization of the magnetic actuator.
The optimization of the electromagnetic actuator is a typical multi-objective optimization problem, different electromagnetic actuators have different optimization targets due to different working modes, and the optimization targets are usually obtained by researching dynamic and static characteristics. The optimization of the electromagnetic actuator generally adopts an equivalent magnetic circuit method for calculation, but for the electromagnetic actuator containing the permanent magnet, the situation of the combined action of permanent magnet excitation and coil excitation exists in the working process, so that the phenomena of magnetic leakage, magnetic saturation and the like exist, the phenomenon that the coil excitation influences the working point of the permanent magnet also exists, and the coupling relation between the optimization target and the optimization factor is more complex. How to quickly and accurately form a function expression which can be programmed by an optimized program by using the dynamic and static characteristics to be optimized and each optimization factor is a problem which still needs to be solved, and meanwhile, the problem of how to construct a quick calculation model containing a permanent magnet also exists.
Disclosure of Invention
Aiming at the defects and shortcomings of the prior art, the invention provides a multi-objective optimization method for an electromagnetic actuator containing a permanent magnet.
In order to achieve the purpose, the invention specifically adopts the following technical scheme:
a multi-objective optimization method for an electromagnetic actuator containing permanent magnets is characterized by comprising the following steps: fitting the relation between the performance indexes and the parameters of the electromagnetic actuator through the improved OLS-RBF neural network rapid algorithm, and combining with the improved NSGA-II algorithm to obtain a Pareto solution set of the performance of the electromagnetic actuator; because of the mutual influence among the optimization targets, one is increased, the other is also increased, and when the optimization size directions of a plurality of optimization targets are different, an optimal solution does not exist; finding a compromise solution in a Pareto solution set by adopting a fuzzy membership method, and then selecting a compromise optimal solution by using a membership function to obtain an optimal structure parameter;
the improved OLS-RBF neural network rapid algorithm optimizes the width of the central point of the radial basis function by using a gradient descent operator, so that the width of the central point of each iteration can enable the contribution degree of the hidden layer output matrix to error descent to be maximum, and the OLS-RBF neural network is improved;
the improved NSGA-II algorithm widens the search space of the NSGA-II algorithm through an orthogonal crossover operator, and introduces self-adaptive crossover and mutation probability to ensure that the number of individuals generated by crossover behavior and mutation behavior changes along with the genetic algebra; when the iteration times are less than 50, the cross probability is 0.9, and the specific variation probability is 0.1; when the iteration times exceed 50 times, the cross probability is 0.4, and the variation probability is 0.6.
Further, the improved OLS-RBF neural network rapid algorithm uses a gradient descent operator to correct the central point width σ of the neuron, and the operator formula is as follows:
σ * ＝σ-ωΔσ (1)
Δσ＝(δ MSE1 -δ MSE2 )/(σ * -σ) (2)
Figure BDA0003811102150000021
wherein σ * For correction values obtained after introduction of the down operator, delta MSE Is the mean square error of the weight λ, ω is the descent rate; according to actual needsAnd after the optimization factor is solved, fitting the performance index and the optimization factor by using the improved OLS-RBF neural network to obtain an approximate model.
Further, the formula of the orthogonal crossover operator is as follows:
when the random number is less than 0.5:
Figure BDA0003811102150000022
when the random number is greater than 0.5:
Figure BDA0003811102150000023
further, the step of finding a compromise solution in the Pareto solution set by using a fuzzy membership method, and then selecting a compromise optimal solution by using a membership function to obtain an optimal structure parameter specifically includes:
fuzzifying a Pareto solution set by adopting a fuzzy membership function, and expressing the satisfaction degree of the ith target function fi of the kth individual in the Pareto optimal solution set by using the fuzzy membership function as follows:
Figure BDA0003811102150000031
wherein f is i max Is the maximum value of the ith objective function, f i min Is the minimum of the ith objective function; for each solution in the Pareto solution set, judging whether the target is good or bad by calculating the sum of fuzzy membership function of each solution; the normalized value of the fuzzy membership function is:
Figure BDA0003811102150000032
the larger the fuzzy membership degree value is, the better the individual compromise performance is, and the optimal parameter is the optimal parameter selected from the optimal parameter with the maximum membership degree value.
Compared with the prior art, the invention and the optimized scheme thereof have the following beneficial effects:
(1) In order to solve the problem that model overfitting is easily caused by selecting the center width, an improved OLS-RBF algorithm for optimizing the center width by using a gradient descent operator is provided, and a direct functional relation between a performance index and a structural parameter is provided for a multi-objective optimization algorithm.
(2) Aiming at the problems that the NSGA-II multi-objective optimization algorithm is slow in searching speed and easy to fall into local optimization, a normal distribution crossover operator and self-adaptive variation and crossover probability are used for improvement, the searching speed is increased, and errors are reduced.
Drawings
FIG. 1 is a flow chart of an improved OLS-RBF neural network according to an embodiment of the present invention;
FIG. 2 is a flow chart of the NSGA-II algorithm modified by the embodiment of the present invention.
Detailed Description
In order to make the features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail as follows:
it should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
As shown in fig. 1 and fig. 2, the embodiment provides a multi-objective optimization method for an electromagnetic actuator with permanent magnets, which is used for implementing optimization design on an electromagnetic actuator with permanent magnets. In order to carry out multi-objective optimization on the electromagnetic actuating mechanism containing the permanent magnet, the invention improves the OLS-RBF neural network, and fits the performance index and the optimization factor which need to be optimized to obtain an approximate model.
And selecting an NSGA-II algorithm to carry out multi-objective optimization on the approximate model, and improving by using a normal distribution crossover operator, adaptive mutation and crossover probability in order to solve the problems that the NSGA-II algorithm is slow in search speed and easy to fall into local optimum. And performing multi-objective optimization on the approximate model through the improved NSGA-II algorithm to obtain optimal structure parameters.
The invention aims to improve the existing OLS-RBF neural network through a gradient descent operator to obtain an accurate approximate model, and then perform multi-objective optimization on the approximate model through an improved NSGA-II algorithm. The implementation of the method mainly comprises two aspects of establishing an approximate model and optimizing multiple targets:
(1) Establishing an approximate model: in order to avoid the overfitting condition of the neural network, the width of the central point of the radial basis function is optimized by using a gradient descent operator, so that the contribution degree of the hidden layer output matrix to error descent is maximized by the width of the central point of each iteration, and the OLS-RBF neural network is improved. Wherein, the OLS-RBF neural network refers to a Radial Basis Function (RBF) neural network model constructed based on an Orthogonal Least Square (OLS) method.
And (3) correcting the width sigma of the central point of the neuron by using a gradient descent operator, wherein the operator formula is as follows:
σ * ＝σ-ωΔσ (1)
Δσ＝(δ MSE1 -δ MSE2 )/(σ * -σ) (2)
Figure BDA0003811102150000041
wherein σ * For correction values obtained after introduction of the down-scaling operator, delta MSE Is the mean square error of the weight λ, ω is the rate of decrease, which can be set larger at the beginning of the procedure to widen the search range of σ. After the optimization factors are selected according to actual requirements, the performance indexes and the optimization factors are fitted by using an improved OLS-RBF neural network to obtain an approximate model, and the steps are shown in FIG. 1.
(2) Improved multi-objective optimization algorithm: when the traditional NSGA-II algorithm uses a simulated binary crossing algorithm, the crossing efficiency is low, if the variation probability is kept unchanged in the whole program running process, the crossing behavior can enable offspring to be concentrated in a smaller interval, the overall searching speed of the algorithm is reduced, and when the problem of complex high latitude is faced, the program running speed is slow. In addition, the traditional NSGA-II algorithm sets the crossover probability to be large, the mutation probability design is extremely small, and the probabilities of the two are fixed, which allows the program to converge very quickly in the early stage, and also causes the program to converge to a local extreme point easily in the later stage. The invention solves the problems by introducing normal distribution crossover operators and self-adaptive crossover and mutation probabilities. The cross mode is improved, and the normal distribution cross operator is introduced, so that the cross mode of parent individuals belongs to normal distribution, the sampling space of filial generations is enlarged, and the time required for traversing the sampling space is greatly reduced. The formula for the orthogonal crossover operator is as follows:
when the random number is less than 0.5:
Figure BDA0003811102150000051
when the random number is greater than 0.5:
Figure BDA0003811102150000052
wherein, P 1 And P 2 Is two parent populations, S 1 And S 2 For the generated offspring population, N (0, 1) is a random quantity that follows a standard normal distribution.
The search space of the NSGA-II algorithm is widened through the orthogonal crossover operator, and self-adaptive crossover and mutation probabilities are introduced, so that the number of individuals generated by crossover behaviors and mutation behaviors changes along with genetic algebra. When the iteration times are lower than 50 times, the cross probability is 0.9, the specific variation probability is 0.1, and most individuals in the filial generation population are generated by the cross behavior; when the iteration times exceed 50 times, the cross probability is 0.4, the variation probability is 0.6, although the speed of generating filial generations is reduced, the phenomenon that the program sinks and deepens in the local minimum is effectively avoided. The fitting model obtained by the neural network is calculated through an improved NSGA-II algorithm, multi-objective optimization is realized, and optimal structure parameters are obtained, wherein a flow chart of the method is shown in figure 2.
Further, in this embodiment, the relationship between the performance index and the parameter of the electromagnetic actuator is fitted through the improved OLS-RBF neural network fast algorithm, and the Pareto solution set of the performance of the electromagnetic actuator is obtained by combining with the improved NSGA-II algorithm. Because of the mutual influence among the optimization targets, one is increased, the other is increased, and when the optimization size directions of the optimization targets are different, the optimal solution does not exist. Therefore, the Pareto solution needs to rely on a fuzzy membership method when finding the compromise solution in a Pareto solution set, and then the membership function is used for selecting the compromise optimal solution to obtain the optimal structure parameters.
The method fuzzifies a Pareto solution set by adopting a fuzzy membership function, and the satisfaction degree of the ith target function fi of the kth individual in the Pareto optimal solution set can be expressed by using the fuzzy membership function as follows:
Figure BDA0003811102150000061
wherein f is i max Is the maximum value of the ith objective function, f i min Is the minimum of the ith objective function. And for each solution in the Pareto solution set, judging whether the target is good or bad by calculating the sum of fuzzy membership function of each solution. The normalized value of the fuzzy membership function is:
Figure BDA0003811102150000062
the larger the fuzzy membership degree value is, the better the compromise performance of the individual is, and the optimal parameter is selected as the optimal parameter with the maximum membership degree value.
Based on the above design, as a specific embodiment, the present embodiment can be implemented on five optimization factors, namely, the iron core width Dz, the permanent magnet height Lm, the permanent magnet width Dm, the air gap Lg and the coil ampere-turn, of the electromagnetic actuator with the multi-armature structure and including the permanent magnet, and the constraint conditions are as shown in the following table and in units of mm.
Figure BDA0003811102150000063
Particularly, the average suction force borne by two adjacent armatures of the working armatures can be reduced under the working condition of multiple armatures
Figure BDA0003811102150000071
And the suction force F borne by the armature under the working condition of single armature 1 1 As two goals for multi-objective optimization. For convenient optimization, the optimization objective is selected as
Figure BDA0003811102150000072
And F 1 1 I.e. both objectives are optimized towards minimization. And (3) constructing an approximate model between an optimization target and an optimization factor through the graph 1, performing multi-target optimization on the approximate model by utilizing the step of the graph 2, and finally obtaining an optimal structure parameter by adopting a fuzzy membership method.
The foregoing is directed to preferred embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution of the present invention.
The present invention is not limited to the above-mentioned preferred embodiments, and other various forms of the multi-objective optimization method for the electromagnetic actuator with permanent magnets can be obtained by anyone who follows the teaching of the present invention.

Claims (4)

1. A multi-objective optimization method for an electromagnetic actuator containing permanent magnets is characterized by comprising the following steps: fitting the relation between the performance indexes and the parameters of the electromagnetic actuator through the improved OLS-RBF neural network rapid algorithm, and combining with the improved NSGA-II algorithm to obtain a Pareto solution set of the performance of the electromagnetic actuator; because of mutual influence among the optimization targets, one is increased, the other is also increased, and when the optimization directions of a plurality of optimization targets are different, an optimal solution does not exist; finding a compromise solution in a Pareto solution set by adopting a fuzzy membership method, and then selecting a compromise optimal solution by using a membership function to obtain an optimal structure parameter;
the improved OLS-RBF neural network rapid algorithm optimizes the width of the central point of the radial basis function by using a gradient descent operator, so that the width of the central point of each iteration can enable the contribution degree of the hidden layer output matrix to error descent to be maximum, and the OLS-RBF neural network is improved;
the improved NSGA-II algorithm widens the search space of the NSGA-II algorithm through an orthogonal crossover operator, and introduces self-adaptive crossover and mutation probability to ensure that the number of individuals generated by crossover behavior and mutation behavior changes along with genetic algebra; when the iteration times are less than 50, the cross probability is 0.9, and the specific variation probability is 0.1; when the iteration times exceed 50 times, the cross probability is 0.4, and the variation probability is 0.6.
2. The multi-objective optimization method for the electromagnetic actuator with the permanent magnet according to claim 1, characterized in that:
the improved OLS-RBF neural network rapid algorithm corrects the central point width sigma of the neuron by using a gradient descent operator, wherein the operator formula is as follows:
σ * ＝σ-ωΔσ (1)
Δσ＝(δ MSE1 -δ MSE2 )/(σ * -σ) (2)
Figure FDA0003811102140000011
wherein σ * For correction values obtained after introduction of the down operator, delta MSE Is the mean square error of the weight lambda, omega is the rate of decrease; and after the optimization factors are selected according to actual requirements, fitting the performance indexes and the optimization factors by using the improved OLS-RBF neural network to obtain an approximate model.
3. The multi-objective optimization method for the electromagnetic actuator with the permanent magnet according to claim 1, characterized in that:
the formula of the orthogonal crossover operator is as follows:
when the random number is less than 0.5:
Figure FDA0003811102140000012
Figure FDA0003811102140000021
when the random number is greater than 0.5:
Figure FDA0003811102140000022
wherein, P 1 And P 2 Is two parent populations, S 1 And S 2 For the generated progeny population, N (0, 1) is a random quantity that follows a standard normal distribution.
4. The multi-objective optimization method for the electromagnetic actuator with the permanent magnet according to claim 1, characterized in that:
the method for finding the compromise solution in the Pareto solution set by adopting the fuzzy membership method and then selecting the compromise optimal solution by using the membership function to obtain the optimal structure parameters specifically comprises the following steps:
fuzzifying the Pareto solution set by adopting a fuzzy membership function, wherein the satisfaction degree of the ith target function fi of the kth individual in the Pareto optimal solution set is expressed by using the fuzzy membership function as follows:
Figure FDA0003811102140000023
wherein f is i max Is the maximum value of the ith objective function, f i min Is the minimum of the ith objective function; for each solution in the Pareto solution set, calculating a fuzzy membership function of each solutionJudging whether the target is good or bad by counting the sum; the normalized value of the fuzzy membership function is:
Figure FDA0003811102140000024
the larger the fuzzy membership degree value is, the better the compromise performance of the individual is, and the optimal parameter is selected as the optimal parameter with the maximum membership degree value.
CN202211011529.4A 2022-08-23 2022-08-23 Multi-objective optimization method for electromagnetic actuator containing permanent magnet Pending CN115310364A (en)

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