WO2023029446A1

WO2023029446A1 - Genetic algorithm-based resonant converter design parameter selection method

Info

Publication number: WO2023029446A1
Application number: PCT/CN2022/082272
Authority: WO
Inventors: 陈健斌; 杨程喻; 唐升宗; 邹建俊
Original assignee: 广东泰坦智能动力有限公司
Priority date: 2021-09-02
Filing date: 2022-03-22
Publication date: 2023-03-09
Also published as: CN113806884A; CN113806884B

Abstract

Disclosed is a genetic algorithm-based resonant converter design parameter selection method. According to the present invention, multi-target parameter solution vectors can be naturally obtained in an initial solution global solution set population space under a convergence condition by using a genetic algorithm; a BP neural network can adaptively obtain a population space φ* by means of the initial solution global solution set population space; by means of a proper hybridization operator and mutation operator, according to a roulette wheel selection operator, proper male parents and female parents are selected from these solution vectors having higher fitness, and genes of the male parents and the female parents are disassembled and recombined, so as to generate solution vectors in a sub-generation; then the fitness of these solution vectors in the sub-generation is calculated by means of a natural selection function; and generations of heredity is performed in the same way, and finally convergence is performed to obtain an optimal value of a target resonant converter. The present invention is applied to the technical field of design, selection and optimization of circuit parameters.

Description

Selection Method of Resonant Converter Design Parameters Based on Genetic Algorithm

technical field

The invention relates to a method for selecting design parameters of a resonant converter based on a genetic algorithm.

Background technique

LLC resonant converter is a DC/DC converter topology with advantages of high efficiency, high power density, low EMI and wide voltage range. The basic working principle of the LLC resonant converter is to change the voltage gain of the resonant cavity by controlling the frequency of the switching device, so as to achieve the purpose of outputting the target power. Among them, the parameter design of a resonant tank that can meet the requirements of engineering indicators such as gain adjustable range, resonant frequency, excitation frequency, characteristic impedance range, device temperature rise, and inductance device volume is a multi-dimensional process. The problem of a target parameter and complex boundary conditions is also a difficult problem for circuit engineers. Usually, circuit engineers can only roughly calculate the gain-frequency relationship function of the resonant cavity, and after obtaining some approximate inductance ratio K and load quality factor Q solutions, obtain the optimal value through engineering experience and prototype tests. Parameter design of the resonator. This method is usually time-consuming, and usually requires multiple trials before obtaining satisfactory design parameters. At the same time, it is also necessary to make some trade-offs and compromises among multiple engineering variables that will affect each other. This not only requires engineers to have extremely rich engineering experience and extremely advanced circuit design knowledge, but also greatly prolongs the time for circuit design and verification.

In addition, the relationship between the AC voltage gain of the LLC resonant tank and the actual engineering design parameters is very complicated, and each target parameter will affect each other. Finding the appropriate design parameters requires a lot of calculations and experiments, which is a time-consuming and labor-intensive task. Work.

Contents of the invention

The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art, and provide a method for selecting design parameters of a resonant converter based on a genetic algorithm, which can quickly find out the solution of suitable design parameters in the overall situation.

The technical solution adopted in the present invention is: the design parameters in the present invention include K and Q values, K is the inductance ratio, and Q is the load quality factor, and the method for selecting the design parameters of the resonant converter of the present invention includes the following steps:

a. Initialize the global solution set population space, and create several two-dimensional solution vectors;

b. Construct the above-mentioned several two-dimensional solution vectors into a four-dimensional initial solution global solution set population space φ;

c. Adaptively transform this initial solution global solution set population space φ through the BP neural network to obtain a global solution set population space φ*, which contains the genetic information of the entire population of this generation;

d. Input the solution vectors in the global solution set population space φ* into the natural selection function one by one, and calculate their fitness;

e. According to the analysis and fitting of several target parameters, a fitness function with variable weight is obtained, and the fitness of the solution vectors in the population space φ* of these global solution sets is calculated and sorted under the specified engineering conditions, and obtained The fitness of several numbers is higher than the set solution vector as the elite population space φe;

f. Eliminate other solution vectors whose fitness is lower than the setting, and retain the elite population space φe that satisfies the setting as the male parent solution vector and the female parent solution vector to be paired;

g. Select the paired paternal solution vector and female parent solution vector in the elite population space φe through the mate selection strategy operator;

h. Dismantling and recombining the genes of each pair of paternal solution vector and maternal solution vector, and synthesizing the solution vector of the offspring;

i. With the solution vector of one of the sub-generations being the specified mutation probability, the parameter mutation is performed on the solution vector in the global solution set population space of the entire sub-generation, and the randomly selected solution vector will undergo gene mutation through the mutation operator, that is, cause individual elements in the solution vector to change in unpredictable directions;

j. Obtain the global solution set population space of the sub-generation solution vector;

k. Judging whether the number of generational alternations reaches the target value, if not, continue to step c-j, thereby obtaining the final global solution set population space of the new child generation solution vector, if the number of generational alternations reaches the target value, proceed to step l;

l. Judge whether the solution of the population space of the final global solution set is convergent. If it converges, output the solution of the population space of the global solution set. If it does not converge, return to step c-j. Usually, the convergent eigenvalue C first becomes larger and then becomes smaller. C If C is too large, it means that the population space of the final global solution set loses its tendency to be stable under certain circumstances. On the contrary, if C is too small, it means that the population space of the final global solution set has no variation randomness. When the convergence eigenvalue C corresponds to the convergence eigenvector matrix When the eigenvalues of the result matrix of the cross product of C* and the engineering boundary condition vector matrix B* meet a certain range, the solution of the population space of the final global solution set converges under the specified engineering conditions;

m. Obtain the target solution vector, which contains the design parameters K and Q values of the resonant cavity of the designed resonant converter;

n. The algorithm ends, and the solution vector including the design parameters of the resonant cavity of the target resonant converter is obtained.

Further, the resonant converter is an LLC resonant converter, and the two-dimensional solution vector in step a is composed of K and Q in the design parameters of the LLC resonant converter as basic elements, and the method for forming the solution vector is:

Further, the natural selection function in step d is a set of operators that obtain a series of fitness parameters.

Further, the expression of the fitness function is:

Wherein kn is a weight coefficient, Xmn is a two-dimensional solution vector, the fitness function is a kind of inner product algorithm, the size of the result can arrange the ranking of the fitness of the global solution set population under the engineering conditions, it can be assumed A ratio is screened to obtain the elite population space φe.

Further, the mate selection strategy operator adopts a classic roulette wheel selection method or a proportional selection method.

Further, the gene disassembly and recombination in step h is an intermediate recombination method using a real-valued recombination algorithm.

Further, the parameter variation in the step i refers to the process of forming a new solution vector by changing some elements in the solution vector, and the variation algorithm adopted is Gaussian variation, and Gaussian variation means that the result of the variation obeys a normal distribution.

The beneficial effects of the present invention are: the genetic algorithm can be used to naturally obtain the solution vector of multi-objective parameters (including the solution vector of the target design parameters) in the initial solution global solution set population space under the convergence condition, which can effectively reduce the LLC resonance transformation The design and verification time of the resonant cavity parameters of the device, and the accuracy of the design parameters are improved; the BP neural network can adaptively obtain a population space φ* through the initial solution of the global solution set population space, which contains the genes of the entire population of this generation At the same time, through appropriate hybridization operators and mutation operators, it is possible to find parameter combinations that engineers have never imagined in the global solution set space. Although the set of these parameter solution vectors is not necessarily correct most of the time (even Sometimes it is outrageously wrong), but sometimes it has unexpected effects; through a natural selection function that can be changed according to actual engineering needs, it can objectively reflect the circuit operation status and characterization parameters, and make these more vague and complicated Qualitatively and quantitatively evaluate the relationship of engineering characterization parameters, and calculate the fitness of these solution vectors in the population space of the global solution set, arrange them, and decide to keep the solution vectors for hybridization and mutation in the next generation; In these solution vectors with high fitness, the appropriate male and female parents are selected according to the roulette selection operator (an operator of a mating strategy), and their genes (those containing basic circuit design elements in the solution vector) are selected. Components) are disassembled and recombined to generate the solution vectors of the sub-epochs; then the solution vectors of the sub-epochs are then used to calculate their fitness through the natural selection function; and so on for several generations of inheritance, and finally converge to obtain the target LLC resonance transformation The preferred value of the device.

Description of drawings

Fig. 1 is a schematic flow chart of the selected method of the present invention;

Fig. 2 is the circuit diagram of the LLC resonant tank;

Fig. 3 is a possible descendant diagram of the intermediate reorganization method of the real value reorganization algorithm;

Figure 4 is a graph of the change of the average fitness of the population with the number of generations;

Fig. 5 is a relationship diagram of the voltage gain and the load quality factor Q of the characteristics of the LLC converter;

Fig. 6 is a graph showing the relationship between the voltage gain and the inductance ratio K of the LLC converter characteristic.

Detailed ways

In this embodiment, before introducing how the genetic algorithm realizes the design parameter selection of the resonant cavity of the LLC resonant converter, first introduce the design principle of the resonant cavity parameters of the LLC resonant converter:

The input voltage of the LLC resonant tank, that is, the Vs of the voltage source generated by the switch network as shown in Figure 1. According to Fourier analysis, the equation relationship is established by employing the first harmonic approximation (FHA). Obviously, the Vs of the resonant tank can be expressed by the following formula.

Among them, Vg is the peak value of the square wave voltage output by the switching network, and ωs is the angular switching frequency. The input voltage of the LLC resonant tank contains harmonics of order 2n-1 (n=integer). By assuming that the input voltage Vs is applied to one of the LLC resonant tanks, the equivalent circuit shown in Figure 2, the AC voltage gain of the LLC resonant tank can be obtained by the voltage ratio between the input and output impedances. The gain equation of the converter can be expressed as the following formula.

where Rac is the effective AC resistance, ωs is the angular switching frequency, and NS/NP is the turns ratio of the secondary to primary section. The effective resistance Rac is converted from the secondary section to the primary section using the transformer winding ratio and is determined in the following way.

The design parameters of the resonant tank can be defined by the following expressions:

Resonance frequency function:

Excitation frequency function:

Characteristic impedance function:

Inductance Ratio:

Load quality factor:

Among them, Lr is the resonant inductance, Lm is the magnetizing inductance, and Cr is the resonant capacitor. In addition, the expression for the converter voltage gain can be obtained as:

Among them, the load quality factor Q is defined as the ratio between the characteristic impedance ZO and the effective resistance Rac. Inductance K is the ratio between the resonance frequency and the magnetization frequency. Wherein, the normalized frequency x is the ratio of the switching frequency to the resonant frequency, that is, x=fs/fr.

And the design parameter of the present invention comprises K and Q value, and described resonant converter is LLC resonant converter, and selected method of the present invention comprises the following steps:

Realization principle of the present invention:

In order to confirm the design parameters of the LLC resonant converter, such as the resonant inductance Lr in the resonant tank, the magnetizing inductance Lm and the resonant capacitor Cr, it is mainly to study the influence of K and Q on the voltage gain, and the design parameters of these resonant tanks will show Complex trends that influence each other. In the present invention, the solution vector is formed by the key design parameters K and Q of the design parameters of the LLC resonant converter as basic elements, and the solution vector composition method is as follows:

Then, a number of solution vectors Xmn(m, n∈N) constitute an initial solution global solution set population space φ:

Such an initial solution global solution set population space φ includes n*m solution vectors Xmn to form a two-dimensional matrix, and each matrix element contains two degrees of freedom, so this initial solution global solution set population space φ is a four-dimensional space.

Then it is analyzed into a global solution set population space φ* by BP neural network, and thus BP neural network completes the approximate mapping of 4-dimensional space vectors to 2-dimensional space. The BP neural network consists of three layers, namely the input layer, the hidden layer, and the output layer. There are connection weights between the hidden layer, the input layer, and the output layer. The transfer function is a nonlinear transformation function. The nonlinear transformation is as follows formula:

(net=x1ω1+x2ω2+...+xnωn)

Among them, net is the input value of the hidden layer, f(x) is the output value of the hidden layer, xn is the input value of the input layer, and ωn is the connection weight of the input layer and the hidden layer.

The size of the population (that is, the number of individuals in the population) is represented by N; the chromosome length of the population is represented by L. Usually, in order to make the calculation of the convergent eigenvalue C easier, n=m is selected to form an n-order matrix φ.

When initializing the population space of the global solution set, it is necessary to limit the value range of the solution vector Xmn (for example, the value of K cannot be too large, because the actual resonant inductance cannot be too large), and then a certain number of solution vectors are defined by a random number algorithm, and the These solution vectors are combined into the global solution set population space φ.

The natural selection function is a group of operators that obtain a series of fitness parameters. In the present invention, the expression function of the converter voltage gain is used as the first objective function, and one of the weight coefficients k1 of the fitness function of its variable weight for:

Others take the resonant frequency function, excitation frequency function and characteristic impedance function as objective functions to construct other weight coefficients k2~k4 of the corresponding fitness function

The expression of the fitness function fitness is:

The fitness function fitness is an inner product algorithm whose result is a scalar. According to the size of the fitness results, the ranking of the fitness of the global solution cluster population under the project conditions can be arranged, and a ratio can be assumed to be screened to obtain the elite population space φe.

In addition, in order to limit the boundary conditions and increase the proportion of feasible solutions in the solution set population space φ, a penalty function is added to solve the optimization problem with complex constraints. The penalty function reduces the survival probability of infeasible solution individuals who do not meet the constraint conditions in the next generation by imposing penalties on infeasible solutions.

However, in the genetic algorithm of the present invention, we do not completely negate infeasible solutions. Because in the search solution set population space φ, the infeasible solution may be very close to the optimal feasible solution. However, in many practical problems, in order to evaluate the quality of an individual, multiple criteria must be considered to determine the superiority of the individual. This involves multi-objective optimization problems. We can use the linear weighting method to weight the objective function values of multiple single objectives to obtain the objective function values of multiple objectives, and then use the fitness calculation methods for some single-objective problems described above. Special methods, such as Pareto non-dominated sorting, can also be used.

Paternal and maternal selection methods

The selection method of the male parent and the female parent of the population space Φe of the global solution set of the elite population generally adopts the classic roulette selection method (or called the proportional selection method), and its specific operation is as follows:

(1) Calculate the fitness (i=1, 2, ..., M) of each individual in the group, where M is the size of the group;

(2) Calculate the probability that each individual is inherited into the next generation population;

(3) Calculate the cumulative probability of each individual;

(q[i] is called the cumulative probability of chromosome x[i] (i=1,2,...,n))

(4) Generate a uniformly distributed pseudo-random number r in the interval [0, 1];

(5) If r<q[1], select individual 1, otherwise, select individual k, so that: q[k-1]<r≤q[k] holds true;

(6) Repeat (4) and (5) a total of M times.

Crossover operator and mutation operator

Because the design parameters of the resonant cavity of the LLC resonant converter calculated by the present invention are located in the real number space. Therefore, what the crossover operator of the present invention uses is the intermediate recombination method of the classic real value recombination algorithm, and the specific process is as follows:

The intermediate reorganization can slightly exceed the boundary of the hypercube where the parent is located, as shown in Figure 3, the position of the possible child variables in the solution space after the intermediate reorganization:

For example, the parent chromosome is:

Parent individual 1: 0.41.2-0.3

Parent individual 2: 0.20.70.6

The generated daughter individual chromosome can be: 0.30.90.4. Intermediate reorganization is a reorganization algorithm that works only on real variable individuals. Here the variable value of the offspring is selected on the interval of the generation variable. The formula for generating offspring individuals is as follows:

Among them, αi is a random number between [-d, 1+d], which is a proportional factor selected randomly and uniformly.

The value of parameter d represents the size of the region of possible offspring. d = 0 means that the size of the region of variable values of the offspring is the same as that of the parent, which is called "(standard) intermediate recombination"; however, since most variables of the offspring are not generated on the boundary of the possible region, so The area covered by variables may become smaller and smaller. Thus, this variable space shrinkage occurs with only standard intermediate reorganization with d = 0. Therefore, this phenomenon can be prevented by setting a larger d value. Generally, d=0.25 is set, at this time, it can be statistically guaranteed that the range of variable values of the offspring will not shrink.

Parameter mutation refers to the process of forming a new solution vector by changing some elements in the solution vector. It can improve the diversity of the population and reduce the risk of the evolutionary algorithm falling into a local optimal solution.

The mutation operator of the present invention uses Gaussian mutation. Gaussian variation means that the results of the variation obey the normal distribution. It includes Gaussian variation centered on the current value and Gaussian variation centered on the center of the search domain. Gaussian variation provides a σ (standard deviation of a normal distribution) to control the size of the variation. But it does not strictly limit the scope of variation like uniform variation. In the case of large samples, the probability of the variation result falling in the neighborhood of length α near the center point is about 68.27%; Neighborhood probability is about 99.73%. The embodiment uses the Gaussian variation function used in the Geatpy genetic algorithm box.

Convergence of the population space of the final global solution set

After several generations of alternation, it is necessary to judge whether the solution of the population space of the final global solution set is convergent, and then obtain the solution vector of the design parameters of the target resonator.

The method of finding the convergent eigenvalue C is as follows:

The n-order matrix φ, there is a number C and a non-zero vector x, satisfying the relationship:

φx＝Cx (22)

Usually, the convergence eigenvalue C first increases and then decreases, and if C is too large, it means that the population space of the global solution set loses its "stability tendency" under certain circumstances. Conversely, if C is too small, it means that there is no "mutation randomness" in the population space of the global solution set. When the eigenvalues of the result matrix of the cross product of the convergent eigenvector matrix C ^* corresponding to the convergent eigenvalue C and the engineering boundary condition vector matrix B* meet a certain range (this range is limited by actual engineering needs), it will be explained The solution of the population space of the global solution set converges under the specified engineering conditions.

The algorithm realization of the present invention is realized by python language, and the IDE used is PyCharm Community Edition, has used the Geatpy2 genetic algorithm toolbox provided by South China University of Technology to realize various genetic algorithm operators and the inductance ratio K of the LLC resonant cavity And the calculation of the load quality factor Q, wherein the natural selection function is also one of the toolkits of the Geatpy2 genetic algorithm toolbox, and the Geatpy2 genetic algorithm toolbox is an open prior art, and will not be described here.

The architecture of the artificial neural network is realized through the open source Theano library, and on this basis, there are toolkits for training neural networks such as PDNN.

First, as shown in Figure 4, let’s see how the convergence effect of the algorithm is. By calculating the average fitness of the fitness function fitness of the global solution set population space of each generation, we can find that as the number of generations increases, the entire The average fitness of the population is constantly rising and infinitely close to 1, which shows that the solution of the population space of the global solution set converges under the specified engineering conditions.

The specified engineering design conditions are shown in Table 1, which is used as a standard to modify the engineering boundary condition vector matrix B* and the fitness function fitness. The calculated optimal inductance ratio K and load quality factor Q solution (the preferred value is the optimum marked in Figure 4 and Figure 5) and its similar values, and use matlab to plot their frequency-voltage under the specified K and Q conditions The changes of the gain curve are shown in Figure 5 and Figure 6. Table 1

Specified Specifications for LLC Resonant Converters

In summary, the present invention can quickly and accurately obtain the design parameters of the resonant cavity of the LLC resonant converter, and can even obtain many parameters that even senior engineers have never imagined; originally, the genetic algorithm is a very simple random iteration An algorithm that can solve many problems by sifting through the Fitness function and simulating the biological evolution process in nature;

For example, the steel structure of the Bird's Nest Stadium in Beijing was iterated by genetic algorithms, and the overall structure is very stable; the antenna on the X-Band satellite in the United States was designed using evolutionary algorithms, and its volume was only the size of a coin.

The genetic algorithm has a natural advantage in answering the mathematical problems of this kind of multi-objective parameters. At the same time, the present invention uses the BP artificial neural network to approximate the population space formed by the solution vector, and optimizes the interpretation ability of the population space of the global solution set for practical engineering problems. .

The invention is applied to the technical field of design, selection and optimization of circuit parameters.

Although the embodiment of the present invention is described in terms of actual solutions, it does not constitute a limitation to the meaning of the present invention. For those skilled in the art, it is obvious to those skilled in the art that the modifications to the embodiments and the combination with other solutions are obvious according to the description .

Claims

A method for selecting design parameters of a resonant converter based on a genetic algorithm, the design parameters include K and Q values, K is an inductance ratio, and Q is a load quality factor, characterized in that it includes the following steps:

a. Initialize the global solution set population space, and create several two-dimensional solution vectors;

b. Construct the above-mentioned several two-dimensional solution vectors into a four-dimensional initial solution global solution set population space φ;

c. Adaptively transform this initial solution global solution set population space φ through the BP neural network to obtain a global solution set population space φ*, which contains the genetic information of the entire population of this generation;

d. Input the solution vectors in the global solution set population space φ* into the natural selection function one by one, and calculate their fitness;

e. According to the analysis and fitting of several target parameters, a fitness function with variable weight is obtained, and the fitness of the solution vectors in the population space φ* of these global solution sets is calculated and sorted under the specified engineering conditions, and obtained The fitness of several numbers is higher than the set solution vector as the elite population space φe;

f. Eliminate other solution vectors whose fitness is lower than the setting, and retain the elite population space φe that satisfies the setting as the male parent solution vector and the female parent solution vector to be paired;

g. Select the paired paternal solution vector and female parent solution vector in the elite population space φe through the mate selection strategy operator;

h. Dismantling and recombining the genes of each pair of paternal solution vector and maternal solution vector, and synthesizing the solution vector of the offspring;

i. With the solution vector of one of the sub-generations being the specified mutation probability, the parameter mutation is performed on the solution vector in the global solution set population space of the entire sub-generation, and the randomly selected solution vector will undergo gene mutation through the mutation operator, that is, cause individual elements in the solution vector to change in unpredictable directions;

j. Obtain the global solution set population space of the sub-generation solution vector;

k. Judging whether the number of generational alternations reaches the target value, if not, continue to step c-j, thereby obtaining the final global solution set population space of the new child generation solution vector, if the number of generational alternations reaches the target value, proceed to step l;

l. Judge whether the solution of the population space of the final global solution set is convergent. If it converges, output the solution of the population space of the global solution set. If it does not converge, return to step c-j. Usually, the convergent eigenvalue C first becomes larger and then becomes smaller. C If C is too large, it means that the population space of the final global solution set loses its tendency to be stable under certain circumstances. On the contrary, if C is too small, it means that the population space of the final global solution set has no variation randomness. When the convergence eigenvalue C corresponds to the convergence eigenvector matrix When the eigenvalues of the result matrix of the cross product of C* and the engineering boundary condition vector matrix B* meet a certain range, the solution of the population space of the final global solution set converges under the specified engineering conditions;

m. Obtain the target solution vector, which contains the design parameters K and Q values of the resonant cavity of the designed resonant converter;

n. The algorithm ends, and the solution vector including the design parameters of the resonant cavity of the target resonant converter is obtained.
The method for selecting design parameters of a resonant converter based on a genetic algorithm according to claim 1, wherein the resonant converter is an LLC resonant converter, and the two-dimensional solution vector in step a is obtained from the LLC resonant converter The K and Q in the design parameters are formed as basic elements, and the method of forming the solution vector is as follows:
The method for selecting design parameters of a resonant converter based on genetic algorithm according to claim 2, characterized in that: the natural selection function in the step d is a group of operators to obtain a series of fitness parameters.
The method for selecting design parameters of a resonant converter based on a genetic algorithm according to claim 2, wherein the expression of the fitness function is:
Wherein kn is a weight coefficient, Xmn is a two-dimensional solution vector, the fitness function is a kind of inner product algorithm, the size of the result can arrange the ranking of the fitness of the global solution set population under the engineering conditions, it can be assumed A ratio is screened to obtain the elite population space φe.
The method for selecting design parameters of a resonant converter based on genetic algorithm according to claim 2, characterized in that: said mate selection strategy operator adopts a classic roulette wheel selection method or a proportional selection method.
The method for selecting design parameters of a resonant converter based on a genetic algorithm according to claim 2, characterized in that: the disassembly and recombination of the genes in the step h is an intermediate recombination method using a real-valued recombination algorithm.
The method for selecting design parameters of a resonant converter based on genetic algorithm according to claim 2, characterized in that: the parameter variation in the step i refers to the process of forming a new solution vector by changing some elements in the solution vector , the mutation algorithm used is Gaussian mutation, which means that the result of the mutation obeys the normal distribution.