Proton exchange membrane fuel cell model parameter identification method based on optimization algorithm

Abstract

The invention relates to a proton exchange membrane fuel cell model parameter identification method based on an optimization algorithm, which adopts the following steps: 1. establishing a semi-empirical model of a proton exchange membrane fuel cell; importing model parameters, and generating an initial population in a search space; 2. constructing an optimization algorithm objective function, and calculating the fitness value of the initial population; 3. calculating the fuzzy membership function value of the best individual as its dual fitness index; 4. calculating the weighted average of population individuals and the best individual to achieve the unique guidance of the search individual; 5. updating the speed and position of the search population individual; 6. outputting the optimal solution; the invention combines a GMO algorithm with a chaotic mapping and an SCA algorithm, balances exploration and convergence performance, improves the stability and accuracy of the improved algorithm operation, achieves a more accurate and stable proton exchange membrane fuel cell model parameter identification effect, and improves the accuracy and stability of the optimization algorithm in the proton exchange membrane fuel cell parameter identification.

Description

Technical Field

[0001] The invention relates to a proton exchange membrane fuel cell model parameter identification method based on an optimization algorithm. Background Art

[0002] Proton Exchange Membrane Fuel Cells (PEMFC) use hydrogen as fuel and directly convert the chemical energy in it into electrical energy. Due to its low operating temperature, high power density, stability, and pollution-free characteristics, it is widely believed to have good development prospects and has become a research hotspot for alternative energy sources for mobile devices such as automobiles.

[0003] The working principle of proton exchange membrane fuel cells involves a lot of content and a wide range. It is a multi-domain coupling system integrating thermodynamics, fluid, electrochemistry and other domains. The fuel cell is a complex dynamic system with nonlinearity and strong multi-parameter coupling.

[0004] When studying fuel cell stacks, it is necessary to rely on modeling to predict the operating conditions of fuel cells, but due to its complex reaction mechanism, the modeling is difficult and complex. Semi-empirical models are often used to describe the output performance of fuel cells in a steady state, but the detailed parameters of proton exchange membrane fuel cells are not easy to obtain, and they have strong nonlinear characteristics under operation. Therefore, it is necessary to use traditional analysis methods or optimization algorithms to identify the unknown parameters in the semi-empirical model in order to obtain a more accurate steady-state model of the fuel cell.

[0005] Traditional analysis methods include fractional-order models and least squares identification, but they have certain limitations in practical applications: gradient information is required, and the computational complexity is high in multi-parameter identification applications; the accuracy of the calculation results depends on the initial solution of the problem; when applied to nonlinear systems, the identification results are prone to fall into local optimal solutions, resulting in poor accuracy of the final identification results.

[0006] Optimization algorithms can be divided into simple heuristic algorithms and meta-heuristic algorithms. Simple heuristic algorithms are oriented to specific problems and have poor versatility; meta-heuristic algorithms are used in the field of parameter identification, but the accuracy of meta-heuristic algorithm identification results is low, sometimes with a large gap; the convergence speed is slow; it has high randomness and the output results are unstable.

[0007] Publication number CN117410523A Name: A Chinese patent for a method for identifying unknown parameters of a semi-empirical model of a proton exchange membrane fuel cell, including the following steps: establishing a semi-empirical model of a proton exchange membrane fuel cell, determining the parameters to be identified in the semi-empirical model, and importing the specification parameters and experimental data of the fuel cell stack; constructing an objective function, wherein the objective function is the square sum of the errors between the output voltage of the semi-empirical model of the proton exchange membrane fuel cell and the actual voltage, and determining the constraints of the objective function; introducing a simplex tuning method of p-dimensional extreme values, searching for the optimal parameters to be identified, constructing a semi-empirical model of the proton exchange membrane fuel cell, and obtaining the theoretical value of the model output; comparing the measured data with the theoretical value to determine the degree of fit. The above technical solution does not take into account the stability of the algorithm. Since the optimization algorithm has a high degree of randomness, its stability is a relatively important performance indicator of the algorithm performance, and the stability of the algorithm should be verified.

[0008] Publication number CN115392139A Name: A Chinese patent for a method for identifying fuel cell parameters, comprising the following steps: determining the parameters to be identified in the semi-empirical model of the proton exchange membrane fuel cell, and importing experimental data and stack data; constructing an objective function, wherein the objective function is the sum of the square errors between the output voltage of the semi-empirical model of the proton exchange membrane fuel cell and the actual voltage, and determining the constraints of the output of the objective function; introducing the optimized tree seed algorithm to search for the optimal parameters to be identified; and constructing the semi-empirical model of the proton exchange membrane fuel cell based on the output optimal parameters to be identified. The above technical solution has a certain degree of randomness, and it cannot be ensured that the algorithm is applicable to different cases and has good results. Summary of the invention

[0009] The technical problem to be solved by the present invention is to provide a proton exchange membrane fuel cell model parameter identification method based on an optimization algorithm to improve the accuracy and stability of parameter identification, quickly and accurately obtain parameters of different fuel cells, and establish an accurate fuel cell model.

[0010] The present invention adopts the following technical solution:

[0011] The present invention provides a proton exchange membrane fuel cell model parameter identification method based on an optimization algorithm, which adopts the following steps:

[0012] S1. Establish a semi-empirical model of proton exchange membrane fuel cells; import model parameters and generate an initial population in the search space;

[0013] S2. Construct the objective function of the optimization algorithm, calculate the fitness value of the initial population, and take the minimum target value as the current best individual;

[0014] S3, calculating the fuzzy membership function value of the best individual as its dual fitness index;

[0015] S4, using the dual fitness index as weight, calculate the weighted average of the population individuals and the best individual to achieve the unique guidance of the search individual;

[0016] S5, apply mutation to each individual in the population, determine the mutation direction through guidance, and limit the step length of the mutation in combination with the SCA algorithm, and update the speed and position of the search population individuals;

[0017] S6. Output the optimal solution.

[0018] The specific process of generating the initial population in the search space in S1 of the present invention is as follows:

[0019] According to the constraints of the parameters to be identified, the search space is set, initialized at the initial stage of the search, and the initial parameters of the algorithm are set, and the search individuals are randomly distributed in the search space;

[0020] When initializing the search position, the chaotic map is integrated, based on Rossler chaos, and nonlinear factors are added to produce a uniform search population in the initial period;

[0021] The ordinary differential equations of basic Rossler chaos in the three-dimensional space coordinate system are:

[0022]

[0023]

[0024] Among them, a1, a2, β and δ are adjustable parameters; x is the horizontal axis coordinate value, y is the vertical axis coordinate value, and z is the vertical axis coordinate value;

[0025] The improved Rossler chaos after adding nonlinear factors in the three-dimensional space coordinate system is:

[0026] X n+1 =X n +a1(Y n -Z n )

[0027] Y n+1 =Y n +a1(cos(X n )-Y n )

[0028]

[0029] Among them, a1, a2, β, δ are adjustable parameters;

[0030] The initial area is set and expanded in equal increments. The number of chaotic points in the area after each expansion is counted to calculate the uniformity. When the average value of the ratio of all two adjacent statistical values ​​of a chaotic distribution graph approaches 1, the distribution uniformity is considered to be higher.

[0031] The S2 of the present invention is specifically as follows:

[0032] The population includes X1=(x 11 ,x 12 ,…,x 1D ) and V1=(v 11 ,v 12 ,…,v 1D ) is the position and speed of the individual in the i-th search population, D is the matrix dimension, that is, the number of parameters to be identified in the identification process;

[0033] After the initial population is obtained, the fitness value SSE of the initial population is calculated by the objective function, where the objective function is the sum of the square errors between the output voltage of the semi-empirical model of the proton exchange membrane fuel cell and the actual test voltage:

[0034]

[0035] Among them, V exp is the actual test voltage, V sim is the output voltage of the semi-empirical model;

[0036] Solve the mean and variance of the objective function value SSE corresponding to the individuals in the population to calculate the population dual fitness value;

[0037] Set the objective function value SSE calculated by the population to Z best .

[0038] The present invention S3 is specifically as follows:

[0039] The similarity between variables can be expressed by multiplying the fuzzy membership function (MF) values ​​of these variables;

[0040] Calculate the fuzzy membership function value (MF) of the individual,

[0041]

[0042] The geometric mean of n fuzzy membership function values ​​(MF) can be expressed as:

[0043]

[0044] The dual fitness index (DFI) is constructed based on the geometric mean of the fuzzy membership function values:

[0045]

[0046] in, is the objective function value of the current optimal individual in the tth iteration, μ t With σ t is the mean and standard deviation of the objective function value in the tth iteration, j is the jth individual in the population, 1...N is the range of individual values, and N is the number of individuals in the population;

[0047] Sort the fitness of the individuals in the population in descending order, select the individual with the smallest double fitness value as the best individual, and set the position of the best individual as X best .

[0048] S4 of the present invention is specifically as follows:

[0049] In order to make all the best individuals up to the tth iteration contribute to the generation of the global guiding individual, the weighted average of all the opposite best individuals up to now is defined,

[0050]

[0051] in, is the best individual in the population, DFI is the dual fitness index, and to avoid singularity, a small positive number ε is added to the denominator;

[0052] The global guides individuals to achieve the only direction of group variation and imposes variation on individuals within the group.

[0053] S5 of the present invention is specifically as follows:

[0054] By integrating with the SCA algorithm, the mutation coefficient is limited by the value range of the sine function and the cosine function, that is, the step limit of the mutation is added to prevent the algorithm from falling into the local optimal solution;

[0055] The individual mutation update formula in the basic SCA algorithm is:

[0056]

[0057] in, is the t-th iteration position of the k-th dimension of the current individual, r1, r2, r3, and r4 are random numbers. When r1>1, it is the global exploration stage of the algorithm, and when r1<1, it is the local development stage of the algorithm. The value range of r2 is 0-2π, the value range of r3 is 0-2, and the value range of r4 is 0-1. is the k-th dimension position of the optimal individual position variable at the t-th iteration;

[0058] The individual update formula in the basic GMO algorithm is:

[0059]

[0060] The speed update formula in the GMO algorithm is combined with the individual mutation update formula in the SCA algorithm to obtain the population individual update strategy in the SCAGMO algorithm.

[0061] The individual speed and position variation equations in the optimized SCAGMO algorithm are:

[0062]

[0063] Among them, r1, r2, r3 are random numbers, and γ is an adjustable parameter, and the value range is 0-1;

[0064] The iterative process S2-S5 is repeated until the maximum number of iterations is reached.

[0065] The semi-empirical model in S1 of the present invention includes the output voltage of the fuel cell, and the parameters to be identified in the model are determined according to the output voltage of the fuel cell; the program parameters are initialized, and the output voltage of the single fuel cell includes the Nernst electromotive force, activation polarization loss, ohmic polarization loss and concentration polarization loss;

[0066] The Nernst electromotive force formula is:

[0067]

[0068] In the formula, E Nerst is the Nernst potential of a monolithic proton exchange membrane fuel cell, T PEM is the fuel cell operating temperature, and is the pressure of hydrogen and oxygen;

[0069] The activation polarization loss formula is:

[0070]

[0071] In the formula, V act is the activation polarization loss, β1, β2, β3, and β4 are all semi-empirical coefficients. is the oxygen concentration at the cathode catalyst interface, I PEM is the fuel cell current; the oxygen concentration at the cathode catalyst interface is: in, is the oxygen pressure;

[0072] The formula for ohmic polarization loss is: V ohm =i cell (R c +R m ), where V ohm is the ohmic polarization loss, R c is the constant resistance of the membrane, R mis the membrane equivalent resistance, R m It is expressed as:

[0073] Where, I is the thickness of the proton exchange membrane (μm), A is the area of ​​the proton exchange membrane (cm 2 ), ρ m is the resistivity of the proton exchange membrane (Ω·cm), ρ m It is expressed as:

[0074]

[0075] where i cell is the battery current, A is the battery activation area, T PEM is the operating temperature of the fuel cell, and Λ is the parameter to be identified.

[0076] The concentration polarization loss formula is:

[0077] In the formula, V cons is the concentration polarization loss, b is the parameter coefficient, J is the current density (A / cm 2 ),J max is the maximum current density (A / cm 2 ), Λ is the parameter to be identified;

[0078] The battery stack output voltage is: V stack =n×V T , in the formula, V stack is the output voltage of the battery stack, and n is the number of single cells in the battery stack;

[0079] The output voltage formula of a single fuel cell is: V T =E Nerst -V act -V ohm -V cons In the formula, V T is the output voltage of a single fuel cell.

[0080] The parameters that need to be identified in the semi-empirical model of the proton exchange membrane fuel cell of the present invention include: β1, β2, β3, β4, R c ,∧and b.

[0081] The positive effects of the present invention are as follows: the present invention introduces nonlinear factors into Rossler chaos, increases complex behaviors through nonlinear factor alienation, generates an initial population with a more uniform distribution, and performs statistics on the uniformity of distribution, combines the GMO algorithm (geometric mean optimizer, referred to as GMO) with chaos mapping and the SCA algorithm (sine-cosine optimization algorithm), balances exploration and convergence performance, and improves the stability and accuracy of the improved algorithm operation. Through the improved optimization algorithm, a more accurate and stable proton exchange membrane fuel cell model parameter identification effect is achieved, and good identification effects can be achieved under different verification cases, which improves the accuracy and stability of the optimization algorithm in the proton exchange membrane fuel cell parameter identification. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Attached Figure 1 It is a flowchart of the SCAGMO (Sin-Cosine-Geometric Mean Optimization) algorithm of the present invention;

[0083] Attached Figure 2 This is a graph showing the change of the objective function value of the BSC 500W fuel cell parameter identification process using SCAGMO identification according to an embodiment of the present invention;

[0084] Attached Figure 3 This is a comparison chart of the output of a BSC 500W fuel cell model after SCAGMO identification and a test curve according to an embodiment of the present invention;

[0085] Attached Figure 4 This is a graph showing the change of the objective function value of the SR-12 fuel cell parameter identification process using SCAGMO identification according to an embodiment of the present invention;

[0086] Attached Figure 5 This is a comparison diagram of the output of the SR-12 fuel cell model after SCAGMO identification and the test curve in an embodiment of the present invention;

[0087] Attached Figure 6 This is a graph showing the change in the objective function value of the Horizen 500W fuel cell parameter identification process using SCAGMO identification according to an embodiment of the present invention;

[0088] Attached Figure 7 A comparison chart of the output of the Horizen 500W fuel cell model after SCAGMO identification and the test curve according to an embodiment of the present invention;

[0089] Attached Figure 8 This is a graph showing the change of the objective function value of the 250W fuel cell parameter identification process using SCAGMO identification according to an embodiment of the present invention;

[0090] Attached Fig. 9This is a comparison chart of the output of a 250W fuel cell model after SCAGMO identification and the test curve according to an embodiment of the present invention;

[0091] Attached Fig.10 A graph showing a change in the objective function value of a Ballard Mark V fuel cell parameter identification process using SCAGMO identification according to an embodiment of the present invention;

[0092] Attached Fig.11 This is a comparison chart of the output of the Ballard Mark V fuel cell model after SCAGMO identification and the test curve in an embodiment of the present invention;

[0093] Attached Fig.12 This is a comparison diagram of the initial distribution of Rossler chaos after nonlinear factor optimization in an embodiment of the present invention. DETAILED DESCRIPTION

[0094] As attached Figure 1 As shown, the present invention adopts the following steps:

[0095] S1. Establishing a semi-empirical model of a proton exchange membrane fuel cell; the semi-empirical model includes the output voltage of the fuel cell, and the parameters to be identified in the model are determined according to the output voltage of the fuel cell; the output voltage of a monolithic fuel cell includes Nernst electromotive force, activation polarization loss, ohmic polarization loss and concentration polarization loss;

[0096] The Nernst electromotive force formula is:

[0097]

[0098] In the formula, E Nerst is the Nernst potential of a monolithic proton exchange membrane fuel cell, T PEM is the fuel cell operating temperature, and is the pressure of hydrogen and oxygen;

[0099] The activation polarization loss formula is:

[0100] V act =β1+β2×T PEM +β3×T PEM ×ln(CO2)+β4×T PEM ×ln(I PEM )

[0101] In the formula, V act is the activation polarization loss, β1, β2, β3, and β4 are all semi-empirical coefficients. is the oxygen concentration at the cathode catalyst interface, I PEM is the fuel cell current; the oxygen concentration at the cathode catalyst interface is: in, is the oxygen pressure;

[0102] The formula for ohmic polarization loss is: V ohm =i cell (R c +R m ), where V ohm is the ohmic polarization loss, R c is the constant resistance of the membrane, R m is the membrane equivalent resistance, R m It is expressed as: Where, l is the thickness of the proton exchange membrane (μm), A is the area of ​​the proton exchange membrane (cm 2 ), ρ m is the resistivity of the proton exchange membrane (Ω·cm), ρ m It is expressed as:

[0103]

[0104] The concentration polarization loss formula is: In the formula, V cons is the concentration polarization loss, b is the parameter coefficient, J is the current density (A / cm 2 ),J max is the maximum current density (A / cm 2 );

[0105] The battery stack output voltage is: V stack =n×V T , where V stack is the output voltage of the battery stack, and n is the number of single cells in the battery stack;

[0106] The output voltage formula of a single fuel cell is: V T =E Nerst -V act -V ohm -V cons In the formula, V T is the output voltage of a single fuel cell.

[0107] In summary, the parameters that need to be identified in the semi-empirical model of proton exchange membrane fuel cells include: β1, β2, β3, β4, R c ,∧and b.

[0108] Initialize program parameters, import model parameters, and generate the initial population in the search space;

[0109] According to the constraints of the parameters to be identified, the search space is set, initialized at the initial stage of the search, and the initial parameters of the algorithm are set, and the search individuals are randomly distributed in the search space;

[0110] When initializing the search position, the chaotic map is integrated, based on Rossler chaos, and nonlinear factors are added to produce a uniform search population in the initial period;

[0111] The ordinary differential equations of basic Rossler chaos in the three-dimensional space coordinate system are:

[0112]

[0113] Among them, a1, a2, β and δ are adjustable parameters; x is the horizontal axis coordinate value, y is the vertical axis coordinate value, and z is the vertical axis coordinate value;

[0114] The improved Rossler chaos after adding nonlinear factors in the three-dimensional space coordinate system is:

[0115] X n+1 =X n +a1(Y n -Z n )

[0116] Y n+1 =Y n +a1(cos(X n )-Y n )

[0117]

[0118] Among them, a1, a2, β, δ are adjustable parameters;

[0119] The initial area is set and expanded in equal increments. The number of chaotic points in the area after each expansion is counted to calculate the uniformity. When the average value of the ratio of all two adjacent statistical values ​​of a chaotic distribution graph approaches 1, the distribution uniformity is considered to be higher.

[0120] S2. Construct the objective function of the optimization algorithm, calculate the fitness value of the initial population, and take the minimum target value as the current best individual; the details are as follows:

[0121] The population includes X1=(x 11 ,x 12 ,…,x 1D ) and V1=(v 11 ,v 12 ,…,v 1D ) is the position and speed of the individual in the i-th search population, D is the matrix dimension, that is, the number of parameters to be identified in the identification process;

[0122] After the initial population is obtained, the fitness value SSE of the initial population is calculated by the objective function, where the objective function is the sum of the square errors between the output voltage of the semi-empirical model of the proton exchange membrane fuel cell and the actual test voltage:

[0123]

[0124] Where V exp is the actual test voltage, V sim Output voltage for the semi-empirical model;

[0125] Solve the mean and variance of the objective function value SSE corresponding to the individuals in the population to calculate the population dual fitness value;

[0126] Set the objective function value SSE calculated by the population to Z best ;

[0127] During the parameter identification process, the parameters to be identified are restricted to the following search space:

[0128]

[0129] Λ min ≤Λ≤Λ max

[0130] b min ≤b≤b max ;

[0131] S3. Calculate the fuzzy membership function value of the best individual as its dual fitness index; the specific operation is as follows:

[0132] The geometric mean optimizer (GMO) can simultaneously evaluate the fitness and diversity of search individuals in the search space. In the GMO algorithm, when solving the optimization problem, the geometric mean of the scaled target values ​​of the opposite sides of an individual is assigned to the individual as its weight, representing its total qualification to guide other individuals during the search process. The details and formula of the algorithm are as follows:

[0133] Assume X i =(x i1 ,x i2 ,…,x iD ) and V i =(v i1 ,v i2 ,…,v iD) is the position and speed of the individual in the i-th search population. In order to solve the optimization problem, GMO can evaluate the fitness and diversity of the search individuals in the search space through a single indicator, called the dual-fitness index (DFI). In order to calculate DFI, referring to the concept of fuzzy logic, the similarity between several variables can be expressed by multiplying the fuzzy membership function (MF) values ​​belonging to these variables; this multiplication is called the product-based Larsen implicit function and is widely used in fuzzy systems. The geometric mean formula of n fuzzy membership functions (MF) is:

[0134]

[0135] The MFs formula is:

[0136]

[0137] Substituting x into the objective function value calculated by the current best search individual, the fuzzy value MF of the individual can be calculated according to the formula:

[0138]

[0139] Among them, j is the jth individual in the population, 1...N is the range of individual values, and N is the number of individuals in the population;

[0140] Referring to the geometric mean concept of the above fuzzy membership function values, a new index is constructed and named Dual-Fitness Index:

[0141]

[0142] in is the objective function value of the current optimal individual in the tth iteration, μ t With σ t is the mean and standard deviation of the objective function value in the tth iteration;

[0143] Sort the fitness of the individuals in the population in descending order, select the individual with the smallest double fitness value as the best individual, and set the position of the best individual as X best ;

[0144] S4. Using the dual fitness index as weight, calculate the weighted average of the population relative to the best individual to achieve the unique orientation of the agent; the details are as follows:

[0145] In order to make all the best individuals up to the tth iteration contribute to the generation of the global guiding individual, the weighted average of all the opposite best individuals so far is defined, and the dual fitness index is used as the weight to calculate the guidance. When solving the elitism problem when searching for guiding individuals, the formula is:

[0146]

[0147] in is the best individual in the population, DFI is the dual fitness index, and to avoid singularity, a small positive number ε is added to the denominator;

[0148] The global guides individuals to achieve the only direction of group variation and imposes variation on individuals within the group;

[0149] S5. Apply mutation to each individual in the population, determine the mutation direction through guidance, and limit the step length of the mutation in combination with the SCA algorithm, and update the speed and position of the search population individuals; the details are as follows:

[0150] By integrating with the SCA algorithm, the coefficient of variation is limited by the value range of the sine function and the cosine function, that is, the step limit of the variation is added to prevent the algorithm from falling into the local optimal solution;

[0151] The individual update formula in the basic SCA algorithm is:

[0152]

[0153] in, is the t-th iteration position of the k-th dimension of the current individual, r1, r2, r3, and r4 are random numbers. When r1>1, it is the global exploration stage of the algorithm, and when r1<1, it is the local development stage of the algorithm. The value range of r2 is 0-2π, the value range of r3 is 0-2, and the value range of r4 is 0-1. is the k-th dimension position of the optimal individual position variable at the t-th iteration;

[0154] The individual update formula in the basic GMO algorithm is:

[0155]

[0156] The speed update formula in the GMO algorithm is combined with the individual update formula in the SCA algorithm to obtain the individual update strategy in the SCAGMO algorithm.

[0157] The optimized SCAGMO algorithm update equation is:

[0158]

[0159] Among them, r1, r2, r3 are random numbers, and γ is an adjustable parameter, and the value range is 0-1;

[0160] S6. If the maximum number of iterations has not been reached, repeat steps S2-S5. If the maximum number of iterations has been reached, output the optimal result.

[0161] Example:

[0162] The improved optimization algorithm of the present invention is verified by simulation experiments; the results are verified by comparing it with the whale optimization algorithm (WOA), particle swarm optimization algorithm (PSO), ant colony optimization algorithm (ALO), dragonfly optimization algorithm (DA), multiverse optimizer (MVO), equilibrium optimization algorithm (EO), sparrow search optimization algorithm (SSA), gray wolf optimization algorithm (GWO), sine-cosine optimization algorithm (SCA) and basic geometric mean optimization algorithm (GMO) in different cases of BCS500W, Modular SR-12, Horizen 500W, 250W and BallardMark V; to avoid the randomness of the algorithm, 30 tests are carried out for each case, and the optimal value of the result is taken as the final result.

[0163] In this embodiment, a BCS 500W fuel cell is used for implementation. Figure 2 The objective function value change curve during the algorithm iteration process of the BCS 500W fuel cell model identified by the SCAGMO algorithm that integrates the improved Rossler chaotic map. It can be seen from the figure that the algorithm has a high convergence accuracy.

[0164] Attached Figure 3 The output of the BCS 500W fuel cell model identified by the SCAGMO algorithm that integrates the improved Rossler chaotic map is compared with the experimental results. It can be seen from the figure that the output results of the model established by parameter identification have a good fit with the experimental curve, and the parameter identification accuracy is high.

[0165] In this embodiment, an SR-12 fuel cell is used for implementation. Figure 4 The objective function value change curve during the algorithm iteration process of the SR-12 fuel cell model operation identified by the SCAGMO algorithm that integrates the improved Rossler chaotic map. It can be seen from the figure that the algorithm has a high convergence accuracy.

[0166] Attached Figure 5 The output of the SR-12 fuel cell model identified by the SCAGMO algorithm that integrates the improved Rossler chaotic map is compared with the experimental results. It can be seen from the figure that the output result of the model established by parameter identification has a good fit with the experimental curve, and the parameter identification accuracy is high.

[0167] Attached Figure 6 The objective function value change curve during the algorithm iteration process of the SR-12 fuel cell model operation identified by the SCAGMO algorithm that integrates the improved Rossler chaotic map is shown in the figure. It can be seen from the figure that the algorithm has the best convergence accuracy compared with other algorithms.

[0168] In this embodiment, a Horizen 500W fuel cell is used for implementation. Figure 6 The objective function value change curve of the Horizen 500W fuel cell model identified by the SCAGMO algorithm that integrates the improved Rossler chaotic map during the algorithm iteration process. It can be seen from the figure that the algorithm has the best convergence accuracy compared with other algorithms.

[0169] Attached Figure 7 The output of the Horizen 500W fuel cell model identified by the SCAGMO algorithm that integrates the improved Rossler chaotic map is compared with the experimental results. It can be seen from the figure that the output results of the model established by parameter identification have a good fit with the experimental curve, and the parameter identification accuracy is high.

[0170] In this example, a 250W fuel cell is used for implementation. Figure 8 The objective function value change curve of the 250W fuel cell model identified by the SCAGMO algorithm that integrates the improved Rossler chaotic map during the algorithm iteration process is shown in the figure. It can be seen that the algorithm has a high convergence accuracy.

[0171] Attached Fig. 9 The output of the 250W fuel cell model identified by the SCAGMO algorithm that integrates the improved Rossler chaotic map is compared with the experimental results. It can be seen from the figure that the output results of the model established by parameter identification have a good fit with the experimental curve, and the parameter identification accuracy is high.

[0172] In this example, a Ballard Mark V fuel cell is used for implementation. Fig.11 The output of the Ballard Mark V fuel cell model identified by the SCAGMO algorithm that integrates the improved Rossler chaotic map is compared with the experimental results. It can be seen from the figure that the output result of the model established by parameter identification has a good fit with the experimental curve, and the parameter identification accuracy is high.

[0173] Attached Fig.12 The curve of the objective function value change during the algorithm iteration process of the Ballard Mark V fuel cell model identified by the SCAGMO algorithm that integrates the improved Rossler chaotic map. It can be seen from the figure that the algorithm has a high convergence accuracy.

[0174] Attached Fig.12The particle distribution diagram of the Rossler chaotic map improved by integrating nonlinear factors. The average value of the ratio of all two adjacent statistical values ​​of the Rossler chaotic map is calculated to be 1.035714286. After integrating the nonlinear factors, the average value of the ratio of all two adjacent statistical values ​​of the Rossler chaotic map is 1.018571429, and the distribution uniformity is improved.

[0175] The optimal parameters and objective function values ​​(SSE) obtained by each algorithm are shown in Table 1:

[0176] Table 1: Solution results of different algorithms for fuel cell model parameters in different cases

[0177] SSE BCS500 Modular SR-12 Horizen 500W 250W Ballard Mark V WOA 0.11862 0.02376 0.53998 0.35037 0.50042 PSO 0.1715 0.00802 0.4996 0.34907 0.4443 ALO 0.10557 0.00248 0.48001 0.34931 0.41873 DA 0.12004 0.01226 0.51734 0.35119 0.40595 SCA 0.15895 0.09064 0.50306 0.36633 0.44438 MVO 0.09896 0.00147 0.47938 0.35093 0.39619 EO 0.09772 <![CDATA[6.75*10 -04 ]]> 0.48069 0.346 0.3506 SSA 0.60542 0.00196 0.48234 0.35252 0.40219 GWO 0.09951 0.00182 0.47119 0.35069 0.36223 GMO 0.1015 0.00117 0.5187 0.3905 0.4099 SCAGMO 0.09799 <![CDATA[3.77*10 -04 ]]> 0.4789 0.3464 0.3646

[0178] It can be seen from Table 1 that compared with other algorithms, the improved SCAGMO (sine-cosine-geometric mean optimization) algorithm has achieved a significant advantage in SSE. Under Modular SR-12, SCAGMO has achieved the smallest SSE. In the remaining four embodiments, the difference between the SSE obtained by SCAGMO and the optimal result is controlled within 4%, and the SSE of the SCAGMO algorithm has been greatly optimized compared with the improved geometric mean optimization algorithm. The SCAGMO algorithm has a good optimization effect and high robustness. The improved SCAGMO algorithm has a more significant advantage in the optimization ability of proton exchange membrane fuel cell parameters compared with other algorithms. The standard deviations of SCAGMO under the five embodiments are: 0.000612983, 0.002898536, 0.006005107, 0.003470268 and 0.021361693, respectively, with high stability.

[0179] The present invention introduces nonlinear factors into Rossler chaos, increases complex behaviors through nonlinear factor alienation, generates an initial population with more uniform distribution, and performs statistics on the uniformity of distribution, combines the GMO algorithm (geometric mean optimizer, referred to as GMO) with chaos mapping and SCA algorithm (sine-cosine optimization algorithm), balances exploration and convergence performance, and improves the stability and accuracy of the improved algorithm operation. Through the improved optimization algorithm, a more accurate and stable proton exchange membrane fuel cell model parameter identification effect is achieved, and good identification effects can be achieved under different verification cases, which improves the accuracy and stability of the optimization algorithm in proton exchange membrane fuel cell parameter identification.

Claims

1. A proton exchange membrane fuel cell model parameter identification method based on an optimization algorithm, characterized in that: Use the following steps: S1. Establish a semi-empirical model of proton exchange membrane fuel cells; import model parameters and generate an initial population in the search space; The specific process of generating the initial population in the search space is as follows: According to the constraints of the parameters to be identified, the search space is set, initialized at the initial stage of the search, and the initial parameters of the algorithm are set, and the search individuals are randomly distributed in the search space; When initializing the search position, the chaotic map is integrated, based on Rossler chaos, and nonlinear factors are added to produce a uniform search population in the initial period; The ordinary differential equations of basic Rossler chaos in the three-dimensional space coordinate system are: Among them, a1, a2, β and δ are adjustable parameters; x is the horizontal axis coordinate value, y is the vertical axis coordinate value, and z is the vertical axis coordinate value; The improved Rossler chaos after adding nonlinear factors in the three-dimensional space coordinate system is: X n+1 =X n +a1(Y n -Z n ) AND n+1 =And n +a1(cos(X n )-AND n ) Among them, a1, a2, β, δ are adjustable parameters; Set the initial area and expand it in equal increments. Count the number of chaotic points in the area after each expansion to calculate the uniformity. When the average value of the ratio of all two adjacent statistical values ​​of a chaotic distribution graph approaches 1, the distribution uniformity is considered to be higher. S2. Construct the objective function of the optimization algorithm, calculate the fitness value of the initial population, and take the minimum target value as the current best individual; the details are as follows: The population includes X1=(x 11 ,x 12 ,…,x 1D ) and V1=(v 11 ,v 12 ,…,v 1D ) is the position and speed of the individual in the i-th search population, D is the matrix dimension, that is, the number of parameters to be identified in the identification process; After the initial population is obtained, the fitness value SSE of the initial population is calculated by the objective function, where the objective function is the sum of the square errors between the output voltage of the semi-empirical model of the proton exchange membrane fuel cell and the actual test voltage: Among them, V exp is the actual test voltage, V sim is the output voltage of the semi-empirical model; Solve the mean and variance of the objective function value SSE corresponding to the individuals in the population to calculate the population dual fitness value; Set the objective function value SSE calculated by the population to Z best ; S3. Calculate the fuzzy membership function value of the best individual as its dual fitness index; the details are as follows: The similarity between variables can be expressed by multiplying the fuzzy membership function (MF) values ​​of these variables; Calculate the fuzzy membership function value (MF) of the individual; The geometric mean of n fuzzy membership function values ​​(MF) can be expressed as: The dual fitness index (DFI) is constructed based on the geometric mean of the fuzzy membership function values: in, is the objective function value of the current optimal individual in the tth iteration, μ t With σ t is the mean and standard deviation of the objective function value in the tth iteration, j is the jth individual in the population, 1...N is the range of individual values, and N is the number of individuals in the population; Sort the fitness of the individuals in the population in descending order, select the individual with the smallest double fitness value as the best individual, and set the position of the best individual as X best ; S4. Using the dual fitness index as weight, calculate the weighted average of the population individuals and the best individual to achieve the unique guidance of the search individual; the details are as follows: In order to make all the best individuals up to the tth iteration contribute to the generation of the global guiding individual, the weighted average of all the opposite best individuals up to now is defined, in, is the best individual in the population, DFI is the dual fitness index, and to avoid singularity, a small positive number ε is added to the denominator; The global guides individuals to achieve the only direction of group variation and imposes variation on individuals within the group; S5. Apply mutation to each individual in the population, determine the mutation direction through guidance, and limit the step length of the mutation in combination with the SCA algorithm, and update the speed and position of the search population individuals; the details are as follows: By integrating with the SCA algorithm, the mutation coefficient is limited by the value range of the sine function and the cosine function, that is, the step limit of the mutation is added to prevent the algorithm from falling into the local optimal solution; The individual mutation update formula in the basic SCA algorithm is: in, is the t-th iteration position of the k-th dimension of the current individual, r1, r2, r3, and r4 are random numbers. When r1>1, it is the global exploration stage of the algorithm, and when r1<1, it is the local development stage of the algorithm. The value range of r2 is 0-2π, the value range of r3 is 0-2, and the value range of r4 is 0-1. is the k-th dimension position of the optimal individual position variable at the t-th iteration; The individual update formula in the basic GMO algorithm is: The speed update formula in the GMO algorithm is combined with the individual mutation update formula in the SCA algorithm to obtain the population individual update strategy in the SCAGMO algorithm. The individual speed and position variation equations in the optimized SCAGMO algorithm are: Among them, r1, r2, r3 are random numbers, and γ is an adjustable parameter, and the value range is 0-1; The iterative process S2-S5 is repeated until the maximum number of iterations is reached; S6. Output the optimal solution.

2. The method for identifying parameters of a proton exchange membrane fuel cell model based on an optimization algorithm according to claim 1, characterized in that: The semi-empirical model in S1 includes the output voltage of the fuel cell, and the parameters to be identified in the model are determined according to the output voltage of the fuel cell; the program parameters are initialized, and the output voltage of the single fuel cell includes the Nernst electromotive force, activation polarization loss, ohmic polarization loss and concentration polarization loss; The Nernst electromotive force formula is: In the formula, E Nerst is the Nernst potential of a monolithic proton exchange membrane fuel cell, T PEM is the fuel cell operating temperature, and is the pressure of hydrogen and oxygen; The activation polarization loss formula is: In the formula, V act is the activation polarization loss, β1, β2, β3, and β4 are all semi-empirical coefficients. is the oxygen concentration at the cathode catalyst interface, I PEM is the fuel cell current; the oxygen concentration at the cathode catalyst interface is: in, is the oxygen pressure; The formula for ohmic polarization loss is: V ohm =i cell (R c +R m ), In the formula, V ohm is the ohmic polarization loss, R c is the constant resistance of the membrane, R m is the membrane equivalent resistance, R m It is expressed as: Where, l is the thickness of the proton exchange membrane (μm), A is the area of ​​the proton exchange membrane (cm 2 ), ρ m is the resistivity of the proton exchange membrane (Ω·cm), ρ m It is expressed as: where i cell is the battery current, A is the battery activation area, T PEM is the operating temperature of the fuel cell, Λ is the parameter to be identified; The concentration polarization loss formula is: In the formula, V cons is the concentration polarization loss, b is the parameter coefficient, J is the current density (A / cm 2 ),J max is the maximum current density (A / cm 2 ), Λ is the parameter to be identified; The battery stack output voltage is: V stack =n×V T , in the formula, V stack is the output voltage of the battery stack, and n is the number of single cells in the battery stack; The output voltage formula of a single fuel cell is: V T =E Nerst -V act -V ohm -V cons In the formula, V T is the output voltage of a single fuel cell.

3. The method for identifying parameters of a proton exchange membrane fuel cell model based on an optimization algorithm according to claim 2, characterized in that: The parameters that need to be identified in the semi-empirical model of proton exchange membrane fuel cells include: β1, β2, β3, β4, R c and b.

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