Fuel cell parameter identification method and apparatus, and device and storage medium

Abstract

The present invention relates to the technical field of proton exchange membrane fuel cells. Disclosed are a fuel cell parameter identification method and apparatus, and a device and a storage medium. The method comprises the following steps: constructing a semi-empirical model for a proton exchange membrane fuel cell; calculating a theoretical value of an output voltage of the semi-empirical model, and constructing an objective function by means of a mean square error between the theoretical value and an actual value of the output voltage of the semi-empirical model; on the basis of the semi-empirical model, determining a plurality of parameters to be identified, and using said plurality of parameters as decision variables to construct a plurality of constraint conditions for the objective function; on the basis of the plurality of constraint conditions, constructing an optimization model for the proton exchange membrane fuel cell by using the minimization of the objective function as an optimization objective and using said plurality of parameters as variables to be solved; and solving the optimization model by means of a multi-policy sparrow search optimization algorithm, so as to obtain a plurality of optimal parameters to be identified. In the multi-policy sparrow search optimization algorithm in the present invention, Tent chaotic mapping is introduced to initialize a population, the number of populations is increased, and then the two populations are merged. An adaptive feedback mechanism is added in a follower position update stage and a vigilant position update stage, thereby reducing the convergence accuracy under a limited number of iterations. A DE / best / 1 mutation policy and a dynamic scaling factor sf are used to update the position of a sparrow. The global optimization capability and the local optimization capability of an algorithm are improved, thereby also improving the accuracy of fuel cell parameter identification.

Description

Fuel cell parameter identification method, device, equipment and storage medium Technical Field

[0001] The present invention relates to the technical field of proton exchange membrane fuel cells, and in particular to a fuel cell parameter identification method, device, equipment and storage medium. Background Art

[0002] In recent years, with increasing energy demand, the gradual depletion of traditional fuel resources, and increasingly serious environmental pollution, researchers have increasingly focused on new energy conversion devices such as hydrogen fuel cells. Hydrogen fuel cells convert hydrogen directly into electricity through a series of electrochemical reactions. Compared to traditional energy conversion methods, they avoid the limitations of the Carnot cycle, improve energy conversion efficiency, and produce only water as a byproduct, without any environmental pollution.

[0003] Especially in the field of proton exchange membrane fuel cells (PEMFC), its advantages such as low operating temperature, zero pollution, low noise, fast response, and high power density make it an ideal energy conversion device. However, PEMFC still has some shortcomings that need to be addressed. Therefore, it is particularly important to establish a semi-empirical model close to the actual fuel cell to study and improve the performance of PEMFC. At present, PEMFC models are mainly divided into semi-empirical models, mechanistic models, and data-driven models. Because the mechanistic model relies on thermodynamics, electrochemistry, and fluid mechanics equations, the solution process through CFD commercial software simulation is very complex and time-consuming. The data-driven model relies on a large amount of experimental data and is essentially a black box, without interpretability. Semi-empirical models have the characteristics of high simulation accuracy and speed, and are more widely used in engineering practice. Semi-empirical models of PEMFC are often used in simulation research. However, since the parameters of the semi-empirical model are generally unknown, and this type of fuel cell itself has high complexity and nonlinear characteristics, it is necessary to identify the coefficients of the semi-empirical model to establish an accurate PEMFC semi-empirical model.

[0004] Traditional analytical methods for PEMFC parameter identification, such as the Gauss-Newton method and gradient descent, suffer from limitations such as cumbersome gradient calculations, high complexity, weak global optimization capabilities, and a high degree of reliance on initial iteration values. While metaheuristic algorithms are widely used in parameter identification, they are prone to falling into local optima, premature convergence, and randomness in the optimal solution. Further improvements are needed to achieve stable and accurate results.

[0005] Metaheuristic algorithms have emerged as an effective solution to the challenge of PEMFC parameter identification. These algorithms require no gradient information or specific initial conditions, significantly reducing computational resources and time. However, intelligent algorithms such as the sparrow search optimization algorithm (SSA) still suffer from low search efficiency, premature convergence, and a tendency to fall into local optimal solutions.

[0006] In summary, as an important future energy conversion device, PEMFC faces complexities and challenges in semi-empirical model parameter identification. Researchers urgently need to find more accurate and efficient methods to identify the parameters of the PEMFC semi-empirical model to promote its widespread application and development in the energy sector. Summary of the Invention

[0007] The present invention provides a fuel cell parameter identification method, device, equipment and storage medium, which solves the problems of low search efficiency, premature convergence and easy falling into local optimal solution when the existing sparrow search optimization algorithm (SSA) is used to identify parameters.

[0008] The present invention provides a fuel cell parameter identification method, comprising the following steps:

[0009] Construct a semi-empirical model of proton exchange membrane fuel cells;

[0010] Calculating a theoretical value of the output voltage of the semi-empirical model, and constructing an objective function through a mean square error between the theoretical value and an actual value of the output voltage of the semi-empirical model;

[0011] Determining a plurality of parameters to be identified according to the semi-empirical model, and using the plurality of parameters to be identified as decision variables to construct a plurality of constraint conditions of the objective function;

[0012] Based on multiple constraints, an optimization model of a proton exchange membrane fuel cell is constructed with minimizing the objective function as the optimization goal and multiple parameters to be identified as the variables to be solved;

[0013] The optimization model is solved by a multi-strategy sparrow search optimization algorithm to obtain multiple optimal parameters to be identified;

[0014] The multi-strategy sparrow search optimization algorithm adopts an elite population strategy to replace the random initialization strategy generation mechanism, explores the solution space through the Lévy flight perturbation strategy in the discoverer position update phase, adds an adaptive feedback mechanism in the follower position update phase and the sentinel position update phase, and adopts the DE / best / 1 mutation strategy to update the sparrow position again after the sentinel position update phase;

[0015] Among them, the elite population strategy adopts uniform random distribution method and Tent chaos mapping method to generate two initial sparrow populations, let the two compete, calculate the fitness values ​​of all individuals in the two populations, and then sort them from small to large, and take the first N individuals as the final initial population P.

[0016] Preferably, constructing a semi-empirical model of a proton exchange membrane fuel cell specifically includes the following steps:

[0017] Calculate the voltage of a monolithic proton exchange membrane fuel cell: V cell =E nerst -V act -V ohm -V con

[0018] Where V cell is the voltage of the monolithic proton exchange membrane fuel cell, E nerst is the thermodynamic voltage, V act is the activation loss, V ohm is the ohmic loss, V con is the concentration loss;

[0019] in, V ohm =IR int =I(R m +R c )

[0020] Where ΔG is the Gibbs free energy of the reaction, n is the number of moles of electrons transferred by the proton exchange membrane fuel cell, F is the Faraday constant, ξ1, ξ2, ξ3, and ξ4 are activation loss parameters. is the interface oxygen concentration, T is the stack temperature, I is the operating current, R C is the electronic resistance, R m is the membrane equivalent resistance, R int is the total resistance, b is the concentration loss coefficient, J max is the maximum current density, J is the current density, ρ m is the membrane resistivity, l is the membrane thickness, A is the membrane area, and λ is the water content of the exchange membrane;

[0021] The semi-empirical model of the proton exchange membrane fuel cell is as follows:

[0022] Where N cell is the number of cells in the proton exchange membrane fuel cell.

[0023] Preferably, the multiple parameters to be identified include activation loss parameters ξ1, ξ2, ξ3, ξ4, electronic resistance R C, concentration loss coefficient b, maximum current density J max , current density J, exchange membrane water content λ.

[0024] Preferably, the optimization model of the proton exchange membrane fuel cell is as follows: f(ξ1, ξ2, ξ3, ξ4, R c ,b,λ,J max , J) = min(MSE)

[0025] in, λ min ≤λ≤λ max b min ≤b≤b max J min ≤J≤J max

[0026] Where min is the minimization function, V cell (k) is the theoretical value of the output voltage, V m (k) is the actual value of the output voltage, m is the subscript of the activation loss parameter, k is the kth operating point, num is the number of operating points, f is the optimization target, is the lower bound of the mth activation loss parameter, is the upper limit of the mth activation loss parameter, is the lower limit of electronic resistance, is the upper limit of electronic resistance, λ min is the lower limit of water content of the exchange membrane, λ max is the upper limit of water content of the exchange membrane, b min is the lower limit of the concentration loss coefficient, b max is the upper limit of the concentration loss coefficient, is the lower limit of the maximum current density, is the upper limit of the maximum current density, J min is the lower limit of current density, J max is the upper limit of the current density.

[0027] Preferably, solving the optimization model by a multi-strategy sparrow search optimization algorithm to obtain multiple optimal parameters to be identified includes the following steps:

[0028] S1: Set the search space and dimension of the sparrows according to multiple constraints, set the number of sparrows in the population, the maximum number of iterations, the proportion of discoverers, the proportion of alerters, and the safety threshold;

[0029] S2: Use the elite population strategy to obtain the elite population and enter the cycle;

[0030] S3: Calculate the fitness values ​​of individual sparrows in the elite population, sort multiple fitness values, divide the sparrows into discoverers and followers based on the proportion of discoverers, and find the sparrows and their positions corresponding to the best and worst fitness values;

[0031] S4: The discoverer position update phase, in which the discoverer position is updated according to the Levy flight perturbation strategy;

[0032] S5: Follower position update phase, update the follower position according to the follower formula;

[0033] S6: Sentinel position update phase, randomly generate sentinels in the population based on the sentinel ratio, and update the sentinel position according to the sentinel formula;

[0034] S7: DE / best / 1 mutation phase, for all sparrow individuals, the positions are updated according to the DE / best / 1 mutation strategy and the dynamic scaling factor sf;

[0035] S8: Update the individual fitness values ​​of sparrows and re-rank them to determine the best and worst fitness values ​​and their positions;

[0036] S9: Determine whether the algorithm end condition is met. If not, jump to S3. If met, proceed to S10.

[0037] S10: Record the optimal result and end the operation.

[0038] Preferably, the Tent chaos mapping method formula is as follows:

[0039] Where, and is the i-th sparrow individual in the new population The jth dimension of The upper and lower limits of φ n is a random number in [0,1], φ n+1 Generate a new random number. The position of the sparrow after the Tent chaos map.

[0040] Preferably, the Levy flight disturbance strategy is as follows:

[0041] in,

[0042] Where, is the position of the i-th sparrow in the t+1th generation, is the position of the i-th sparrow in the t-th generation, is the optimal sparrow position of the tth generation, S is the step size, l is the Levy flight direction, levy is the Levy flight perturbation function, μ is the expected value of 0, and the variance is σ μ The normal distribution, σ μ To satisfy the expectation of 0 and the variance of σ v Normal distribution, γ = 1.5, σ v =1,λ=1.5,Γ is the Gamma function;

[0043] The follower formula is as follows:

[0044] Among them, A + =A T (AA T ) -1

[0045] Where, is the global worst position of the t+1 generation, is the optimal position explored by the t+1th generation discoverer, a is the adaptive coefficient, e is the minimum constant to avoid the division error to be zero, A is a 1×d matrix whose elements are randomly assigned to -1 or 1, T is the transpose symbol, L is a 1×d matrix, where all elements in the matrix are 1, and Q is a random number that obeys the normal distribution. is the position of the i-th sparrow in the j-th dimension of the t+1-th generation, is the position of the i-th sparrow in the t-th generation in the j-th dimension, and n is the total number of sparrows;

[0046] The Vigilant formula is as follows:

[0047] Where α is a normal distribution random value with mean 0 and variance 1, K is a random number in the range [-1, 1], and ε is the minimum constant to avoid the division error being zero. represents the current global optimal position, f i ,f g and f w are the current individual fitness, the current global optimal and the worst fitness values, respectively. is the optimal position of the t+1 generation sparrow;

[0048] The DE / best / 1 mutation strategy and dynamic scaling factor sf are as follows:

[0049] Where, is the dynamic scaling factor, sfintial and sfintial are two constants, is the mutant individual of the i-th sparrow in the t-th generation, p1 and p2 are random integers and p1≠p2∈[1,2,…,n], is a test vector generated by crossover operation, is the position of the i-th sparrow in the t-th generation in the r-th dimension, The worst fitness value in the t-th generation population, p c is the crossover probability in the range [0,1], r is a d-dimensional vector, and r0∈{1,2,…,d} describes a random dimension.

[0050] A fuel cell parameter identification device, comprising:

[0051] The first module is used to build a semi-empirical model of proton exchange membrane fuel cells;

[0052] The second module is used to calculate the theoretical value of the output voltage of the semi-empirical model and construct an objective function through the mean square error between the theoretical value and the actual value of the output voltage of the semi-empirical model;

[0053] A third module is used to determine a plurality of parameters to be identified according to the semi-empirical model, and to construct a plurality of constraint conditions of the objective function by using the plurality of parameters to be identified as decision variables;

[0054] The fourth module is used to construct an optimization model of a proton exchange membrane fuel cell based on multiple constraints, with minimization of the objective function as the optimization goal and multiple parameters to be identified as variables to be solved;

[0055] The fifth module is used to solve the optimization model through a multi-strategy sparrow search optimization algorithm to obtain multiple optimal parameters to be identified;

[0056] The multi-strategy sparrow search optimization algorithm adopts an elite population strategy to replace the random initialization strategy generation mechanism, explores the solution space through the Lévy flight perturbation strategy in the discoverer position update phase, adds an adaptive feedback mechanism in the follower position update phase and the sentinel position update phase, and adopts the DE / best / 1 mutation strategy to update the sparrow position again after the sentinel position update phase;

[0057] Among them, the elite population strategy adopts uniform random distribution method and Tent chaos mapping method to generate two initial sparrow populations, let the two compete, calculate the fitness values ​​of all individuals in the two populations, and then sort them from small to large, and take the first N individuals as the final initial population P.

[0058] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the above-mentioned fuel cell parameter identification method is implemented.

[0059] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the fuel cell parameter identification method is implemented.

[0060] Compared with the prior art, the present invention has the following beneficial effects:

[0061] The present invention first constructs a semi-empirical model of a proton exchange membrane fuel cell, then obtains a corresponding plurality of parameters to be identified, and constructs an optimization model of the proton exchange membrane fuel cell. The optimization model is solved by a multi-strategy sparrow search optimization algorithm to obtain a plurality of optimal parameters to be identified. The multi-strategy sparrow search optimization algorithm introduces a tent chaos map to initialize the population, increases the number of populations, and then merges the two populations. Next, an elite population is obtained using an elite strategy to improve the quality of the initial solution. In the discoverer position update phase, the solution space is explored using the Levy flight perturbation strategy. During the levy flight process, there will be a larger range of motion and high search efficiency. An adaptive feedback mechanism is added in the follower position update phase and the sentinel position update phase, which reduces the convergence accuracy under a limited number of iterations. In order to avoid premature convergence, a DE / best / 1 mutation strategy and a dynamic scaling factor sf are adopted to update the sparrow position. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0063] FIG1 is a flow chart of a fuel cell parameter identification method according to the present invention;

[0064] FIG2 is a schematic diagram of a process of solving an optimization model by the multi-strategy sparrow search optimization algorithm of the present invention;

[0065] FIG3 is a comparison diagram of theoretical and actual output current-voltage values ​​of a proton exchange membrane fuel cell according to an embodiment of the present invention;

[0066] Figure 4 is a comparison curve chart of the optimization model search of the multi-strategy sparrow search optimization algorithm (MOSSA), adaptive sparrow search algorithm (ASSA), sparrow search algorithm (SSA), hunger games search algorithm (HGS), vulture search algorithm (BES), improved print fish optimization algorithm (IROA), dung beetle optimization algorithm based on quantum computing and mutation fusion (QHDBO), print fish optimization algorithm (ROA), and improved artificial bee colony optimization algorithm (IABC) used in the simulation experiment of an embodiment of the present invention. DETAILED DESCRIPTION

[0067] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0068] The present invention provides a fuel cell parameter identification method, referring to FIG1 , comprising the following steps:

[0069] Step 1: Construct a semi-empirical model of proton exchange membrane fuel cells based on the principles of proton exchange membrane fuel cells.

[0070] The anode reaction equation of the proton exchange membrane fuel cell is as follows: H2→2H + +2e -

[0071] The cathode reaction equation of the proton exchange membrane fuel cell is as follows:

[0072] The overall chemical reaction equation of the proton exchange membrane fuel cell is as follows:

[0073] In the anode catalyst layer, H2 decomposes into protons and electrons, of which electrons reach the cathode through the external circuit, and protons pass through the exchange membrane to the cathode. In the cathode catalyst layer, O2 combines with protons and electrons to generate H2O.

[0074] By analyzing the working principle and structural characteristics of proton exchange membrane fuel cells, a semi-empirical model of proton exchange membrane fuel cells is established, the experimental values ​​of the proton exchange membrane fuel cell output voltage at multiple working points are collected, and the theoretical value of the proton exchange membrane fuel cell output voltage at each working point is calculated.

[0075] The theoretical value of the output voltage of the proton exchange membrane fuel cell at each operating point is calculated by the following formula: V cell (k) = N cell ·(E nerst (k)-V act (k)-V ohm (k)-V con (k))

[0076] Where V cell (k) represents the output voltage of the proton exchange membrane fuel cell at the kth operating point, N cell is the number of cells in the proton exchange membrane fuel cell, E nerst (k) represents the Nernst voltage of the proton exchange membrane fuel cell at the kth operating point, Vact (k) represents the activation loss of the proton exchange membrane fuel cell at the kth operating point, V ohm (k) represents the ohmic loss of the proton exchange membrane fuel cell at the kth operating point, V con (k) represents the concentration loss of the proton exchange membrane fuel cell at the kth operating point.

[0077] E nerst is the thermodynamic voltage calculated by the following formula:

[0078] Wherein, ΔG is the Gibbs free energy of the reaction, n is the number of moles of electrons transferred by the proton exchange membrane fuel cell, and F is the Faraday constant, F = 96485.33289 ± 0.00059 C / mol.

[0079] The activation loss is calculated as follows:

[0080] I=i+i n

[0081] Among them, ξ1, ξ2, ξ3, ξ4 are activation loss parameters, is the interface oxygen concentration, i n is the no-load current; the oxygen concentration at the catalyst layer interface is defined as follows:

[0082] The calculation of ohmic loss is shown in the following formula: V ohm =IR int =I(R m +R c )

[0083] Among them, R C is the electronic resistance, R m is the equivalent resistance of the membrane, and the membrane resistivity ρ m , membrane thickness l and membrane area A are defined as follows:

[0084] Where λ is the water content of the exchange membrane.

[0085] Since the speed of electron transfer is much greater than the mass transfer speed of hydrogen and oxygen reaction, the concentration loss occurs, which is calculated as follows:

[0086] Where b is the concentration loss coefficient, J max is the maximum current density, and J is the current density.

[0087] The semi-empirical model of proton exchange membrane fuel cell is shown as follows:

[0088] Step 2: Calculate the theoretical value of the output voltage of the semi-empirical model and construct the objective function through the mean square error between the theoretical value and the actual value of the output voltage of the semi-empirical model.

[0089] The objective function is shown as follows:

[0090] Where, MSE is the mean square error, num is the number of working points, V cell (k) is the theoretical value of the output voltage, V n (k) is the actual value of the output voltage.

[0091] As can be seen from FIG3 , the theoretical output current-voltage value of the proton exchange membrane fuel cell of the present invention is substantially the same as the actual value.

[0092] Step 3: Determine multiple parameters to be identified based on the semi-empirical model, and use the multiple parameters to be identified as decision variables to construct multiple constraints of the objective function.

[0093] Then the activation loss parameters ξ1, ξ2, ξ3, ξ4, and electronic resistance R c , concentration loss coefficient b, exchange membrane water content λ, maximum current density J max , current density J is the parameter to be identified.

[0094] The multiple constraints are as follows: λ min ≤λ≤λ max b min ≤b≤b max J min ≤J≤J max

[0095] Specifically,

[0096] Where min is the minimization function, m is the activation loss parameter subscript, k is the kth working point, num is the number of working points, f is the optimization target, is the lower bound of the mth activation loss parameter, is the upper limit of the mth activation loss parameter, is the lower limit of electronic resistance, is the upper limit of electronic resistance, λ min is the lower limit of water content of the exchange membrane, λ max is the upper limit of water content of the exchange membrane, b min is the lower limit of the concentration loss coefficient, b max is the upper limit of the concentration loss coefficient, is the lower limit of the maximum current density, is the upper limit of the maximum current density, J min is the lower limit of current density, J max is the upper limit of the current density.

[0097] Specifically, in this embodiment, is the upper limit of the activation loss parameter 1, is the lower bound of the activation loss parameter 1, is the upper limit of the activation loss parameter 2, is the lower bound of the activation loss parameter 2, is the upper limit of activation loss parameter 3, is the lower bound of the activation loss parameter 3, is the upper limit of the activation loss parameter 4, is the lower limit of the activation loss parameter 4; is the upper limit of electronic resistance, is the lower limit of electronic resistance, λ max =0.03 is the upper limit of the water content of the exchange membrane, λ min =0.001 is the lower limit of water content of exchange membrane, b max =5V is the upper limit of the concentration loss coefficient, b min =0.5V is the lower limit of the concentration loss coefficient, is the upper limit of the maximum current density, is the lower limit of the maximum current density, J max =0.0008A / cm 2 is the upper limit of no-load current density, J min =0.0001A / cm 2 is the lower limit of the no-load current density.

[0098] Step 4: Based on multiple constraints, an optimization model of the proton exchange membrane fuel cell is constructed with minimizing the objective function as the optimization goal and multiple parameters to be identified as variables to be solved.

[0099] Taking the minimum mean square error of the difference between the theoretical output voltage and the actual output voltage of the semi-empirical model as the optimization goal, four activation loss parameters, electronic resistance, concentration loss coefficient, exchange membrane water content, limiting current density, and no-load current density are selected as constraint conditions for decision variables to construct parameters, and an optimization model of proton exchange membrane fuel cell is constructed.

[0100] The optimization model of proton exchange membrane fuel cell is as follows: f(ξ1, ξ2, ξ3, ξ4, R c ,b,λ,J max , J) = min(MSE)

[0101] Where f is the optimization objective and min is the minimization function.

[0102] Step 5: Solve the optimization model through the multi-strategy sparrow search optimization algorithm to obtain multiple optimal parameters to be identified;

[0103] 2 , the proton exchange membrane fuel cell optimization model is solved using a multi-strategy sparrow search optimization algorithm to obtain the four optimized activation loss parameters, the optimized electronic resistance, the optimized concentration loss coefficient, the optimized exchange membrane water content, the optimized no-load current density, and the optimized limiting current density.

[0104] S1: Set the search space of the sparrow according to the parameter constraints<Lb,Ub> and dimension, where Lb is the lower limit of the search space and Ub is the upper limit of the search space; set the number of sparrows in the initial population to N, the maximum number of iterations to G, the number of discoverers and sentinels to PD and SD respectively, and the safety threshold to ST;

[0105] S2: Use the elite population strategy to obtain the elite population.

[0106] The elite population strategy specifically involves generating two initial sparrow populations, denoted as RP and CP, using a uniform random distribution method and a Tent Chaos Map method, respectively. These two populations compete with each other, calculating the fitness values ​​of all individuals in the population RPUCP, sorting them from smallest to largest, and taking the top N individuals as the final initial population P, which is called the Chaos Elite Population. The formula for the Tent Chaos Map method is as follows:

[0107] in, and is the i-th sparrow individual in the new population The jth dimension of The upper and lower limits of φ n is a random number in [0,1], φ n+1 Generate a new random number. The position of the sparrow after the Tent chaos map.

[0108] S3: Calculate the fitness values ​​of sparrow individuals in the chaotic elite population, sort them, and find the individuals with the best and worst fitness values ​​and their positions.

[0109] S4: Update the discoverer's position according to the Levy flight perturbation strategy. The formula is as follows:

[0110] Where, is the position of the t+1 generation sparrow, is the position of the t-th generation sparrow, is the optimal sparrow position of the tth generation, S is the step size, l is the Levy flight direction, levy is the Levy flight perturbation function, μ is the expected value of 0, and the variance is σ μ The normal distribution, σ μ To satisfy the expectation of 0 and the variance of σ v Normal distribution; where γ = 1.5, σ v =1,λ=1.5,Γ is the Gamma function.

[0111] S5: Update the follower position according to the follower formula, the formula is as follows: A + =A T (AA T ) -1

[0112] Where, is the global worst position of the t+1 generation, is the optimal position explored by the t+1th generation discoverer, a is the adaptive coefficient, e is the minimum constant to avoid the division error to be zero, A is a 1×d matrix whose elements are randomly assigned to -1 or 1, T is the transpose symbol, L is a 1×d matrix, where all elements in the matrix are 1, and Q is a random number that obeys the normal distribution. is the position of the i-th sparrow in the j-th dimension of the t+1-th generation, is the position of the i-th sparrow of the t-th generation in the j-th dimension, and n is the total number of sparrows.

[0113] S6: Update the sentinel position according to the sentinel formula.

[0114] Here, α is a random number in [0,1].

[0115] S7: Update the position according to the DE / best / 1 mutation strategy and the dynamic scaling factor sf.

[0116] Where, is the dynamic scaling factor, sfintial and sfintial are two constants, is the mutant individual of the i-th sparrow in the t-th generation, p1 and p2 are random integers and p1≠p2∈[1,2,...,n], is a test vector generated by crossover operation, is the position of the i-th sparrow in the t-th generation in the r-th dimension, The worst fitness value in the t-th generation population, p cis the crossover probability in the range [0,1], r is a d-dimensional vector, and r0∈{1,2,…,d} describes a random dimension.

[0117] S8: Update the individual fitness values ​​of the sparrows and re-sort them to determine the best and worst fitness values ​​and their positions.

[0118] S9: Determine whether the algorithm end condition is met. If not, jump to step S3. If so, proceed to the next step.

[0119] S10: Record the optimal result and end the operation.

[0120] Output the optimized four activation loss parameters, optimized electronic resistance, optimized concentration loss coefficient, optimized exchange membrane water content, optimized no-load current density and optimized limiting current density.

[0121] Based on the same concept, the present invention also provides a fuel cell parameter identification device, including a first module, a second module, a third module, a fourth module and a fifth module.

[0122] The first module is used to construct a semi-empirical model of proton exchange membrane fuel cells.

[0123] The second module is used to calculate the theoretical value of the output voltage of the semi-empirical model and construct the objective function through the mean square error between the theoretical value and the actual value of the output voltage of the semi-empirical model.

[0124] The third module is used to determine multiple parameters to be identified based on the semi-empirical model, and use the multiple parameters to be identified as decision variables to construct multiple constraints of the objective function.

[0125] The fourth module is used to construct an optimization model of a proton exchange membrane fuel cell based on multiple constraints, with minimizing the objective function as the optimization goal and multiple parameters to be identified as variables to be solved.

[0126] The fifth module is used to solve the optimization model through a multi-strategy sparrow search optimization algorithm to obtain multiple optimal parameters to be identified.

[0127] The multi-strategy sparrow search optimization algorithm adopts an elite population strategy to replace the random initialization strategy generation mechanism. In the discoverer position update phase, the Lévy flight perturbation strategy is used to explore the solution space. In the follower position update phase and the sentinel position update phase, an adaptive feedback mechanism is added. After the sentinel position update phase, the DE / best / 1 mutation strategy is used to update the sparrow position again.

[0128] The elite population strategy uses a uniform random distribution method and a tent chaotic mapping method to generate two initial sparrow populations, which are then allowed to compete. The fitness values ​​of all individuals in the two populations are calculated, and after sorting them from smallest to largest, the top N individuals are selected as the final initial population P.

[0129] The present invention also provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the above-mentioned fuel cell parameter identification method is implemented.

[0130] The present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the above-mentioned fuel cell parameter identification method is implemented.

[0131] Example

[0132] The solid oxide fuel cell parameter identification method of the present invention is analyzed through simulation experiments.

[0133] The solid oxide fuel cell in the simulation experiment is at an ambient temperature of 298.15 K. The relevant parameters are brought in and the Hunger Game Search Algorithm (HGS), the Vulture Search Algorithm (BES), the Improved Indo-Ocean Optimization Algorithm (IROA), the Adaptive Sparrow Search Algorithm (ASSA) and the Multi-Strategy Sparrow Search Optimization Algorithm (MOSSA) are used to solve the proton exchange membrane fuel cell model. The optimal parameters and MSE obtained by each algorithm are shown in Table 1.

[0134] Table 1: Solution results of each algorithm for the proton exchange membrane fuel cell model parameters

[0135] Table 1 shows that the multi-strategy sparrow search optimization algorithm achieves a lower MSE value than other algorithms, and the improved sparrow search optimization algorithm achieves a significantly better MSE value than the unimproved sparrow search optimization algorithm. The results show that the algorithm has a good optimization effect and has a significant advantage over other algorithms in optimizing proton exchange membrane fuel cell parameters.

[0136] As shown in Figure 4 (currently referring to the convergence diagram of the algorithm results), the multi-strategy sparrow optimization algorithm has stronger search capabilities than other algorithms. It can improve the global and local optimization capabilities of the original algorithm, improve the algorithm's solution efficiency, and can well identify the parameters of the proton membrane exchange fuel cell, and obtain good identification results.

[0137] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0138] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. A fuel cell parameter identification method, characterized in that: The following steps are involved: Construct a semi-empirical model of proton exchange membrane fuel cells; Calculating a theoretical value of the output voltage of the semi-empirical model, and constructing an objective function through a mean square error between the theoretical value and an actual value of the output voltage of the semi-empirical model; Determining a plurality of parameters to be identified according to the semi-empirical model, and using the plurality of parameters to be identified as decision variables to construct a plurality of constraint conditions of the objective function; Based on multiple constraints, an optimization model of a proton exchange membrane fuel cell is constructed with minimizing the objective function as the optimization goal and multiple parameters to be identified as the variables to be solved; The optimization model is solved by a multi-strategy sparrow search optimization algorithm to obtain multiple optimal parameters to be identified; The multi-strategy sparrow search optimization algorithm adopts an elite population strategy to replace the random initialization strategy generation mechanism, explores the solution space through the Lévy flight perturbation strategy in the discoverer position update phase, adds an adaptive feedback mechanism in the follower position update phase and the sentinel position update phase, and adopts the DE / best / 1 mutation strategy to update the sparrow position again after the sentinel position update phase; Among them, the elite population strategy adopts uniform random distribution method and Tent chaos mapping method to generate two initial sparrow populations, let the two compete, calculate the fitness values of all individuals in the two populations, and then sort them from small to large, and take the first N individuals as the final initial population P.

2. A fuel cell parameter identification method according to claim 1, characterized in that: Constructing a semi-empirical model of a proton exchange membrane fuel cell includes the following steps: Calculate the voltage of a monolithic proton exchange membrane fuel cell: V cell =E nerst -V act -V ohm -V con Where V cell is the voltage of the monolithic proton exchange membrane fuel cell, E nerst is the thermodynamic voltage, V act is the activation loss, V ohm is the ohmic loss, V con is the concentration loss; in, V ohm =AND int =I(R m +R c ) Where ΔG is the Gibbs free energy of the reaction, n is the number of moles of electrons transferred by the proton exchange membrane fuel cell, F is the Faraday constant, ξ1, ξ2, ξ3, and ξ4 are activation loss parameters. is the interface oxygen concentration, T is the stack temperature, I is the operating current, R C is the electronic resistance, R m is the membrane equivalent resistance, R int is the total resistance, b is the concentration loss coefficient, J max is the maximum current density, J is the current density, ρ m is the membrane resistivity, l is the membrane thickness, A is the membrane area, and λ is the water content of the exchange membrane; The semi-empirical model of the proton exchange membrane fuel cell is as follows: Where N cell is the number of cells in the proton exchange membrane fuel cell.

3. A fuel cell parameter identification method according to claim 2, characterized in that: The multiple parameters to be identified include activation loss parameters ξ1, ξ2, ξ3, ξ4, electronic resistance R C , concentration loss coefficient b, maximum current density J max , current density J, exchange membrane water content λ.

4. A fuel cell parameter identification method according to claim 3, characterized in that: The optimization model of the proton exchange membrane fuel cell is as follows: f(ξ1, ξ2, ξ3, ξ4, R c ,b,λ,J max , J) = min(MSE) in, l min ≤λ≤λ max b min ≤b≤b max J min ≤J≤J max Where min is the minimization function, V cell (k) is the theoretical value of the output voltage, V m (k) is the actual value of the output voltage, m is the subscript of the activation loss parameter, k is the kth operating point, num is the number of operating points, f is the optimization target, is the lower bound of the mth activation loss parameter, is the upper limit of the mth activation loss parameter, is the lower limit of electronic resistance, is the upper limit of electronic resistance, λ min is the lower limit of water content of the exchange membrane, λ max is the upper limit of water content of the exchange membrane, b min is the lower limit of the concentration loss coefficient, b max is the upper limit of the concentration loss coefficient, is the lower limit of the maximum current density, is the upper limit of the maximum current density, J min is the lower limit of current density, J max is the upper limit of the current density.

5. A fuel cell parameter identification method according to claim 1, characterized in that: The optimization model is solved by a multi-strategy sparrow search optimization algorithm to obtain multiple optimal parameters to be identified, including the following steps: S1: Set the search space and dimension of the sparrows according to multiple constraints, set the number of sparrows in the population, the maximum number of iterations, the proportion of discoverers, the proportion of alerters, and the safety threshold; S2: Use the elite population strategy to obtain the elite population and enter the cycle; S3: Calculate the fitness values of individual sparrows in the elite population, sort multiple fitness values, divide the sparrows into discoverers and followers based on the proportion of discoverers, and find the sparrows and their positions corresponding to the best and worst fitness values; S4: The discoverer position update phase, in which the discoverer position is updated according to the Levy flight perturbation strategy; S5: Follower position update phase, update the follower position according to the follower formula; S6: Sentinel position update phase, randomly generate sentinels in the population based on the sentinel ratio, and update the sentinel position according to the sentinel formula; S7: DE / best / 1 mutation phase, for all sparrow individuals, the positions are updated according to the DE / best / 1 mutation strategy and the dynamic scaling factor sf; S8: Update the individual fitness values of sparrows and re-rank them to determine the best and worst fitness values and their positions; S9: Determine whether the algorithm end condition is met. If not, jump to S3. If met, proceed to S10. S10: Record the optimal result and end the operation.

6. A fuel cell parameter identification method according to claim 5, characterized in that: The Tent chaos mapping method formula is as follows: Where, and is the i-th sparrow individual in the new population The jth dimension of The upper and lower limits of φ n is a random number in [0,1], φ n+1 Generate a new random number. The position of the sparrow after the Tent chaos map.

7. A fuel cell parameter identification method according to claim 5, characterized in that: The Levy flight perturbation strategy is as follows: in, Where, is the position of the i-th sparrow in the t+1th generation, is the position of the i-th sparrow in the t-th generation, is the optimal sparrow position of the tth generation, S is the step size, l is the Levy flight direction, levy is the Levy flight perturbation function, μ is the expected value of 0, and the variance is σ μ The normal distribution, σ μ To satisfy the expectation of 0 and the variance of σ v Normal distribution, γ = 1.5, σ v =1,λ=1.5,Γ is the Gamma function; The follower formula is as follows: in, A + =A T (CHALLENGE ACCEPTED T ) -1 Where, is the global worst position of the t+1 generation, is the optimal position explored by the t+1th generation discoverer, a is the adaptive coefficient, e is the minimum constant to avoid the division error to be zero, A is a 1×d matrix whose elements are randomly assigned to -1 or 1, T is the transpose symbol, L is a 1×d matrix where all elements in the matrix are 1, and Q is a random number that obeys the normal distribution. is the position of the i-th sparrow in the j-th dimension of the t+1-th generation, is the position of the i-th sparrow in the t-th generation in the j-th dimension, and n is the total number of sparrows; The Vigilant formula is as follows: Where α is a normal distribution random value with mean 0 and variance 1, K is a random number in the range [-1, 1], and ε is the minimum constant to avoid the division error being zero. represents the current global optimal position, f i ,f g and f w are the current individual fitness, the current global optimal and the worst fitness values, respectively. is the optimal position of the t+1 generation sparrow; The DE / best / 1 mutation strategy and dynamic scaling factor sf are as follows: Where, is the dynamic scaling factor, sfintial and sfintial are two constants, is the mutant individual of the i-th sparrow in the t-th generation, p1 and p2 are random integers and p1≠p2∈[1,2,…,n], is a test vector generated by crossover operation, is the position of the i-th sparrow in the t-th generation in the r-th dimension, The worst fitness value in the t-th generation population, p c is the crossover probability in the range [0,1], r is a d-dimensional vector, and r0∈{1,2,…,d} describes a random dimension.

8. A fuel cell parameter identification device, characterized in that: include: The first module is used to build a semi-empirical model of proton exchange membrane fuel cells; The second module is used to calculate the theoretical value of the output voltage of the semi-empirical model and construct an objective function through the mean square error between the theoretical value and the actual value of the output voltage of the semi-empirical model; A third module is used to determine a plurality of parameters to be identified according to the semi-empirical model, and to construct a plurality of constraint conditions of the objective function by using the plurality of parameters to be identified as decision variables; The fourth module is used to construct an optimization model of a proton exchange membrane fuel cell based on multiple constraints, with minimization of the objective function as the optimization goal and multiple parameters to be identified as variables to be solved; The fifth module is used to solve the optimization model through a multi-strategy sparrow search optimization algorithm to obtain multiple optimal parameters to be identified; The multi-strategy sparrow search optimization algorithm adopts an elite population strategy to replace the random initialization strategy generation mechanism, explores the solution space through the Lévy flight perturbation strategy in the discoverer position update phase, adds an adaptive feedback mechanism in the follower position update phase and the sentinel position update phase, and adopts the DE / best / 1 mutation strategy to update the sparrow position again after the sentinel position update phase; Among them, the elite population strategy adopts uniform random distribution method and Tent chaos mapping method to generate two initial sparrow populations, let the two compete, calculate the fitness values of all individuals in the two populations, and then sort them from small to large, and take the first N individuals as the final initial population P.

9. A computer device, characterized in that: The method comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the fuel cell parameter identification method according to any one of claims 1 to 7 is implemented.

10. A computer-readable storage medium, characterized in that The storage medium stores a computer program, and when the computer program is executed by a processor, the fuel cell parameter identification method according to any one of claims 1 to 7 is implemented.

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