A fuel cell parameter identification method, device, equipment and storage medium
Through the multi-strategy sparrow search optimization algorithm, the problem of low search efficiency and easy to fall into local optimal solutions in PEMFC parameter identification is solved, and more accurate and efficient parameter identification is achieved, improving the recognition effect of fuel cell model.
Patent Information
- Application Number
- CN202410541053.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-04-30
- Publication Date
- 2024-12-17
- Estimated Expiration
- 2044-04-30
AI Technical Summary
In the identification of the parameter of proton exchange membrane fuel cell (PEMFC), traditional methods such as the Gaussian Newton method and the gradient descent method have complicated gradient information calculation, high complexity, and weak global optimization ability. Metaheuristic algorithms are prone to fall into local optimal solutions and convergence. Precocious puberty leads to low parameter identification efficiency and makes it difficult to obtain stable and accurate results.
Multi-strategy sparrow search optimization algorithm is adopted to initialize the population through elite population strategies, use Levi flight perturbation and adaptive feedback mechanism to explore the solution space, and use DE/best/1 mutation strategy in the alerter position update stage to improve search efficiency and avoid Converge prematurely, and then obtain multiple optimal identification parameters.
It improves the accuracy and efficiency of parameter identification, reduces the consumption of computing resources and computing time, avoids local optimal solutions, and significantly improves the parameter identification effect of fuel cell model.
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Figure CN118428221B_ABST
Abstract
Description
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, as energy demand increases, researchers have gradually increased their attention to new energy conversion devices such as hydrogen fuel cells. Hydrogen fuel cells convert hydrogen energy directly into electrical energy through a series of electrochemical reactions. Compared with traditional energy conversion methods, they avoid the limitations of the Carnot cycle, improve energy conversion efficiency, and their final byproduct is only water, without any pollution to the environment.
[0003] Especially in the field of proton exchange membrane fuel cells (PEMFC), its advantages such as low operating temperature, no pollution, low noise, fast response, and high power density make it the most ideal energy conversion device. However, PEMFC still has some shortcomings that need to be solved, so 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, the models of PEMFC are mainly divided into semi-empirical models, mechanism models, and data-driven models. Since the mechanism model depends on thermodynamics, electrochemistry, and fluid mechanics equations, the solution process is very complicated and time-consuming through CFD commercial software simulation. The data-driven model depends on a large amount of experimental data and is essentially a black box without interpretability. The semi-empirical model has the characteristics of high simulation accuracy and rapidity, and the semi-empirical model is more widely used in engineering practice. The semi-empirical model of PEMFC is 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] In PEMFC parameter identification, traditional analysis methods such as Gauss-Newton method and gradient descent method have limitations such as cumbersome gradient information calculation, high complexity, weak global optimization ability, and high dependence on initial values of iteration. Although metaheuristic algorithms are widely used in the field of parameter identification, they are prone to fall into local optimal solutions, premature convergence, and randomness of optimal solutions. Further improvements are needed to obtain stable and accurate results.
[0005] Metaheuristic algorithms have become an efficient solution to the problem of PEMFC parameter identification. Such algorithms do not require gradient information or specific initial conditions, and can greatly save computing resources and operation time. However, intelligent algorithms such as the sparrow search optimization algorithm (SSA) still have problems such as low search efficiency, premature convergence, and easy to fall into local optimal solutions.
[0006] In summary, as an important energy conversion device in the future, the identification of semi-empirical model parameters of PEMFC faces complexity and challenges. 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 field. 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] Determine a plurality of parameters to be identified according to the semi-empirical model, and use 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 minimization of an objective function as the optimization goal and multiple parameters to be identified as 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 Levy flight perturbation strategy in the discoverer position update stage, adds an adaptive feedback mechanism in the follower position update stage and the vigilant position update stage, and adopts the DE / best / 1 mutation strategy to update the sparrow position again after the vigilant position update stage;
[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 comprises the following steps:
[0017] Calculate the voltage of a monolithic proton exchange membrane fuel cell:
[0018] V cell =E nerst -V act -V ohm -V con
[0019] Where V cell is the voltage of a single 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;
[0020] in,
[0021]
[0022]
[0023] V ohm =IR int =I(R m +R c )
[0024]
[0025] 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, and ξ 1 , 2 , 3 , 4 is the activation loss parameter, C O2 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;
[0026] The semi-empirical model of the proton exchange membrane fuel cell is as follows:
[0027]
[0028] Where N cell is the number of cells in the proton exchange membrane fuel cell.
[0029] Preferably, the plurality of parameters to be identified include an activation loss parameter ξ 1 , 2 ,3 , 4 、Electronic resistance R C , concentration loss coefficient b, maximum current density J max , current density J, exchange membrane water content λ.
[0030] Preferably, the optimization model of the proton exchange membrane fuel cell is as follows:
[0031] f(ξ 1 , 2 , 3 , 4 , R c , b, λ, J max , J) = min(MSE)
[0032] in,
[0033]
[0034] λ min ≤λ≤λ max
[0035] b min ≤b≤b max
[0036]
[0037] J min ≤J≤J max
[0038] In the formula, 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 activation loss parameter subscript, k is the kth operating point, num is the number of operating points, f is the optimization target, is the lower limit 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.
[0039] 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:
[0040] S1: Set the search space and dimension of 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;
[0041] S2: Use the elite population strategy to obtain the elite population and enter the cycle;
[0042] S3: Calculate the fitness values of individual sparrows in the elite population, sort multiple fitness values, divide the individual sparrows into discoverers and followers according to the proportion of discoverers, and find the sparrow individuals and their positions corresponding to the best and worst fitness values;
[0043] S4: The discoverer position update phase, in which the discoverer position is updated according to the Levy flight disturbance strategy;
[0044] S5: Follower position update phase, update the follower position according to the follower formula;
[0045] S6: Sentinel position update stage, randomly generate sentinels in the population according to the sentinel ratio, and update the sentinel position according to the sentinel formula;
[0046] 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;
[0047] S8: Update the individual fitness values of sparrows, re-rank to determine the best and worst fitness values and their positions;
[0048] S9: Determine whether the algorithm end condition is met. If not, jump to S3. If met, proceed to S10.
[0049] S10: Record the optimal result and end the operation.
[0050] Preferably, the Tent chaos mapping method formula is as follows:
[0051]
[0052] In the formula, and is the i-th sparrow individual in the new population The jth dimension of The upper and lower limits of n is a random number in [0,1], φ n+1 To generate a new random number, The position of the sparrow after the Tent chaos map.
[0053] Preferably, the Levy flight disturbance strategy is as follows:
[0054]
[0055] in,
[0056]
[0057]
[0058] In the formula, 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 of 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;
[0059] The follower formula is as follows:
[0060]
[0061] in,
[0062] A + =A T (AA T ) -1
[0063]
[0064] In the formula, is the global worst position of the t+1th 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 -1 or 1, T is the transpose symbol, L is a 1×d matrix, in which 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;
[0065] The Vigilant formula is as follows:
[0066]
[0067] In the formula, α is a normal distribution random value with a mean of 0 and a variance of 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 value, respectively. is the optimal position of the t+1th generation sparrow;
[0068] The DE / best / 1 mutation strategy and dynamic scaling factor sf are as follows:
[0069]
[0070] In the formula, 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, p 1 and p 2 is a random integer and p 1 ≠p 2 ∈[1,2,…,n], is a test vector generated by crossover operation, is the position of the i-th sparrow of the t-th generation in the r-th dimension, The worst fitness value in the tth generation population, p c is the crossover probability in the range [0,1], r is a d-dimensional vector, r 0 ∈{1,2,…,d} describes a random dimension.
[0071] A fuel cell parameter identification device, comprising:
[0072] The first module is used to build a semi-empirical model of proton exchange membrane fuel cells;
[0073] The second module is used to calculate the theoretical value of the output voltage of the semi-empirical model, and to 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;
[0074] The 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;
[0075] The fourth module is used to construct an optimization model of a proton exchange membrane fuel cell based on multiple constraints, with minimization of an objective function as an optimization goal and multiple parameters to be identified as variables to be solved;
[0076] 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;
[0077] 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 Levy flight perturbation strategy in the discoverer position update stage, adds an adaptive feedback mechanism in the follower position update stage and the vigilant position update stage, and adopts the DE / best / 1 mutation strategy to update the sparrow position again after the vigilant position update stage;
[0078] 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.
[0079] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned fuel cell parameter identification method when executing the program.
[0080] 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.
[0081] Compared with the prior art, the present invention has the following beneficial effects:
[0082] 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 chaotic map to initialize a 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 stage, the solution space is explored by 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 stage and the sentinel position update stage, and the convergence accuracy is reduced 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 used to update the sparrow position. BRIEF DESCRIPTION OF THE DRAWINGS
[0083] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. 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 creative work.
[0084] Figure 1 A flow chart of a fuel cell parameter identification method of the present invention;
[0085] Figure 2 A schematic diagram of the process of solving the optimization model by the multi-strategy sparrow search optimization algorithm of the present invention;
[0086] Figure 3 A comparison diagram of the output current-voltage theoretical value and the actual value of the proton exchange membrane fuel cell according to an embodiment of the present invention;
[0087] Figure 4 This is a comparison curve chart of optimization model optimization using the multi-strategy sparrow search optimization algorithm (MOSSA), adaptive sparrow search algorithm (ASSA), sparrow search algorithm (SSA), hunger game search algorithm (HGS), vulture search algorithm (BES), improved sealfish optimization algorithm (IROA), dung beetle optimization algorithm based on quantum computing and mutation fusion (QHDBO), sealfish optimization algorithm (ROA), and improved artificial bee colony optimization algorithm (IABC) used in the simulation experiment of the embodiment of the present invention. DETAILED DESCRIPTION
[0088] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 creative work are within the scope of protection of the present invention.
[0089] The present invention provides a fuel cell parameter identification method, referring to Figure 1 , including the following steps:
[0090] Step 1: Construct a semi-empirical model of proton exchange membrane fuel cells based on the principles of proton exchange membrane fuel cells.
[0091] The anode reaction equation of the proton exchange membrane fuel cell is as follows:
[0092] H 2 →2H + +2e -
[0093] The cathode reaction equation of the proton exchange membrane fuel cell is as follows:
[0094]
[0095] The overall chemical reaction equation of the proton exchange membrane fuel cell is as follows:
[0096]
[0097] In the anode catalyst layer, H 2 Decomposed into protons and electrons, where electrons reach the cathode through the external circuit and protons reach the cathode through the exchange membrane. 2 Combines with protons and electrons to form H 2 O.
[0098] 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 output voltage of the proton exchange membrane fuel cell at multiple working points are collected, and the theoretical value of the output voltage of the proton exchange membrane fuel cell at each working point is calculated.
[0099] The theoretical value of the output voltage of the proton exchange membrane fuel cell at each operating point is calculated by the following formula:
[0100] V cell (k) = N cell ·(E nerst (k)-V act (k)-V ohm (k)-V con (k))
[0101] 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, V act (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.
[0102] E nerst is the thermodynamic voltage calculated by the following formula:
[0103]
[0104] 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.
[0105] The activation loss is calculated as follows:
[0106]
[0107] I=i+i n
[0108] where ξ 1 , 2 , 3 , 4 is the activation loss parameter, is the interface oxygen concentration, i n is the no-load current; the oxygen concentration at the catalyst layer interface is defined as follows:
[0109]
[0110] The calculation of ohmic loss is shown below:
[0111] V ohm =IR int =I(R m +R c )
[0112] Among them, R C is the electronic resistance, R m is the equivalent resistance of the membrane, and the membrane resistivity ρ m , film thickness l and film area A are defined as shown in the following formula:
[0113]
[0114] Where λ is the water content of the exchange membrane.
[0115] Since the speed of electron transfer is much greater than the mass transfer rate of hydrogen and oxygen reaction, the concentration loss occurs, which is calculated as follows:
[0116]
[0117] Where b is the concentration loss coefficient, J max is the maximum current density, and J is the current density.
[0118] The semi-empirical model of proton exchange membrane fuel cell is shown as follows:
[0119]
[0120] 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.
[0121] The objective function is as follows:
[0122]
[0123] 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.
[0124] according to Figure 3 It can be seen that the output current-voltage theoretical value of the proton exchange membrane fuel cell of the present invention is substantially the same as the actual value.
[0125] 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.
[0126] Then the activation loss parameter ξ 1 , 2 , 3 , 4 、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.
[0127] The multiple constraints are as follows:
[0128]
[0129] λ min ≤λ≤λ max
[0130] b min ≤b≤b max
[0131]
[0132] J min ≤J≤J max
[0133] Specifically,
[0134]
[0135] In the formula, 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 limit 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.
[0136] Specifically, in this embodiment, is the upper limit of the activation loss parameter 1, is the lower limit of the activation loss parameter 1, is the upper limit of activation loss parameter 2, is the lower limit of activation loss parameter 2, is the upper limit of activation loss parameter 3, is the lower limit of 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 the 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 no-load current density.
[0137] 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 the variables to be solved.
[0138] 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 decision variables to construct parameter constraints, and a proton exchange membrane fuel cell optimization model is constructed.
[0139] The proton exchange membrane fuel cell optimization model is as follows:
[0140] f(ξ 1 , 2 , 3 , 4 , R c , b, λ, J max , J) = min(MSE)
[0141] In the formula, f is the optimization objective and min is the minimization function.
[0142] Step 5: Solve the optimization model through the multi-strategy sparrow search optimization algorithm to obtain multiple optimal parameters to be identified;
[0143] Reference Figure 2 The proton exchange membrane fuel cell optimization model is solved by a multi-strategy sparrow search optimization algorithm, and 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 are obtained.
[0144] S1: Set the search space of the sparrow according to the constraint conditions of the parameters<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 alerters to PD and SD respectively, and the safety threshold to ST;
[0145] S2: Use the elite population strategy to obtain the elite population.
[0146] The elite population strategy specifically includes: using the uniform random distribution method and the Tent chaos mapping method to generate two initial sparrow populations, and record them as RP and CP, and let the two compete, that is, calculating the fitness values of all individuals in the population RP∪CP, and then sorting them from small to large, taking the first N individuals as the final initial population P, and calling it the chaotic elite population. Among them, the formula of the Tent chaos mapping method is as follows:
[0147]
[0148] in, and is the i-th sparrow individual in the new population The jth dimension of The upper and lower limits of n is a random number in [0,1], φ n+1 To generate a new random number, The position of the sparrow after the Tent chaos map.
[0149] 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.
[0150] S4: Update the discoverer position according to the Levy flight perturbation strategy. The formula is as follows:
[0151]
[0152] In the formula, 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 of 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.
[0153] S5: Update the follower position according to the follower formula, the formula is as follows:
[0154]
[0155] A + =A T (AA T ) -1
[0156]
[0157] In the formula, is the global worst position of the t+1th 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 -1 or 1, T is the transpose symbol, L is a 1×d matrix, in which all elements in the matrix are 1, 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.
[0158] S6: Update the sentinel position according to the sentinel formula.
[0159]
[0160] Here, α is a random number in [0,1].
[0161] S7: Update the position according to the DE / best / 1 mutation strategy and the dynamic scaling factor sf.
[0162]
[0163] In the formula, 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, p 1 and p 2 is a random integer and p 1 ≠p 2 ∈[1,2,…,n], is a test vector generated by crossover operation, is the position of the i-th sparrow of the t-th generation in the r-th dimension, The worst fitness value in the tth generation population, p c is the crossover probability in the range [0,1], r is a d-dimensional vector, r 0 ∈{1,2,…,d} describes a random dimension.
[0164] S8: Update the individual fitness values of the sparrows, and re-sort them to determine the best and worst fitness values and their positions.
[0165] S9: Determine whether the algorithm end condition is met. If not, jump to step S3. If met, proceed to the next step.
[0166] S10: Record the optimal result and end the operation.
[0167] Output the four optimized 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.
[0168] 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.
[0169] The first module is used to construct a semi-empirical model of proton exchange membrane fuel cells.
[0170] The second module is used to calculate the theoretical value of the output voltage of the semi-empirical model, and to 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.
[0171] The 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 taking the plurality of parameters to be identified as decision variables.
[0172] 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 with multiple parameters to be identified as variables to be solved.
[0173] 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.
[0174] The multi-strategy sparrow search optimization algorithm adopts the elite population strategy to replace the random initialization strategy generation mechanism, explores the solution space through the Levy flight perturbation strategy in the discoverer position update stage, adds an adaptive feedback mechanism in the follower position update stage and the vigilant position update stage, and adopts the DE / best / 1 mutation strategy to update the sparrow position again after the vigilant position update stage.
[0175] Among them, the elite population strategy uses 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.
[0176] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned fuel cell parameter identification method when executing the program.
[0177] 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.
[0178] Example
[0179] The solid oxide fuel cell parameter identification method of the present invention is analyzed through simulation experiments.
[0180] The solid oxide fuel cell in the simulation experiment is at an ambient temperature of 298.15K. The relevant parameters are introduced, and the Hunger Game Search Algorithm (HGS), Vulture Search Algorithm (BES), Improved Indo-European Fish Optimization Algorithm (IROA), Adaptive Sparrow Search Algorithm (ASSA) and Multi-Strategy Sparrow Search Optimization Algorithm (MOSSA) are used to solve the proton exchange membrane fuel cell model. The optimal parameters and MSE solved by each algorithm are shown in Table 1.
[0181] Table 1: Solution results of each algorithm for the proton exchange membrane fuel cell model parameters
[0182]
[0183] It can be seen from Table 1 that the multi-strategy sparrow search optimization algorithm has achieved a smaller MSE value than other algorithms, and the improved sparrow optimization algorithm has achieved a great optimization in the MSE value compared to the unimproved sparrow optimization algorithm. The results show that this algorithm has a good optimization effect, and the multi-strategy sparrow search optimization algorithm has a more obvious advantage in the optimization ability of proton exchange membrane fuel cell parameters compared to other algorithms.
[0184] Depend on Figure 4 (Currently it refers to the convergence diagram of the algorithm results) It can be seen that the multi-strategy sparrow optimization algorithm has a stronger search capability compared with other algorithms, can improve the global optimization 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.
[0185] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other 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.
[0186] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.
Claims
1. A fuel cell parameter identification method, It is 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; Determine a plurality of parameters to be identified according to the semi-empirical model, and use 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 minimization of an objective function as the optimization goal and multiple parameters to be identified as 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 Levy flight perturbation strategy in the discoverer position update stage, adds an adaptive feedback mechanism in the follower position update stage and the vigilant position update stage, and adopts the DE / best / 1 mutation strategy to update the sparrow position again after the vigilant position update stage; The elite population strategy uses uniform random distribution and Tent chaos mapping to generate two initial sparrow populations, which are then allowed to compete with each other. The fitness values of all individuals in the two populations are calculated, and then the first N individuals are sorted from small to large, and the final initial population P is taken. 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 a single 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, and ξ 1 , 2 , 3 , 4 is the activation loss parameter, 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 of the proton exchange membrane fuel cell; The plurality of parameters to be identified include an activation loss parameter ξ 1 , 2 , 3 , 4 、Electronic resistance R C , concentration loss coefficient b, maximum current density J max , current density J, exchange membrane water content λ; The optimization model of the proton exchange membrane fuel cell is as follows: f(ξ 1 ,x 2 ,x 3 ,x 4 、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 In the formula, 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 activation loss parameter subscript, k is the kth operating point, num is the number of operating points, f is the optimization target, is the lower limit 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 current density; 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 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 individual sparrows into discoverers and followers according to the proportion of discoverers, and find the sparrow individuals 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 disturbance strategy; S5: Follower position update phase, update the follower position according to the follower formula; S6: Sentinel position update stage, randomly generate sentinels in the population according to 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, re-rank 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.
2. A fuel cell parameter identification method as claimed in claim 1, It is characterized in that The Tent chaos mapping method formula is as follows: In the formula, and is the i-th sparrow individual in the new population The jth dimension of The upper and lower limits of n is a random number in [0,1], φ n+1 To generate a new random number, The position of the sparrow after the Tent chaos map.
3. A fuel cell parameter identification method as claimed in claim 1, It is characterized in that The Levy flight perturbation strategy is as follows: in, In the formula, 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 of 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 In the formula, is the global worst position of the t+1th 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 -1 or 1, T is the transpose symbol, L is a 1×d matrix, in which 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; The Vigilant formula is as follows: In the formula, α is a normal distribution random value with a mean of 0 and a variance of 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 value, respectively. is the optimal position of the t+1th generation sparrow; The DE / best / 1 mutation strategy and dynamic scaling factor sf are as follows: In the formula, sf i t 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, p 1 and p 2 is a random integer and p 1 ≠p 2 ∈[1,2,…,n], is a test vector generated by crossover operation, is the position of the i-th sparrow of the t-th generation in the r-th dimension, The worst fitness value in the tth generation population, p c is the crossover probability in the range [0,1], r is a d-dimensional vector, r 0 ∈{1,2,…,d} describes a random dimension.
4. A fuel cell parameter identification device, It is 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 to 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; The 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 an objective function as an 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 Levy flight perturbation strategy in the discoverer position update stage, adds an adaptive feedback mechanism in the follower position update stage and the vigilant position update stage, and adopts the DE / best / 1 mutation strategy to update the sparrow position again after the vigilant position update stage; The elite population strategy uses uniform random distribution and Tent chaos mapping to generate two initial sparrow populations, which are then allowed to compete with each other. The fitness values of all individuals in the two populations are calculated, and then the first N individuals are sorted from small to large, and the final initial population P is taken. 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 a single 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, and ξ 1 , 2 , 3 , 4 is the activation loss parameter, 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 of the proton exchange membrane fuel cell; The plurality of parameters to be identified include an activation loss parameter ξ 1 , 2 , 3 , 4 、Electronic resistance R C , concentration loss coefficient b, maximum current density J max , current density J, exchange membrane water content λ; The optimization model of the proton exchange membrane fuel cell is as follows: f(ξ 1 ,x 2 ,x 3 ,x 4 、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 In the formula, 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 activation loss parameter subscript, k is the kth operating point, num is the number of operating points, f is the optimization target, is the lower limit 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 current density; 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 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 individual sparrows into discoverers and followers according to the proportion of discoverers, and find the sparrow individuals 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 disturbance strategy; S5: Follower position update phase, update the follower position according to the follower formula; S6: Sentinel position update stage, randomly generate sentinels in the population according to 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, re-rank 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.
5. A computer device, It is 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 3 is implemented.
6. A computer-readable storage medium, It is 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 3 is implemented.