CN118428221B - Fuel cell parameter identification method, device, equipment and storage medium - Google Patents
Fuel cell parameter identification method, device, equipment and storage medium Download PDFInfo
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Abstract
The invention discloses a fuel cell parameter identification method, a device, equipment and a storage medium, which relate to the technical field of proton exchange membrane fuel cells and comprise the following steps of constructing a semi-empirical model of a proton exchange membrane fuel cell, calculating a theoretical value of output voltage of the semi-empirical model, 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, constructing a plurality of constraint conditions of the objective function by taking the plurality of parameters to be identified as decision variables, constructing an optimization model of the proton exchange membrane fuel cell by taking a minimized objective function as an optimization target and taking the plurality of parameters to be identified as variables to be solved based on the plurality of constraint conditions, and solving the optimization model through 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 Tent chaotic mapping to initialize the population, increases the number of the population, and then combines the two populations. The adaptive feedback mechanism is added in the follower position updating stage and the alerter position updating stage, and the convergence accuracy is reduced under the limited iteration number. The sparrow position is updated using the DE/best/1 mutation strategy and dynamic scaling factor sf. The global and local optimizing capability of the algorithm is improved, so that the accuracy of fuel cell parameter identification is improved.
Description
Technical Field
The present invention relates to the technical field of proton exchange membrane fuel cells, and in particular, to a method, an apparatus, a device and a storage medium for identifying parameters of a fuel cell.
Background
In recent years, with the increase in energy demand, researchers have been attracting attention to new energy conversion devices such as hydrogen fuel cells. The hydrogen fuel cell directly converts hydrogen energy into electric energy through a series of electrochemical reactions, compared with the traditional energy conversion mode, the limitation of Carnot cycle is avoided, the energy conversion efficiency is improved, and the final byproduct is only water, so that the hydrogen fuel cell has no pollution to the environment.
Particularly in the field of Proton Exchange Membrane Fuel Cells (PEMFCs), the advantages of low working temperature, no pollution, low noise, quick response, high power density and the like make the PEMFC become the most ideal energy conversion device. However, the PEMFC has some disadvantages to be solved, so it is important to build a semi-empirical model close to the actual fuel cell to study and improve the performance of the PEMFC. At present, the models of PEMFCs are mainly divided into semi-empirical models, mechanism models, and data-driven models. Since the mechanism model relies on thermodynamic, electrochemical and hydrodynamic equations, the solution process is very complex and time consuming by CFD commercial software simulation. The data driven model relies on a large amount of experimental data and is essentially a black box with no interpretability. The semi-empirical model has the characteristics of high simulation accuracy and rapidity, and is widely applied to engineering practice. Semi-empirical models of PEMFC are commonly used for simulation studies, however, since parameters of the semi-empirical model are generally unknown and the type of fuel cell itself has high complexity and nonlinear characteristics, coefficients of the semi-empirical model need to be identified to build an accurate semi-empirical model of PEMFC.
In the parameter identification of the PEMFC, the traditional analysis method such as the Gauss Newton method, the gradient descent method and the like has the limitations of complicated gradient information calculation, high complexity, weak global optimizing capability, high iteration initial value dependence degree and the like. Although meta heuristic algorithm is widely applied in the field of parameter identification, it is easy to fall into the problems of local optimal solution, convergence premature, randomness of optimal solution and the like, and further improvement is needed to obtain stable and accurate results.
Aiming at the difficult problem of parameter identification of the PEMFC, the meta-heuristic algorithm becomes an efficient solution. The algorithm does not need gradient information or specific initial conditions, and can greatly save calculation resources and calculation time. However, intelligent algorithms such as sparrow search optimization algorithm (SSA) still have the problems of low search efficiency, premature convergence, easy sinking into local optimal solution, and the like.
In summary, PEMFC, which is an important energy conversion device in the future, faces complexity and challenges in semi-empirical model parameter identification. Researchers are urgent to find a more accurate and efficient method to identify parameters of a semi-empirical model of PEMFC, so as to promote the wide application and development of the PEMFC in the energy field.
Disclosure of Invention
The invention provides a fuel cell parameter identification method, a device, equipment and a storage medium, which solve the problems that the existing sparrow search optimization algorithm (SSA) still has low search efficiency, early convergence, easy sinking into a local optimal solution and the like when identifying parameters.
The invention provides a fuel cell parameter identification method, which comprises the following steps:
Constructing a semi-empirical model of the proton exchange membrane fuel cell;
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 the 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 constructing a plurality of constraint conditions of an objective function by taking the plurality of parameters to be identified as decision variables;
Based on a plurality of constraint conditions, constructing an optimization model of the proton exchange membrane fuel cell by taking a minimized objective function as an optimization target and taking a plurality of parameters to be identified as variables to be solved;
Solving the optimization model through a multi-strategy sparrow search optimization algorithm to obtain a plurality of optimal waiting identification parameters;
The multi-strategy sparrow search optimization algorithm adopts elite population strategy to replace a generation mechanism of a random initialization strategy, explores a solution space through a Lewy flight disturbance strategy in a finder position updating stage, adds a self-adaptive feedback mechanism in a follower position updating stage and an alerter position updating stage, and updates the sparrow position again by adopting a DE/best/1 variation strategy after the alerter position updating stage;
The elite population strategy adopts a uniform random distribution method and a Tent chaotic mapping method to generate two initial sparrow populations, so that the two initial sparrow populations compete, the fitness value of all individuals in the two populations is calculated, and after the two populations are ordered from small to large, the first N individuals are taken as a final initial population P.
Preferably, a semi-empirical model of the proton exchange membrane fuel cell is constructed, specifically comprising the following steps:
calculating the voltage of the monolithic proton exchange membrane fuel cell:
Vcell＝Enerst-Vact-Vohm-Vcon
Wherein V cell is the voltage of a monolithic proton exchange membrane fuel cell, E nerst is the thermodynamic voltage, V act is the activation loss, V ohm is the ohmic loss, and V con is the concentration loss;
Wherein,
Vohm＝IRint＝I(Rm+Rc)
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, F is faraday constant, ζ 1、ξ2、ξ3、ξ4 is the activation loss parameter, C O2 is the interfacial oxygen concentration, T is the stack temperature, I is the working 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, λ is the exchange membrane water content;
The semi-empirical model of a proton exchange membrane fuel cell is as follows:
Wherein N cell is the number of the cells of the proton exchange membrane fuel cell.
Preferably, the plurality of parameters to be identified include an activation loss parameter ζ 1、ξ2、ξ3、ξ4, an electronic resistance R C, a concentration loss coefficient b, a maximum current density J max, a current density J, and an exchange membrane water content λ.
Preferably, the optimization model of the proton exchange membrane fuel cell is as follows:
f(ξ1、ξ2、ξ3、ξ4、Rc、b、λ、Jmax、J)=min(MSE)
Wherein,
λmin≤λ≤λmax
bmin≤b≤bmax
Jmin≤J≤Jmax
Wherein min is a minimization function, V cell (k) is a theoretical value of the output voltage, V m (k) is an actual value of the output voltage, m is an activation loss parameter index, k is a kth working point, num is the number of working points, f is an optimization target,Is the lower limit of the mth activation loss parameter,Is the upper limit of the mth activation loss parameter,As a lower limit of the electrical resistance,Is the upper limit of the electronic resistance, lambda min is the lower limit of the water content of the exchange membrane, lambda max is the upper limit of the 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,As a lower limit of the maximum current density,For the upper limit of the maximum current density, J min is the lower limit of the current density and J max is the upper limit of the current density.
Preferably, the optimization model is solved by a multi-strategy sparrow search optimization algorithm to obtain a plurality of optimal recognition parameters, and the method comprises the following steps:
S1, setting search space and dimension of sparrows according to a plurality of constraint conditions, and setting the number of sparrows in a population, the maximum iteration number, the finder proportion, the alerter proportion and a safety threshold;
S2, obtaining elite population by utilizing elite population strategy, and entering circulation;
S3, calculating fitness values of sparrow individuals in elite population, sequencing a plurality of fitness values, dividing the sparrow individuals into discoverers and followers according to the ratio of the discoverers, and finding out the sparrow individuals and positions thereof corresponding to the optimal and worst fitness values;
S4, in a finder position updating stage, the finder position is updated according to the Lewy flight disturbance strategy;
s5, updating the position of the follower according to a follower formula;
s6, an alerter position updating stage, namely randomly generating alerters in the population according to the proportion of the alerters, and updating the positions of the alerters according to an alerter formula;
S7, in the DE/best/1 mutation stage, updating positions of all sparrow individuals according to a DE/best/1 mutation strategy and a dynamic scaling factor sf;
S8, updating individual fitness values of sparrows, and reordering to determine optimal and worst fitness values and positions of the optimal and worst fitness values;
S9, judging whether an algorithm ending condition is met, if not, jumping to S3, and if so, performing S10;
and S10, recording an optimal result and ending the operation.
Preferably, the Tent chaotic mapping method formula is as follows:
in the formula, AndFor the ith sparrow individual in the new population of individualsIs the jth dimension of (2)Phi n is a random number within [0,1], phi n+1 is a newly generated random number,And the sparrow position is obtained after Tent chaotic mapping.
Preferably, the Lewy flight disturbance strategy is as follows:
Wherein,
In the formula,For the ith sparrow position of the t+1st generation,For the ith sparrow position of the t generation,For the t generation of optimal sparrow position, S is a step length, l is a Layvern flight direction, levy is a Layvern flight disturbance function, mu is a normal distribution meeting expectations of 0 and variance of sigma μ, sigma μ is a normal distribution meeting expectations of 0 and variance of sigma v, gamma=1.5, sigma v =1, lambda=1.5, and Gamma is a Gamma function;
The follower formula is as follows:
Wherein,
A+＝AT(AAT)-1
In the formula,For the t +1 generation global worst position,For the optimal position explored by the t+1st generation finder, a is an adaptive coefficient, e is a minimum constant for avoiding division errors to be zero, A is a1×d matrix, its elements are randomly allocated-1 or 1, T is a transpose symbol, L is a1×d matrix, each element in the matrix is all 1, Q is a random number obeying normal distribution,For the position of the ith sparrow in the j-th dimension of the t+1st generation,The position of the ith sparrow in the j-th dimension is the t generation, and n is the total number of sparrows;
The alerter formula is as follows:
Where alpha is a normal distribution random value representing a mean value of 0 and a variance of 1, K is a random number of [ -1,1], ε is a minimum constant that avoids division errors of zero, Representing the current global optimal position, f i,fg and f w are the fitness of the current individual, the current global optimal and worst fitness values respectively,The optimal position of the t+1st generation sparrow;
the DE/best/1 mutation strategy and dynamic scaling factor sf are as follows:
in the formula, For dynamic scaling factors, sfintial and sfintial are two constants,For variants of the ith sparrow of the t generation, p 1 and p 2 are random integers and p 1≠p2 e [1, 2., n ],To generate a test vector using the crossover operation,For the position of the ith sparrow of the t generation in the r dimension,The worst fitness value in the t-th generation population, p c, is the crossover probability in the range of 0,1, r is the d-dimensional vector, r 0 e {1, 2.
A fuel cell parameter identification device, comprising:
the first module is used for constructing a semi-empirical model of the proton exchange membrane fuel cell;
the second module is used for calculating the theoretical value of the output voltage of the semi-empirical model and constructing 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 for determining a plurality of parameters to be identified according to the semi-empirical model, and constructing a plurality of constraint conditions of an objective function by taking the plurality of parameters to be identified as decision variables;
the fourth module is used for constructing an optimization model of the proton exchange membrane fuel cell by taking the minimized objective function as an optimization target and taking a plurality of parameters to be identified as variables to be solved based on a plurality of constraint conditions;
The fifth module is used for solving the optimization model through a multi-strategy sparrow search optimization algorithm to obtain a plurality of optimal recognition parameters;
The multi-strategy sparrow search optimization algorithm adopts elite population strategy to replace a generation mechanism of a random initialization strategy, explores a solution space through a Lewy flight disturbance strategy in a finder position updating stage, adds a self-adaptive feedback mechanism in a follower position updating stage and an alerter position updating stage, and updates the sparrow position again by adopting a DE/best/1 variation strategy after the alerter position updating stage;
The elite population strategy adopts a uniform random distribution method and a Tent chaotic mapping method to generate two initial sparrow populations, so that the two initial sparrow populations compete, the fitness value of all individuals in the two populations is calculated, and after the two populations are ordered from small to large, the first N individuals are taken as a final initial population P.
A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the fuel cell parameter identification method described above when executing the program.
A computer readable storage medium storing a computer program which when executed by a processor implements the fuel cell parameter identification method described above.
Compared with the prior art, the invention has the beneficial effects that:
The invention firstly builds a semi-empirical model of the proton exchange membrane fuel cell, then obtains a plurality of corresponding parameters to be identified, and builds an optimized model of the proton exchange membrane fuel cell. And solving the optimization model through 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 Tent chaotic mapping to initialize the population, increases the number of the population, and then combines the two populations. Then, elite population is obtained by utilizing elite strategy to improve the quality of initial solution. In the position updating stage of the finder, the solution space is explored through the Lev flight disturbance strategy, and in the levy flight process, a larger movement range is provided, so that the searching efficiency is high. The adaptive feedback mechanism is added in the follower position updating stage and the alerter position updating stage, and the convergence accuracy is reduced under the limited iteration number. To avoid premature convergence, the sparrow location is updated using the DE/best/1 mutation strategy and dynamic scaling factor sf.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a fuel cell parameter identification method according to the present invention;
FIG. 2 is a schematic diagram of a process of solving an optimization model by using the multi-strategy sparrow search optimization algorithm of the invention;
FIG. 3 is a graph showing the theoretical and actual values of the output current-voltage of a PEM fuel cell according to an embodiment of the present invention;
Fig. 4 is a graph of optimizing and comparing a multi-strategy sparrow search optimization algorithm (MOSSA), an Adaptive Sparrow Search Algorithm (ASSA), a Sparrow Search Algorithm (SSA), a hunger game search algorithm (HGS), a bald hawk search algorithm (BES), an improved seal fish optimization algorithm (IROA), a dung beetle optimization algorithm (QHDBO) based on quantum computation and mutation fusion, a seal fish optimization algorithm (ROA), and an improved artificial bee colony optimization algorithm (IABC) to an optimization model in a simulation experiment according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention provides a fuel cell parameter identification method, referring to fig. 1, comprising the following steps:
the first step is to construct a semi-empirical model of the proton exchange membrane fuel cell based on the principle of the proton exchange membrane fuel cell.
The anode reaction equation for a proton exchange membrane fuel cell is as follows:
H2→2H++2e-
the cathode reaction equation for a proton exchange membrane fuel cell is as follows:
the general chemical reaction equation for a proton exchange membrane fuel cell is as follows:
at the anode catalytic layer, H 2 breaks down into protons and electrons, wherein the electrons pass through an external circuit to the cathode and the protons pass through the exchange membrane to the cathode. At the cathode catalytic layer, O 2 combines with protons and electrons to produce H 2 O.
By analyzing the working principle and the structural characteristics of the proton exchange membrane fuel cell, a semi-empirical model of the proton exchange membrane fuel cell is established, experimental values of the output voltages of the proton exchange membrane fuel cell at a plurality of working points are collected, and theoretical values of the output voltages of the proton exchange membrane fuel cell at each working point are calculated.
The theoretical value of the output voltage of the proton exchange membrane fuel cell for each operating point is calculated by:
Vcell(k)＝Ncell·(Enerst(k)-Vact(k)-Vohm(k)-Vcon(k))
Wherein 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 of 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, and V con (k) represents the concentration loss of the proton exchange membrane fuel cell at the kth operating point.
E nerst is the thermodynamic voltage calculated from the following formula:
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 f= 96485.33289 ± 0.00059C/mol.
The activation loss was calculated as shown in the following formula:
I=i+in
where ζ 1、ξ2、ξ3、ξ4 is the activation loss parameter, I n is no-load current, and the definition of the oxygen concentration of the interface of the catalytic layer is shown in the following formula:
Calculation of ohmic losses, as shown in the following formula:
Vohm＝IRint＝I(Rm+Rc)
Wherein, R C is electronic resistance, R m is film equivalent resistance, which is defined by film resistivity ρ m, film thickness l and film area A, as shown in the following formula:
wherein lambda is the water content of the exchange membrane.
The concentration loss due to the fact that the electron transport speed is far greater than the mass transfer speed of the oxyhydrogen reaction is calculated as follows:
where b is the concentration loss factor, J max is the maximum current density, and J is the current density.
The semi-empirical model of a proton exchange membrane fuel cell is shown in the following formula:
And secondly, 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 the actual value of the output voltage of the semi-empirical model.
The objective function is shown as follows:
Where MSE is the mean square of the error, num is the number of operating points, V cell (k) is the theoretical value of the output voltage, and V n (k) is the actual value of the output voltage.
As can be seen from fig. 3, the theoretical value and the actual value of the output current-voltage of the proton exchange membrane fuel cell according to the present invention are substantially the same.
And thirdly, determining a plurality of parameters to be identified according to the semi-empirical model, and constructing a plurality of constraint conditions of the objective function by taking the parameters to be identified as decision variables.
Then the activation loss parameter ζ 1、ξ2、ξ3、ξ4, the electronic resistance R c, the concentration loss coefficient b, the water content lambda of the exchange membrane, the maximum current density J max and the current density J are parameters to be identified.
The various constraints are as follows:
λmin≤λ≤λmax
bmin≤b≤bmax
Jmin≤J≤Jmax
In particular, the method comprises the steps of,
Wherein min is a minimization function, m is an activation loss parameter index, k is a kth working point, num is the number of working points, f is an optimization target,Is the lower limit of the mth activation loss parameter,Is the upper limit of the mth activation loss parameter,As a lower limit of the electrical resistance,Is the upper limit of the electronic resistance, lambda min is the lower limit of the water content of the exchange membrane, lambda max is the upper limit of the 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,As a lower limit of the maximum current density,For the upper limit of the maximum current density, J min is the lower limit of the current density and J max is the upper limit of the current density.
Specifically, in the present embodiment, the first and second embodiments,For the upper limit of the activation loss parameter 1, To activate the lower limit of the loss parameter 1,For the upper limit of the activation loss parameter 2,To activate the lower limit of the loss parameter 2,For the upper limit of the activation loss parameter 3,For the lower limit of the activation loss parameter 3,For the upper limit of the activation loss parameter 4,A lower limit for the activation loss parameter 4; Is the upper limit of the electrical resistance, As the lower limit of the electron 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 the 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,As an upper limit of the maximum current density,As a lower limit of the maximum current density, J max＝0.0008A/cm2 is an upper limit of the no-load current density, and J min＝0.0001A/cm2 is a lower limit of the no-load current density.
And fourthly, constructing an optimization model of the proton exchange membrane fuel cell by taking the minimized objective function as an optimization target and taking a plurality of parameters to be identified as variables to be solved based on a plurality of constraint conditions.
And taking the minimum mean square deviation of the difference between the theoretical output voltage and the actual output voltage of the semi-empirical model as an optimization target, selecting four activation loss parameters, electronic resistance, concentration loss coefficient, water content of the exchange membrane, limiting current density and no-load current density as constraint conditions of decision variable construction parameters, and constructing a proton exchange membrane fuel cell optimization model.
The proton exchange membrane fuel cell optimization model is as follows:
f(ξ1、ξ2、ξ3、ξ4、Rc、b、λ、Jmax、J)=min(MSE)
Where f is the optimization objective and min is the minimization function.
Fifthly, solving an optimization model through a multi-strategy sparrow search optimization algorithm to obtain a plurality of optimal recognition parameters;
Referring to fig. 2, the proton exchange membrane fuel cell optimization model is solved by a multi-strategy sparrow search optimization algorithm, and four optimized activation loss parameters, an optimized electronic resistance, an optimized concentration loss coefficient, an optimized exchange membrane water content, an optimized no-load current density and an optimized limiting current density are obtained.
S1, setting search space < Lb, ub > and dimension of sparrows according to constraint conditions of parameters, wherein Lb is the lower limit of the search space, ub is the upper limit of the search space, setting the number of sparrows in an initial population as N, the maximum iteration number as G, and the numbers of discoverers and alerters as PD, SD and a safety threshold ST respectively;
s2, obtaining elite population by utilizing elite population strategy.
The elite population strategy specifically comprises the steps of respectively adopting a uniform random distribution method and a Tent chaotic mapping method to generate two initial sparrow populations, marking the two initial sparrow populations as RP and CP, competing the two initial sparrow populations, namely calculating the fitness value of all individuals in the population RP and CP, sequencing from small to large, and taking the first N individuals as a final initial population P, namely the chaotic elite population. The Tent chaotic mapping method has the following formula:
Wherein, AndFor the ith sparrow individual in the new population of individualsIs the jth dimension of (2)Phi n is a random number within [0,1], phi n+1 is a newly generated random number,And the sparrow position is obtained after Tent chaotic mapping.
And S3, calculating fitness values of sparrow individuals in the chaotic elite population, sequencing the fitness values, and finding out individuals and positions of individuals with optimal and worst fitness values.
S4, updating the position of the finder according to the Lewy flight disturbance strategy, wherein the formula is as follows:
in the formula, For the t+1st generation sparrow position,For the position of the t-th generation sparrow,For the t generation of optimal sparrow position, S is a step length, l is a Layvern flight direction, levy is a Layvern flight disturbance function, mu is a normal distribution meeting expectations of 0 and variance of sigma μ, sigma μ is a sigma v normal distribution meeting expectations of 0 and variance of sigma v, wherein gamma=1.5, sigma v =1, lambda=1.5 and Gamma is a Gamma function.
S5, updating the follower position according to a follower formula, wherein the formula is as follows:
A+＝AT(AAT)-1
in the formula, For the t +1 generation global worst position,For the optimal position explored by the t+1st generation finder, a is an adaptive coefficient, e is a minimum constant for avoiding division errors to be zero, A is a1×d matrix, its elements are randomly allocated-1 or 1, T is a transpose symbol, L is a1×d matrix, each element in the matrix is all 1, Q is a random number obeying normal distribution,For the position of the ith sparrow in the j-th dimension of the t+1st generation,The position of the ith sparrow in the j-th dimension is the t generation, and n is the total number of sparrows.
And S6, updating the position of the alerter according to the alerter formula.
Wherein alpha is a random number within [0,1 ].
And S7, updating the position according to the DE/best/1 mutation strategy and the dynamic scaling factor sf.
In the formula,For dynamic scaling factors, sfintial and sfintial are two constants,For variants of the ith sparrow of the t generation, p 1 and p 2 are random integers and p 1≠p2 e [1, 2., n ],To generate a test vector using the crossover operation,For the position of the ith sparrow of the t generation in the r dimension,The worst fitness value in the t-th generation population, p c, is the crossover probability in the range of 0,1, r is the d-dimensional vector, r 0 e {1, 2.
And S8, updating individual fitness values of sparrows, and reordering to determine optimal and worst fitness values and positions of the optimal and worst fitness values.
And S9, judging whether the algorithm ending condition is met, if not, jumping to the step S3, and if so, carrying out the next step.
And S10, recording an optimal result and ending the operation.
Outputting four optimized activation loss parameters, an optimized electronic resistor, an optimized concentration loss coefficient, an optimized water content of the exchange membrane, an optimized no-load current density and an optimized limiting current density.
Based on the same conception, the invention also provides a fuel cell parameter identification device which comprises a first module, a second module, a third module, a fourth module and a fifth module.
The first module is used to construct a semi-empirical model of a proton exchange membrane fuel cell.
The second module is used for calculating the theoretical value of the output voltage of the semi-empirical model, and constructing 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 for determining a plurality of parameters to be identified according to the semi-empirical model, and constructing a plurality of constraint conditions of the objective function by taking the parameters to be identified as decision variables.
The fourth module is used for constructing an optimization model of the proton exchange membrane fuel cell by taking the minimized objective function as an optimization target and taking a plurality of parameters to be identified as variables to be solved based on a plurality of constraint conditions.
And the fifth module is used for solving the optimization model through a multi-strategy sparrow search optimization algorithm to obtain a plurality of optimal parameters to be identified.
The multi-strategy sparrow search optimization algorithm adopts elite population strategy to replace a generation mechanism of a random initialization strategy, explores a solution space through a Lewy flight disturbance strategy in a finder position updating stage, adds a self-adaptive feedback mechanism in a follower position updating stage and an alerter position updating stage, and updates the sparrow position again by adopting a DE/best/1 variation strategy after the alerter position updating stage;
The elite population strategy adopts a uniform random distribution method and a Tent chaotic mapping method to generate two initial sparrow populations, so that the two initial sparrow populations compete, the fitness value of all individuals in the two populations is calculated, and after sorting from small to large, the first N individuals are taken as a final initial population P. .
The invention also provides a computer device, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor realizes the fuel cell parameter identification method when executing the program.
The invention also provides a computer readable storage medium, wherein the storage medium stores a computer program, and the computer program realizes the fuel cell parameter identification method when being executed by a processor.
Examples
The solid oxide fuel cell parameter identification method is analyzed through simulation experiments.
The solid oxide fuel cell in the simulation experiment is at the ambient temperature of 298.15k, related parameters are brought in, and a proton exchange membrane fuel cell model is solved by adopting a hunger game search algorithm (HGS), a balying search algorithm (BES), an improved fish printing optimization algorithm (IROA), an Adaptive Sparrow Search Algorithm (ASSA) and a multi-strategy sparrow search optimization algorithm (MOSSA), wherein the optimal parameters and MSE solved by the algorithms are shown in a table 1.
TABLE 1 results of solutions of algorithms to proton exchange membrane fuel cell model parameters
As can be seen from Table 1, the multi-strategy sparrow search optimization algorithm achieved a smaller MSE value than the other decorrelation algorithms, and the improved sparrow optimization algorithm achieved a greater optimization than the unmodified sparrow optimization algorithm. The result shows that the algorithm has a good optimizing effect, and the multi-strategy sparrow searching optimizing algorithm has obvious advantages for optimizing the parameters of the proton exchange membrane fuel cell compared with other algorithms.
Compared with other algorithms, the multi-strategy sparrow optimization algorithm has stronger searching capability, can improve the global optimizing and local optimizing capabilities of the original algorithm, improves the solving efficiency of the algorithm, can well identify the parameters of the proton membrane exchange fuel cell, and obtains good identification results.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. It is therefore intended that the following claims be interpreted as including the preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
Claims (6)
1. A fuel cell parameter identification method, characterized by comprising the steps of:
Constructing a semi-empirical model of the proton exchange membrane fuel cell;
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 the 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 constructing a plurality of constraint conditions of an objective function by taking the plurality of parameters to be identified as decision variables;
Based on a plurality of constraint conditions, constructing an optimization model of the proton exchange membrane fuel cell by taking a minimized objective function as an optimization target and taking a plurality of parameters to be identified as variables to be solved;
Solving the optimization model through a multi-strategy sparrow search optimization algorithm to obtain a plurality of optimal waiting identification parameters;
The multi-strategy sparrow search optimization algorithm adopts elite population strategy to replace a generation mechanism of a random initialization strategy, explores a solution space through a Lewy flight disturbance strategy in a finder position updating stage, adds a self-adaptive feedback mechanism in a follower position updating stage and an alerter position updating stage, and updates the sparrow position again by adopting a DE/best/1 variation strategy after the alerter position updating stage;
The elite population strategy adopts a uniform random distribution method and a Tent chaotic mapping method to generate two initial sparrow populations, so that the two initial sparrow populations compete, the fitness value of all individuals in the two populations is calculated, and after the two populations are sequenced from small to large, the first N individuals are taken as a final initial population P;
the method for constructing the semi-empirical model of the proton exchange membrane fuel cell specifically comprises the following steps:
calculating the voltage of the monolithic proton exchange membrane fuel cell:
Vcell＝Enerst-Vact-Vohm-Vcon
Wherein V cell is the voltage of a monolithic proton exchange membrane fuel cell, E nerst is the thermodynamic voltage, V act is the activation loss, V ohm is the ohmic loss, and V con is the concentration loss;
Wherein,
Vohm＝IRint＝I(Rm+Rc)
Wherein, delta G 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 Faraday constant, xi 1、ξ2、ξ3、ξ4 is the activation loss parameter,The interface oxygen concentration is T, the stack temperature is I, the working current is R C, the electronic resistance is R m, the membrane equivalent resistance is R int, the concentration loss coefficient is b, the maximum current density is J max, the current density is J, the membrane resistivity is rho m, the membrane thickness is l, the membrane area is A, and the water content of an exchange membrane is lambda;
The semi-empirical model of a proton exchange membrane fuel cell is as follows:
Wherein N cell is the number of the cells of the proton exchange membrane fuel cell;
The parameters to be identified comprise an activation loss parameter xi 1、ξ2、ξ3、ξ4, an electronic resistance R C, a concentration loss coefficient b, a maximum current density J max, a current density J and an exchange membrane water content lambda;
The optimization model of the proton exchange membrane fuel cell is as follows:
f(ξ1、ξ2、ξ3、ξ4、Rc、b、λ、Jmax、J)=min(MSE)
Wherein,
λmin≤λ≤λmax
bmin≤b≤bmax
Jmin≤J≤Jmax
Wherein min is a minimization function, V cell (k) is a theoretical value of the output voltage, V m (k) is an actual value of the output voltage, m is an activation loss parameter index, k is a kth working point, num is the number of working points, f is an optimization target,Is the lower limit of the mth activation loss parameter,Is the upper limit of the mth activation loss parameter,As a lower limit of the electrical resistance,Is the upper limit of the electronic resistance, lambda min is the lower limit of the water content of the exchange membrane, lambda max is the upper limit of the 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,As a lower limit of the maximum current density,As an upper limit of the maximum current density, J min is a lower limit of the current density, and J max is an upper limit of the current density;
Solving an optimization model through a multi-strategy sparrow search optimization algorithm to obtain a plurality of optimal recognition parameters, wherein the method comprises the following steps of:
S1, setting search space and dimension of sparrows according to a plurality of constraint conditions, and setting the number of sparrows in a population, the maximum iteration number, the finder proportion, the alerter proportion and a safety threshold;
S2, obtaining elite population by utilizing elite population strategy, and entering circulation;
S3, calculating fitness values of sparrow individuals in elite population, sequencing a plurality of fitness values, dividing the sparrow individuals into discoverers and followers according to the ratio of the discoverers, and finding out the sparrow individuals and positions thereof corresponding to the optimal and worst fitness values;
S4, in a finder position updating stage, the finder position is updated according to the Lewy flight disturbance strategy;
s5, updating the position of the follower according to a follower formula;
s6, an alerter position updating stage, namely randomly generating alerters in the population according to the proportion of the alerters, and updating the positions of the alerters according to an alerter formula;
S7, in the DE/best/1 mutation stage, updating positions of all sparrow individuals according to a DE/best/1 mutation strategy and a dynamic scaling factor sf;
S8, updating individual fitness values of sparrows, and reordering to determine optimal and worst fitness values and positions of the optimal and worst fitness values;
S9, judging whether an algorithm ending condition is met, if not, jumping to S3, and if so, performing S10;
and S10, recording an optimal result and ending the operation.
2. The fuel cell parameter identification method according to claim 1, wherein the Tent chaotic mapping method formula is as follows:
in the formula, AndFor the ith sparrow individual in the new population of individualsIs the jth dimension of (2)Phi n is a random number within [0,1], phi n+1 is a newly generated random number,And the sparrow position is obtained after Tent chaotic mapping.
3. The fuel cell parameter identification method according to claim 1, wherein the lewy flight disturbance strategy is as follows:
Wherein,
In the formula,For the ith sparrow position of the t+1st generation,For the ith sparrow position of the t generation,For the t generation of optimal sparrow position, S is a step length, l is a Layvern flight direction, levy is a Layvern flight disturbance function, mu is a normal distribution meeting expectations of 0 and variance of sigma μ, sigma μ is a normal distribution meeting expectations of 0 and variance of sigma v, gamma=1.5, sigma v =1, lambda=1.5, and Gamma is a Gamma function;
The follower formula is as follows:
Wherein,
A+＝AT(AAT)-1
In the formula,For the t +1 generation global worst position,For the optimal position explored by the t+1st generation finder, a is an adaptive coefficient, e is a minimum constant for avoiding division errors to be zero, A is a1×d matrix, its elements are randomly allocated-1 or 1, T is a transpose symbol, L is a1×d matrix, each element in the matrix is all 1, Q is a random number obeying normal distribution,For the position of the ith sparrow in the j-th dimension of the t+1st generation,The position of the ith sparrow in the j-th dimension is the t generation, and n is the total number of sparrows;
The alerter formula is as follows:
Where alpha is a normal distribution random value representing a mean value of 0 and a variance of 1, K is a random number of [ -1,1], ε is a minimum constant that avoids division errors of zero, Representing the current global optimal position, f i,fg and f w are the fitness of the current individual, the current global optimal and worst fitness values respectively,The optimal position of the t+1st generation sparrow;
the DE/best/1 mutation strategy and dynamic scaling factor sf are as follows:
Where sf i t is the dynamic scaling factor, sfintial and sfintial are two constants, For variants of the ith sparrow of the t generation, p 1 and p 2 are random integers and p 1≠p2 e [1, 2., n ],To generate a test vector using the crossover operation,For the position of the ith sparrow of the t generation in the r dimension,The worst fitness value in the t-th generation population, p c, is the crossover probability in the range of 0,1, r is the d-dimensional vector, r 0 e {1, 2.
4. A fuel cell parameter identification device, characterized by comprising:
the first module is used for constructing a semi-empirical model of the proton exchange membrane fuel cell;
the second module is used for calculating the theoretical value of the output voltage of the semi-empirical model and constructing 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 for determining a plurality of parameters to be identified according to the semi-empirical model, and constructing a plurality of constraint conditions of an objective function by taking the plurality of parameters to be identified as decision variables;
the fourth module is used for constructing an optimization model of the proton exchange membrane fuel cell by taking the minimized objective function as an optimization target and taking a plurality of parameters to be identified as variables to be solved based on a plurality of constraint conditions;
The fifth module is used for solving the optimization model through a multi-strategy sparrow search optimization algorithm to obtain a plurality of optimal recognition parameters;
The multi-strategy sparrow search optimization algorithm adopts elite population strategy to replace a generation mechanism of a random initialization strategy, explores a solution space through a Lewy flight disturbance strategy in a finder position updating stage, adds a self-adaptive feedback mechanism in a follower position updating stage and an alerter position updating stage, and updates the sparrow position again by adopting a DE/best/1 variation strategy after the alerter position updating stage;
The elite population strategy adopts a uniform random distribution method and a Tent chaotic mapping method to generate two initial sparrow populations, so that the two initial sparrow populations compete, the fitness value of all individuals in the two populations is calculated, and after the two populations are sequenced from small to large, the first N individuals are taken as a final initial population P;
the method for constructing the semi-empirical model of the proton exchange membrane fuel cell specifically comprises the following steps:
calculating the voltage of the monolithic proton exchange membrane fuel cell:
Vcell＝Enerst-Vact-Vohm-Vcon
Wherein V cell is the voltage of a monolithic proton exchange membrane fuel cell, E nerst is the thermodynamic voltage, V act is the activation loss, V ohm is the ohmic loss, and V con is the concentration loss;
Wherein,
Vohm＝IRint＝I(Rm+Rc)
Wherein, delta G 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 Faraday constant, xi 1、ξ2、ξ3、ξ4 is the activation loss parameter,The interface oxygen concentration is T, the stack temperature is I, the working current is R C, the electronic resistance is R m, the membrane equivalent resistance is R int, the concentration loss coefficient is b, the maximum current density is J max, the current density is J, the membrane resistivity is rho m, the membrane thickness is l, the membrane area is A, and the water content of an exchange membrane is lambda;
The semi-empirical model of a proton exchange membrane fuel cell is as follows:
Wherein N cell is the number of the cells of the proton exchange membrane fuel cell;
The parameters to be identified comprise an activation loss parameter xi 1、ξ2、ξ3、ξ4, an electronic resistance R C, a concentration loss coefficient b, a maximum current density J max, a current density J and an exchange membrane water content lambda;
The optimization model of the proton exchange membrane fuel cell is as follows:
f(ξ1、ξ2、ξ3、ξ4、Rc、b、λ、Jmax、J)=min(MSE)
Wherein,
λmin≤λ≤λmax
bmin≤b≤bmax
Jmin≤J≤Jmax
Wherein min is a minimization function, V cell (k) is a theoretical value of the output voltage, V m (k) is an actual value of the output voltage, m is an activation loss parameter index, k is a kth working point, num is the number of working points, f is an optimization target,Is the lower limit of the mth activation loss parameter,Is the upper limit of the mth activation loss parameter,As a lower limit of the electrical resistance,Is the upper limit of the electronic resistance, lambda min is the lower limit of the water content of the exchange membrane, lambda max is the upper limit of the 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,As a lower limit of the maximum current density,As an upper limit of the maximum current density, J min is a lower limit of the current density, and J max is an upper limit of the current density;
Solving an optimization model through a multi-strategy sparrow search optimization algorithm to obtain a plurality of optimal recognition parameters, wherein the method comprises the following steps of:
S1, setting search space and dimension of sparrows according to a plurality of constraint conditions, and setting the number of sparrows in a population, the maximum iteration number, the finder proportion, the alerter proportion and a safety threshold;
S2, obtaining elite population by utilizing elite population strategy, and entering circulation;
S3, calculating fitness values of sparrow individuals in elite population, sequencing a plurality of fitness values, dividing the sparrow individuals into discoverers and followers according to the ratio of the discoverers, and finding out the sparrow individuals and positions thereof corresponding to the optimal and worst fitness values;
S4, in a finder position updating stage, the finder position is updated according to the Lewy flight disturbance strategy;
s5, updating the position of the follower according to a follower formula;
s6, an alerter position updating stage, namely randomly generating alerters in the population according to the proportion of the alerters, and updating the positions of the alerters according to an alerter formula;
S7, in the DE/best/1 mutation stage, updating positions of all sparrow individuals according to a DE/best/1 mutation strategy and a dynamic scaling factor sf;
S8, updating individual fitness values of sparrows, and reordering to determine optimal and worst fitness values and positions of the optimal and worst fitness values;
S9, judging whether an algorithm ending condition is met, if not, jumping to S3, and if so, performing S10;
and S10, recording an optimal result and ending the operation.
5. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the fuel cell parameter identification method of any one of the preceding claims 1-3 when executing the program.
6. A computer-readable storage medium, characterized in that the storage medium stores a computer program which, when executed by a processor, implements the fuel cell parameter identification method of any one of the preceding claims 1-3.
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