Fuel cell parameter estimation method based on improved doliolaria algorithm

Abstract

The invention relates to a fuel cell parameter estimation method based on an improved doliolaria algorithm. Parameter estimation is crucial to modeling, design and operation of a proton exchange membrane fuel cell (PEMFC) system. However, the inherent nonlinearity and complex dynamic characteristics of the PEMFC system bring huge challenges to the traditional optimization technology, and accurate and effective parameter optimization is difficult to realize. In order to solve the problems, the invention provides a novel optimization method which is called as an improved dogvessel squirt algorithm (HSSA). In HSSA, an orthogonal learning strategy is adopted to help a leader to avoid falling into local optimum, and the ability of the leader to explore new fields and fields with prospects is improved. Meanwhile, a dynamic control parameter mechanism is introduced into a position updating equation of the follow-up cable so as to keep proper balance between exploration capacity and mining capacity. And a Levy flight strategy is adopted, so that the population diversity is increased, and the SSA detection efficiency is improved. The method can be effectively applied to fuel cell parameter identification, and has good estimation precision and robust performance.

Description

Technical Field

[0001] The invention relates to the technical field of fuel cells, and in particular to a fuel cell parameter estimation method based on an improved salp algorithm. Background Art

[0002] With the increasing severity of the energy crisis and environmental degradation, it is necessary to develop and utilize clean and renewable energy on a global scale. Among these sustainable energy sources, fuel cells have become a viable solution to solve the energy crisis and reduce carbon dioxide emissions due to their unique advantages, including high conversion efficiency, less environmental pollution, excellent reliability and lifespan. In particular, proton exchange membrane fuel cells (PEMECs) have gained great attention due to their excellent power density, efficiency and minimal or reduced emissions, making them potential power sources for a variety of applications such as distributed power stations, automotive systems and portable power devices.

[0003] Generally, the parameter determination process of the PEMFC model can be formalized as an optimization problem, and various optimization methods can be used to solve this problem. However, due to the highly nonlinear, multivariable and strongly coupled characteristics of the PEMFC system, traditional parameter estimation methods such as the least squares method and Kalman filtering often have problems such as slow convergence and low accuracy when dealing with complex nonlinear problems, making it extremely challenging to determine the optimal values ​​of the model parameters. Summary of the invention

[0004] In view of this, the object of the present invention is to provide a fuel cell parameter estimation method based on an improved salp algorithm, which can be effectively applied to fuel cell parameter identification and has good estimation accuracy and robust performance.

[0005] To achieve the above object, the present invention adopts the following technical solution: a fuel cell parameter estimation method based on an improved salp algorithm, comprising the following steps:

[0006] Step 1: Modeling based on the fuel cell mathematical model and determining the parameter identification target;

[0007] Step 2: Select the Salp algorithm for parameter identification, and improve the Salp algorithm through orthogonal learning strategy, dynamic control parameter strategy and Levy flight;

[0008] Step 3: Determine the parameter identification objective function, which is expressed as the difference between the experimental data and the output voltage of the predicted model; import the voltage and current data of the relevant fuel cell, perform iterative calculations through the improved Salp Algorithm until convergence is reached, stop outputting the corresponding parameter identification value of the model, and compare it with the actual data.

[0009] In a preferred embodiment, in step 1, the PEMFC is composed of anode and cathode electrodes separated by a polymer electrolyte membrane that promotes proton transport while blocking electron flow;

[0010] The overall electrochemical reaction occurring within the FC is expressed as:

[0011] anode:

[0012] H 2 →2H + +e - (1)

[0013] cathode:

[0014]

[0015] overall:

[0016]

[0017] In PEMFC, three types of losses occur: ohmic loss, concentration loss and activation loss; the terminal voltage is expressed by equation (4):

[0018] V cell =E nernst -V ohmic -V conc -V act (4)

[0019] Where V ohmic 、V conc and V act They represent ohmic loss, concentration loss and activation loss respectively; Enernst is the reversible open circuit voltage, which is described as follows:

[0020]

[0021] Where T is the electrolytic cell temperature, are the effective partial pressures of oxygen and hydrogen, respectively, expressed as:

[0022]

[0023] In the formula, is the water vapor saturation pressure, calculated using the following formula:

[0024]

[0025] The activation voltage loss is expressed by equation 8:

[0026]

[0027] Where η 1 ,η 2,η 3 ,η 4 are parameter coefficients, where: is the oxygen concentration, ii is the PEMFC output current, expressed as:

[0028]

[0029] The equivalent resistance of FC results in ohmic voltage loss; expressed by equation (10):

[0030] V ohmic =i(R M +R C ) (10)

[0031] In the formula, R M is the membrane resistance, R C is the contact resistance, expressed as:

[0032]

[0033] Where l is the membrane thickness, A is the cell active area, ρ M is the membrane resistivity, λ is the membrane water content. Formula (13) defines the concentrated voltage loss:

[0034]

[0035] Among them J max represents the maximum current density, b is a constant;

[0036] The PEMFC stack consists of a number of n cells connected in series; therefore, the voltage output of the stack is expressed by equation (14):

[0037] V s =n×V cell (14)

[0038] Therefore, based on the above equations, a mathematical model of PEMFC is constructed.

[0039] In a preferred embodiment, the salp chain in the salp algorithm in step 2 is divided into two categories: leaders and followers; the first salp in the chain is determined as the leader, and all other salps are considered followers; the food source is used as the foraging target to guide the leader to update its position; the leader's position is updated by formula (15):

[0040]

[0041] In the formula represents the position of the leader in the jth dimension; F j Lb is the food source in this dimension; j and Lb j are the upper and lower bounds respectively; c2 and c 3 are two random numbers in the range [0,1]. In the whole optimization process, the coefficient c 1 It is a key parameter to ensure the balance between algorithm exploration and development capabilities; it is defined as follows:

[0042]

[0043] Where T represents the maximum number of iterations and t represents the current iteration; the position of the follower is updated using formula (17):

[0044]

[0045] In the formula represents the position of the i-th driven term in the j-th dimension, and i>2;

[0046] In the following phases, both the leader and the follower adjust their positions to move toward a more desirable location; this process continues until a specified termination condition is met.

[0047] In a preferred embodiment, in step 2, first, in the population update stage, the OL strategy is used to generate more feasible candidate solutions to guide the leader to move to the feasible search area, help the leader avoid local optimality, and improve its search ability; secondly, an improved follower position update mechanism based on dynamic control parameter strategy is proposed; thirdly, the Levy flight strategy is adopted to enrich the movement pattern of salps and make their distribution more dispersed.

[0048] In a preferred embodiment, the OED method is used to formulate the leader's OL strategy; the OL strategy uses the different dimensional information of the leader and the guide vector, and uses the OED method to generate more feasible candidate solutions; the implementation of the OL strategy starts with two agents: the current leader X 1 and the guide vector T s , derived from formula (18):

[0049] T s =X k +rand(0,1)(FX k ) (18)

[0050] Where rand(0,1) represents a random value uniformly generated in the interval [0,1]; k is a random integer in [1,N], excluding 1; F represents the food source of the current population;

[0051] In generating the guidance vector T s Afterwards, use the OL strategy to 1 and T s Combine the information of s, as follows:

[0052]

[0053] Wherein represents an OL operation;

[0054] Consider two candidate solutions, the leader X 1 =(x 11 , x 12 , …, x 1D ) and the guiding vector T s = T 11 , T 12 , …, T 1D ), defining the solution space [lb, ub], where lb and ub are given as follows:

[0055]

[0056] Then, the solution space is converted to the Q level, and the formula is as follows:

[0057]

[0058] The D dimensions of the provided problem are divided into F subgroups by the following formula:

[0059]

[0060] r 1 , r 2 , …, r F -1 is a random integer satisfying 1 < r 1 < r 2 < … < r F -1 < D; thus, each group corresponds to a factor, and the i-th group G i can be quantified to Q levels by the following formula:

[0061]

[0062] Therefore, M candidate solutions are obtained by OAL M (Q F ); according to the FA method, (M + 1) candidate solutions are developed using the previous M candidate solutions; then, the fitness values of all (M + 1) candidate solutions are calculated. Then, the solution with the lowest fitness value is selected as the new candidate solution V s .

[0063] In a preferred embodiment, a dynamic control parameter w based on the sine function is introduced to adjust the movement of the follower; this method is represented by formulas (24) and (25):

[0064]

[0065]

[0066] where w ini and w fin They represent the initial value and final value of w(t) respectively; t represents the current iteration, and T represents the maximum number of iterations;

[0067] It can be seen from formula (25) that the dynamic control parameter w(t) decreases nonlinearly with the increase of the number of iterations.

[0068] In a preferred embodiment, in each iteration, when all sea squirts complete the position update process, the Levy flight strategy is m r The mutation rate is realized; if a random number is generated in the interval [0,1] and is less than m r , then apply the Levy flight strategy to the i-th individual to generate a new candidate solution

[0069]

[0070] where x i represents the i-th sample, <e:1>represents point-to-point multiplication, l = 0.01 (x i -x best ), x best represents the best individual in the current population; Levy(λ) represents the path that obeys the Levy distribution, satisfying Levy~u=t -λ , 0<λ≤3;

[0071] The Levy distribution simplifies to

[0072]

[0073] Where μ and ν are standard normal distributions, defined as follows:

[0074]

[0075] σ ν =1(30

[0076] Where γ is set to 1.5;

[0077] Then the newly obtained candidate solution The corresponding original solution x i Comparison is made in terms of fitness; if has a better fitness, it will replace the original solution x in the next generation i ; Otherwise, the original solution x i Remain unchanged. The formal description is as follows:

[0078]

[0079] In a preferred embodiment, the objective function is expressed as the difference between the experimental data and the predicted model output voltage:

[0080]

[0081] In the formula, M represents the data size, V data Represents measured data, V model represents the model output, x = [η 1 ,η 2 ,η 3 ,η 4 ,η,b,R C ] is a vector containing 7 unknown parameters; the considered constraints are defined by:

[0082]

[0083] Compared with the prior art, the present invention has the following beneficial effects:

[0084] 1. The present invention transforms the fuel cell parameter estimation problem into a nonlinear, multivariable and strongly coupled optimization problem, and adopts an intelligent algorithm to perform parameter estimation, which simplifies the complexity of the parameter estimation problem on the one hand, and improves the accuracy of parameter estimation on the other hand;

[0085] 2. The present invention adopts three improvement strategies to improve the standard Salp algorithm, effectively solving the problem of low precision of parameter estimation and further improving the system stability;.

[0086] 3. Compared with other intelligent optimization algorithms, the present invention has better estimation accuracy and reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Figure 1 An improved flowchart of the algorithm of the preferred embodiment of the present invention;

[0088] Figure 2 A schematic diagram of parameter identification of a preferred embodiment of the present invention;

[0089] Figure 3 This is a parameter identification structure of a preferred embodiment of the present invention, wherein (a) is a convergence curve and (b) is a fitting curve. DETAILED DESCRIPTION

[0090] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0091] It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0092] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application; as used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or their combinations.

[0093] The present invention provides a fuel cell parameter estimation method based on an improved salp algorithm, referring to Figure 1-3 , including the following steps:

[0094] 1. Model building

[0095] Specifically, a PEMFC consists of an anode and a cathode electrode, separated by a polymer electrolyte membrane that facilitates proton transport while blocking the flow of electrons. The basic structure of a PEMFC is shown above.

[0096] The overall electrochemical reaction occurring within the FC can be expressed as:

[0097] anode:

[0098] H 2 →2H + +e - (1)

[0099] cathode:

[0100]

[0101] overall:

[0102]

[0103] In PEMFC, three types of losses occur: ohmic loss, concentration loss, and activation loss. The terminal voltage can be expressed by equation 4:

[0104] V cell =E nernst -V ohmic -V conc -V act (4)

[0105] Where V ohmic 、V conc and V act They represent ohmic loss, concentration loss and activation loss respectively. E_nernst is the reversible open circuit voltage, which is described as follows:

[0106]

[0107] Where T is the electrolytic cell temperature, are the effective partial pressures of oxygen and hydrogen, respectively, which can be expressed as:

[0108]

[0109] In the formula, is the water vapor saturation pressure, which can be calculated using the following formula:

[0110]

[0111] The activation voltage loss can be expressed by equation 8:

[0112]

[0113] Where η 1 ,η 2 ,η 3 ,η 4 are parameter coefficients, where: is the oxygen concentration, ii is the PEMFC output current, expressed as:

[0114]

[0115] The equivalent resistance of FC results in an ohmic voltage loss. This can be expressed by Equation 10.

[0116] V ohmic =i(R M +R C ) (10)

[0117] In the formula, R M is the membrane resistance, R C is the contact resistance, expressed as:

[0118]

[0119] Where l is the membrane thickness, A is the cell active area, ρ M is the membrane resistivity, and λ is the membrane water content.

[0120] Equation 13 defines the concentrated voltage loss:

[0121]

[0122] Among them J max represents the maximum current density and b is a constant.

[0123] The PEMFC stack consists of a number of n cells connected in series. Therefore, the voltage output of the stack is expressed by equation 14:

[0124] V s =n×V cell (14)

[0125] Therefore, based on the above equations, a mathematical model of PEMFC can be constructed.

[0126] 2. Improvement of Salp Algorithm

[0127] 2.1 Salp Algorithm

[0128] The salp algorithm mimics the collective behavior of salps in the ocean, where they often gather in groups and habitually form a cluster called a salp chain during foraging and navigation. Mathematically, a salp chain can be divided into two categories: leaders and followers. The first salp in the chain is identified as the leader, while all other salps are considered followers. Food sources serve as foraging targets to guide the leader to update its position. The leader's position is updated by Equation 15:

[0129]

[0130] In the formula represents the position of the leader in the jth dimension; F j Lb is the food source in this dimension; j and Lb j are the upper and lower bounds respectively; c 2 and c 3 are two random numbers in the range [0,1]. In the whole optimization process, the coefficient c 1 It is a key parameter to ensure the balance between the algorithm's exploration and development capabilities. It is defined as follows:

[0131]

[0132] Where T represents the maximum number of iterations and t represents the current iteration. Use formula 17 to update the position of the follower:

[0133]

[0134] In the formula represents the position of the i-th driven term in the j-th dimension, and i>2.

[0135] Like other swarm intelligence algorithms, SSA first initializes a swarm of salps in a given solution space. In the following phase, both the leader and followers adjust their positions to move towards a more ideal position. This process will continue until the specified termination condition is met.

[0136] 2.2 Improvement strategies

[0137] Although SSA has shown excellent performance in global optimization and various engineering problems, it has problems such as insufficient population diversity, slow convergence speed, and unbalanced development and exploration when dealing with complex problems. In response to these limitations, the present invention proposes HSSA and integrates three enhancement strategies into HSSA. First, in the population update stage, the OL strategy is used to guide the leader to move to the feasible search area by generating more feasible candidate solutions, helping the leader to avoid local optimality and improve its search ability; secondly, an improved follower position update mechanism based on dynamic control parameter strategy is proposed. This mechanism is conducive to the balance between local development and global exploration, thereby improving the optimization accuracy of the algorithm. Third, the Levy flight strategy is adopted to enrich the movement mode of salps and make their distribution more dispersed. This enhances their exploration ability, diversifies the population, and enables the population to find better solutions. With the synergistic effect of these three modifications, the overall performance of the SSA algorithm has been greatly improved in terms of convergence speed and solution accuracy.

[0138] 2.2.1 Orthogonal Learning Strategy

[0139] It is obvious from formula (15) that the leader adjusts its position only according to the direction received from the food source. In the absence of prior knowledge, it becomes challenging to verify whether the current food source is located at the global optimal solution. When a food source is determined to be a local optimum, the entire population will inevitably converge in that area, resulting in a loss of population diversity and ultimately causing the algorithm to converge to the local optimum. To alleviate this problem, the OL strategy is used to help the leader bypass the local optimum and turn it to a better search direction, thereby improving its exploration ability.

[0140] In this paper, the OED method is used to formulate the OL strategy of the leader. This strategy makes full use of the different dimensional information of the leader and the guide vector, and uses the OED method to generate more feasible candidate solutions. It can effectively guide the leader to a more promising search area, leading to the global optimum, thereby improving the performance of SSA. In addition, the OL strategy enables the leader to avoid the local optimum and enhances its exploration ability.

[0141] The implementation of the OL strategy in this study starts with two agents: the current leader X 1 and the guide vector T s , derived from formula (18):

[0142] T s =X k +rand(0,1)(FX k ) (18)

[0143] Where rand(0,1) represents a random value uniformly generated in the interval [0,1]; k is a random integer in [1,N], excluding 1; and F represents the food source of the current population.

[0144] In generating the guidance vector T s Afterwards, use the OL strategy to 1 and T s Combine the information of s , as shown below:

[0145]

[0146] in Indicates OL operation.

[0147] The next section introduces the implementation details of the orthogonal strategy. Considering two candidate solutions, the leader X 1 =x 11 ,x 12 ,…,x 1D ) and the guide vector T s =(T 11 ,T 12 ,…,T 1D ), which define the solution space [lb, ub], where lb and ub are given as follows:

[0148]

[0149] Then, the solution space is transformed into Q levels, and the formula is as follows:

[0150]

[0151] Since the dimension of problem D is generally greater than the number of factors F, OAL M (Q F ) cannot be directly used. To solve this problem, we can use the following formula to divide the D dimension of the provided problem into F subgroups:

[0152]

[0153] r 1 , r 2 , …, r F -1 are random integers satisfying 1 < r 1 < r 2 < … < r F -1 < D. Therefore, each group corresponds to a factor, and the i-th group G i can be quantified into Q levels by the following formula:

[0154]

[0155] Therefore, M candidate solutions are obtained by OAL M (Q F ). According to the FA method, (M + 1) candidate solutions can be developed using the previous M candidate solutions. Then, the fitness values of all (M + 1) candidate solutions are calculated. Then, the solution with the lowest fitness value is selected as the new candidate solution V s .

[0156] 2.2.2 Dynamic control parameter strategy

[0157] It can be seen from the follower position update formula (17) that the current follower's position only depends on its own and the positions of adjacent followers in the previous iteration. However, this position update mechanism lacks dynamics and has a certain blindness. If adjacent individuals fall into a local optimum, the current follower will inevitably follow into this local optimum region, which may lead to premature convergence of the algorithm. Therefore, to enhance the adaptability of the follower position update mechanism, a dynamic control parameter w based on the sine function is introduced to adjust the movement of the follower. This method can be expressed by formulas 24 and 25:

[0158]

[0159] where w ini and w fin They represent the initial value and final value of w(t) respectively; t represents the current iteration, and T represents the maximum number of iterations.

[0160] As can be seen from Equation 25, the dynamic control parameter w(t) decreases nonlinearly with the number of iterations. This feature enables the algorithm to expand the global search domain in the initial stage, thereby avoiding the risk of premature convergence to the local optimum. In the subsequent stages of the search process, the algorithm shifts its focus to using local neighbors to improve the accuracy of the solution. This enhancement achieves a more favorable balance between exploration and exploitation capabilities, thereby improving the algorithm's performance in terms of convergence.

[0161] 2.2.3 Levi Flight

[0162] Like other swarm intelligence algorithms, SSA sometimes experiences a rapid decline in population diversity as it evolves to late stages. The reduction in diversity within the search space usually causes most sea squirts to stagnate near a local optimum. As a result, only a limited number of agents continue their exploration, which may lead to premature convergence and evolutionary stagnation. To address this issue, this paper proposes a Levy flight strategy with the goal of increasing the diversity of the SSA population and enhancing its global exploration capability.

[0163] Levy flight, characterized by occasional long jumps interspersed with short walks, has been intensively studied for its potential to enhance the performance of swarm intelligence algorithms.

[0164] In each iteration, when all sea squirts complete the position update process, the Levy flight strategy is r Specifically, if a random number is generated in the interval [0,1] and is less than m r , then apply the Levy flight strategy to the i-th individual to generate a new candidate solution

[0165]

[0166] where x i represents the i-th sample, <e:1>represents point-to-point multiplication, l = 0.01 (x i -x best ), x best represents the best individual in the current population. Levy(λ) represents the path that obeys the Levy distribution, satisfying Levy~u=t -λ , 0<λ≤3.

[0167] The Levy distribution can be simplified to

[0168]

[0169] Where μ and ν are standard normal distributions, defined as follows:

[0170]

[0171] σ ν =1(30

[0172] Here γ is set to 1.5.

[0173] Then the newly obtained candidate solution The corresponding original solution x i Compare in terms of fitness. If has a better fitness, it will replace the original solution x in the next generation i Otherwise, the original solution x i Remain unchanged. The formal description is as follows:

[0174]

[0175] Figure 1 Algorithm Improvement Flowchart

[0176] 3. Parameter Estimation

[0177] In the present invention, the objective function is expressed as the difference between the experimental data and the output voltage of the prediction model:

[0178]

[0179] In the formula, M represents the data size, V data Represents measured data, V model represents the model output, x = [η 1 ,η 2 ,η 3 ,η 4 ,η,b,R C ] is a vector containing 7 unknown parameters. The considered constraints can be defined as follows:

[0180]

[0181] In order to effectively solve the parameter estimation problem, an appropriate optimization algorithm is required. The present invention adopts the improved Salp algorithm to accurately determine the unknown parameters of the PEMFC model, thereby improving the accuracy of the model. The parameter estimation steps are as follows Figure 2 As shown:

[0182] 4. Result Verification

[0183] The effectiveness of the proposed HSSA was further studied by applying it to determine the unknown parameters of four PEMFC models. The PEMFC models tested were 250W, NedStackPS6, SR-12500W and BCS 500W models, and their electrical specifications are shown in Table 1. In order to evaluate the effectiveness of HSSA, the present invention extensively compared HSSA with five mature metaheuristic algorithms (i.e., GWO, WOA, MVO, PSO and SSA) and the results obtained from existing studies. In order to ensure a fair comparison between all the algorithms considered, a population size of 30 and a fixed number of iterations (1000) were set. All algorithms were independently implemented using MATLAB2020a, and 30 runs were performed on each of the four PEMFC models.

[0184] Table 1 PEMFC electrical specifications and operating conditions

[0185]

[0186] Taking the identification result of model 250W as an example, as mentioned above, the algorithm is first tested by the 250W PEMFC model, using four sets of voltage and current data. Among them, two sets of data (3 / 5bar353.15K, 1 / 1bar 343.15K) are used to estimate 7 unknown model parameters, and the remaining data sets (2.5 / 3bar343.15K, 1.5 / 1.5bar 343.15K) are used to evaluate the effectiveness of the obtained model.

[0187] The best identification parameters and their corresponding values ​​of SSE identified by HSSA, SSA, GWO, WOA, MVO and PSO, as well as the existing results reported for range 1, are presented in Table 2, and the most favorable results are highlighted in bold. As shown in Table 2, HSSA outperforms all compared algorithms and has the lowest SSE value of 13.7958 in range 1. GWO and WOA rank second and third, respectively. For range 2, as shown in Table 8, HSSA also provides the lowest SSE (7.545) and is therefore ranked first. WOA, PSO and GWO rank second, third and fourth, respectively. These results show that the proposed HSSA outperforms the existing algorithms when dealing with the PEMFC parameter estimation problem, highlighting its superior performance.

[0188] Table 2 Optimal parameters and SEE obtained by different algorithms in range 1

[0189]

[0190] The following are the convergence curve and fitting curve of HSSA parameter identification

[0191] For the range 1 of 250W fuel cell, the convergence curves of all the algorithms considered are shown in Figure 3 (a). As shown in the figure, it can be seen that while GWO can quickly identify high-quality solutions in the initial stage of the iterative process, it tends to converge prematurely and struggle to achieve global optimality at the end of the iteration. In contrast, HSSA shows superior convergence speed and consistently obtains high-quality solutions.

[0192] In order to verify the consistency between the actual and predicted characteristics of the PEMFC model derived from the optimal parameters identified by HSSA, Figure 3 (b) shows the polarization curve for range 1. It can be clearly seen from the figure that the simulated polarization curves generated by HSSA are remarkably consistent with the experimental data in terms of both parameter identification and model validation.

[0193] The previous discussion shows that the proposed HSSA consistently demonstrates excellent performance in identifying the optimal parameters of a fuel cell with a signal of 250W. This is particularly evident in terms of convergence speed, accuracy, and reliability compared to other algorithms. Therefore, the HSSA is able to accurately determine the optimal parameters of a PEMFC.

Claims

1. A fuel cell parameter estimation method based on an improved salp algorithm, characterized in that: The following steps are involved: Step 1: Modeling based on the fuel cell mathematical model and determining the parameter identification target; Step 2: Select the Salp algorithm for parameter identification, and improve the Salp algorithm through orthogonal learning strategy, dynamic control parameter strategy and Levy flight; Step 3: Determine the parameter identification objective function, which is expressed as the difference between the experimental data and the output voltage of the predicted model; import the voltage and current data of the relevant fuel cell, perform iterative calculations through the improved Salp Alpine algorithm until convergence is reached, stop outputting the corresponding parameter identification value of the model, and compare it with the actual data.

2. A fuel cell parameter estimation method based on an improved salp algorithm according to claim 1, characterized in that: In step 1, the PEMFC consists of anode and cathode electrodes separated by a polymer electrolyte membrane that facilitates proton transport while blocking the flow of electrons; The overall electrochemical reaction occurring within the FC is expressed as: anode: H2→2H + +and - (1) cathode: overall: In PEMFC, three types of losses occur: ohmic loss, concentration loss and activation loss; the terminal voltage is expressed by equation (4): V cell =E nernst -V oHmic -V conc -V act (4) Where V ohmic 、V conc and V act They represent ohmic loss, concentration loss and activation loss respectively; Enernst is the reversible open circuit voltage, which is described as follows: Where T is the electrolytic cell temperature, P O2 , P H2 are the effective partial pressures of oxygen and hydrogen, respectively, expressed as: Where P H2O is the water vapor saturation pressure, calculated using the following formula: The activation voltage loss is expressed by equation 8: In the formula, η1, η2, η3, η4 are parameter coefficients, among which: is the oxygen concentration, ii is the PEMFC output current, expressed as: The equivalent resistance of FC results in ohmic voltage loss; expressed by equation (10): V ohmic =i(R M +R C ) (10) In the formula, R M is the membrane resistance, R C is the contact resistance, expressed as: Where l is the membrane thickness, A is the cell active area, ρ M is the membrane resistivity, λ is the membrane water content. Formula (13) defines the concentrated voltage loss: Among them J max represents the maximum current density, b is a constant; The PEMFC stack consists of a number of n cells connected in series; therefore, the voltage output of the stack is expressed by equation (14): In s =n×V cell (14) Therefore, based on the above equations, a mathematical model of PEMFC is constructed.

3. A fuel cell parameter estimation method based on an improved salp algorithm according to claim 1, characterized in that: In step 2, the salp chain in the salp algorithm is divided into two categories: leaders and followers; the first salp in the chain is determined as the leader, while all other salps are considered followers; the food source is used as the foraging target to guide the leader to update its position; the leader's position is updated by formula (15): Where x j 1 represents the position of the leader in the jth dimension; F j Lb is the food source in this dimension; j and Lb j are the upper and lower bounds respectively; c2 and c3 are two random numbers in the range of [0,1]; in the entire optimization process, the coefficient c1 is the key parameter to ensure the balance between the algorithm's exploration ability and development ability; it is defined as follows: Where T represents the maximum number of iterations and t represents the current iteration; the position of the follower is updated using formula (17): Where x j i represents the position of the i-th driven term in the j-th dimension, and i>2; In the following phases, both the leader and the follower adjust their positions to move toward a more desirable location; this process continues until a specified termination condition is met.

4. A fuel cell parameter estimation method based on an improved salp algorithm according to claim 3, characterized in that: In step 2, first, in the population update phase, the OL strategy is used to generate more feasible candidate solutions to guide the leader to move to the feasible search area, helping the leader avoid local optimality and improve its search ability; Secondly, an improved follower position update mechanism based on dynamic control parameter strategy is proposed; thirdly, the Levy flight strategy is adopted to enrich the movement mode of salps and make their distribution more dispersed.

5. The fuel cell parameter estimation method based on the improved salp algorithm according to claim 3, characterized in that: The OED method is used to formulate the leader's OL strategy; the OL strategy uses the different dimensional information of the leader and the guidance vector to generate more feasible candidate solutions using the OED method; The implementation of the OL strategy starts with two agents: the current leader X1 and the guidance vector T s , derived from formula (18): T s =X k +rand(0,1)(F-X k ) (18) Where rand(0,1) represents a random value uniformly generated in the interval [0,1]; k is a random integer in [1,N], excluding 1; F represents the food source of the current population; In generating the guidance vector T s Afterwards, the OL strategy is used to transform X1 and T s Combine the information of s , as shown below: Where ⊕ represents OL operation; Consider two candidate solutions, leader X1 = (x 11 ,x 12 ,…,x 1D ) and the guide vector T s =T 11 ,T 12 ,…,T 1D ), define the solution space [lb,ub], where lb and ub are given as follows: Then, the solution space is converted to Q level, the formula is as follows: The D dimensions of the provided problem are divided into F subgroups using the following formula: r1, r2, …, r F -1 are random integers satisfying 1 < r1 < r2 < … < r F -1 < D; thus, each group corresponds to a factor, and the i-th group G i can be quantified into Q levels by the following formula: Therefore, by OA L M (Q F ) to obtain M candidate solutions; according to the FA method, use the previous M candidate solutions to develop (M+1) candidate solutions; then calculate the fitness values ​​of all (M+1) candidate solutions. Then select the solution with the lowest fitness value as the new candidate solution V s .

6. A fuel cell parameter estimation method based on improved salp algorithm according to claim 3, characterized in that: A dynamic control parameter w based on a sinusoidal function is introduced to regulate the motion of the follower; this method is expressed by equations (24) and (25): where w ini and w fin represent the initial and final values ​​of w(t) respectively; t represents the current iteration, and T represents the maximum number of iterations; It can be seen from formula (25) that the dynamic control parameter w(t) decreases nonlinearly with the increase of the number of iterations.

7. A fuel cell parameter estimation method based on improved salp algorithm according to claim 3, characterized in that: In each iteration, when all sea squirts complete the position update process, the Levy flight strategy is r The mutation rate is realized; if a random number is generated in the interval [0,1] and is less than m r , then apply the Levy flight strategy to the i-th individual to generate a new candidate solution where x i represents the i-th sample, <e:1>represents point-to-point multiplication, l = 0.01 (x i -x best ), x best represents the best individual in the current population; Levy(λ) represents the path that obeys the Levy distribution, satisfying Levy~u=t -λ , 0<λ≤3; The Levy distribution simplifies to Where μ and ν are standard normal distributions, defined as follows: s ν =1(30 Where γ is set to 1.5; Then the newly obtained candidate solution The corresponding original solution x i Comparison is made in terms of fitness; if has a better fitness, it will replace the original solution x in the next generation i ; Otherwise, the original solution x i Remain unchanged. The formal description is as follows:

8. The fuel cell parameter estimation method based on the improved salp algorithm according to claim 1, characterized in that: The objective function is expressed as the difference between the experimental data and the predicted model output voltage: In the formula, M represents the data size, V data Represents measured data, V model represents the model output, x=[η1,η2,η3,η4,η,b,R C ] is a vector containing 7 unknown parameters; the considered constraints are defined by:

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