Fuel cell electrochemical impedance spectroscopy estimation method for water management fault diagnosis

Abstract

The application discloses a fuel cell electrochemical impedance spectrum estimation method for water management fault diagnosis, comprising the following steps: S1, establishing an equivalent circuit model; S2, equivalent circuit model parameter identification; S3, single model impedance estimation; S4, impedance fusion estimation; and S5, electrochemical impedance spectrum estimation. The impedance estimation method of the application can combine the advantages of each equivalent circuit model, realize high precision and reliability of impedance estimation in a full frequency range, and provide a more complete basis for fuel cell water management fault diagnosis based on EIS.

Description

Technical Field

[0001] This invention relates to the field of proton exchange membrane fuel cell technology, and more specifically to a fuel cell electrochemical impedance spectroscopy estimation method for water management fault diagnosis. Background Technology

[0002] Because a proton exchange membrane fuel cell (PEMFC) is a complex nonlinear system involving multiple domains, variables, and strong coupling, establishing an accurate mechanistic model is quite difficult. Electrochemical impedance spectroscopy (EIS), as an effective tool for analyzing electrochemical reaction processes, can reflect the internal information of the fuel cell during operation and is commonly used for PEMFC water management fault diagnosis, health estimation, and aging prediction.

[0003] To ensure the accuracy of the measurement results, electrochemical impedance spectroscopy (EIS) measurements are initiated after the PEMFC system reaches equilibrium. This requires ensuring a linear and approximately stable system response, and the measurement time is relatively long. Furthermore, in the process of simulating flooding and membrane dryness faults followed by EIS measurement during fuel cell water management fault diagnosis based on EIS, the resulting simulations can cause damage to the fuel cell. Effective equivalent circuit models can be used to estimate EIS, providing accurate and reliable estimations across the ultra-low to high frequency range, thus offering data support for fuel cell water management fault diagnosis. However, a single equivalent circuit model cannot guarantee optimal impedance estimation accuracy across the entire frequency range. Combining the advantages of each equivalent circuit model to achieve high accuracy and reliability in impedance estimation across the entire frequency range is of great significance for researching fuel cell water management fault diagnosis based on EIS. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a fuel cell electrochemical impedance spectroscopy (EIS) estimation method for water management fault diagnosis. This multi-model fusion impedance estimation method combines the advantages of each equivalent circuit model, achieving high accuracy and reliability of impedance estimation across the entire frequency range, thus providing a more complete basis for EIS-based fuel cell water management fault diagnosis.

[0005] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution:

[0006] A method for estimating the electrochemical impedance spectroscopy of a fuel cell for water management fault diagnosis includes:

[0007] S1. Establish equivalent circuit models: Establish three equivalent circuit models suitable for water management fault diagnosis, including RLC-W equivalent circuit model, RC-RC equivalent circuit model and second-order RQ-RLC equivalent circuit model.

[0008] S2. Equivalent Circuit Model Parameter Identification: Based on the electrochemical impedance spectroscopy (EIS) data of PEMFC measured under three water management conditions (normal, flooded, and dry membrane), the parameters of the three equivalent circuit models were identified. The parameter identification method used was the chaotic particle swarm optimization algorithm DIW-CPSO based on dynamic inertial weights, which identified the optimal parameters of the three models under the three water management conditions (normal, flooded, and dry membrane).

[0009] S3. Single Model Impedance Estimation: Using three equivalent circuit models identified based on parameters, impedance data for each equivalent model under three states—normal, flooded, and membrane dry—can be estimated, with a total of nine sets.

[0010] S4. Impedance fusion estimation: Based on the impedance estimation data of the three equivalent circuit models measured under each water management state, the real and imaginary parts of the impedance estimation data are fused using the covariance cross-correlation (CI) algorithm to obtain the real and imaginary parts of the impedance after model fusion estimation. The final impedance fusion estimate is then calculated from the real and imaginary parts of the fused impedance.

[0011] S5. Electrochemical impedance spectroscopy estimation: Under the three water management conditions of normal, flooded and membrane dry, the electrochemical impedance spectra of the fuel cell under these three water management conditions are plotted based on the impedance fusion estimation values ​​corresponding to each frequency point in the range from ultra-low frequency to low frequency and then to high frequency.

[0012] Preferably, in step S1, the equivalent model of the RLC-W circuit mainly consists of an RLC parallel circuit and a Warburg impedance. The RLC parallel circuit is used to describe the first impedance arc in the impedance spectrum, and the Warburg impedance is used to describe the second impedance arc; the equivalent impedance Z of the RLC-W model model1 (jω) is:

[0013]

[0014] In the RLC-W model, the parameter vector that needs to be identified is: θ=[R ohm L2,R b ,L1,C,R a ,R d ,τ d ] T ;R ohm L1 is an ohmic resistor, L2 is an inductor, and R is an ohmic resistor. a and R b R is the resistance in the RLC circuit, C is the capacitance in the RLC circuit, and R... d For the Warburg impedance, τ d It is a function of the diffusion coefficient and the diffusion length.

[0015] Preferably, in step S1, the impedance Z of the RC-RC equivalent circuit model model2 (jω) is:

[0016]

[0017] Among them, the parameter vector that needs to be identified in the RC-RC equivalent circuit model is: θ=[R ohm ,R a ,R b [C1,C2,L] T ;R ohm R is an ohm resistor, L is the cable inductance, R1 and R2 are the resistors in the RC circuit, and C1 and C2 are the capacitors in the RC circuit.

[0018] Preferably, in step S1, the impedance Z of the second-order RQ-RLC equivalent circuit model model3 (jω) is:

[0019]

[0020] In the second-order RQ-RLC equivalent circuit model, the parameter vector that needs to be identified is: θ=[R,L,Rct,α,Q,C,Lmt,Rmt] T R is the ohmic resistance, R ct For charge transfer resistance, α and Q are constants of the phase-constant element, C represents the amount of reactant stored in water / ions, and L mt R is the resistance to the dissolution of reactants. mt L represents the diffusion resistance of the reactants, and L represents the cable inductance.

[0021] Preferably, in step S2, the DIW-CPSO (Disorderly Particle Swarm Optimization) algorithm with dynamic inertia weights is used to identify the parameters of the three equivalent circuit models. The specific steps are as follows:

[0022] S21. Set the weighted sum of squares of the measured impedance and the model-estimated impedance errors as the objective function:

[0023]

[0024] Among them, Re k Re is the measured value of the real part of the impedance. k Im is an estimate of the real part of the impedance. k and Im k These are the measured and estimated values ​​of the imaginary part of the impedance, w. Im and w Re These are the residual weights for the imaginary and real parts of the impedance, respectively.

[0025] S22. Initialize the parameters of the equivalent circuit to be identified, and obtain the Logistic chaotic sequence using the improved Logistic mapping formula. The improved Logistic mapping mathematical model is as follows:

[0026]

[0027] Where μ is the growth rate parameter, x n The magnitude of the chaotic mapping;

[0028] S23, Take the chaotic sequence x n The initial parameter range of the equivalent circuit is merged to obtain the initial population after chaos.

[0029] S24. When the preset number of iterations has not been reached, update the dynamic inertia weight. The formula for the dynamic inertia weight is:

[0030]

[0031] Among them, W max It is the maximum value of the inertial weight, W min It is the minimum value of the inertia weight, iter and ger are the current iteration number and the total iteration number, respectively, and σ and B(b1,b2) refer to the inertia weight coefficient and the beta function, respectively;

[0032] S25. Calculate the fitness value f = F(X) of the particle according to the objective function F. t+1 );

[0033] S26. Calculate the individual historical best value and the group historical best value, and update the particle velocity and particle position at the same time.

[0034] S27. The loop iterates until the preset total number of iterations is reached, thereby identifying the optimal parameters of the three equivalent circuit models under the three states of normal, flooded and dry.

[0035] Preferably, in step S4, the covariance crossover (CI) algorithm is as follows:

[0036]

[0037]

[0038] in, It is the impedance estimate after fusing the three models, P n P is the variance of the estimation error of model n. CI It is the estimation error variance of the fusion model, and 0≤ω n ≤1, Simultaneous fusion coefficient ω n It is determined by minimizing the index function J = tr(P) CI The calculation yielded:

[0039]

[0040] Therefore, the CI fusion algorithm yielded the fusion impedance estimates of the fuel cell under three conditions: normal operation, flooding, and membrane dryness. and

[0041] Compared with the electrochemical impedance spectra estimated by existing equivalent circuit models, the present invention has the following advantages:

[0042] This method first establishes three different electrochemical equivalent circuit models for proton exchange membrane fuel cells (PEMFCs). Then, based on electrochemical impedance spectroscopy (EIS) data measured under three water management conditions (normal, flooded, and dry), parameter identification is performed on the three equivalent circuit models to obtain their parameters under different water management conditions, thereby estimating the impedance of the three equivalent circuit models under these conditions. Finally, a covariance cross-validation (CI) algorithm is used to fuse the impedance estimation results of the three equivalent circuit models under different water management conditions to obtain the EIS of the fuel cell under these three water management conditions. The beneficial effects of this invention are: the multi-model fusion impedance estimation method combines the advantages of each equivalent circuit model, achieving high accuracy and reliability of impedance estimation across the entire frequency range, providing a more complete basis for EIS-based fuel cell water management fault diagnosis. Attached Figure Description

[0043] Figure 1 This is a flowchart of the steps involved in estimating the electrochemical impedance spectroscopy of a fuel cell for water management fault diagnosis.

[0044] Figure 2 This is the RLC-W equivalent circuit model in this invention.

[0045] Figure 3 This is the RC-RC equivalent circuit model in this invention.

[0046] Figure 4 This is the second-order RQ-RLC equivalent circuit model in this invention.

[0047] Figure 5 This is a flowchart of the parameter identification process in this invention.

[0048] Figure 6 This is the electrochemical impedance spectroscopy of the fuel cell in this invention under normal water management conditions. Detailed Implementation

[0049] To enable those skilled in the art to better understand the technical solutions of the present invention, the preferred embodiments of the present invention are described below in conjunction with specific examples. However, it should be understood that the accompanying drawings are for illustrative purposes only and should not be construed as limiting the present patent.

[0050] The specific implementation steps of the present invention will be described in detail below with reference to the accompanying drawings. A method for estimating the electrochemical impedance spectroscopy of a fuel cell for water management fault diagnosis includes the following steps:

[0051] Step 1: Establish equivalent circuit models. Three equivalent circuit models suitable for water management fault diagnosis are established, including the RLC-W equivalent circuit model, the RC-RC equivalent circuit model, and the second-order RQ-RLC equivalent circuit model.

[0052] The specific model structure is as follows:

[0053] like Figure 2 As shown, the equivalent model of the RLC-W circuit mainly consists of an RLC parallel circuit and a Warburg impedance. The former is used to describe the first impedance arc in the impedance spectrum, and the latter is used to describe the second impedance arc.

[0054] The impedance Z of the RLC-W equivalent circuit model model1 (jω) is:

[0055]

[0056] Among them, the parameter vectors in the RLC-W equivalent circuit model are: θ=[R ohm L2,R b ,L1,C,R a ,R d ,τ d ] T ;R ohm L1 is an ohmic resistor, L2 is an inductor, and R is an ohmic resistor. a and R b R is the resistance in the RLC circuit, C is the capacitance in the RLC circuit, and R... d For the Warburg impedance, τ d It is a function of the diffusion coefficient and the diffusion length.

[0057] like Figure 3 As shown, the impedance Z of the RC-RC equivalent circuit model model2 (jω) is:

[0058]

[0059] Among them, the parameter vectors in the RC-RC equivalent circuit model are: θ=[R ohm ,R a ,Rb [C1,C2,L] T ;R ohm R is an ohm resistor, L is the cable inductance, R1 and R2 are the resistors in the RC circuit, and C1 and C2 are the capacitors in the RC circuit.

[0060] like Figure 4 As shown, the impedance Z of the second-order RQ-RLC equivalent circuit model model3 (jω) is:

[0061]

[0062] The parameter vectors in the second-order RQ-RLC equivalent circuit model are: θ=[R,L,Rct,α,Q,C,Lmt,Rmt] T R is the ohmic resistance, R ct For charge transfer resistance, α and Q are constants of the phase-constant element, C represents the amount of reactant stored in water / ions, and L mt R is the resistance to the dissolution of reactants. mt L represents the diffusion resistance of the reactants, and L represents the cable inductance.

[0063] Step 2: Equivalent Circuit Model Parameter Identification. Based on the electrochemical impedance spectroscopy (EIS) data measured under three water management conditions (normal, flooded, and dry membrane) of PEMFC, the parameters of the three equivalent circuit models are identified. The parameter identification method used is a chaotic particle swarm optimization algorithm based on dynamic inertia weights (DIW-CPSO), which identifies the optimal model parameters for the three models under the three water management conditions (normal, flooded, and dry membrane).

[0064] The parameter identification of three equivalent circuit models is performed using the Chaotic Particle Swarm Optimization (DIW-CPSO) algorithm with dynamic inertia weight. The specific steps are as follows:

[0065] First, the weighted sum of squares of the measured impedance and the model-estimated impedance errors is set as the objective function:

[0066]

[0067] Among them, Re k Re is the measured value of the real part of the impedance. k Im is an estimate of the real part of the impedance. k and Im k These are the measured and estimated values ​​of the imaginary part of the impedance, w. Im and w Re These are the residual weights for the imaginary and real parts of the impedance, respectively.

[0068] Then, the parameters of the equivalent circuit to be identified are initialized, and the Logistic chaotic sequence is obtained using the improved Logistic mapping formula. The improved Logistic mapping mathematical model is as follows:

[0069]

[0070] Where μ is the growth rate parameter, x n The magnitude of the chaotic mapping.

[0071] Then take the chaotic sequence x n By integrating the initial parameter ranges of the equivalent circuit, the initial population after chaos is obtained.

[0072] If the preset number of iterations has not been reached, the dynamic inertia weight is updated. The formula for the dynamic inertia weight is:

[0073]

[0074] Among them, W max It is the maximum value of the inertial weight, W min It represents the minimum value of the inertia weight, where iter and ger are the current iteration number and the total number of iterations, respectively. σ and B(b1,b2) refer to the inertia weight coefficient and the beta function, respectively.

[0075] Then, calculate the particle's fitness value f = F(X) according to the objective function F. t+1 ).

[0076] Calculate the individual historical best value and the group historical best value, and update the particle velocity and particle position at the same time.

[0077] The loop iterates until the preset total number of iterations is reached, thereby identifying the optimal parameters of the three equivalent circuit models under the three states of normal, flooded and dry.

[0078] Step 3: Single model impedance estimation. Using the three equivalent circuit models identified based on the parameters, the impedance estimation results of each equivalent circuit model under the three states of normal, flooded and membrane dry are estimated. There are a total of nine sets.

[0079] Step 4: Impedance fusion estimation. Based on the impedance estimation data of the three equivalent circuit models measured under each water management condition, the real and imaginary parts of the impedance estimation data are fused using the covariance cross (CI) algorithm to obtain the real and imaginary parts of the impedance after model fusion estimation. The final impedance fusion estimate is then calculated using the real and imaginary parts of the fused impedance.

[0080] Based on the impedance estimation data of three equivalent circuit models measured under each water management condition, the real and imaginary parts of the impedance estimation data are fused using the covariance crossover (CI) algorithm. The specific steps of the covariance crossover (CI) algorithm fusion are as follows:

[0081]

[0082]

[0083] in, It is the impedance estimate after fusing the three models, P n P is the variance of the estimation error of model n. CI It is the estimation error variance of the fusion model, and 0≤ω n ≤1, Simultaneous fusion coefficient ω n It is determined by minimizing the index function J = tr(P) CI The calculation yielded:

[0084]

[0085] The CI fusion algorithm yielded fusion impedance estimates for the fuel cell under three conditions: normal operation, flooding, and membrane dryness. and

[0086] Step 5: Electrochemical impedance spectroscopy estimation. Under three water management conditions—normal, flooded, and membrane dry—the electrochemical impedance spectra of the fuel cell are plotted based on the impedance fusion estimates corresponding to each frequency point from ultra-low frequency to low frequency to high frequency.

[0087] like Figure 6 As shown, the electrochemical impedance spectroscopy of the fuel cell under normal water management conditions was plotted.

[0088] The implementation steps of the present invention have been described in detail above, and the impedance spectrum of a proton exchange membrane fuel cell based on multi-model fusion was finally obtained, which is of great significance for analyzing water management fault diagnosis of fuel cells.

[0089] Based on the description and accompanying drawings of this invention, those skilled in the art can readily use the fuel cell electrochemical impedance spectroscopy estimation method for water management fault diagnosis according to this invention, and can achieve the positive effects described in this invention.

[0090] The above description is merely a preferred embodiment of the present invention, but the present invention is not limited to the specific embodiments described above. Those skilled in the art can make various modifications, additions, or substitutes with similar methods without departing from the principles of the present invention, and these should also be considered within the scope of protection of the present invention.

Claims

1. A method for estimating the electrochemical impedance spectroscopy of a fuel cell for water management fault diagnosis, characterized in that, include: S1. Establish equivalent circuit models: Establish three equivalent circuit models suitable for water management fault diagnosis, including RLC-W equivalent circuit model, RC-RC equivalent circuit model and second-order RQ-RLC equivalent circuit model. S2. Equivalent Circuit Model Parameter Identification: Based on the electrochemical impedance spectroscopy (EIS) data of PEMFC measured under three water management conditions (normal, flooded, and dry membrane), the parameters of the three equivalent circuit models were identified. The parameter identification method used was the chaotic particle swarm optimization algorithm DIW-CPSO based on dynamic inertial weights, which identified the optimal parameters of the three models under the three water management conditions (normal, flooded, and dry membrane). In step S2, the DIW-CPSO optimization algorithm with dynamic inertia weights is used to identify the parameters of the three equivalent circuit models. The specific steps are as follows: S21. Set the weighted sum of squares of the measured impedance and the model-estimated impedance errors as the objective function: ； in, This is the measured value of the real part of the impedance. This is an estimate of the real part of the impedance. and These are the measured and estimated values ​​of the imaginary part of the impedance, respectively. and These are the residual weights for the imaginary and real parts of the impedance, respectively. S22. Initialize the parameters of the equivalent circuit to be identified, and obtain the Logistic chaotic sequence using the improved Logistic mapping formula. The improved Logistic mapping mathematical model is as follows: ； in, It is a growth rate parameter. The magnitude of the chaotic mapping; S23, the chaotic sequence The initial parameter range of the equivalent circuit is merged to obtain the initial population after chaos. S24. When the preset number of iterations has not been reached, update the dynamic inertia weight. The formula for the dynamic inertia weight is: ； in It is the maximum value of the inertia weight. It is the minimum value of the inertia weight. and These are the current iteration number and the total number of iterations, respectively, σ and B( b 1, b 2) These refer to the inertia weighting coefficient and the beta function, respectively. S25. According to the objective function F Calculate the fitness value of the particles. ; S26. Calculate the individual historical best value and the group historical best value, and update the particle velocity and particle position at the same time. S27. The loop iterates until the preset total number of iterations is reached, thereby identifying the optimal parameters of the three equivalent circuit models under the three states of normal, flooding and membrane dryness. S3. Single model impedance estimation: Using three equivalent circuit models identified based on parameters, the impedance data of each equivalent model under three states of normal, flooded and membrane dry are estimated, for a total of nine sets. S4. Impedance fusion estimation: Based on the impedance estimation data of the three equivalent circuit models measured under each water management state, the real and imaginary parts of the impedance estimation data are fused using the covariance cross-correlation (CI) algorithm to obtain the real and imaginary parts of the impedance after model fusion estimation. The final impedance fusion estimate is then calculated from the real and imaginary parts of the fused impedance. S5. Electrochemical impedance spectroscopy estimation: Under the three water management conditions of normal, flooded and membrane dry, the electrochemical impedance spectra of the fuel cell under these three water management conditions are plotted based on the impedance fusion estimation values ​​corresponding to each frequency point in the range from ultra-low frequency to low frequency and then to high frequency.

2. The method for estimating the electrochemical impedance spectroscopy of a fuel cell for water management fault diagnosis according to claim 1, characterized in that: In step S1, the equivalent model of the RLC-W circuit mainly consists of an RLC parallel circuit and a Warburg impedance. The RLC parallel circuit is used to describe the first impedance arc in the impedance spectrum, and the Warburg impedance is used to describe the second impedance arc; the equivalent impedance Z of the RLC-W model is... model1 (j) ω )for: ； The parameter vector that needs to be identified in the RLC-W model is: ; R ohm For ohmic resistance, L 1 and L 2 represents inductance. R a and R b The resistor in the RLC circuit. C This refers to the capacitor in the RLC circuit. R d For Warburg impedance, It is a function of the diffusion coefficient and the diffusion length.

3. The method for estimating the electrochemical impedance spectroscopy of a fuel cell for water management fault diagnosis according to claim 1, characterized in that: In step S1, the impedance Z of the RC-RC equivalent circuit model model2 (jω) is: ; Among them, the parameter vector that needs to be identified in the RC-RC equivalent circuit model is: ; R ohm For ohmic resistance, L For cable inductance, R 1 and R 2 for RC The resistance in the circuit, C 1 , C 2 is RC The capacitor in the circuit.

4. The method for estimating the electrochemical impedance spectroscopy of a fuel cell for water management fault diagnosis according to claim 1, characterized in that: In step S1, the impedance Z of the second-order RQ-RLC equivalent circuit model model3 (jω) is: ； In the second-order RQ-RLC equivalent circuit model, the parameter vector that needs to be identified is: θ = [ R, L, Rct α Q, C, Lmt, Rmt ] T ; R For ohmic resistance, R ct For charge transfer resistance, α and Q For constant phase elements, C Indicates the amount of reactants stored in water / ions. L mt Resistance to reactant dissolution R m t For the diffusion resistance of reactants, L This refers to the cable inductance.

5. The method for estimating the electrochemical impedance spectroscopy of a fuel cell for water management fault diagnosis according to claim 1, characterized in that: In step S4, the covariance crossover (CI) algorithm is as follows: ； ； in, This is the impedance estimate after fusing the three models. It is a model n The estimation error variance It is the variance of the estimation error of the fusion model, and, , Simultaneous fusion coefficient It is made by minimizing the index function The calculation yielded: ； Therefore, the CI fusion algorithm yielded the fusion impedance estimates of the fuel cell under three conditions: normal operation, flooding, and membrane dryness. , and .

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