A method, system and medium for evaluating the health state of a proton exchange membrane fuel cell

Abstract

The technical scheme adopted by the present application is: a proton exchange membrane fuel cell health state evaluation method, system and medium, comprising the following steps: S1: establishing a semi-empirical aging model of the voltage of the proton exchange membrane fuel cell and identifying the model parameters; S2: constructing an evaluation matrix for characterizing the health state of the proton exchange membrane fuel cell; S3: introducing model uncertainty candidate positions and uncertainty values into the state space equation, calling experimental data of the proton exchange membrane fuel cell, and calculating the model uncertainty of the output semi-empirical aging model and the calculation results of the evaluation matrix based on the Bayesian framework. The present application considers the influence of the uncertainty of the semi-empirical model of the fuel cell on the battery health state evaluation, quantifies the uncertainty, and can realize more accurate evaluation effect of the fuel cell health state.

Description

Technical Field

[0001] This invention belongs to the field of fuel cell technology, specifically relating to a method, system, and medium for assessing the health status of a proton exchange membrane fuel cell. Background Technology

[0002] The complex structure and material properties of proton exchange membrane fuel cells (PEMFCs) result in high operating costs and short lifespans, hindering their commercial application. Accurate estimation of the health status of PEMFCs can provide a basis for developing effective control and lifespan extension strategies, thereby improving fuel cell lifespan and reducing operating costs. Current methods for assessing the health status of PEMFCs mainly include model-based methods, data-driven methods, and hybrid model-data-driven methods. Among these, model-based methods combine mechanistic models, empirical models, or semi-empirical models with filtering estimation algorithms to estimate the health status of fuel cells.

[0003] Uncertainty arising from the accuracy of the model itself can affect the accuracy of health status estimation. Currently, there is no method for estimating the health status of proton exchange membrane fuel cells that considers model uncertainty. Quantitatively evaluating the model uncertainty in health status estimation methods is necessary to more accurately and reliably estimate the health status and aging of fuel cells. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of the aforementioned background technology and provide a method, system, and medium for assessing the health status of a proton exchange membrane fuel cell. This invention considers the impact of the uncertainty of the fuel cell semi-empirical model on the assessment of the fuel cell's health status and quantifies the uncertainty, thereby achieving a more accurate assessment of the fuel cell's health status.

[0005] The technical solution adopted in this invention is: a method for assessing the health status of a proton exchange membrane fuel cell, comprising the following steps: S1: Establish a semi-empirical aging model for the voltage of a proton exchange membrane fuel cell and identify the model parameters; S2: Construct an evaluation matrix to characterize the health status of proton exchange membrane fuel cells; S3: In the state-space equation, the product of the model uncertainty value and the matrix of the i-th uncertainty candidate position is superimposed on the state transition matrix as a correction term to obtain the state-space equation that introduces the model uncertainty candidate position and uncertainty value; the experimental data of the proton exchange membrane fuel cell are called, and the calculation results of the model uncertainty and evaluation matrix of the semi-empirical aging model are calculated based on the Bayesian framework.

[0006] In the above technical solution, in step S1, the semi-empirical aging model of the proton exchange membrane fuel cell voltage is as follows: Among them, V st R is the voltage of the proton exchange membrane fuel cell stack, n is the number of cells, E0 is the open-circuit voltage of the stack at a given temperature and gas pressure, and R is the open-circuit voltage of the stack. ohm Let i be the total internal resistance of the battery in ohms, i be the stack current, a be Tafel's constant, T be the stack temperature, and i0 be the exchange current. L Let be the limiting current, and b be the concentration constant.

[0007] In the above technical solution, in step S1, the existing expectation-maximization algorithm is used to optimize the voltage semi-empirical model of the proton exchange membrane fuel cell based on the model equations and experimental data. E 0、 R ohm , a , b , i L Perform parameter identification.

[0008] In the above technical solution, in step S2, based on the degree and trend of the change of the parameters identified in step S1 with aging time, the parameters that change significantly with time and have similar magnitudes among the identified parameters are grouped into a single variable containing a unified variable. α The formula for (t) is used to represent the degree of battery aging over time; this variable is used to characterize the degree of battery aging; the matrix composed of this variable and its rate of change is used as the evaluation matrix.

[0009] In the above technical solution, step S2 uses the following formula to construct the evaluation matrix: Where c represents the parameters identified by the model parameters that change significantly over time with similar magnitudes. c 0 is a parameter c The initial value; f ( α ( t )) is included α ( t The function has the following form: f ( α ( t ))=1+ α ( t ), f ( α ( t ))=1- α ( t ); β Let α be the rate of change; set the matrix [ α , β ]T An evaluation matrix used to characterize the health status of a proton exchange membrane fuel cell system. x ,Right now x =[ α , β ] T If the parameter gradually increases with aging time, then f ( α ( t ))=1+ α ( t If the parameter gradually decreases with aging time, then... f ( α ( t ))=1- α ( t Then the parameters c Use c0× f ( α ( t Substitute back into the semi-empirical model and initialize the parameters. c 0 is used for identification.

[0010] In the above technical solution, the state-space equations for the location and value of model uncertainty are expressed as follows: in x k Let A be the health status evaluation matrix at time k; let A be the state transition matrix; and let δ be the uncertainty value. d i Let x be the candidate position matrix for the i-th uncertainty; k-1 The health status evaluation matrix at time k-1; w k-1 The process noise at time k-1; y k Let be the voltage measurement at time k; h() is the observation equation; uk is the input of the fuel cell, i.e., the stack current; v k For measuring noise.

[0011] In the above technical solution, step S3 specifically includes the following steps: S3.1, Initialize the model uncertainty. 0|0 The initial value of the evaluation matrix x 0|0 Initial estimate of model uncertainty covariance Pδ 0|0, the initial estimated covariance of the evaluation matrix x Px 0|0, Evaluation Matrix x and model uncertainty d Cross covariance P x dx 0|0, S3.2, perform a one-step prediction of the model uncertainty and health status and their estimated covariance at the current aging time at the candidate position with given uncertainty; S3.3, Given the fuel cell voltage measurement value, determine the uncertainty value at the current aging time. d With evaluation matrix x The one-step predicted values ​​together construct the amplification state. d , x T ] T The amplification state is then updated using a nonlinear optimization algorithm. S3.4, Calculate the probability that the model uncertainty is at different candidate positions given the voltage measurement at the current aging time, based on Bayes' rule: S3.5, based on the probability of uncertainty being at different candidate positions, the uncertainty at the current aging moment is fused and estimated with the evaluation matrix to obtain the model uncertainty and health status of the fuel cell at the current aging moment; S3.6, Repeat steps S3.2-S3.5 until no voltage measurement value is available. Based on the fuel cell model uncertainty and health state at each time point, generate and output the complete fuel cell model uncertainty and health state curves that change over time.

[0012] The beneficial effects of this invention are: (1) This invention identifies parameters of a semi-empirical model of a proton exchange membrane fuel cell, eliminating the need to study the internal mechanism of the battery. It can reflect changes in internal variables and health status of the system while reducing the complexity of the model.

[0013] (2) The present invention takes into account the model uncertainty when assessing the health status of proton exchange membrane fuel cells, and can directly use the original data obtained by sampling, thus preserving the information in the data to the greatest extent.

[0014] (3) In evaluating the health status of proton exchange membrane fuel cells, the present invention uses the Gauss-Newton method to update the state and uncertainty, resulting in a smoother state curve that can reflect the aging trend of the battery.

[0015] (4) This invention considers the impact of the uncertainty of the semi-empirical model of fuel cell on the assessment of battery health status, and quantifies the uncertainty, which can achieve a more accurate assessment of the health status of fuel cell. Attached Figure Description

[0016] Figure 1This is a schematic diagram of a health status assessment method for a proton exchange membrane fuel cell system that considers the quantification of uncertainty according to the present invention. Figure 2 This is a flowchart of the proton exchange membrane fuel cell health status observer algorithm based on a Bayesian framework that considers model uncertainty, according to the present invention.

[0017] Figure 3 The model uncertainty in this invention d Probability estimation diagram of each candidate position.

[0018] Figure 4 The model uncertainty in this invention d A graph showing the estimated numerical values.

[0019] Figure 5 This is a graph showing the estimated health status of the fuel cell in this invention.

[0020] Figure 6 The method proposed in this invention, along with extended Kalman filtering and unscented Kalman filtering, substitutes the estimated fuel cell health state back into the voltage tracking graph obtained from the semi-empirical model. Figure 7 A comparison table of the voltage tracking performance of fuel cell stacks using the method proposed in this invention, extended Kalman filtering, and unscented Kalman filtering. Detailed Implementation

[0021] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments to facilitate a clear understanding of the present invention, but these descriptions do not constitute a limitation on the present invention.

[0022] like Figure 1 As shown, the technical solution adopted in this invention is a method for assessing the health status of a proton exchange membrane fuel cell considering the quantification of uncertainty, the steps of which include: S1: Establish a semi-empirical aging model for the voltage of a proton exchange membrane fuel cell and identify the model parameters; S2: Construct an evaluation matrix to characterize the health status of proton exchange membrane fuel cells; S3: The state-space equation introduces candidate locations and values ​​for model uncertainty, calls experimental data from proton exchange membrane fuel cells, and calculates the model uncertainty and evaluation matrix of the semi-empirical aging model based on a Bayesian framework.

[0023] In step S1, the parameters of the semi-empirical model of the proton exchange membrane fuel cell voltage are identified using the existing expectation-maximization (EM) algorithm based on the model equations and experimental data. The following semi-empirical aging model for fuel cells is adopted: (1) Among them, V st R is the voltage of the proton exchange membrane fuel cell stack, n is the number of cells, E0 is the open-circuit voltage of the stack at a given temperature and gas pressure, and R is the open-circuit voltage of the stack. ohm Let Ω be the total internal resistance of the battery in ohms, i be the stack current, a be Tafel's constant, T be the stack temperature, and i0 be the exchange current. L Let be the limiting current, and b be the concentration constant.

[0024] The parameters to be identified are E 0、 R ohm , a , b , i L .

[0025] In step S2, based on the degree and trend of change of the parameters identified in step S1 with aging time, the parameters that change significantly with time and have similar magnitudes are grouped into a single variable. α The health status of a proton exchange membrane fuel cell can be represented by the formula (t), which consists of a matrix of the variable and its rate of change, as shown in the following equation: (2) (3) Where c is a parameter obtained from the semi-empirical model parameter identification mentioned above that changes significantly over time and has a similar magnitude of change. c 0 is a parameter c The initial value; f ( α ( t )) includes the uniform variables mentioned above α ( t The function has the following form: f ( α ( t ))=1+ α ( t ), f ( α ( t ))=1- α ( t ); β for α The rate of change. The matrix [ α , β ] T The health state x of a proton exchange membrane fuel cell system. If parameter c gradually increases with aging time, then f ( α ( t ))=1+ α (t If parameter c gradually decreases with aging time, then f ( α ( t ))=1- α ( t Then the parameters c Use c0* f ( α ( t Substitute the values ​​back into the semi-empirical model and use the measurement data at the initial moment of stack operation to initialize the parameter c. c 0 is used for identification.

[0026] In step S3, the battery health state estimation process considering uncertainty can be regarded as an observer.

[0027] The state-space equations for introducing the location and value of model uncertainties are as follows: in x k Let A be the health status evaluation matrix at time k; let A be the state transition matrix; and let δ be the uncertainty value. d i Let x be the candidate position matrix for the i-th uncertainty; k-1 The health status evaluation matrix at time k-1; w k-1 The process noise at time k-1; y k Let be the voltage measurement at time k; h() is the observation equation; uk is the input of the fuel cell, i.e., the stack current; v k For measuring noise.

[0028] First, let's discuss the model uncertainty. d The existing candidate position matrix is ​​preset: The Bayesian framework for the observer is as follows: (4) (5) (6) (7) in d Indicates model uncertainty. x k This represents the health status of PEMFC at time k. x k-1 Indicates the first k PEMFC health status at time -1d i Indicates the first i A matrix of candidate positions, Y k-1 Indicates the first k The measurement value obtained at time -1 Y k Indicates the first k The measurement value obtained at time 10:00 y k Represents the PEMFC health state at time k. x k The voltage estimate obtained from the observation equation. Equation (4) addresses the model uncertainty. d and health status x The joint conditional probability density is used for one-step prediction. Equation (5) is based on the observed values. Y k If available, update the probability density function predicted by equation (4). Equations (6) and (7) estimate the model uncertainty. d In each candidate position matrix d The probability and d The probability density function and probability mass function of matrix d at different preset positions are fused.

[0029] The following Gaussian assumptions are made regarding the conditions satisfied by the probabilities on the left side of equations (4)-(7): (8) (9) (10) i,k|k-1 and i,k|k-1 The i-th candidate position matrix is ​​respectively d i and estimate covariance Pδ i,k|k -1k and P xi,k|k -1 The first obtained k Model uncertainty at time d and health status x k The one-step prediction value. In the formula... i,k|k and i,k|k They are respectively from the first i Candidate position matrix d i and error covariance Pδ i,k|k k and Pxi,k|k and measured value of stack voltage Y k The first k Moment i,k|k-1 and i,k|k-1 The updated value.

[0030] At the i-th candidate position d i and stack voltage observations Y k Below x k and d When making a one-step prediction based on formula (4), the problem can be transformed into a maximum a posteriori probability problem, and the one-step prediction value [ i,k|k-1 , T i,k | k-1 ] T Solve using the following formula: (11) Furthermore, in step S3, the fuel cell stack voltage measurement value is used based on formula (5). Y k Uncertainty on the i-th candidate position matrix at time k d With health status x k One-step prediction of the amplification state [ i,k | k-1 , T i,k | k-1 ] T Update: (12) This problem is transformed into a nonlinear optimization problem, and the Gauss-Newton method, a nonlinear optimization algorithm, is applied to expand the state constructed from the model uncertainty and health state. i,k|k-1 , T i,k | k-1 ] T Perform an update, and the result of the update is [ i,k|k , T i,k | k ] T .

[0031] Furthermore, in step S3, based on formula (6), due to uncertainty... d If the sum of the probabilities of being at a candidate position is 1, then the uncertainty obtained from the fuel cell voltage observation data is... d Located in the candidate position matrix d i The probability p( d i | Y k The uncertainty based on voltage observation data for all candidate locations can be calculated using Bayes' rule. d The position with the highest probability is the uncertainty. d The true location M Let be the set of candidate position indices containing uncertainty δ. M ={1, 2, 3…, M}, M=4, let m i,k = p ( d i | Y k ), l i,k = p ( y k | d i , Y k-1 Then, using the kth voltage measurement value Y k The calculated first k Model uncertainty at time d The probability of being located in the i-th candidate position matrix is ​​calculated using the following formula: (13) Model uncertainty d The candidate position matrix with the highest probability is the model uncertainty. d The position matrix, i.e.: (14) (15) in, d k To utilize the first k Voltage measurement value Y k The true location of the model uncertainty δ at time k.

[0032] Furthermore, in step S3, based on formula (7), the true values ​​of uncertainty and health status are fused and estimated according to the probability of uncertainty being in different candidate positions. The fused estimate of uncertainty and health status is the sum of its value in each candidate position matrix multiplied by the probability of uncertainty being in the corresponding candidate position matrix.

[0033] The calculation formula is as follows: (16) (17) in, The augmented state is constructed by fusing the uncertainty δ and the health state x at time k. Let be the updated values ​​of the model uncertainty δ and the expanded state of the health state at time k on the i-th candidate position matrix. i,k|k , T i,k | k ] T .

[0034] Therefore, in combination Figure 2 The flowchart of the constructed proton exchange membrane fuel cell health status observer algorithm, specifically step S3, includes the following steps: ① S3.1, Initialization: Initial values ​​of model uncertainty 0|0 Initial health status 0|0 The estimated covariance of the model uncertainty δ Pδ 0|0, Estimated covariance of health status x Px 0|0, the cross-covariance of health status x and model uncertainty δ Pxd 0|0.

[0035] ② S3.2, perform a one-step prediction of the model uncertainty δ and health state x at time k and their estimated covariance: (18) (19) (20) (twenty one) (twenty two) (twenty three) in and This is a one-step prediction of the health status and uncertainty δ at the i-th candidate position matrix at time k-1; and This represents the updated values ​​of the health status and uncertainty δ at the i-th candidate position matrix at time k. A Here is the state transition matrix. A =[1, T S [; 0, 1],T S T is the sampling frequency. S =1h; d i Let be the matrix of the i-th candidate positions; and This is a one-step prediction of the estimated covariance of the health status and uncertainty δ at the i-th candidate position matrix at time k. and This is the updated value of the estimated covariance of the health status and uncertainty δ at the i-th candidate position matrix at time k-1; This is the updated value of the cross-covariance of health status and uncertainty at the i-th candidate position matrix at time k-1; Q k For process noise covariance; This is the updated value of the cross-covariance of health status and uncertainty at time k on the i-th candidate position matrix; F k-1 The right side of the process equation for introducing the location and value of model uncertainty at time k-1 is the Jacobian matrix of uncertainty δ and health state x.

[0036] ③ S3.3, construct the augmented state by combining the model uncertainty at the i-th candidate position with the one-step prediction of the health state. i,k|k-1 , T i,k | k-1 ] T The update is performed using a nonlinear optimization algorithm; in this example, the Gauss-Newton method is used. Initialize the number of iterations a =0, x (0) i,k|k k =[ i,k|k-1 , T i,k | k-1 ] T Set the maximum number of iterations. a max exist a < a max When updating, use the following formula: (twenty four) In the formula: (25) (26) (27) Among them, R k To measure the noise covariance.

[0037] ④ S3.4, Calculate the probability that the model uncertainty δ at time k is at different candidate positions according to formula (6): (28) In the formula: (29) (30) S 3.5, perform a fusion estimation of the uncertainty and health status at time k; (31) (32) Repeat steps ②-⑤ above until no voltage measurement value is available. Based on the fuel cell model uncertainty and health state at each time point, generate a complete fuel cell model uncertainty and time-varying health state curve and output the repeatable curve. Furthermore, in step S3, the experimentally measured voltage and current of the fuel cell stack are input into the observer to obtain the model uncertainty. d In the health status of fuel cells α ( t The curve of change over time, when α ( t A value greater than 0.25 indicates that the fuel cell is in a failed state. Substituting the health state estimated by the observer back into the empirical model yields the estimated voltage. The smaller the error in tracking the test voltage with the estimated voltage, the more accurate the observer's estimation of the health state.

[0038] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. A method for assessing the health status of a proton exchange membrane fuel cell, characterized in that: Includes the following steps: S1: Establish a semi-empirical aging model for proton exchange membrane fuel cell voltage and identify the model parameters; S2: Construct an evaluation matrix to characterize the health status of proton exchange membrane fuel cells; S3: In the state-space equation, the product of the model uncertainty value and the matrix of the i-th uncertainty candidate position is superimposed on the state transition matrix as a correction term to obtain the state-space equation that introduces the model uncertainty candidate position and uncertainty value; the experimental data of the proton exchange membrane fuel cell are called, and the calculation results of the model uncertainty and evaluation matrix of the semi-empirical aging model are calculated based on the Bayesian framework.

2. The method according to claim 1, characterized in that: In step S1, the semi-empirical aging model of the proton exchange membrane fuel cell voltage is as follows: Among them, V st R is the voltage of the proton exchange membrane fuel cell stack, n is the number of cells, E0 is the open-circuit voltage of the stack at a given temperature and gas pressure, and R is the open-circuit voltage of the stack. ohm Let Ω be the total internal resistance of the battery in ohms, i be the stack current, a be Tafel's constant, T be the stack temperature, and i0 be the exchange current. L Let be the limiting current, and b be the concentration constant.

3. The method according to claim 2, characterized in that: In step S1, based on the model equations and experimental data, the existing expectation-maximization algorithm is used to evaluate the voltage semi-empirical aging model of the proton exchange membrane fuel cell. E 0、 R ohm , a , b , i L Perform parameter identification.

4. The method according to claim 2, characterized in that: In step S2, based on the degree and trend of change of the parameters identified in step S1 with aging time, the parameters that change significantly with time and have similar magnitudes are grouped into a single variable. α The formula (t) is used to represent this variable; this variable is used to characterize the degree of battery aging over time. The matrix consisting of the variable and its rate of change serves as the evaluation matrix.

5. The method according to claim 4, characterized in that: In step S2, the evaluation matrix is ​​constructed using the following formula: Where c represents the parameters identified by the model parameters, which show significant changes over time and have similar magnitudes of change. c 0 is a parameter c The initial value; f ( α ( t )) is included α ( t The function has the following form: f ( α ( t ))=1+ α ( t ), f ( α ( t ))=1- α ( t ); β Let α be the rate of change; set the matrix [ α , β ] T An evaluation matrix used to characterize the health status of a proton exchange membrane fuel cell system. x ,Right now x =[ α , β ] T If the parameter gradually increases with aging time, then f ( α ( t ))=1+ α ( t If the parameter gradually decreases with aging time, then... f ( α ( t ))=1- α ( t Then the parameters c Use c0× f ( α ( t Substitute back into the semi-empirical model and initialize the parameters. c 0 is used for identification.

6. The method according to claim 5, characterized in that: The state-space equations for introducing the location and value of model uncertainties are as follows: in x k Let A be the health status evaluation matrix at time k; let A be the state transition matrix; and let δ be the uncertainty value. d i Let x be the candidate position matrix for the i-th uncertainty; k-1 The health status evaluation matrix at time k-1; w k-1 The process noise at time k-1; y k Let be the voltage measurement at time k; h() is the observation equation; uk is the input of the fuel cell, i.e., the stack current; v k For measuring noise.

7. The method according to claim 6, characterized in that: Step S3 details Includes the following steps: S3.1 Initialize the initial values ​​of the evaluation matrix, the initial covariance of the model uncertainty, the initial covariance of the evaluation matrix x, and the cross-covariance of the evaluation matrix and the model uncertainty. S3.2, perform a one-step prediction of the model uncertainty and health status and their estimated covariance at the current aging time at the candidate position with given uncertainty; S3.3, The expansion state is constructed by combining the uncertainty value at the current aging time with the one-step prediction value of the evaluation matrix based on the given fuel cell voltage measurement value, and the expansion state is updated by using a nonlinear optimization algorithm; S3.4, Calculate the probability that the model uncertainty is at different candidate positions given the voltage measurement at the current aging time, based on Bayes' rule: S3.5, based on the probability of uncertainty being at different candidate positions, the uncertainty at the current aging moment is fused and estimated with the evaluation matrix to obtain the model uncertainty and health status of the fuel cell at the current aging moment; S3.6, Repeat steps S3.2-S3.5 until no voltage measurement value is available. Based on the fuel cell model uncertainty and health state at each time point, generate and output the complete fuel cell model uncertainty and health state curves that change over time.

8. A health status assessment system for a proton exchange membrane fuel cell, characterized in that... include: This system is used to implement the proton exchange membrane fuel cell health status assessment method according to any one of claims 1-7.

9. A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the proton exchange membrane fuel cell health status assessment method as described in any one of claims 1-7.

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