Fuel cell health state estimation method and system based on adaptive extended Kalman filtering

Abstract

The invention relates to a fuel cell health state estimation method and system based on adaptive extended Kalman filtering. The method comprises the following steps: firstly, based on a polarization curve, performing parameter identification by using a genetic algorithm to obtain initial parameters; considering ohmic resistance aging and limiting current density aging, establishing a semi-empirical aging formula based on the initial parameters, and discretizing the semi-empirical aging formula to obtain a state space; then setting an initial value, jointly constructing a Kalman filter model by using the initial value and the state space, and fusing time updating, filtering measurement updating and self-adaptive updating into the model to obtain a self-adaptive extended Kalman filter model; inputting the voltage sequence of the fuel cell into the self-adaptive extended Kalman filter model, and outputting the rated voltage of the current prediction point location of the fuel cell; and finally, calculating the health degree of the fuel cell according to the rated voltage of the current prediction point location. Compared with the prior art, the method has the advantages of high accuracy, strong robustness and the like.

Description

Technical Field

[0001] The present invention relates to the field of fuel cell technology, and in particular to a fuel cell health state estimation method and system based on adaptive extended Kalman filtering. Background Art

[0002] As a clean energy transportation tool, the health of the core component of fuel cell vehicles is crucial to the performance of the entire vehicle. With the long-term operation of the fuel cell, its internal components such as the catalyst layer and proton exchange membrane will degrade to varying degrees. This degradation not only affects the electrochemical active surface area (ECSA), resulting in a reduction in active sites, but also causes the voltage of the fuel cell to decrease at the same current density, that is, the polarization curve shifts downward. The downward shift of the polarization curve is directly related to the performance attenuation of the fuel cell, so monitoring the health of the fuel cell is extremely critical to maintaining its efficient operation and extending its service life.

[0003] When estimating the health status of fuel cells in real time, voltage is an easily achievable indicator. Through the controller on the real vehicle, the voltage data of the battery can be collected online and transmitted back to the monitoring system. This real-time monitoring not only helps to detect abnormal changes in battery performance in a timely manner, but also provides data support for battery maintenance and replacement. Therefore, it is very important to introduce health status monitoring in the operation of the fuel cell system.

[0004] The invention patent with publication number CN115983084A discloses a method for predicting the remaining service life of a fuel cell. The method predicts the aging life of the remaining sequence processed by EMD by combining the aging model and the particle filter method. However, it does not take into account the noise interference generated during the fuel cell voltage measurement process, and is prone to algorithm estimation problems caused by inaccurate estimation of the statistical characteristics of the process noise covariance matrix and the measurement noise covariance, and unreasonable initial value settings, resulting in inaccurate prediction results. Summary of the invention

[0005] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a fuel cell health status estimation method and system based on adaptive extended Kalman filtering.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] According to one aspect of the present invention, a method for estimating the health status of a fuel cell based on an adaptive extended Kalman filter is provided, and the method steps include:

[0008] 1. A method for estimating the health status of a fuel cell based on an adaptive extended Kalman filter, characterized in that the method steps include:

[0009] S1. Obtaining a polarization curve of the vehicle-mounted fuel cell, and based on the polarization curve, using a genetic algorithm to perform parameter identification to obtain initial parameters;

[0010] S2. Considering the aging of ohmic resistance and limiting current density, a semi-empirical aging formula is established based on the initial parameters, and the semi-empirical aging formula is discretized to obtain the state space;

[0011] S3, setting initial values, using the initial values ​​and the state space to jointly construct a Kalman filter model, in which time update, filter measurement update, and adaptive update processes are integrated to obtain an adaptive extended Kalman filter model;

[0012] S4, inputting the fuel cell voltage sequence into the adaptive extended Kalman filter model, and outputting the rated voltage of the fuel cell at the current predicted point;

[0013] S5. Calculate the health of the fuel cell based on the rated voltage at the current prediction point.

[0014] As a preferred technical solution, the parameter identification process using genetic algorithm in S1 is as follows: first, a fitness function is established, and the objective function of the genetic algorithm is set to the minimization function of the fitness function, and then the initial parameters of the genetic algorithm are set, and the steps of initializing the population, fitness evaluation, single-point crossover, random selection and mutation are repeated until the fitness meets the preset error requirements, and finally the initial parameters are output.

[0015] As a preferred technical solution, the objective function and constraints of the genetic function are:

[0016]

[0017] Among them, f fitness is the fitness function; E ocv is the open circuit voltage; R 0 is the initial impedance; A is the Tafel constant; B is the concentration constant; i 0 is the exchange current density; i L0 is the initial limiting current density; V st,k is the actual value of the sampling point of the polarization curve; is the genetic algorithm estimated value of the polarization curve sampling point; i k is the current density at time k.

[0018] As a preferred technical solution, the specific formula of the semi-empirical aging formula established in S2 is:

[0019]

[0020] Among them, V st is the current output voltage; n cell is the number of fuel cells; E ocv is the open circuit voltage; i is the current output current density; R 0 is the initial impedance; α is the aging amount; A is the Tafel constant; T is the temperature; i 0 is the exchange current density; B is the concentration constant; i L0 is the initial limiting current density.

[0021] As a preferred technical solution, the state space in S2 includes state variables, state transfer functions and output functions, and its specific formula is:

[0022]

[0023] Among them, T s is the sampling time; α k is the degradation rate at time k; β k is the aging rate at time k; w k-1 is the system process noise; u k is the input of the system; i k is the current density at time k; y k is the output at time k; V st,k is the actual value of the sampling point of the polarization curve; n cell is the number of fuel cells; E ocv is the open circuit voltage; R 0 is the initial impedance; A is the Tafel constant; T is the temperature; i 0 is the exchange current density; B is the concentration constant; v k To measure noise.

[0024] As a preferred technical solution, the time update in S3 includes state prediction and error covariance prediction, and the filter measurement update is to correct the state value and error covariance matrix predicted by the time update according to the Kalman gain.

[0025] As a preferred technical solution, in time updating, the specific formulas for state prediction and error covariance prediction are:

[0026]

[0027] Among them, x k|k-1 is the estimated predicted value of the fuel cell aging state variable; P k|k-1 is the filtering error covariance matrix in the system estimation recursion; A is the parameter matrix of the state equation; Q is the process noise.

[0028] As a preferred technical solution, in the filter measurement update, according to the Kalman gain, the specific formula for correcting the state value and the error covariance matrix predicted by the time update is:

[0029]

[0030] x k|k =x k|k-1 +K k (V st,k -g(x k ,u k ))

[0031] P k|k =(IK k C k ) k|k-1

[0032] Among them, K k is the gain matrix of the Kalman filter; x k|k is the corrected state filter value; P k|k is the corrected error covariance matrix; x k|k-1 is the estimated predicted value of the fuel cell aging state variable; P k|k-1 is the filter error covariance matrix in the system estimation recursion; I is the identity matrix, C k is the parameter matrix of the state equation; V st,k is the actual value of the sampling point of the polarization curve; g(x k ,u l ) is the output function of the polarization curve aging model.

[0033] As a preferred technical solution, the adaptive update in S3 is to set the deviation between the model prediction and the actual observation as the new information during the filtering process, and correct the update process noise and measurement noise according to the new information. The specific formula for the correction update is:

[0034]

[0035] Among them, v l is the measurement noise; V st,k is the actual value of the sampling point of the polarization curve; C k is the observation matrix; x k is the estimated value of the state at time step k; is the covariance matrix of the new information; v j is the new information of step j in the past N time steps; 0 is the initial step of the past N time steps; K k is the Kalman gain; R k is the difference between the innovation covariance and the prediction error covariance, which is used to adjust the estimate of the measurement noise covariance; Pk|k-1 is the covariance matrix; N = 2; Q k is the system process noise at the current k moment; R k is the measurement noise at the current time k.

[0036] As a preferred technical solution, the specific process of calculating the health of the fuel cell according to the predicted aging voltage in S4 is: firstly, a fuel cell performance degradation index is established, and the fuel cell performance degradation index is calculated according to the predicted aging voltage, and then the health status index is calculated according to the fuel cell performance degradation index, that is, the health of the fuel cell is obtained; wherein, the specific formulas of the fuel cell performance degradation index and the health status index are:

[0037]

[0038] SOH=1-D

[0039] Among them, D is the fuel cell performance degradation index; SOH is the health status index; U rated,new is the total rated voltage attenuation of the fuel cell from the beginning to the end of its life, U rated,degraded The rated voltage of the fuel cell at the current predicted point.

[0040] According to another aspect of the present invention, a fuel cell health state estimation system based on an adaptive extended Kalman filter is provided, the system works by applying the fuel cell health state estimation method based on an adaptive extended Kalman filter as described above, the system comprises a parameter identification module, an aging modeling module, a Kalman filter module and a health degree calculation module;

[0041] Among them, the parameter identification module is used to obtain the polarization curve of the vehicle-mounted fuel cell, and then use the genetic algorithm to perform parameter identification based on the polarization curve to obtain the initial parameters; the aging modeling module is used to consider the aging of the ohmic resistance and the limiting current density, and establish a semi-empirical aging formula; the Kalman filter model module is composed of the initial value, the state space obtained after the discretization of the semi-empirical aging formula, the time update, the filter measurement update and the adaptive update. The fuel cell voltage sequence is input into the module, and the rated voltage of the current predicted point of the fuel cell is obtained as output; the health calculation module is used to calculate the health of the fuel cell according to the rated voltage of the current predicted point.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] 1. In the present invention, firstly, based on the polarization curve, the genetic algorithm is used to identify the parameters to obtain the initial parameters; then, considering the aging of the ohmic resistance and the limiting current density, a semi-empirical aging formula is established based on the initial parameters, and the semi-empirical aging formula is discretized to obtain the state space; then, the initial value is set, and the Kalman filter model is constructed by using the initial value and the state space, and the time update, filter measurement update and adaptive update are integrated into the model to obtain the adaptive extended Kalman filter model; the fuel cell voltage sequence is input into the adaptive extended Kalman filter model, and the rated voltage of the current predicted point of the fuel cell is output; finally, the health of the fuel cell is calculated according to the rated voltage of the current predicted point. The present invention realizes the estimation of the health state of the fuel cell through the adaptive extended Kalman filter method, and at the same time, effectively eliminates the noise interference generated in the process of measuring the fuel cell voltage, thereby ensuring the accuracy of the health state estimation.

[0044] 2. The present invention establishes an adaptive Kalman filter model and integrates time update, filter measurement update and adaptive update process into the model, wherein process noise is considered in time update, measurement noise is considered in filter measurement update, the deviation between model prediction and actual observation is set as new information, and the process noise and measurement noise are corrected and updated according to the new information. Time update includes state prediction and error covariance prediction, and filter measurement update is to correct the state value and error covariance matrix predicted by time update according to Kalman gain. Through time update, filter measurement update and adaptive update process, the algorithm estimation effect problem caused by inaccurate estimation of the statistical characteristics of process noise covariance matrix and measurement noise covariance and unreasonable initial value setting is reduced, and the robustness of calculating fuel cell health is improved.

[0045] 3. In the present invention, based on the polarization curve, a genetic algorithm is used to identify parameters to obtain initial parameters; with these initial parameters, a semi-empirical aging formula is established to obtain the state space of the Kalman filter. The process of parameter identification using a genetic algorithm is as follows: first, a fitness function is established, and the objective function of the genetic algorithm is set as the minimization function of the fitness function, and then the initial parameters of the genetic algorithm are set, and the steps of initializing the population, fitness evaluation, single-point crossover, random selection and mutation are repeated until the fitness meets the preset error requirements, and the initial parameters are finally output. By using a genetic algorithm to identify the initial parameters required to establish the Kalman filter, the acquisition of the initial parameters is made more accurate and reliable, thereby providing a solid foundation for the subsequent establishment of the semi-empirical aging formula and the construction of the state space of the Kalman filter, and improving the accuracy and reliability of the fuel cell health status assessment.

[0046] 4. In the present invention, the specific process of calculating the health of a fuel cell using the predicted aging voltage is as follows: first, a fuel cell performance degradation index is established, and the fuel cell performance degradation index is calculated using the predicted aging voltage, and then a health status index is calculated using the fuel cell performance degradation index, thereby obtaining the health of the fuel cell; wherein, the fuel cell performance degradation index is simple in form, and is determined only by the total rated voltage attenuation of the fuel cell from the beginning to the end of its life and the rated voltage of the fuel cell at the current predicted point. By establishing the fuel cell performance degradation index and the health status index, the health of the fuel cell can be calculated in real time based on the output voltage of the fuel cell, thereby improving the efficiency of the fuel cell health status estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a schematic diagram of the method steps of the present invention;

[0048] Figure 2 It is a schematic diagram of the method flow of the present invention;

[0049] Figure 3 It is a schematic diagram of the genetic algorithm parameter identification process of the semi-empirical formula of the polarization curve in the present invention;

[0050] Figure 4 Flow chart of adaptive extended Kalman filtering in an embodiment;

[0051] Figure 5 It is a schematic diagram of applying the adaptive extended Kalman filter to estimate the health state of a fuel cell in an embodiment. DETAILED DESCRIPTION

[0052] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0053] As a clean energy transportation tool, the health of the core component of fuel cell vehicles is crucial to the performance of the entire vehicle. With the long-term operation of the fuel cell, its internal components such as the catalyst layer and proton exchange membrane will degrade to varying degrees. This degradation not only affects the electrochemically active surface area (ECSA), resulting in a reduction in active sites, but also causes the voltage of the fuel cell to decrease at the same current density, that is, the polarization curve shifts downward. The downward shift of the polarization curve is directly related to the performance attenuation of the fuel cell, so monitoring the health of the fuel cell is extremely critical to maintaining its efficient operation and extending its service life.

[0054] When estimating the health status of fuel cells in real time, voltage is an easily achievable indicator. Through the controller on the real vehicle, the voltage data of the battery can be collected online and transmitted back to the monitoring system. This real-time monitoring not only helps to detect abnormal changes in battery performance in a timely manner, but also provides data support for battery maintenance and replacement. Therefore, it is very important to introduce health status monitoring in the operation of the fuel cell system.

[0055] Example 1

[0056] This scheme proposes a fuel cell health status estimation method based on adaptive extended Kalman filtering to monitor the health status of the fuel cell. Figure 1 As shown, the steps include:

[0057] S1. Obtaining a polarization curve of the vehicle-mounted fuel cell, and based on the polarization curve, using a genetic algorithm to perform parameter identification to obtain initial parameters;

[0058] S2. Considering the aging of ohmic resistance and limiting current density, a semi-empirical aging formula is established based on the initial parameters, and the semi-empirical aging formula is discretized to obtain the state space;

[0059] S3, setting initial values, using the initial values ​​and the state space to jointly construct a Kalman filter model, in which time update, filter measurement update, and adaptive update processes are integrated to obtain an adaptive extended Kalman filter model;

[0060] S4, inputting the fuel cell voltage sequence into the adaptive extended Kalman filter model, and outputting the rated voltage of the fuel cell at the current predicted point;

[0061] S5. Calculate the health of the fuel cell based on the rated voltage at the current prediction point.

[0062] In this embodiment, the scheme is applied to estimate the health status of the fuel cell. First, the initial polarization curve of the fuel cell without attenuation is obtained, and based on the polarization curve, the genetic algorithm is used in the semi-empirical formula model to perform parameter identification to obtain the amount of unknown parameters. The specific expression of the semi-empirical formula model is:

[0063]

[0064] Among them, V st is the current output voltage; n cell is the number of fuel cells; E ocv is the open circuit voltage; i is the current output current density; R ohm is the ohmic internal resistance; A is the Tafel constant; T is the temperature; i 0 is the exchange current density; B is the concentration constant; i Lis the limiting current density.

[0065] In this embodiment, a genetic algorithm is used for rapid parameter identification, and the process is as follows: Figure 3 As shown, first initialize the population: (e ocv ,R 0 ,A,B,i 0 ,i L0 ), and then calculate the fitness function based on it, repeat the process of calculating the fitness function, selecting, crossing, mutating and updating the population until the accuracy is achieved, at which time, the optimal solution and parameters are output. Among them, the fitness function of the genetic algorithm is defined as the sum of the squares of the differences between the sampled voltages of the aging experiment at all measurement points and the voltages predicted by the genetic algorithm. The purpose of the genetic algorithm is to globally explore various possibilities of the parameters to be identified and optimize in the direction of the minimum value of the fitness function. The mathematical formula of the fitness function and the constraints of the parameters to be identified are as follows:

[0066]

[0067] Among them, f fitness is the fitness function; E ocv is the open circuit voltage; R 0 is the initial impedance; A is the Tafel constant; B is the concentration constant; i 0 is the exchange current density; i L0 is the initial limiting current density; V st,k is the actual value of the sampling point of the polarization curve; is the genetic algorithm estimated value of the polarization curve sampling point; i k is the current density at time k.

[0068] In this embodiment, the initial parameters of the genetic algorithm are set, specifically including: setting the population size to 200, the crossover rate to 0.8, and the mutation rate to 0.1.

[0069] In this embodiment, the operations of population initialization, fitness evaluation, single-point crossover, random selection and mutation are repeated until the fitness value meets the error requirement, and the value of the parameter to be identified can be obtained as the initial parameter.

[0070] In this embodiment, after the initial parameters are obtained, a Kalman filter model for ohmic resistance aging and limiting current density aging is established using the initial parameters;

[0071] First, a polarization curve formula model considering real-time aging is constructed. It is found that the aging degradation rates of the two are similar and both are linear. Therefore, the semi-empirical degradation formula only considers the decay of ohmic internal resistance and limiting current density. The two decay variables are modeled as follows:

[0072]

[0073] Among them, R ohm is the ohmic internal resistance; i L is the limiting current density; R 0 is the initial impedance; i L0 is the initial limiting current density; α(t)=βt, is the aging amount, β is the aging rate, which is a constant.

[0074] Therefore, the relationship between the semi-empirical formula of the fuel cell polarization curve and time is as follows:

[0075]

[0076] Further, construct the Kalman filter model:

[0077]

[0078] Among them, x k is the state variable of the system; u k is the input of the system; is the output of the system; w k-1 is the system process noise; v k is the measurement noise; f is the state transfer function of the polarization curve aging model; g(x k ,u k ) is the output function of the polarization curve aging model; k is the current moment, and k-1 is the previous moment.

[0079] In this embodiment, w k-1 and v k are the system process noise and measurement noise, which are independent, have zero mean and covariance matrices Q and R respectively.

[0080] In this embodiment, the continuous variables of the semi-empirical aging formula of the fuel cell are constructed as the extended Kalman filter discrete variables as the state variables, that is, the space equation expression of the nonlinear system can be converted into the state transfer function and output function of the discrete time state. The state variable, the state transfer function and the output function are all

[0081]

[0082] as follows:

[0083]

[0084] Among them, T s is the sampling time; α k is the degradation rate at time k; β k is the aging rate at time k; w k-1 is the system process noise; u k is the input of the system; i k is the current density at time k; yk is the output at time k; V st,k is the actual value of the sampling point of the polarization curve; n cell is the number of fuel cells; E ocv is the open circuit voltage; R 0 is the initial impedance; A is the Tafel constant; T is the temperature; i 0 is the exchange current density; B is the concentration constant; v k To measure noise.

[0085] The Kalman filter algorithm continuously estimates the size of the state by performing time updates and measurement updates according to the established formula under the given initial value. The initial value of the Kalman filter is set as follows:

[0086]

[0087] Among them, x 0|0 is the state space value of the initial state; P 0|0 is the covariance matrix value of the initial state; Q is the process noise; R is the measurement noise.

[0088] Further, according to the state equation and initial value of the given Kalman filter model, time update and filter measurement update are performed. The time update estimation includes one-step state value estimation and one-step error covariance matrix estimation. The measurement update correction includes correcting the state value and error covariance matrix estimated by time update according to the Kalman gain. The specific expression is:

[0089]

[0090] Among them, x k|k-1 is the estimated predicted value of the fuel cell aging state variable; x k|k is the corrected state filter value; K k is the gain matrix of the Kalman filter; P k|k-1 is the filter error covariance matrix in the system estimation recursion; P k|k is the corrected error covariance matrix; I is the identity matrix, A and C k is the parameter matrix of the state equation; Q is the process noise; R is the measurement noise; V st,k is the actual value of the sampling point of the polarization curve; g(x k ,u k ) is the output function of the polarization curve aging model.

[0091] Formula 1 is the state prediction, that is, according to the state estimate x at the previous moment k-1|k-1 and the state transfer matrix A to predict the current state x k|k-1 ; Formula 2 is the error covariance prediction, that is, predicting the error covariance P at the current moment k|k-1; Formula 3 is the Kalman gain calculation, calculate the Kalman gain K k , which is used as the weight to weigh the predicted value and the actual measured value when updating the measurement; Formula 4 is the state update, which is based on the Kalman gain K k and the measured value V st,k , update the state estimate x k|k ; Formula 5 is the error covariance update, and is the updated error covariance P k|k ; reflects the uncertainty of the state estimate after taking into account the new measurement values.

[0092] In this embodiment, in order to further improve the robustness of the Kalman filter algorithm, a Kalman filter algorithm that adaptively updates the process noise covariance matrix and the measurement noise covariance matrix is ​​used, so that the initial values ​​of Q and R no longer interfere with the accuracy of the long-term life estimation of the fuel cell. They will automatically correct the Q and R values ​​according to the new information, reducing the algorithm estimation effect problems caused by inaccurate estimation of the statistical characteristics of the process noise covariance matrix and the measurement noise covariance and unreasonable initial value settings. The update formulas for Q and R are as follows:

[0093]

[0094] Among them, v k is the measurement noise; V st,k is the actual value of the sampling point of the polarization curve; C k is the observation matrix; x k is the estimated value of the state at time step k; is the covariance matrix of the new information; v j is the new information of step j in the past N time steps; 0 is the initial step of the past N time steps; K k is the Kalman gain; R k is the difference between the innovation covariance and the prediction error covariance, which is used to adjust the estimate of the measurement noise covariance; P k|k-1 is the covariance matrix; N = 2; Q k is the system process noise at the current k moment; R k is the measurement noise at the current time k.

[0095] In this embodiment, the specific process of adaptive extended Kalman filtering is as follows: Figure 4 As shown in the figure, the state variable is input, the state is estimated, and the new information is calculated from the observed value and the actual value. Then, based on the new information, it is selected whether to perform adaptive noise covariance matching. If so, the state error covariance is updated and the state error covariance matrix is ​​calculated. The state estimation covariance is then calculated, and the Kalman gain is calculated. The state estimate is further updated by the Kalman gain at this time to generate a model-based online estimate and output parameters or states.

[0096] In this embodiment, the output voltage of the fuel cell is input into the adaptive extended Kalman filter model, and the aging voltage of the fuel cell at the current prediction point is output. The steps are: first, the output voltage data of each time period is obtained from the fuel cell system to form an hourly voltage sequence. The hourly voltage sequence is input into the adaptive extended Kalman filter model; then the adaptive extended Kalman filter model is used to predict the aging voltage of the fuel cell in the current time period, and the rated voltage result of the fuel cell at the current prediction point is output. As new time series data is obtained, the parameters of the adaptive extended Kalman filter model are updated to improve the prediction accuracy.

[0097] In this embodiment, the process of applying the scheme to estimate the battery state is as follows: Figure 5 As shown, the historical fuel cell output voltage is first input to form the fuel cell output voltage time series, and then the adaptive extended Kalman filter model is trained. After training, the historical fuel cell output voltage is input into the model to output the current rated voltage of the fuel cell, and the current health status of the fuel cell is calculated using the on-board chip, and the health of the fuel cell is output by the instrument panel. In this process, the fuel cell output voltage time series and the training adaptive extended Kalman filter model are continuously updated over time.

[0098] In this embodiment, the health of the fuel cell is finally calculated based on the predicted rated voltage; first, it is defined that the fuel cell ends its life when it decays to 10% of the initial rated voltage under the rated current, that is, the health state is 0 at this time. The fuel cell performance degradation index D and health state index SOH defined accordingly are as follows:

[0099]

[0100] SOH=1-D

[0101] Among them, U rated,new is the total rated voltage attenuation of the fuel cell from the beginning to the end of its life, U rated,degraded is the rated voltage of the fuel cell at the SOH prediction point.

[0102] In this embodiment, SOH and D are output to the fuel cell control core and displayed on the instrument panel.

[0103] In summary, this scheme can realize the estimation of the health state of the fuel cell, and through the Kalman filtering method, effectively eliminate the noise interference generated in the process of fuel cell voltage measurement, thereby ensuring the accuracy of the fuel cell health state estimation.

[0104] Example 2

[0105] This scheme proposes a fuel cell health state estimation system based on adaptive extended Kalman filtering to monitor the health state of the fuel cell. The system includes a parameter identification module, an aging modeling module, a Kalman filter module and a health calculation module;

[0106] Among them, the parameter identification module is used to obtain the polarization curve of the vehicle-mounted fuel cell, and then use the genetic algorithm to perform parameter identification based on the polarization curve to obtain the initial parameters; the aging modeling module is used to consider the aging of the ohmic resistance and the limiting current density, and establish a semi-empirical aging formula; the Kalman filter model module is composed of the initial value, the state space obtained after the discretization of the semi-empirical aging formula, the time update, the filter measurement update and the adaptive update. The fuel cell voltage sequence is input into the module, and the rated voltage of the current predicted point of the fuel cell is obtained as output; the health calculation module is used to calculate the health of the fuel cell according to the rated voltage of the current predicted point.

[0107] In this embodiment, the scheme is applied to estimate the health status of the fuel cell, and the system is applied to estimate the health status of the fuel cell. Figure 2 As shown, firstly, the initial polarization curve of the fuel cell is obtained, and the genetic algorithm is used to identify the parameters. Then, the semi-empirical formula of the fuel cell is matched. Considering the aging of the ohmic resistance and the limiting current density, a semi-empirical formula for the real-time aging of the fuel cell is established, which is discretized to obtain the state space. The state space, the update of the initial value, the time update and the filter measurement update are used to jointly construct an adaptive extended Kalman filter model. The obtained fuel cell voltage sequence is input into it, and the rated voltage of the fuel cell is output. The health status of the output fuel cell is calculated using the current rated voltage of the fuel cell.

[0108] In this embodiment, first, the initial polarization curve of the fuel cell without attenuation is obtained, and based on the polarization curve, a genetic algorithm is used in a semi-empirical formula model to perform parameter identification to obtain the amount of unknown parameters. The specific expression of the semi-empirical formula model is:

[0109]

[0110] Among them, V st is the current output voltage; n cell is the number of fuel cells; E ocv is the open circuit voltage; i is the current output current density; R ohm is the ohmic internal resistance; A is the Tafel constant; T is the temperature; i 0 is the exchange current density; B is the concentration constant; i L is the limiting current density.

[0111] In this embodiment, a genetic algorithm is used for rapid parameter identification, wherein the fitness function of the genetic algorithm is defined as the sum of the squares of the differences between the sampled voltages of the aging experiment at all measurement points and the voltages predicted by the genetic algorithm. The purpose of the genetic algorithm is to globally explore various possibilities of the parameters to be identified and optimize in the direction of the minimum value of the fitness function. The mathematical formula of the fitness function and the constraints of the parameters to be identified are as follows:

[0112]

[0113] Among them, f fitness is the fitness function; E ocv is the open circuit voltage; R 0 is the initial impedance; A is the Tafel constant; B is the concentration constant; i 0 is the exchange current density; i L0 is the initial limiting current density; V st,k is the actual value of the sampling point of the polarization curve; is the genetic algorithm estimated value of the polarization curve sampling point; i k is the current density at time k.

[0114] In this embodiment, the initial parameters of the genetic algorithm are set, specifically including: setting the population size to 200, the crossover rate to 0.8, and the mutation rate to 0.1.

[0115] In this embodiment, the operations of population initialization, fitness evaluation, single-point crossover, random selection and mutation are repeated until the fitness value meets the error requirement, and the value of the parameter to be identified can be obtained as the initial parameter.

[0116] In this embodiment, after the initial parameters are obtained, a Kalman filter model for ohmic resistance aging and limiting current density aging is established using the initial parameters;

[0117] First, a polarization curve formula model considering real-time aging is constructed. It is found that the aging degradation rates of the two are similar and both are linear. Therefore, the semi-empirical degradation formula only considers the decay of ohmic internal resistance and limiting current density. The two decay variables are modeled as follows:

[0118]

[0119] Among them, R ohm is the ohmic internal resistance; i L is the limiting current density; R 0 is the initial impedance; i L0 is the initial limiting current density; α(t)=βt, is the aging amount, β is the aging rate, which is a constant.

[0120] Therefore, the relationship between the semi-empirical formula of the fuel cell polarization curve and time is as follows:

[0121]

[0122] Further, construct the Kalman filter model:

[0123]

[0124] Among them, x k is the state variable of the system; u k is the input of the system; is the output of the system; w k-1 is the system process noise; v k is the measurement noise; f is the state transfer function of the polarization curve aging model; g(x k ,u k ) is the output function of the polarization curve aging model; k is the current moment, and k-1 is the previous moment.

[0125] In this embodiment, w k-1 and v k are the system process noise and measurement noise, which are independent, have zero mean and covariance matrices Q and R respectively.

[0126] In this embodiment, the continuous variables of the semi-empirical aging formula of the fuel cell are constructed as the extended Kalman filter discrete variables as the state variables, that is, the space equation expression of the nonlinear system can be converted into the state transfer function and output function of the discrete time state. The state variable, the state transfer function and the output function are all

[0127]

[0128] as follows:

[0129]

[0130] Among them, T s is the sampling time; α k is the degradation rate at time k; β k is the aging rate at time k; w k-1 is the system process noise; u k is the input of the system; i k is the current density at time k; y k is the output at time k; V st,k is the actual value of the sampling point of the polarization curve; n cell is the number of fuel cells; E ocv is the open circuit voltage; R 0 is the initial impedance; A is the Tafel constant; T is the temperature; i 0 is the exchange current density; B is the concentration constant; v k To measure noise.

[0131] The Kalman filter algorithm continuously estimates the size of the state by performing time updates and measurement updates according to the established formula under the given initial value. The initial value of the Kalman filter is set as follows:

[0132]

[0133] Among them, x 0|0 is the state space value of the initial state; P 0|0 is the covariance matrix value of the initial state; Q is the process noise; R is the measurement noise.

[0134] Further, according to the state equation and initial value of the given Kalman filter model, time update and filter measurement update are performed. The time update estimation includes one-step state value estimation and one-step error covariance matrix estimation. The measurement update correction includes correcting the state value and error covariance matrix estimated by time update according to the Kalman gain. The specific expression is:

[0135]

[0136]

[0137] Among them, x k|k-1 is the estimated predicted value of the fuel cell aging state variable; x k|k is the corrected state filter value; K k is the gain matrix of the Kalman filter; P k|k-1 is the filter error covariance matrix in the system estimation recursion; P k|k is the corrected error covariance matrix; I is the identity matrix, A and C k is the parameter matrix of the state equation; Q is the process noise; R is the measurement noise; V st,k is the actual value of the sampling point of the polarization curve; g(x k ,u k ) is the output function of the polarization curve aging model.

[0138] Formula 1 is the state prediction, that is, according to the state estimate x at the previous moment k-1|k-1 and the state transfer matrix A to predict the current state x k|k-1 ; Formula 2 is the error covariance prediction, that is, predicting the error covariance P at the current moment k|k-1 ; Formula 3 is the Kalman gain calculation, calculate the Kalman gain K k , which is used as the weight to weigh the predicted value and the actual measured value when updating the measurement; Formula 4 is the state update, which is based on the Kalman gain K k and the measured value V st,k , update the state estimate x k|k; Formula 5 is the error covariance update, and is the updated error covariance P k|k ; reflects the uncertainty of the state estimate after taking into account the new measurement values.

[0139] In this embodiment, in order to further improve the robustness of the Kalman filter algorithm, a Kalman filter algorithm that adaptively updates the process noise covariance matrix and the measurement noise covariance matrix is ​​used, so that the initial values ​​of Q and R no longer interfere with the accuracy of the long-term life estimation of the fuel cell. They will automatically correct the Q and R values ​​according to the new information, reducing the algorithm estimation effect problems caused by inaccurate estimation of the statistical characteristics of the process noise covariance matrix and the measurement noise covariance and unreasonable initial value settings. The update formulas for Q and R are as follows:

[0140]

[0141] Among them, v k is the measurement noise; V st,l is the actual value of the sampling point of the polarization curve; C k is the observation matrix; x k is the estimated value of the state at time step k; is the covariance matrix of the new information; v j is the new information of step j in the past N time steps; 0 is the initial step of the past N time steps; K k is the Kalman gain; R k is the difference between the innovation covariance and the prediction error covariance, which is used to adjust the estimate of the measurement noise covariance; P k|k-1 is the covariance matrix; N = 2; Q k is the system process noise at the current k moment; R k is the measurement noise at the current time k.

[0142] In this embodiment, the specific process of adaptive extended Kalman filtering is as follows: Figure 4 As shown, the output voltage of the fuel cell is input into the adaptive extended Kalman filter model, and the aging voltage of the fuel cell at the current predicted point is output.

[0143] The steps are as follows: first, the output voltage data of each time period is obtained from the fuel cell system to form an hourly voltage sequence. The hourly voltage sequence is input into the adaptive extended Kalman filter model; the adaptive extended Kalman filter model is then used to predict the fuel cell aging voltage of the current time period, and the rated voltage result of the fuel cell at the current prediction point is output. As new time series data is obtained, the parameters of the adaptive extended Kalman filter model are updated to improve the prediction accuracy.

[0144] In this embodiment, the process of applying the scheme to estimate the battery state is as follows: Figure 5 As shown, the historical fuel cell output voltage is first input to form the fuel cell output voltage time series, and then the adaptive extended Kalman filter model is trained. After training, the historical fuel cell output voltage is input into the model to output the current rated voltage of the fuel cell, and the current health status of the fuel cell is calculated using the on-board chip, and the health of the fuel cell is output by the instrument panel. In this process, the fuel cell output voltage time series and the training adaptive extended Kalman filter model are continuously updated over time.

[0145] In this embodiment, the health of the fuel cell is finally calculated based on the predicted rated voltage; first, it is defined that the fuel cell ends its life when it decays to 10% of the initial rated voltage under the rated current, that is, the health state is 0 at this time. The fuel cell performance degradation index D and health state index SOH defined accordingly are as follows:

[0146]

[0147] SOH=1-D

[0148] Among them, U rated,new is the total rated voltage attenuation of the fuel cell from the beginning to the end of its life, U rated,degraded is the rated voltage of the fuel cell at the SOH prediction point.

[0149] In this embodiment, SOH and D are output to the fuel cell control core and displayed on the instrument panel.

[0150] In summary, this scheme can realize the estimation of the health status of the fuel cell through the Kalman filtering method, and through the time update, filter measurement update and adaptive update process, it reduces the algorithm estimation effect problems caused by inaccurate estimation of the statistical characteristics of the process noise covariance matrix and the measurement noise covariance and unreasonable initial value setting, thereby improving the robustness of calculating the health of the fuel cell.

[0151] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present invention, and these modifications or replacements should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A fuel cell health state estimation method based on adaptive extended Kalman filtering, characterized in that: The method steps include: S1. Obtaining a polarization curve of the vehicle-mounted fuel cell, and based on the polarization curve, using a genetic algorithm to perform parameter identification to obtain initial parameters; S2. Considering the aging of ohmic resistance and limiting current density, a semi-empirical aging formula is established based on the initial parameters, and the semi-empirical aging formula is discretized to obtain the state space; S3, setting initial values, using the initial values ​​and the state space to jointly construct a Kalman filter model, in which time update, filter measurement update, and adaptive update processes are integrated to obtain an adaptive extended Kalman filter model; S4, inputting the fuel cell voltage sequence into the adaptive extended Kalman filter model, and outputting the rated voltage of the fuel cell at the current predicted point; S5. Calculate the health of the fuel cell based on the rated voltage at the current prediction point.

2. A fuel cell health state estimation method based on adaptive extended Kalman filtering according to claim 1, characterized in that: The parameter identification process using the genetic algorithm in S1 is as follows: first, a fitness function is established, and the objective function of the genetic algorithm is set to be the minimization function of the fitness function, then the initial parameters of the genetic algorithm are set, and the steps of initializing the population, fitness evaluation, single-point crossover, random selection and mutation are repeated until the fitness meets the preset error requirements, and finally the initial parameters are output.

3. A fuel cell health state estimation method based on adaptive extended Kalman filtering according to claim 2, characterized in that: The objective function and constraints of the genetic algorithm are: Among them, f fitness is the fitness function; E ocv is the open circuit voltage; R0 is the initial impedance; A is the Tafel constant; B is the concentration constant; i0 is the exchange current density; i L0 is the initial limiting current density; V st,k is the actual value of the sampling point of the polarization curve; is the genetic algorithm estimated value of the polarization curve sampling point; i k is the current density at time k.

4. The method for estimating the health status of a fuel cell based on an adaptive extended Kalman filter according to claim 1, characterized in that: The state space in S2 includes state variables, state transfer function and output function, and its specific formula is: Among them, T s is the sampling time; α k is the degradation rate at time k; β k is the aging rate at time k; w k-1 is the system process noise; u k is the input of the system; i k is the current density at time k; y k is the output at time k; V st，k is the actual value of the sampling point of the polarization curve; n cell is the number of fuel cells; E ocv is the open circuit voltage; R0 is the initial impedance; A is the Tafel constant; T is the temperature; i0 is the exchange current density; B is the concentration constant; v k To measure noise.

5. The method for estimating the health status of a fuel cell based on an adaptive extended Kalman filter according to claim 1, characterized in that: The time update in S3 includes state prediction and error covariance prediction, and the filter measurement update is to correct the state value and error covariance matrix predicted by the time update according to the Kalman gain.

6. A fuel cell health status estimation method based on adaptive extended Kalman filtering according to claim 5, characterized in that: In the time update, the specific formulas for state prediction and error covariance prediction are: Among them, x k|k-1 is the estimated predicted value of the fuel cell aging state variable; P k|k-1 is the filtering error covariance matrix in the system estimation recursion; A is the parameter matrix of the state equation; Q is the process noise.

7. A fuel cell health status estimation method based on adaptive extended Kalman filtering according to claim 5, characterized in that: In the filtering measurement update, the specific formula for correcting the state value and the error covariance matrix predicted by the time update according to the Kalman gain is: x k|k =x k|k-1 +K k (V st，k -g(x k ,u k )) P k|k =(I-K k C k )P k|k-1 Among them, K k is the gain matrix of the Kalman filter; x k|k is the corrected state filter value; P k|k is the corrected error covariance matrix; x k|k-1 is the estimated predicted value of the fuel cell aging state variable; P k|k-1 is the filter error covariance matrix in the system estimation recursion; I is the identity matrix, C k is the parameter matrix of the state equation; V st，k is the actual value of the sampling point of the polarization curve; g(x k ,u k ) is the output function of the polarization curve aging model; R is the measurement noise;.

8. The method for estimating the health status of a fuel cell based on an adaptive extended Kalman filter according to claim 1, characterized in that: The adaptive update in S3 is to set the deviation between the model prediction and the actual observation as the new information during the filtering process, and correct the update process noise and measurement noise according to the new information. The specific formula for the correction update is: Among them, v k is the measurement noise; V st，k is the actual value of the sampling point of the polarization curve; C k is the observation matrix; x k is the estimated value of the state at time step k; is the covariance matrix of the new information; v j is the new information of step j in the past N time steps; j0 is the initial step of the past N time steps; K k is the Kalman gain; R k is the difference between the innovation covariance and the prediction error covariance, which is used to adjust the estimate of the measurement noise covariance; P k|k-1 is the covariance matrix; N = 2; Q k is the system process noise at the current k moment; R k is the measurement noise at the current time k.

9. The method for estimating the health status of a fuel cell based on an adaptive extended Kalman filter according to claim 1, characterized in that: The specific process of calculating the health of the fuel cell according to the predicted aging voltage in S4 is: firstly, a fuel cell performance degradation index is established, and the fuel cell performance degradation index is calculated according to the predicted aging voltage, and then the health status index is calculated according to the fuel cell performance degradation index, so as to obtain the health of the fuel cell; wherein, the specific formulas of the fuel cell performance degradation index and the health status index are: SOH=1-D Among them, D is the fuel cell performance degradation index; SOH is the health status index; U rated,new is the total rated voltage attenuation of the fuel cell from the beginning to the end of its life, U rated,deg raded The rated voltage of the fuel cell at the current predicted point.

10. A fuel cell health status estimation system based on adaptive extended Kalman filtering, characterized in that: The system applies a fuel cell health state estimation method based on an adaptive extended Kalman filter as described in any one of claims 1 to 9, and the system includes a parameter identification module, an aging modeling module, a Kalman filter module and a health calculation module; The parameter identification module is used to obtain the polarization curve of the vehicle-mounted fuel cell and then perform parameter identification based on the polarization curve using a genetic algorithm to obtain initial parameters; The aging modeling module is used to consider ohmic resistance aging and limiting current density aging, and establish a semi-empirical aging formula; The Kalman filter model module is composed of initial value, state space obtained by discretization of semi-empirical aging formula, time update, filter measurement update and adaptive update. The fuel cell voltage sequence is input into the module, and the rated voltage of the fuel cell at the current predicted point is output; The health calculation module is used to calculate the health of the fuel cell according to the rated voltage of the current prediction point.

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