CN111880100A - Remaining life prediction method of fuel cell based on adaptive extended Kalman filter - Google Patents

Abstract

The invention relates to a method for predicting the remaining life of a fuel cell based on an adaptive extended Kalman filter, comprising the following steps: 1) obtaining an estimated value of the average single-chip voltage of the fuel cell at the current moment through the adaptive extended Kalman filtering algorithm; 2) Collect the time proportion and decay rate of the fuel cell under each working condition, and calculate the total decay rate of the fuel cell; 3) Calculate the environmental factor according to the estimated value of the average single-chip voltage at the current moment and the actual value of the average single-chip voltage at the current moment; 4) According to the estimated value of the average single-chip voltage at the current moment, the total decay rate and the environmental factor, and through the calculation formula of the remaining service life, the prediction result of the remaining service life of the fuel cell at the current moment is obtained. Compared with the prior art, the present invention has the advantages of high precision, good stability, and greatly reduced calculation amount.

Description

Remaining life prediction method of fuel cell based on adaptive extended Kalman filter

technical field

The invention relates to the technical field of fuel cell system control, in particular to a method for predicting the remaining life of a fuel cell based on an adaptive extended Kalman filter.

Background technique

Proton exchange membrane fuel cells (PEMFCs) use hydrogen and oxygen as fuels, and the entire energy conversion process has little negative impact on the environment. However, the limited lifetime limits the further development of fuel cell industrialization. Lifetime prediction is one of the most effective measures in fuel cell health management. Because it helps to develop mitigation measures by estimating the remaining useful life before the fuel cell fails, improving the durability of the fuel cell. However, existing fuel cell residual life prediction methods mainly focus on constant operating conditions. That is, a constant current input is given to the fuel cell on the experimental bench, the voltage change is measured over a long period of time, and the voltage change is used as an indicator for life prediction. These prediction methods cannot be applied to dynamic conditions such as online prediction of fuel cell life. At present, there are few online prediction methods for fuel cell life, but online prediction has important practical value for evaluating the durability of fuel cell vehicles.

A variety of prediction methods have been applied to the prediction of fuel cell life, including: particle filter, Kalman filter, echo state network and correlation vector machine. These prediction methods also have the following problems: (1) The evaluation methods for the end of life are not uniform. Different forecasting methods define this problem differently. Some life evaluation indicators are difficult to measure in practical application and are not suitable for online prediction. (2) There is a lack of evaluation of the actual working conditions of fuel cells. The operation mode (start-stop, idle speed, high power, etc.), load and external parameters (intake pressure, air humidity, operating temperature, etc.) have a significant impact on the durability of the PEMFC system. The above prediction methods rarely consider the operating conditions and external environment of fuel cell vehicles, so it is difficult to directly apply to online prediction of vehicle fuel cell life. (3) Most of the prediction tools do not have the adaptive ability. The actual operating conditions of fuel cells are highly dynamic, so prediction methods are required to be adaptive to dynamic data to improve the accuracy and stability of online prediction.

A forecast is defined as a time estimate of a future failure scenario. For PEMFCs, the purpose of forecasting is to predict the remaining useful life in order to prevent failures. The forecast method uses test data from a large number of actual fuel cell stacks to indicate future decline trends. According to the decline trend of the PEMFC system, the remaining life of the PEMFC system can be predicted to prevent the occurrence of failures. The processing methods for fuel cell decay data mainly include model-driven methods and data-driven methods. The data-driven approach is based on a large amount of fuel cell decay data, using artificial intelligence tools to learn the behavior of the system and give an estimate of the changing trend of fuel cell life. This method has high accuracy but too much computation and is not suitable for online prediction. Therefore, data processing methods under online conditions should mainly consider model-driven methods.

The main problems of online prediction of the remaining service life of fuel cells are: (1) A reasonable life evaluation index; under dynamic conditions, the index must be easy to measure. (2) Evaluation of actual operating conditions; typical operating conditions and changes in the external environment have a significant impact on the life of the fuel cell, so the operating conditions of the fuel cell vehicle must be considered. (3) The calculation amount of the prediction method should not be too large, and the prediction method needs to have adaptive processing ability for the data collected under dynamic conditions.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a method for predicting the remaining life of a fuel cell based on an adaptive extended Kalman filter with adaptive processing capability and considering the operating conditions of the fuel cell in order to overcome the above-mentioned defects of the prior art.

The object of the present invention can be realized through the following technical solutions:

A method for predicting the remaining life of a fuel cell based on an adaptive extended Kalman filter, comprising the following steps:

The voltage estimation step at the current moment: obtain the estimated value of the average single-chip voltage of the fuel cell at the current moment through the adaptive extended Kalman filter algorithm;

Total decay rate calculation step: collect the time proportion and decay rate of the fuel cell under each working condition, and calculate the total decay rate of the fuel cell;

The step of calculating the environmental factor: calculating the environmental factor according to the estimated value of the average single-chip voltage at the current moment and the actual value of the average single-chip voltage at the current moment;

Remaining service life prediction step: According to the estimated value of the average single-chip voltage at the current moment, the total decay rate and environmental factors, and through the remaining service life calculation formula, the prediction result of the remaining service life of the fuel cell at the current moment is obtained.

Further, the input of the adaptive extended Kalman filter algorithm includes the actual measured value and the model predicted value,

The actual measured value is the average monolithic voltage-time curve data of the fuel cell under the rated current obtained by recording the voltage and current changes of the fuel cell in real time;

The predicted value of the model is the calculated value of the average single-chip voltage of the fuel cell obtained by fitting the polarization curves at different times during the operation of the fuel cell and loading it into a pre-established empirical model.

Further, the polarization curves at different times during the operation of the fuel cell are fitted by the polarization curve expression, and the polarization curve expression is:

where V is the output voltage of the fuel cell, E is the reversible open-circuit voltage, i is the output current of the fuel cell, i ₀ is the exchange current density, A is the Tafel slope, B is the concentration polarization constant, and i _l is the limiting current density, r is the total resistance of the fuel cell.

Further, the expression of the empirical model is:

In the formula, g(x _k , u _k ) is the voltage at the current moment (model prediction value), r ₀ is the initial value of the total resistance, α _k is the total resistance change rate (linear change), and i _k is the current value at the current moment.

Further, the expression of the adaptive extended Kalman filter algorithm is:

x _k+1 =Fx _k|k +w _k

x _k =[α _k β _k ] ^T

y _k =g(x _k ,u _k )+v _k

P(w)～N(0,Q)

P(v)～N(0,R)

where x _k is the state, u _k is the input, y _k is the output, F is the state transition matrix of the system, T _s is the sampling time, x _k|k is the state matrix of the system, w _k is the system error noise, α _k is the total resistance change rate, β _k is the change rate constant, v _k is the measurement error noise, g(x _k , u _k ) is the current voltage (model prediction value), P(w) is the probability function of the system error, Q is the system noise covariance matrix, P(v) is the probability function of the measurement error, and R is the measurement noise covariance matrix;

The time update expression of the adaptive extended Kalman filter algorithm is:

x _k|k-1 =Fx _k-1|k-1

P _k|k-1 =FP _k-1|k-1 F ^T +Q

In the formula, x _k|k-1 is the predicted value of the system state at the next moment, x _k-1|k-1 is the system state at the current moment, and P _k|k-1 is the coordination value corresponding to x _k|k-1 . variance, P _k-1|k-1 is the covariance corresponding to x _k-1|k-1 ;

The measurement update expression of the adaptive extended Kalman filter algorithm is:

P _k|k =(IK _k H _k )P _k|k-1

x _k|k =x _k|k-1 +K _k (V _stk -g(x _k ,u _k ))

In the formula, K _k is the Kalman gain, H _k is the Jacobian matrix corresponding to the observation equation (model) in the adaptive extended Kalman filter algorithm, x _k|k-1 is the system state, and V _stk is the current moment voltage (actual Measurements);

The covariance adaptive update expression of the adaptive extended Kalman filter algorithm is:

v _k =V _stk -H _k x _k

为采样窗口为N时新息残差协方差的估计，N为采样窗口的长度，j₀为采样的起始时刻，k为采样的当前时刻，v_j为当前的残差序列，Q_k为更新后的系统噪声协方差矩阵，R_k为更新后的测量噪声协方差矩阵。In the formula,

is the estimation of the innovation residual covariance when the sampling window is N, N is the length of the sampling window, j ₀ is the starting time of sampling, k is the current time of sampling, v _j is the current residual sequence, and Q _k is The updated system noise covariance matrix, R _k is the updated measurement noise covariance matrix.

Further, in the step of calculating the total decay rate, the working conditions include a load change working condition, a start-stop working condition, a low-power load working condition and a high-power load working condition;

The calculation expression of the total decay rate of the fuel cell is:

Total decay rate = V(d ₁ g ₁ +d ₂ g ₂ +d ₃ g ₃ +d ₄ g ₄ )

In the formula, V is the estimated value of the average single-chip voltage, d ₁ is the decay rate of the load change condition, g ₁ is the time weight coefficient of the load change condition, d ₂ is the decay rate of the start-stop condition, and g ₂ is the time weight coefficient of the start-stop condition, d ₃ is the decay rate of the low power load condition, g ₃ is the time weight coefficient of the low power load condition, d ₄ is the decay rate of the high power load condition, and g ₄ is Time weighting factor for high power load conditions.

Further, in the environmental factor calculation step, the calculation expression of the environmental factor is:

为t+1时刻的平均单片电压估计值，V_t+2为t+1时刻的平均单片电压实际值。In the formula, k _t+1 is the environmental factor at time t+1, k _t is the environmental factor at time t,

is the estimated value of the average single-chip voltage at time t+1, and V _t+2 is the actual value of the average single-chip voltage at time t+1.

Further, the initial value of the environmental factor is in the range of 1 to 1.2.

Further, in the remaining service life prediction step, the remaining service life calculation formula is:

In the formula, T is the remaining service life of the fuel cell at the current moment, ΔV is the difference between the estimated value of the average single-chip voltage at the current moment and the estimated value of the average single-chip voltage at the end of the life, k is the environmental factor at the current moment, and V is the current The estimated value of the average single-chip voltage at the time, d is the decay rate under each working condition, and g is the time ratio under each working condition.

Further, the criterion for judging the end of life is the time point when the average single-chip voltage value of the fuel cell declines to 90% of the initial value of the average single-chip voltage.

Compared with the prior art, the present invention has the following advantages:

(1) The present invention comprehensively considers various difficulties in online prediction of the remaining service life of the fuel cell, and provides the evaluation standard of the service life, the evaluation of the operating condition and the processing method of the dynamically collected data; Filtering to obtain a voltage estimate for the current moment, which improves the accuracy and stability of online prediction

(2) A prediction formula for the remaining service life is proposed, which takes into account the nonlinear decay factors of the fuel cell during use. The estimated value of the remaining service life at each moment can be given during the use process, and at the same time, the driving conditions of the vehicle at the current stage can be reflected; this method greatly reduces the amount of calculation and is easy to implement in real vehicles.

Description of drawings

1 is a flowchart of a method for predicting the remaining life of a fuel cell based on an adaptive extended Kalman filter according to the present invention;

Fig. 2 is the solution proposed by the present invention for the difficulty of online prediction;

FIG. 3 is a flowchart of a method for online prediction of the remaining service life of a fuel cell according to a specific embodiment.

Detailed ways

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and provides a detailed implementation manner and a specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

Example 1

As shown in FIG. 1 , the present invention provides a method for predicting the remaining life of a fuel cell based on an adaptive extended Kalman filter, which specifically solves the three main difficulties that need to be solved in online prediction: the life evaluation index under dynamic conditions; Evaluation of operating conditions and adaptive capabilities of predictive tools. The average single-chip voltage at rated current is used as the life evaluation index under dynamic conditions. Load change condition, start-stop condition, low power load condition and high power load condition are introduced to evaluate the working conditions of fuel cell vehicles, and the influence of different working conditions on fuel cell degradation is considered respectively. The adaptive extended Kalman filter is used to remove the noise of the data collected online, which has a certain adaptive and anti-interference ability, and improves the accuracy and stability of the prediction algorithm.

The fuel cell residual life prediction method based on adaptive extended Kalman filter includes the following steps:

S1: When the fuel cell stack is running, measure the polarization curves at different times to obtain the parameters in the empirical model; collect the voltage-time data, extract the voltage data of the fuel cell operating at the rated current, and calculate the average value under the rated current. Monolithic voltage-time data; Substitute the voltage data calculated in the model and the collected voltage data into the adaptive extended Kalman filter algorithm to obtain the estimated value of the average monolithic voltage at the current moment;

S2: Obtain the running time of the fuel cell vehicle in the load change condition, the start-stop condition, the low power load condition and the high power load condition in the driving record, and calculate the time ratio of the four working conditions; from the fuel cell test database Obtain the decay rate of the fuel cell under four working conditions; calculate the total decay rate according to the time proportion and decay rate of the four working conditions;

S3: Substitute the environmental factor at the current moment, the total decay rate of the fuel cell and the current estimated voltage value obtained by the adaptive extended Kalman filter algorithm into the remaining service life prediction formula to obtain the estimated value of the remaining service life at the current moment.

The objective of the method for predicting the remaining service life of the fuel cell in this embodiment is to provide an estimate of the remaining service life at the current moment in real time during the online process, and display it through the display module. At the same time, the display module can also output the current usage status of the vehicle, including the load spectrum of the four working conditions, the time proportion of the four working conditions, and the external environmental influence factors. The remaining service life of the fuel cell is the time interval from the current moment to the defined end of the life of the fuel cell; the end of the life of the fuel cell is the time when the average single-chip voltage of the fuel cell decays to 90% of the initial value under the rated current point.

Each step is described in detail below:

1. Step S1

In step S1, an adaptive extended Kalman filter algorithm is used to estimate the average monolithic voltage of the fuel. The input of the adaptive extended Kalman filter is the model predicted value and the actual measured value of the average single-chip voltage of the fuel cell, and the output of the filter is the optimal estimated value of the average single-chip voltage of the fuel cell. Specifically include the following steps:

S101 : data acquisition: during the working process of the fuel cell, the voltage and current changes of the fuel cell are recorded in real time. Take out the data points of the fuel cell operating at the rated current, and calculate the average monolithic voltage-time curve at the rated current. Take this part of the data as the actual measurement of the input to the Adaptive Extended Kalman Filter.

S102: Parameter determination: when the fuel cell stack is running, measure the polarization curves at different times,

Fit the actual polarization curve with the following polarization curve expression, and obtain the parameters in the polarization curve, which are substituted into the empirical model described in the next step.

where V is the output voltage of the fuel cell, E is the reversible open-circuit voltage, i is the output current of the fuel cell, i ₀ is the exchange current density, A is the Tafel slope, B is the concentration polarization constant, and i _l is the limiting current density, r is the total resistance of the fuel cell.

S103: Model establishment: According to the relevant parameters obtained from the polarization curve, an empirical model conforming to the polarization theory is established, and the model considers the effects of activation loss, ohmic loss and concentration loss. It is considered that the changes of the total resistance r and the limiting current i _l with time are approximately linear, and the changes of these two parameters are regarded as having the same rate of change. The empirical model described is:

In the formula, g(x _k , u _k ) is the voltage at the current moment (model prediction value), r ₀ is the initial value of the total resistance, α _k is the total resistance change rate (linear change), and i _k is the current value at the current moment.

The calculated value of the fuel cell voltage in the empirical model is used as the model prediction value in the input of the adaptive extended Kalman filter.

S104: Filtering processing: take the collected data as the actual measured value input by the adaptive extended Kalman filter, and use the calculated value of the fuel cell voltage in the empirical model as the model predicted value in the input of the adaptive extended Kalman filter.

The adaptive extended Kalman filter algorithm is:

x _k+1 =Fx _k|k +w _k

x _k =[α _k β _k ] ^T

y _k =g(x _k ,u _k )+v _k

P(w)～N(0,Q)

P(v)～N(0,R)

where x _k is the state of the system, _{uk is the input, and y k is} the output. The noises w _k and v _k are assumed to be Gaussian noises and are independent of each other. In particular, the noise w _k is the system error, the noise v _k is the measurement error, F is the state transition matrix of the system, T _s is the sampling time, x _k|k is the state matrix of the system, α _k is the total resistance change rate, β _k is the rate of change constant, g(x _k , u _k ) is the current voltage (model prediction value), P(w) is the probability function of the system error, Q is the system noise covariance matrix, and P(v) is the measurement error The probability function of , R is the measurement noise covariance matrix; in the algorithm, the process noise covariance Q and measurement noise covariance R matrix may change with time, which enhances the adaptive ability of the algorithm.

The time update expression of the adaptive extended Kalman filter algorithm is:

x _k|k-1 =Fx _k-1|k-1

P _k|k-1 =FP _k-1|k-1 F ^T +Q

In the formula, x _k|k-1 is the predicted value of the system state at the next moment, x _k-1|k-1 is the system state at the current moment, and P _k|k-1 is the coordination value corresponding to x _k|k-1 . variance, P _k-1|k-1 is the covariance corresponding to x _k-1|k-1 ;

The measurement update expression of the adaptive extended Kalman filter algorithm is:

P _k|k =(IK _k H _k )P _k|k-1

x _k|k =x _k|k-1 +K _k (V _stk -g(x _k ,u _k ))

In the formula, K _k is the Kalman gain, H _k is the Jacobian matrix corresponding to the observation equation (model) in the adaptive extended Kalman filter algorithm, x _k|k-1 is the system state, and V _stk is the current moment voltage (actual Measurements);

The covariance adaptive update expression of the adaptive extended Kalman filter algorithm is:

v _k =V _stk -H _k x _k

为采样窗口为N时新息残差协方差的估计，N为采样窗口的长度，j₀为采样的起始时刻，k为采样的当前时刻，v_j为当前的残差序列，Q_k为更新后的系统噪声协方差矩阵，R_k为更新后的测量噪声协方差矩阵。In the formula,

is the estimation of the innovation residual covariance when the sampling window is N, N is the length of the sampling window, j ₀ is the starting time of sampling, k is the current time of sampling, v _j is the current residual sequence, and Q _k is The updated system noise covariance matrix, R _k is the updated measurement noise covariance matrix.

2. Step S2

Step S2 obtains the running time of the fuel cell vehicle in the load change condition, the start-stop condition, the low power load condition and the high power load condition in the driving record, and calculates the time ratio of the four working conditions; from the fuel cell test database Obtain the decay rate of the fuel cell under the four working conditions; calculate the total decay rate according to the time proportion and decay rate of the four working conditions, which includes the following steps:

S201: Obtaining the decay rate: the decay rate of the fuel cell is different under the load change condition, the start-stop condition, the low power load condition and the high power load condition. The experimental results of four different degradation rates of the fuel cell can be obtained from the database in an offline state.

d={d ₁ ,d ₂ ,d ₃ ,d ₄ }

d _i represents the decay rate of the fuel cell under load changing conditions, start-stop conditions, low-power load conditions and high-power load conditions, respectively.

S202: Weight calculation: According to the load spectrum record of the fuel cell, the time weight of the fuel cell under load change conditions, start-stop conditions, low power load conditions and high power load conditions is calculated in real time. The higher the weight factor of the working condition, the longer the fuel cell stack will work under this working condition.

g={g ₁ , g ₂ , g ₃ , g ₄ }

g _i represents the time weighting factor of the fuel cell working under load change condition, start-stop condition, low power load condition and high power load condition, respectively.

S203: Calculation of total decay rate: According to the time weight coefficient and decay rate of the four working conditions, the total decay rate is calculated:

V(d ₁ g ₁ +d ₂ g ₂ +d ₃ g ₃ +d ₄ g ₄ )

Among them, V is the estimated value of the average single-chip voltage calculated by the adaptive extended Kalman filter, d ₁ is the decay rate of the load change condition, g ₁ is the time weight coefficient of the load change condition, and d ₂ is the start-stop The decay rate of the working condition, g ₂ is the time weight coefficient of the start-stop condition, d ₃ is the decay rate of the low power load condition, g ₃ is the time weight coefficient of the low power load condition, and d ₄ is the high power load condition. The decay rate of the condition, g ₄ is the time weighting factor of the high-power load condition.

The total decay rate will be used in the remaining useful life prediction formula.

3. Step S3

Step S3: Substitute the environmental factor at the current moment, the total decay rate of the fuel cell and the current estimated voltage value obtained by the adaptive extended Kalman filter algorithm into the remaining service life prediction formula to obtain the estimated value of the remaining service life at the current moment. The specific calculation process is:

S301: Calculate the environmental factor: compare the actual measured voltage value with the predicted voltage value, calculate the environmental factor at the current moment,

为t+1时刻的平均单片电压估计值，V_t+1为t+1时刻的平均单片电压实际值。In the formula, k _t+1 is the environmental factor at time t+1, k _t is the environmental factor at time t,

is the estimated value of the average single-chip voltage at time t+1, and V _t+1 is the actual value of the average single-chip voltage at time t+1.

The initial value of k is recommended to be 1.1 because the voltage degradation is nonlinear. Considering that the nonlinear degradation factor is not significant at the beginning of life, the initial value is slightly higher than 1. This also leaves a safe threshold for the lifetime prediction of fuel cells. k reflects long-term changes in external conditions, so it is recommended to update the k value every 100 hours.

S302: Substitute the prediction formula: Substitute the environmental factor at the current moment, the total decay rate of the fuel cell and the estimated value of the average single-chip voltage at the current moment obtained by the adaptive extended Kalman filter algorithm into the remaining service life prediction formula to obtain the current moment pair. An estimate of the remaining useful life. The remaining service life prediction formula is:

In the formula, T is the remaining service life of the fuel cell at the current moment, ΔV is the difference between the estimated value of the average single-chip voltage at the current moment and the estimated value of the average single-chip voltage at the end of the life, k is the environmental factor at the current moment, and V is the current The estimated value of the average single-chip voltage at the time, d is the decay rate under each working condition, and g is the time ratio under each working condition.

4. Summary

As shown in Figure 2, the main difficulties of online prediction are pointed out: life evaluation index under dynamic conditions; evaluation of real operating conditions and adaptive ability of prediction tools. The method provided in this embodiment provides corresponding solutions to these three difficulties. An empirical model was built to predict the lifetime of fuel cells, which considered activation loss, ohmic loss, and concentration loss. This model is combined with Adaptive Extended Kalman Filtering (AEKF) to obtain an estimate of the average monolithic voltage at the current moment. Four operating conditions are defined: variable load condition, start-stop condition, idle speed condition and high power load condition. The total voltage degradation rate of the fuel cell is calculated based on the degradation rate under each operating condition and the time fraction of each operating condition. A residual service life prediction formula is proposed, which takes into account the operating conditions and the influence of the external environment under actual use conditions. The online calculation amount of the method is greatly reduced, and the remaining service life of the fuel cell can be quickly estimated, and the current usage status of the fuel cell vehicle can be given at the same time.

In step S1, when the fuel cell stack is running, the polarization curves at different times are measured to obtain the parameters in the empirical model; the voltage-time data is collected, the voltage data of the fuel cell operating at the rated current is extracted, and the rated current is calculated. The average single-chip voltage-time data under the current; the voltage data calculated in the model and the collected voltage data are substituted into the adaptive extended Kalman filter algorithm, and the estimated value of the voltage at the current moment is obtained. Then step S2 is performed.

In step S2, the running time of the fuel cell vehicle in the load change condition, the start-stop condition, the low power load condition and the high power load condition in the driving record is obtained, and the time ratio of the four working conditions is calculated; The decay rate of the fuel cell under four working conditions is obtained from the battery test database; the total decay rate is calculated according to the time proportion and decay rate of the four working conditions. Then step S3 is performed.

In step S3, the environmental factor at the current moment, the total decay rate of the fuel cell and the current voltage estimate obtained by the adaptive extended Kalman filter algorithm are substituted into the remaining service life prediction formula to obtain the remaining service life at the current moment.

As shown in FIG. 3 , in this embodiment, there is a specific online prediction method for the remaining service life of the fuel cell. An empirical model is established from the polarization curve, and a model-based average monolithic voltage-time database is obtained. Combined with the collected average monolithic voltage-time database, an adaptive extended Kalman filter is applied to obtain an estimate of the current voltage. The voltage decay rate under different working conditions is obtained from the decay test data. The time proportion of the four working conditions is obtained from the vehicle driving data, and the total voltage decay rate is calculated. Finally, the environmental factors at the current moment, the total decay rate of the fuel cell and the current voltage estimate obtained by the adaptive extended Kalman filter algorithm are substituted into the remaining service life prediction formula to obtain the remaining service life at the current moment.

The method for predicting the remaining service life of the fuel cell can quickly give the estimated value of the remaining service life at the current moment in real time under the online condition, and the calculation amount is small, which is convenient to be applied in real vehicle conditions.

The preferred embodiments of the present invention have been described above in detail. It should be understood that those skilled in the art can make numerous modifications and changes according to the concept of the present invention without creative efforts. Therefore, any technical solutions that can be obtained by those skilled in the art through logical analysis, reasoning or limited experiments on the basis of the prior art according to the concept of the present invention shall fall within the protection scope determined by the claims.

Claims (10)

1. A method for predicting the residual life of a fuel cell based on adaptive extended Kalman filtering is characterized by comprising the following steps:

estimating the voltage at the current moment: acquiring an average monolithic voltage estimated value of the fuel cell at the current moment through a self-adaptive extended Kalman filtering algorithm;

calculating the total decay rate: collecting the time proportion and the attenuation rate of the fuel cell under each working condition, and calculating the total attenuation rate of the fuel cell;

calculating an environment factor: calculating an environmental factor according to the average single-chip voltage estimated value at the current moment and the average single-chip voltage actual value at the current moment;

and (3) predicting the residual service life: and obtaining a prediction result of the residual service life of the fuel cell at the current moment through a residual service life calculation formula according to the average monolithic voltage estimation value, the total attenuation rate and the environmental factor at the current moment.

2. The method of claim 1, wherein the input of the adaptive extended Kalman Filter algorithm comprises actual measurement values and model prediction values,

the actual measurement value is the average monolithic voltage-time curve data of the fuel cell under the rated current obtained by recording the voltage and current changes of the fuel cell in real time;

the model predicted value is a calculated value of the average single-chip voltage of the fuel cell, which is obtained by fitting polarization curves of the fuel cell at different moments during operation and loading the fitted polarization curves into a pre-established empirical model.

3. The method for predicting the remaining life of the fuel cell based on the adaptive extended kalman filter according to claim 2, wherein the polarization curves at different moments when the fuel cell operates are fitted through a polarization curve expression, and the polarization curve expression is as follows:

where V is the fuel cell output voltage, E is the reversible open circuit voltage, i is the fuel cell output current, i is the voltage of the fuel cell output₀For exchange of current density, A is the Tafel slope, B is the concentration polarization constant, i_lIs the limiting current density and r is the total resistance of the fuel cell.

4. The method for predicting the remaining life of the fuel cell based on the adaptive extended kalman filter according to claim 3, wherein the empirical model has the expression:

in the formula, g (x)_k，u_k) For the current time voltage (model prediction), r₀As an initial value of the total resistance, α_kAs the rate of change of the total resistance, i_kThe current value at the present moment.

5. The method for predicting the remaining life of the fuel cell based on the adaptive extended kalman filter according to claim 1, wherein the expression of the adaptive extended kalman filter algorithm is as follows:

x_k+1＝Fx_k|k+w_k

x_k＝[α_kβ_k]^T

y_k＝g(x_k，u_k)+v_k

P(w)～N(0，Q)

P(v)～N(0，R)

in the formula, x_kIs state, u_kTo input, y_kFor output, F is the state transition matrix of the system, T_sIs a sampling time, x_k|kIs a state matrix of the system, w_kFor systematic error noise, α_kAs the rate of change of the total resistance, beta_kIs a constant of rate of change, v_kTo measure error noise, g (x)_k，u_k) For the voltage (model prediction value) at the current moment, P (w) is a probability function of a system error, Q is a system noise covariance matrix, P (v) is a probability function of a measurement error, and R is a measurement noise covariance matrix;

the time updating expression of the self-adaptive extended Kalman filtering algorithm is as follows:

x_k|k-1＝Fx_k-1|k-1

P_k|k-1＝FP_k-1|k-1F^T+Q

in the formula, x_k|k-1Is a predicted value, x, of the system state at the next time_k-1|k-1As the current timeSystem state of (1), P_k|k-1Is x_k|k-1Corresponding covariance, P_k-1|k-1Is x_k-1|k-1A corresponding covariance;

the measurement updating expression of the self-adaptive extended Kalman filtering algorithm is as follows:

P_k|k＝(I-K_kH_k)P_k|k-1

x_k|k＝x_k|k-1+K_k(V_stk-g(x_k，u_k))

in the formula, K_kAs Kalman gain, H_kIs a Jacobian matrix, x, corresponding to an observation equation in an adaptive extended Kalman filtering algorithm_k|k-1Is the system state, V_stkThe voltage at the current moment (actual measurement value);

the covariance adaptive updating expression of the adaptive extended Kalman filtering algorithm is as follows:

v_k＝V_stk-H_kx_k

in the formula (I), the compound is shown in the specification,

when the sampling window is NEstimation of innovation residual covariance, N is the length of the sampling window, j₀Is the starting time of sampling, k is the current time of sampling, v_jFor the current residual sequence, Q_kFor the updated system noise covariance matrix, R_kThe noise covariance matrix is measured for the updated.

6. The method for predicting the remaining life of the fuel cell based on the adaptive extended kalman filter according to claim 1, wherein in the step of calculating the total attenuation rate, the working conditions include a load change working condition, a start-stop working condition, a low-power load working condition and a high-power load working condition;

the computational expression of the total decay rate of the fuel cell is:

total decay rate ═ V (d)₁g₁+d₂g₂+d₃g₃+d₄g₄)

Where V is the average monolithic voltage estimate, d₁Is the rate of decline of the load change condition, g₁Time-weighted coefficient of load variation behavior, d₂Degradation rate for start-stop conditions, g₂Time weight coefficient for start-stop conditions, d₃The rate of decay, g, for low power load conditions₃Time weighting factor for low power load conditions, d₄Is the degradation rate of the high power load condition, g₄The time weight coefficient of the working condition of the high-power load is shown.

7. The method for predicting the remaining life of the fuel cell based on the adaptive extended kalman filter according to claim 1, wherein in the step of calculating the environmental factor, the calculation expression of the environmental factor is as follows:

in the formula, k_t+1Is the environmental factor, k, at time t +1_tIs the environmental factor at the time of t,

is the average monolithic voltage estimate, V, at time t +1_t+1Is the average monolithic voltage actual value at time t + 1.

8. The fuel cell remaining life prediction method based on the adaptive extended kalman filter according to claim 7, wherein the initial value of the environmental factor is in a range of 1 to 1.2.

9. The method for predicting the remaining life of the fuel cell based on the adaptive extended kalman filter according to claim 1, wherein in the step of predicting the remaining life, the remaining life calculation formula is as follows:

in the formula, T is the remaining service life of the fuel cell at the current time, Δ V is the difference between the average monolithic voltage estimate at the current time and the average monolithic voltage estimate at the end of the life, k is the environmental factor at the current time, V is the average monolithic voltage estimate at the current time, d is the decay rate under each working condition, and g is the time ratio under each working condition.

10. The method of claim 9, wherein the criterion of the end of life is a time point when the average cell voltage value of the fuel cell decays to 90% of the initial value of the average cell voltage.

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