Method for predicting residual life of fuel cell

Abstract

The invention provides a method for predicting the residual life of a fuel cell, which belongs to the technical field of fuel cells, and comprises the following steps: carrying out data preprocessing on collected fuel cell operation time-voltage data to obtain output voltage data of a time sequence; introducing the verified EIS data, and further analyzing and extracting attenuation characteristic parameters of the fuel cell through relaxation time distribution; analyzing a peak value and a frequency of relaxation time distribution analysis and a Pearson's correlation coefficient of output voltage data, distributing a weight, performing nonlinear fitting on a recession characteristic parameter, and establishing a time-frequency health index; constructing a fuel cell attenuation model, and performing optimization training; the attenuation characteristic parameters and the output voltage data are used as input and are sent into the fuel cell attenuation model after optimization training, and the residual life of the fuel cell is predicted and output. The defect that a conventional prediction method based on data driving cannot be suitable for fuel cell attenuation prediction is overcome, and the attenuation process can be quantitatively analyzed.

Description

Technical Field

[0001] The present invention relates to the technical field of fuel cells, and in particular to a method for predicting the remaining life of a fuel cell. Background Art

[0002] As one of the key technologies in the hydrogen energy industry, proton exchange membrane fuel cells (PEMFCs) are gradually emerging as an ideal alternative to traditional power generation technologies due to their excellent high efficiency and extremely low emission characteristics. The degradation prediction of proton exchange membrane fuel cells can provide a scientific basis for the internal state observation and maintenance of fuel cells. The degradation process of fuel cells is a multi-dimensional complex process involving physics, chemistry, and electrochemistry, and the degradation processes of different components of the battery have different degrees of influence on the degradation of PEMFCs. Such as irreversible degradation such as catalyst agglomeration and carbon corrosion; reversible degradation such as flooding, hydrogen crossover, and insufficient gas supply. Among them, irreversible attenuation such as carbon corrosion significantly affects the distribution and structural integrity of the catalyst in the catalytic layer, resulting in blocked mass transfer, changing the pore properties, and reducing the hydrophobicity. Reversible attenuation is a recoverable voltage drop caused by improper experimental operation and can be restored by changing experimental conditions, etc. Therefore, ensuring that the proton exchange membrane fuel cell is in a healthy state is crucial for continuous and stable operation.

[0003] Existing data-driven prediction methods are mostly point predictions and cannot comprehensively capture the volatility and uncertainty in the attenuation process. To obtain accurate prediction results, these methods usually require a large amount of training data, which may be difficult to meet in practical applications. In the case of limited data, these methods may not be able to effectively perform attenuation prediction, limiting their application in practical scenarios. In addition, existing data-driven methods rarely can explain the mechanism of the attenuation process and cannot quantitatively analyze the attenuation process.

[0004] Therefore, it is very necessary to provide a method for predicting the remaining life of a fuel cell, which can quantitatively analyze the attenuation process in terms of the mechanism of the attenuation process, can perform high-precision testing in a short training time, and can measure the volatility and uncertainty of the attenuation. Summary of the Invention

[0005] In view of this, the present invention proposes a method for predicting the remaining life of a fuel cell that constructs a high-order time-frequency health index to improve the accuracy of life prediction and involves a quantile-based bidirectional long short-term memory network to achieve multi-interval prediction, thereby reducing the uncertainty of life prediction.

[0006] The technical solution of the present invention is implemented as follows: The present invention provides a method for predicting the remaining life of a fuel cell, including the following steps:

[0007] S1: preprocessing the collected time-voltage data of the fuel cell operation to obtain output voltage data of the time series;

[0008] S2: Introduce the verified EIS data, and further extract the decay characteristic parameters of the fuel cell through relaxation time distribution analysis; analyze the Pearson correlation coefficient of the peak value, frequency and output voltage data of the relaxation time distribution analysis, assign weights according to the Pearson correlation coefficient, and perform nonlinear fitting on the decay characteristic parameters to establish a time-frequency health index;

[0009] S3: Build a fuel cell attenuation model and perform optimization training;

[0010] S4: Use the attenuation characteristic parameters and output voltage data as inputs to the optimized and trained fuel cell attenuation model to predict the remaining life of the output fuel cell.

[0011] On the basis of the above technical scheme, preferably, the data preprocessing described in step S1 is to perform Gaussian filtering on the collected time-voltage data of the fuel cell operation to eliminate abnormal data: the filter width of the Gaussian filter is set to ±3σ, σ is the standard deviation of the time-voltage data, and the abnormal data outside the Gaussian distribution curve of the time-voltage data is eliminated; through the cubic interpolation function, a polynomial is constructed to smoothly connect the time-voltage data before and after the abnormal data, and the abnormal data at the eliminated position is filled to obtain a data set of the processed time series voltage data, and the data set is normalized according to the Min-Max method and converted to [0,1] as the output voltage data of the time series.

[0012] Preferably, the introduced verified EIS data in step S2 is to verify the Kramers-Kronig relationship of the electrochemical impedance spectroscopy EIS data obtained in the experiment, and the electrochemical impedance satisfies the following constraints:

[0013] Where ω is the actual frequency of the EIS data, ω' is the integral variable, and Z Re (ω) is the real part of the impedance spectrum, Z Im (ω) is the imaginary part of the impedance spectrum; errors in EIS data are detected and corrected through verification.

[0014] Further preferably, the further extraction of the attenuation characteristic parameter of the fuel cell by relaxation time distribution analysis in step S2 is to perform relaxation time distribution analysis DRT on the verified EIS data, and quantitatively analyze the attenuation process of the proton exchange membrane fuel cell using the corresponding changes in the peak value and the number of peak values ​​of the relaxation time distribution analysis, and the expression is: Where Z DRT is the total impedance, R ∞is the ohmic internal resistance, γ(lnτ) is a distribution function describing the relaxation time characteristics, τ is the relaxation time, I is the imaginary unit, and f is the characteristic frequency;

[0015] The discretization process of the regularization function for the data set is expressed as a Dirac distribution centered on a finite number of relaxation time characteristics, and the discretization formula is expressed as: where x k is the first weight coefficient; τ k is the time corresponding to the peak representing the relaxation time distribution analysis, which determines the position of the Dirac function; δ(lnτ - lnτ k ) is the expression of the Dirac function; M represents the number of peaks, k = 1, 2,..., M; Using the peaks and frequency changes of the relaxation time distribution, the peak frequency and peak data are extracted as the fuel cell degradation characteristic parameters.

[0016] More preferably, step S2 further includes optimizing the discretization process of the regularization function using a radial basis function, and the optimization expression is; where φ u (|lnτ - lnτ k |) is a kernel function with a central time scale of τ k and a shape parameter of u.

[0017] Further preferably, in step S2, the weights are assigned according to the Pearson correlation coefficient, and the degradation characteristic parameters are non-linearly fitted to establish a time-frequency health index. The time-frequency health index HI is constructed, and the expression is: i = arg max[R 2 (HI)], HI = β0 + β1U + β2U 2 +... + β i U i , where α 1.1 , α 2.1 ,..., α n.1 are the weights of the frequencies, and α 1.2 , α 2.2 ,..., α n.2 are the weights of the fuel cell output power; f1, f2,..., f n and P1, P2,..., P n are the peak frequencies and peak data obtained by performing a relaxation time distribution analysis DRT on the verified EIS data, respectively; i represents the order of the health index; β0, β1, β2,..., β i represent the polynomial coefficients of the health index; U represents the output voltage data of the time series; By comparing the fitting degrees R 2, determine the polynomial coefficients of the health indicators; analyze the linear relationship between the peak frequency and peak data obtained by the relaxation time distribution analysis DRT through the Pearson correlation coefficient and the output voltage data of the time series, and determine the corresponding weights α of the fuel cell decay characteristic parameters 1.1 , α 2.1 ,..., α n.1 and α 1.2 , α 2.2 ,..., α n.2 .

[0018] Further preferably, the content of step S3 is to construct a fuel cell decay model based on a quantile regression-based bidirectional long short-term memory network, use the time-frequency health indicator HI corresponding to the fuel cell decay characteristic parameters as the input of the fuel cell decay model, divide the normalized data set according to time sequence, divide the data set into two parts in chronological order, the first part is used as the training set, and the second part is used as the test set; call the hippopotamus optimization algorithm to optimize the hyperparameters of the fuel cell decay model, and the hyperparameters include the number of input and output nodes, the size of each batch, hidden units, the maximum number of training rounds, and the learning rate; traverse different quantiles to construct a quantile regression layer, and construct a bidirectional long short-term memory network BiLSTM layer by layer; use the hippopotamus optimization algorithm to adjust the parameters of the fuel cell decay model during the training of the neural network;

[0019] The process of quantile regression is as follows:

[0020] Assume that the input independent variable is X = [x1, x2,..., x N , the dependent variable Y = [y1, y2,..., y N , N is the total number of samples, and the quantile regression is expressed as: Q y (T|X) = Xβ(T), where Q y (T|X) is the predicted value of the conditional quantile at the quantile T, β(T) is the regression coefficient corresponding to the quantile, and the quantile regression obtains the regression coefficient β(T) by minimizing the quantile loss function. The loss function of the quantile is expressed as where v = Y - Xβ(T) is the error between the predicted value and the true value;

[0021] Construct a prediction interval according to the multiple predicted values output by the dynamic quantile; then start the training of the fuel cell decay model, save the trained fuel cell decay model through the output sequence of the bidirectional long short-term memory network BiLSTM, and obtain different prediction results according to different quantiles.

[0022] Further preferably, during the training process, the Hippopotamus Optimization Algorithm is used to adjust the parameters of the fuel cell degradation model. Specifically, the fitness function of the Bidirectional Long Short-Term Memory Network (BiLSTM) is replaced with: Fit HO = K(∑loss QR + MSE), where Fit HO represents the fitness function of the Hippopotamus Optimization Algorithm; ∑loss QR represents the total quantile loss; MSE represents the prediction error; K represents the adaptive weight allocation function, which minimizes the fitness function Fit HO .

[0023] Further preferably, multiple predicted values are output according to the dynamic quantiles to construct interval prediction. Specifically, Q y (T|X,t) = w(t)·Q y (T all |X) + [1 - w(t)]·Q y (T local |X), where Q y (T|X,t) is the constructed interval prediction; Q y (T all |X) is the predicted value of the conditional quantile at the global quantile T all . The value range of the global quantile is T all ∈[0.02, 0.98], and the step size of each adjustment is 0.05; β(T all ) is the regression coefficient corresponding to the global quantile; w(t) is a function based on the operating conditions; Q y (T local |X) is the predicted value of the conditional quantile at the local quantile T local ; the global quantile T all represents the uncertainty under all data. The local quantile T local including local constraint conditions is introduced to realize the uncertainty analysis under local constraint conditions;

[0024] The local quantile T local including local constraint conditions is first defined as the load state of the fuel cell, including: when the output power of the fuel cell is 0, it represents the fuel cell is unloaded; when the output power of the fuel cell is in the range of (0, 15%) of the rated output power, it represents the fuel cell is lightly loaded; when the output power of the fuel cell is in the range of [15%, 90%] of the rated output power, it represents the fuel cell is normally loaded; when the output power of the fuel cell is in the range of (90%, 120%) of the rated output power, it represents the fuel cell is heavily loaded; Given where t0 is the designed life of the fuel cell, t1 is the cumulative working duration of the fuel cell under light load, t2 is the cumulative working duration of the fuel cell with the cumulative rated output power, and t3 is the cumulative working duration of the fuel cell under heavy load.

[0025] Further preferably, for predicting the remaining life of the fuel cell in step S4, the prediction results output by the optimized and trained fuel cell degradation model are integrated into a matrix, the maximum and minimum values of the prediction results are found, the median of the prediction result interval is calculated, and the median is used as the predicted value for comparison. Specifically, the remaining life is estimated using the RUL formula: Error is used to measure the remaining useful life RUL of the fuel cell prediction pred and the actual remaining useful life RUL of the fuel cell actual The relative error between them, the remaining useful life RUL of the fuel cell prediction pred is calculated by the following formula: lifetime represents an approximation of the remaining life of the fuel cell, H represents the total number of approximations of the remaining life of the fuel cell, h = 1, 2,..., H, and the prediction interval coverage probability PICP is: where δ t is the indicator function, y t represents the actual remaining life, and are the upper and lower limits of the prediction interval respectively; the prediction interval normalized average width PINAW is where R is the scale factor.

[0026] A method for predicting the remaining life of a fuel cell provided by the present invention has the following beneficial effects compared with the prior art:

[0027] (1) The present invention provides a method for preprocessing the time-voltage data of the fuel cell operation into a data set, then verifying the electrochemical impedance spectroscopy EIS data, performing relaxation time distribution analysis DRT on the verified EIS data, quantitatively analyzing the degradation process of the proton exchange membrane fuel cell by using the corresponding changes in the DRT peaks and the number of peaks, taking the relaxation time distribution peak and frequency changes in advance as the fuel cell degradation characteristic parameters, establishing the corresponding relationship between the time-voltage data and the fuel cell degradation characteristic parameters, and thus fitting the time-frequency health index of the corresponding order as the input of the fuel cell degradation model;

[0028] (2) The fuel cell degradation model is constructed by a bidirectional long short-term memory network based on quantile regression. During the training process, the hippopotamus optimization algorithm is used for parameter tuning, considering the global quantile and the local quantile including local constraint conditions, analyzing the uncertainty under specific conditions, and reducing the uncertainty of life prediction. Description of the Drawings

[0029] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required for the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can also be obtained based on these drawings.

[0030] Figure 1 It is a step flow chart of a method for predicting the remaining life of a fuel cell according to the present invention;

[0031] Figure 2 It is a peak value diagram of the relaxation time distribution of a method for predicting the remaining life of a fuel cell according to the present invention;

[0032] Figure 3 It is a comparison diagram of fuel cell predictions under the conditions of an embodiment of a method for predicting the remaining life of a fuel cell according to the present invention. Specific embodiments

[0033] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention.

[0034] In the case of limited data, data-driven prediction methods may not be able to effectively perform attenuation prediction, which limits their application in actual scenarios. In view of this, as Figure 1 shown, the present invention provides a method for predicting the remaining life of a fuel cell, including the following steps:

[0035] S1: Preprocess the time-voltage data of the fuel cell operation collected to obtain the output voltage data of the time series.

[0036] The data preprocessing described in step S1 is to perform Gaussian filtering on the collected time-voltage data of the fuel cell operation to remove abnormal data: set the filtering width of Gaussian filtering to ±3σ, where σ is the standard deviation of the time-voltage data, and remove the abnormal data outside the Gaussian distribution curve of the time-voltage data; through a cubic interpolation function, construct a polynomial to smoothly connect the time-voltage data before and after the abnormal data, and fill in the abnormal data at the removed positions to obtain a dataset of the processed time series voltage data, and perform normalization processing on the dataset according to the Min-Max method, converting it to between [0,1] as the output voltage data of the time series.

[0037] The Min - Max method is used for normalization. The current data sample A in the dataset is normalized using the following formula: A' is the normalized data, and A max and A min are the maximum and minimum values in the dataset respectively. The normalization process can simplify the computational complexity of later life prediction.

[0038] S2: Introduce the verified EIS data, and further extract the attenuation characteristic parameters of the fuel cell through relaxation time distribution analysis; analyze the Pearson correlation coefficients of the peak, frequency, and output voltage data of the relaxation time distribution analysis, assign weights according to the Pearson correlation coefficients, and perform non - linear fitting on the decay characteristic parameters to establish a time - frequency health index.

[0039] Specifically, step S2 includes the following content:

[0040] S21: Introduce the verified EIS data. It is to verify the Kramers - Kronig relationship for the electrochemical impedance spectrum EIS data obtained from experiments. The electrochemical impedance satisfies the following constraints:

[0041] where ω is the actual frequency of the EIS data, ω' is the integration variable, Z Re (ω) is the real part of the impedance spectrum, and Z Im (ω) is the imaginary part of the impedance spectrum; errors in the EIS data are detected and corrected through verification. The Kramers - Kronig relationship verification can ensure the causality and linear response characteristics of the impedance data, thereby effectively monitoring and correcting errors in the electrochemical impedance spectrum EIS data and enhancing the credibility of this data.

[0042] S22: Further extract the attenuation characteristic parameters of the fuel cell through relaxation time distribution analysis. It is to perform relaxation time distribution analysis DRT on the verified EIS data, and quantitatively analyze the attenuation process of the proton exchange membrane fuel cell using the corresponding changes in the peak and the number of peaks of the relaxation time distribution analysis. The expression is: where Z DRT is the total impedance, R ∞ is the ohmic internal resistance, γ(lnτ) is the distribution function describing the relaxation time characteristics, τ is the relaxation time, I is the imaginary unit, and f is the characteristic frequency; this process can be understood as an equivalent circuit model consisting of the ohmic internal resistance and the sum of infinitely - series RC elements. The relaxation time distribution diagram is obtained by solving the distribution function γ(lnτ) corresponding to the relaxation time τ.

[0043] The discretization process of the regularization function for the dataset is expressed as a Dirac distribution centered on a finite number of relaxation time characteristics. The discretization formula is expressed as: where x kis the first weight coefficient; τ k is the time corresponding to the peak of the relaxation time distribution analysis, which determines the position of the Dirac function; δ(lnτ - lnτ k ) is the expression of the Dirac function; M represents the number of peaks, k = 1, 2,..., M; the larger M is, the higher the accuracy. Using the peaks and frequency changes of the relaxation time distribution, the peak frequency and peak data are extracted as the fuel cell attenuation characteristic parameters. Introduce a regularization parameter to solve the optimization problem. If the relaxation time distribution function is too smooth or oscillates, then readjust the regularization parameter.

[0044] Step S22 also includes further optimizing the discretization process of the regularization function using a radial basis function, and the optimization expression is; where φ u (|lnτ - lnτ k |) is a kernel function with a central time scale of τ k and a shape parameter of u.

[0045] Step S23: Assign weights according to the Pearson correlation coefficient and perform non-linear fitting on the decay characteristic parameters to establish a time-frequency health index. Specifically, the content is to construct a high-order time-frequency health index HI expression as: i = argmax[R 2 (HI)], HI = β0 + β1U + β2U 2 +... + β i U i , where α 1.1 、α 2.1 、...、α n.1 are the weights of the frequency, α 1.2 、α 2.2 、...、α n.2 are the weights of the fuel cell output power; f1, f2,..., f n and P1, P2,..., P n are the peak frequencies and peak data obtained from the relaxation time distribution analysis DRT of the verified EIS data respectively; i represents the order of the health index; β0, β1, β2,..., β i represent the polynomial coefficients of the health index; U represents the output voltage data of the time series; by comparing the fitting degree R 2 at different orders, determine the polynomial coefficients of the health index; by analyzing the linear relationship between the peak frequencies and peak data obtained from the relaxation time distribution analysis DRT and the output voltage data of the time series through the Pearson correlation coefficient, determine the corresponding weights α 1.1 、α 2.1 、...、α n.1 and α1.2 、 α 2.2 、...、 α n.2 。 The fuel cell degradation characteristic parameters can be used as the input of the subsequent fuel cell degradation model. The reason for fitting is that the order of the output voltage data U of the time series is unknown before fitting.

[0046] S3: Construct a fuel cell degradation model and perform optimization training.

[0047] The content of step S3 is to construct a fuel cell degradation model based on a two-way long short-term memory network with quantile regression, use the time-frequency health index HI corresponding to the weights of the obtained fuel cell degradation characteristic parameters as the input of the fuel cell degradation model, divide the normalized data set according to time sequence, divide the data set into two parts in chronological order, the first part as the training set and the second part as the test set; call the hippopotamus optimization algorithm to optimize the hyperparameters of the fuel cell degradation model, and the hyperparameters include the number of input and output nodes, the size of each batch, the hidden units, the maximum number of training epochs, and the learning rate; traverse different quantiles to construct a quantile regression layer, and construct a two-way long short-term memory network BiLSTM layer by layer; use the hippopotamus optimization algorithm to adjust the parameters of the fuel cell degradation model during the training of the neural network;

[0048] The process of quantile regression is as follows:

[0049] Assume that the input independent variable is X = [x1, x2,..., x N , the dependent variable Y = [y1, y2,..., y N , N is the total number of samples, and the quantile regression is expressed as: Q y (T|X) = Xβ(T), where Q y (T|X) is the predicted value of the conditional quantile at quantile T, β(T) is the regression coefficient corresponding to the quantile, and the quantile regression obtains the regression coefficient β(T) by minimizing the quantile loss function. The loss function of the quantile is expressed as where v = Y - Xβ(T) is the error between the predicted value and the true value;

[0050] Construct a prediction interval according to the multiple predicted values output by the dynamic quantile; then start the training of the fuel cell degradation model, save the trained fuel cell degradation model through the output sequence of the two-way long short-term memory network BiLSTM, and output different prediction results according to different quantiles.

[0051] Among them, during the training process, the hippopotamus optimization algorithm is used to adjust the parameters of the fuel cell degradation model. Specifically, the fitness function of the two-way long short-term memory network BiLSTM is replaced by: Fit HO = K(∑lossQR + MSE), where Fit HO represents the fitness function of the hippopotamus optimization algorithm; ∑loss QR represents all quantile losses; MSE represents the prediction error; K represents the adaptive weight allocation function that minimizes the fitness function Fit HO to the minimum.

[0052] Among them, interval prediction is constructed by outputting multiple prediction values according to dynamic quantiles. The specific content is Q y (T|X,t) = w(t)·Q y (T all |X) + [1 - w(t)]·Q y (T local |X), where Q y (T|X,t) is the constructed interval prediction; Q y (T all |X) is the predicted value of the conditional quantile at the global quantile T all . The value range of the global quantile is T all ∈[0.02, 0.98], and the step size of each adjustment is 0.05; β(T all ) is the regression coefficient corresponding to the global quantile; w(t) is a function based on operating conditions; Q y (T local |X) is the predicted value of the conditional quantile at the local quantile T local ; the global quantile T all represents the uncertainty under all data. The local quantile T local containing local constraint conditions is introduced to realize the uncertainty analysis under local constraint conditions.

[0053] Specifically, the local quantile T local containing local constraint conditions is defined as follows: the load-carrying state of the fuel cell is first defined as follows: when the output power of the fuel cell is 0, it represents the fuel cell in an unloaded state; when the output power of the fuel cell is in the range of (0, 15%) of the rated output power, it represents the fuel cell in a low-load state; when the output power of the fuel cell is in the range of [15%, 90%] of the rated output power, it represents the fuel cell in a normal load state; when the output power of the fuel cell is in the range of (90%, 120%) of the rated output power, it represents the fuel cell in a high-load state; given where t0 is the designed life of the fuel cell, t1 is the cumulative working duration of the fuel cell under light load, t2 is the cumulative working duration of the fuel cell at the cumulative rated output power, and t3 is the cumulative working duration of the fuel cell under high load. It can be seen that the local quantile T localIts value has a direct relationship with the cumulative working duration under the fuel cell load conditions. When the cumulative operating time of the fuel cell is combined with the corresponding life reduction weights and weighted and summed, the local quantile T of the corresponding working duration is obtained. local 。

[0054] S4: Use the attenuation characteristic parameters and output voltage data as inputs and send them into the optimized and trained fuel cell attenuation model to predict and output the remaining life of the fuel cell.

[0055] Specifically, the prediction results output by the optimized and trained fuel cell attenuation model are integrated into a matrix, the maximum and minimum values of the prediction results are found, the median of the prediction result interval is calculated, and the median is used as the predicted value for comparison. The specific content is to use the RUL formula for life estimation: Error is used to measure the remaining useful life RUL of the fuel cell prediction pred and the actual remaining useful life RUL of the fuel cell actual The relative error between them, the remaining useful life RUL of the fuel cell prediction pred is calculated by the following formula: lifetime represents an approximation of the remaining life of the fuel cell. The remaining life of the fuel cell refers to that after the defined attenuation percentage is reached, for example, a 4% decrease. An average value is taken from the data within 5% of the corresponding voltage value after attenuation, and the network training time is deducted to obtain the remaining life of the fuel cell. For example, the initial voltage of the fuel cell is 3.5V, and the current fuel cell voltage drops by 5% as the life stop time for this interval. The life stop time obtained by taking an average value of the life data within 5% of the corresponding voltage drop is 888h, but the network training time is 400h. Then its remaining life time is 488h. The purpose of the fuel cell prediction remaining life formula is to reduce errors during prediction because it is possible that the overall curve is good and the accuracy is high, but the prediction effect at this point is not ideal. Therefore, the average value within the neighborhood range is used as the life stop time. H represents the total number of approximations of the remaining life of the fuel cell, h = 1, 2,..., H, and the prediction interval coverage probability PICP is: where δ t is the indicator function, y t represents the actual remaining life, and are the upper and lower limits of the prediction interval respectively; the prediction interval normalized average width PINAW is where R is the scale factor. By introducing the prediction interval coverage probability PICP and the prediction interval normalized average width PINAW, the uncertainty of the fusion prediction interval prediction method is evaluated.

[0056] The following combines specific embodiments to supplement and explain the actual process of the present invention.

[0057] 1. Data preprocessing:

[0058] In the IEEE PHM 2014 dataset, the static operating condition dataset and the dynamic operating condition dataset are respectively identified as FC1 and FC2. In this study, the EIS data at 0h, 48h, 185h, 348h, 515h, 658h, 823h, 991h in the FC1 dataset and 0h, 35h, 182h, 343h, 515h, 666h, 830h, 1016h in the FC2 dataset are selected for analysis. To reduce the interference of abnormal data, the smooth function is used to preprocess the data. To ensure the physical consistency and integrity of the processed data, the Kramers-Kronig relationship is used for verification.

[0059] 2. Relaxation time distribution analysis DRT

[0060] For the EIS data of the static operating condition dataset FC1 and the dynamic operating condition dataset FC2, discrete calculations are performed and approximated as Dirac distributions centered on a finite number of relaxation time characteristics. As described in the previous step S2, the radial basis functions (RBFs) are used to optimize the discretization process of the appropriate function, improve the convergence speed, and reduce the experimental error. Defining RBFs over the entire frequency spectrum can extend the DRT interval from to the relaxation time 0 ≤ τ ≤ ∞, f max and f min are respectively the maximum and minimum values of the peak frequencies obtained from the relaxation time distribution analysis DRT. Therefore, the shape and width of the RBF may change with the change of the relaxation time, so that more accurate DRT analysis data can be obtained.

[0061] Solving the relaxation time corresponding function of PEMFC involves an ill-posed problem, and a regularization parameter is introduced for solution. The regularization parameter is reasonably adjusted to find the appropriate degree of regularization to avoid false peaks and error problems. When the regularization parameter is too large, some impedance information will be filtered out, resulting in the relaxation time distribution function being too smooth; when the regularization parameter is small, overfitting occurs during impedance analysis, and oscillations occur in the function solution. The correlation coefficient analysis is performed on the obtained DRT peaks and the frequencies corresponding to the peaks and the voltage parameters to obtain the correlation coefficient between the attenuation parameter and the voltage. The weight is assigned according to the correlation coefficient relationship to nonlinearly fit the attenuation characteristic parameters, and a high-order time-frequency health index HI is established.

[0062] The results are as shown in the appendix Figure 2 As shown, the DRT results of the EIS data of the datasets FC1 and FC2 are shown in the figure. Different peaks represent the impedance relationships at different time scales. The attenuation mechanism of the fuel cell is quantitatively analyzed by analyzing the peak changes and the corresponding frequencies.

[0063] 3. Method Prediction Process

[0064] Take the attenuation characteristic parameters and the output voltage data of the time series as inputs, and simultaneously initialize the network hyperparameters: learning rate, number of input and output nodes, batch size, number of hidden units, maximum number of training epochs, etc. At the same time, set the target quantile of quantile regression. Quantile regression provides richer information than mean regression by estimating different quantiles and can capture the overall shape of the data distribution. Set the MSE as the loss function, and use the hippopotamus optimization algorithm to iteratively adjust the hyperparameters of the bidirectional long short-term memory network (BiLSTM network), including the learning rate, number of hidden units, etc., to find the optimal hyperparameter configuration that minimizes the loss function. Use the preprocessed data to train the network, and output multiple predicted values according to different quantiles to construct interval prediction. Use the mean squared error (MSE), mean absolute error (MAE), PICP, and PINWP to measure the accuracy of attenuation prediction and interval prediction. The results are as Figure 3 shown. The comparison of the accuracy of different comparative interval prediction methods proves that it is feasible to use the fuel cell relaxation time characteristic as the attenuation prediction parameter, and the method has high accuracy.

[0065] The technical effects are as Figure 2 , Figure 3 shown. Figure 2 is the frequency domain feature information,[[]] Figure 3 is the comparison effect diagram of short-term training and normal training. The experimental accuracy and short-term training performance of this prediction method are proved through experiments. Figure 3 The bandwidth in [[ ]] represents the interval prediction range. The following table shows the prediction accuracy and RUL error of different prediction methods. The information in the table shows that the RUL error during short-term training is within 0.5%, and the R 2 coefficient represents the fitting degree of the method. It can be seen that the experimental method has a significant improvement compared with the comparative algorithm. PICP and PINWP are used to measure the interval prediction performance. PICP focuses on the coverage ability of the prediction interval and reflects the reliability of the model; PINWP focuses on the compactness of the prediction interval and reflects the accuracy of the model. It is proved through experiments that it has good performance in measuring uncertainty and volatility in interval prediction.

[0066] As Figure 3 shown in (a) and (b), the training time is 300h,[[]] Figure 3 shown in (c) and (d), the training time is increased to 600h, and the prediction accuracy gradually improves, which conforms to common sense judgment. At the same time, the prediction accuracy of the quantization regression prediction neural network based on DRT degradation is all below 0.009. Among them, the prediction accuracy of the hybrid prediction of the bidirectional long short-term memory network HO-QRBiLSTM combined with the quantile regression - hippopotamus optimization algorithm adopted in this application is the best, and the R under static conditions (FC1) and dynamic conditions (FC2)2 All are above 0.95, and the RMSE errors are 0.0025 and 0.0053 respectively. Comparing PICP and PINWP, HO-QRBiLSTM is closer to the 95% confidence interval in both FC1 and FC2, while PINWP is the smallest. This indicates that HO improves the performance of the fusion prediction method when making interval predictions. Among them, QR-BiLSTM is a bidirectional long short-term memory network based on quantile regression, QR-LSTM is a long short-term memory network based on quantile regression, and QR-GRU is a gated recurrent unit based on quantile regression.

[0067] This embodiment is implemented based on the matlab simulation platform, and the parameters related to the fuel cell in the simulation process are as follows in the table.

[0068]

[0069] The above is only the preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for predicting the remaining life of a fuel cell, characterized in that: The steps include: S1: preprocessing the collected time-voltage data of the fuel cell operation to obtain output voltage data of the time series; S2: Introduce the verified EIS data, and further extract the decay characteristic parameters of the fuel cell through relaxation time distribution analysis; analyze the Pearson correlation coefficient of the peak value, frequency and output voltage data of the relaxation time distribution analysis, assign weights according to the Pearson correlation coefficient, and perform nonlinear fitting on the decay characteristic parameters to establish a time-frequency health index; S3: Build a fuel cell attenuation model and perform optimization training; S4: Use the attenuation characteristic parameters and output voltage data as inputs to the optimized and trained fuel cell attenuation model to predict the remaining life of the output fuel cell.

2. A method for predicting the remaining life of a fuel cell according to claim 1, characterized in that: The data preprocessing described in step S1 is to perform Gaussian filtering on the collected time-voltage data of the fuel cell operation to eliminate abnormal data: the filter width of the Gaussian filter is set to ±3σ, σ is the standard deviation of the time-voltage data, and the abnormal data outside the Gaussian distribution curve of the time-voltage data is eliminated; a polynomial is constructed through a cubic interpolation function to smoothly connect the time-voltage data before and after the abnormal data, and the abnormal data at the eliminated position is filled to obtain a data set of the processed time series voltage data, and the data set is normalized according to the Min-Max method and converted to between [0,1] as the output voltage data of the time series.

3. A method for predicting the remaining life of a fuel cell according to claim 2, characterized in that: The introduced verified EIS data in step S2 is to verify the Kramers-Kronig relationship of the electrochemical impedance spectroscopy EIS data obtained in the experiment, and the electrochemical impedance satisfies the following constraints: Where ω is the actual frequency of the EIS data, ω' is the integral variable, and Z Re (ω) is the real part of the impedance spectrum, Z Im (ω) is the imaginary part of the impedance spectrum; errors in EIS data are detected and corrected through verification.

4. A method for predicting the remaining life of a fuel cell according to claim 3, characterized in that: The further extraction of the fuel cell attenuation characteristic parameter by relaxation time distribution analysis described in step S2 is to perform relaxation time distribution analysis DRT on the verified EIS data, and quantitatively analyze the proton exchange membrane fuel cell attenuation process by using the corresponding changes of the peak value and the number of peak values ​​of the relaxation time distribution analysis, and the expression is: Where Z DRT is the total impedance, R ∞ is the ohmic internal resistance, γ(lnτ) is the distribution function describing the relaxation time characteristics, τ is the relaxation time, I is the imaginary unit, and f is the characteristic frequency; the data set is discretized by the regularization function and expressed as a Dirac distribution centered on a finite number of relaxation time characteristics. The discretization formula is expressed as: where x k is the first weight coefficient; τ k To represent the time corresponding to the peak value of the relaxation time distribution analysis, the position of the Dirac function is determined; δ(lnτ-lnτ k ) is the expression of Dirac function; M represents the number of peaks, k=1, 2, ..., M; using the peak value and frequency changes of relaxation time distribution, the peak frequency and peak data are extracted as the fuel cell attenuation characteristic parameters.

5. A method for predicting the remaining life of a fuel cell according to claim 4, characterized in that: Step S2 also includes optimizing the discretization process of the regularization function using a radial basis function, and the optimization expression is: where φ u (|lnτ-lnτ k |) is a central time scale τ k , a kernel function with shape parameter u.

6. A method for predicting the remaining life of a fuel cell according to claim 4, characterized in that: The method described in step S2, which allocates weights according to the Pearson correlation coefficient and performs nonlinear fitting on the decay characteristic parameters to establish a time-frequency health index, is to construct a time-frequency health index HI, which is expressed as: i=argmax[R 2 (HI)],HI=β0+β1U+β2U 2 +...+β i U i , where α 1.1 , α 2.1 , ..., α n.1 is the frequency weight, α 1.2 , α 2.2 , ..., α n.2 is the weight of the fuel cell output power; f1, f2, ..., f n and P1, P2, ..., P n are the peak frequency and peak data obtained by DRT of the verified EIS data; i represents the order of the health index; β0, β1, β2, ..., β i Represents the health index polynomial coefficient; U represents the output voltage data of the time series; by comparing the degree of fit R at different orders 2 , determine the polynomial coefficients of the health index; analyze the linear relationship between the peak frequency and peak data obtained by DRT and the output voltage data of the time series through the Pearson correlation coefficient analysis of the relaxation time distribution, and determine the corresponding weight α of the fuel cell attenuation characteristic parameter 1.1 , α 2.1 , ..., α n.1 and α 1.2 , α 2.2 , ..., α n.2 .

7. A method for predicting the remaining life of a fuel cell according to claim 6, characterized in that: The content of step S3 is to construct a fuel cell attenuation model based on a bidirectional long short-term memory network of quantile regression, and use the time-frequency health index HI of the corresponding weight of the fuel cell attenuation characteristic parameter as the input of the fuel cell attenuation model, divide the normalized data set according to the time sequence, and divide the data set into two parts in chronological order, the first part as a training set, and the second part as a test set; call the Hippo optimization algorithm to optimize the hyperparameters of the fuel cell attenuation model, the hyperparameters include the number of input and output nodes, the size of each batch, the hidden unit, the maximum number of training rounds and the learning rate; traverse different quantiles to construct a quantile regression layer, and construct a bidirectional long short-term memory network BiLSTM by layer; use the Hippo optimization algorithm to adjust the parameters of the fuel cell attenuation model during the training process of the neural network; The prediction interval is constructed based on multiple prediction values ​​outputted according to the dynamic quantile; then the training of the fuel cell attenuation model is started, and the trained fuel cell attenuation model is saved through the output sequence of the bidirectional long short-term memory network BiLSTM, and different prediction results are outputted according to different quantiles.

8. A method for predicting the remaining life of a fuel cell according to claim 7, characterized in that: During the training process, the Hippo optimization algorithm is used to adjust the parameters of the fuel cell attenuation model. Specifically, the fitness function of the bidirectional long short-term memory network BiLSTM is replaced by: Fit HO =K(∑loss QR +MSE), where Fit HO Represents the fitness function of the Hippo optimization algorithm; ∑loss QR represents the total quantile loss; MSE represents the prediction error; K represents the adaptive weight distribution function, making the fitness function Fit HO Minimum.

9. A method for predicting the remaining life of a fuel cell according to claim 7, characterized in that: Output multiple prediction values ​​based on dynamic quantiles to construct interval predictions. The specific content is Q y (T|X,t)=w(t)·Q y (T all |X)+[1-w(t)]·Q y (T local |X), where Q y (T|X,t) is the constructed interval prediction; Q y (T all |X) is the conditional quantile in the global quantile T all The predicted value at , the global quantile range is T all ∈[0.02,0.98], each adjustment step is 0.05; β(T all ) is the regression coefficient corresponding to the global quantile; w(t) is a function based on the operating conditions; Q y (T local |X) is the conditional quantile in the local quantile T local The predicted value at; global quantile T all Represents the uncertainty under all data, and introduces the local quantile T containing local constraints local , realize uncertainty analysis under local constraints; The local quantile T containing local constraints local , is to first define the fuel cell load state, including: when the fuel cell output power is 0, it represents the fuel cell no-load; when the fuel cell output power is in the interval of (0, 15%) of the rated output power, it represents the fuel cell low load; when the fuel cell output power is in the interval of [15%, 90%] of the rated output power, it represents the fuel cell normal load; when the fuel cell output power is in the interval of (90%, 120%) of the rated output power, it represents the fuel cell high load; given Among them, t0 is the design life of the fuel cell, t1 is the cumulative working time of the fuel cell at light load, t2 is the cumulative working time of the fuel cell at the rated output power, and t3 is the cumulative working time of the fuel cell at high load.

10. A method for predicting the remaining life of a fuel cell according to claim 7, characterized in that: The prediction and output of the remaining life of the fuel cell described in step S4 is to integrate the prediction results output by the optimized and trained fuel cell attenuation model into a matrix, find the maximum and minimum values ​​of the prediction results, calculate the median of the prediction result interval, and use the median as the prediction value for comparison. Specifically, the RUL formula is used to estimate the life: Error is used to measure the remaining life (RUL) of the fuel cell prediction pred The actual remaining life of the fuel cell RUL actual The relative error between the predicted remaining life (RUL) of the fuel cell pred Calculated by the following formula: Lifetime represents the approximate value of the remaining life of the fuel cell, H represents the total number of approximate values ​​of the remaining life of the fuel cell, h = 1, 2, ..., H, and the prediction interval coverage rate PICP is: where δ t is the indicator function, y t Indicates the actual remaining life, and are the upper and lower limits of the prediction interval respectively; The normalized average width of the prediction interval PINAW is Where R is the scale factor.

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