A method for predicting remaining life of fuel cells based on robust model

Abstract

The present invention discloses a method for predicting the remaining life of a fuel cell based on a robust model. First, an approximate Markov blanket method based on maximum information coefficient and fused Lasso is used to perform feature selection on the original data. Second, a local mean decomposition method is used to perform noise reduction on the data after feature selection. The continuous root mean square error is calculated to determine the demarcation point of high and low frequency components. The chaotic reverse learning strategy and the golden sine strategy are used to improve the slime mold algorithm to obtain ISMA. Then, the parameters of the robust weighted least squares model are optimized using ISMA. Then, the optimized RWLS is used to model the low frequency components and the robust integrated deep random vector function link network model is used to model the complex high frequency components. Finally, the test data is input into the model, and the prediction results are stacked and reorganized to obtain the final prediction result of the fuel cell life. The present invention can effectively improve the accuracy of the fuel cell life prediction model and also provide a reliable basis for the prediction of the fuel cell life.

Description

Technical Field

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

[0002] The global energy structure is currently dominated by fossil fuels. However, with the gradual depletion of fossil energy and the increasing environmental problems, the development of new energy has become crucial. In order to save energy, reduce emissions and alleviate energy shortages, the development of new energy has become more and more extensive. With the use of fuel cells, each component will age to a certain extent over time, resulting in a decrease in life. Therefore, proper system maintenance is essential to improve the durability, long-term safety and reliability of fuel cells, so the life prediction of fuel cells has become crucial.

[0003] In recent years, fuel cell life prediction has become an important research topic with practical application value. The existing fuel cell prediction methods cannot effectively extract and select the collected fuel cell data, which will affect the accuracy of the model's remaining life prediction; the diversity of fuel cell data often interferes with the model's prediction, so the use of targeted modeling methods for different data can improve the reliability of fuel cell remaining life prediction. In order to improve the accuracy of fuel cell life prediction, it is necessary to establish a prediction method that is suitable for fuel cell characteristics and has high prediction accuracy. Summary of the invention

[0004] Purpose of the invention: In view of the problems existing in the prior art, the present invention provides a method for predicting the remaining life of a fuel cell based on a robust model, which can improve the accuracy of the fuel cell life prediction model.

[0005] Technical solution: The present invention provides a method for predicting the remaining life of a fuel cell based on a robust model, comprising the following steps:

[0006] (1) Using the pre-acquired fuel cell life prediction related data as input variables, the approximate Markov blanket method based on the maximum information coefficient and fused Lasso is used for feature selection, and the capacitance data closely related to the remaining life of the fuel cell is selected as the output variable;

[0007] (2) For the noise reduction method using local mean decomposition, the capacitance data is decomposed into several low-frequency product function components and residuals, and the continuous root mean square error is calculated as the dividing point between the high-frequency component and the low-frequency component;

[0008] (3) The slime mold algorithm SMA is improved by using a chaotic reverse learning strategy to improve the population initialization of the SMA. The golden sine is integrated into the food surrounding stage of the slime mold algorithm to obtain the ISMA algorithm.

[0009] (4) The ISMA algorithm is used to optimize the penalty coefficient γ and kernel function parameter δ of the robust weighted least squares model RWLS, and at the same time, a model is built for the low-frequency components obtained after decomposition in step (2);

[0010] (5) The robust integrated deep random vector function link network model ORedRVFL is used to model the high-frequency components obtained after decomposition in step (2);

[0011] (6) The training sets are input into the corresponding two prediction models for prediction, and the prediction results of the two models are stacked to obtain the final prediction result of the fuel cell capacitance. Finally, RMSE and MAE are used as evaluation indicators to judge the reliability of the two models;

[0012] (7) When the predicted value of the fuel cell capacitance obtained in step (6) reaches the failure threshold, the predicted value of the remaining life of the fuel cell is obtained based on the predicted value of the fuel cell capacity.

[0013] Furthermore, the fuel cell life prediction related data described in step (1) includes fuel cell usage time, voltage, current, temperature, output power and capacitance.

[0014] Furthermore, the implementation process of step (1) is as follows:

[0015] (11) One-stage correlation analysis, the correlation information formula is:

[0016]

[0017] Q = {q i ,i=1,2,…,n}、W={w i , i=1,2,…,n} is a data set; q and w are two-dimensional random variables; p(q,w) is the joint probability density function of q and w; p(q) and p(w) are marginal probability density functions;

[0018] (12) Data set D = {(q i ,w i ),i=1,2,...n}, its maximum information coefficient is:

[0019] EIC(D)=max qw<B(m) {M(D) Q,W}

[0020] The sample size is m; B(m) is the value of the sample size;

[0021] (13) Given a feature set F = {f1,f2,…,f n,c}, the number of features is n, the category is c; between [0,1], for any category c and feature f i The correlation between them is defined as EIC(f i ,c), calculate the correlation EIC (f i ,c), the calculation formula is as follows:

[0022]

[0023] The features with higher correlation scores are more important, and the features are sorted in descending order according to the correlation scores to construct the fuel cell feature group after one stage;

[0024] (14) Two-stage redundancy analysis, select the main element f i , and put it into the most characteristic subset;

[0025] Main element: a feature f i , if and only if no element is f i An approximate Markov blanket of

[0026] (15) According to the concept of approximate Markov blanket, all redundant features with the current main element as the approximate Markov blanket are deleted. The conditional formula is:

[0027] EIC(f i ,R)≥EIC(f j ,R)||EIC(f i ,f j )≥EIC(f j ,R)

[0028] Among them, R is the target variable; f i Yes j The approximate Markov blanket, f j To eliminate redundant features;

[0029] (16) Repeat steps (14) and (15) until there is no principal element in the feature set F. The feature subset consisting of all principal elements is the suboptimal feature subset, in which the correlation between features and categories is high.

[0030] (17) The Lasso method is used to introduce the penalty function L1 norm term on the basis of the loss function, compressing the insignificant regression coefficients to 0 while reducing the excessive compression of important regression coefficients. The specific formula is as follows:

[0031]

[0032] Among them, n is the number of features, m is the number of samples, o is the regression coefficient vector, x is the feature matrix, y is iis the true value of the sample, and α is the degree of compression. After constructing the suboptimal feature subset of the fuel cell by approximating the Markov blanket, the Lasso method is applied to the suboptimal feature subset to iteratively delete the redundant features related to the fuel cell life prediction, and the optimal feature subset for fuel cell life prediction is obtained.

[0033] Furthermore, the implementation process of step (2) is as follows:

[0034] (21) The original signal of the fuel cell is x(t), and the local extreme point g in x(t) is calculated i and the corresponding extreme value x(g i ), then the local mean J i and the local amplitude A i It is expressed as:

[0035]

[0036] The local amplitude and local mean are processed to obtain the local mean function J 11 (t) and the local amplitude function A 11 (t);

[0037] (22) The local mean function J 11 (t) is removed from the original signal x(t):

[0038] H 11 (t) = x(t) - J 11 (t)

[0039] Using the local amplitude function A 11 (t) Solve H 11 (t), there are:

[0040]

[0041] Calculate S 11 (t) Local amplitude function A 12 (t), determine whether it is 1; if not, set S 11 (t) is regarded as the input signal and the local mean function J is calculated 12 (t), and remove J from it 12 (t) thus obtain H 12 (t), and then use A 12 (t) Solve H 12 (t); Repeat the above steps to get the pure FM signal S 1n (t);

[0042] The final local amplitude signal is:

[0043]

[0044] t represents the tth iteration;

[0045] (23) The product of the pure FM signal and the local amplitude signal represents the first product function:

[0046] PF1(t)=A1(t)S 1n (t)

[0047] (24) Remove PF1(t) from the original signal x(t) to obtain a new signal x(t) * , the new signal x(t) * is the smoothed signal; repeat steps (21) to (24) to obtain the monotonic function x k (t) * , stop iteration;

[0048] (25)x(t) is represented by k PFs and a residual x k (t) * The superposition of, that is:

[0049]

[0050] The basis of LMD decomposition is the extreme value of the signal itself, and the corresponding PF is obtained by continuous iteration. The signal is finally decomposed into the residual signal and part of the PF;

[0051] (26) The dividing point between high-frequency and low-frequency components is determined by calculating the continuous root mean square error, and the p value corresponding to the global minimum of CMSE is used as the dividing point between high-frequency and low-frequency components. The formula is as follows:

[0052]

[0053] The fuel cell data after LMD denoising is divided into high-frequency components and low-frequency components.

[0054] Furthermore, the implementation process of step (3) is as follows:

[0055] (31) The chaotic reverse learning strategy is used to initialize the population position of the SMA algorithm. The improved initialization formula is:

[0056]

[0057] P i =rand(0,1)·(LB+UB)

[0058] Among them, y i is a cubic sequence; X i The range is from the lower limit to the upper limit; UB represents the lower position boundary of the slime mold; LB represents the upper position boundary of the slime mold; P i is the reverse solution;

[0059] (32) When the slime mold is approaching food, the position update formula is as follows:

[0060]

[0061] p=tanh|S i -DF|

[0062]

[0063] Where W is the weight of the slime mold algorithm; VB is a random number between [-a, a]; VC is a parameter that decreases linearly from 1 to 0; r is a random number between [0, 1]; X b is the current optimal individual position; X A and X B are two random slime mold individuals; p = tanh|S i -DF| is a parameter that affects the update method of the slime mold position; DF represents the optimal fitness of the current individual; i represents the slime mold individual; S i is the fitness value of the i-th slime mold individual; condition represents the slime molds ranked in the top 50 percentile in fitness; BF and WF represent the currently obtained optimal fitness and worst fitness respectively; SmellIndex represents that the fitness values ​​are sorted in ascending order;

[0064] The calculation formula of a is as follows:

[0065]

[0066] Among them, t max Represents the maximum number of iterations;

[0067] (33) The golden sine division coefficient is introduced into the SMA algorithm to improve the original position update formula. The improved position update formula is as follows:

[0068]

[0069] R1∈(0,2π); R2∈(0,π); X1=-π+(1-π); X2=-π+(τ×2π);

[0070] Among them, X1 and X2 are coefficients calculated by the golden ratio, and τ is the golden section coefficient;

[0071] After two stages of position updates, the slime mold achieves a better position, which is the optimal position of multiple fuel cell life prediction data input variables, and also the optimal solution for the fuel cell output variables.

[0072] Furthermore, the optimization process of the penalty coefficient γ and kernel function parameter δ of the robust weighted least squares model RWLS using the ISMA algorithm in step (4) is as follows:

[0073] Initialize the relevant parameters of the ISMA algorithm, including population size, initial population size, upper and lower limits of the search space, maximum number of iterations, and current number of iterations;

[0074] The fuel cell training set is input into the RWLS model, the penalty coefficient γ of the model is optimized, and the predicted value f after the model training is calculated. v and the actual value of the sample a v , the fitness value Fit of each individual in the population is represented by the root mean square error between the predicted value and the actual value, and the formula is as follows:

[0075]

[0076] The new position obtained by the ISMA algorithm uses the above fitness value formula to calculate the fitness value of each individual and sort them in descending order. When the preset termination condition of the model is met, the best population position is selected, which is the optimal value of the model parameter penalty coefficient γ.

[0077] Furthermore, the process of modeling the low-frequency components obtained after decomposition in step (2) in step (4) is as follows:

[0078] The function to be optimized for the weighted least squares model WLS is as follows:

[0079]

[0080] Among them, ν i represents the weighting factor; the Lagrangian function can be obtained, and the formula is:

[0081]

[0082] To the error term e i The weighting factor ν is introduced into i , to improve the robustness of weighted least squares WLS, after introducing the Lagerlangi operator, the formula is:

[0083]

[0084] Among them, α represents the Lagrange multiplier; α i represents the Lagrange multiplier vector; according to the optimization condition, the linear matrix is:

[0085]

[0086] Ω is an n-order matrix;

[0087] Calculate the above equations and get the prediction function of the robust weighted least squares model RWLS:

[0088]

[0089] Furthermore, the implementation process of step (5) is as follows:

[0090] (51) In the random vector function link neural network RVFL, the data input in the input layer traverses through the nodes in the hidden layer, undergoes nonlinear mapping in the hidden layer, and is finally output through the output function, as shown in the formula:

[0091]

[0092] w j is the weight of the jth hidden node, X = [x1, x2, ..., x2] input matrix, b j is the threshold, β j is the output layer weight, g() is the activation function;

[0093] (52) The deep random vector function link neural network dRVFL is obtained by adding hidden layers to RVFL. The data input formula of the hidden layer is:

[0094]

[0095] Y in represents the hidden layer output, W represents the hidden layer weight, [Y in (i-1) ; X] represents the concatenation of the output of the hidden layer and the input features of the input layer;

[0096] (53) The integrated deep random vector function link neural network edRVFL adds an integration method to dRVFL. The final output β in edRVFL is decomposed into several small βs that are calculated independently. That is, each hidden layer calculates a β and finally takes the average value:

[0097]

[0098] (54) The outlier robust integrated deep random vector function link neural network ORedRVFL is designed to address the outlier problem that often occurs in fuel cell data. It uses regularization and normalization to improve the robustness of the model and transforms the model risk minimization problem into the l2 norm output weight β minimization problem. The purpose is to make the error e sparse. The formula is:

[0099]

[0100] Y in is the hidden layer output;

[0101] (55) The l0 norm is replaced by the l1 norm to ensure the overall minimization of the convexity and the sparsity of the error e. The formula is as follows:

[0102]

[0103] (56) To solve the convex optimization constraint problem, the enhanced Lagrange multiplier method is used, and the formula is:

[0104]

[0105] λ is the enhanced Lagrangian multiplier vector, μ is the penalty parameter;

[0106] (57) After iteration and solution of the Lagrange multiplier method, the prediction function of ORedRVFL is finally obtained:

[0107]

[0108] Furthermore, the implementation process of step (6) is as follows:

[0109] (61) The decomposed fuel cell data set is input into the corresponding robust weighted least squares model RWLS and outlier robust integrated deep random vector function link neural network model (ORedRVFL) for fuel cell capacitance prediction, and the prediction results are stacked and reorganized as follows:

[0110]

[0111] The prediction results of RWLS and ORedRVFL are solved together to obtain the prediction results of fuel cell capacitance. The formula is as follows:

[0112]

[0113] (62) RMSE and MAE are selected as the judgment indicators of the model, and the formula is as follows:

[0114]

[0115] Among them, the smaller the values ​​of the two evaluation indicators, RMSE and MAE, the more reliable and accurate the RWLS and ORedRVFL models are in predicting the fuel cell capacitance.

[0116] Furthermore, the implementation process of step (7) is as follows:

[0117]

[0118] RUL=Noc Max safe -Noc current

[0119] Among them, Noc Max safe is the maximum safe cycle number of the fuel cell, Noc current is the current fuel cell cycle number, Noc Max safe -Noc current The remaining safe cycle number obtained is the remaining life of the fuel cell.

[0120] Beneficial effects: Compared with the prior art, the present invention has the following beneficial effects:

[0121] The invention aims at the fact that the fuel cell life prediction data has the characteristics of correlation and large data volume, which will interfere with the prediction accuracy of the prediction model. Therefore, the invention performs feature selection on the collected data based on the maximum information coefficient and the approximate Markov blanket method fused with Lasso, which can efficiently process high-dimensional data sets, improve the operation efficiency of the model, and achieve the effect of improving the prediction accuracy of the model.

[0122] Aiming at the limitations of the traditional SMA algorithm, the chaotic reverse learning strategy is used to improve the population initialization of SMA. The golden sine is integrated in the food surrounding stage of the slime mold algorithm to obtain the ISMA algorithm. The multi-strategy fusion helps the algorithm to jump out of the local optimal value in the later stage of iteration, improve the local and global search capabilities, and obtain better convergence effect.

[0123] This paper uses the ISMA algorithm to optimize the penalty coefficient γ of the robust weighted least squares model (RWLS), which improves the performance of the RWLS model, enables the model to better fit the fuel cell capacitance data, improves the generalization ability of the model, and improves the accuracy and reliability of the prediction;

[0124] The present invention adopts a local decomposition method to decompose fuel cell data into complex high-frequency components and low-frequency components, uses a robust weighted least squares model (RWLS) and an outlier robust integrated deep random vector function link network model (ORedVFL) to model different components, inputs the data set into the model to obtain the prediction results, and then stacks and reorganizes the prediction results, which can increase the reliability and accuracy of the fuel cell life prediction output results, effectively improve the accuracy of the fuel cell life prediction model, and accurately evaluate the life degradation trend of the fuel cell. BRIEF DESCRIPTION OF THE DRAWINGS

[0125] Figure 1 is a flow chart of the present invention;

[0126] Figure 2 A flow chart of the improved LMD denoising algorithm provided by the present invention;

[0127] Figure 3 This is a flow chart of the improved SMA algorithm provided by the present invention. DETAILED DESCRIPTION

[0128] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0129] like Figure 1 As shown, the present invention provides a method for predicting the remaining life of a fuel cell based on a robust model, and adopts an approximate Markov blanket method based on maximum information coefficient and fused Lasso to perform feature selection on the original data; according to the complexity of the data, a local mean v decomposition method (local mean v decomposition, LMD) is adopted to decompose the signal into high-frequency components and low-frequency components; according to the influence of the selection of the penalty coefficient γ and the kernel function parameter δ in the robust weighted least squares model (Robust Weighted Least Sauares, RWLS) on the model performance, a slime mold algorithm (Slime Mould Algorithm, SMA) algorithm is used to optimize it, and at the same time, in order to solve the defects of the SMA algorithm, a multi-strategy fusion method is used to improve the SMA to obtain an improved SMA algorithm (ISMA); ISMA is used to optimize the penalty coefficient γ of RWLS; the optimized RWLS and the outlier robust ensembles deep random vector function link neural network (Outlier Robust Ensembles Deep Random Vector Functional Link, ORedRVFL) are used to model different components, and the two models are tested using a test set, and the prediction results are stacked and reorganized into the final prediction results. The specific steps are as follows:

[0130] Step 1: Use data monitoring equipment to collect data related to fuel cell life prediction, such as usage time, voltage, current, temperature, output power, capacitance and other data, and use the approximate Markov blanket method based on maximum information coefficient and fused Lasso to perform feature selection on the collected battery capacity data, and select capacitance data that is closely related to the remaining life prediction of the fuel cell from the collected fuel cell data.

[0131] Step 1.1: First-stage correlation analysis, feature selection is performed based on the correlation between the features and categories of the collected fuel cell data. The correlation information formula is:

[0132]

[0133] Q = {q i ,i=1,2,…,n}、W={w i ,i=1,2,…,n} is the data set; q and w are two-dimensional random variables; p(q,w) is the joint probability density function of q and w; p(q) and p(w) are marginal probability density functions.

[0134] Step 1.2: Assume that the dataset D = {(q i ,w i ),i=1,2,...n}, its maximum information coefficient is:

[0135] EIC(D)=max qw<B(m) {M(D) Q,W}

[0136] The sample size is m; the best effect is achieved when B(m) is equal to 0.6 of the sample size.

[0137] Step 1.3: Use the maximum information coefficient to define the correlation between features and between features and categories for fuel cell data. Given a feature set F = {f1, f2, …, f n ,c}, the number of features is n, the category is c; between [0,1], for any category c and feature f i The correlation between them is defined as EIC(f i ,c), calculate the correlation EIC (f i ,c), the calculation formula is as follows:

[0138]

[0139] The features with higher correlation scores are more important, and the features are sorted in descending order according to the correlation scores to construct the fuel cell feature group after one stage.

[0140] Step 1.4: Second-stage redundancy analysis, select the main element f i , and put it into the most characteristic subset;

[0141] Main element: a feature f i , if and only if no element is f i An approximate Markov blanket.

[0142] Step 1.5: According to the concept of approximate Markov blanket, all redundant features with the current main element as the approximate Markov blanket are deleted. The conditional formula is:

[0143] EIC(f i ,R)≥EIC(f j ,R)||EIC(f i ,f j )≥EIC(f j ,R)

[0144] R is the target variable; f i Yes j The approximate Markov blanket, f j To eliminate redundant features.

[0145] Step 1.6: Repeat steps 1.4 and 1.5 until there are no principal elements in the feature set F. The feature subset consisting of all principal elements is the suboptimal feature subset, in which the correlation between features and categories is high.

[0146] Step 1.7: To constrain the complexity of the model, the Lasso method is used to introduce the penalty function L1 norm term on the basis of the loss function, compressing the insignificant regression coefficients to 0 while reducing the excessive compression of important regression coefficients, so that a better model can be obtained. The specific formula is as follows:

[0147]

[0148] n is the number of features, m is the number of samples, o is the regression coefficient vector, x is the feature matrix, y is the i is the true value of the sample, and α is the degree of compression.

[0149] After constructing the suboptimal feature subset of fuel cells by approximating the Markov blanket, the Lasso method is applied to the suboptimal feature subset to iteratively delete the redundant features related to fuel cell life prediction, and finally the optimal feature subset for fuel cell life prediction is obtained.

[0150] Step 2: If Figure 2 As shown, the local mean decomposition (LMD) denoising method is used for the data after feature selection in step 1 to decompose the fuel cell capacitance into several low-frequency product function (PF) components and residuals, and the continuous root mean square error is calculated as the dividing point between high and low frequency components.

[0151] Step 2.1: Assume that the original signal of the fuel cell is x(t), calculate the local extreme point g in x(t) i and the corresponding extreme value x(g i ), then the local mean J i and the local amplitude A i It can be expressed as:

[0152]

[0153] The local amplitude and local mean are processed to obtain the local mean function J 11 (t) and the local amplitude function A 11 (t).

[0154] Step 2.2: Set the local mean function J 11 (t) is removed from the original signal x(t), and the formula is:

[0155] H 11 (t) = x(t) - J 11 (t)

[0156] Using the local amplitude function A 11 (t) Solve H 11 (t), there are:

[0157]

[0158] Calculate S 11 (t) Local amplitude function A 12 (t), determine whether it is 1; if not, set S 11 (t) is regarded as the input signal and the local mean function J is calculated 12 (t), and remove J from it 12 (t) thus obtain H 12 (t), and then use A 12 (t) Solve H 12 (t); Repeat the above steps to get the pure FM signal S 1n (t).

[0159] The final local amplitude signal is:

[0160]

[0161] t represents the tth iteration.

[0162] Step 2.3: The product of the pure FM signal and the local amplitude signal is expressed as the first product function, and the formula is as follows:

[0163] PF1(t)=A1(t)S 1n (t)

[0164] Step 2.4: Remove PF1(t) from the original signal x(t) to get the new signal x(t) * , the new signal x(t) * For smoothing the signal, repeat steps 1 to 4 to obtain the monotonic function x k (t) * , stop the iteration.

[0165] Step 2.5: x(t) can be represented as k PFs and a residual x k (t) * The superposition of, that is:

[0166]

[0167] The basis of LMD decomposition is the extreme value of the signal itself. The corresponding PF is obtained by continuous iteration, and the signal is finally decomposed into a residual signal and a partial PF.

[0168] Step 2.6: Determine the dividing point between high-frequency and low-frequency components by calculating the continuous root mean square error (CMSE), and use the p value corresponding to the global minimum of CMSE as the dividing point between high-frequency and low-frequency components. The formula is as follows:

[0169]

[0170] The fuel cell capacitance data after LMD denoising decomposition is divided into high-frequency components and low-frequency components. The subsequent use of appropriate models to model the high-frequency components and low-frequency components respectively can improve the accuracy and stability of the fuel cell life prediction results.

[0171] Step 3: If Figure 3 As shown in the figure, the slime mold algorithm (SMA) is improved, the chaotic reverse learning strategy is used to improve the population initialization of the SMA, and the golden sine is integrated in the food surrounding stage of the slime mold algorithm to obtain the ISMA algorithm. The fusion of multiple strategies helps the algorithm to jump out of the local optimal value in the later stage of iteration, improve the local and global search capabilities, and obtain better convergence effect.

[0172] Step 3.1: Use the chaotic reverse learning strategy to initialize the population position of the MOSMA algorithm. The improved initialization formula is:

[0173]

[0174] P i =rand(0,1)·(LB+UB)

[0175] y i is a cubic sequence; X i The range is from the lower limit to the upper limit; UB represents the lower position boundary of the slime mold; LB represents the upper position boundary of the slime mold; P i For the reverse solution.

[0176] Step 3.2: When the slime mold is approaching food, the position update formula is as follows:

[0177]

[0178] p=tanh|S i -DF|

[0179]

[0180] Where W is the weight of the slime mold algorithm; VB is a random number between [-a, a]; VC is a parameter that decreases linearly from 1 to 0; r is a random number between [0, 1]; X b is the current optimal individual position; X A and X B are two random slime mold individuals; p = tanh|Si -DF| is a parameter that affects the update method of the slime mold position; DF represents the optimal fitness of the current individual; i represents the slime mold individual; S i is the fitness value of the i-th slime mold individual; condition represents the slime molds with the top 50 fitness rankings; BF and WF represent the currently obtained optimal fitness and worst fitness respectively; SmellIndex indicates that the fitness values ​​are sorted in ascending order.

[0181] The calculation formula of a is as follows:

[0182]

[0183] t max Represents the maximum number of iterations.

[0184] Step 3.3: As the slime mold approaches the food, the concentration of food in contact with the vein increases, which leads to the enhancement of the wave generated by the biological oscillator, the acceleration of cytoplasmic flow, and the increase of vein thickness. At this time, the relevant weight increases; conversely, when the food concentration decreases, the relevant weight decreases; when the slime mold surrounds the food, in order to effectively jump out of the local optimum, the golden sine strategy is integrated at this stage, the golden sine segmentation coefficient is introduced into the MOSMA algorithm, and the original position update formula is improved. The improved position update formula is as follows:

[0185]

[0186] R1∈(0,2π); R2∈(0,π); X1=-π+(1-π); X2=-π+(τ×2π)

[0187] X1 and X2 are coefficients calculated by the golden ratio, and τ is the golden section coefficient.

[0188] After two stages of position updates, the slime mold achieves a better position, that is, the optimal position of multiple fuel cell life prediction data input variables such as charging and discharging voltage, current, and temperature, which is also the optimal solution for the fuel cell output variables.

[0189] Step 4: The ISMA algorithm is used to optimize the penalty coefficient γ of the robust weighted least squares model (RWLS), and at the same time, a model is built for the low-frequency components obtained after decomposition in step 2.

[0190] Step 4.1: The function to be optimized in the weighted least squares model (WLS) is as follows:

[0191]

[0192] ν i represents the weighting factor. So the Lagrangian function can be obtained, the formula is:

[0193]

[0194] Step 4.2: Add the error term e i The weighting factor ν is introduced into i , to improve the robustness of weighted least squares (WLS), after introducing the Lagrange operator, the formula is:

[0195]

[0196] α represents the Lagrange multiplier; α i represents the Lagrange multiplier vector; according to the optimization condition, the linear matrix is:

[0197]

[0198] Ω is an n-order matrix.

[0199] Step 4.3: Calculate the above equations to obtain the robust weighted least squares model (RWLS) and the prediction function is:

[0200]

[0201] Step 4.4: Use the ISMA algorithm to optimize the penalty coefficient γ of the robust weighted least squares model (RWLS), the steps are as follows:

[0202] Initialize the relevant parameters of the ISMA algorithm, including population size, initial population size, upper and lower limits of the search space, maximum number of iterations, and current number of iterations.

[0203] The fuel cell training set is input into the RWLS model, the penalty coefficient γ of the model is optimized, and the predicted value f after the model training is calculated. v and the actual value of the sample a v , the fitness value Fit of each individual in the population is represented by the root mean square error between the predicted value and the actual value, and the formula is as follows:

[0204]

[0205] The new position obtained by the ISMA algorithm uses the above fitness value formula to calculate the fitness value of each individual and sort them in descending order. When the preset termination condition of the model is met, the best population position is selected, which is the optimal value of the model parameter penalty coefficient γ.

[0206] Step 5: Use the robust integrated deep random vector function link neural network model (ORedRVFL) to model the complex high-frequency components obtained after decomposition in step 2.

[0207] Step 5.1: The random vector function link neural network (RVFL) not only has an input layer, a hidden layer, and an output layer, but also has a linear link connecting the input layer and the output layer. In the RVFL model, the data input in the input layer traverses through the nodes in the hidden layer, undergoes nonlinear mapping in the hidden layer, and is finally output through the output function, the formula is:

[0208]

[0209] w j is the weight of the jth hidden node, X = [x1, x2, ..., x2] input matrix, b j is the threshold, β j is the output layer weight and g() is the activation function.

[0210] Step 5.2: The deep random vector function link neural network (dRVFL) is obtained by adding hidden layers to RVFL. The data input formula of the hidden layer is:

[0211]

[0212] Y in represents the hidden layer output, W represents the hidden layer weight, [Y in (i-1) ; X] represents the concatenation of the output of the hidden layer and the input features of the input layer.

[0213] Step 5.3: The integrated deep random vector function link neural network (edRVFL) adds an integration method to dRVFL, decomposing the final output β in edRVFL into several small βs that are calculated independently, that is, each hidden layer calculates a β and finally takes the average value:

[0214]

[0215] Step 5.4: Outlier robust integrated deep random vector function link neural network (ORedRVFL) is an improved version of edRVFL. In view of the outlier problem that often appears in fuel cell data, regularization and normalization are used to improve the robustness of the model. The problem of minimizing model risk is transformed into the problem of minimizing the l2 norm output weight β. The purpose is to make the error e sparse. The formula is:

[0216]

[0217] Y in is the hidden layer output.

[0218] Step 5.5: Replace the l0 norm with the l1 norm, which not only ensures the overall minimization of the convexity, but also ensures the sparsity of the error e. The formula is as follows:

[0219]

[0220] Step 5.6: To solve the convex optimization constraint problem, the enhanced Lagrange multiplier method is used, and the formula is:

[0221]

[0222] λ is the augmented Lagrangian multiplier vector and μ is the penalty parameter.

[0223] Step 5.7: After iteration and solution of the Lagrange multiplier method, the prediction function of ORedRVFL is finally obtained:

[0224]

[0225] Step 6: Input the training set into the corresponding two prediction models for prediction, stack the prediction results of the two models, and obtain the final prediction result of the fuel cell capacitance prediction. Finally, RMSE and MAE are used as evaluation indicators to judge the reliability of the two models.

[0226] Step 6.1: Input the decomposed fuel cell data set into the corresponding robust weighted least squares model (RWLS) and outlier robust integrated deep random vector function link neural network model (ORedRVFL) to predict the fuel cell capacitance, and stack and reorganize the prediction results. The formula is as follows:

[0227]

[0228] The prediction results of RWLS and ORedRVFL are solved together to obtain the prediction results of fuel cell capacitance. The formula is as follows:

[0229]

[0230] Step 6.2: Select RMSE and MAE as the judgment indicators of the model. The formula is as follows:

[0231]

[0232] The smaller the values ​​of RMSE and MAE, the more reliable and accurate the RWLS and ORedRVFL models are in predicting fuel cell capacitance.

[0233] Step 7: Define a suitable failure threshold according to different fuel cell capacitance data. When the capacitance prediction value reaches the set failure threshold, calculate the remaining life of the fuel cell. The formula is as follows:

[0234]

[0235] RUL=Noc Max safe -Noc current

[0236] Noc Max sa fe represents the maximum safe cycle number of the fuel cell, Noc curren t represents the current fuel cell cycle number, Noc Max safe -Noc current The remaining safe cycle number obtained is the remaining life of the fuel cell.

[0237] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable people familiar with the technology to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. Any equivalent transformation or modification made according to the spirit of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for predicting the remaining life of a fuel cell based on a robust model, characterized in that: The following steps are involved: (1) Using the pre-acquired fuel cell life prediction related data as input variables, the approximate Markov blanket method based on the maximum information coefficient and fused Lasso is used for feature selection, and the battery capacity data closely related to the remaining life of the fuel cell is selected as the output variable; (2) For the noise reduction method using local mean decomposition, the battery capacity data is decomposed into several low-frequency product function components and residuals, and the continuous root mean square error is calculated as the dividing point between the high-frequency component and the low-frequency component; (3) The slime mold algorithm SMA is improved by using a chaotic reverse learning strategy to improve the population initialization of the SMA. The golden sine is integrated into the food surrounding stage of the slime mold algorithm to obtain the ISMA algorithm. (4) The ISMA algorithm is used to optimize the penalty coefficient γ and kernel function parameter δ of the robust weighted least squares model RWLS, and at the same time, a model is built for the low-frequency components obtained after decomposition in step (2); (5) The robust integrated deep random vector function link network model ORedRVFL is used to model the high-frequency components obtained after decomposition in step (2); (6) The training sets are input into the corresponding two prediction models for prediction, and the prediction results of the two models are stacked to obtain the final prediction result of the fuel cell battery capacity. Finally, RMSE and MAE are used as evaluation indicators to judge the reliability of the two models; (7) when the predicted value of the fuel cell battery capacity obtained in step (6) reaches the failure threshold, obtaining a predicted value of the remaining life of the fuel cell according to the fuel cell battery capacity prediction result; The implementation process of step (1) is as follows: (11) One-stage correlation analysis, the correlation information formula is: Q = {q i ,i=1,2,…,n}、W={w i , i=1,2,…,n} is a data set; q and w are two-dimensional random variables; p(q,w) is the joint probability density function of q and w; p(q) and p(w) are marginal probability density functions; (12) Data set D = {(q i ,w i ),i=1,2,...n}, its maximum information coefficient is: EIC(D)=max qw＜B(m) {M(D) Q,W } The sample size is m; B(m) is the value of the sample size; (13) Given a feature set F = {f1,f2,…,f n ,c}, the number of features is n, the category is c; between [0,1], for any category c and feature f i The correlation between them is defined as EIC(f i ,c), calculate the correlation EIC (f i ,c), the calculation formula is as follows: The features with higher correlation scores are more important, and the features are sorted in descending order according to the correlation scores to construct the fuel cell feature group after one stage; (14) Two-stage redundancy analysis, select the main element f i , and put it into the optimal feature subset; Main element: a feature f i , if and only if no element is f i An approximate Markov blanket of (15) According to the concept of approximate Markov blanket, all redundant features with the current main element as the approximate Markov blanket are deleted. The conditional formula is: EIC(f i ,R)≥EIC(f j ,R)||EIC(f i ,f j )≥EIC(f j ,R) Among them, R is the target variable; f i Yes j The approximate Markov blanket, f j To eliminate redundant features; (16) Repeat steps (14) and (15) until there is no principal element in the feature set F. The feature subset consisting of all principal elements is the suboptimal feature subset, in which the correlation between features and categories is high. (17) The Lasso method is used to introduce the penalty function L1 norm term on the basis of the loss function, compressing the insignificant regression coefficients to 0 while reducing the excessive compression of important regression coefficients. The specific formula is as follows: Among them, n is the number of features, m is the number of samples, and o j is the regression coefficient vector, q ij is the feature matrix, w i is the true value of the sample, and α is the degree of compression; after constructing the suboptimal feature subset of the fuel cell by approximating the Markov blanket, the Lasso method is applied to the suboptimal feature subset to iteratively delete the redundant features related to the fuel cell life prediction, and the optimal feature subset for fuel cell life prediction is obtained; The implementation process of step (3) is as follows: (31) The chaotic reverse learning strategy is used to initialize the population position of the SMA algorithm. The improved initialization formula is: P i =rand(0,1)·(LB+UB) Among them, y i is a cubic sequence; X i The range is from the lower limit to the upper limit; UB represents the lower position boundary of the slime mold; LB represents the upper position boundary of the slime mold; P i is the reverse solution; (32) When the slime mold approaches food, the position update formula is as follows: p=tanh|S i -DF Where W is the weight of the slime mold algorithm; VB is a random number between [-a, a]; VC is a parameter that decreases linearly from 1 to 0; r is a random number between [0, 1]; X b is the current optimal individual position; X A and X B are two random slime mold individuals; p = tanh|S i -DF| is a parameter that affects the update method of the slime mold position; DF represents the optimal fitness of the current individual; i represents the slime mold individual; S i is the fitness value of the i-th slime mold individual; condition represents the slime molds ranked in the top 50 percentile in fitness; BF and WF represent the currently obtained optimal fitness and worst fitness respectively; SmellIndex represents that the fitness values ​​are sorted in ascending order; The calculation formula of a is as follows: Among them, t max Represents the maximum number of iterations; (33) The golden sine division coefficient is introduced into the SMA algorithm to improve the original position update formula. The improved position update formula is as follows: R1∈(0,2π); R2∈(0,π); X1=-π+(1-π); X2=-π+(τ×2π); Among them, X1 and X2 are coefficients calculated by the golden ratio, and τ is the golden section coefficient; After the two-stage position update, the slime mold obtains a better position, which is the best position of the multiple fuel cell life prediction data input variables, and the optimal solution of the fuel cell output variables; The optimization process of the penalty coefficient γ and kernel function parameter δ of the robust weighted least squares model RWLS using the ISMA algorithm in step (4) is as follows: Initialize the relevant parameters of the ISMA algorithm, including population size, initial population size, upper and lower limits of the search space, maximum number of iterations, and current number of iterations; The fuel cell training set is input into the RWLS model, the penalty coefficient γ of the model is optimized, and the predicted value f after the model training is calculated. v and the actual value of the sample a v , the fitness value Fit of each individual in the population is represented by the root mean square error between the predicted value and the actual value, and the formula is as follows: The new position obtained by the ISMA algorithm uses the above fitness value formula to calculate the fitness value of each individual and sort them in descending order. When the preset termination condition of the model is met, the best population position is selected, which is the optimal value of the model parameter penalty coefficient γ; The process of modeling the low-frequency components obtained after decomposition in step (2) in step (4) is as follows: The function to be optimized for the weighted least squares model WLS is as follows: Among them, ν i represents the weighting factor; the Lagrangian function can be obtained, and the formula is: To the error term e i The weighting factor ν is introduced into i , to improve the robustness of weighted least squares WLS, after introducing the Lagerlangi operator, the formula is: Among them, α represents the Lagrange multiplier; α i represents the Lagrange multiplier vector; according to the optimization condition, the linear matrix is: Ω is an n-order matrix; The prediction function of the robust weighted least squares model RWLS is obtained as: The implementation process of step (5) is as follows: (51) In the random vector function link neural network RVFL, the data input in the input layer traverses through the nodes in the hidden layer, undergoes nonlinear mapping in the hidden layer, and is finally output through the output function, as shown in the formula: w j is the weight of the jth hidden node, X = [x1, x2, ..., x2] input matrix, b j is the threshold, β j is the output layer weight, g() is the activation function; (52) The deep random vector function link neural network dRVFL is obtained by adding hidden layers to RVFL. The data input formula of the hidden layer is: Y in represents the hidden layer output, W represents the hidden layer weight, [Y in (i-1) ; X] represents the concatenation of the output of the hidden layer and the input features of the input layer; (53) The integrated deep random vector function link neural network edRVFL adds an integration method to dRVFL. The final output β in edRVFL is decomposed into several small βs that are calculated independently. That is, each hidden layer calculates a β and finally takes the average value: (54) The outlier robust integrated deep random vector function link neural network ORedRVFL is designed to address the outlier problem that often occurs in fuel cell data. It uses regularization and normalization to improve the robustness of the model and transforms the model risk minimization problem into the l2 norm output weight β minimization problem. The purpose is to make the error e sparse. The formula is: Y in is the hidden layer output; (55) The l0 norm is replaced by the l1 norm to ensure the overall minimization of the convexity and the sparsity of the error e. The formula is as follows: (56) To solve the convex optimization constraint problem, the enhanced Lagrange multiplier method is used, and the formula is: λ is the enhanced Lagrangian multiplier vector, μ is the penalty parameter; (57) After iteration and solution of the Lagrange multiplier method, the prediction function of ORedRVFL is finally obtained:

2. The method for predicting the remaining life of a fuel cell based on a robust model according to claim 1, characterized in that: The fuel cell life prediction related data described in step (1) includes fuel cell usage time, voltage, current, temperature, output power and battery capacity.

3. The method for predicting the remaining life of a fuel cell based on a robust model according to claim 1, characterized in that: The implementation process of step (2) is as follows: (21) The original signal of the fuel cell is x(t), and the local extreme point g in x(t) is calculated i and the corresponding extreme value x(g i ), then the local mean J i and the local amplitude A i It is expressed as: The local amplitude and local mean are processed to obtain the local mean function J 11 (t) and the local amplitude function A 11 (t); (22) The local mean function J 11 (t) is removed from the original signal x(t): H 11 (t)=x(t)-J 11 (t) Using the local amplitude function A 11 (t) Solve H 11 (t), there are: Calculate S 11 (t) Local amplitude function A 12 (t), determine whether it is 1; if not, set S 11 (t) is regarded as the input signal and the local mean function J is calculated 12 (t), and from S 11 Remove J from (t) 12 (t) thus obtain H 12 (t), and then use A 12 (t) Solve H 12 (t); Repeat the above steps to get the pure FM signal S 1n (t); The final local amplitude signal is: t represents the tth iteration; (23) The product of the pure FM signal and the local amplitude signal represents the first product function: PF1(t)=A1(t)S 1n (t) (24) Remove PF1(t) from the original signal x(t) to obtain a new signal x(t) * , the new signal x(t) * is the smoothed version of the original signal; repeat steps (21) to (24) to obtain the monotonic function x k (t) * , stop iteration; (25)x(t) is represented by k PFs and a residual x k (t) * The superposition of, that is: The basis of LMD decomposition is the extreme value of the signal itself, and the corresponding PF is obtained by continuous iteration. The signal is finally decomposed into the residual signal and part of the PF; (26) The dividing point between high-frequency and low-frequency components is determined by calculating the continuous root mean square error, and the p value corresponding to the global minimum of CMSE is used as the dividing point between high-frequency and low-frequency components. The formula is as follows: The fuel cell data after LMD denoising is divided into high-frequency components and low-frequency components.

4. The method for predicting the remaining life of a fuel cell based on a robust model according to claim 1, characterized in that: The implementation process of step (6) is as follows: (61) The decomposed fuel cell data set is input into the corresponding robust weighted least squares model RWLS and outlier robust integrated deep random vector function link neural network model ORedRVFL to predict the fuel cell battery capacity, and the prediction results are stacked and reorganized. The formula is as follows: The prediction result functions of RWLS and ORedRVFL are solved simultaneously, and the final fuel cell battery capacity prediction result is obtained as follows: (62) RMSE and MAE are selected as the judgment indicators of the model, and the formula is as follows: Among them, the smaller the values ​​of RMSE and MAE are, the better the prediction results of fuel cell battery capacity by RWLS and ORedRVFL models are. final The greater the reliability and accuracy.

5. The method for predicting the remaining life of a fuel cell based on a robust model according to claim 4, characterized in that: The implementation process of step (7) is as follows: RUL=Night Maxsafe -Night current Among them, Noc Maxsafe is the maximum safe cycle number of the fuel cell, Noc current is the current fuel cell cycle number, Noc Maxsafe -Noc current The remaining safe cycle number obtained is the remaining life of the fuel cell.

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