Method and system for predicting remaining service life of fuel cell based on long-term operation data

Abstract

The invention discloses a method and system for predicting the remaining service life of a fuel cell based on long-term operation data, and the method comprises the steps: collecting the historical operation data of the fuel cell, and carrying out the preprocessing; performing feature selection on the preprocessed data through inverse nonlinear principal component analysis INLPCA to obtain an optimal input data set; a simplex method SM and an elite reverse learning strategy EOBL are introduced for improvement, and an improved hybrid simplex lightning search algorithm LSA-SM is obtained; a fuel cell remaining service life prediction model based on an ITransform model is established; an improved mixed simplex lightning search algorithm (LSA-SM algorithm) is utilized to optimize hyper-parameters of the fuel cell remaining service life prediction model, an optimal hyper-parameter is obtained, and an optimized LSA-SM-ITransform model is obtained; and predicting the service life of the battery by using the optimized LSA-SM-ITransform model. The energy efficiency can be improved, the maintenance cost is reduced, the service life of the battery is effectively prolonged, and energy waste is reduced.

Description

Technical Field

[0001] The present invention relates to a method and system for predicting the remaining service life of a fuel cell, and in particular to a method and system for predicting the remaining service life of a fuel cell based on long-term operation data, and belongs to the technical field of fuel cell technology. Background Art

[0002] With the profound changes in the global energy structure and the increasing awareness of environmental protection, proton exchange membrane fuel cells (hereinafter referred to as fuel cells), as a clean and efficient energy conversion device, are gradually becoming an important part of the future energy system. In the context of global energy transformation, reducing dependence on fossil fuels and increasing the use of clean energy has become a global consensus. As a representative of new energy technology, the long-term stable operation of fuel cells is an important guarantee for optimizing the energy structure.

[0003] Fuel cells have many advantages, but their deployment and commercialization are significantly hindered by their short lifespan, rapid performance degradation, high maintenance costs, and expensive hydrogen fuel caused by temporary or permanent degradation of the battery. In order to overcome these challenges, it is particularly important to predict the battery degradation trend and estimate the remaining service life. Summary of the invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a method and system for predicting the remaining useful life of a fuel cell based on long-term operating data, which can shorten the prediction time and improve the prediction efficiency.

[0005] Technical solution: A method for predicting the remaining service life of a fuel cell based on long-term operation data according to the present invention comprises:

[0006] Step 1: Collect historical operation data of the fuel cell and perform preprocessing, wherein the preprocessing is to remove abnormal data using a divergence-based calibration method;

[0007] Step 2: Perform feature selection on the preprocessed data through inverse nonlinear principal component analysis (INLPCA), eliminate redundant and irrelevant feature information, and reconstruct it to obtain the optimal input data set;

[0008] Step 3: Based on the lightning search LSA algorithm, the simplex method SM and the elite reverse learning strategy EOBL are introduced to improve it, and the improved hybrid simplex lightning search algorithm LSA-SM is obtained;

[0009] Step 4: Establish a fuel cell remaining service life prediction model based on the ITransformer model;

[0010] Step 5: Use the improved hybrid simplex lightning search algorithm LSA-SM algorithm to optimize the hyperparameters of the fuel cell remaining service life prediction model, obtain the optimal hyperparameters, and obtain the optimized LSA-SM-ITransformer model;

[0011] Step 6: Use the optimized LSA-SM-ITransformer model to predict the battery life and obtain the prediction result of the remaining battery life.

[0012] Furthermore, the step 1 of removing abnormal data by using a divergence-based calibration method includes:

[0013] The historical operation data of the fuel cell is standardized, and the Z score is calculated to measure the number of standard deviations between a data point and the mean:

[0014]

[0015] Among them, Z represents the Z score; X is the value of a single data point; μ is the mean of the data set; σ is the standard deviation of the data set; when the Z score of a data point is greater than 3 or less than -3, the data point is considered to be an outlier.

[0016] Furthermore, the step (2) comprises:

[0017] Step 2.2: Normalize the preprocessed data and map it to [0,1]:

[0018]

[0019] Among them, x is the preprocessed data, x max is the maximum value of the data, x min is the minimum value of the data;

[0020] Step 2.2: During INLPCA training, the normalized data is set as the network input value, and the output value is given To reversely estimate the principal component z of the training data and the weights w∈W3∪W4 of the network:

[0021]

[0022] Where: g is a nonlinear activation function, w∈W3∪W4, W3 and W4 are the weight matrices of the network;

[0023] Step 2.3: Express the mean square error function of INLPCA training as:

[0024]

[0025] Where: d′ is the number of data dimensions; N is the number of samples; i, j, k are the number of neurons in the output layer, reconstruction layer and bottleneck layer respectively, and w ij is the weight from the jth neuron in the reconstruction layer to the ith neuron in the output layer, Represents the principal component value of the nth sample in the kth dimension;

[0026] Step 2.4: INLPCA passes the mean square error back to the input layer to obtain the gradient; at this time, the weight w ij ∈W4,w jk ∈W3, with the principal component The gradients are expressed as:

[0027]

[0028]

[0029] Where: is the training error on the i-th dimension of the n-th sample data;

[0030] Step 2.5: Minimize the error function E(w,z) to solve the network weight w and the principal component z; for the principal component extraction of data x, fix w and then To search for the best result;

[0031] Use weight decay coefficient to regularize the neural network:

[0032]

[0033] Where: E total is the total model error; v is the weight penalty coefficient;

[0034] Step 2.6: Randomly extract data from several dimensions from the validation set data, take the extracted values ​​as the true values, use INLPCA to estimate the missing values, and calculate the estimated mean square error E MS :

[0035]

[0036] Finally, by adjusting v, the mean square error of the estimated value of the missing value is minimized; the true value is sorted in descending order. The larger the value, the more important the component. The top several are selected as the principal components according to the ranking to form the best input data set.

[0037] Furthermore, the step (3) includes:

[0038] Step 3.1: LSA algorithm process:

[0039] Transition discharge body: Assume a ladder leader SL with a population size of G = [sl1, sl2, ...., sl G ], the transition discharge body is expressed as sl g is the value of the Gth dimension of the ladder leader, is the value of the Gth dimension of the transition discharge body; in the early stage of the formation of the step leader, the transition discharge body propagates downward from the bottom of the thunderstorm cloud in a random direction. The transition discharge body obeys a uniform distribution, creates an initial random population, and converts the probability density function f(x T ) is expressed as:

[0040]

[0041] Among them, x T is a candidate solution, a and b are the lower and upper bounds of the solution space respectively;

[0042] Space discharge body: Assume that the space discharge body is represented by is the value of the g-th dimension of the space discharge body, and the position uses the exponential distribution probability density function express:

[0043]

[0044] Wherein, μ is a shape parameter, which is used to control the position or direction of the next iteration of the space discharge body; in the LSA algorithm, μ is considered to be the guiding discharge body p L and space discharge body The distance between them, g = 1, 2, ..., G, space discharge body The position at the next iteration is expressed as:

[0045]

[0046] Among them, exprand is the random number generated by the exponential distribution function, and μ is the mean;

[0047] Guide discharge body: Assume that the guide discharge body is represented by p L , the position is represented by the normal probability density function f(x L )express:

[0048]

[0049] Among them, x L is the value of the guiding discharge body in a certain dimension, μ is the mean, and σ is the standard deviation;

[0050] Leading discharge body L The position at the next iteration is expressed as:

[0051]

[0052] Among them, Fitness(·) is the fitness function, normrand(μ,σ) is a random number generated based on normal distribution, μ is the mean, and σ is the standard deviation;

[0053] Step 3.2: Use the simplex method to optimize the positions of K lightning leaders with the worst target values, improve the local search capability of the algorithm and speed up the convergence of the algorithm. Specifically:

[0054] Step 3.2.1: Calculate the fitness function values ​​of all leading individuals in the population, assume that the one with the smallest fitness value is the best, determine the best point as xg, the second best point as xb and K worst points, and take one of the worst points as xw;

[0055] Step 3.2.2: Calculate the center position of the optimal point xg and the suboptimal point xb

[0056]

[0057] Step 3.2.3: The worst point xw is based on the center point Perform reflection operations:

[0058]

[0059] Where xr is the reflection point and α is the reflection coefficient; calculate the fitness function value f(xr) of the z reflection point xr:

[0060] Step 3.2.4: If f(xr) < f(xg), the reflection direction is correct and perform the following operations; otherwise, proceed to step 3.2.5:

[0061]

[0062] Where xe is the expansion point and γ is the expansion coefficient. Calculate the fitness function value f(xe) of the expansion point xe. If f(xe) < f(xg), xe replaces xw, otherwise xr replaces xw.

[0063] Step 3.2.5: If f(xr)>f(xw), it means the reflection direction is wrong, and perform the following operations. Otherwise, proceed to step 3.2.6:

[0064]

[0065] Where xc is the compression point and β1 is the compression coefficient. Calculate the fitness function value f(xc) of the compression point xc. If f(xc) < f(xw), replace xw with xc.

[0066] Step 3.2.6: When f(xg)<f(xr)<f(xw), perform the contraction operation:

[0067]

[0068] Where xs is the contraction point, β2 is the contraction coefficient, and the contraction coefficient and the compression coefficient have the same value; calculate the fitness function value f(xs) of the contraction point xs, if f(xs) < f(xw), replace xw with xs, otherwise replace xw with xr;

[0069] Step 3.3: Assume that the solution with the best current fitness value in the population is defined as the elite leader, denoted as X ε =(x ε,1 ,x ε,2 ,...,x ε,D ), x ε,D is the position of the elite leader in dimension D. For a leader X g =(x g,1 ,x g,2 ,...,x g,D ), its elite reverse solution is defined into the formula:

[0070] x g ' ,d = k·(Lb d +Ub d )-x ε,d ,g=1,2,....,G; d=1,2,....,D(20)

[0071] Where N is the population size, D is the dimension of the search space, k∈U(0,1), (Lb d ,Ub d ) is the search boundary; if the elite reverse solution x g ' ,d If the search boundary is exceeded, adjust it using the following formula:

[0072] x g ' ,d = rand(Lb d ,Ub d ), if x g ' ,d <Lb d x g ' ,d >Ub d (twenty one).

[0073] Furthermore, the step 4 comprises:

[0074] Step 4.1: Embed the input time series data into a high-dimensional space to capture the characteristics of the sequence, through a linear layer:

[0075] X′=X :,n W E +b E (twenty two)

[0076] Among them, X :,n is the original data, X′ is the embedded data, W E and b E are the weights and biases of the embedding layer respectively;

[0077] H l+1 =TrmBlock(H l ),l=0,...,L-1 (23)

[0078] Among them, H l+1 represents the embedding representation of layer l, which is processed by the Transformer module TrmBlock();

[0079] Step 4.2: Add positional encoding to provide position information for each time step in the sequence:

[0080]

[0081] Where PE is the position code; pos is the position of the time step, i is the dimension index, d model is the dimension of the model;

[0082] Step 4.3: Perform multi-head self-attention calculation:

[0083] MultiHead(Q,K,V)=Concat(head1,…,head h )W O (26)

[0084] Where Q, K, and V are query, key, and value matrices, respectively, and W i Q , W i K and W i V is the learnable weight matrix, h is the number of heads;

[0085] The calculation for each head is:

[0086] head i =Attention(QW i Q ,KW i K ,VW iV )

[0087]

[0088] Among them, d model is the dimension of the model, d q ,d k and d v is the dimension of query, key and value in each attention head, R is a matrix;

[0089] Step 4.4: Introduce self-attention mechanism:

[0090]

[0091] Among them, softmax() is the transfer function, QK T It is a dot product operation, which calculates the attention weight of Q on V; Used to scale dot products to prevent the vanishing gradient problem;

[0092] Step 4.5: Perform residual connection and layer normalization, input X :,n The output of the multi-head self-attention layer is recorded as Sublayer(X :,n ), and then make a residual connection:

[0093] X res =X :,n +Sublayer(X :,n ) (29)

[0094] Among them, X res is the output after residual connection, where X :,n represents the input data set;

[0095] Step 4.6: Normalize all inputs in each sample:

[0096]

[0097] Where μ′ is X res The mean of X res The standard deviation of

[0098] Step 4.7: Let the normalized data be x, and perform a linear transformation through two different weight matrices W1 and W2 and two bias terms b1 and b2; between the two linear transformations, apply the ReLU activation function: ReLU(x) = max(0,x), set all negative values ​​to 0, and keep the positive values ​​unchanged; pass the output of ReLU through the second linear layer, weight matrix W2 and bias b2, and get the output of the feedforward network FFN:

[0099] FFN(x)=max(0,xW1+b1)W2+b2 (31)

[0100] Step 4.8: Perform reverse normalization:

[0101] X=0.5[x′(x max -x min )+(x max +x min )] (32)

[0102] Step 4.9: Output the prediction results through the mapping layer:

[0103] Y=XW O +b O (33)

[0104] Among them, Y is the prediction result of the model, which represents the remaining service life of the fuel cell; X is the internal representation after model processing, which is the output of the last model layer; b O is the bias vector of the mapping layer; W O is the weight matrix of the mapping layer, which is used to decide how to transform the internal representation into the prediction result.

[0105] Furthermore, the step 5 comprises:

[0106] Step 5.1: Use the improved hybrid simplex lightning search algorithm LSA-SM algorithm to optimize the hyperparameters of the fuel cell remaining service life prediction model based on the LSA-SM-ITransformer model, and initialize the LSA algorithm hyperparameters;

[0107] Step 5.2: Randomly generate transition discharge bodies as the initial leader population;

[0108] Step 5.3: Execute the space discharge body and the guide discharge body model, and check whether bifurcation occurs;

[0109] Step 5.4: Evaluate and update the lead individuals;

[0110] Step 5.5: Use the simplex method to update the positions of the T worst leaders;

[0111] Step 5.6: Use the elite reverse learning strategy to generate an elite reverse population and compete with the original population;

[0112] Step 5.7: Determine whether the maximum number of iterations has been reached. If yes, proceed to step 5.8. If no, proceed to step 5.3 again for iterative calculation.

[0113] Step 5.8: Output the optimal hyperparameters and obtain the optimized LSA-SM-ITransformer model.

[0114] Furthermore, the step 6 comprises:

[0115] Step 6.1: Divide the best input data set into training set, validation set, and test set according to the preset ratio;

[0116] Step 6.2: Use the divided training set to train the improved LSA-SM-ITransformer model to enable the model to learn patterns and relationships in the data;

[0117] Step 6.3: Use the validation set to verify the model, adjust the model parameters, and complete the training;

[0118] Step 6.4: Use the trained model to predict the test set and obtain the prediction result of the remaining battery life.

[0119] Based on the same inventive concept, the present invention also provides a fuel cell remaining service life prediction system based on long-term operation data, comprising:

[0120] A data acquisition module, used to collect historical operation data of the fuel cell and perform preprocessing, wherein the preprocessing is to eliminate abnormal data using a divergence-based calibration method;

[0121] The data processing module is used to perform feature selection on the preprocessed data through inverse nonlinear principal component analysis (INLPCA), eliminate redundant and irrelevant feature information, and reconstruct the data to obtain the best input data set;

[0122] The algorithm improvement module is used to improve the LSA algorithm based on the lightning search algorithm by introducing the simplex method SM and the elite reverse learning strategy EOBL to obtain the improved hybrid simplex lightning search algorithm LSA-SM;

[0123] A model building module is used to build a fuel cell remaining service life prediction model based on the ITransformer model;

[0124] The model optimization module is used to optimize the hyperparameters of the fuel cell remaining service life prediction model using the improved hybrid simplex lightning search algorithm LSA-SM algorithm to obtain the optimal hyperparameters and obtain the optimized LSA-SM-ITransformer model;

[0125] The prediction module is used to predict the battery life using the optimized LSA-SM-ITransformer model to obtain the prediction result of the remaining battery life.

[0126] Based on the same inventive concept, the present invention also provides a computing device, comprising: one or more processors, one or more memories and one or more programs, wherein the programs are stored in the memories and configured to be executed by the processors, and when the programs are loaded into the processors, the steps of the method for predicting the remaining service life of a fuel cell based on long-term operation data according to any one of the above items are implemented.

[0127] Based on the same inventive concept, the present invention also provides a storage medium, which stores a computer program, and the computer program includes program instructions, which, when executed by a processor, enable the processor to perform the steps of the method for predicting the remaining service life of a fuel cell based on long-term operation data according to any of the above-mentioned items.

[0128] Beneficial effects: Compared with the prior art, the present invention uses the ITransformer model to improve prediction accuracy through optimized architecture and training strategies; in addition, the ITransformer model performs well in nonlinear data processing, feature extraction, and generalization capabilities, and can adapt to battery data under different types and conditions, providing more stable prediction results. Its improved algorithm also enhances the robustness of the model. Compared with the traditional Transformer model, the ITransformer model reduces the risk of overfitting and improves the model's reasoning speed and data processing capabilities in practical applications; the present invention uses inverse nonlinear principal component analysis (INLPCA) to perform nonlinear dimensionality reduction on the original data. Since a large amount of nonlinear data is generated during the charging and discharging process of a fuel cell, this method can reduce the number of characteristic signals, eliminate redundant characteristic information, and thus reduce the complexity of the model. At the same time, dimensionality reduction can also help improve the operating efficiency of the model and shorten the prediction time. The present invention improves the lightning search (LSA) algorithm and significantly improves the solution accuracy of the algorithm by introducing the simplex method (SM), especially when dealing with complex optimization problems, it can more accurately approach the global optimal solution. The introduction of the simplex method greatly enhances the local search capability of the algorithm, enabling LSA-SM to systematically explore potential areas in the solution space, quickly narrow the search range and accurately locate the optimal solution. In addition, the algorithm is shown in the later stage. The invention has a faster convergence speed and higher convergence accuracy, reduces the number of iterations required to reach the optimal solution, and improves the data processing capability of the algorithm when processing large-scale data sets or complex data structures; the improved LSA-SM algorithm also shows strong adaptability and robustness; in the process of improving the LSA-SM algorithm, the present invention also introduces an elite reverse learning strategy (EOBL) to improve the global search performance of the algorithm and avoid premature convergence of the algorithm; in addition, the guidance of elite individuals accelerates the convergence speed of the algorithm, improves the ability and practicability of the algorithm to process multimodal problems, and increases the flexibility and interpretability of the algorithm, so that the improved LSA-SM algorithm is more efficient and reliable in solving practical complex problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0129] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0130] Figure 2 A schematic diagram of a hybrid simplex lightning search algorithm according to an embodiment of the present invention;

[0131] Figure 3 It is a schematic diagram of the inverse nonlinear principal component analysis process of an embodiment of the present invention;

[0132] Figure 4 Schematic diagram of the optimized LSA-SM-ITransformer model according to an embodiment of the present invention. DETAILED DESCRIPTION

[0133] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0134] As attached Figure 1 As shown, the method for predicting the remaining service life of a fuel cell based on long-term operation data of this embodiment includes:

[0135] Step 1: Collect historical operation data of the fuel cell and perform preprocessing, wherein the preprocessing is to remove abnormal data using a divergence-based calibration method;

[0136] Step 2: Perform feature selection on the preprocessed data through inverse nonlinear principal component analysis (INLPCA), eliminate redundant and irrelevant feature information, and reconstruct it to obtain the optimal input data set;

[0137] Step 3: Based on the lightning search LSA algorithm, the simplex method SM and the elite reverse learning strategy EOBL are introduced to improve it, and the improved hybrid simplex lightning search algorithm LSA-SM is obtained;

[0138] Step 4: Establish a fuel cell remaining service life prediction model based on the ITransformer model;

[0139] Step 5: Use the improved hybrid simplex lightning search algorithm LSA-SM algorithm to optimize the hyperparameters of the fuel cell remaining service life prediction model, obtain the optimal hyperparameters, and obtain the optimized LSA-SM-ITransformer model;

[0140] Step 6: Use the optimized LSA-SM-ITransformer model to predict the battery life and obtain the prediction result of the remaining battery life.

[0141] The specific steps are as follows:

[0142] Step 1: Collect the long-term operation data of the fuel cell: voltage, current, temperature, capacity, relative humidity, and air metering. Preprocess the data and use the divergence-based calibration method to remove abnormal data to improve the overall data quality.

[0143] Step 1.1: The data is normalized and the Z score is calculated to measure the number of standard deviations between a data point and the mean. The formula for calculating the Z score is as follows:

[0144]

[0145] Where Z is the Z score of data point X; X is the value of a single data point; μ is the mean of the data set; σ is the standard deviation of the data set. If a data point has a Z score greater than 3 or less than -3, it is considered an outlier.

[0146] Step 1.2: Construct a scatter plot to show the correlation between variables. Outliers are usually represented by data points that deviate from the overall distribution trend. In the scatter plot, these deviated data points can be observed intuitively.

[0147] Step 1.3: Keep the data (normal data) where the overall part of the scatter plot is relatively concentrated and keep the output.

[0148] Finally, keep the data (normal data) that are relatively concentrated in the overall part of the scatter plot and keep the output.

[0149] Step 2: If Figure 3 As shown, for the data obtained in step 1 after abnormal elimination, feature selection is performed on the data through inverse nonlinear principal component analysis (INLPCA), redundant and irrelevant feature information in the original data is eliminated, and feature information data is effectively selected. The data is reconstructed to obtain the best input data set.

[0150] Step 2.1: Normalize the long-term operation data of the fuel cell after the abnormalities are eliminated and map it to [0,1]. The formula is as follows:

[0151]

[0152] In the formula, x is the original data, x max is the maximum value of the data, x min is the minimum value of the data.

[0153] Step 2.2: During INLPCA training, the normalized data (voltage, current, temperature, capacity, relative humidity, air metering) is set as the network input value, and the output value is given by (voltage, current, temperature, capacity) to reversely estimate the principal component z of the training data and the weights w∈W3∪W4 of the network:

[0154]

[0155] Where: g is a nonlinear activation function, w∈W3∪W4, W3 and W4 are the weight matrices of the network;

[0156] Step 2.3: Express the mean square error function of INLPCA training as:

[0157]

[0158] Where: d′ is the number of data dimensions; N is the number of samples; i, j, k are the number of neurons in the output layer, reconstruction layer and bottleneck layer respectively, and w ij is the weight from the jth neuron in the reconstruction layer to the ith neuron in the output layer, Represents the principal component value of the nth sample in the kth dimension;

[0159] Step 2.4: INLPCA passes the mean square error back to the input layer to obtain the gradient; at this time, the weight w ij ∈W4,w jk ∈W3, with the principal component The gradients are expressed as:

[0160]

[0161] Where: is the training error on the i-th dimension of the n-th sample data.

[0162] Step 2.5: Minimize the error function E(w,z) to solve the network weight w and the principal component z. For the principal component extraction of data x, by fixing w and then To find the best solution.

[0163] The weight decay coefficient is used to regularize the neural network. That is:

[0164]

[0165] Where: E total is the total model error; ν is the weight penalty coefficient.

[0166] Step 2.6: Randomly extract data from some dimensions of the validation set data. Take the extracted values ​​as the true values, use INLPCA to estimate the missing values, and calculate the estimated mean square error (E MS ).Right now:

[0167]

[0168] Finally, by adjusting ν, the mean square error of the estimated value of the missing value is minimized. Sort by the true value in descending order. The larger the value, the more important the component. Find the main components (voltage, current, temperature, capacity) according to the importance to form the best input data set.

[0169] The above steps process the complex nonlinear data generated during the charging and discharging process of the fuel cell to achieve nonlinear dimensionality reduction. This method can effectively reduce the total amount of characteristic signals, eliminate redundant characteristic data, and simplify the model structure. The dimensionality reduction process not only improves the operational efficiency of the model, but also significantly shortens the time required for prediction.

[0170] Step 3.1: LSA algorithm process:

[0171] Transition discharge body: Assume a ladder leader SL with a population size of G = [sl1, sl2, ...., sl G ], the transition discharge body is expressed as sl g is the value of the Gth dimension of the ladder leader, is the value of the Gth dimension of the transition discharge body. In the early stage of the formation of the step leader, the transition discharge body propagates downward from the bottom of the thunderstorm cloud in a random direction. Therefore, the transition discharge body obeys a uniform distribution, creating an initial random population with a probability density function f(x T ) can be expressed as:

[0172]

[0173] Among them, x T is a candidate solution, a and b are the lower and upper bounds of the solution space respectively.

[0174] Space discharge body: Assume that the space discharge body is represented by Exponential distribution probability density function for position express:

[0175]

[0176] Wherein, μ is a shape parameter, which is used to control the position or direction of the next iteration of the space discharge body; in the LSA algorithm, μ is considered to be the guiding discharge body p L and space discharge body The distance between them, g = 1, 2, ..., G, space discharge body The position at the next iteration is expressed as:

[0177]

[0178] Among them, exprand is the random number generated by the exponential distribution function, and μ is the mean;

[0179] Guide discharge body: Assume that the guide discharge body is represented by p L , the position is represented by the normal probability density function f(x L )express:

[0180]

[0181] Among them, x L is the value of the guiding discharge body in a certain dimension, μ is the mean, and σ is the standard deviation;

[0182] Leading discharge body L The position at the next iteration is expressed as:

[0183]

[0184]

[0185] Among them, Fitness(·) is the fitness function, normrand(μ,σ) is a random number generated based on normal distribution, μ is the mean, and σ is the standard deviation;

[0186] Step 3.2: Use the simplex method to optimize the positions of the K lightning leaders with the worst target values, improve the local search capability of the algorithm and speed up the convergence of the algorithm, such as Figure 2 As shown, the steps are as follows:

[0187] Step 3.2.1: Calculate the fitness function values ​​of all vertices, i.e., all leading individuals in the population. Assume that the one with the smallest fitness value is the best. Determine the best point as xg, the second best point as xb, and K worst points. Take one of the worst points and record it as xw.

[0188] Step 3.2.2: Calculate the center position of the optimal point xg and the suboptimal point xb

[0189]

[0190] Step 3.2.3: The worst point xw is based on the center point Perform reflection operations:

[0191]

[0192] Where xr is the reflection point and α=1 is the reflection coefficient. Calculate the fitness function value f(xr) of the reflection point xr:

[0193] Step 3.2.4: If f(xr) < f(xg), the direction of reflection is correct and the operation is as follows. Otherwise, proceed to step 3.2.5:

[0194]

[0195] Where xe is the expansion point and γ = 1.5 is the expansion coefficient. Calculate the fitness function value f(xe) of the expansion point xe. If f(xe) < f(xg), replace xw with xe, otherwise replace xw with xr;

[0196] Step 3.2.5: If f(xr)>f(xw), it means the direction of reflection is wrong. Perform the following operation. Otherwise, go to step 3.2.6:

[0197]

[0198] Where xc is the compression point and β1=0.5 is the compression coefficient. Calculate the fitness function value f(xc) of the compression point xc. If f(xc)<f(xw), replace xw with xc;

[0199] Step 3.2.6: f(xg)<f(xr)<f(xw), perform the contraction operation of the following equation:

[0200]

[0201] Where xs is the contraction point, β2=0.5 is the contraction coefficient, and the contraction coefficient and the compression coefficient have the same value. Calculate the fitness function value f(xs) of the contraction point xs. If f(xs) < f(xw), replace xw with xs, otherwise replace xw with xr.

[0202] Step 3.3: In addition to using the simplex method to improve the convergence accuracy of the LSA algorithm, the present invention also introduces an elite reverse learning strategy to improve the global search performance of the algorithm and avoid premature convergence of the algorithm. Assume that the solution with the best current fitness value in the population is defined as the elite leader, represented by X ε =(x ε,1 ,x ε,2 ,...,x ε,D ), x ε,D is the position of the elite leader in dimension D. For a leader X g =(x g,1 ,x g,2 ,...,x g,D ), its elite reverse solution is defined into the formula:

[0203] x g ' ,d = k·(Lb d +Ub d )-x ε,d ,g=1,2,....,G; d=1,2,....,D(20)

[0204] Where N is the population size, D is the dimension of the search space, k∈U(0,1), (Lb d ,Ub d ) is the search boundary; if the elite reverse solution x g ' ,d If the search boundary is exceeded, adjust it using the following formula:

[0205] x g ' ,d = rand(Lb d ,Ub d ), if x g ' ,d <Lb d xg ' ,d >Ub d (twenty one)

[0206] Step 4: Establish a fuel cell remaining service life prediction model based on the ITransformer model, and input the newly formed optimal input data set into the model. Use its multivariate self-attention mechanism to capture the local time series characteristics of the fuel cell during the charging and discharging process, and establish a global association between local features and the overall remaining service life of the battery through an objective function that comprehensively considers prediction accuracy and global dependencies.

[0207] Step 4.1: Input time series data X :,n is embedded into a high-dimensional space to capture the characteristics of the sequence. This is usually achieved through a linear layer:

[0208] X′=X :,n W E +b E (twenty two)

[0209] Among them, X :,n is the original data, X′ is the embedded data, W E and b E are the weights and biases of the embedding layer, respectively.

[0210] H l+1 =TrmBlock(H l ),l=0,...,L-1 (23)

[0211] Among them, H l+1 Represents the embedding representation of layer l, which is processed by TrmBlock (Transformer module).

[0212] Step 4.2: Since the ITransformer model itself does not process the order information of the sequence, it is necessary to add position encoding to provide the position information of each time step in the sequence:

[0213]

[0214] Where PE is the position code; pos is the position of the time step, i is the dimension index, d model is the dimension of the model.

[0215] Step 4.3: Perform multi-head self-attention calculation. Each ITransformer module starts with a multi-head self-attention mechanism, which allows the model to capture dependencies within the sequence in different representation subspaces at the same time:

[0216] MultiHead(Q,K,V)=Concat(head1,…,head h )W O (26)

[0217] The calculation for each head is:

[0218] head i =Attention(QW i Q ,KW i K ,VW i V ).

[0219]

[0220] Step 4.4: Introduce the Self-Attention Mechanism, which is calculated as follows:

[0221]

[0222] Among them, Q, K, V are query, key and value matrices respectively, and W i Q ,W i K ,W i V is the learnable weight matrix and h is the number of heads. QK T It is a dot product operation, which calculates the attention weight of Q on V; Used to scale the dot product to prevent the vanishing gradient problem.

[0223] Step 4.5: Perform residual connection and layer normalization, input X :,n It will pass through the multi-head self-attention layer, and the output of this sublayer is denoted as Sublayer(X :,n ), and then make a residual connection:

[0224] X res =X :,n +Sublayer(X :,n ) (29)

[0225] Among them, X res is the output after the residual connection. The purpose of this is to alleviate the gradient disappearance or gradient explosion problem in deep network training, allowing the gradient to flow through the network more directly.

[0226] Step 4.6: After the residual connection, layer normalization is applied to normalize all inputs in each sample:

[0227]

[0228] Where μ′ is X res The mean of X res The standard deviation of .

[0229] Step 4.7: Pass the data through the feedforward neural network again, which contains two linear transformations. The data will be transformed by two different weight matrices (W1 and W2) and bias terms (b1 and b2). Between the two linear transformations, the ReLU (Rectified Linear Unit) activation function is applied: ReLU(x) = max(0,x), any negative value will be set to 0, while positive values ​​remain unchanged. Pass the output of ReLU through the second linear layer, weight matrix W2 and bias b 2， Finally, we get the output of the feedforward network:

[0230] FFN(x)=max(0,xW1+b1)W2+b2 (31)

[0231] Step 4.8: In order to convert these data back to their original physical meaning range, perform inverse normalization, which is the inverse operation of the normalization process:

[0232] X=0.5[x′(x max -x min )+(x max +x min )] (32)

[0233] Step 4.9: At the end of the model, the prediction results are output through the mapping layer:

[0234] Y=XW O +b O (33)

[0235] Where Y is the prediction result of the model, i.e., the remaining service life of the fuel cell; X is the internal representation after being processed by the model, i.e., the output of the last model layer; b O is the bias vector of the mapping layer; W O is the weight matrix of the mapping layer, which determines how to transform the internal representation into the prediction result.

[0236] Step 5.1: Use the improved LSA-SM algorithm to optimize the hyperparameters of the fuel cell remaining service life prediction model and initialize the relevant parameters of the LSA algorithm.

[0237] Step 5.2: Randomly generate the initial leader population (transition discharger).

[0238] Step 5.3: Execute the space discharge body and the guided discharge body model and check whether bifurcation occurs.

[0239] Step 5.4: Evaluate and update the pilot individuals.

[0240] Step 5.5: Update the positions of the T worst leaders using the simplex method.

[0241] Step 5.6: Generate an elite reverse population using the elite reverse learning strategy and compete with the original population.

[0242] Step 5.7: Determine whether the maximum number of iterations has been reached. If so, proceed to step 5.8. If not, re-enter step 5.3 for iterative calculation.

[0243] Step 5.8: Output the optimal hyperparameters and obtain the optimized LSA-SM-ITransformer model, as shown in Figure 4 shown.

[0244] Step 6.1: After the data is processed in step 2, the optimal input data set is established and divided into training set, validation set, and test set in a ratio of 7:1:2.

[0245] Step 6.2: Use the divided training set to train the improved LSA-SM-ITransformer fusion model to let the model learn the patterns and relationships in the data.

[0246] Step 6.3: Use the validation set to validate the model, help adjust the model parameters, prevent overfitting, and improve the generalization ability of the model.

[0247] Step 6.4: Use the fusion model to predict the test set and obtain the prediction result of the remaining battery life.

[0248] Based on the same inventive concept, this embodiment also provides a fuel cell remaining service life prediction system based on long-term operation data, including:

[0249] A data acquisition module, used to collect historical operation data of the fuel cell and perform preprocessing, wherein the preprocessing is to eliminate abnormal data using a divergence-based calibration method;

[0250] The data processing module is used to perform feature selection on the preprocessed data through inverse nonlinear principal component analysis (INLPCA), eliminate redundant and irrelevant feature information, and reconstruct the data to obtain the best input data set;

[0251] The algorithm improvement module is used to improve the LSA algorithm based on the lightning search algorithm by introducing the simplex method SM and the elite reverse learning strategy EOBL to obtain the improved hybrid simplex lightning search algorithm LSA-SM;

[0252] A model building module is used to build a fuel cell remaining service life prediction model based on the ITransformer model;

[0253] The model optimization module is used to optimize the hyperparameters of the fuel cell remaining service life prediction model using the improved hybrid simplex lightning search algorithm LSA-SM algorithm to obtain the optimal hyperparameters and obtain the optimized LSA-SM-ITransformer model;

[0254] The prediction module is used to predict the battery life using the optimized LSA-SM-ITransformer model to obtain the prediction result of the remaining battery life.

[0255] Based on the same inventive concept, this embodiment also provides a computing device, including: one or more processors, one or more memories and one or more programs, wherein the programs are stored in the memories and configured to be executed by the processors, and when the programs are loaded into the processors, the steps of the method for predicting the remaining service life of a fuel cell based on long-term operation data according to any one of the above items are implemented.

[0256] Based on the same inventive concept, this embodiment also provides a storage medium, which stores a computer program, and the computer program includes program instructions. When the program instructions are executed by a processor, the processor executes the steps of the method for predicting the remaining service life of a fuel cell based on long-term operation data according to any one of the above-mentioned items.

[0257] The method and system proposed in the present invention realize the real-time prediction of the remaining service life of the battery by collecting and analyzing the data generated during the long-term operation of the fuel cell. Through the system, users can intuitively understand the current status of the fuel cell, including key information such as battery capacity, performance degradation degree, and remaining service life. Based on these data, users can formulate more scientific and reasonable maintenance strategies, such as regularly replacing key components, optimizing battery use conditions, etc., thereby effectively extending the service life of the fuel cell, reducing energy loss, and improving the efficiency of the entire energy system.

[0258] The practical significance of this invention lies in that this remaining service life prediction system for long-term operation data of fuel cells has great practical significance. It can not only improve energy efficiency and reduce maintenance costs, but also effectively extend battery life and reduce energy waste. In addition, it supports the transformation of energy structure, promotes the development of clean energy technology, and meets the urgent global demand for sustainable energy solutions. The application of this technology helps to reduce dependence on fossil fuels, reduce greenhouse gas emissions, and combat climate change. At the same time, it enhances the market competitiveness of fuel cell manufacturers, improves system safety, optimizes resource allocation, and contributes to achieving global emission reduction goals and environmental protection.

Claims

1. A method for predicting the remaining service life of a fuel cell based on long-term operation data, characterized in that: include: Step 1: Collect historical operation data of the fuel cell and perform preprocessing, wherein the preprocessing is to remove abnormal data using a divergence-based calibration method; Step 2: Perform feature selection on the preprocessed data through inverse nonlinear principal component analysis (INLPCA), eliminate redundant and irrelevant feature information, and reconstruct it to obtain the optimal input data set; Step 3: Based on the lightning search LSA algorithm, the simplex method SM and the elite reverse learning strategy EOBL are introduced to improve it, and the improved hybrid simplex lightning search algorithm LSA-SM is obtained; Step 4: Establish a fuel cell remaining service life prediction model based on the ITransformer model; Step 5: Use the improved hybrid simplex lightning search algorithm LSA-SM algorithm to optimize the hyperparameters of the fuel cell remaining service life prediction model, obtain the optimal hyperparameters, and obtain the optimized LSA-SM-ITransformer model; Step 6: Use the optimized LSA-SM-ITransformer model to predict the battery life and obtain the prediction result of the remaining battery life.

2. The method for predicting the remaining service life of a fuel cell based on long-term operation data according to claim 1, characterized in that: The step 1 of removing abnormal data by using the divergence-based calibration method includes: The historical operation data of the fuel cell is standardized, and the Z score is calculated to measure the number of standard deviations between a data point and the mean: Among them, Z represents the Z score; X is the value of a single data point; μ is the mean of the data set; σ is the standard deviation of the data set; when the Z score of a data point is greater than 3 or less than -3, the data point is considered to be an outlier.

3. The method for predicting the remaining service life of a fuel cell based on long-term operation data according to claim 1, characterized in that: The step (2) comprises: Step 2.1: Normalize the preprocessed data and map it to [0,1]: Among them, x is the preprocessed data, x max is the maximum value of the data, x min is the minimum value of the data; Step 2.2: During INLPCA training, the normalized data is set as the network input value, and the output value is given To reversely estimate the principal component z of the training data and the weights w∈W3∪W4 of the network: Where: g is a nonlinear activation function, w∈W3∪W4, W3 and W4 are the weight matrices of the network; Step 2.3: Express the mean square error function of INLPCA training as: Where: d′ is the number of data dimensions; N is the number of samples; i, j, k are the number of neurons in the output layer, reconstruction layer and bottleneck layer respectively, and w ij is the weight from the jth neuron in the reconstruction layer to the ith neuron in the output layer, Represents the principal component value of the nth sample in the kth dimension; Step 2.4: INLPCA passes the mean square error back to the input layer to obtain the gradient; at this time, the weight w ij ∈W4,w jk ∈W3, with the principal component The gradients are expressed as: Where: is the training error on the i-th dimension of the n-th sample data; Step 2.5: Minimize the error function E(w,z) to solve the network weight w and the principal component z; for the principal component extraction of data x, fix w and then To search for the best result; Use weight decay coefficient to regularize the neural network: Where: E total is the total model error; v is the weight penalty coefficient; Step 2.6: Randomly extract data from several dimensions from the validation set data, take the extracted values ​​as the true values, use INLPCA to estimate the missing values, and calculate the estimated mean square error E MS : Finally, by adjusting v, the mean square error of the estimated value of the missing value is minimized; the true value is sorted in descending order. The larger the value, the more important the component. The top several are selected as the principal components according to the ranking to form the best input data set.

4. The method for predicting the remaining service life of a fuel cell based on long-term operation data according to claim 1, characterized in that: The step (3) includes: Step 3.1: LSA algorithm process: Transition discharge body: Assume a ladder leader SL with a population size of G = [sl1, sl2, ...., sl G ], the transition discharge body is expressed as sl g is the value of the Gth dimension of the ladder leader, is the value of the Gth dimension of the transition discharge body; in the early stage of the formation of the step leader, the transition discharge body propagates downward from the bottom of the thunderstorm cloud in a random direction. The transition discharge body obeys a uniform distribution, creates an initial random population, and converts the probability density function f(x T ) is expressed as: Among them, x T is a candidate solution, a and b are the lower and upper bounds of the solution space respectively; Space discharge body: Assume that the space discharge body is represented by is the value of the g-th dimension of the space discharge body, and the position uses the exponential distribution probability density function express: Wherein, μ is a shape parameter, which is used to control the position or direction of the next iteration of the space discharge body; in the LSA algorithm, μ is considered to be the guiding discharge body p L and space discharge body The distance between them, g = 1, 2, ..., G, space discharge body The position at the next iteration is expressed as: Among them, exprand is the random number generated by the exponential distribution function, and μ is the mean; Guide discharge body: Assume that the guide discharge body is represented by p L , the position is represented by the normal probability density function f(x L )express: Among them, x L is the value of the guiding discharge body in a certain dimension, μ is the mean, and σ is the standard deviation; Leading discharge body L The position at the next iteration is expressed as: Among them, Fitness(·) is the fitness function, normrand(μ,σ) is a random number generated based on normal distribution, μ is the mean, and σ is the standard deviation; Step 3.2: Use the simplex method to optimize the positions of K lightning leaders with the worst target values, improve the local search capability of the algorithm and speed up the convergence of the algorithm. Specifically: Step 3.2.1: Calculate the fitness function values ​​of all leading individuals in the population, assume that the one with the smallest fitness value is the best, determine the best point as xg, the second best point as xb and K worst points, and take one of the worst points as xw; Step 3.2.2: Calculate the center position of the optimal point xg and the suboptimal point xb Step 3.2.3: The worst point xw is based on the center point Perform reflection operations: Where xr is the reflection point and α is the reflection coefficient; calculate the fitness function value f(xr) of the z reflection point xr: Step 3.2.4: If f(xr) < f(xg), the reflection direction is correct and perform the following operations; otherwise, proceed to step 3.2.5: Where xe is the expansion point and γ is the expansion coefficient. Calculate the fitness function value f(xe) of the expansion point xe. If f(xe) < f(xg), xe replaces xw, otherwise xr replaces xw. Step 3.2.5: If f(xr)>f(xw), it means the reflection direction is wrong, and perform the following operations. Otherwise, proceed to step 3.2.6: Where xc is the compression point and β1 is the compression coefficient. Calculate the fitness function value f(xc) of the compression point xc. If f(xc) < f(xw), replace xw with xc. Step 3.2.6: When f(xg)<f(xr)<f(xw), perform the contraction operation: Where xs is the contraction point, β2 is the contraction coefficient, and the contraction coefficient and the compression coefficient have the same value; calculate the fitness function value f(xs) of the contraction point xs, if f(xs) < f(xw), replace xw with xs, otherwise replace xw with xr; Step 3.3: Assume that the solution with the best current fitness value in the population is defined as the elite leader, denoted as X ε =(x ε,1 ,x ε,2 ,...,x ε,D ), x ε,D is the position of the elite leader in dimension D. For a leader X g =(x g,1 ,x g,2 ,...,x g,D ), its elite reverse solution is defined into the formula: x g ′ ,d =k·(Lb d +Ub d )-x ε,d ,g=1,2,....,G;d=1,2,....,D(20) Where N is the population size, D is the dimension of the search space, k∈U(0,1), (Lb d ,Ub d ) is the search boundary; if the elite reverse solution x g ' ,d If the search boundary is exceeded, adjust it using the following formula: x g ′ ,d =rand(Lb d ,Ub d ), if x g ′ ,d <Lb d or x g ′ ,d >Ub d (21)。 5. The method for predicting the remaining service life of a fuel cell based on long-term operation data according to claim 1, characterized in that: The step 4 comprises: Step 4.1: Embed the input time series data into a high-dimensional space to capture the characteristics of the sequence, through a linear layer: X′=X :,n W E +b E (22) Among them, X :,n is the original data, X′ is the embedded data, W E and b E are the weights and biases of the embedding layer respectively; H l+1 =TrmBlock(H l ),l=0,...,L-1 (23) Among them, H l+1 represents the embedding representation of layer l, which is processed by the Transformer module TrmBlock(); Step 4.2: Add positional encoding to provide position information for each time step in the sequence: Where PE is the position code; pos is the position of the time step, i is the dimension index, d model is the dimension of the model; Step 4.3: Perform multi-head self-attention calculation: MultiHead(Q,K,V)=Concat(head1,…,head h )W O (26) Where Q, K, and V are query, key, and value matrices, respectively, and W i Q , W i K and W i V is the learnable weight matrix, h is the number of heads; The calculation for each head is: head i =Attention(QW i Q ,KW i K ,VW i V ) Among them, d model is the dimension of the model, d q ,d k and d v is the dimension of query, key and value in each attention head, R is a matrix; Step 4.4: Introduce self-attention mechanism: Among them, softmax() is the transfer function, QK T It is a dot product operation, which calculates the attention weight of Q on V; Used to scale dot products to prevent the vanishing gradient problem; Step 4.5: Perform residual connection and layer normalization, input X :,n The output of the multi-head self-attention layer is recorded as Sublayer(X :,n ), and then make a residual connection: X res =X :,n +Sublayer(X :,n ) (29) Among them, X res is the output after residual connection, where X :,n represents the input data set; Step 4.6: Normalize all inputs in each sample: Where μ′ is X res The mean of X res The standard deviation of Step 4.7: Let the normalized data be x, and perform a linear transformation through two different weight matrices W1 and W2 and two bias terms b1 and b2; between the two linear transformations, apply the ReLU activation function: ReLU(x) = max(0,x), set all negative values ​​to 0, and keep the positive values ​​unchanged; pass the output of ReLU through the second linear layer, weight matrix W2 and bias b2, and get the output of the feedforward network FFN: FFN(x)=max(0,xW1+b1)W2+b2 (31) Step 4.8: Perform reverse normalization: X=0.5[x′(x max -x min )+(x max +x min )] (32) Step 4.9: Output the prediction results through the mapping layer: Y=XW O +b O (33) Among them, Y is the prediction result of the model, which represents the remaining service life of the fuel cell; X is the internal representation after model processing, which is the output of the last model layer; b O is the bias vector of the mapping layer; W O is the weight matrix of the mapping layer, which is used to decide how to transform the internal representation into the prediction result.

6. The method for predicting the remaining service life of a fuel cell based on long-term operation data according to claim 1, characterized in that: The step 5 comprises: Step 5.1: Use the improved hybrid simplex lightning search algorithm LSA-SM algorithm to optimize the hyperparameters of the fuel cell remaining service life prediction model based on the LSA-SM-ITransformer model, and initialize the LSA algorithm hyperparameters; Step 5.2: Randomly generate transition discharge bodies as the initial leader population; Step 5.3: Execute the space discharge body and the guide discharge body model, and check whether bifurcation occurs; Step 5.4: Evaluate and update the lead individuals; Step 5.5: Use the simplex method to update the positions of the T worst leaders; Step 5.6: Use the elite reverse learning strategy to generate an elite reverse population and compete with the original population; Step 5.7: Determine whether the maximum number of iterations has been reached. If yes, proceed to step 5.

8. If no, proceed to step 5.3 again for iterative calculation. Step 5.8: Output the optimal hyperparameters and obtain the optimized LSA-SM-ITransformer model.

7. The method for predicting the remaining service life of a fuel cell based on long-term operation data according to claim 1, characterized in that: The step 6 comprises: Step 6.1: Divide the best input data set into training set, validation set, and test set according to the preset ratio; Step 6.2: Use the divided training set to train the improved LSA-SM-ITransformer model to enable the model to learn patterns and relationships in the data; Step 6.3: Use the validation set to verify the model, adjust the model parameters, and complete the training; Step 6.4: Use the trained model to predict the test set and obtain the prediction result of the remaining battery life.

8. A fuel cell remaining service life prediction system based on long-term operation data, characterized in that: include: A data acquisition module, used to collect historical operation data of the fuel cell and perform preprocessing, wherein the preprocessing is to eliminate abnormal data using a divergence-based calibration method; The data processing module is used to perform feature selection on the preprocessed data through inverse nonlinear principal component analysis (INLPCA), eliminate redundant and irrelevant feature information, and reconstruct the data to obtain the best input data set; The algorithm improvement module is used to improve the LSA algorithm based on the lightning search algorithm by introducing the simplex method SM and the elite reverse learning strategy EOBL to obtain the improved hybrid simplex lightning search algorithm LSA-SM; A model building module is used to build a fuel cell remaining service life prediction model based on the ITransformer model; The model optimization module is used to optimize the hyperparameters of the fuel cell remaining service life prediction model using the improved hybrid simplex lightning search algorithm LSA-SM algorithm to obtain the optimal hyperparameters and obtain the optimized LSA-SM-ITransformer model; The prediction module is used to predict the battery life using the optimized LSA-SM-ITransformer model to obtain the prediction result of the remaining battery life.

9. A computing device, characterized in that include: One or more processors, one or more memories, and one or more programs, wherein the programs are stored in the memories and configured to be executed by the processors, and when the programs are loaded into the processors, the steps of the method for predicting the remaining service life of a fuel cell based on long-term operation data according to any one of claims 1 to 7 are implemented.

10. A storage medium storing a computer program, characterized in that: The computer program includes program instructions, which, when executed by a processor, cause the processor to perform the steps of the method for predicting the remaining service life of a fuel cell based on long-term operation data according to any one of claims 1 to 7.

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