Long-term prediction method for proton exchange membrane fuel cell based on multi-step prediction strategy

Abstract

The application relates to the technical field of fuel cells, and discloses a long-term prediction method for a proton exchange membrane fuel cell based on a multi-step prediction strategy, which comprises the following steps: experimental data preprocessing, obtaining a model training data set and long-term prediction initial input data; establishing a model and training the model to obtain a trained mixed probability data-driven voltage degradation trend prediction model; long-term prediction based on the multi-step prediction strategy; prediction result and uncertainty analysis: taking the average value of the same prediction position as a point estimation result, taking the standard error range of the 95% confidence level as an interval estimation result, analyzing the point estimation and the interval estimation result through an error evaluation index, and simultaneously calculating the interval estimation concentration rate to evaluate the prediction uncertainty. The long-term prediction method for the proton exchange membrane fuel cell based on the multi-step prediction strategy has good long-term prediction effect, and the prediction result has high precision and reliability.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of fuel cell technology, and particularly relates to a long-term prediction method for a proton exchange membrane fuel cell based on a multi-step prediction strategy. BACKGROUND

[0002] Proton exchange membrane fuel cell (PEMFC) systems are the preferred solution for new energy vehicle power sources, and have shown significant application value in vehicle energy fields due to their high energy conversion efficiency, low noise, and zero emissions.

[0003] However, the industrialization process of this technology is still subject to two major bottlenecks: first, the high cost of key materials leads to insufficient economy; second, the durability degradation mechanism of the stack under dynamic conditions is complex, which limits the service life. In particular, in the actual operation of electric vehicles, the stack needs to frequently withstand dynamic load changes, and its state of health (SOH) is affected by the interaction of current density fluctuations, voltage response abnormalities, temperature and pressure coupling changes, and other multi-physical field parameters, ultimately leading to system performance degradation and directly affecting the remaining useful life (RUL). Therefore, the intelligent diagnosis system based on prognosis and health management (PHM) has become an important research direction in the industry. By integrating mechanism models and machine learning algorithms, a predictable model of the degradation state of the stack is constructed, and then an active health management strategy is implemented.

[0004] In the stack state monitoring index system, the voltage parameter is the core characteristic quantity for SOH evaluation due to its ease of measurement, high sensitivity, and strong correlation. The current mainstream voltage decay prediction methods can be divided into three technical routes: model-driven method based on electrochemical mechanism, model-free method based on big data, and hybrid method combining the two. Among them, the model-driven method needs to accurately establish a numerical model containing multi-scale degradation mechanisms such as proton conduction, double-layer effect, and catalyst deactivation. However, the inherent nonlinear time-varying characteristics of the PEMFC system and the randomness of the operating conditions make it difficult for traditional mechanism models to accurately describe the actual dynamic decay process. In contrast, the data-driven method avoids the difficulties of complex mechanism modeling by deeply mining the evolution law of voltage time series data, and shows stronger adaptability in engineering practice.

[0005] In recent years, with the breakthrough of deep learning technology, prediction methods based on neural networks have made significant progress in PEMFC degradation analysis. Typical algorithm architectures include long short-term memory networks (LSTM) and gated recurrent units (GRU) with time series feature extraction capabilities, convolutional neural networks (CNN) with spatial correlation modeling, spatiotemporal convolutional networks (TCN), and Gaussian process regression (GPR) integrated with probabilistic inference. Existing technical solutions mostly adopt a single-step long rolling prediction mechanism: historical monitoring data is input into the trained model in the form of a sliding window, and the voltage value at the next moment is predicted hour by hour. Although this method can ensure short-term prediction accuracy, it has two inherent defects: (1) the prediction time domain is limited and cannot meet the needs of full life cycle management; (2) in recursive long-term prediction, the error accumulates exponentially with the number of iterations, which ultimately causes the prediction trajectory to deviate seriously from the actual degradation curve. This prediction inaccuracy problem directly affects the reliability of RUL estimation, making it difficult for health management systems based on traditional methods to implement accurate preventive maintenance strategies. Summary of the Invention

[0006] The purpose of the present invention is to address the deficiencies of the above-mentioned technologies and provide a long-term prediction method for proton exchange membrane fuel cells based on a multi-step prediction strategy, which has good long-term prediction effect and high prediction result accuracy and credibility.

[0007] To achieve the above-mentioned object, the present invention relates to a long-term prediction method for proton exchange membrane fuel cells based on a multi-step prediction strategy, comprising the following steps:

[0008] S1) Experimental Data Preprocessing: Based on the PEMFC durability experimental dataset, voltage data is sampled and filtered, then divided into a training set and a test set. The training set is normalized to obtain the model training dataset. The test set is also normalized, and the voltage data of the sliding window size before the test set is taken as the initial input data for long-term prediction.

[0009] S2) Model building and training: replacing neurons in the common neural network of the hybrid data-driven model with neurons composed of a long short-term memory network, a gated recurrent unit, and a minimum gated unit structure, using a self-attention mechanism as a connection medium and combining it with probabilistic Bayesian theory, replacing model parameters of the hybrid data-driven model with probability distributions to obtain a hybrid probabilistic data-driven model. Combined with the training data set obtained in step S1), a trained hybrid probabilistic data-driven voltage decay trend prediction model is obtained.

[0010] S3) Long-term prediction based on a multi-step prediction strategy: The initial long-term prediction input data obtained in step S1) is input into the trained hybrid probability data-driven voltage decay trend prediction model obtained in step S2) to obtain the model output. The average value of the data at the same prediction location at different times is added to the end of the hybrid probability data-driven voltage decay trend prediction model input data. The hybrid probability data-driven voltage decay trend prediction model input data is updated by sliding the input window until all predictions are completed.

[0011] S4) Forecast results and uncertainty analysis: The average value of the same forecast position is used as the point estimate result, and the standard error range of the 95% confidence level is used as the interval estimate result. The point estimate and interval estimate results are analyzed using error assessment indicators, and the interval estimate concentration rate is calculated to evaluate the forecast uncertainty.

[0012] Preferably, in step S1), when sampling the voltage data, a three-spline interpolation method is adopted, and the sampling interval is 1 hour.

[0013] Preferably, in step S1), a weighted average filtering algorithm is used to filter the voltage data.

[0014] Preferably, in step S1), after the training set is normalized, a model training data set is constructed according to the sliding window size and prediction step size.

[0015] Preferably, in step S2), the expression of the long short-term memory network is as follows:

[0016] LSTM: Where LSTM is a long short-term memory network, f k is the forget gate of LSTM, σ is the sigmoid function, W f is the weight matrix of the LSTM forget gate, x k For the current moment k Enter information, is the hidden state passed to the self-attention mechanism by LSTM, is the hidden state of LSTM at the previous moment, b f is the bias matrix of the LSTM forget gate, i k is the input gate of LSTM, W i is the weight matrix of the LSTM input gate, b i is the bias matrix of the LSTM input gate, c kMemory state of LSTM, c k-1 Memory state of LSTM at last time, Candidate memory state of LSTM, tanh is tanh function, W c Weight matrix of candidate memory state of LSTM, b c Bias matrix of candidate memory state of LSTM, o k Output gate of LSTM, W o Weight matrix of output gate of LSTM, b o Bias matrix of output gate of LSTM;

[0017] The expression of gated recurrent unit is as follows:

[0018] GRU: In the formula, GRU is a gated recurrent unit, z k Update gate of GRU, σ Sigmoid function, W z Weight matrix of update gate of GRU, x k Current time k Input information, Hidden state of GRU passed to self-attention mechanism, Hidden state of GRU at last time, b z Bias matrix of update gate of GRU, r k Reset gate of GRU, W r Weight matrix of reset gate of GRU, b r Bias matrix of reset gate of GRU, Candidate hidden state of GRU, tanh is tanh function, W h1 Weight matrix of candidate hidden state of GRU, b h1 Bias matrix of candidate hidden state of GRU;

[0019] The expression of minimum gate unit is as follows:

[0020] MGU: In the formula, MGU is a minimum gate unit, u k Update gate of MGU,σ sigmoid is sigmoid function, W u Wu is a weight matrix of the update gate of the MGU, x k t is a current time k input information, h is a hidden state of the MGU passed to the self-attention mechanism, ht-1 is a hidden state of the MGU at a previous time, ht is a candidate hidden state of the MGU, b u bu is a bias matrix of the update gate of the MGU, tanh is tanh function, W h2 Wu is a weight matrix of the update gate of the MGU, f k fi is a forget gate of a long short-term memory network LSTM, b h2 bu is a bias matrix of the update gate of the MGU;

[0021] The expression of the self-attention mechanism is as follows:

[0022] SA: In the formula, SA is the self-attention mechanism, X k t is a current time k information input to the SA, Q k q is a query vector, K k k is an index vector, V k v is a content vector, W Q Wq is a weight matrix of the query vector, W K Wk is a weight matrix of the index vector, W V Wv is a weight matrix of the content vector, Attention( Q k , K k , V k ) is an output of the SA, softmax is softmax function, d dim(k) is a dimension of the index vector.

[0023] Preferably, in the step S2), the model parameters of the hybrid data-driven model are replaced by a probability distribution to obtain a hybrid probability data-driven model:

[0024] The model parameters of the hybrid probability data-driven model are obtained based on Bayes' theorem ωposterior distribution of the model parameters where, p ( ω | D ) are the model parameters ω , D is the model training dataset, p ( ω ) is the prior distribution of the model parameters ω , p ( D | ω ) is the likelihood function of the model parameters ω , p ( D ) is the prior distribution of the model training dataset, parameters ω include W f , W i , W c , W o , b f , b i , b c , b o , W z , W r , b z , b r , W h1 , b h1 , W u , b u , W h2 , b h2 , W Q , W K , W V , D in combination with the model training dataset , x is the input data, y is the model output, p( y | x , D ) is the output distribution under the given model training data set D and input data x , p ( y | x , ω ) is the output distribution under the given parameter ω and input data x .

[0025] Preferably, in the step S3, the long-term prediction initial input data at time 1 is x 1, x 2, …, x M-1 , x M ), M is the model input window size, the model output is obtained, N is the model output step size, at time 2, the average value of the prediction position 1 is added to the tail of the input data, the model input data is x 2, x 3, …, x M , ), the model output is , similarly, at time 3, the average value of the prediction position 2 is added to the tail of the input data, the model input data is x 3, x 4, …, , ), the model output is , through the above steps, all predictions are completed at time k .

[0026] Preferably, in the step S4, the calculation formula is as follows:

[0027] In the formula, i is the prediction position, Mean is the sample mean function, Var is the sample variance function, y i is the point estimate result when the prediction position is i , is the upper limit of the interval estimate, is the lower limit of the interval estimate.

[0028] Compared with the prior art, the present application has the following advantages:

[0029] 1. The hybrid probabilistic data-driven model has excellent PEMFC voltage decay trend prediction capabilities. Combined with a multi-step prediction strategy, it can achieve long-term prediction of voltage decay trends without relying on real historical data. It has achieved good prediction results in durability test data sets under static and dynamic load cycles.

[0030] 2. Based on the multi-step prediction strategy, point estimation and interval estimation prediction results can be obtained simultaneously. The interval estimation can provide the 95% confidence interval range of the voltage attenuation trend, which improves the credibility of the prediction results;

[0031] 3. It has a large plastic space and can adapt to different needs by adjusting the model structure, sliding input window size, and model output steps. When there is a large amount of historical data, the sliding window size and model output steps can be increased. The increase in the number of model output steps will further improve the accuracy of multi-step prediction results at the same time, reduce the cumulative error in the recursive process, and thus further improve the accuracy of long-term predictions as a whole. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 Schematic diagram of the process of the long-term prediction method of proton exchange membrane fuel cells based on the multi-step prediction strategy of the present invention;

[0033] Figure 2 Schematic diagram of long-term prediction based on multi-step prediction strategy. DETAILED DESCRIPTION

[0034] The technical solutions of the present invention will be described clearly and completely below with reference to the accompanying drawings and embodiments. It is obvious that the embodiments described are only a portion of the embodiments of the present invention, not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort are also within the scope of protection of the invention.

[0035] like Figure 1 As shown, a long-term prediction method for proton exchange membrane fuel cells based on a multi-step prediction strategy includes the following steps:

[0036] S1) Experimental Data Preprocessing: Based on the PEMFC durability experimental dataset, voltage data is sampled and filtered, then divided into a training set and a test set. The training set is normalized to obtain the model training dataset. The test set is also normalized, and the voltage data of the sliding window size before the test set is taken as the initial input data for long-term prediction.

[0037] S2) Model establishment and model training: replace the neurons of the hybrid data-driven model ordinary neural network with neurons composed of long short-term memory network, gated recurrent unit and minimum gate unit structure, use self-attention mechanism as the connection medium, replace the model parameters of the hybrid data-driven model with probability distribution according to the probability Bayesian theory, obtain a hybrid probability data-driven model, and train the hybrid probability data-driven voltage degradation trend prediction model according to the training data set obtained in step S1);

[0038] S3) Long-term prediction based on multi-step prediction strategy: input the long-term prediction initial input data obtained in step S1) into the trained hybrid probability data-driven voltage degradation trend prediction model obtained in step S2), obtain the model output, and add the average value of the same prediction position at different times to the tail of the hybrid probability data-driven voltage degradation trend prediction model input data, update the hybrid probability data-driven voltage degradation trend prediction model input data through a sliding input window until all predictions are completed.

[0039] S4) Prediction results and uncertainty analysis: take the average value of the same prediction position as the point estimate result, take the standard error range of the 95% confidence level as the interval estimate result, analyze the point estimate and interval estimate results through the error evaluation index, and calculate the interval estimate concentration rate to evaluate the prediction uncertainty.

[0040] In step S1), when sampling the voltage data, a three-spline interpolation method is used, and the sampling interval is 1h. Other time intervals can also be used. When filtering the voltage data, a weighted average filtering algorithm is used. After normalizing the training set, the model training data set is constructed according to the sliding window size and the prediction step.

[0041] In step S2), the expression of the long short-term memory network is as follows:

[0042] LSTM: In the formula, LSTM is the long short-term memory network, f k is the forgetting gate of LSTM, σ is a sigmoid function, W f is the weight matrix of the LSTM forgetting gate, x k is the current time k input information, is the hidden state of the LSTM transmitted to the self-attention mechanism, is the hidden state of the LSTM at the previous time, b f is the bias matrix of the LSTM forgetting gate, i kinput gate of the LSTM, W i weight matrix for the input gate of the LSTM, b i bias matrix for the input gate of the LSTM, c k memory state of the LSTM, c k-1 previous memory state of the LSTM, candidate memory state of the LSTM, tanh is a tanh function, W c weight matrix for the candidate memory state of the LSTM, b c bias matrix for the candidate memory state of the LSTM, o k output gate of the LSTM, W o weight matrix for the output gate of the LSTM, b o bias matrix for the output gate of the LSTM;

[0043] The expression of the gated recurrent unit is as follows:

[0044] GRU: In the formula, GRU is a gated recurrent unit, z k update gate of the GRU, σ sigmoid function, W z weight matrix for the update gate of the GRU, x k input information at the current moment, k input information, hidden state of the GRU passed to the self-attention mechanism, previous hidden state of the GRU, b z bias matrix for the update gate of the GRU, r k reset gate of the GRU, W r weight matrix for the reset gate of the GRU, b r bias matrix for the reset gate of the GRU, candidate hidden state of the GRU, tanh is a tanh function, W h1 weight matrix for the candidate hidden state of the GRU, b h1 bias matrix for the candidate hidden state of the GRU;

[0045] The expression of the minimum gating unit is as follows:

[0046] MGU: In the formula, MGU is a minimum gating unit, u k is the update gate of the MGU, σ is a sigmoid function, W u is the weight matrix of the MGU update gate, x k is the input information at the current moment k , is the hidden state of the MGU passed to the self-attention mechanism, is the hidden state of the MGU at the previous moment, is the candidate hidden state of the MGU, b u is the bias matrix of the MGU update gate, and tanh is a tanh function, W h2 is the weight matrix of the MGU candidate hidden state, f k is the forget gate of the long short-term memory network LSTM, b h2 is the bias matrix of the MGU candidate hidden state;

[0047] The expression of the self-attention mechanism is as follows:

[0048] SA: In the formula, SA is a self-attention mechanism, X k is the information input to the SA at the current moment k , Q k is a query vector, K k is an index vector, V k is a content vector, W Q is the weight matrix of the query vector, W K is the weight matrix of the index vector, W V is the weight matrix of the content vector, Attention( Q k , K k , V k ) is the output of the SA, and softmax is a softmax function, d is the dimension of the index vector.

[0049] Then, in step S2), the model parameters of the hybrid data-driven model are replaced by the probability distribution, and a hybrid probability data-driven model is obtained:

[0050] Based on Bayes' theorem, the posterior distribution of the model parameters of the hybrid probability data-driven model is obtained: ω where, p ω D is the posterior distribution of the model parameters, ω is the model training data set, D p ω is the prior distribution of the model parameters, ω p D is the likelihood function of the model parameters, ω ω p D is the prior distribution of the model training data set, and the parameters ω include W f , W i , W c , W o , b f , b i , b c , b o in the LSTM expression W z , W r , b z , b r , W h1 , b h1 in the GRU expression W u , b u , W h2 , b h2 in the SA expression W Q , W K , W V ​​​​​​​​​​, combined model training dataset D , the trained hybrid probability data-driven voltage degradation trend prediction model is obtained: wherein, x is the input data, y is the model output, p y x , D is the output distribution under the given model training dataset D and the input data x , p y x , ω is the output distribution under the given parameters ω and the input data x .

[0051] In step S3, the long-term prediction initial input data at time 1 is x 1, x 2, …, x M-1 , x M , M is the model input window size, the model output is obtained, N is the model output step size, at time 2, the average value of the prediction position 1 is added to the tail of the input data, through the sliding input window, the model input data is x 2, x 3, …, x M , , the model output is , similarly, at time 3, the average value of the prediction position 2 is added to the tail of the input data, through the sliding input window, the model input data is x 3, x 4, …, , , the model output is , through the above steps, all predictions are completed recursively at time k .

[0052] In step S4, the calculation formula is as follows:

[0053] wherein, i is the prediction position, Mean is the sample mean function, Var is the sample variance function, y i is the point estimate result when the prediction position is i , ​​​​The upper limit of the interval estimation is calculated as follows, The lower limit of the interval estimation is calculated as follows.

[0054] The average of the prediction values at the same prediction position at different times is taken as the point estimation result of the prediction position, the point estimation result is added to the tail of the input data, and the prediction value is recursively output through the sliding window to complete the long-term prediction of the voltage decay trend. A multi-step prediction strategy is adopted to replace the traditional single-step iteration mode, and a multi-step prediction sequence is generated by expanding the output step; secondly, a prediction value fusion mechanism is innovatively designed, the prediction values at the same prediction position at different times are averaged, and the random deviation of the prediction result at the same time is suppressed; finally, the credibility modeling of the prediction process is realized under the probability Bayesian deep learning framework, the model parameters are replaced by probability distribution, and the prediction result with 95% confidence interval is output. By averaging the prediction values at the same prediction position at different times, the cumulative error in long-term prediction is effectively reduced, the stability of long-term prediction is significantly improved, and a reliable solution for PEMFC voltage decay prediction is provided.

[0055] The long-term prediction method of the proton exchange membrane fuel cell based on the multi-step prediction strategy can realize long-term prediction of the voltage decay trend without relying on real historical data through the hybrid probability data-driven model with excellent PEMFC voltage decay trend prediction capability and the multi-step prediction strategy, and good prediction effect is achieved in static and dynamic load cycle durability experimental data sets; based on the multi-step prediction strategy, point estimation and interval estimation prediction results can be obtained at the same time, the interval estimation can give the 95% confidence interval range of the voltage decay trend, and the credibility of the prediction result is improved; the plastic space is large, and different requirements can be adapted by adjusting the model structure, the sliding input window size and the model output step number, when there is a large amount of historical data, the sliding window size and the model output step number can be increased, the increase of the model output step number will further improve the accuracy of the multi-step prediction result at the same time, reduce the cumulative error in the recursive process, and thus further improve the accuracy of the long-term prediction as a whole.

[0056] Here, it should be noted that the description of the above technical solutions is exemplary, and the specification can be embodied in different forms, and should not be interpreted as being limited to the technical solutions set forth herein. On the contrary, providing these descriptions will make the present disclosure thorough and complete, and will fully convey the scope disclosed by the specification to those skilled in the art. In addition, the technical solutions of the present application are limited only by the scope of the claims.

[0057] The aspects disclosed in the specification and claims are merely exemplary and the specification and claims are not limited to the details given. In the above description, detailed description of related known functions or configurations will be omitted when it is determined that such detailed description will make the focus of the specification and claims ambiguous.

[0058] Finally, it should be noted that the above content is a further detailed description of the application in combination with the specific embodiments, and the specific embodiments of the application should not be considered as limiting the application. Simple substitutions made by those skilled in the art without departing from the concept of the application should be considered as falling within the protection scope of the application. The above examples are only more representative examples of the application. Obviously, the application is not limited to the above examples, and there can be many variations. Any simple modification, equivalent change and modification made according to the technical essence of the application to the above examples should be considered as falling within the protection scope of the application.

Claims

1. A long-term prediction method for proton exchange membrane fuel cells based on a multi-step prediction strategy, characterized by: The steps include: S1) Experimental data preprocessing: Based on the PEMFC durability experimental dataset, voltage data is sampled and filtered, then divided into a training set and a test set. The training set is normalized to obtain the model training dataset. The test set is normalized, and the voltage data of the sliding window size before the test set is taken as the initial input data for long-term prediction. S2) establishing and training a model: replacing neurons of a common neural network in the hybrid data-driven model with neurons composed of a long short-term memory network, a gated recurrent unit, and a minimum gated unit structure; using a self-attention mechanism as a connection medium; combining probabilistic Bayesian theory; replacing model parameters of the hybrid data-driven model with probability distributions to obtain a hybrid probabilistic data-driven model; and combining the training data set obtained in step S1) to obtain a trained hybrid probabilistic data-driven voltage decay trend prediction model; S3) Long-term prediction based on multi-step prediction strategy: The long-term prediction initial input data obtained in step S1) is input into the trained mixed probability data driven voltage decay trend prediction model obtained in step S2) to obtain the model output, and the average value at the same prediction position at different times is added to the end of the mixed probability data driven voltage decay trend prediction model input data. The mixed probability data driven voltage decay trend prediction model input data is updated by sliding the input window until all predictions are completed. The long-term prediction initial input data at time 1 is (x1, x2, ..., x M-1 ,x M ), M is the model input window size, and the model output is N is the number of steps of model output. At time 2, the average value of the predicted position 1 is taken. Add to the end of the input data, through the sliding input window, the model input data is The model output is Similarly, at time 3, take the average value of predicted position 2 Add to the end of the input data, through the sliding input window, the model input data is The model output is Through the above steps, recursively complete all predictions at time k; S4) Forecast results and uncertainty analysis: The average value of the same forecast position is taken as the point estimate result, and the standard error range of the 95% confidence level is taken as the interval estimate result. The point estimate and interval estimate results are analyzed using error evaluation indicators, and the interval estimate concentration rate is calculated to evaluate the forecast uncertainty.

2. The long-term prediction method for proton exchange membrane fuel cells based on a multi-step prediction strategy according to claim 1, characterized in that: In the step S1), when sampling the voltage data, a three-spline interpolation method is used, and the sampling interval is 1 hour.

3. The long-term prediction method for proton exchange membrane fuel cells based on a multi-step prediction strategy according to claim 1, characterized in that: In step S1), a weighted average filtering algorithm is used to filter the voltage data.

4. The long-term prediction method for proton exchange membrane fuel cells based on a multi-step prediction strategy according to claim 1, characterized in that: In step S1), after the training set is normalized, a model training data set is constructed according to the sliding window size and prediction step size.

5. The long-term prediction method for proton exchange membrane fuel cells based on a multi-step prediction strategy according to claim 1, characterized in that: In step S2), the expression of the long short-term memory network is as follows: LSTM: Where LSTM is a long short-term memory network, f k is the forget gate of LSTM, σ is the sigmoid function, W f is the weight matrix of the LSTM forget gate, x k Input information for the current time k, is the hidden state passed to the self-attention mechanism by LSTM, is the hidden state of LSTM at the previous moment, b f is the bias matrix of the LSTM forget gate, i k is the input gate of LSTM, W i is the weight matrix of the LSTM input gate, b i is the bias matrix of the LSTM input gate, c k is the memory state of LSTM, c k-1 It is the memory state of LSTM at the previous moment. is the candidate memory state of LSTM, tanh is the tanh function, W c is the weight matrix of the LSTM candidate memory state, b c is the bias matrix of the LSTM candidate memory state, o k is the output gate of LSTM, W o is the weight matrix of the LSTM output gate, b o is the bias matrix of the LSTM output gate; The expression of the gated recurrent unit is as follows: GRU: In the formula, GRU is the gated recurrent unit, z k is the update gate of GRU, σ is the sigmoid function, W z Update the weight matrix of the GRU gate, x k Input information for the current time k, is the hidden state passed to the self-attention mechanism by GRU, is the hidden state of GRU at the previous moment, b z Update the bias matrix of the GRU gate, r k is the reset gate of GRU, W r Reset the gate weight matrix for GRU, b r Reset the bias matrix of the gate for GRU, is the candidate hidden state of GRU, tanh is the tanh function, W h1 is the weight matrix of the GRU candidate hidden state, b h1 is the bias matrix of the GRU candidate hidden state; The expression of the minimum gate unit is as follows: MGU: Where MGU is the minimum gate control unit, u k is the update gate of MGU, σ is the sigmoid function, W u Update the gate weight matrix for the MGU, x k Input information for the current time k, is the hidden state passed to the self-attention mechanism by MGU, The hidden state of MGU at the last moment. is the candidate hidden state of MGU, b u is the bias matrix of the MGU update gate, tanh is the tanh function, W h2 is the weight matrix of the MGU candidate hidden state, f k is the forget gate of the long short-term memory network LSTM, b h2 is the bias matrix of the MGU candidate hidden state; The expression of the self-attention mechanism is as follows: SA: Q k =X k W Q K k =X k W K V k =X k W V Where SA is the self-attention mechanism, X k is the information input to SA at the current moment k, Q k is the query vector, K k is the index vector, V k is the content vector, W Q is the weight matrix of the query vector, W K is the weight matrix of the index vector, W V is the weight matrix of the content vector, Attention(Q k ,K k ,V k ) is the output of SA, softmax is the softmax function, and d is the dimension of the index vector.

6. The long-term prediction method for proton exchange membrane fuel cells based on a multi-step prediction strategy according to claim 5, characterized in that: In step S2), the model parameters of the hybrid data-driven model are replaced with probability distribution to obtain a hybrid probability data-driven model: Based on Bayes' theorem, the posterior distribution of the model parameter ω of the mixed probability data-driven model is obtained: Where p(ω|D) is the posterior distribution of the model parameter ω, D is the model training data set, p(ω) is the prior distribution of the model parameter ω, p(D|ω) is the likelihood function of the model parameter ω, p(D) is the prior distribution of the model training data set, and the parameter ω includes W in the LSTM expression f , W i , W c , W o , b f , b i , b c , b o , W in the GRU expression z , W r , b z , b r , W h1 , b h1 , W in the MGU expression u , b u , W h2 , b h2 , W in SA expression Q , W K , W V , combined with the model training data set D, the trained mixed probability data driven voltage decay trend prediction model is obtained: p(y|x,D)=∫p(y|x,ω)p(ω,D)dω Where x is the input data, y is the model output, p(y|x,D) is the output distribution under the given model training dataset D and input data x, and p(y|x,ω) is the output distribution under the given parameter ω and input data x.

7. The long-term prediction method for proton exchange membrane fuel cells based on a multi-step prediction strategy as claimed in claim 1, characterized in that: In the step S4), the calculation formula is as follows: Where i is the predicted position, Mean is the sample mean function, Var is the sample variance function, and y i is the point estimation result of the predicted position i, is the upper limit of the interval estimate, Estimated lower bound of the interval.

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