Fuel cell performance degradation prediction method and system

Abstract

The invention discloses a fuel cell performance degradation prediction method and system. The method belongs to the technical field of proton exchange membrane fuel cells, and comprises the following operation steps: firstly, acquiring output voltage data and characteristic variables of the proton exchange membrane fuel cell, and observing and filtering acquired signals by using an SKF in order to improve the accuracy of the data, removing measurement noise and system noise and enhancing a control effect; secondly, carrying out feature selection on the feature variables by adopting BRFE; then, a Stacking model is established, XGBoost, Stan HopNet and DHKELM are selected as a base learning device, and AESELM enhanced by an automatic encoder is used as a meta learning device; and finally, an improved artemisinin optimization algorithm is introduced to carry out parameter optimization on the meta-learner model so as to enhance the prediction performance and the generalization ability of the model. The method not only can effectively predict performance degradation of the PEMFC, but also can provide a scientific basis for maintenance and management of the fuel cell, so that the service life of the fuel cell is prolonged, and the overall efficiency is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of proton exchange membrane fuel cells, and relates to a method for predicting performance degradation of proton exchange membrane fuel cells; specifically, it relates to a method and system for predicting performance degradation of fuel cells. Background Art

[0002] At present, the energy composition is mainly mineral fuels, but due to the depletion of mineral resources, the situation is getting worse and worse. Therefore, it is very important to develop new energy. In order to cope with energy shortages, improve energy utilization, and reduce greenhouse gas emissions, new energy is becoming increasingly popular.

[0003] Proton exchange membrane fuel cells (PEMFCs) are considered to be the most promising energy source for achieving carbon neutrality due to their high energy conversion efficiency, low operating temperature, high specific power, and environmental friendliness. Hydrogen and fuel cells are important development directions for my country's energy industry. However, the poor stability of PEMFCs is the main bottleneck restricting the large-scale application and industrialization of PEMFCs. In engineering practice, the prediction and health management of fuel cell life decay are important means to solve their reliability and durability. Accurate and efficient PEMFC life decay prediction methods are key scientific issues that need to be solved urgently, and provide theoretical support for maintenance strategy formulation, operating condition optimization, and operation status evaluation.

[0004] As a complex electrochemical system with strong coupling involving multiple physical quantities, multiple components and multiple factors, the strong nonlinearity, randomness and uncertainty in the performance degradation process of PEMFC greatly increase the difficulty of prediction. At present, the PEMFC performance degradation prediction method still has problems such as low prediction accuracy, poor generalization and lack of uncertainty expression. In order to solve the above problems, a PEMFC performance degradation prediction based on base feature selection and ensemble learning is established. By making full use of PEMFC degradation data and effectively mining the deep features in the data, the accuracy and reliability of PEMFC performance degradation prediction can be improved. Summary of the invention

[0005] In view of the above problems, the purpose of the present invention is to propose a fuel cell performance degradation prediction method and system, aiming to improve the prediction accuracy and reliability of proton exchange membrane fuel cell performance degradation, and at the same time improve the accuracy of proton exchange membrane fuel cell performance degradation prediction through feature selection and ensemble learning.

[0006] The technical solution of the present invention is: a method for predicting fuel cell performance degradation according to the present invention, the operation steps of which are as follows:

[0007] Step (1): collecting the output voltage data and characteristic variables of the proton exchange membrane fuel cell and preprocessing the data;

[0008] To improve the accuracy of the data, SKF is used to observe and filter the collected signals;

[0009] Step (2): In order to improve the performance and efficiency of the model, BRFE is used to select the feature variables, and the threshold is set to select the best feature to obtain a new feature subset as the input variable;

[0010] Step (3): Establish a Stacking model, where the base learners are XGBoost, StanHop_Net and DHKELM;

[0011] Input the preprocessed data into each base learner; obtain three differently trained weak learners; use the validation set to verify the performance of each weak learner and obtain three different sets of prediction results;

[0012] Step (4): Input the three sets of prediction results and the original data labels as new training sets into the meta-learner for secondary training;

[0013] The meta-learner uses the AESELM model enhanced by the autoencoder, and finally uses the test set to verify the performance of the AESELM model to obtain the final prediction result;

[0014] Step (5): Introduce the improved artemisinin optimization algorithm, tune the model parameters, add a periodic oscillation mutation strategy in the initialization stage, introduce Adaptive Loop Fusion and Splitting for optimization and improvement in the comprehensive elimination stage, and dynamically adjust the number of clusters according to data characteristics when processing large-scale data.

[0015] Furthermore, in step (1), the characteristic variables of the proton exchange membrane fuel cell include current, temperature, humidity, degradation time and gas supply pressure.

[0016] Furthermore, the implementation process of step (1) is as follows:

[0017] SKF is introduced to improve filtering accuracy, computational efficiency and reduce computational complexity. The SKF approximates the output distribution of nonlinear functions by using Sigma Points.

[0018] The SKF operation process is as follows:

[0019] Initialize Select an initial state estimate And the initial covariance matrix P0 generates Sigma Points, a central point 2n diffusion points;

[0020] Where n is the dimension of the state vector, and the points are symmetrically distributed around the center point;

[0021] Propagate each Sigma Point to the next time step through a nonlinear function to obtain a predicted set of Sigma Points;

[0022] The propagated Sigma Points set is used to calculate the mean and covariance of the predicted state, as shown in the following formula:

[0023]

[0024] Where W i c and W i m is the weight, is the i-th Sigma Points, Q is the process noise covariance;

[0025] Observation update: propagate each Sigma Point through the observation model h to obtain the observed Sigma Points set; use the observed Sigma Points set to calculate the Kalman gain K:

[0026]

[0027] In the formula, H k is the Jacobian matrix of the observation model, R is the observation noise covariance;

[0028] Iterations are repeated until the state estimation of all time steps is completed; the acquired signal after observation and filtering is output and feature extraction is performed on it.

[0029] Furthermore, the operation steps of step (2) are as follows: Assume that the initial sample is X∈S N×M ; Where N is the number of samples and M is the number of features; On this basis, BRFE is proposed to recursively select the best feature subset from the features of the original samples, which is divided into two parts: dynamic calculation of feature importance and recursive selection of the best feature subset;

[0030] The dynamic calculation of feature importance is as follows: First, prepare the decision tree training data set, randomly take N' samples from the original sample with replacement, and get a small sample X N' , randomly selected from the M features of the sample The features are the feature subsets in a single decision tree. The Gini index is used to represent the importance of the features and the decision tree node splitting strategy. The Gini index at a node is calculated as shown in formula (1); that is:

[0031]

[0032] In the formula, p i Indicates the proportion of feature category i on the node;

[0033] The change in the Gini index before and after the node split is expressed as follows:

[0034] ΔGI=Gini-Gini i -Gini r (5)

[0035] In the formula, Gini i Represents the Gini index of the left node after the node splits, Gini r Represents the Gini index of the right node after splitting;

[0036] The importance of a feature at this node is as follows:

[0037]

[0038] The importance on the jth decision tree is the importance of all nodes, that is:

[0039] VIM j =ΣVIM (7)

[0040] Assuming that there are Q decision trees in the random forest, the importance of this feature is as follows:

[0041]

[0042] In the formula, VIM i Indicates the importance of the i-th feature category in the random forest among all features, VIM Q Represents the normalized result of the importance score of a feature in the random forest;

[0043] The recursive selection of the best feature subset: using the feature selection idea of ​​random forest, a BRFE is proposed; by sorting the importance of each feature in the random forest algorithm, and using the recursive feature elimination method to remove the least important feature;

[0044] Through multiple learning of random forests, the minimum importance is removed to obtain a new feature subset until the optimal feature setting threshold is reached.

[0045] Furthermore, in step (3), the implementation steps of establishing the XGBoost model are as follows:

[0046] Assume training set, loss function Train = {(x1, y1), (x2, y2), ... (xn, yn)}, loss function Regularization term Ω(fk ), then the objective function is recorded as:

[0047]

[0048] Where L(Φ) is the representation in linear space, i represents the i-th sample, k is the k-th tree, is the i-th sample x i The predicted value of

[0049] Based on the existing trees, new trees are continuously added to grow a tree by performing feature splitting, and then the prediction results of each tree are used to fit the residual between the prediction results of the previous tree and the true value, that is:

[0050]

[0051] Numerically, the prediction result of the t-th tree is equal to the sum of the prediction results of the previous t-1 trees and the performance of the t-th tree. For the t-th tree, the objective function is updated as:

[0052]

[0053] Use Taylor expansion to approximate the original objective function, and f t (x i ) as Δx, let:

[0054]

[0055] make Represents the sample on the jth leaf node, and finds the optimal solution of the objective function:

[0056]

[0057] Furthermore, in step (3), the implementation steps of establishing the StanHop_Net model are as follows:

[0058] StanHop_Net is a recursive neural network that attempts to process and store information by simulating the working mode of human brain neurons. In the connection between neurons, not every neuron is connected to all other neurons, but only a part of them is randomly or selectively connected.

[0059] Among them, sparse connections include random connections and structured connections; sparse connections not only reduce the number of connections, but also affect the dynamic behavior of the network by adjusting the connection strength or weight;

[0060] The core of the StanHop_Net is its energy function, which is defined as:

[0061]

[0062] In the formula, E represents the energy value function describing the network state, X(t) represents the state vector of the network at time t, W represents the connection weight matrix between neurons, and X T (t) is the transpose of X(t).

[0063] Furthermore, in step (3), the implementation steps of establishing the DHKELM model are as follows: the DHKELM is a hybrid model combining DELM and HKELM;

[0064] Among them, DELM constructs a feature learning layer by connecting multiple ELM-AEs in series;

[0065] Use multiple ELM-AEs to build feature learning layers and connect autoencoders in series to capture complex mapping relationships in the data;

[0066] In the initialization stage, for each ELM-AE, the input weight w is randomly initialized i and the bias term b i ; ELM-AE calculates the output matrix H of each hidden layer in cascade order by the following formula i and the output weight β i :

[0067] H i =g(w in X+b i ) (19)

[0068]

[0069] Update H according to the following formula i , take the hidden layer output of each ELM-AE as the input of the next layer of ELM-AE, and continue forward propagation until the hidden layer outputs of all ELM-AEs are calculated:

[0070]

[0071] The output matrix of the last hidden layer is used as the decision input of HKELM, and the output weight of HKELM is calculated according to the following formula:

[0072] β i =(W ELM +I / C) -1 H i (twenty two)

[0073] The output Q(x) of DHKELM is:

[0074]

[0075] In the formula, represents the hidden layer activation function; x represents sample data; C represents the regularization parameter; I represents the unit matrix; T represents the training level target vector.

[0076] Furthermore, the implementation process of establishing the meta-learner prediction model in step (4) is as follows:

[0077] During the training process, if the training set of the base learner is used to generate the secondary training set, the risk of overfitting will increase. To avoid repeated learning, the K-fold cross-validation method is used to generate the secondary training set. The specific process is as follows:

[0078] The original data set is divided into K equal-sized and non-overlapping subsets, denoted as D = {D1, D2, ..., D q ,...,D K}, where D k is the Kth cross-validation set, and the remaining subsets D -q =D / D q is the validation set for the qth cross-validation; for each base learner, the model is trained on the training set and the results are predicted on the validation set. After K rounds of training and testing, the prediction results are stacked vertically to generate a secondary training set, and the sample size of the secondary training set is the same as that of the original data;

[0079] The meta-learner is used to combine the strategies or algorithms of the base learners. By combining the outputs of the base learners, the prediction results of the final ensemble model are generated. Therefore, the autoencoder-enhanced AESELM is selected as the meta-learner of the second layer in the Stacking ensemble model.

[0080] In the AESELM framework, AE constitutes the first layer and performs unsupervised pre-training tasks. AE discovers the core features of data through encoding and decoding operations, giving AESELM the ability to perceive data structure.

[0081] In AESELM, AE is first used to preprocess the raw data and learn the low-dimensional representation of the data; then, these representations are used as the input of S-ELM for further classification or regression tasks; after several layers of stacking, the output of S-ELM is the final output of AESELM;

[0082] The training strategy of AESELM is as follows: in the initial stage, ELM-AE is used to implement unsupervised learning, where the weights and biases of the input layer are initialized by random orthogonal matrices, and the least squares method is used to optimize the weights of the output layer;

[0083] Subsequently, the AESELM model is fully initialized based on the output weights of ELM-AE. The specific output weights of ELM-AE are used as the input weights of AESELM to generate the feature vectors of the first hidden layer. These features are then input into the next extreme learning machine model, and so on. By stacking layer by layer, AESELM gradually extracts more complex data features.

[0084] Furthermore, the implementation process of step (5) is as follows: an artemisinin optimization algorithm is introduced to tune the parameters of the meta-learner, and a meta-heuristic algorithm of AOA is proposed; it includes three optimization stages: a comprehensive elimination stage simulating global exploration, a local elimination stage of local development, and a post-consolidation stage to enhance the algorithm's ability to escape local optimality;

[0085] Initialization, like other algorithms, uses random initialization:

[0086]

[0087] In the formula, T and B represent the boundaries of the solution space; R represents a set of random number sequences, whose value range is [0,1]; AOA uses the common method in meta-heuristic algorithms to generate the initial solution using random number sequences;

[0088] The periodic oscillation mutation strategy is applied to the initialization stage, the sine function sin(ω·t+Φ) is selected as the basis of the oscillation function, and the initial solution is generated using random numbers and the oscillation function; that is:

[0089] X i =T+(BT)·R+A·sin(ω·t+Φ) (25)

[0090] Where, X i represents the initial position of the i-th search agent, T and B represent the boundaries of the solution space, R represents a random number in the range [0, 1], A represents the oscillation amplitude, ω, t, Φ represent the parameters of the sine function;

[0091] Simulating the comprehensive elimination phase of global exploration: In the initial stage of malaria treatment, a larger dose of the drug is given and artemisinin is absorbed; the distribution of the drug is affected by blood flow, vascular permeability, and the binding affinity of the drug to the protein, as shown in the following formula:

[0092]

[0093] In the formula, and They represent the search agents before and after the update respectively; best represents the current best; c represents the attenuation index of the drug concentration in the human body;

[0094] Improve the adaptive loop fusion and splitting by adding them to the comprehensive elimination stage and adjust the loop structure;

[0095] Fusion means reducing the number of iterations and merging the search steps when the performance index is below the threshold;

[0096] Splitting means increasing the number of iterations and subdividing the search steps when the performance index is higher than the threshold;

[0097] Automatically adjust the fusion and splitting of loops based on the comparison between the actual value of the performance indicator and the threshold;

[0098] Local elimination phase of local development: The goal is to eliminate any remaining malarial parasites in the body, i.e.:

[0099]

[0100] In the formula, Fit norm (i) represents the normalized fitness value, which is converted into a probability distribution as the relative weight between individuals; d represents the coefficient, which takes a random value between [0.1, 0.6];

[0101] Post-consolidation phase to enhance the algorithm's ability to escape local optimality: As the condition improves, the frequency and dosage of medication will be reduced or even stopped, which will lead to disease relapse, as shown in the following formula:

[0102]

[0103] In the formula, The subvector representing the current optimal solution of the j-th dimension.

[0104] Further, a fuel cell performance degradation prediction system includes a data acquisition module, a data processing module, a model training module and an optimization model module;

[0105] Data acquisition module: collects the output voltage data and characteristic variables of proton exchange membrane fuel cells;

[0106] Data processing module: To improve the accuracy of data, SKF is used to observe and filter the collected signals, remove measurement noise and system noise, and enhance the control effect;

[0107] In order to improve the performance and efficiency of the model, BRFE is used to select the feature variables, and the threshold is set to select the best feature to obtain a new feature subset as the input variable;

[0108] Model training module: A Stacking model is established, in which the base learners are extreme gradient boosting XGBoost, sparse tandem Hopfield network StanHop_Net and DHKELM, and the meta-learner uses the autoencoder enhanced AESELM. The processed low-dimensional data set is input into the integrated model for training;

[0109] Optimization model module: Introducing an improved artemisinin optimization algorithm, tuning the parameters of the meta-learner, adding a periodic oscillation mutation strategy in the initialization phase, increasing the diversity of the population, improving the convergence speed, and the searched global optimal value is of high quality;

[0110] In the comprehensive elimination stage, adaptive loop fusion and splitting are introduced for optimization and improvement.

[0111] The beneficial effects of the present invention are as follows: 1. The present invention proposes to use a new simplex Kalman filter (SKF) to improve filtering accuracy, improve calculation efficiency and reduce calculation complexity, remove measurement noise and system noise and enhance control effect; 2. The present invention proposes to use a recursive feature elimination method (BRFE) to select features from the original PEMFC data set, effectively reducing the feature space, and usually finding the best feature subset with less calculation time. The model training time is reduced, and the detection accuracy is improved to a certain extent. By removing irrelevant or redundant features, BRFE can improve the generalization ability of the model, reduce overfitting, and thus improve the performance of the model; 3. The Stacking ensemble model is used to predict the performance degradation of PEMFC. Among them, XGBoost, sparse tandem Hopfield network (StanHop_Net) and deep hybrid kernel extreme learning machine (DHKELM) are selected as the base learners, and the autoencoder enhanced stacked extreme learning machine (AESELM) is selected as the meta-learner, allowing model selection and tuning on the second layer (meta-learner) to find the best model combination. The complementarity of these models can be used to improve the overall performance, thereby reducing the deviation of model prediction and improving the prediction performance; 4. The improved artemisinin optimization algorithm is introduced to tune the parameters of the meta-learner model, and a periodic oscillation mutation strategy is added in the initialization stage, which can increase the diversity of the population, improve the convergence speed, and the global optimal value searched is of high quality, and the algorithm has good stability. In the comprehensive elimination stage, adaptive loop fusion and splitting are introduced for optimization and improvement. When processing large-scale data, the number of clusters can be dynamically adjusted according to data characteristics, making the algorithm more efficient. BRIEF DESCRIPTION OF THE DRAWINGS

[0112] Figure 1 is a model flow chart of the present invention;

[0113] Figure 2 is an operation diagram of a novel simplex Kalman filter in an embodiment of the present invention;

[0114] Figure 3 It is a structural diagram of the Stacking integration model in an embodiment of the present invention;

[0115] Figure 4 It is a flow chart of the artemisinin optimization algorithm in an embodiment of the present invention. DETAILED DESCRIPTION

[0116] The specific technical scheme of the present invention is further described in detail below with reference to specific examples.

[0117] As shown in the figure, a method and system for predicting fuel cell performance degradation according to the present invention includes the following steps:

[0118] Step (1), collecting the output voltage data and characteristic variables of the proton exchange membrane fuel cell, preprocessing the data, using a new simplex Kalman filter (SKF) to observe and filter the collected signals to improve the accuracy of the data, remove measurement noise and system noise, enhance the control effect, and reduce random interference in the data;

[0119] Wherein, the characteristic variables of the proton exchange membrane fuel cell include current, temperature, humidity, degradation time, gas supply pressure, etc.;

[0120] Step (2): In order to improve the performance and efficiency of the model, a recursive feature elimination method (BRFE) is used to select the feature variables, and the threshold is set to select the best feature to obtain a new feature subset as the input variable;

[0121] Step (3), establishing a stacking ensemble learning model, in which the base learners selected extreme gradient boosting (XGBoost), sparse tandem Hopfield network (StanHop_Net) and deep hybrid kernel extreme learning machine (DHKELM);

[0122] Input the preprocessed data into each base learner to obtain three differently trained weak learners; use the validation set to verify the performance of each weak learner and obtain three different sets of prediction results;

[0123] Step (4), the three sets of prediction results and the original data labels are input into the meta-learner as new training sets for secondary training; the meta-learner uses the autoencoder enhanced stacked extreme learning machine (AESELM), and finally the performance of the AESELM model is verified using the test set to obtain the final prediction results;

[0124] Step (5), introduce the improved artemisinin optimization algorithm, tune the model parameters, add the periodic oscillation mutation strategy in the initialization stage, which can increase the diversity of the population, improve the convergence speed, and the global optimal value searched is of high quality, and the algorithm has good stability. In the comprehensive elimination stage, adaptive loop fusion and splitting are introduced for optimization and improvement. When processing large-scale data, the number of clusters can be dynamically adjusted according to the data characteristics, making the algorithm more efficient.

[0125] Furthermore, the implementation process of step (1) is as follows: In order to improve filtering accuracy, improve calculation efficiency and reduce calculation complexity, a new simplex Kalman filter (SKF) is introduced. SKF is an algorithm for nonlinear state estimation, which approximates the output distribution of nonlinear functions by using Sigma Points. The following are the specific steps of SKF:

[0126] Initialize Select an initial state estimate and the initial covariance matrix P0, generating sigma points, a central point 2n diffusion points, where n is the dimension of the state vector, are symmetrically distributed around the center point; each sigma point is propagated to the next time step through a nonlinear function to obtain a predicted set of sigma points;

[0127] Use the propagated sigma point set to calculate the mean and covariance of the predicted state:

[0128]

[0129] Where W i c and W i m represents the weight, It represents the i-th sigma point, Q represents the process noise covariance;

[0130] Observation update: propagate each sigma point through the observation model h to obtain the observed sigma point set;

[0131] The Kalman gain K is calculated using the observed sigma point set:

[0132]

[0133] In the formula, H k It represents the Jacobian matrix of the observation model, and R is the observation noise covariance;

[0134] Iterations are repeated until the state estimation of all time steps is completed; the acquired signal after observation and filtering is output and feature extraction is performed on it.

[0135] Furthermore, the implementation process of step (2) is as follows:

[0136] Assume the initial sample is X∈S N×M , where N is the number of samples and M is the number of features. On this basis, a recursive feature elimination method is proposed to recursively select the best feature subset from the features of the original samples. The algorithm is mainly divided into two parts: dynamic calculation of feature importance and recursive selection of the best feature subset;

[0137] Dynamically calculate feature importance: First, prepare the decision tree training data set, randomly select N' samples from the original sample with replacement, and get a small sample X N' , randomly selected from the M features of the sample The features are a subset of features in a single decision tree;

[0138] The Gini index is used to represent the importance of features and the decision tree node splitting strategy. The Gini index at a node is calculated as follows:

[0139]

[0140] In the formula, p i Indicates the proportion of feature category i on the node;

[0141] The change in the Gini index before and after the node split is expressed as:

[0142] ΔGI=Gini-Gini i -Gini r (5)

[0143] In the formula, Gini i Represents the Gini index of the left node after the node splits, Gini r Represents the Gini index of the right node after splitting;

[0144] The importance of a feature at this node is:

[0145]

[0146] The importance on the jth decision tree is the importance of all nodes:

[0147] VIM j =ΣVIM (7)

[0148] Assuming there are Q decision trees in the random forest, the importance of this feature is:

[0149]

[0150] In the formula, VIM i Indicates the importance of the i-th feature category in the random forest among all features, VIM Q Represents the normalized result of the importance score of a feature in the random forest;

[0151] Recursively select the best feature subset: On this basis, a recursive feature elimination method BRFE is proposed using the feature selection idea of ​​random forest; by sorting the importance of each feature in the random forest algorithm, and using the recursive feature elimination method to remove the minimum importance feature; on this basis, through multiple learning of random forests, a minimum importance is removed to obtain a new feature subset until the optimal feature setting threshold is reached.

[0152] Furthermore, in step (3), the implementation process of establishing the extreme gradient boosting (XGBoost) model is as follows:

[0153] Assume training set, loss function Train = {(x1, y1), (x2, y2), ... (xn, yn)}, loss function Regularization term Ω(f k ), then the objective function can be written as:

[0154]

[0155] Where L(Φ) is the representation in linear space, i represents the i-th sample, k is the k-th tree, is the i-th sample x i The predicted value of

[0156] Based on the existing trees, new trees are continuously added to grow a tree by performing feature splitting, and then the prediction results of each tree are used to fit the residual between the prediction results of the previous tree and the true value:

[0157]

[0158] Numerically, the prediction result of the t-th tree is equal to the sum of the prediction results of the previous t-1 trees and the performance of the t-th tree. For the t-th tree, the objective function can be updated as:

[0159]

[0160] Use Taylor expansion to approximate the original objective function, and f t (x i ) as Δx, let:

[0161]

[0162] make Represents the sample on the jth leaf node, and finds the optimal solution of the objective function:

[0163]

[0164] Furthermore, in step (3), the implementation process of establishing a sparse series Hopfield network (StanHop_Net) is as follows:

[0165] StanHop_Net is a recurrent neural network that attempts to process and store information by simulating the working mode of human brain neurons. Compared with the traditional Hopfield network, it is more sparse in the connection between neurons, which means that not every neuron is connected to all other neurons, but only a part of them is randomly or selectively connected.

[0166] Sparse connections include random connections and structured connections;

[0167] Sparse connections not only reduce the number of connections, but also affect the dynamic behavior of the network by adjusting the connection strength (weight);

[0168] The core of the StanHop_Net is its energy function, which is defined as:

[0169]

[0170] Where E is the energy value function describing the network state, X(t) is the state vector of the network at time t, W is the connection weight matrix between neurons, and X T (t) is the transpose of X(t).

[0171] Furthermore, in step (3), the implementation process of establishing a deep hybrid kernel extreme learning machine (DHKELM) is as follows:

[0172] The deep hybrid kernel extreme learning machine (DHKELM) is a hybrid model that combines DELM and HKELM; DELM constructs a feature learning layer by connecting multiple extreme learning machine autoencoders (ELM-AE) in series. This structure can effectively capture the complex mapping relationship between data, especially when processing high-dimensional and nonlinear data.

[0173] Use multiple extreme learning machine autoencoders (ELM-AE) to build feature learning layers, which are connected in series to capture complex mapping relationships in the data;

[0174] In the initialization stage, for each ELM-AE, the input weight w is randomly initialized i and the bias term b i; ELM-AE calculates the output matrix H of each hidden layer in cascade order by the following formula i and the output weight β i :

[0175] H i =g(w in X+b i ) (19)

[0176]

[0177] Update H according to the following formula i , take the hidden layer output of each ELM-AE as the input of the next layer of ELM-AE, and continue forward propagation until the hidden layer outputs of all ELM-AEs are calculated;

[0178]

[0179] The output matrix of the last hidden layer is used as the decision input of HKELM, and the output weight of HKELM is calculated according to the following formula:

[0180] β i =(W ELM +I / C) -1 H i (twenty two)

[0181] The output Q(x) of DHKELM is:

[0182]

[0183] In the formula, is the hidden layer activation function; x is the sample data; C is the regularization parameter; I is the unit matrix; T is the training level target vector.

[0184] Furthermore, the implementation process of step (4) of establishing the meta-learner prediction model is as follows:

[0185] During the training process, if the training set of the base learner is directly used to generate the secondary training set, the risk of overfitting will increase, greatly reducing the performance of the integrated model on the test set;

[0186] To avoid repeated learning, K-fold cross-validation is used to generate a secondary training set. The specific steps are as follows: Divide the original data set into K equal-sized and non-overlapping subsets, denoted as D = {D1, D2, ..., D q ,...,D K}, where D k is the Kth cross-validation set, and the remaining subsets D -q =D / D q is the validation set for the qth cross validation;

[0187] For each base learner, the model is trained on the training set and the results are predicted on the validation set. After K rounds of training and testing, the predicted results are stacked vertically to generate a secondary training set, and the sample size of the secondary training set is the same as the sample size of the original data. This method can ensure that the meta-learner has sufficient training samples while reducing the risk of overfitting. The meta-learner is used to combine the strategies or algorithms of the base learners, and generates the prediction results of the final integrated model by combining the outputs of the base learners. Therefore, the autoencoder enhanced stacked extreme learning machine (AESELM) is selected as the meta-learner of the second layer in the Stacking integrated model. Compared with the standard ELM, AESELM can more finely map and understand the relationships between data while maintaining memory efficiency. AESELM also combines the advantages of AE and S-ELM. AE can help learn useful representations from raw data, while S-ELM can use these representations for complex classification or regression tasks. This combination makes AESELM more effective in processing large-scale, unstructured and complex data.

[0188] In the AESELM framework, the autoencoder (AE) constitutes its first layer and performs unsupervised pre-training tasks. AE aims to discover the core features of the data through encoding and decoding operations, thereby giving AESELM a deeper data structure perception capability.

[0189] In AESELM, AE is first used to preprocess the raw data and learn the low-dimensional representation of the data; then, these representations are used as the input of S-ELM for further classification or regression tasks; after several layers of stacking, the output of S-ELM is the final output of AESELM;

[0190] The training strategy of AESELM is as follows: In the initial stage, an extreme learning machine autoencoder (ELM-AE) is used to implement unsupervised learning, where the weights and biases of the input layer are initialized by random orthogonal matrices, and the least squares method is used to optimize the weights of the output layer; this step enables AESELM to abstract useful features from the original data;

[0191] Subsequently, the AESELM model is fully initialized based on the output weights of ELM-AE; specifically, the output weights of ELM-AE are used as the input weights of AESELM to generate the feature vectors of the first hidden layer; these features are then input into the next extreme learning machine model, and so on. By stacking layer by layer, AESELM can gradually extract more complex data features.

[0192] It is worth noting that when training AESELM, the input layer weights and biases of ELM-AE remain unchanged, and only the output layer weights are adjusted. This fixity may affect the prediction performance of the model, so it is particularly important to optimize the input layer weights and biases.

[0193] Furthermore, the implementation process of establishing the meta-learner prediction model in step (5) is as follows:

[0194] The artemisinin optimization algorithm is introduced to tune the parameters of the meta-learner. This method can effectively predict the performance degradation of PEMFC and provide a scientific basis for the maintenance and management of fuel cells, thereby extending their service life and improving their overall efficiency.

[0195] Inspired by the efficacy of artemisinin in treating malaria, a meta-heuristic algorithm named Artemisinin Optimization Algorithm (AOA) is proposed to effectively solve the optimization dilemma; AOA includes three optimization stages: a comprehensive elimination stage that simulates global exploration, a local elimination stage that exploits local conditions, and a post-consolidation stage that enhances the algorithm's ability to escape local optimality;

[0196] Initialization: Like other algorithms, random initialization is used:

[0197]

[0198] In the formula, T and B represent the boundaries of the solution space; R represents a set of random number sequences, whose value range is [0,1]. The artemisinin optimization algorithm adopts the common method in metaheuristic algorithms and uses random number sequences to generate initial solutions;

[0199] The periodic oscillation mutation strategy is applied to the initialization stage, the sine function sin(ω·t+Φ) is selected as the basis of the oscillation function, and the initial solution is generated using random numbers and the oscillation function:

[0200] X i =T+(BT)·R+A·sin(ω·t+Φ) (25)

[0201] Where, X i is the initial position of the i-th search agent, T and B are the boundaries of the solution space, R is a random number in the range [0, 1], A is the oscillation amplitude, ω, t, Φ are the parameters of the sine function;

[0202] The above initialization process is directly integrated into the AOA algorithm as the first step of the algorithm startup; this means that at the beginning of each run of the algorithm, a new initial solution is generated based on the sine oscillation function;

[0203] Complete elimination stage: In the initial stage of malaria treatment, larger doses of drugs are given to quickly control the progression of the disease; once artemisinin is absorbed, it is transported to various parts of the body through the blood; the distribution of the drug is affected by factors such as blood flow, vascular permeability, and the binding affinity of the drug to proteins:

[0204]

[0205] In the formula, and They represent the search agents before and after the update respectively; best is the current best; c represents the attenuation index of the drug concentration in the human body;

[0206] Add Adaptive Loop Fusion and Splitting to the comprehensive elimination stage to improve and adjust the loop structure;

[0207] Fusion means reducing the number of iterations and merging the search steps when the performance index is below the threshold;

[0208] Splitting means increasing the number of iterations and subdividing the search steps when the performance index is higher than the threshold;

[0209] Automatically adjust the fusion and splitting of loops based on the comparison between the actual value of the performance indicator and the threshold;

[0210] Local elimination phase: The goal is to eliminate any remaining malarial parasites in the body, preventing their reproduction and the recurrence of malarial symptoms:

[0211]

[0212] In the formula, Fit norm (i) represents the normalized fitness value, which converts the fitness value into a probability distribution as the relative weight between individuals; it ensures that the higher the fitness, the greater the probability corresponding to the individual; d represents the coefficient, which takes a random value between [0.1, 0.6];

[0213] Post-consolidation phase: Indifference to the severity of the disease and laxity during treatment are dangerous and harmful factors. As the condition improves, vigilance against malaria may gradually decrease, the frequency and dosage of medication may be reduced, or even treatment may be stopped, which may lead to a relapse of the disease:

[0214]

[0215] In the formula, The subvector representing the current optimal solution of the j-th dimension.

[0216] Further, a fuel cell performance degradation prediction system includes a data acquisition module, a data processing module, a model training module, and an optimization model module;

[0217] Data acquisition module: collects the output voltage data of proton exchange membrane fuel cells and its characteristic variables. The characteristic variables of proton exchange membrane fuel cells include current, temperature, humidity, degradation time, gas supply pressure, etc.

[0218] Data processing module: To improve the accuracy of data, a new simplex Kalman filter (SKF) is used to observe and filter the collected signals, remove measurement noise and system noise and enhance the control effect, thereby reducing random interference in the data; to improve the performance and efficiency of the model, a recursive feature elimination method (BRFE) is used to select feature variables, select the best feature to set the threshold, and obtain a new feature subset as the input variable;

[0219] Model training module: A stacking ensemble learning model is established, in which the base learners are extreme gradient boosting (XGBoost), sparse tandem Hopfield network (StanHop_Net) and deep hybrid kernel extreme learning machine (DHKELM), and the meta-learner uses the autoencoder enhanced stacking extreme learning machine (AESELM). The processed low-dimensional data set is input into the ensemble model for training;

[0220] Optimization model module: Introduce an improved artemisinin optimization algorithm, tune the parameters of the meta-learner, and add a periodic oscillation mutation strategy in the initialization phase, which can increase the diversity of the population, improve the convergence speed, and the global optimal value searched is of high quality, and the algorithm has good stability. In the comprehensive elimination phase, introduce adaptive loop fusion and splitting for optimization and improvement.

Claims

1. A method for predicting fuel cell performance degradation, characterized in that: The operation steps are as follows: Step (1): collecting the output voltage data and characteristic variables of the proton exchange membrane fuel cell and preprocessing the data; To improve the accuracy of the data, SKF is used to observe and filter the collected signals; Step (2): In order to improve the performance and efficiency of the model, BRFE is used to select the feature variables, and the threshold is set to select the best feature to obtain a new feature subset as the input variable; Step (3): Establish a Stacking model, where the base learners are XGBoost, StanHop_Net and DHKELM; Input the preprocessed data into each base learner; obtain three differently trained weak learners; use the validation set to verify the performance of each weak learner and obtain three different sets of prediction results; Step (4): Input the three sets of prediction results and the original data labels as new training sets into the meta-learner for secondary training; The meta-learner uses the AESELM model enhanced by the autoencoder, and finally uses the test set to verify the performance of the AESELM model to obtain the final prediction result; Step (5): Introduce the improved artemisinin optimization algorithm, tune the model parameters, add a periodic oscillation mutation strategy in the initialization stage, introduce Adaptive Loop Fusion and Splitting for optimization and improvement in the comprehensive elimination stage, and dynamically adjust the number of clusters according to data characteristics when processing large-scale data.

2. A fuel cell performance degradation prediction method according to claim 1, characterized in that: In step (1), the characteristic variables of the proton exchange membrane fuel cell include current, temperature, humidity, degradation time and gas supply pressure.

3. A fuel cell performance degradation prediction method according to claim 1, characterized in that: The implementation process of the step (1) is as follows: SKF is introduced to improve filtering accuracy, improve calculation efficiency and reduce calculation complexity, and the SKF approximates the output distribution of the nonlinear function by using Sigma Points; The SKF operation process is as follows: Initialize Select an initial state estimate And the initial covariance matrix P0 generates Sigma Points, a central point 2n diffusion points; Where n is the dimension of the state vector, and the points are symmetrically distributed around the center point; Propagate each Sigma Point to the next time step through a nonlinear function to obtain a set of predicted Sigma Points; The propagated Sigma Points set is used to calculate the mean and covariance of the predicted state, as shown in the following formula: In the formula, and is the weight, is the i-th Sigma Points, Q is the process noise covariance; Observation update: propagate each Sigma Point through the observation model h to obtain the observed Sigma Points set; use the observed Sigma Points set to calculate the Kalman gain K: In the formula, H k is the Jacobian matrix of the observation model, R is the observation noise covariance; Iterations are repeated until the state estimation of all time steps is completed; the acquired signal after observation and filtering is output and feature extraction is performed on it.

4. A fuel cell performance degradation prediction method according to claim 1, characterized in that: The operation steps of step (2) are as follows: Let the initial sample be X∈S N×M ; Where N is the number of samples and M is the number of features; On this basis, BRFE is proposed to recursively select the best feature subset from the features of the original samples, which is divided into two parts: dynamic calculation of feature importance and recursive selection of the best feature subset; The dynamic calculation of feature importance is as follows: First, prepare the decision tree training data set, randomly take N' samples from the original sample with replacement, and get a small sample X N' , randomly selected from the M features of the sample The features are the feature subsets in a single decision tree. The Gini index is used to represent the importance of the features and the decision tree node splitting strategy. The Gini index at a node is calculated as shown in formula (1); that is: In the formula, p i Indicates the proportion of feature category i on the node; The change in the Gini index before and after the node split is expressed as follows: ΔGI=This-This i -This is it r (5) In the formula, Gini i Represents the Gini index of the left node after the node splits, Gini r Represents the Gini index of the right node after splitting; The importance of a feature at this node is as follows: The importance on the jth decision tree is the importance of all nodes, that is: BECAUSE j =∑VIM (7) Assuming that there are Q decision trees in the random forest, the importance of this feature is as follows: Where VIM i Indicates the importance of the i-th feature category in the random forest among all features, VIM Q Represents the normalized result of the importance score of a feature in the random forest; The recursive selection of the best feature subset: using the feature selection idea of ​​random forest, a BRFE is proposed; by sorting the importance of each feature in the random forest algorithm, and using the recursive feature elimination method to remove the least important feature; Through multiple learning of random forests, the minimum importance is removed to obtain a new feature subset until the optimal feature setting threshold is reached.

5. A fuel cell performance degradation prediction method according to claim 1, characterized in that: In step (3), the implementation steps of establishing the XGBoost model are as follows: Assume that the training set and loss function Train = {(x1,y1),(x2,y2),…(x n ,y n )}, loss function Regularization term Ω(f k ), then the objective function is recorded as: Where L(Φ) is the representation in linear space, i represents the i-th sample, k is the k-th tree, is the i-th sample x i The predicted value of Based on the existing trees, new trees are continuously added to grow a tree by performing feature splitting, and then the prediction results of each tree are used to fit the residual between the prediction results of the previous tree and the true value, that is: Numerically, the prediction result of the t-th tree is equal to the sum of the prediction results of the previous t-1 trees and the performance of the t-th tree. For the t-th tree, the objective function is updated as: Use Taylor expansion to approximate the original objective function, and f t (x i ) as Δx, let: make Represents the sample on the jth leaf node, and finds the optimal solution of the objective function:

6. A fuel cell performance degradation prediction method according to claim 1, characterized in that: In step (3), the implementation steps of establishing the StanHop_Net model are as follows: StanHop_Net is a recursive neural network that attempts to process and store information by simulating the working mode of human brain neurons; in terms of the connection between neurons, not every neuron is connected to all other neurons, but only a part of them is randomly or selectively connected; Among them, sparse connections include random connections and structured connections; sparse connections not only reduce the number of connections, but also affect the dynamic behavior of the network by adjusting the connection strength or weight; The core of the StanHop_Net is its energy function, which is defined as: In the formula, E represents the energy value function describing the network state, X(t) represents the state vector of the network at time t, W represents the connection weight matrix between neurons, and X T (t) is the transpose of X(t).

7. A fuel cell performance degradation prediction method according to claim 1, characterized in that ； In step (3), the implementation steps of establishing the DHKELM model are as follows: the DHKELM is a hybrid model combining DELM and HKELM; Among them, DELM constructs a feature learning layer by connecting multiple ELM-AEs in series; Use multiple ELM-AEs to build feature learning layers and connect autoencoders in series to capture complex mapping relationships in the data; In the initialization stage, for each ELM-AE, the input weight w is randomly initialized i and the bias term b i ; ELM-AE calculates the output matrix H of each hidden layer in cascade order by the following formula i and the output weight β i : H i =g(w in X+b i ) (19) Update H according to the following formula i , take the hidden layer output of each ELM-AE as the input of the next layer of ELM-AE, and continue forward propagation until the hidden layer outputs of all ELM-AEs are calculated: The output matrix of the last hidden layer is used as the decision input of HKELM, and the output weight of HKELM is calculated according to the following formula: β i =(W ELM +I / C) -1 H i (22) The output Q(x) of DHKELM is: In the formula, represents the hidden layer activation function; x represents sample data; C represents the regularization parameter; I represents the unit matrix; T represents the training level target vector.

8. A fuel cell performance degradation prediction method according to claim 1, characterized in that: The implementation process of establishing the meta-learner prediction model in step (4) is as follows: During the training process, if the training set of the base learner is used to generate the secondary training set, the risk of overfitting will increase. In order to avoid repeated learning, the K-fold cross-validation method is used to generate the secondary training set; the specific process is as follows: The original data set is divided into K equal-sized and non-overlapping subsets, denoted as D = {D1, D2, ..., D q ,...,D K }, where D k is the Kth cross-validation set, and the remaining subsets D -q =D / D q is the validation set for the qth cross-validation; for each base learner, the model is trained on the training set and the results are predicted on the validation set. After K rounds of training and testing, the prediction results are stacked vertically to generate a secondary training set, and the sample size of the secondary training set is the same as that of the original data; The meta-learner is used to combine the strategies or algorithms of the base learners. By combining the outputs of the base learners, the prediction results of the final ensemble model are generated. Therefore, the autoencoder-enhanced AESELM is selected as the meta-learner of the second layer in the Stacking ensemble model. In the AESELM framework, AE constitutes the first layer and performs unsupervised pre-training tasks. AE discovers the core features of data through encoding and decoding operations, giving AESELM the ability to perceive data structure. In AESELM, AE is first used to preprocess the raw data and learn the low-dimensional representation of the data; then, these representations are used as the input of S-ELM for further classification or regression tasks; after several layers of stacking, the output of S-ELM is the final output of AESELM; The training strategy of AESELM is as follows: in the initial stage, ELM-AE is used to implement unsupervised learning, where the weights and biases of the input layer are initialized by random orthogonal matrices, and the least squares method is used to optimize the weights of the output layer; Subsequently, the AESELM model is fully initialized based on the output weights of ELM-AE. The specific output weights of ELM-AE are used as the input weights of AESELM to generate the feature vectors of the first hidden layer. These features are then input into the next extreme learning machine model, and so on. By stacking layer by layer, AESELM gradually extracts more complex data features.

9. A fuel cell performance degradation prediction method according to claim 1, characterized in that: The implementation process of step (5) is as follows: an artemisinin optimization algorithm is introduced to tune the parameters of the meta-learner, and a meta-heuristic algorithm of AOA is proposed; it includes three optimization stages: a comprehensive elimination stage simulating global exploration, a local elimination stage of local development, and a post-consolidation stage to enhance the algorithm's ability to escape local optimality; Initialization, like other algorithms, uses random initialization: In the formula, T and B represent the boundaries of the solution space; R represents a set of random number sequences, whose value range is [0,1]; AOA uses the common method in meta-heuristic algorithms to generate the initial solution using random number sequences; The periodic oscillation mutation strategy is applied to the initialization stage, the sine function sin(ω·t+Φ) is selected as the basis of the oscillation function, and the initial solution is generated using random numbers and the oscillation function; Right now: X i =T+(BT)·R+A·sin(ω·t+Φ) (25) Where, X i represents the initial position of the i-th search agent, T and B represent the boundaries of the solution space, R represents a random number in the range [0, 1], A represents the oscillation amplitude, ω, t, Φ represent the parameters of the sine function; Simulating the comprehensive elimination phase of global exploration: In the initial stage of malaria treatment, a larger dose of the drug is given and artemisinin is absorbed; the distribution of the drug is affected by blood flow, vascular permeability, and the binding affinity of the drug to the protein, as shown in the following formula: In the formula, and They represent the search agents before and after the update respectively; best represents the current best; c represents the attenuation index of the drug concentration in the human body; Improve the adaptive loop fusion and splitting by adding them to the comprehensive elimination stage and adjust the loop structure; Fusion means reducing the number of iterations and merging the search steps when the performance index is below the threshold; Splitting means increasing the number of iterations and subdividing the search steps when the performance index is higher than the threshold; Automatically adjust the fusion and splitting of loops based on the comparison between the actual value of the performance indicator and the threshold; Local elimination phase of local development: The goal is to eliminate any remaining malarial parasites in the body, i.e.: In the formula, Fit norm (i) represents the normalized fitness value, which is converted into a probability distribution as the relative weight between individuals; d represents the coefficient, which takes a random value between [0.1, 0.6]; Post-consolidation phase to enhance the algorithm's ability to escape local optimality: As the condition improves, the frequency and dosage of medication will be reduced or even stopped, which will lead to disease relapse, as shown in the following formula: In the formula, The subvector representing the current optimal solution of the j-th dimension.

10. A fuel cell performance degradation prediction system, characterized in that: It includes data acquisition module, data processing module, model training module and model optimization module; Data acquisition module: collects the output voltage data and characteristic variables of proton exchange membrane fuel cells; Data processing module: To improve the accuracy of data, SKF is used to observe and filter the collected signals, remove measurement noise and system noise, and enhance the control effect; In order to improve the performance and efficiency of the model, BRFE is used to select the feature variables, and the threshold is set to select the best feature to obtain a new feature subset as the input variable; Model training module: A Stacking model is established, in which the base learners are extreme gradient boosting XGBoost, sparse tandem Hopfield network StanHop_Net and DHKELM, and the meta-learner uses the autoencoder enhanced AESELM. The processed low-dimensional data set is input into the integrated model for training; Optimization model module: Introducing an improved artemisinin optimization algorithm, tuning the parameters of the meta-learner, adding a periodic oscillation mutation strategy in the initialization phase, increasing the diversity of the population, improving the convergence speed, and the searched global optimal value is of high quality; In the comprehensive elimination stage, adaptive loop fusion and splitting are introduced for optimization and improvement.

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