Method and system for predicting performance degradation trend of proton exchange membrane fuel cell

Abstract

The invention relates to a method and a system for predicting a performance degradation trend of a proton exchange membrane fuel cell. The method comprises the following steps: acquiring state monitoring data of the proton exchange membrane fuel cell; a power spectrum threshold-Kalman joint algorithm PST-KF is adopted to carry out noise reduction smoothing processing on the state monitoring data; key feature parameter extraction is carried out on the output voltage degradation data after noise reduction by adopting a regular mutual information selection method; dividing the key feature parameter set into data sample subsets based on different performance degradation degrees by adopting a TG-ISODATA clustering algorithm, and dividing the data sample subsets into a training set and a test set; a performance degradation trend model SK-Mama is constructed; an improved WSA algorithm is adopted to optimize the SK-Mama model, and an IWSA-SK-Mama prediction model is constructed; performing training and performance evaluation on the IWSA-SK-Mama prediction model by using the training set and the test set; and then the performance degradation trend of the proton exchange membrane fuel cell is predicted through the trained model and the tested model. The method and the system can improve the prediction precision of the performance degradation trend of the proton exchange membrane fuel cell.

Description

Technical Field

[0001] This invention relates to the field of fuel cell technology, and specifically to a method and system for predicting the performance degradation trend of proton exchange membrane fuel cells. Background Technology

[0002] With the continuous growth of global energy demand and the increasing severity of environmental problems, proton exchange membrane fuel cells (PEMFCs), as a highly efficient and clean energy conversion technology, have received widespread attention. PEMFCs directly convert chemical energy into electrical energy through the electrochemical reaction of hydrogen and oxygen, offering advantages such as high energy conversion efficiency, zero pollution emissions, and rapid start-up. They have broad application prospects in distributed power generation, electric vehicles, and backup power supplies.

[0003] However, the performance of proton exchange membrane fuel cells (PEMFCs) gradually degrades during long-term operation. This degradation is caused by a variety of factors, including decreased catalyst activity, membrane aging, changes in electrode structure, and variations in operating conditions. Performance degradation not only affects the power output and energy conversion efficiency of the fuel cell but may also lead to premature system failure, increasing maintenance costs and replacement frequency. Therefore, accurately predicting the performance degradation trend of PEMFCs is of great significance for optimizing their operation and management, extending their service life, and improving overall system performance.

[0004] Existing proton exchange membrane fuel cell (PEMFC) performance degradation prediction techniques have several shortcomings, such as low prediction accuracy, poor robustness to data noise, inaccurate feature extraction, and susceptibility to local optima in optimization algorithms. These issues limit the development and application of PEMFC performance degradation prediction techniques. To overcome these shortcomings, improve prediction accuracy, and extend the lifespan of PEMFCs, developing a more accurate performance degradation prediction method is currently an important research direction in this field. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the performance degradation trend of proton exchange membrane fuel cells. This method and system can improve the accuracy of predicting the performance degradation trend of proton exchange membrane fuel cells.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is: a method for predicting the performance degradation trend of a proton exchange membrane fuel cell, comprising the following steps:

[0007] Step S1: Collect state monitoring data of the proton exchange membrane fuel cell;

[0008] Step S2: The power spectrum threshold-Kalman joint algorithm PST-KF, which combines Kalman filtering (KF) and improved singular value decomposition (SVD), is used to denoise and smooth the condition monitoring data. The PST-KF algorithm removes periodic narrowband interference through improved singular value decomposition (SVD), and then uses the SVD reconstructed signal as the observation value to input the Kalman filter model for dynamic filtering.

[0009] Step S3: Use the regular mutual information selection method to extract key feature parameters from the noise-reduced output voltage degradation data, including: calculating the MIC value between all input variables and the output voltage, sorting the input variables in descending order according to the MIC value and selecting the top K variables, and then using LASSO regression to perform secondary screening on the selected K variables to retain the features corresponding to non-zero coefficients.

[0010] Step S4: The TG-ISODATA clustering algorithm is used to divide the key feature parameter set into data sample subsets based on different performance degradation degrees, and each subset obtained by TG-ISODATA clustering is divided into training set and test set according to the ratio; the TG-ISODATA clustering algorithm includes: using TimeGAN to generate synthetic degradation trajectory, and performing ISODATA dynamic clustering in combination with real data;

[0011] Step S5: Construct the performance degradation trend model SK-Mamba, including: Under the TimeKAN framework, STL decomposition is used as a preprocessing step before the cascaded frequency decomposition module. First, the trend, seasonality, and residual components are extracted by STL decomposition. Then, the multi-scale frequency information in each component is extracted step by step by the cascaded frequency decomposition module. Next, multi-order KAN is used to perform nonlinear modeling with complexity matching for different frequency bands. The Mamba module is then connected after each subsequence to endow local features with global temporal memory and cross-segment interaction capabilities. Finally, all features are fused and the prediction is output.

[0012] Step S6: Improve the wave search algorithm WSA by using the Cat chaotic mapping strategy to initialize the population and introducing the Cauchy inverse cumulative distribution mutation strategy in the position update stage to avoid local optima, thus obtaining the IWSA algorithm;

[0013] Step S7: Optimize the hyperparameters of the SK-Mamba model using the IWSA algorithm to construct the IWSA-SK-Mamba prediction model;

[0014] Step S8: Train the IWSA-SK-Mamba prediction model using the training set and evaluate the performance of the IWSA-SK-Mamba prediction model using the test set; then predict the performance degradation trend of the proton exchange membrane fuel cell using the trained and tested IWSA-SK-Mamba prediction model.

[0015] Further, in step S1, the status monitoring data includes real-time monitoring data and historical degradation data; the real-time monitoring data includes aging time, single cell temperature, stack temperature, stack voltage, current, current density, cathode inlet air flow rate, anode inlet air flow rate, hydrogen inlet temperature, hydrogen outlet temperature, air inlet temperature, air outlet temperature, cooling water inlet temperature, cooling water outlet temperature, hydrogen inlet pressure, hydrogen outlet pressure, air inlet pressure, air outlet pressure, hydrogen inlet flow rate, hydrogen outlet flow rate, air inlet flow rate, air outlet flow rate, and cooling water flow rate;

[0016] The historical degradation data includes output voltage degradation data; let the historical degradation data be X, and resample the degradation data using a half-hour interval rule, the specific formula is as follows:

[0017]

[0018] In the formula: X t x represents the sampled value at time t; i N represents the i-th observation of the degraded data; t Indicates the number of observations.

[0019] Further, step S2 specifically includes:

[0020] Step S2.1: Perform Fourier transform on the noisy PD signal to obtain the power spectrum, calculate the absolute difference of the spectral amplitude, and then filter and remove narrowband interference singular values ​​by using the singular value thresholding method.

[0021] First, we substitute the noisy simulation signal into the analysis. We first perform a Fourier transform on the simulation signal to obtain the power spectrum. The specific calculation formula is as follows:

[0022]

[0023] In the formula: F(ω) is the Fourier transform of the simulated signal; f(t) is the simulated signal in the time domain; g(t) is the weighting function; ω is the angular frequency of the signal; t is time; P(ω) is the power spectrum;

[0024] Step S2.2: In the FFT power spectrum, periodic narrowband interference and PD signals are distinguished by calculating the absolute value of the difference between the amplitudes of two adjacent points in the spectrum; the power spectrum difference ΔP(n) is expressed as:

[0025]

[0026] In the formula: P(n) is the amplitude of the nth signal data sampling point in the spectrum; N is the total number of signal data sampling points;

[0027] Step S2.3: Filter out the singular values ​​of periodic narrowband interference using the classical threshold method and threshold formula. The periodic narrowband interference amplitude is greater than the set threshold T. SVD The expression is as follows:

[0028]

[0029] In the formula: σ is the standard deviation of the signal; τ is the noise level in the sample; ψ(n) is the intermediate variable; η is the number of periodic narrowband interferences; and the power spectrum with amplitude greater than the threshold T is considered as an intermediate variable. SVD At that time, it is periodic narrowband interference;

[0030] Step S2.4: Reorganize the denoised singular value matrix into a diagonal matrix ∑ Hessen Combining the left singular vector matrix U and the right singular vector matrix V T Calculate the reconstruction matrix X Hessen The antidiagonal elements are averaged to restore the time-domain signal, yielding the clean PD signal X after filtering out periodic narrowband interference. SVD (t), the calculation formula is as follows:

[0031] X Hessen =U·∑ Hessen ·V T (8)

[0032] Step S2.5: Reconstruct the SVD signal X SVD Using (t) as the observed value, a KF state-space model is established, and the calculation formula is as follows:

[0033]

[0034] In the formula, x k Let x be the system state vector at time k; F is the state transition matrix; x k-1 w is the system state vector at time k-1; k Let Y be the process noise vector; Y is the process noise covariance; the process noise covariance Y is estimated by the variance of the SVD reconstruction error;

[0035]

[0036] In the formula: z k Let v be the vector of observations at time k; H is the observation matrix; v k Here, N is the observation noise vector; N is the observation noise covariance; the observation noise covariance N is estimated by the residual noise power not filtered out by SVD.

[0037] Step S2.6: Perform state prediction based on the system's previous state and the system's dynamic equations. The formula for calculating the prior estimated state is as follows:

[0038]

[0039] In the formula: A represents the prior estimate of the state at time k based on information from time k-1, where A is the state transition matrix. B represents the posterior estimated state at time k-1. k For the control matrix, u k-1 This is the control input vector at time k-1; To estimate the covariance matrix a priori, P k-1|k-1 Let be the posterior estimated covariance matrix at time k-1, and Q be the noise introduced by the prediction model itself;

[0040] Step S2.7: Update the state estimate using Kalman gain based on the observation equation and the predicted value. The specific calculation formula is as follows:

[0041] Kalman gain: K k =P k|k-1 H T HP k|k-1 H T +R) -1 (13)

[0042] State estimation update:

[0043] Covariance update estimate: P k|k =(IK k H)P k|k-1 (15)

[0044] In the formula: K k denoted by Kalman coefficients; R is the covariance matrix of the observation noise; The residual between the actual observed value and the expected observed value;

[0045] Step S2.8: After Kalman filtering, the state estimate obtained for each frame is as follows: Take the first component of the state vector As the denoised signal of this sampling point

[0046] Furthermore, step S3 specifically includes:

[0047] Step S3.1: Determine the N samples D = {(x...} related to the predicted input variable X and the predicted output variable Y. i ,y i ,)|i=1,2,…,N}, divide the samples into m and n different intervals to form an m×n grid G;

[0048] Step S3.2: Determine the empirical marginal distributions p(x) and p(y) of the predicted input variable X and predicted output variable Y based on the empirical joint probability distribution p(x,y) of the predicted input variable X and predicted output variable Y; under the conditions of sample D and grid G, the mutual information MI(X,Y|D,G) between the predicted input variable X and predicted output variable Y is expressed as:

[0049]

[0050] Step S3.3: Calculate the normalized maximum mutual information I in grid G. * (D,m,n) is represented as:

[0051]

[0052] Based on the pre-set MIC value, select the first K input variables as the optimal set of input variables;

[0053] Step S3.4: Calculate the maximum mutual information coefficient between the predicted input variable X and the predicted output variable Y, expressed as:

[0054]

[0055] In the formula: k(N) represents a function of the number of samples;

[0056] Step S3.5: Construct matrix x from the K variables selected by MIC. MIC ∈R N×K The output voltage is y∈R N ;

[0057] Step S3.6: After completing the initial screening of MIC, retain the K-dimensional feature matrix x MIC The output voltage y is directly fed into the LASSO model: by minimizing the objective function with L1 penalty, the model achieves an optimal balance between fitting residuals and coefficient sparsity, thereby completing the secondary extraction of key features. The LASSO model is represented as follows:

[0058]

[0059] In the formula: J represents the objective function value, the value to be minimized; n represents the number of samples; y i x represents the true value of the i-th sample; ij β represents the j-th feature value of the i-th sample; j Represents the regression coefficient of the j-th feature; α represents the regularization strength; |β j | represents the absolute value of the j-th regression coefficient; p represents the total number of features; Used to standardize the residual sum of squares so that it is consistent with the unit of the regularization term;

[0060] Step S3.7: Retain the variables corresponding to non-zero coefficients, if β j If the variable is not equal to 0, then the j-th MIC initial screening variable is retained; otherwise, it is discarded, forming the final feature subset X. FIN ∈R N×K .

[0061] Further, in step S4, the TG-ISODATA clustering algorithm is used to divide the key feature parameter set into subsets of data samples based on different degrees of performance degradation, including the following steps:

[0062] Step S4.1: Collect N real PEMFC capacity-cycle degradation curves, amplify M synthetic trajectories using TimeGAN, merge the real and synthetic data, and perform ISODATA dynamic clustering on them to adaptively classify battery performance degradation modes; TimeGAN generates data using time-series correlation, and its embedded network calculates static and dynamic features as follows:

[0063]

[0064] Where: h ζ and h t They represent the corresponding feature spaces ζ and χ, respectively. t The latent vector; e ζ and e t These are recurrent embedding networks for static and dynamic features, respectively; w0 and b0 are the weights at the initial time step.

[0065] Step S4.2: Calculate the static and dynamic features of the reproduced network, as shown below:

[0066]

[0067] In the formula: and To reproduce the static and dynamic feature vectors of the network; r ζ (.) and r χ (.) represents the recurrence network constructed from the autoregressive network;

[0068] Step S4.3: The TimeGAN generator first maps the random input to an embedding space, and then indirectly generates data through an intermediate representation; the generator's calculation formula is as follows:

[0069]

[0070] Where: h ζ and h t h represents the latent feature vector of the generator; t-1 The hidden state from the previous moment; g ζ and gχ Recurrent generative networks for static and dynamic features, respectively; z ζ and z t It is a uniform random vector sequence in the range [0,1].

[0071] Step S4.4: The discriminator distinguishes between the original and newly generated time series in the embedding space to ensure that the output has battery degradation trend characteristics; the classification is as follows:

[0072]

[0073] In the formula: and The classifications are static and dynamic synthetic data, respectively; d ζ and d χ These are the classification functions for the static and dynamic output layers, respectively; 0 t1 and 0 t2 These represent the forward hidden state and the reverse hidden state, respectively.

[0074] Step S4.5: Select high-density and uniformly distributed battery data sample points as initial cluster centers; the importance of battery trajectory nodes is defined as follows:

[0075] CORE j =εR ij +σQ ij +ζL ij ,ε,σ,ζ>0,ε+σ+ζ=1,j=1,2,3,…,N

[0076] In the formula: CORE represents the coreness of the node; Q represents the significance of the battery degradation trend; N represents the total number of battery samples; ε, σ, and ζ are all set parameters;

[0077] Step S4.6: By calculating the degree of overlap of the capacity degradation curves of the two batteries in the same cycle interval, the similarity of their degradation modes is evaluated. The formula for calculating the similarity between the two batteries is as follows:

[0078]

[0079] In the formula: B i This represents the set of cyclic numbers for battery i whose capacity retention rate is not lower than the threshold θ; |.| represents the number of elements in the set;

[0080] Step S4.7: Calculate the distance between the two batteries using the following formula:

[0081]

[0082] In the formula: d(i,j) represents the distance between the degradation curves of the two batteries. The larger the value, the greater the difference between the two degradation curves.

[0083] Step S4.8: Without presetting the number of clusters, based on the battery sample size, dynamically adjust the clustering by comparing indicators such as intra-cluster distance and inter-cluster distance to match the density differences of different degradation trends; calculate the average intra-cluster distance of each cluster as follows:

[0084]

[0085] In the formula: D J c represents the average intra-cluster distance; c represents the initial number of clusters. Represents the total number of nodes; τ J Represents clustering;

[0086] Step S4.9: Calculate the average distance between all samples and the cluster centers, and then calculate the average distance between the two classes. The calculation formula is as follows:

[0087]

[0088] In the formula: D represents the average distance between the two clusters; D(·) represents the distance between the two clusters.

[0089] Step S4.10: Calculate the global average inter-class distance, expressed as follows:

[0090]

[0091] In the formula: Represents the global average inter-class distance; This represents the average distance between all samples and the cluster center.

[0092] Furthermore, step S5 specifically includes:

[0093] Step S5.1: Decompose the time series using an additive model based on STL decomposition, construct a weighting function through a kernel function, and estimate the trend component based on Losses local weighted regression. The calculation formula is as follows:

[0094]

[0095] In the formula: T t This is a trend estimate; α i and ω i As weight; Y i The original values ​​of the time series are given, and μ is the regularization parameter.

[0096] Step S5.2: After removing the trend term from the original sequence, seasonal estimation is performed using Losses. Losses-weighted regression is performed independently within each period, and the calculation formula is as follows:

[0097]

[0098] In the formula: S t This is a trend estimate; ω i (t,s) represents the seasonal weight s calculated at time t; Y i -T i This is a detrended value;

[0099] Step S5.3: After removing the trend and seasonal terms from the original data, the remaining terms are obtained. The remaining terms represent the portion of the time series that cannot be explained by trend and seasonality. The formula is as follows:

[0100] R t =Y t -T t -S t (34)

[0101] Step S5.4: To reduce the interference of seasonal and trend aliasing in the original sequence on frequency extraction, STL decomposition is used to extract the observed values ​​Y. t Explicitly split into trend T t Season S t Residual R t Three components are then fed in parallel into the cascaded frequency decomposition module.

[0102] Step S5.5: The cascaded frequency decomposition module accurately decomposes each frequency component in a series manner; firstly, for x... i+1 A fast Fourier transform is performed to obtain the frequency domain representation, and then zero-padding is used to extend the length of the frequency domain sequence to ensure that it matches the original sequence X after being transformed back to the time domain. i Consistent length;

[0103] Step S5.6: Convert the frequency domain signal back to the time domain using the inverse fast Fourier transform to achieve frequency upsampling, ensuring that the frequency information remains unchanged before and after upsampling; the frequency upsampling process is represented as:

[0104]

[0105] In the formula: and x i The sequence length is the same as x. i compared to, The i-th frequency component is missing; size is the padding size; type is the padding type; w is the window function.

[0106] Step S5.7: For the multi-level frequency components {f1,f2,…,f...} generated by the cascaded frequency decomposition module k The multi-order KAN representation learning module with a dual-branch parallel architecture learns specific representations of each frequency component through multi-order KAN, and captures temporal dependencies by using deep convolution, so as to model temporal representation learning and temporal dependency learning separately.

[0107] Step S5.8: Depthwise convolution uses D sets of convolution kernels to perform independent convolution operations on the sequence of each channel; the process of depthwise convolution is as follows:

[0108] f i,1 =Conv D→D (f i ,group=D) (36)

[0109] Step S5.9: Use ChebyshevKAN to learn the representation of the frequency components, that is, use a linear combination of Chebyshev polynomials of different orders to generate a learnable univariate function. The Chebyshev polynomial is defined as:

[0110] T n (x)=cos(n·arccos(x)) (37)

[0111] Where n is the highest order of the Chebyshev polynomial, and the complexity of the Chebyshev polynomial increases with the order.

[0112] Step S5.10: Apply a 1-layer ChebyshevKAN to the channel dimension, represented as:

[0113]

[0114] In the formula: o is the index of the output neuron; Θ∈R D×D×(n+1) These are the learnable coefficients used for linear combinations of Chebyshev polynomials;

[0115] Step S5.11: Align the KAN complexity with the Chebyshev polynomial order increasing from low to high according to the frequency components to form a multi-order KAN; set a lower bound order b, x i The learning process can be represented as:

[0116] f i,2 =KAN(f i ,order=b+ki) (40)

[0117] Step S5.12: The final output of the multi-order KAN representation learning module is the sum of the multi-order KAN and the depthwise convolution output:

[0118]

[0119] Step S5.13: Through the state variable h(t)∈R N Define the process from input X(t)∈R to output The linear mapping transforms the continuous SSM into the corresponding discrete SSM, as shown in the following formula:

[0120]

[0121] In the formula: Δ represents the discretization step size; C represents the discrete matrix obtained by the zero-order preservation technique;

[0122] Step S5.14: Obtain the final output feature map using the discretized matrix. The calculation formula is as follows:

[0123]

[0124] Where: h (t-1) h represents the initial state. (t) Indicates the current update status;

[0125] Step S5.15: Construct a mixer block and use frequency upsampling again to reintegrate the information increment into a higher frequency component:

[0126] x i =IFFT(Padding(FFT(x)) i+1 ),N,type))·w+g(f i (46)

[0127] In the formula: N is the size of the fill, g(f i Used to process or suppress noise f i ;

[0128] Step S5.16: For the last mixing block, extract the highest-level sequence x1 and use a linear layer to generate the prediction result X. O :

[0129] X O =Linear(x1) (47).

[0130] Further, step S6 specifically includes:

[0131] Step S6.1: Set the size, dimension, number of iterations, and upper and lower limits of the search space for the simulated electromagnetic wave particles in the WSA algorithm;

[0132] Step S6.2: For an optimization problem with d dimensions and n individual particles, use matrices to simulate the positional distribution of the electromagnetic particle swarm W in the search space:

[0133]

[0134] Step S6.3: Using f([W n1 W n2 ,…W nd ]) represents the fitness value of the nth individual, and the fitness value of the population is represented as:

[0135] F = [f([W] 11 W 12 ,…W 1d ]); f([W 21 W 22 ,…W 2d ])…f([W n1 W n2 ,…W nd (49)

[0136] Step S6.4: Introduce the Cat chaotic mapping strategy to generate the chaotic sequence q. n v n Mapped to the j-th dimension of the optimization problem [l j u j Using the points generated by the Cat chaotic mapping strategy as the initial population, the improved formula is as follows:

[0137]

[0138] x j =l j +(u j -l j )·q n (51)

[0139] In the formula: q n v n ∈[0,1] represents the chaotic value generated in the nth iteration; mod1 indicates taking the fractional part; x j Let l be the initial individual position in the j-th dimension; j u j Let be the lower and upper bounds of the j-th dimension;

[0140] Step S6.5: Conduct a local exploration phase search, using an electromagnetic wave emission search model, as shown below:

[0141]

[0142] In the formula: f(·) represents the individual fitness value; ρ controls the magnitude of the electromagnetic wave; m is the standard normal distribution vector; W best The current optimal position; W L The rearranged group position matrix; f max This is the maximum fitness value;

[0143] Step S6.6: Simulate some particles encountering obstacles and moving towards W. best Reflection, while the remaining particles move away from W. best Continuing to diffuse outwards, a search model using reflected electromagnetic waves is employed, as follows:

[0144]

[0145] In the formula: β is the reflection intensity coefficient; r2 is a random value between 0 and 1; n w2 W represents the number of particles that reflect electromagnetic waves. fi It is a position matrix arranged in ascending order of fitness values;

[0146] Step S6.7: Direct the particle swarm towards the current optimal direction, while simultaneously deflecting the particle swarm in other directions with a certain probability to reduce the possibility of getting trapped in local optima; a search model using received electromagnetic waves is adopted, as follows:

[0147]

[0148] In the formula: δ is the receiving coefficient; η is a random number following a normal distribution; n w3 To simulate the number of particles receiving electromagnetic waves; The historical best position is obtained through convolution; λ is the correction factor; r3, r4, r5, and r6 are random numbers between 0 and 1.

[0149] Step S6.8: Estimate the gradient of the problem using the central difference method, and then adjust the search path according to the fitted gradient direction to gradually approach the optimal solution; its mathematical expression is:

[0150] g i =(f(W) +εi )-f(W -εi )) / 2ε (58)

[0151] W i =W i -α·g i (59)

[0152] In the formula: W +εi =W i +ε,W -εi =W i -ε; g is the gradient; α is the step size coefficient;

[0153] Step S6.9: Randomly set particles that exceed the boundary within the search range, as shown in the following expression:

[0154] W i =lb+r·(ub-lb) ifWi i >ub or W i <lb (60)

[0155] Where: lb and ub are the lower and upper bounds of the search range, respectively, and r is a d-dimensional randomized column vector;

[0156] Step S6.10: Perform a global search: An improved greedy algorithm ensures efficient searching for the global optimum; by gradually narrowing the search range, the newly generated particle swarm is confined to a new search region, limiting the particle swarm to the vicinity of the global optimum; the search model is as follows:

[0157]

[0158] In the formula: W min and W max f represents the vectors formed by the minimum and maximum values ​​of individuals in the population, respectively; mean This represents the average fitness of all particles in the swarm; r is a random number between 0 and 1.

[0159] Step S6.11: After generating the next generation of particle swarms, apply the Cauchy inverse cumulative distribution mutation strategy to the globally optimal particles and particles with fitness worse than the average value. The specific formula is as follows:

[0160] η=tan[π(u-0.5)],u~U(0,1)

[0161]

[0162] In the formula: η is an independent and identically distributed Cauchy random vector in each dimension; t is the current iteration number; T max γ is the maximum number of iterations; max Take 5% of the search space width uj-lj; ⊙ indicates element-wise multiplication;

[0163] Step S6.12: Calculate fitness after perturbation If it is better than f(W) i If the optimal particle position is not found, the new position is accepted. If the convergence is not achieved, the current optimal particle position is retained, and the process returns to step S6.5 to continue iterative optimization and output the optimal parameter configuration. The SK-Mamba model uses the optimal parameter configuration to predict the components and obtain the prediction results of the components.

[0164] Further, step S7 specifically includes:

[0165] Step S7.1: Initialize the relevant parameters of the IWSA algorithm, including population size, problem dimension, upper and lower bounds of the search space, current iteration count, and maximum iteration count;

[0166] Step S7.2: Input the training set obtained in step S4 into the SK-Mamba model to optimize the hyperparameters in the SK-Mamba model; calculate the predicted value P after training the SK-Mamba model. v and sample actual value A v The fitness value Fit of each individual in the population is represented by the root mean square error between the predicted and actual values, as shown in the following formula:

[0167]

[0168] Step S7.3: Obtain the new position using the IWSA algorithm, calculate the fitness value of each individual, and sort them. After reaching the maximum number of iterations, select the best population position, which is the optimal hyperparameter of the model.

[0169] Step S7.4: Use mean squared error (MSE) and mean absolute error (MAE) as evaluation metrics to assess the accuracy of the current proton exchange membrane fuel cell performance degradation prediction model:

[0170]

[0171] Where MSE is the mean squared error, MAE is the mean absolute error, and A v For the actual value, P v These are predicted values.

[0172] Furthermore, in step S7, the hyperparameters of the SK-Mamba model include: state dimension expansion factor, time step, input window size, number of hidden layer units, regularization parameter, number of frequency band decompositions, polynomial order of KAN, moving average window size, embedding dimension, model depth, frequency upsampling method, and learning rate η.

[0173] The present invention also provides a proton exchange membrane fuel cell performance degradation trend prediction system, including a memory, a processor, and computer program instructions stored in the memory and executable by the processor. When the processor executes the computer program instructions, it can implement the above-described method.

[0174] Compared with the prior art, the present invention has the following beneficial effects:

[0175] 1. This invention employs a PST-KF hybrid algorithm to denoise and smooth state monitoring data, effectively removing noise interference and improving data accuracy and reliability. The combination of Kalman filtering and improved singular value decomposition leverages both the real-time tracking and estimation advantages of Kalman filtering for dynamic systems and the powerful dimensionality reduction and denoising capabilities of singular value decomposition.

[0176] 2. This invention uses the regular mutual information selection method to extract features from the noise-reduced data, which can effectively identify key feature variables closely related to the performance degradation of proton exchange membrane fuel cells. The LASSO regression module is introduced to perform secondary screening of the variables selected by MIC. LASSO regression achieves the optimal balance between fitting residuals and coefficient sparsity, making the model more concise and efficient.

[0177] 3. This invention uses the TG-ISODATA clustering algorithm to divide the key feature parameter set into data sample subsets based on different performance degradation levels, which can effectively classify battery performance degradation modes and realize refined analysis and modeling of different types of degradation modes.

[0178] 4. In the SK-Mamba model of this invention, STL decomposition effectively separates the trend, seasonal and residual components in the data, reducing the interference of seasonal and trend aliasing on frequency extraction; the CFD module accurately decomposes each frequency component, providing clearer frequency information for subsequent feature learning; the M-KAN module uses multi-order KANs to learn specific representations of each frequency component and captures temporal dependencies, realizing separate modeling of temporal representation learning and temporal dependency learning; the Mamba module endows local features with global temporal memory and cross-segment interaction capabilities, further improving the model's ability to capture and predict complex decline trends.

[0179] 5. This invention improves upon the original Wave Search Algorithm (WSA) to obtain the IWSA algorithm, which is then used to optimize the hyperparameters of the performance degradation trend model SK-Mamba. A Cat chaotic mapping strategy is introduced to improve the original population initialization process, increasing population diversity and global search capability. A Cauchy inverse cumulative distribution mutation strategy is introduced in the algorithm's position update stage to avoid getting trapped in local optima. Attached Figure Description

[0180] Figure 1 This is a schematic diagram of the SK-Mamba model in an embodiment of the present invention;

[0181] Figure 2 This is a schematic diagram of the implementation process of the IWSA algorithm in an embodiment of the present invention;

[0182] Figure 3This is a schematic diagram illustrating the process of optimizing the SK-Mamba model using the WSA algorithm in an embodiment of the present invention. Detailed Implementation

[0183] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0184] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0185] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0186] This embodiment provides a method for predicting the performance degradation trend of a proton exchange membrane fuel cell, including the following steps:

[0187] Step S1: Collect state monitoring data of the proton exchange membrane fuel cell; the state monitoring data includes output voltage data and its characteristic variables.

[0188] Step S2: The power spectrum threshold-Kalman joint algorithm (PST-KF), which combines Kalman filtering (KF) and improved singular value decomposition (SVD), is used to denoise and smooth the condition monitoring data. The PST-KF algorithm removes periodic narrowband interference through improved singular value decomposition (SVD), and then uses the SVD reconstructed signal as the observation value to input the Kalman filtering (KF) model for dynamic filtering.

[0189] Step S3: Use the regular mutual information selection method to extract key feature parameters from the noise-reduced output voltage degradation data, including: calculating the MIC value between all input variables and the output voltage, sorting the input variables in descending order according to the MIC value and selecting the top K variables that are closely related to the performance degradation of the proton exchange membrane fuel cell, and then using LASSO regression to perform secondary screening on the selected K variables to retain the features corresponding to non-zero coefficients.

[0190] Step S4: The TG-ISODATA clustering algorithm is used to divide the key feature parameter set into data sample subsets based on different performance degradation degrees, and each subset obtained by TG-ISODATA clustering is divided into training set and test set according to the ratio; the TG-ISODATA clustering algorithm includes: using TimeGAN to generate synthetic degradation trajectory, and performing ISODATA dynamic clustering in combination with real data.

[0191] Step S5: Construct the performance degradation trend model SK-Mamba, the structure of which is as follows: Figure 1 As shown, the SK-Mamba model includes: within the TimeKAN framework, STL decomposition is used as a preprocessing step before the Cascaded Frequency Decomposition (CFD) module. First, the trend, seasonal, and residual components are extracted through STL decomposition. Then, the Cascaded Frequency Decomposition (CFD) module is used to progressively extract multi-scale frequency information from each component. Next, multi-order KAN (M-KAN) is used to perform nonlinear modeling with complexity matching for different frequency bands. The Mamba module is then connected after each subsequence to endow local features with global temporal memory and cross-segment interaction capabilities. Finally, all features are fused and a prediction is output.

[0192] Step S6: Improve the Wave Search Algorithm (WSA). Initialize the population using the Cat chaotic mapping strategy and introduce the Cauchy inverse cumulative distribution mutation strategy during the position update stage to avoid local optima, resulting in the IWSA algorithm. The implementation flow of the IWSA algorithm is as follows: Figure 2 As shown.

[0193] Step S7: As Figure 3 As shown, the IWSA algorithm is used to optimize the hyperparameters of the SK-Mamba model, and the IWSA-SK-Mamba prediction model is constructed.

[0194] Step S8: Train the IWSA-SK-Mamba prediction model using the training set and evaluate the performance of the IWSA-SK-Mamba prediction model using the test set; then predict the performance degradation trend of the proton exchange membrane fuel cell using the trained and tested IWSA-SK-Mamba prediction model.

[0195] Compared with existing technologies, this invention provides more accurate prediction results for the performance degradation of proton exchange membrane fuel cells, provides a scientific basis for the maintenance and management of fuel cells, thereby extending their service life and improving overall efficiency.

[0196] In this embodiment, in step S1, the status monitoring data includes real-time monitoring data and historical degradation data.

[0197] The real-time monitoring data includes aging time, single cell temperature, stack temperature, stack voltage, current, current density, cathode inlet air flow rate, anode inlet air flow rate, hydrogen inlet temperature, hydrogen outlet temperature, air inlet temperature, air outlet temperature, cooling water inlet temperature, cooling water outlet temperature, hydrogen inlet pressure, hydrogen outlet pressure, air inlet pressure, air outlet pressure, hydrogen inlet velocity, hydrogen outlet velocity, air inlet velocity, air outlet velocity, and cooling water velocity.

[0198] The historical degradation data includes output voltage degradation data; let the historical degradation data be X, and resample the degradation data using a half-hour interval rule, the specific formula is as follows:

[0199]

[0200] In the formula: X t x represents the sampled value at time t; i N represents the i-th observation of the degraded data; t Indicates the number of observations.

[0201] In this embodiment, the specific implementation steps of step S2 are as follows.

[0202] Step S2.1: Perform Fourier transform on the noisy PD signal to obtain the power spectrum, calculate the absolute difference of the spectral amplitude, and then filter and remove narrowband interference singular values ​​to reduce noise using the singular value thresholding method.

[0203] First, we substitute the noisy simulation signal into the analysis. We first perform a Fourier transform on the simulation signal to obtain the power spectrum. The specific calculation formula is as follows:

[0204]

[0205] In the formula: F(ω) is the Fourier transform of the simulated signal; f(t) is the simulated signal in the time domain; g(t) is the weighting function; ω is the angular frequency of the signal; t is time; P(ω) is the power spectrum.

[0206] Step S2.2: In the FFT power spectrum, by calculating the absolute value of the difference between the amplitudes of two adjacent points in the spectrum, periodic narrowband interference (spiking pulses) and PD signals (hilly waveforms) can be effectively distinguished. Specifically, the amplitude difference of gentle hilly waveforms is smaller after differential analysis, and the overall amplitude is suppressed; while steep spikes, due to their drastic edge changes, still maintain a significant amplitude difference after differential analysis, thus standing out in the new power spectrum. The power spectrum difference ΔP(n) is expressed as:

[0207]

[0208] In the formula: P(n) is the amplitude of the nth signal data sampling point in the spectrum; N is the total number of signal data sampling points.

[0209] Step S2.3: Filter out the singular values ​​of periodic narrowband interference using the classical threshold method and threshold formula. The periodic narrowband interference amplitude is greater than the set threshold T. SVD The expression is as follows:

[0210]

[0211] In the formula: σ is the standard deviation of the signal; τ is the noise level in the sample; ψ(n) is the intermediate variable; η is the number of periodic narrowband interferences; and the power spectrum with amplitude greater than the threshold T is considered as an intermediate variable. SVD At that time, it is periodic narrowband interference.

[0212] Step S2.4: Reorganize the denoised singular value matrix into a diagonal matrix ∑ Hessen Combining the left singular vector matrix U and the right singular vector matrix V T Calculate the reconstruction matrix X Hessen The antidiagonal elements are averaged to restore the time-domain signal, yielding the clean PD signal X after filtering out periodic narrowband interference. SVD (t), the calculation formula is as follows:

[0213] X Hessen =U·∑ Hessen ·V T (8)

[0214] Step S2.5: Reconstruct the SVD signal X SVD Using (t) as the observed value, a KF state-space model is established, and the calculation formula is as follows:

[0215]

[0216] In the formula, x k Let x be the system state vector at time k; F is the state transition matrix; if the signal changes slowly, let F = 1 (identity matrix); k-1 w is the system state vector at time k-1; k Let Y be the process noise vector; Y is the process noise covariance; the process noise covariance Y is estimated by the variance of the SVD reconstruction error;

[0217]

[0218] In the formula: z k Let v be the vector of observations at time k; H is the observation matrix; the observation matrix H = 1; v k is the observation noise vector; N is the observation noise covariance; the observation noise covariance N is estimated by the residual noise power not filtered out by SVD.

[0219] Step S2.6: Prediction (Time Update): Based on the previous state of the system and the system dynamic equations, state prediction is performed. The prior estimated state calculation formula is as follows:

[0220]

[0221] In the formula: A represents the prior estimate of the state at time k based on information from time k-1, where A is the state transition matrix. B represents the posterior estimated state at time k-1. k For the control matrix, u k-1 This is the control input vector at time k-1; To estimate the covariance matrix a priori, P k-1|k-1 Let be the posterior estimated covariance matrix at time k-1, and Q be the noise introduced by the prediction model itself.

[0222] Step S2.7: Prediction (Measurement Update): Based on the observation equation and the predicted value, the state estimate is updated using the Kalman gain. The specific calculation formula is as follows:

[0223] Kalman gain: K k =P k|k-1 H T HP k|k-1 H T +R) -1 (13)

[0224] State estimation update:

[0225] Covariance update estimate: P k|k =(IK k H)P k|k-1 (15)

[0226] In the formula: K k denoted by Kalman coefficients; R is the covariance matrix of the observation noise; This represents the residual between the actual observed value and the expected observed value.

[0227] Step S2.8: After Kalman filtering, the state estimate obtained for each frame is as follows: Take the first component of the state vector As the denoised signal of this sampling point

[0228] In this embodiment, the specific implementation steps of step S3 are as follows.

[0229] Step S3.1: Determine the N samples D = {(x...} related to the predicted input variable X and the predicted output variable Y. i ,y i,)∣i=1,2,…,N}, divide the samples into m and n different intervals to form an m×n grid G.

[0230] Step S3.2: Determine the empirical marginal distributions p(x) and p(y) of the predicted input variable X and predicted output variable Y based on the empirical joint probability distribution p(x,y) of the predicted input variable X and predicted output variable Y; under the conditions of sample D and grid G, the mutual information MI(X,Y|D,G) between the predicted input variable X and predicted output variable Y is expressed as:

[0231]

[0232] Step S3.3: Calculate the normalized maximum mutual information I in grid G. * (D,m,n) is represented as:

[0233]

[0234] In the formula: I * The larger (D,m,n) is, the closer it is to 1, and the stronger the correlation between the fuel cell input variable x and the output variable y; based on the pre-set MIC value, the first K input variables are selected as the optimal set of input variables.

[0235] Step S3.4: Calculate the maximum mutual information coefficient between the predicted input variable X and the predicted output variable Y, expressed as:

[0236]

[0237] In the formula: k(N) represents a function of the number of samples.

[0238] Step S3.5: Construct matrix x from the K variables selected by MIC. MIC ∈R N×K The output voltage is y∈R N .

[0239] Step S3.6: After completing the initial screening of MIC, retain the K-dimensional feature matrix x MIC The output voltage y is directly fed into the LASSO model: by minimizing the objective function with L1 penalty, the model achieves an optimal balance between fitting residuals and coefficient sparsity, thereby completing the secondary extraction of key features. The LASSO model is represented as follows:

[0240]

[0241] In the formula: J represents the objective function value, the value to be minimized; n represents the number of samples; y i x represents the true value of the i-th sample; ij β represents the j-th feature value of the i-th sample;j Represents the regression coefficient of the j-th feature; α represents the regularization strength; |β j | represents the absolute value of the j-th regression coefficient; p represents the total number of features; Used to standardize the sum of squared residuals so that it is consistent with the units of the regularization term.

[0242] Step S3.7: Retain the variables corresponding to non-zero coefficients, if β j If the variable is not equal to 0, then the j-th MIC initial screening variable is retained; otherwise, it is discarded, forming the final feature subset X. FIN ∈R N×K .

[0243] In this embodiment, in step S4, the TG-ISODATA clustering algorithm is used to divide the set of key feature parameters into subsets of data samples based on different degrees of performance degradation. The specific implementation steps are as follows.

[0244] Step S4.1: Collect N real PEMFC capacity-cycle degradation curves, amplify M synthetic trajectories using TimeGAN, merge the real and synthetic data, and perform ISODATA dynamic clustering on them to adaptively classify battery performance degradation modes; TimeGAN generates data using time-series correlation, and its embedded network calculates static and dynamic features as follows:

[0245]

[0246] Where: h ζ and h t They represent the corresponding feature spaces ζ and χ, respectively. t The latent vector; e ζ and e t These are recurrent embedding networks for static and dynamic features, respectively; w0 and b0 are the weights at the initial time step.

[0247] Step S4.2: Calculate the static and dynamic features of the reproduced network, as shown below:

[0248]

[0249]

[0250] In the formula: and To reproduce the static and dynamic feature vectors of the network; r ζ (.) and r χ (.) represents the recurrence network constructed from the autoregressive network.

[0251] Step S4.3: The TimeGAN generator first maps the random input to an embedding space, and then indirectly generates data through an intermediate representation; the generator's calculation formula is as follows:

[0252]

[0253] Where: h ζ and h t h represents the latent feature vector of the generator; t-1 The hidden state from the previous moment; g ζ and g χ Recurrent generative networks for static and dynamic features, respectively; z ζ and z t Let be a uniform random vector sequence in the range [0,1].

[0254] Step S4.4: The discriminator distinguishes between the original and newly generated time series in the embedding space to ensure that the output has battery degradation trend characteristics; the classification is as follows:

[0255]

[0256] In the formula: and The classifications are static and dynamic synthetic data, respectively; d ζ and d χ These are the classification functions for the static and dynamic output layers, respectively; 0 t1 and 0 t2 These represent the forward hidden state and the reverse hidden state, respectively.

[0257] Step S4.5: Select battery data sample points with high density and uniform distribution as initial cluster centers to achieve more effective structural partitioning; the importance of battery trajectory nodes is defined as follows:

[0258] CORE j =εR ij +σQ ij +ζL ij ,ε,σ,ζ>0,ε+σ+ζ=1,j=1,2,3,…,N

[0259] In the formula: CORE represents the coreness of the node; Q represents the significance of the battery degradation trend; N represents the total number of battery samples; ε, σ, and ζ are all set parameters. The centrality index is arranged from largest to smallest. The higher the value, the better the cluster center.

[0260] Step S4.6: By calculating the degree of overlap of the capacity degradation curves of two batteries in the same cycle interval, the similarity of their degradation patterns is evaluated, effectively realizing battery clustering based on degradation trends. The similarity calculation formula between two batteries is as follows:

[0261]

[0262] In the formula: B i Let represent the set of cyclic numbers for battery i whose capacity retention rate is not lower than the threshold θ; |.| represents the number of elements in the set.

[0263] Step S4.7: The higher the similarity between the degradation curves of the two batteries, the smaller their distance; the distance between the two batteries is calculated using the following formula:

[0264]

[0265] In the formula: d(i,j) represents the distance between the two battery degradation curves. The larger the value, the greater the difference between the two degradation curves.

[0266] Step S4.8: Research and adjust clustering rules. Instead of pre-setting the number of clusters, the clustering is dynamically adjusted based on the battery sample size by comparing indicators such as intra-cluster distance and inter-cluster distance to match the density differences of different degradation trends. The average intra-cluster distance of each cluster is calculated as follows:

[0267]

[0268] In the formula: D J c represents the average intra-cluster distance; c represents the initial number of clusters. Represents the total number of nodes; τ J Represents clustering.

[0269] Step S4.9: Calculate the average distance between all samples and the cluster centers, and then calculate the average distance between the two classes. The calculation formula is as follows:

[0270]

[0271] In the formula: D represents the average distance between the two clusters; D(·) represents the distance between the two clusters.

[0272] Step S4.10: Calculate the global average inter-class distance, expressed as follows:

[0273]

[0274] In the formula: Represents the global average inter-class distance; This represents the average distance between all samples and the cluster center.

[0275] Based on the performance degradation trend of proton exchange membrane fuel cells, the sample set is divided into three subsets: rapid early degradation followed by slow later degradation; uniform degradation throughout the process; and fluctuating degradation.

[0276] In this embodiment, the specific implementation steps of step S5 are as follows.

[0277] Step S5.1: STL decomposition is a data decomposition method based on locally weighted regression; STL typically includes two models: additive and multiplicative models, as shown in the following formula:

[0278] Y t =T t +S t +R t ,t∈(0,n] (30)

[0279] Y t =T t ×S t ×R t ,t∈(0,n] (31)

[0280] In the formula: Y t This is the original data; T t The trend term derived from the decomposition; S t R represents the seasonal terms derived from the decomposition. t This is the irregular remaining item after removing trend and seasonal items.

[0281] This embodiment uses an additive model based on STL decomposition to decompose the time series, constructs a weighting function through a kernel function, and estimates the trend component based on Losses local weighted regression. The calculation formula is as follows:

[0282]

[0283] In the formula: T t This is a trend estimate; α i and ω i As weight; Y i represents the original values ​​of the time series, and μ is the regularization parameter.

[0284] Step S5.2: After removing the trend term from the original sequence, seasonal estimation is performed using Losses. Periodicity needs to be considered, meaning that Losses-weighted regression is performed independently within each period. The calculation formula is as follows:

[0285]

[0286] In the formula: S t This is a trend estimate; ω i (t,s) represents the seasonal weight s calculated at time t; Y i -T i This is the detrended value.

[0287] Step S5.3: After removing the trend and seasonal terms from the original data, the remaining terms are obtained. The remaining terms represent the portion of the time series that cannot be explained by trend and seasonality, as shown in the following formula:

[0288] R t =Y t -T t -S t (34)

[0289] Step S5.4: To reduce the interference of seasonal and trend aliasing in the original sequence on frequency extraction, STL decomposition is used to extract the observed values ​​Y. t Explicitly split into trend T t Season S t Residual R t Three components are then fed in parallel into the cascaded frequency decomposition (CFD) module.

[0290] Step S5.5: The cascaded frequency decomposition (CFD) module accurately decomposes each frequency component in a cascade manner; firstly, for x... i+1 A Fast Fourier Transform (FFT) is performed to obtain the frequency domain representation. Then, Zero-Padding is used to extend the length of the frequency domain sequence, ensuring that it matches the original sequence X after being transformed back to the time domain. i The lengths are consistent.

[0291] Step S5.6: Frequency upsampling is achieved by converting the frequency domain signal back to the time domain using Inverse Fast Fourier Transform (IFFT), ensuring that the frequency information remains unchanged before and after upsampling; each sub-band sequence f1 output by the cascaded frequency decomposition (CFD) module retains a clear frequency domain label (low / medium / high frequency) and has a consistent time step; the frequency upsampling process is represented as:

[0292]

[0293] In the formula: and x i The sequence length is the same as x. i compared to, The i-th frequency component is missing; size is the size of the padding; type is the type of padding; w is the window function.

[0294] Step S5.7: For the multi-level frequency components {f1, f2, ..., f...} generated by the cascaded frequency decomposition (CFD) module k The multi-order KAN representation learning (M-KAN) module, which utilizes a dual-branch parallel architecture, learns specific representations for each frequency component through multi-order KAN, while using deep convolution to capture temporal dependencies, thus enabling separate modeling of temporal representation learning and temporal dependency learning.

[0295] Step S5.8: Depthwise convolution uses D sets of convolutional kernels to perform independent convolution operations on the sequence of each channel; this allows the model to focus on capturing temporal patterns without being disturbed by the relationships between channels; the process of depthwise convolution is as follows:

[0296] f i,1 =Conv D→D (f i ,group=D) (36)

[0297] Step S5.9: Use ChebyshevKAN to learn the representation of the frequency components, that is, use a linear combination of Chebyshev polynomials of different orders to generate a learnable univariate function. The Chebyshev polynomial is defined as:

[0298] T n (x)=cos(n·arccos(x)) (37)

[0299] Where n is the highest order of the Chebyshev polynomial, and the complexity of the Chebyshev polynomial increases with the order.

[0300] Step S5.10: Apply a 1-layer ChebyshevKAN to the channel dimension, represented as:

[0301]

[0302] In the formula: o is the index of the output neuron; Θ∈R D×D×(n+1) represents the learnable coefficients used for linear combinations of Chebyshev polynomials.

[0303] Step S5.11: Align the KAN complexity with the Chebyshev polynomial order increasing from low to high according to the frequency components to form a multi-order KAN; set a lower bound order b, x i The learning process can be represented as:

[0304] f i,2 =KAN(f i ,order=b+ki) (40)

[0305] Step S5.12: The final output of the multi-order KAN representation learning (M-KAN) module is the sum of the multi-order KAN and the depthwise convolution output:

[0306]

[0307] Step S5.13: The core of the selective SSM layer is the state representation equation and the prediction output equation, through the state variable h(t)∈R NDefine the process from input X(t)∈R to output The linear mapping is used; to adapt to discrete data, the continuous SSM needs to be converted into the corresponding discrete SSM, and the specific formula is as follows:

[0308]

[0309] In the formula: Δ represents the discretization step size; C represents the discrete matrix obtained by the zero-order preservation technique.

[0310] Step S5.14: Obtain the final output feature map using the discretized matrix. The calculation formula is as follows:

[0311]

[0312] Where: h (t-1) h represents the initial state. (t) This indicates the current update status.

[0313] Step S5.15: Construct a mixer block to mix the frequency components of the i-th stage. To convert the sequence into a multi-level sequence xi, we only need to supplement the frequency information from level i+1 to level k back to level i; therefore, we use frequency upsampling again to reintegrate the information increment into higher frequency components:

[0314] x u =IFFT(Padding(FFT(x)) u+1 ),N,type))·w+g(f i (46)

[0315] In the formula: N is the size of the fill, g(f i Used to process or suppress noise f i .

[0316] Step S5.16: For the last mixing block, extract the highest-level sequence x1 and use a simple linear layer to produce the prediction result X. O :

[0317] X O =Linear(x1) (47).

[0318] In this embodiment, the specific implementation steps of step S6 are as follows.

[0319] Step S6.1: Set the size, dimension, number of iterations, and upper and lower limits of the search space for the simulated electromagnetic wave particles in the WSA algorithm.

[0320] Step S6.2: In the wave search algorithm, massless particles are used to simulate electromagnetic waves; for a d-dimensional optimization problem and n individual particles, a matrix is ​​used to simulate the position distribution of the electromagnetic wave particle swarm W in the search space:

[0321]

[0322] Step S6.3: Using f([W n1 W n2 ,…W nd ]) represents the fitness value of the nth individual, and the fitness value of the population is represented as:

[0323] F = [f([W] 11 W 12 ,…W 1d ]); f([W 21 W 22 ,…W 2d ])…f([W n1 W n2 ,…W nd (49)

[0324] Step S6.4: Introduce the Cat chaotic mapping strategy to generate the chaotic sequence q. n v n Mapped to the j-th dimension of the optimization problem [l j u j Using the points generated by the Cat chaotic mapping strategy as the initial population, the improved formula is as follows:

[0325]

[0326] x j =l j +(u j -l j )·q n (51)

[0327] In the formula: q n v n ∈[0,1] represents the chaotic value generated in the nth iteration; mod1 indicates taking the fractional part; x j Let l be the initial individual position in the j-th dimension; j u j Let be the lower and upper bounds of the j-th dimension.

[0328] Step S6.5: Perform a local exploration phase search. To avoid getting trapped in local optima and to improve the efficiency of the local search, an electromagnetic wave emission search model is adopted, as follows:

[0329]

[0330] In the formula: f(·) represents the individual fitness value; ρ controls the magnitude of the electromagnetic wave; m is the standard normal distribution vector; W best The current optimal position; W L The rearranged group position matrix; f max This represents the maximum fitness value.

[0331] Step S6.6: Simulate some particles (particles with low fitness values) encountering obstacles and moving towards W. best Reflection occurs, while the remaining particles (particles with higher fitness values) move away from W. best Continuing to diffuse outwards, a search model using reflected electromagnetic waves is employed, as follows:

[0332]

[0333] In the formula: β is the reflection intensity coefficient; r2 is a random value between 0 and 1; n w2 W represents the number of particles that reflect electromagnetic waves. fi It is a position matrix arranged in ascending order of fitness values.

[0334] Step S6.7: Radars typically receive electromagnetic waves normally, but sometimes they are subject to interference, requiring correction and processing. The particle swarm is directed to search in the current optimal direction, while simultaneously deflecting in other directions with a certain probability to reduce the possibility of getting trapped in local optima. An electromagnetic wave reception search model is used, as follows:

[0335]

[0336] In the formula: δ is the receiving coefficient; η is a random number following a normal distribution; n w3 To simulate the number of particles receiving electromagnetic waves; λ represents the historical best position obtained through convolution; λ is the correction factor; r3, r4, r5, and r6 are random numbers between 0 and 1.

[0337] Step S6.8: Estimate key information such as the gradient of the problem using the central difference method, and then adjust the search path according to the fitted gradient direction to gradually approach the optimal solution; its mathematical expression is:

[0338] g i =(f(W) +εi )-f(W -εi )) / 2ε (58)

[0339] W i =W i -α·g i (59)

[0340] In the formula: W +εi=W i +ε,W -εi =W i -ε; g is the gradient; α is the step size coefficient.

[0341] Step S6.9: The generalized boundary constraint rule places particles that cross the boundary on the boundary itself. This method reduces the diversity of the particle swarm. Therefore, we randomly set particles that exceed the boundary within the search range, as shown in the following expression:

[0342] W i =lb+r·(ub-lb) ifW i >ub or W i <lb (60)

[0343] Where: lb and ub are the lower and upper bounds of the search range, respectively, and r is a d-dimensional randomized column vector.

[0344] Step S6.10: Perform a global search: An improved greedy algorithm ensures efficient searching for the global optimum. By gradually narrowing the search range, the newly generated particle swarm is confined to a new search region, keeping the particle swarm near the global optimum, thus greatly improving search efficiency. The search model is as follows:

[0345]

[0346] In the formula: W min and W max f represents the vectors formed by the minimum and maximum values ​​of individuals in the population, respectively; mean This represents the average fitness of all particles in the population; r is a random number between 0 and 1.

[0347] Step S6.11: To suppress premature convergence that may be caused by the greedy mechanism, after generating the new generation of particle swarm, a Cauchy inverse cumulative distribution mutation strategy is applied to the globally optimal particles and particles with fitness worse than the average value to enhance their ability to escape local optima. The specific formula is as follows:

[0348] η=tan[π(u-0.5)],u~U(0,1)

[0349]

[0350] In the formula: η is an independent and identically distributed Cauchy random vector in each dimension; t is the current iteration number; T max γ is the maximum number of iterations; max Take 5% of the search space width uj-lj; ⊙ indicates element-wise multiplication.

[0351] Step S6.12: Calculate fitness after perturbation If it is better than f(W)i If the optimal particle position is not found, the new position is accepted. If the convergence is not achieved, the current optimal particle position is retained, and the process returns to step S6.5 to continue iterative optimization and output the optimal parameter configuration. The SK-Mamba model uses the optimal parameter configuration to predict the components and obtain the prediction results of the components.

[0352] In this embodiment, the specific implementation steps of step S7 are as follows.

[0353] Step S7.1: Initialize the relevant parameters of the IWSA algorithm, including population size, problem dimension, upper and lower bounds of the search space, current iteration count, and maximum iteration count.

[0354] Step S7.2: Input the training set obtained in step S4 into the SK-Mamba model to optimize the hyperparameters in the SK-Mamba model; calculate the predicted value P after training the SK-Mamba model. v and sample actual value A v The fitness value Fit of each individual in the population is represented by the root mean square error between the predicted and actual values, as shown in the following formula:

[0355]

[0356] Step S7.3: Obtain the new position using the IWSA algorithm, calculate the fitness value of each individual using the above formula, and sort them. After reaching the maximum number of iterations, select the best population position, which is the optimal hyperparameter of the model.

[0357] Step S7.4: Use mean squared error (MSE) and mean absolute error (MAE) as evaluation metrics to assess the accuracy of the current proton exchange membrane fuel cell performance degradation prediction model:

[0358]

[0359] Where MSE is the mean squared error, MAE is the mean absolute error, and A v For the actual value, P v These are predicted values.

[0360] In this embodiment, the hyperparameters of the SK-Mamba model include: state dimension expansion factor (N), time step (Δ), input window size (L), number of hidden layer units, regularization parameter (γ), number of frequency band decompositions (k), polynomial order of KAN, moving average window size (d), embedding dimension (D), model depth (L), frequency upsampling method, and learning rate η.

[0361] In step S8, the training set obtained in step S4 is input into the IWSA-SK-Mamba prediction model for training, and the performance of the IWSA-SK-Mamba prediction model is evaluated through the test set.

[0362] Then, the IWSA-SK-Mamba prediction model, which has been trained and tested, is used to predict the health indicators of proton exchange membrane fuel cells and the degradation trend of fuel cell usage time, thus obtaining the prediction results of the performance degradation trend of proton exchange membrane fuel cells.

[0363] The improved wave search algorithm optimizes the SK-Mamba combinatorial model, which exhibits better robustness in predicting fuel cell health indicators, avoids overfitting, increases prediction accuracy, and provides a favorable foundation for fuel cell life prediction.

[0364] This embodiment also provides a proton exchange membrane fuel cell performance degradation trend prediction system, including a memory, a processor, and computer program instructions stored in the memory and executable by the processor. When the processor executes the computer program instructions, it can implement the above-described method.

[0365] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0366] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0367] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0368] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0369] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for predicting the performance degradation trend of a proton exchange membrane fuel cell, characterized in that, Includes the following steps: Step S1: Collect state monitoring data of the proton exchange membrane fuel cell; Step S2: The power spectrum threshold-Kalman joint algorithm PST-KF, which combines Kalman filtering (KF) and improved singular value decomposition (SVD), is used to denoise and smooth the condition monitoring data. The PST-KF algorithm removes periodic narrowband interference through improved singular value decomposition (SVD), and then uses the SVD reconstructed signal as the observation value to input the Kalman filter model for dynamic filtering. Step S3: Use the regular mutual information selection method to extract key feature parameters from the noise-reduced output voltage degradation data, including: calculating the MIC value between all input variables and the output voltage, sorting the input variables in descending order according to the MIC value and selecting the top K variables, and then using LASSO regression to perform secondary screening on the selected K variables to retain the features corresponding to non-zero coefficients. Step S4: The TG-ISODATA clustering algorithm is used to divide the key feature parameter set into data sample subsets based on different performance degradation degrees, and each subset obtained by TG-ISODATA clustering is divided into training set and test set according to the ratio; the TG-ISODATA clustering algorithm includes: using TimeGAN to generate synthetic degradation trajectory, and performing ISODATA dynamic clustering in combination with real data; Step S5: Construct the performance degradation trend model SK-Mamba, including: Under the TimeKAN framework, STL decomposition is used as a preprocessing step before the cascaded frequency decomposition module. First, the trend, seasonality, and residual components are extracted by STL decomposition. Then, the multi-scale frequency information in each component is extracted step by step by the cascaded frequency decomposition module. Next, multi-order KAN is used to perform nonlinear modeling with complexity matching for different frequency bands. The Mamba module is then connected after each subsequence to endow local features with global temporal memory and cross-segment interaction capabilities. Finally, all features are fused and the prediction is output. Step S6: Improve the wave search algorithm WSA by using the Cat chaotic mapping strategy to initialize the population and introducing the Cauchy inverse cumulative distribution mutation strategy in the position update stage to avoid local optima, thus obtaining the IWSA algorithm; Step S7: Optimize the hyperparameters of the SK-Mamba model using the IWSA algorithm to construct the IWSA-SK-Mamba prediction model; Step S8: Train the IWSA-SK-Mamba prediction model using the training set and evaluate the performance of the IWSA-SK-Mamba prediction model using the test set; then predict the performance degradation trend of the proton exchange membrane fuel cell using the trained and tested IWSA-SK-Mamba prediction model.

2. The method for predicting the performance degradation trend of a proton exchange membrane fuel cell according to claim 1, characterized in that, In step S1, the status monitoring data includes real-time monitoring data and historical degradation data; the real-time monitoring data includes aging time, single cell temperature, stack temperature, stack voltage, current, current density, cathode inlet flow rate, anode inlet flow rate, hydrogen inlet temperature, hydrogen outlet temperature, air inlet temperature, air outlet temperature, cooling water inlet temperature, cooling water outlet temperature, hydrogen inlet pressure, hydrogen outlet pressure, air inlet pressure, air outlet pressure, hydrogen inlet flow rate, hydrogen outlet flow rate, air inlet flow rate, air outlet flow rate, and cooling water flow rate; the historical degradation data includes output voltage degradation data.

3. The method for predicting the performance degradation trend of a proton exchange membrane fuel cell according to claim 1, characterized in that, Step S2 specifically includes: Step S2.1: Perform Fourier transform on the noisy PD signal to obtain the power spectrum, calculate the absolute difference of the spectral amplitude, and then filter and remove narrowband interference singular values ​​using the singular value thresholding method; First, substitute the noisy simulation signal for analysis, and first perform Fourier transform on the simulation signal to obtain the power spectrum. Step S2.2: In the FFT power spectrum, periodic narrowband interference and PD signals are distinguished by calculating the absolute value of the difference between the amplitudes of two adjacent points in the spectrum; Step S2.3: Filter out the singular values ​​of periodic narrowband interference, where the amplitude in the power spectrum is greater than the set threshold T. SVD At that time, it is a periodic narrowband interference; Step S2.4: Reorganize the denoised singular value matrix into a diagonal matrix ∑ Hessen Combining the left singular vector matrix U and the right singular vector matrix V T Calculate the reconstruction matrix X Hessen The antidiagonal elements are averaged to restore the time-domain signal, yielding the clean PD signal X after filtering out periodic narrowband interference. SVD (t); Step S2.5: Reconstruct the SVD signal X SVD Using (t) as the observed value, a KF state-space model is established; Step S2.6: Perform state prediction based on the system's previous state and the system's dynamic equations; Step S2.7: Update the state estimate using Kalman gain based on the observation equation and the predicted value; Step S2.8: After Kalman filtering, the state estimate obtained for each frame is as follows: Take the first component of the state vector As the denoised signal of this sampling point 4. The method for predicting the performance degradation trend of a proton exchange membrane fuel cell according to claim 1, characterized in that, Step S3 specifically includes: Step S3.1: Determine N samples D related to the predicted input variable X and the predicted output variable Y, and divide the samples into m and n different intervals to form an m×n grid G; Step S3.2: Determine the empirical marginal distributions p(x) and p(y) of the predicted input variable X and predicted output variable Y based on the empirical joint probability distribution p(x,y) of the predicted input variable X and predicted output variable Y; predict the mutual information MI(X,Y|D,G) between the predicted input variable X and predicted output variable Y under the conditions of sample D and grid G; Step S3.3: Calculate the normalized maximum mutual information I in grid G. * (D,m,n); Based on the pre-set MIC value, select the first K input variables as the optimal set of input variables; Step S3.4: Calculate the maximum mutual information coefficient between the predicted input variable X and the predicted output variable Y; Step S3.5: Construct matrix x from the K variables selected by MIC. MIC The output voltage is y; Step S3.6: After completing the initial screening of MIC, retain the K-dimensional feature matrix x MIC The output voltage y is directly fed into the LASSO model: by minimizing the objective function with L1 penalty, the model achieves an optimal balance between fitting residuals and coefficient sparsity, thereby completing the secondary extraction of key features; the LASSO model is represented as follows: In the formula: J represents the objective function value, the value to be minimized; n represents the number of samples; y i x represents the true value of the i-th sample; ij β represents the j-th feature value of the i-th sample; j Represents the regression coefficient of the j-th feature; α represents the regularization strength; |β j | represents the absolute value of the j-th regression coefficient; p represents the total number of features; Used to standardize the residual sum of squares so that it is consistent with the unit of the regularization term; Step S3.7: Retain the variables corresponding to non-zero coefficients, if β j If the variable is not equal to 0, then the j-th MIC initial screening variable is retained; otherwise, it is discarded, forming the final feature subset X. FIN .

5. The method for predicting the performance degradation trend of a proton exchange membrane fuel cell according to claim 1, characterized in that, In step S4, the TG-ISODATA clustering algorithm is used to divide the set of key feature parameters into subsets of data samples based on different degrees of performance degradation, including the following steps: Step S4.1: Collect N real PEMFC capacity-cycle degradation curves, amplify M synthetic trajectories using TimeGAN, merge the real and synthetic data and perform ISODATA dynamic clustering on them to adaptively classify battery performance degradation modes. Step S4.2: Calculate the static and dynamic characteristics of the reproduced network; Step S4.3: The TimeGAN generator first maps the random input to an embedding space, and then indirectly generates data through an intermediate representation; Step S4.4: The discriminator identifies the original and newly generated time series in the embedding space to ensure that the output has characteristics of battery degradation trends; Step S4.5: Select high-density and uniformly distributed battery data sample points as the initial cluster centers; Step S4.6: By calculating the degree of overlap of the capacity degradation curves of the two batteries in the same cycle interval, the similarity of their degradation modes is evaluated; Step S4.7: Calculate the distance between the two batteries; Step S4.8: Without presetting the number of clusters, based on the battery sample size, dynamically adjust the clusters by comparing indicators such as intra-cluster distance and inter-cluster distance to match the density differences of different degradation trends; Step S4.9: Calculate the average distance between all samples and the cluster center, and then calculate the average distance between the two classes; Step S4.10: Calculate the global average inter-class distance; Based on the performance degradation trend of proton exchange membrane fuel cells, the sample set is divided into three subsets: rapid early degradation followed by slow later degradation; uniform degradation throughout the process; and fluctuating degradation.

6. The method for predicting the performance degradation trend of a proton exchange membrane fuel cell according to claim 1, characterized in that, Step S5 specifically includes: Step S5.1: Decompose the time series using an additive model with STL decomposition, construct a weighting function through a kernel function, and estimate the trend components based on Losses local weighted regression; Step S5.2: After removing the trend term from the original sequence, seasonal estimation is performed using Losses, and Losses weighted regression is performed independently in each period; Step S5.3: After removing the trend and seasonal terms from the original data, the remaining terms are obtained. The remaining terms represent the part of the time series that cannot be explained by the trend and seasonality. Step S5.4: To reduce the interference of seasonal and trend aliasing in the original sequence on frequency extraction, STL decomposition is used to extract the observed values ​​Y. t Explicitly split into trend T t Season S t Residual R t Three components are then fed in parallel into the cascaded frequency decomposition module. Step S5.5: The cascaded frequency decomposition module accurately decomposes each frequency component in a series manner; firstly, for x... i+1 A fast Fourier transform is performed to obtain the frequency domain representation, and then zero-padding is used to extend the length of the frequency domain sequence to ensure that it matches the original sequence X after being transformed back to the time domain. i Consistent length; Step S5.6: Convert the frequency domain signal back to the time domain through inverse fast Fourier transform to achieve frequency upsampling, ensuring that the frequency information remains unchanged before and after upsampling; Step S5.7: For the multi-level frequency components {f1,f2,…,f...} generated by the cascaded frequency decomposition module k The multi-order KAN representation learning module with a dual-branch parallel architecture learns specific representations of each frequency component through multi-order KAN, and captures temporal dependencies by using deep convolution, so as to model temporal representation learning and temporal dependency learning separately. Step S5.8: Depthwise convolution uses D sets of convolution kernels to perform independent convolution operations on the sequence of each channel; Step S5.9: Use ChebyshevKAN to learn the representation of the frequency components, that is, use a linear combination of Chebyshev polynomials of different orders to generate a learnable univariate function. Step S5.10: Apply a 1-layer ChebyshevKAN to the channel dimension; Step S5.11: Align the KAN complexity by increasing the order of the Chebyshev polynomial according to the frequency components from low to high to form a multi-order KAN; Step S5.12: The final output of the multi-order KAN representation learning module is the sum of the multi-order KAN and the depthwise convolution output; Step S5.13: Define the state variable from input X(t) to output. A linear mapping; converting a continuous SSM into its corresponding discrete SSM; Step S5.14: Obtain the final output feature map using the discretized matrix. Step S5.15: Construct a mixer block and use frequency upsampling again to reintegrate the information increment into a higher frequency component; Step S5.16: For the last mixing block, extract the highest-level sequence x1 and use a linear layer to generate the prediction result X. O .

7. The method for predicting the performance degradation trend of a proton exchange membrane fuel cell according to claim 1, characterized in that, Step S6 specifically includes: Step S6.1: Set the size, dimension, number of iterations, and upper and lower limits of the search space for the simulated electromagnetic wave particles in the WSA algorithm; Step S6.2: For an optimization problem with d dimensions and n individual particles, use a matrix to simulate the position distribution of the electromagnetic wave particle swarm W in the search space; Step S6.3: Calculate the fitness value of the population; Step S6.4: Introduce the Cat chaotic mapping strategy to map the generated chaotic sequence to the j-th dimension search space of the optimization problem, and use the points generated by the Cat chaotic mapping strategy as the initial population; Step S6.5: Conduct a local exploration phase search using an electromagnetic wave emission search model; Step S6.6: Simulate some particles encountering obstacles and reflecting back to the current optimal position, while the remaining particles continue to diffuse outward away from the current optimal position, using a reflected electromagnetic wave search model; Step S6.7: Make the particle swarm search in the current optimal direction, while the particle swarm deflects in other directions with a certain probability to reduce the possibility of getting trapped in local optima; Step S6.8: Estimate the gradient of the problem using the central difference method, and then adjust the search path according to the fitted gradient direction to gradually approach the optimal solution; Step S6.9: Randomly set particles that exceed the boundary within the search range; Step S6.10: Perform a global search: By using an improved greedy algorithm, the search efficiency for the global optimum is guaranteed; by gradually narrowing the search range, the newly generated particle swarm is restricted to the new search area, and the particle swarm is restricted to the vicinity of the global optimum position; Step S6.11: After generating the next generation of particle swarms, apply the Cauchy inverse cumulative distribution mutation strategy to the globally optimal particles and particles with fitness worse than the average value. Step S6.12: Calculate the fitness after perturbation. If it is better than the current optimal particle position, accept the new position. If it does not converge, retain the current optimal particle position and return to step S6.5 to continue iterative optimization and output the optimal parameter configuration. The SK-Mamba model uses the optimal parameter configuration to predict the components and obtain the prediction results of the components.

8. The method for predicting the performance degradation trend of a proton exchange membrane fuel cell according to claim 1, characterized in that, Step S7 specifically includes: Step S7.1: Initialize the relevant parameters of the IWSA algorithm, including population size, problem dimension, upper and lower bounds of the search space, current iteration count, and maximum iteration count; Step S7.2: Input the training set obtained in step S4 into the SK-Mamba model and optimize the hyperparameters in the SK-Mamba model; calculate the predicted value and the actual value of the sample after training with the SK-Mamba model. The fitness value of each individual in the population is represented by the root mean square error of the predicted value and the actual value. Step S7.3: Obtain the new position using the IWSA algorithm, calculate the fitness value of each individual, and sort them. After reaching the maximum number of iterations, select the best population position, which is the optimal hyperparameter of the model. Step S7.4: Use mean square error (MSE) and mean absolute error (MAE) as evaluation indicators to assess the accuracy of the current proton exchange membrane fuel cell performance degradation prediction model.

9. The method for predicting the performance degradation trend of a proton exchange membrane fuel cell according to claim 1, characterized in that, In step S7, the hyperparameters of the SK-Mamba model include: state dimension expansion factor, time step, input window size, number of hidden layer units, regularization parameter, number of frequency band decompositions, polynomial order of KAN, moving average window size, embedding dimension, model depth, frequency upsampling method, and learning rate η.

10. A system for predicting the performance degradation trend of a proton exchange membrane fuel cell, characterized in that, It includes a memory, a processor, and computer program instructions stored in the memory and executable by the processor, wherein when the processor executes the computer program instructions, it can implement the method as described in any one of claims 1-9.

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