Fuel cell multi-dimensional state prediction method based on multi-task probability network and dynamic gate pruning

Abstract

The application discloses a fuel cell multi-dimensional state prediction method based on a multi-task probability network and dynamic gate pruning, belongs to the technical field of fuel cell health management, and specifically relates to the following: obtaining fuel cell state data, including multi-cell voltage, partitioned cell current density and multi-dimensional operating condition parameters, performing double-target collaborative feature screening on the multi-dimensional operating condition parameters to obtain an optimal collaborative feature subset; constructing a parallel multi-task probability neural network architecture containing multiple base models, and independently training each base model based on a training set; and utilizing an online rolling monitoring and dynamic gate collaborative pruning integrated mechanism to output final multi-cell voltage global probability prediction curves and cell current density global probability prediction curves. The application can improve the accuracy, robustness and reliability of fuel cell multi-dimensional state prediction.

Description

Technical Field

[0001] This invention belongs to the field of fuel cell health management technology, specifically involving a multi-dimensional state prediction method for fuel cells based on multi-task probabilistic networks and dynamic gating pruning. Background Technology

[0002] Proton exchange membrane fuel cells (PEMFCs) have become a key focus for green transformation and high-power power equipment development in the transportation sector due to their high energy conversion efficiency, excellent power density, and fast dynamic response. However, under actual on-board or high-power dynamic operating conditions, fuel cells undergo irreversible physical degradation throughout their lifespan due to complex internal electrochemical reactions. This internal degradation manifests macroscopically as a continuous deterioration of the state of health (SOH), leading to a gradual decrease in the output voltage of multiple individual cells in the stack, uneven local current density distribution, and even failures such as thermal runaway and flooding. Therefore, accurately and proactively predicting the multi-dimensional state evolution and degradation trends of fuel cells, and issuing early warnings before risks occur, is a core technological bottleneck in fuel cell health management (PHM) and lifespan optimization. In recent years, with the development of artificial intelligence, the use of deep learning to predict fuel cell degradation has received increasing attention.

[0003] However, existing data-driven state prediction methods still have significant shortcomings in multi-dimensional state collaborative modeling and long-term generalization. Traditional methods typically serve only single-objective point prediction tasks (such as predicting voltage decay of the entire stack) during the feature selection stage, tending to use static correlation indicators to evaluate parameters. This makes it difficult to comprehensively reflect the strong coupling interaction between voltage degradation and the dynamic distribution of high-dimensional local current density during actual fuel cell operation. Under actual operating conditions, the health state degradation of fuel cells is usually the result of multi-dimensional state collaborative evolution. The voltage degradation trajectory and internal current density deterioration of each individual cell are mutually causal. Screening mechanisms that only focus on a single state objective are prone to neglecting the balance feature information that takes into account multiple tasks, thus affecting the accuracy of long-term prediction.

[0004] Furthermore, existing technologies mostly employ a single fixed structure or a static combination of multiple models for deterministic point prediction. On the one hand, during the transition of a fuel cell from initial health to deep aging, its internal characteristics undergo drastic degradation. Existing models lack online dynamic elimination and pruning mechanisms, failing to automatically identify and remove degraded models at each stage of the entire lifecycle. This results in the prediction errors of inferior models severely interfering with the final integrated output, making them highly susceptible to severe accuracy collapse in later stages. On the other hand, existing models generally lack uncertainty quantification capabilities, failing to provide probability intervals and risk bandwidths characterizing the reliability of prediction results. This easily leads to decision-making errors in the control system, thus restricting the practical application of data-driven models in online health management of fuel cells.

[0005] Therefore, it is necessary to introduce a multi-dimensional state prediction method for fuel cells based on multi-task probabilistic networks and dynamic gating pruning during the fuel cell state prediction process. This method can fully exploit the coupling characteristics between the voltage of multiple individual cells and high-dimensional current density, generate probability intervals characterizing the predicted risks, and eliminate inferior models generated at different aging stages throughout the entire life cycle. This improves the accuracy and robustness of multi-dimensional state prediction for fuel cells, providing stronger technical support for fuel cell health management and lifespan optimization. Summary of the Invention

[0006] To address the shortcomings of existing fuel cell state prediction methods, which struggle to effectively balance the strong coupling interaction between voltage degradation in multiple individual cells and dynamic distribution of high-dimensional local current density, and lack online dynamic elimination and pruning mechanisms leading to prediction errors from inferior models interfering with the final output, as well as the lack of uncertainty quantification capabilities, this invention provides a fuel cell multidimensional state prediction method based on multi-task probabilistic networks and dynamic gating pruning. This method can improve the accuracy, robustness, and reliability of fuel cell multidimensional state prediction.

[0007] The technical solution adopted in this invention is as follows:

[0008] A multi-dimensional state prediction method for fuel cells based on multi-task probabilistic networks and dynamic gating pruning includes the following steps:

[0009] Step 1: Obtain fuel cell status data, including the voltage of each cell in the fuel cell, the cell current density, and multi-dimensional operating parameters related to fuel cell degradation and state evolution. After removing outlier data and normalizing the data, a dataset is obtained.

[0010] Step 2: Perform dual-objective collaborative feature filtering on the multi-dimensional operating condition parameters of the dataset. The specific process is as follows:

[0011] Step 2.1: Using the Mutual Information (MI) algorithm, calculate the nonlinear correlation between each operating condition parameter and two different prediction targets: single cell voltage and battery current density. Then calculate the minimum voltage feature redundancy and the minimum current feature redundancy to construct a multi-objective optimization function.

[0012] Step 2.2: Solve the multi-objective optimization function to obtain the voltage solution set and the current solution set. Extract the optimal feature subset from them to form a multi-task collaborative feature vector, which is then used to construct a training set together with the voltage and current density of multiple single cells.

[0013] Step 3: Construct a parallel multi-task probabilistic neural network architecture containing multiple base models, and independently train each base model based on the training set. The specific process is as follows:

[0014] Step 3.1: Introduce a shared timing layer, a voltage decoupling prediction head, and a current decoupling prediction head into each base model to form a heterogeneous timing probabilistic base model;

[0015] Step 3.2: Using the multi-task collaborative feature vector of the training set as input, and the voltage and current density of multiple single cells as training objectives, train each heterogeneous time-series probability basis model by constructing a negative log-likelihood (NLL) loss function. Specifically, the first output node of the voltage decoupling prediction head outputs the predicted voltage values ​​of multiple single cells, and the second output node outputs the original non-negative voltage constraint numbers. The first output node of the current decoupling prediction head outputs the predicted battery current density values, and the second output node outputs the original non-negative current constraint numbers. By cascading a Softplus activation function after the second output nodes of the voltage and current decoupling prediction heads, the original non-negative voltage and current constraint numbers are converted into corresponding strictly positive definite voltage prediction variance and battery current density prediction variance, respectively.

[0016] Step 4: Utilizing the integrated mechanism of online rolling monitoring and dynamic gating collaborative pruning, the final global probability prediction curves for multi-cell single-cell voltage and battery current density are generated. The specific process is as follows:

[0017] Step 4.1: Obtain the multi-dimensional operating condition parameters of the fuel cell to be predicted, extract its corresponding multi-task collaborative feature vector, introduce a sliding time window on the operating time axis, and input it to each trained heterogeneous time-series probability base model with fixed model hyperparameters in real time. Based on the model output results, calculate the predicted joint mean residual and predicted joint variance of voltage-current of each trained heterogeneous time-series probability base model in real time.

[0018] Step 4.2: Using a dynamic gating network, the real-time degradation performance of each trained heterogeneous temporal probabilistic base model is evaluated online based on the prediction joint mean residual. Specifically, when the prediction joint mean residual of the current stage is detected to exceed the preset critical threshold, the gating channel corresponding to the base model is automatically set to zero, and it is removed from the parallel multi-task probabilistic neural network architecture as a poor model.

[0019] Step 4.3: For at least one post-training heterogeneous time-series probabilistic basis model retained after online evaluation, normalize the inverse of its joint prediction variance to obtain dynamic real-time gating weight coefficients; based on the dynamic real-time gating weight coefficients, dynamically linearly and collaboratively fuse the multi-cell single-cell voltage prediction values ​​and battery current density prediction values ​​output by each model, and simultaneously fuse the voltage prediction variance and battery current density prediction variance output by each model with dynamic variance uncertainty; based on the preset confidence level, generate global probability prediction curves for multi-cell single-cell voltage and battery current density.

[0020] Further, the multi-dimensional operating condition parameters mentioned in step 1 include hydrogen concentration, load power, hydrogen flow rate, air flow rate, hydrogen inlet pressure, air inlet pressure, hydrogen outlet pressure, air outlet pressure, circulating water inlet pressure, circulating water outlet pressure, anode inlet temperature, anode outlet temperature, cathode inlet temperature, cathode outlet temperature, circulating water inlet temperature, circulating water outlet temperature, anode humidification dew point temperature, cathode humidification dew point temperature, circulating water flow rate, circulating water conductivity, anode humidification water temperature, anode humidification inlet water temperature, anode humidification outlet water temperature, cathode humidification water temperature, cathode humidification inlet water temperature, cathode humidification outlet water temperature, hydrogen inlet humidity, air inlet humidity, hydrogen humidifier inlet pressure, hydrogen humidifier outlet pressure, air humidifier inlet pressure, air humidifier outlet pressure, circulating water tank temperature, air compressor flow rate, and air compressor speed.

[0021] Furthermore, the battery current density mentioned in step 1 is either the spatial partition current density or the single-cell battery current density.

[0022] Furthermore, the formula for the multi-objective optimization function described in step 2.1 is:

[0023]

[0024]

[0025] In the formula, It is a multi-objective optimization function; The voltage target optimization function; Let S be the current target optimization function; S is the subset of operating condition characteristics to be optimized. The total number of feature parameters in S; and All are candidate feature variables; The target variable is the voltage of multiple individual cells; The target variable is the battery current density; and They represent and , The mutual information correlation score between them; This represents the mutual information redundancy among different candidate feature variables within S.

[0026] Furthermore, in step 2.2, a nonlinear multi-objective Pareto optimization algorithm is used to solve the multi-objective optimization function.

[0027] Furthermore, the parallel multi-task probabilistic neural network architecture described in step 3 includes base models such as convolutional neural networks (CNN), long short-term memory networks (LSTM), gated recurrent units (GRU), temporal convolutional networks (TCN), transformer architecture, temporal bidirectional networks with attention mechanisms (Bi-LSTM / Bi-GRU), extreme gradient boosting trees (XGBoost), lightweight gradient boosting machines (LightGBM), random forests (RF), deep belief networks (DBN), support vector regression machines (SVR), and artificial neural networks (ANN).

[0028] Furthermore, the shared temporal layer described in step 3.1 is specifically built on the bottom layer of the parallel multi-task probabilistic neural network architecture and configured as a common temporal feature extractor based on a hard sharing mechanism.

[0029] Furthermore, the specific formula for calculating the predicted joint mean residual in step 4.1 is as follows:

[0030]

[0031] In the formula, For the trained heterogeneous temporal probability base model At any moment The predicted joint mean residuals; and For fuel cells at time The actual voltage and current density of multiple single cells; and These are the heterogeneous temporal probability base models after training. The output includes predicted values ​​for the voltage of multiple single cells and predicted values ​​for the battery current density. and These are the voltage and current reference standard deviations on the training set, respectively, used to eliminate the dimensional differences between voltage and current density; and The preset task weight adjustment coefficient, and satisfies... ;

[0032] The specific formula for calculating the joint variance of predictions is as follows:

[0033]

[0034] In the formula, For the trained heterogeneous temporal probability base model At any moment The predicted joint variance; and These are the heterogeneous temporal probability base models after training. At any moment The voltage prediction variance and the battery current density prediction variance.

[0035] Furthermore, the specific process of step 4.3 is as follows:

[0036] Step 4.3.1, Dynamic Gating Weight Calculation: Assuming that K heterogeneous temporal probability basis models are retained after online evaluation, obtain the k-th... The joint variance of the predictions output by each model at the current time. By analyzing the predicted joint variance The reciprocal of is globally normalized to obtain the th... Dynamic real-time gating weight coefficients for each model The specific calculation formula is as follows:

[0037]

[0038] Step 4.3.2, Multi-task mean linear collaborative fusion: Utilizing dynamic real-time gating weight coefficients , for the The model outputs the predicted voltage values ​​of multiple single-cell batteries. and predicted battery current density Weighted linear combinations are performed separately, and the global voltage prediction value is dynamically decoupled and calculated online. Compared with global current density prediction The specific calculation formula is as follows:

[0039]

[0040] Step 4.3.3, Multi-task variance uncertainty fusion: Based on cluster statistical ensemble theory, the final global prediction variance is composed of an intrinsic random uncertainty term characterizing the inherent physical noise inside the stack and an extrinsic cognitive uncertainty term characterizing the divergence of multi-model predictions.

[0041] Specifically, using dynamic real-time gating weight coefficients By calculating the first Voltage prediction variance of the model output The weighted expected value and Deviation The weighted squared residuals are used to obtain the global voltage prediction variance. , and by calculating the first The predicted variance of the battery current density output by each model The weighted expected value and Deviation The weighted squared residuals are used to obtain the global current density prediction variance. The specific calculation formula is as follows:

[0042]

[0043] Step 4.3.4: Based on the two-tailed quantiles of the standard normal distribution, adaptively obtain the standard deviation factor corresponding to the preset reliability. ;based on , , and By using inverse Gaussian probability reconstruction, the time-varying confidence boundary for multi-task probability prediction at each time step is calculated on a dynamic runtime time axis. The specific calculation formula is as follows:

[0044]

[0045] In the formula, and These represent the upper and lower confidence limits for the global probability prediction of the voltage of multiple single cells at time t, respectively. and These are the upper and lower confidence limits for the global probability prediction of battery current density at time t, respectively.

[0046] Furthermore, based on global voltage prediction values Global current density prediction value With time-varying confidence boundaries for multi-task probability prediction, global probability prediction curves for single-cell voltage and battery current density are generated.

[0047] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0048] This invention proposes a multi-dimensional state prediction method for fuel cells based on multi-task probabilistic networks and dynamic gating pruning. It extracts an optimal subset of coupled features that considers the voltage and current density of multiple individual cells through a multi-objective nonlinear mechanism. Using these features as input, a parallel multi-task probabilistic neural network architecture is constructed that can simultaneously output the mean of future multi-dimensional state predictions and the variance of endogenous uncertainty, enabling online quantitative assessment of prediction risk. Simultaneously, an online dynamic collaborative gating pruning mechanism is introduced into the time-series scheduling. The gating network performs real-time residual rolling monitoring of heterogeneous base models in the model pool, spontaneously eliminating poorly performing models by zeroing the gating channels. Excellent models are dynamically weighted and fused based on their uncertainty feedback, assigning optimal integration weights to perform multi-model dynamic weighted fusion. This effectively improves the modeling capability and prediction accuracy of the prediction model under full lifecycle and strongly coupled conditions. Attached Figure Description

[0049] Figure 1 This is a diagram illustrating the overall framework of the fuel cell multi-dimensional state prediction method based on multi-task probabilistic networks and dynamic gating pruning proposed in Example 1.

[0050] Figure 2 This is a flowchart of the dual-objective feature collaborative screening process based on the Pareto front in Example 1;

[0051] Figure 3 This is a flowchart illustrating the workflow of the parallel multi-task probabilistic neural network architecture in Example 1.

[0052] Figure 4 This is a schematic diagram illustrating the online pruning and weighting of the base model using the integrated mechanism of online rolling monitoring and dynamic gating collaborative pruning in Example 1.

[0053] Figure 5 This is a graph showing the global predicted average voltage of multiple single cells obtained in Example 1;

[0054] Figure 6 The graph shows the global predicted mean curve of the spatial partition current density obtained in Example 1; where (a) to (i) are experimental and model comparison graphs for partitions 54, 87, 120, 153, 186, 219, 252, 285 and 318, respectively.

[0055] Figure 7 The graphs shown in Example 1 are: global prediction variance confidence interval curves for multi-cell single-cell voltage and global prediction variance confidence interval curves for spatial partitioned current density; where (a) is a 3D graph of 319-dimensional partitioned current confidence intervals; and (b) is a 3D graph of 10-cell voltage confidence intervals. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0057] Example 1

[0058] This embodiment proposes a multi-dimensional state prediction method for fuel cells based on multi-task probabilistic networks and dynamic gating pruning. The overall framework is as follows: Figure 1 As shown, it includes the following steps:

[0059] Step 1: Acquire fuel cell status data, including the voltage of each individual cell, spatial partition current density, and multi-dimensional operating parameters related to fuel cell degradation and state evolution. These multi-dimensional operating parameters include hydrogen concentration, load power, hydrogen flow rate, air flow rate, hydrogen inlet pressure, air inlet pressure, hydrogen outlet pressure, air outlet pressure, circulating water inlet pressure, circulating water outlet pressure, anode inlet temperature, anode outlet temperature, cathode inlet temperature, cathode outlet temperature, circulating water inlet temperature, circulating water outlet temperature, anode humidification dew point temperature, cathode humidification dew point temperature, circulating water flow rate, circulating water conductivity, anode humidification water temperature, anode humidification inlet temperature, anode humidification outlet temperature, cathode humidification water temperature, cathode humidification inlet temperature, cathode humidification outlet temperature, hydrogen inlet humidity, air inlet humidity, hydrogen humidifier inlet pressure, hydrogen humidifier outlet pressure, air humidifier inlet pressure, air humidifier outlet pressure, circulating water tank temperature, air compressor flow rate, and air compressor speed.

[0060] The Pautu criterion is used to detect gross errors in the fuel cell state data. The overall mean and standard deviation σ of the data are calculated. Data points that fall outside the confidence interval [−3σ, +3σ] are considered outliers and are removed. The minimax normalization method is used to process the fuel cell state data, mapping features with different dimensions or value ranges to a unified scale to obtain the dataset.

[0061] Step 2: Based on the Pareto front, perform dual-objective collaborative feature selection on the multi-dimensional operating condition parameters of the dataset. The process is as follows: Figure 2 As shown, the specific process is as follows:

[0062] Step 2.1: Using the mutual information algorithm, calculate the nonlinear correlation between each operating condition parameter and two different prediction objectives: multi-cell single-cell voltage and spatial partition current density. Then, calculate the minimum voltage characteristic redundancy and the minimum current characteristic redundancy to construct a multi-objective optimization function. The specific process is as follows:

[0063] First, the nonlinear correlation score between each candidate operating condition parameter and the voltage vector of multiple single cells is calculated using the mutual information operator. Then, the average mutual information between the candidate features is subtracted from this score to construct a comprehensive score function for the voltage feature subset, which characterizes maximizing correlation and minimizing voltage feature redundancy. Similarly, the spatial average mutual information correlation score between each candidate operating condition parameter and the global spatial partition current density matrix containing 319 spatial partitions is calculated, and redundant mutual information between features is also deducted to construct a comprehensive score function of current feature subsets that characterizes maximizing spatial correlation and minimizing current feature redundancy. Finally, the voltage feature subset comprehensive score function and the current feature subset comprehensive score function are combined in parallel to construct a multi-objective optimization function. The formula is:

[0064]

[0065]

[0066] In the formula, S is the subset of working condition features to be optimized; The total number of feature parameters in S; and All are candidate feature variables; The target variable is the voltage of multiple individual cells; The target variable is the battery current density; and They represent and , The mutual information correlation score between them; This represents the mutual information redundancy among different candidate feature variables within S.

[0067] Step 2.2: Solve the multi-objective optimization function using a nonlinear multi-objective Pareto optimization algorithm to obtain the voltage and current solution sets. Extract the optimal feature subset from these solutions. Specifically, use the nonlinear multi-objective Pareto optimization algorithm to solve the multi-objective optimization function. Through multiple generations of non-dominated iterative evolution, a set of non-dominated solutions, namely the Pareto front solution set, is obtained, which achieves a mutually constraining balance between voltage and current feature scores. This front solution set contains multiple independent candidate feature subsets, which constitute the voltage solution set and the current solution set, respectively. Subsequently, in order to achieve cross-task feature collaborative integration, an ideal point decision mechanism is introduced into the Pareto front solution set to dynamically calculate the Euclidean geometric distance from the "voltage-current two-sided score" corresponding to each candidate feature subset to the mathematically ideal optimal score point (i.e., the coordinate point formed by the maximum voltage score and the maximum current score). Finally, the candidate feature subset with the smallest Euclidean geometric distance is determined as the unique optimal feature subset that takes into account the global two-sided prediction accuracy. Through the ideal point decision mechanism, the optimal feature subset is accurately and collaboratively extracted from the front solution set.

[0068] A multi-task collaborative feature vector is constructed based on the optimal feature subset, which includes circulating water outlet temperature, circulating water inlet temperature, air outlet temperature, air outlet pressure, air inlet pressure, hydrogen outlet pressure, hydrogen inlet pressure, hydrogen flow return value, air flow return value, and load current, totaling 10 parameters. This vector, together with the voltage of multiple single cells and the spatial partition current density, is used to construct the dataset to be partitioned.

[0069] Based on the chronological order, the dataset to be divided is divided into a training set and a test set for online validation and rolling monitoring in a 7:3 ratio. The training set has 1000 samples, and the test set has 423 samples.

[0070] Step 3: Construct a parallel multi-task probabilistic neural network architecture containing multiple base models, and independently train each base model based on the training set. The process is as follows: Figure 3 As shown, the specific process is as follows:

[0071] Step 3.1: The parallel multi-task probabilistic neural network architecture includes five base models: Long Short-Term Memory Network (LSTM), One-Dimensional Convolutional Neural Network (1D-CNN), Temporal Convolutional Network (TCN), Transformer architecture, and Bidirectional Gated Recurrent Unit (Bi-GRU). A shared temporal layer is introduced into each base model, and independent voltage decoupling prediction head and current decoupling prediction head are configured for each base model to form a heterogeneous temporal probabilistic base model.

[0072] Step 3.2: Using the multi-task collaborative feature vector of the training set as input, and the voltage of multiple single cells and the spatial partition current density as training objectives, train the heterogeneous time-series probability basis models by constructing a Gaussian negative log-likelihood loss function; wherein, the first output node of the voltage decoupling prediction head is used to output the predicted voltage values ​​of multiple single cells, and the second output node is used to output the original voltage non-negativity constraint number z. v The first output node of the current decoupling prediction head is used to output the predicted current density value for spatial partitioning, and the second output node is used to output the original non-negative current constraint number z. i By cascading a Softplus activation function after the second output node of the voltage decoupling prediction head and the current decoupling prediction head, z v z i Convert them respectively to the corresponding strictly positive definite voltage prediction variance and current density prediction variance .

[0073] The formula for the Softplus activation function is: .

[0074] During model backpropagation and gradient update, a Gaussian negative log-likelihood loss function is constructed as a joint constraint mechanism. The gradient is dynamically adjusted through the residual dilution effect of the negative log-likelihood loss function, so that when the transient polarization reaction residual increases, it forces the corresponding second output node to raise the corresponding original non-negativity constraint number z. v or z i To increase the variance magnitude; when the steady-state response surface is smooth and the residuals decrease, to synergistically reduce the corresponding original nonnegative constraint number z. v or zi To reduce the variance amplitude, the complete probability density distribution of the multidimensional state of the fuel cell is adaptively reconstructed.

[0075] During training, multiple hyperparameters to be optimized and their corresponding candidate value ranges are pre-defined. The specific names and search spaces of each hyperparameter are shown in Table 1, taking the Transformer model as an example:

[0076] Table 1

[0077]

[0078] Five-fold cross-validation and Cartesian product are used to enumerate all combinations of candidate hyperparameter values. Negative log-likelihood loss is used as the core evaluation metric. An independent prediction model is constructed for each set of hyperparameter configurations. Under each configuration, the model sequentially performs multi-task forward computation (simultaneously generating the mean values ​​of 10 voltage sections and 319 partition current sections). Variance constrained by Softplus The process includes NLL error calculation and parameter update based on backpropagation; by comparing the validation results of all hyperparameter combinations, the hyperparameter combination with the minimum total NLL loss is selected as the optimal configuration; based on the optimal hyperparameters obtained from grid search, further settings are made for optimizer and other parameters, resulting in the parameter settings of the final model as shown in Table 2.

[0079] Table 2

[0080]

[0081] Using the parameter settings shown in Table 2, each base model in the parallel multi-task probabilistic neural network architecture was offline initialized and retrained on the complete training dataset. Specifically, the negative log-likelihood loss function (NLL) was used to independently and fully iteratively train the five heterogeneous temporal probabilistic base models in the parallel multi-task probabilistic neural network architecture on 1000 sets of full training samples. Training was stopped after the NLL loss function curves of each heterogeneous temporal probabilistic base model converged smoothly and no overfitting occurred. At this point, all five heterogeneous temporal probabilistic base models independently possessed the basic probability prediction capability of multidimensional states of fuel cells, and the trained heterogeneous temporal probabilistic base models were successfully obtained.

[0082] Step 4: Utilizing the integrated mechanism of online rolling monitoring and dynamic gating collaborative pruning, output the final global probability prediction curves for multi-cell single-cell voltage and spatial partition current density. The process is as follows: Figure 4 As shown, the specific process is as follows:

[0083] Step 4.1: Introduce a sliding time window of length 12 on the runtime axis of the test set, and continuously scroll the input to each trained heterogeneous temporal probability base model with fixed model hyperparameters. Based on the model output results, calculate the joint mean residual and joint variance of voltage-current predictions for each trained heterogeneous temporal probability base model. The specific process is as follows:

[0084] At the current sliding time window, the individual prediction residuals of voltage and current density outputs of each trained heterogeneous temporal probability base model are obtained, and dimensionless normalization is performed on them. Then, the square root of the sum of the squares of the two is used as the current joint mean residual of predictions for each trained heterogeneous temporal probability base model. The specific formula is as follows:

[0085]

[0086] In the formula, For the trained heterogeneous temporal probability base model At any moment The predicted joint mean residuals; and For fuel cells at time The actual voltage of a multi-cell single cell and the spatial partition current density; and These are the heterogeneous temporal probability base models after training. The output includes predicted values ​​for the voltage of multiple single cells and predicted values ​​for the battery current density. and These are the voltage and current reference standard deviations on the training set, respectively, used to eliminate the dimensional differences between voltage and current density; and The preset task weight adjustment coefficient, and satisfies... ;

[0087] Simultaneously, the strictly positive definite voltage prediction variance and spatial partition current density prediction variance of each trained heterogeneous temporal probability basis model are obtained through the Softplus activation function. These two types of variances are then weighted linearly using a preset task balancing coefficient to form the current joint prediction variance of each trained heterogeneous temporal probability basis model. The specific formula is as follows:

[0088]

[0089] In the formula, For the trained heterogeneous temporal probability base model At any moment The predicted joint variance; and These are the heterogeneous temporal probability base models after training. At any moment The voltage prediction variance and the battery current density prediction variance.

[0090] Step 4.2: Using a dynamic gating network, the real-time degradation performance of each trained heterogeneous temporal probabilistic base model is evaluated online based on the prediction joint mean residual. Specifically, when the prediction joint mean residual of the current stage is detected to exceed the preset critical threshold, the gating channel corresponding to the base model is automatically set to zero, and it is removed from the parallel multi-task probabilistic neural network architecture as a poor model.

[0091] In this embodiment, the preset critical threshold is set to 1.5. When the fuel cell system switches from a high-power steady-state condition to a low-power transient drastic condition, the LSTM base model and the Bi-GRU base model lag in the time-series dynamic response to the nonlinear sudden current density, causing their prediction joint mean residuals to spike to 1.82 and 1.95 in three consecutive sliding time windows, respectively, both exceeding the preset critical threshold of 1.5. At this time, the dynamic gating network spontaneously sets the control coefficients of the gating channels corresponding to these two base models directly to 0, thereby treating the LSTM base model and the Bi-GRU base model as poor models with performance degradation and pruning them online from the parallel multi-task probabilistic neural network architecture.

[0092] Step 4.3: Using the aforementioned dynamic real-time gating weight coefficients, perform weighted dynamic online fusion on the heterogeneous temporal probability basis models remaining after online pruning. The specific process is as follows:

[0093] Step 4.3.1, Dynamic Gating Weight Calculation: After online evaluation, three heterogeneous temporal probabilistic basis models were retained: Transformer, TCN, and 1D-CNN. To accurately reflect the confidence differences among the models, the joint variance of the predictions output by each model at the current time t was obtained. By analyzing the predicted joint variance The reciprocal of is globally normalized to obtain the th... Dynamic real-time gating weight coefficients for each model The specific calculation formula is as follows:

[0094]

[0095] In this embodiment, the joint variance of the Transformer's predictions Joint variance of TCN predictions Joint variance of predictions in 1D-CNN Based on the variance reciprocal normalization mechanism, the reciprocals of the joint variances of each prediction are first calculated, yielding 42, 35, and 23 respectively, with a total sum of 100. Then, the dynamic real-time gating weight coefficients of each retained base model at the current time are adaptively calculated. The three models have values ​​of 0.42, 0.35, and 0.23, respectively.

[0096] Step 4.3.2, Multi-task mean linear collaborative fusion: Utilizing dynamic real-time gating weight coefficients , for the The model outputs the predicted voltage values ​​of multiple single-cell batteries. (Single-cell voltage prediction mean vector) and spatially partitioned current density prediction values (The current density prediction mean matrix, containing 319 spatial partitions) is weighted and linearly combined, and the global voltage prediction value is dynamically and online decoupled for calculation. Compared with global current density prediction The specific calculation formula is as follows:

[0097]

[0098] Furthermore, global predicted mean curves of multi-cell single-cell voltage and spatially partitioned global predicted mean curves of current density are generated. The global predicted mean curves of multi-cell single-cell voltage are shown below. Figure 5 As shown, the global predicted mean curve of current density for some partitions is as follows: Figure 6 As shown, both predicted mean curves fit the experimental surface well with relatively small errors.

[0099] Step 4.3.3, Multi-task variance uncertainty fusion: Based on the cluster statistical ensemble theory, the random uncertainty variances output by Transformer, TCN and 1D-CNN are weighted and summed, and the cognitive uncertainty term representing the prediction divergence between models is simultaneously superimposed to calculate the final global voltage prediction variance and global current density prediction variance.

[0100] Specifically, using dynamic real-time gating weight coefficients By calculating the first Voltage prediction variance of the model output The weighted expected value and Deviation The weighted squared residuals are used to obtain the global voltage prediction variance. , and by calculating the first The spatial partition current density prediction variance of the model output The weighted expected value and Deviation The weighted squared residuals are used to obtain the global current density prediction variance. The specific calculation formula is as follows:

[0101]

[0102] Step 4.3.4: Based on the two-tailed quantiles of the standard normal distribution, adaptively obtain the standard deviation factor corresponding to the preset reliability. ;based on , , and By using inverse Gaussian probability reconstruction, the time-varying confidence boundary for multi-task probability prediction at each time step is calculated on a dynamic runtime time axis. The specific calculation formula is as follows:

[0103]

[0104] In the formula, and These represent the upper and lower confidence limits for the global probability prediction of the voltage of multiple single cells at time t, respectively. and These represent the upper and lower confidence limits for the global probability prediction of the battery current density at time t, respectively; when the preset confidence level is set to 95%, take... =1.96;

[0105] Furthermore, a global prediction variance confidence interval curve for multi-cell single-cell voltage (which, together with the global prediction mean curve for multi-cell single-cell voltage, constitutes a global probability prediction curve for multi-cell single-cell voltage) and a global prediction variance confidence interval curve for spatial partitioned current density (which, together with the global prediction mean curve for spatial partitioned current density, constitutes a global probability prediction curve for spatial partitioned current density) are generated, such as... Figure 7 As shown, most of the true values ​​fall within the prediction variance confidence interval, indicating that the prediction variance confidence interval provided by the model has high reliability.

[0106] It should be noted that this is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A multi-dimensional state prediction method for fuel cells based on multi-task probabilistic networks and dynamic gating pruning, characterized in that, Includes the following steps: Step 1: Obtain fuel cell status data, including the voltage of each cell, cell current density, and multi-dimensional operating parameters. After removing outlier data and normalizing the data, a dataset is obtained. Step 2: Perform dual-objective collaborative feature selection on the multi-dimensional operating condition parameters of the dataset. The specific process is as follows: Step 2.1: Using the mutual information algorithm, calculate the nonlinear correlation between each operating condition parameter and two different prediction targets: single cell voltage and battery current density. Then calculate the minimum voltage feature redundancy and the minimum current feature redundancy to construct a multi-objective optimization function. Step 2.2: Solve the multi-objective optimization function to obtain the voltage solution set and the current solution set. Extract the optimal feature subset from them to form a multi-task collaborative feature vector, which is then used to construct a training set together with the voltage and current density of multiple single cells. Step 3: Construct a parallel multi-task probabilistic neural network architecture containing multiple base models, and independently train each base model based on the training set. The specific process is as follows: Step 3.1: Introduce a shared timing layer, a voltage decoupling prediction head, and a current decoupling prediction head into each base model to form a heterogeneous timing probabilistic base model; Step 3.2: Using the multi-task collaborative feature vector as input and the voltage and current density of multiple single cells as training targets, train the heterogeneous time-series probability basis models by constructing a negative log-likelihood loss function. Specifically, the first output node of the voltage decoupling prediction head outputs the predicted voltage values ​​of multiple single cells, and the second output node outputs the original non-negative voltage constraint numbers. Similarly, the first output node of the current decoupling prediction head outputs the predicted battery current density values, and the second output node outputs the original non-negative current constraint numbers. By cascading a Softplus activation function after the second output nodes of the voltage and current decoupling prediction heads, the original non-negative voltage and current constraint numbers are converted into the corresponding voltage prediction variance and battery current density prediction variance, respectively. Step 4: Utilizing the integrated mechanism of online rolling monitoring and dynamic gating collaborative pruning, generate global probability prediction curves for multi-cell single-cell voltage and global probability prediction curves for battery current density. The specific process is as follows: Step 4.1: Obtain the multi-dimensional operating condition parameters of the fuel cell to be predicted, extract its corresponding multi-task collaborative feature vector, introduce a sliding time window on the operating time axis, and input it to each trained heterogeneous time-series probability base model with fixed model hyperparameters in real time. Based on the model output results, calculate the predicted joint mean residual and predicted joint variance of voltage-current of each trained heterogeneous time-series probability base model in real time. Step 4.2: Using a dynamic gating network, the real-time degradation performance of each trained heterogeneous temporal probabilistic base model is evaluated online based on the prediction joint mean residual. Specifically, when the prediction joint mean residual of the current stage is detected to exceed the preset critical threshold, the gating channel corresponding to the base model is automatically set to zero, and it is removed from the parallel multi-task probabilistic neural network architecture as a poor model. Step 4.3: For at least one post-training heterogeneous time-series probabilistic basis model retained after online evaluation, normalize the inverse of its joint prediction variance to obtain dynamic real-time gating weight coefficients; based on the dynamic real-time gating weight coefficients, dynamically linearly and collaboratively fuse the multi-cell single-cell voltage prediction values ​​and battery current density prediction values ​​output by each model, and simultaneously fuse the voltage prediction variance and battery current density prediction variance output by each model with dynamic variance uncertainty; based on the preset confidence level, generate global probability prediction curves for multi-cell single-cell voltage and battery current density.

2. The fuel cell multidimensional state prediction method based on multi-task probabilistic networks and dynamic gating pruning according to claim 1, characterized in that, The multi-dimensional operating condition parameters mentioned in step 1 include hydrogen concentration, load power, hydrogen flow rate, air flow rate, hydrogen inlet pressure, air inlet pressure, hydrogen outlet pressure, air outlet pressure, circulating water inlet pressure, circulating water outlet pressure, anode inlet temperature, anode outlet temperature, cathode inlet temperature, cathode outlet temperature, circulating water inlet temperature, circulating water outlet temperature, anode humidification dew point temperature, cathode humidification dew point temperature, circulating water flow rate, circulating water conductivity, anode humidification water temperature, anode humidification inlet water temperature, anode humidification outlet water temperature, cathode humidification water temperature, cathode humidification inlet water temperature, cathode humidification outlet water temperature, hydrogen inlet humidity, air inlet humidity, hydrogen humidifier inlet pressure, hydrogen humidifier outlet pressure, air humidifier inlet pressure, air humidifier outlet pressure, circulating water tank temperature, air compressor flow rate, and air compressor speed.

3. The fuel cell multidimensional state prediction method based on multi-task probabilistic networks and dynamic gating pruning according to claim 2, characterized in that, The battery current density mentioned in step 1 is either the spatial partition current density or the single-cell battery current density.

4. The fuel cell multidimensional state prediction method based on multi-task probabilistic networks and dynamic gating pruning according to claim 3, characterized in that, The formula for the multi-objective optimization function mentioned in step 2.1 is: In the formula, It is a multi-objective optimization function; The voltage target optimization function; The target optimization function is the current. S is a subset of working condition features to be optimized; The total number of feature parameters in S; and All are candidate feature variables; The target variable is the voltage of multiple individual cells; The target variable is the battery current density; and They represent and , The mutual information correlation score between them; This represents the mutual information redundancy among different candidate feature variables within S.

5. The fuel cell multidimensional state prediction method based on multi-task probabilistic networks and dynamic gating pruning according to claim 3, characterized in that, In step 2.2, a nonlinear multi-objective Pareto optimization algorithm is used to solve the multi-objective optimization function.

6. The fuel cell multidimensional state prediction method based on multi-task probabilistic networks and dynamic gating pruning according to claim 3, characterized in that, The parallel multi-task probabilistic neural network architecture described in step 3 includes base models such as convolutional neural networks, long short-term memory networks, gated recurrent units, temporal convolutional networks, transformer architectures, temporal bidirectional networks with attention mechanisms, extreme gradient boosting trees, lightweight gradient boosting machines, random forests, deep belief networks, support vector regression machines, and artificial neural networks.

7. The fuel cell multidimensional state prediction method based on multi-task probabilistic networks and dynamic gating pruning according to claim 3, characterized in that, The shared temporal layer described in step 3.1 is specifically built on the bottom layer of the parallel multi-task probabilistic neural network architecture and configured as a common temporal feature extractor based on a hard sharing mechanism.

8. The fuel cell multidimensional state prediction method based on multi-task probabilistic networks and dynamic gating pruning according to claim 3, characterized in that, The specific formula for calculating the predicted joint mean residual in step 4.1 is as follows: In the formula, For the trained heterogeneous temporal probability base model At any moment The predicted joint mean residuals; and For fuel cells at time The actual voltage and current density of multiple single cells; and These are the heterogeneous temporal probability base models after training. The output includes predicted values ​​for the voltage of multiple single cells and predicted values ​​for the battery current density. and These are the standard deviations of voltage and current on the training set, respectively, used to eliminate the dimensional differences between voltage and current density; and The preset task weight adjustment coefficient, and satisfies... ; The specific formula for calculating the joint variance of predictions is as follows: In the formula, For the trained heterogeneous temporal probability base model At any moment The predicted joint variance; and These are the heterogeneous temporal probability base models after training. At any moment The voltage prediction variance and the battery current density prediction variance.

9. The fuel cell multidimensional state prediction method based on multi-task probabilistic network and dynamic gating pruning according to claim 8, characterized in that, The specific process of step 4.3 is as follows: Step 4.3.1, Dynamic Gating Weight Calculation: Assuming that K heterogeneous temporal probability basis models are retained after online evaluation, obtain the k-th... The joint variance of the predictions output by each model at the current time. By analyzing the predicted joint variance The reciprocal of the first is globally normalized to obtain the second . Dynamic real-time gating weight coefficients for each model The specific calculation formula is as follows: Step 4.3.2, Multi-task mean linear collaborative fusion: Utilizing dynamic real-time gating weight coefficients , for the The model outputs the predicted voltage values ​​of multiple single-cell cells. and predicted battery current density Weighted linear combinations are performed separately, and the global voltage prediction value is dynamically decoupled and calculated online. Compared with global current density prediction The specific calculation formula is as follows: Furthermore, global prediction curves for the voltage of multiple single cells and global prediction curves for the battery current density are generated. Step 4.3.3, Multi-task variance uncertainty fusion: Based on the cluster statistical ensemble theory, the final global prediction variance is composed of the intrinsic random uncertainty term characterizing the inherent physical noise inside the stack and the extrinsic cognitive uncertainty term characterizing the divergence of multi-model predictions. Specifically, using dynamic real-time gating weight coefficients By calculating the first Voltage prediction variance of the model output The weighted expected value and Deviation The weighted squared residuals are used to obtain the global voltage prediction variance. , and by calculating the first The predicted variance of battery current density output by each model The weighted expected value and Deviation The weighted squared residuals are used to obtain the global current density prediction variance. The specific calculation formula is as follows: Step 4.3.4: Based on the two-tailed quantiles of the standard normal distribution, adaptively obtain the standard deviation factor corresponding to the preset reliability. ;based on , , and By using inverse Gaussian probability reconstruction, the time-varying confidence boundary for multi-task probability prediction at each time step is calculated on a dynamic runtime time axis. The specific calculation formula is as follows: In the formula, and These represent the upper and lower confidence limits for the global probability prediction of the voltage of multiple single cells at time t, respectively. and These are the upper and lower confidence limits for the global probability prediction of battery current density at time t, respectively. Furthermore, global probability prediction curves for the voltage of multiple single cells and global probability prediction curves for the battery current density are obtained.

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