PEMFC online prediction method fusing dynamic physical constraint and physical information neural network

Abstract

The invention provides a PEMFC online prediction method fusing dynamic physical constraints and a physical information neural network, and belongs to the technical field of fuel cell application. The invention aims to solve the problems that the voltage prediction of the proton exchange membrane fuel cell in an online scene is inaccurate and real-time data cannot be used for model self-correction. Comprising the following steps: S1, data acquisition and preprocessing; s2, establishing a loss function library; s3, establishing a PINN model and performing training; s4, establishing a dual-mode triggered online learning and updating module, and carrying out incremental learning; and S5, repeating the step S4, and realizing the online precise prediction of the voltage in the full working condition range of the PEMFC.

Description

Technical Field

[0001] This invention relates to an online prediction method for PEMFC that integrates dynamic physical constraints and physical information neural networks, belonging to the field of fuel cell application technology. Background Technology

[0002] Proton exchange membrane fuel cells (PEMFCs), as the core energy conversion device of the hydrogen economy, have shown broad application prospects in transportation power and stationary power generation due to their advantages such as high energy density, zero carbon emissions, and rapid start-up. However, the complex electrochemical-mass transfer-thermodynamic coupling process inside PEMFCs makes their performance output highly dependent on operating conditions. Especially under dynamic scenarios such as variable load and start-up / shutdown, their voltage response exhibits strong nonlinearity and time-varying characteristics, which poses a severe challenge to real-time status monitoring and precise energy management of the system.

[0003] Currently, modeling and prediction methods for PEMFCs are mainly divided into two paradigms: mechanism-driven and data-driven. Mechanism-driven methods construct numerical models based on first principles of physics, possessing clear physical interpretation and capable of fundamentally describing the dynamic processes inside the battery. However, such models typically involve a large number of internal parameters that are difficult to measure precisely and stringent model assumptions. When facing complex and variable real-world operating environments, prediction accuracy often decreases due to model mismatch. In contrast, data-driven methods do not rely on explicit physical equations. By autonomously learning the mapping relationship between voltage and operating parameters from historical operating data, they exhibit strong nonlinear fitting capabilities and robustness to noise. However, the performance of these methods is highly dependent on the scale and quality of the training data. When data is scarce or the operating conditions exceed the historical range, their generalization ability deteriorates sharply, and the prediction results often lack physical consistency, potentially producing phenomena that violate fundamental physical laws.

[0004] To integrate the advantages of both paradigms, Physics-Informed Neural Networks (PINN) have emerged. PINN successfully combines prior mechanistic knowledge with data-driven learning by introducing the governing physical equations as regularization terms into the loss function of the neural network. This ensures the physical plausibility of predicted solutions even in data-sparse scenarios, providing a new approach for PEMFC modeling. However, the physical constraints in existing PINN studies are typically static and fixed, employing only a set of pre-defined, invariant physical equations throughout the training and prediction process. In actual operation, the dominant physical mechanism within a PEMFC dynamically switches according to operating conditions such as load current. Low-load regions are dominated by electrochemical polarization, medium-load regions by ohmic polarization, and high-load regions by concentration polarization. A static physical loss function cannot accurately characterize this internal state that evolves with operating conditions, leading to poor prediction performance when the model crosses different polarization regions. More importantly, this offline, fixed modeling method lacks the ability to self-correct online using real-time data streams and cannot adapt to the drift of system characteristics caused by factors such as aging and environmental disturbances, which greatly limits its application in online prediction scenarios that require real-time perception and decision-making. Summary of the Invention

[0005] To address the issues of inaccurate voltage prediction in proton exchange membrane fuel cells (PEMFCs) and the inability to apply real-time data for model self-correction in online scenarios, this invention proposes an online PEMFC prediction method that integrates dynamic physical constraints and physical information neural networks.

[0006] The technical solution adopted by the present invention to solve the above problems is as follows: The present invention includes the following steps: Step 1: Collect real-time operating data of the proton exchange membrane fuel cell and perform data preprocessing; Step 2: Based on the electrochemical reaction mechanism of proton exchange membrane fuel cells, a loss function library is constructed. The loss function library is used to store the polarization loss terms between the voltage prediction value of proton exchange membrane fuel cells and the physical process control equations. Step 3: Build the PINN model, train the PINN model based on the preprocessed working condition dataset, and update the total loss of the trained PINN model; Step 4: Establish a dual-mode triggered online learning and update module. When any preset condition is triggered, the module automatically collects the real-time dynamic dataset of the proton exchange membrane fuel cell within a recent window and performs incremental learning on the trained PINN model based on the dynamic dataset. Step 5: Repeat step 4 to achieve accurate online voltage prediction across the entire operating range of PEMFC.

[0007] Furthermore, the preprocessing in step 1 includes: The current density, cell temperature, anode and cathode inlet pressure, and air flow rate are extracted from the operating data of the proton exchange membrane fuel cell as input data for the PINN model, and the stack output voltage of the proton exchange membrane fuel cell is used as the output data for the PINN model. The voltage data in the operating data of proton exchange membrane fuel cells is denoised and smoothed by a moving average filtering algorithm, and the time series of voltage data is resampled by linear interpolation to complete the preprocessing of the proton exchange membrane fuel cell operating data.

[0008] Furthermore, the polarization loss terms in the loss function library in step 2 include: activation polarization loss term, ohmic polarization loss term, and concentration polarization loss term; The activation polarization loss term is used to obtain the voltage drop caused by the activation barrier during charge transfer; The ohmic polarization loss term is used to capture the voltage drop caused by resistance as current flows through the internal components of a proton exchange membrane fuel cell. The concentration polarization loss term is used to obtain the voltage drop caused by the decrease in reactant concentration on the catalyst surface due to the inability of the mass transfer rate of reactants to the electrode surface of a proton exchange membrane fuel cell to keep up with the consumption rate under high current density. The expression for the activation polarization loss term is: (1); In formula (1), R Represents the universal gas constant. T This indicates the absolute operating temperature of the fuel cell. α Represents the charge transfer coefficient. n This indicates the number of electrons transferred during the electrode reaction. F Denotes Faraday's constant. i Indicates current density, i 0 represents the exchange current density; The expression for the Ohmic polarization loss term is: (2); In formula (2), R ohm Represents the area ratio resistance, including proton conduction resistance, electron conduction resistance, and contact resistance between components; The expression for the concentration polarization loss term is: (3); In formula (3), i L This represents the limiting current density.

[0009] Furthermore, the PINN model in step 3 includes: an input layer, a hidden layer, and an output layer; the hidden layer consists of multiple connection layers. The inputs to the PINN model are the current density, cell temperature, anode and cathode inlet pressure, and air flow rate extracted from the proton exchange membrane fuel cell operating data; the output is the predicted voltage value of the proton exchange membrane fuel cell.

[0010] Furthermore, the training of the PINN model includes: Step 3.1: Establish a working condition identification and decision-making module. Take the real-time operating parameters of the proton exchange membrane fuel cell as input, identify the current dominant polarization region online through polarization region discrimination logic, and output the dynamic weight coefficient of the corresponding polarization loss. Step 3.2: Based on the dynamic weight coefficients of the corresponding polarization loss, call the corresponding polarization loss term from the loss function library and configure the weights to generate the real-time optimal dynamic physical loss. Update the total loss of the trained PINN model based on the real-time optimal dynamic physical loss. Step 3.3: Simultaneously optimize the network parameters using the backpropagation algorithm to minimize the total loss of the updated PINN model, and calculate the gradient of each layer parameter in the PINN model using the chain rule, iteratively updating the parameters until the preset training rounds are reached or the total loss is reduced to the preset threshold, thus completing the training of the PINN model.

[0011] Furthermore, step 3.2 specifically includes: Assign corresponding weight coefficients to the activation polarization loss term, ohmic polarization loss term, and concentration polarization loss term, and calculate the optimal physical loss based on the weighted activation polarization loss term, ohmic polarization loss term, and concentration polarization loss term. or physics ; Based on optimal physical loss or physics Voltage reference value for proton exchange membrane fuel cells Obtain the theoretical output voltage value obtained through mechanism characterization at the current moment. U physics ; Based on the voltage value output in the current training round, U physics ( i and theoretical output voltage value U physics Calculate the real-time optimal dynamic physical loss L physics ; Data loss based on the PINN model itself L data and real-time optimal dynamic physical loss L physicsCalculate the total loss of the PINN model L total .

[0012] Furthermore, the preset conditions in step 4 include preset condition one and preset condition two; Preset condition one is that the PINN model reaches the preset running time period; The second preset condition is that the voltage prediction performance of the PINN model reaches the prediction error threshold.

[0013] Furthermore, the incremental learning in step 4 specifically includes: Starting with the parameters of the PINN model at the current stage, and taking the latest total loss of the PINN model as the target, we deeply integrate the PINN model parameters and the real-time optimal dynamic physical loss in the total loss, and perform batch gradient descent iteration on the PINN parameters to achieve fine-tuning of the PINN model parameters.

[0014] The beneficial effects of this invention are: 1. This invention uses a working condition identification and decision-making module to dynamically adapt to different polarization-dominant regions. In dynamic scenarios such as load changes and start-stop, the predicted curve closely matches the actual voltage without significant lag or distortion.

[0015] 2. This invention solves the problem of poor adaptability of traditional PINN static constraints by combining dynamic physical constraints with online updates, and can still maintain stable prediction performance when data is scarce, the system is aging, or the environment is disturbed.

[0016] 3. By setting up a dual-mode triggered online learning and update module, this invention enables the PINN model to track system characteristic drift in real time, continuously optimize parameters, and meet the long-term use requirements of online real-time monitoring and health management of fuel cells. Attached Figure Description

[0017] Figure 1 A flowchart illustrating the PEMFC online prediction method that integrates dynamic physical constraints and physical information neural networks; Figure 2 This is a schematic diagram illustrating the online voltage prediction principle of PEMFC. Figure 3 This is a schematic diagram of the PINN model. Figure 4 This is a schematic diagram of the operation process of the working condition identification and decision-making module; Figure 5 This is a schematic diagram of online voltage prediction for the PEMFC of the present invention; Figure 6 This is a schematic diagram of the traditional PINN prediction results. Detailed Implementation

[0018] The principle of PEMFC online voltage prediction is as follows: Figure 2 As shown, Figure 1 As shown, the steps of the PEMFC online prediction method integrating dynamic physical constraints and physical information neural networks described in this embodiment include: S1: Data acquisition and preprocessing; This implementation uses the FC3 dynamic dataset measured at the Greenlight 20 test station as the basis for experimental verification. This dataset records in detail the key state parameters of the fuel cell stack during long-term aging tests. First, current density, cell temperature, anode and cathode inlet pressure, and airflow are extracted from the original dataset as input feature vectors for the model, and the stack output voltage is used as the model's prediction label. To address sensor noise and inconsistent sampling frequencies in the original data, a moving average filtering algorithm is used to denoise and smooth the voltage signal, and linear interpolation is used to resample the time series to ensure data uniformity across the time dimension. The first 50% of the processed FC3 dataset is used for offline model construction and initial training, while the latter 50% is used as the target domain data to verify the generalization performance and adaptive update capability of the online prediction method.

[0019] S2: Establish a loss function library; Based on the electrochemical reaction mechanism within PEMFCs, a modular physical loss function library incorporating multiple polarization mechanisms is constructed. This implementation method represents and encapsulates the key degradation mechanisms of PEMFCs. Each loss term in the library corresponds to a dominant physical process, the core of which is calculating the residual between the neural network prediction and the governing equation of that physical process. The actual output voltage of the fuel cell... U It can be represented as: (1); (2); In formulas (1) and (2), E nernst This represents the Nernst voltage, which is the theoretical maximum voltage that a fuel cell can achieve under ideal, reversible conditions. or act This represents the activation polarization loss term. or ohm This represents the Ohmic polarization loss term. or conc This represents the concentration polarization loss term. T This indicates the absolute operating temperature of the fuel cell. P H2 This indicates the partial pressure of hydrogen at the anode catalyst / gas interface. P O2This represents the partial pressure of oxygen at the cathode catalyst / gas interface. The definitions, equations, and parameters of the three core dynamic physical loss terms will then be explained in detail.

[0020] The loss function library includes activation polarization loss terms, ohmic polarization loss terms, and concentration polarization loss terms, as detailed below: 1) Activation polarization loss term; Activation polarization loss refers to the voltage drop caused by the kinetic limitations inherent in the electrochemical reaction itself, i.e., the need to overcome a certain activation energy barrier during charge transfer. This loss mainly occurs in the low current density region, where the reaction rate is slow, and reaction kinetic resistance becomes the dominant factor limiting battery performance. Its main influencing factors include catalyst activity, reaction temperature, and the reaction environment at the electrode surface. The main reactions are as follows: (3); In formula (3), R Represents the universal gas constant. T This indicates the absolute operating temperature of the fuel cell. α Represents the charge transfer coefficient. n This indicates the number of electrons transferred during the electrode reaction. F Denotes Faraday's constant. i Indicates current density, i 0 represents the exchange current density; 2) Ohmic polarization loss term; Ohmic polarization loss refers to the voltage drop caused by the resistance encountered by current flowing through the components inside a fuel cell. This loss is significant in the medium current density region, where the cell has moved beyond reaction kinetics control. Increased current leads to a proportional increase in the ohmic voltage drop, becoming the dominant factor in performance degradation at this stage. Its magnitude is primarily determined by the ionic conductivity of the electrolyte, the electronic conductivity of the bipolar plates and diffusion layer, and the contact resistance between the components.

[0021] (4); In formula (4), R ohm Represents the area ratio resistance, including proton conduction resistance, electron conduction resistance, and contact resistance between components; 3) Concentration polarization loss term; Concentration polarization loss refers to the voltage drop caused by a sharp decrease in reactant concentration on the catalyst surface due to the inability of the mass transfer rate of reactants to the electrode surface to keep up with the rate of their consumption at high current densities. This loss is a major cause of performance degradation in the high current density region and directly determines the maximum power of the fuel cell. Its severity depends on the diffusion rate of the reactants and is closely related to the flow field design, the pore structure of the gas diffusion layer, and the operating pressure.

[0022] (5); In formula (5), i L This represents the limiting current density.

[0023] An activation polarization module based on the Butler-Volmer equation is used to calculate the activation overpotential caused by reaction kinetic limitations in low current density regions; an ohmic polarization module based on Ohm's law is used to calculate the ohmic overpotential caused by proton and electron conduction resistance; and a concentration polarization module based on Fick's diffusion law is used to calculate the concentration overpotential caused by mass transfer limitations in high current density regions. This physical loss function library is designed as a callable program interface, capable of receiving current operating parameters such as current density, temperature, and gas partial pressure, and outputting the corresponding theoretical voltage loss value in real time, providing dynamic physical benchmark constraints for subsequent neural network training.

[0024] S3: Build and train the PINN model; PINN is a machine learning paradigm that deeply integrates prior physical knowledge with data-driven models. Unlike traditional neural networks that rely entirely on large amounts of training data, the core innovation of PINN lies in the explicit constraints of fundamental physical principles on its learning process. This mechanism allows the model not only to learn statistical regularities in the data but also to be forced to a solution space that conforms to established physical laws. Consequently, it exhibits significantly stronger generalization ability and prediction reliability in scenarios where training data is scarce, noisy, or requires extrapolation prediction.

[0025] PINN works by embedding the physical governing equations describing the system's behavior as soft constraints into the loss function of the neural network. Specifically, its total loss function typically consists of two parts: data fitting loss and physical equation residual loss. The data loss ensures that the model's output approximates the known observations; while the physical residual loss forces the neural network's predicted solutions to satisfy the partial differential equations or ordinary differential equations that serve as constraints. During training, the network parameters are simultaneously optimized using the backpropagation algorithm to minimize the total loss, ultimately resulting in a surrogate model that is both data-accurate and physically consistent. Figure 3 The network structure of PINN is shown.

[0026] The PINN model is established by first constructing a multi-layer fully connected neural network, setting the feature dimensions of the input layer, and setting the output layer as the predicted voltage. The hyperbolic tangent function (Tanh or Swish) is selected as the activation function to ensure the existence of higher-order derivatives, thus facilitating the backpropagation of physical gradients. Operating condition identification and decision-making logic is embedded in the model's forward propagation path. This logic monitors the input load current density in real time and determines the dominant polarization region. When the system is in the low-current-density activation polarization dominant region, the decision module assigns a dominant weight to the activation polarization loss term; when the system operates in the medium-current-density ohmic polarization dominant region, it assigns a dominant weight to the ohmic polarization loss term; and when the system enters the high-current-density concentration polarization dominant region, it assigns a dominant weight to the concentration polarization loss term. Through this dynamic weight configuration mechanism, a dynamic physical loss that highly matches the current operating state is generated. L physics and compare it with the data fitting loss. L data The summation constitutes the total loss used to guide network optimization. L total .

[0027] Training the PINN model includes: The pre-processed offline training set from S1 is used to initialize and train the constructed physical information neural network. Training data containing operating condition parameters is input into the network, and the residual between the predicted and actual voltages is calculated. Simultaneously, the physical loss function library is used to calculate the residual of the physical equations under the current operating condition. Based on the total loss function, the Adam or L-BFGS optimization algorithm is used to iteratively update the weights and bias parameters of the neural network. This process forces the model to learn the statistical patterns of historical data while simultaneously guiding it towards a solution space that conforms to the laws of electrochemical physics, thus obtaining an initial pre-trained model that possesses both data fitting accuracy and physical consistency.

[0028] S301: Establish a working condition identification and decision-making module, take the real-time operating parameters of the proton exchange membrane fuel cell as input, identify the current dominant polarization region online through polarization region discrimination logic, and output the dynamic weight coefficient of the corresponding polarization loss; S302: Based on the dynamic weight coefficients of the corresponding polarization loss, call the corresponding polarization loss term from the loss function library and configure the weights to generate the real-time optimal dynamic physical loss. Update the total loss of the trained PINN model based on the real-time optimal dynamic physical loss. The operating condition identification and decision-making module is the intelligent hub for achieving dynamic adaptation to physical constraints in this method. This module uses real-time operating parameters of the fuel cell system, primarily output voltage and load current density, supplemented by temperature and gas pressure, as inputs. Through built-in physical state discrimination logic, it diagnoses the dominant polarization region currently in which the system is located online. Its core discrimination criterion is the typical correlation characteristics between different polarization mechanisms and current density. In the low current density range, the voltage drop is extremely sensitive to current changes, and the system is identified as being in the "active polarization dominant region." When the voltage drop and current are approximately linearly related, it is determined to be in the "ohmic polarization dominant region." At high current densities, if the voltage shows an accelerating downward trend, it indicates that the system has entered the "concentration polarization dominant region" or a mixed region.

[0029] Based on the real-time identification results described above, this module performs key decision-making functions by dynamically configuring the combined weights of the physical loss function: (6); (7); In formulas (6) and (7), or physics Represents the optimal physical loss. l act , l ohm and l conc These are the weighting coefficients for the activation polarization loss term, ohmic polarization loss term, and concentration polarization loss term, respectively. U physics This represents the theoretical output voltage value obtained through mechanistic characterization at the current moment. This is the voltage reference value for a proton exchange membrane fuel cell.

[0030] Based on formulas (6) and (7), the dynamic physical loss and total loss are further calculated: (8); (9); In formulas (8) and (9), L physics Represents dynamic physical loss. n Indicates the amount of voltage data. U physics ( i ) indicates the current density i The theoretical output voltage value under the following conditions U p ( i ) represents the output voltage value of PINN during the training phase. L total This represents the total loss during the PINN training process.L data This indicates the data loss of PINN itself. L data This refers to the data loss inherent in the PINN model itself.

[0031] Specifically, the module outputs a set of dynamic weighting coefficients that match the current physical state. l act , l ohm and l conc These coefficients are then assigned to the corresponding loss terms in the physical loss function library to generate the optimal dynamic physical loss at this moment. L physics This leads to the optimal total loss of the model. For example, when the module identifies that the system is in the Ohmic-dominated region, it will... l ohm Set the dominant weight close to 1, while significantly reducing l act and l conc The weights of the PINN algorithm mean that its training and prediction processes are primarily constrained by Ohm's law. The working condition recognition and decision-making module enables the on-demand and precise injection of physical knowledge into the neural network, serving as a bridge connecting real-time working conditions and mechanistic constraints. The specific process is as follows: Figure 4 As shown.

[0032] S303: Simultaneously optimize network parameters through backpropagation algorithm to minimize the total loss of the updated PINN model, and calculate the gradient of parameters of each layer in the PINN model through chain rule, iteratively update parameters until the preset training rounds are reached or the total loss is reduced to the preset threshold, thus completing the training of the PINN model.

[0033] S4: Establish a dual-mode triggered online learning and update module and perform incremental learning; The online learning and update module endows the entire prediction method with the ability to continuously self-optimize and adapt to the slowly changing characteristics of the system. The module's activation mechanism employs a dual-mode triggering mechanism: routine triggering based on a fixed time period and triggering based on threshold events caused by prediction performance deviations. When either condition is met, the module automatically collects real-time system operation data streams within a recent window. This data includes continuous operating parameters and sparse but critical measured voltage values, which together form an incremental dataset for model fine-tuning.

[0034] The core operation of this module is to perform rapid incremental learning on the deployed PINN model using this dynamic dataset. The learning process starts with the current model parameters as the optimization starting point and uses the latest total loss. L totalTo achieve this, a small number of gradient descent iterations are performed. Essentially, this process deeply integrates the information contained in the new data with the latest physical constraints, fine-tuning the network parameters. This allows the model to quickly track and adapt to system characteristic drift caused by membrane dehydration, catalyst aging, or environmental disturbances without excessively forgetting historical knowledge, thus achieving continuous online improvement and maintenance of predictive performance.

[0035] The pre-trained model is deployed to the online prediction environment to perform real-time voltage prediction tasks. The system employs a dual update mechanism combining timed and event-triggered updates. Timed updates activate according to a set runtime period, while event-triggered updates activate when the error between the predicted and measured voltages exceeds a preset threshold. Once the update mechanism is triggered, the system automatically collects data from the most recent time period within a window of [length missing]. N An incremental dataset is constructed using real-time operating conditions and voltage data. This dataset is then used to rapidly incrementally learn the current model, fine-tuning the model parameters with a small learning rate while keeping most historical knowledge parameters stable. Through this closed-loop iterative process, the model can capture and adapt in real time to system characteristic drift caused by membrane dehydration, catalyst aging, or environmental disturbances, thereby achieving accurate voltage prediction throughout its entire lifecycle.

[0036] S5: Repeat S4 to achieve accurate online voltage prediction across the entire operating range of PEMFC.

[0037] like Figure 5 The figure shows the improved PINN prediction results proposed in this invention. As can be seen from the figure, the PINN prediction results using the online mechanism are in high agreement with the actual voltage curve. Even in the transition region of changing current density (such as startup, load surges, and other dynamic scenarios), the model can still accurately track the voltage response without significant hysteresis or distortion, demonstrating excellent prediction accuracy and robustness.

[0038] like Figure 6 The figure shows the prediction results of a traditional PINN. As can be seen, there is a significant deviation between the predicted results and the actual voltage. Especially in the region where the current density changes from low to high, the static physical constraints cannot adapt to the switching of the dominant polarization mechanism, leading to a large error in the model prediction.

[0039] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent substitutions, and improvements made to the above embodiments without departing from the scope of the present invention, based on the technical essence of the present invention and within the spirit and principles of the present invention, shall still fall within the protection scope of the present invention.

Claims

1. A PEMFC online prediction method integrating dynamic physical constraints and physical information neural networks, characterized in that, include: Step 1: Collect real-time operating data of the proton exchange membrane fuel cell and perform data preprocessing; Step 2: Based on the electrochemical reaction mechanism of proton exchange membrane fuel cells, a loss function library is constructed. The loss function library is used to store the polarization loss terms between the voltage prediction value of proton exchange membrane fuel cells and the physical process control equations. Step 3: Build the PINN model, train the PINN model based on the preprocessed working condition dataset, and update the total loss of the trained PINN model; Step 4: Establish a dual-mode triggered online learning and update module. When any preset condition is triggered, the module automatically collects the real-time dynamic dataset of the proton exchange membrane fuel cell within a recent window and performs incremental learning on the trained PINN model based on the dynamic dataset. Step 5: Repeat step 4 to achieve accurate online voltage prediction across the entire operating range of PEMFC.

2. The PEMFC online prediction method based on the fusion of dynamic physical constraints and physical information neural networks according to claim 1, characterized in that, The preprocessing in step 1 includes: The current density, cell temperature, anode and cathode inlet pressure, and air flow rate are extracted from the operating data of the proton exchange membrane fuel cell as input data for the PINN model, and the stack output voltage of the proton exchange membrane fuel cell is used as the output data for the PINN model. The voltage data in the operating data of proton exchange membrane fuel cells is denoised and smoothed by a moving average filtering algorithm, and the time series of voltage data is resampled by linear interpolation to complete the preprocessing of the proton exchange membrane fuel cell operating data.

3. The PEMFC online prediction method based on the fusion of dynamic physical constraints and physical information neural networks according to claim 1, characterized in that, The polarization loss terms in the loss function library in step 2 include: activation polarization loss term, ohmic polarization loss term, and concentration polarization loss term; The activation polarization loss term is used to obtain the voltage drop caused by the activation barrier during charge transfer; The ohmic polarization loss term is used to capture the voltage drop caused by resistance as current flows through the internal components of a proton exchange membrane fuel cell. The concentration polarization loss term is used to obtain the voltage drop caused by the decrease in reactant concentration on the catalyst surface due to the inability of the mass transfer rate of reactants to the electrode surface of a proton exchange membrane fuel cell to keep up with the consumption rate under high current density. The expression for the activation polarization loss term is: （1）； In formula (1), R Represents the universal gas constant. T This indicates the absolute operating temperature of the fuel cell. α Represents the charge transfer coefficient. n This indicates the number of electrons transferred during the electrode reaction. F Denotes Faraday's constant. i Indicates current density, i 0 represents the exchange current density; The expression for the Ohmic polarization loss term is: （2）； In formula (2), R ohm Represents the area ratio resistance, including proton conduction resistance, electron conduction resistance, and contact resistance between components; The expression for the concentration polarization loss term is: （3）； In formula (3), i L This represents the limiting current density.

4. The PEMFC online prediction method based on the fusion of dynamic physical constraints and physical information neural networks according to claim 1, characterized in that, The PINN model in step 3 includes an input layer, hidden layers, and an output layer; the hidden layers consist of multiple connection layers. The inputs to the PINN model are the current density, cell temperature, anode and cathode inlet pressure, and air flow rate extracted from the proton exchange membrane fuel cell operating data; the output is the predicted voltage value of the proton exchange membrane fuel cell.

5. The PEMFC online prediction method based on the fusion of dynamic physical constraints and physical information neural networks according to claim 1, characterized in that, Training the PINN model includes: Step 3.1: Establish a working condition identification and decision-making module. Take the real-time operating parameters of the proton exchange membrane fuel cell as input, identify the current dominant polarization region online through polarization region discrimination logic, and output the dynamic weight coefficient of the corresponding polarization loss. Step 3.2: Based on the dynamic weight coefficients of the corresponding polarization loss, call the corresponding polarization loss term from the loss function library and configure the weights to generate the real-time optimal dynamic physical loss. Update the total loss of the trained PINN model based on the real-time optimal dynamic physical loss. Step 3.3: Simultaneously optimize the network parameters using the backpropagation algorithm to minimize the total loss of the updated PINN model, and calculate the gradient of each layer parameter in the PINN model using the chain rule, iteratively updating the parameters until the preset training rounds are reached or the total loss is reduced to the preset threshold, thus completing the training of the PINN model.

6. The PEMFC online prediction method integrating dynamic physical constraints and physical information neural networks according to claim 3, characterized in that, Step 3.2 specifically includes: Assign corresponding weight coefficients to the activation polarization loss term, ohmic polarization loss term, and concentration polarization loss term, and calculate the optimal physical loss based on the weighted activation polarization loss term, ohmic polarization loss term, and concentration polarization loss term. η physics ; Based on optimal physical loss η physics Voltage reference value for proton exchange membrane fuel cells Obtain the theoretical output voltage value obtained through mechanism characterization at the current moment. U physics ; Based on the voltage value output in the current training round, U physics ( i and theoretical output voltage value U physics Calculate the real-time optimal dynamic physical loss L physics ; Data loss based on the PINN model itself L data and real-time optimal dynamic physical loss L physics Calculate the total loss of the PINN model L total .

7. The PEMFC online prediction method according to claim 1, characterized in that, The preset conditions in step 4 include preset condition one and preset condition two; Preset condition one is that the PINN model reaches the preset running time period; The second preset condition is that the voltage prediction performance of the PINN model reaches the prediction error threshold.

8. The PEMFC online prediction method according to claim 1, characterized in that, The incremental learning in step 4 specifically includes: Starting with the parameters of the PINN model at the current stage, and taking the latest total loss of the PINN model as the target, we deeply integrate the PINN model parameters and the real-time optimal dynamic physical loss in the total loss, and perform batch gradient descent iteration on the PINN parameters to achieve fine-tuning of the PINN model parameters.

Images