Proton exchange membrane fuel cell internal current density distribution reconstruction method based on physical information neural network

Abstract

This invention belongs to the field of proton exchange membrane fuel cell (PEMFC) state monitoring technology, and discloses a method for reconstructing the internal current density distribution of a PEMFC based on a physical information neural network. The method includes constructing an electro-magnetic dataset of the internal current distribution and external magnetic field distribution of the PEMFC under different operating conditions; constructing a physical information neural network model, embedding Biot-Savart's law as a physical loss into the network loss function; training the physical information neural network model using the loss function, and obtaining the trained physical information neural network model when the loss function converges. In practical applications, the current external magnetic field distribution of the PEMFC is input into the trained physical information neural network model to obtain the reconstructed internal current density distribution. This invention solves the problems of ill-posedness and noise sensitivity of traditional inversion methods, and achieves high-precision, non-invasive real-time monitoring of the internal state of the PEMFC.

Description

Technical Field

[0001] This invention belongs to the field of proton exchange membrane fuel cell condition monitoring technology, and more specifically, relates to a method for reconstructing the internal current density distribution of a proton exchange membrane fuel cell based on a physical information neural network. Background Technology

[0002] Proton exchange membrane fuel cells (PEMFCs) face various complex conditions related to water, heat, and gas in real-world operating scenarios. These complexities not only severely impact their performance but also become a key bottleneck for their commercialization. The internal current density distribution (the lateral current on the PEMFC cell) serves as a macroscopic manifestation of the coupling of multiple physical fields such as electricity, gas, heat, and water within the PEMFC, directly mapping its internal state during operation. Therefore, it is one of the main research directions for PEMFC state monitoring.

[0003] Currently, methods for measuring the internal current density distribution of PEMFCs are mainly divided into two categories: invasive measurement methods, such as the battery segmentation method, the gasket measurement method, and the printed circuit board method. These methods are invasive and will alter the internal structure of the PEMFC, thus affecting the normal performance of the battery. The other type is the non-invasive magnetic field inversion method, based on the Biot-Savart law, which calculates the internal current by measuring the external magnetic field of the battery.

[0004] However, while using the external magnetic field of a PEMFC to invert the internal current density distribution is an ideal non-invasive measurement method, this process is essentially the inverse of the Biot-Savart law, a severely ill-posed problem with challenges such as non-unique solutions and sensitivity to noise. Traditional numerical solutions (such as directly solving mathematical equations) suffer from the "curse of dimensionality," and the inversion results are extremely sensitive to noise in the measurement data, resulting in low accuracy and a tendency for non-unique or unstable solutions. With the development of deep learning, data-driven methods are gradually replacing traditional numerical solutions. While existing data-driven methods (such as convolutional neural networks or backpropagation neural networks) avoid solving complex physical equations, they neglect the underlying physical laws (such as the law of electromagnetic induction), leading to the need for massive amounts of data and long training times, and poor model generalization and interpretability. Insufficient data can easily lead to overfitting or underfitting, failing to accurately reflect the physical constraints between the electric and magnetic fields in the PMEFC.

[0005] Therefore, there is an urgent need for a non-intrusive PEMFC current density distribution reconstruction method that can both utilize physical constraints and achieve efficient data-driven solutions. Summary of the Invention

[0006] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a method for reconstructing the internal current density distribution of a proton exchange membrane fuel cell based on a physical information neural network. The aim is to significantly improve the accuracy of current density distribution reconstruction with limited datasets, thereby enabling non-invasive real-time monitoring of the internal conditions of a PEMFC.

[0007] To achieve the above objectives, the present invention provides a method for reconstructing the internal current density distribution of a proton exchange membrane fuel cell based on a physical information neural network, comprising: a training phase and an application phase;

[0008] The training phase includes: constructing an electromagnetic dataset, wherein the samples in the electromagnetic dataset include the internal current density distribution and the corresponding external magnetic field distribution of PEMFC under different operating conditions;

[0009] The external magnetic field distribution in the sample is input into the physical information neural network model to obtain the predicted internal current density distribution of the PEMFC. The physical information neural network model is trained using a loss function. When the loss function converges, the trained physical information neural network model is obtained. The loss function is a weighted sum of a data loss term and a physical loss term. The data loss term is the error between the predicted internal current density distribution of the PEMFC and the internal current density distribution in the sample. The physical loss term is the error between the theoretical external magnetic field distribution calculated using the Biot-Savart law based on the predicted internal current density distribution of the PEMFC and the external magnetic field distribution in the input sample.

[0010] The application phase includes: inputting the current external magnetic field distribution of the PEMFC into the trained physical information neural network model to obtain the reconstructed internal current density distribution.

[0011] Furthermore, the loss function for:

[0012]

[0013]

[0014] in, As a dynamic weighting factor, For the current training process, For data loss items, For physical loss items, The saturation cutoff point dominated by the data loss term. For the total training cycle, This represents the steady-state lower limit of the weighting factor. For data loss items Normalized real-time data loss The dynamic decay rate factor of feedback control, and and They exhibit a linear negative correlation.

[0015] Furthermore, the dynamic decay rate factor for:

[0016]

[0017] in, For rapid decay constant, It is the slow decay constant. and The value of satisfies the condition within a total training cycle. Inside, It is a continuous function, and in Inside, exist It begins to decay in the neighborhood and in Decay within the neighborhood to ,exist Inside, exist Fluctuations within the neighborhood of for decay to The time point is taken from experience.

[0018] Furthermore, the construction of the electro-magnetic dataset includes:

[0019] The PEMFC is divided into n current element regions along its surface by rows and columns, and n magnetic field measurement points are set accordingly. The current density distribution of the n current element regions is measured under each operating condition, and the external magnetic field distribution of each measurement point under each operating condition is calculated according to the Biot-Savart law to obtain the constructed electro-magnetic dataset.

[0020] Furthermore, the data loss item and the physical loss term They are respectively:

[0021]

[0022]

[0023] in, The batch size of the current training samples. The input sample matrix of the physical information neural network model is the matrix composed of the distribution of external magnetic fields in the samples. The output matrix predicted by the physical information neural network model is a matrix composed of the predicted internal current density distribution of the PEMFC. It is a matrix composed of the distribution of external magnetic fields in the sample; Let be the coefficient matrix, satisfying ;in, The current element matrix is ​​composed of the current density distribution in the electromagnetic dataset. Based on The matrix calculated using Biot-Savart's law, which consists of the theoretical external magnetic field distribution.

[0024] Furthermore, the physical information neural network model is a multi-layer fully connected neural network.

[0025] The present invention also provides a method for monitoring the state of a proton exchange membrane fuel cell, including monitoring the internal current density distribution of the proton exchange membrane fuel cell, wherein the internal current density distribution of the proton exchange membrane fuel cell is obtained by the proton exchange membrane fuel cell internal current density distribution reconstruction method described in any one of the above claims.

[0026] The present invention also provides an electronic device, including a computer-readable storage medium and a processor;

[0027] The computer-readable storage medium is used to store executable instructions;

[0028] The processor is used to read executable instructions stored in the computer-readable storage medium to execute the proton exchange membrane fuel cell internal current density distribution reconstruction method based on physical information neural network as described above, or / and to execute the proton exchange membrane fuel cell state monitoring method as described above.

[0029] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the program, when executed by a processor, implements the method for reconstructing the internal current density distribution of a proton exchange membrane fuel cell based on a physical information neural network as described above, or / and implements the method for monitoring the state of a proton exchange membrane fuel cell as described above.

[0030] The present invention also provides a computer program product, including a computer program that, when the computer program is run on a computer, causes the computer to execute the proton exchange membrane fuel cell internal current density distribution reconstruction method based on physical information neural network as described above, or / and execute the proton exchange membrane fuel cell state monitoring method as described above.

[0031] In summary, the above-described technical solutions conceived in this invention can achieve the following beneficial effects:

[0032] (1) Compared with the traditional pure data-driven method, this invention predicts the current density distribution inside PEMFC based on the physical information neural network model. During the model training process, the Biot-Savart physical law is embedded in the network as a physical loss term. The network no longer relies solely on massive data for model training. At the same time, it learns the physical laws based on the feature loss between the theoretical external magnetic field distribution and the actual input external magnetic field distribution. This greatly constrains the original "ill-posed" solution (current density distribution) space, enhances the generalization of the reconstruction results, and can significantly improve the accuracy of reconstruction under limited datasets, realizing non-intrusive real-time monitoring of the internal situation of PEMFC.

[0033] (2) Furthermore, in the technical field of PEMFC magnetic field inversion current, this invention proposes a dynamic weighting strategy that evolves nonlinearly with the number of training iterations, utilizing the idea of ​​"data-guided first, physical correction later": before the data-dominated saturation cutoff point, the dynamic weighting factor is directly adjusted. The threshold is 1, and all data loss terms are used in this stage. Training can accelerate convergence while avoiding the influence of physical loss terms on the direction of gradient descent. Additionally, a dynamic decay rate factor controlled by real-time data loss feedback can be set. , With normalized real-time data loss They exhibit a linear negative correlation; if the network struggles to fit the data (i.e., ... If the value is large, the decay curve will automatically slow down, giving the network more "data learning windows". If the network fits the data well (i.e., (smaller value), physical constraints (physical loss term) This will allow for faster integration into the training process, reducing training time. The designed dynamic weighting factor... It effectively balances the contradiction between data loss terms and physical loss terms, effectively avoiding gradient direction disorder (difficulty in convergence) caused by excessive physical constraints in the early stage of training, and avoiding overfitting caused by excessive data weights in the later stage of training. As a result, the reconstructed current density distribution is close to the true value and has a high degree of physical smoothness.

[0034] (3) Furthermore, this invention innovatively incorporates the weight decay rate (dynamic decay rate factor) ) and normalized real-time data loss Coupling. In the adaptive exponential decay phase ( When the data noise is large or fitting is difficult (corresponding to...) (If the value is large), it will automatically decrease. Values ​​are used to slow down weight decay and extend the "data learning window"; when the data fits well (corresponding to...) (smaller value), increase Values ​​are used to accelerate the introduction of physical constraints. During the steady-state phase of physical constraints ( In the ) stage, based on the set parameters ( and Regardless of the decay rate, All in convergence to Nearby, the forced reconstruction results undergo physical regularization correction to eliminate non-physical oscillations. This mechanism enables "on-demand allocation" of training attention, avoiding non-physical oscillations caused by forced fitting of noise in fixed-weight strategies, and accelerating network training.

[0035] (4) Preferably, when constructing the electromagnetic dataset, the present invention divides the PEMFC into n current element regions along the surface and sets n magnetic field measurement points accordingly. Based on Biot-Savart's law, the magnetic field distribution of each measurement point under various working conditions is calculated. Compared with directly selecting measurement points around the battery cell, the measurement method of the present invention contains richer location information in the dataset, making the prediction results of the model more accurate.

[0036] In general, this invention achieves real-time and effective monitoring of the internal state of PEMFC by embedding electromagnetic physical laws as regularization terms into a neural network and using dynamic constraints to adjust the weights of physical and data losses during training. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the Physical Information Neural Network (PINN) structure in an embodiment of the present invention;

[0038] Figure 2 This is a diagram showing the relationship between the internal current and the external magnetic field of a PEMFC.

[0039] Figure 3 This is a schematic diagram of the PEMFC electro-magnetic equivalent model used to calculate physical losses;

[0040] Figure 4 This describes the change in loss weights under dynamic constraints in this embodiment of the invention. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0042] Example 1

[0043] This invention provides a method for reconstructing the internal current density distribution of a proton exchange membrane fuel cell based on a physical information neural network, comprising a training phase and an application phase.

[0044] The specific steps in the training phase include:

[0045] S1. Construct an electro-magnetic dataset; obtain the "internal current density distribution - external magnetic field distribution" dataset of PEMFC under different operating conditions. The data in the dataset can be obtained through experimental measurement or multiphysics simulation (such as changing the stoichiometry, temperature, humidity and other operating state parameters within an allowable range). The obtained dataset is then divided into a training set, a validation set and a test set for subsequent model training and testing.

[0046] S2. Construct a Physical Information Neural Network (PINN) model; the overall PINN model is as follows: Figure 1 As shown, a multi-layer fully connected neural network is built, with the input... Output the magnetic field distribution data outside the PEMFC. This is the current density distribution data inside the PEMFC.

[0047] S3. Use the loss function The physical information neural network model is trained; where the loss function for network training is... It contains two parts: data loss item and physical loss items , ,in, For weighting factors, data loss terms The physical loss term represents the data error between the current density distribution predicted by PINN and the actual internal current sample corresponding to the input external magnetic field distribution. The physical loss is constructed based on the Biot-Savart law, specifically the error between the theoretical external magnetic field distribution calculated using the Biot-Savart law based on the current density distribution predicted by PINN and the actual input external magnetic field distribution. Figure 2 This is a schematic diagram showing the relationship between the internal current and the external magnetic field of a PEMFC.

[0048] Application phase: Input the current external magnetic field distribution data of PEMFC into the trained PINN model to obtain the reconstructed internal current density distribution, thereby realizing non-invasive monitoring of the internal condition of PEMFC.

[0049] As a further design of the present invention, considering that the existing technology of adding electro-magnetic physical constraints to training still has significant defects in the setting of physical and data loss weights: First, the fixed weight setting throughout the entire cycle cannot take into account the contradictory requirements of using data to quickly lock the solution space (current density distribution) in the early stage of training and using physical constraints to refine the physical consistency of the solution in the later stage of training, which makes the model very easy to get trapped in local optima or produce non-physical oscillations; Second, the existing method based on intelligent optimization weight requires a lot of computation space, wasting a certain amount of computational resources.

[0050] To address the aforementioned issues, this embodiment of the invention constructs a dynamic weight adjustment mechanism based on the training process. Specifically, in phase S3 of the training phase, the weight factors... The dynamic weight factor varies with the number of training iterations (Epochs). At this point, the total loss function for:

[0051] (1)

[0052] In this embodiment of the invention, the designed dynamic weighting factor Following the principle of "data-driven first, physical correction later", the system is dynamically adjusted every certain period (e.g., 20 periods), and the adjustment design satisfies the following equation:

[0053] (2)

[0054] In the formula, The current training process is the normalized current training process in this embodiment of the invention, with a value range of [0,1]. The data-driven saturation cutoff point, i.e., using only data loss terms. The normalization time for training is determined based on the data samples used for model training, and is set in this embodiment of the invention. =0.1, total training cycles Normalization to 1 means that the dynamic weight factor is forced to be normalized in the first 10% of the training cycle. Set it to 1 to speed up convergence while avoiding the influence of the physical loss term on the direction of gradient descent; The steady-state lower limit of the weighting factor is an empirical value, set in this embodiment of the invention. = 0.4, to ensure that the weight of the data loss term in the later stage of training is not less than 0.4, so that the model training can both follow the physical rules and shorten the convergence time; For items affected by real-time data loss The dynamic decay rate factor of feedback control.

[0055] To enable the model to adaptively adjust to different training states, a dynamic decay rate factor is used. With normalized real-time data loss term (Right now Figure 4 The loss in the data shows a linear negative correlation, which makes it difficult for the network to fit the data (i.e., If the value is large, the decay curve will automatically slow down, giving the network more "data learning windows". If the network fits the data well (i.e., (smaller value), physical constraints (physical loss term) This will allow for faster integration into the training process, reducing training time.

[0056] As a specific implementation method, in this embodiment of the invention, Satisfy the following equation:

[0057] (3)

[0058] In the formula, The fast decay constant corresponds to the state of excellent data fitting, i.e. The value is small; This is a slow decay constant, corresponding to a state where data fitting is difficult, i.e. The value is large. When the data fits well ( When the value is small, the weight decays extremely quickly, rapidly introducing physical constraints, while when the fit is out of control ( (If the value is large), the weight decays slowly, maintaining a high data weight to extend the data learning time. and The value of satisfies the condition within a total training cycle. Inside, It is a continuous function, and in Inside, exist It begins to decay at this point, at Within its neighborhood, decay to ,exist Inside, exist Fluctuations within the neighborhood; for decay to The time point is a value derived from experience. In this embodiment of the invention, , , For the total training cycle, To simultaneously include data loss items and physical loss items Training time and data loss terms They gradually declined from a dominant training position to a subordinate one. and The value of ensures that regardless of the size of the data loss term, the weighting factor All were conducted during the training cycle. (Approximately 50%) converges to the lower steady-state limit. Nearby, ensure that the physical loss term can dominate the training at this time.

[0059] In this embodiment of the invention, the strategy implements three stages of control:

[0060] Pure data loss term training phase ( ):regardless How much is it worth? Forced to 1. This stage utilizes pure data-driven methods, avoiding gradient interference caused by physical loss in the initial stage, and using only data loss to guide the training results.

[0061] Adaptive exponential decay phase ( ): It started to decline regularly. The value is controlled by real-time data loss feedback. If the network struggles to fit the data, the decay curve will automatically slow down, giving the network more "data learning windows." If the network fits the data well, physical constraints will be added to the training process more quickly, reducing training time.

[0062] Physically constrained steady state stage ( Based on the set parameters ( and Regardless of the decay rate, All in convergence to Nearby, the forced reconstruction results are physically regularized to eliminate non-physical oscillations.

[0063] The PINN model is iteratively trained using this dynamic weighting strategy. During training, the loss function shifts from "data fitting" to "physical compliance" until the model converges. In practical applications, external magnetic field data measured by a magnetic sensor is input into the trained PINN model, which can quickly output a reconstructed internal current density distribution, enabling non-intrusive monitoring of the internal conditions of a PEMFC.

[0064] The methods in the embodiments of the present invention will be further illustrated below with specific examples.

[0065] First, a three-dimensional cryogenic dual-serpentine flow field simulation model for PEMFC was constructed. This model includes components such as anode and cathode bipolar plates, flow field plates, gas diffusion layers, electrodes, and a proton exchange membrane, using a Nafion® EW1100 proton exchange membrane. To simulate realistic and diverse operating environments, a dataset was generated by changing operating parameters, designing a total of 192 different operating conditions. Subsequently, an electro-magnetic equivalent model was built, such as... Figure 3 As shown, the PEMFC surface is divided into 10 rows and 6 columns, totaling 60 (n=60) current element regions, and 60 magnetic field measurement points are set accordingly. The magnetic field distribution at each measurement point under the above 192 operating conditions is calculated based on Biot-Savart's law. The magnetic field at a certain measurement point outside the PEMFC is also calculated. and internal current The relationship can be represented by the following formula:

[0066] (4)

[0067] In the formula, It is a current element; The distance from the current element to a point in space; It is the unit vector pointing from the current element to a point in space. Represents the cross product of vectors; The value of free permeability is 4π × 10⁻⁶. -7 N / A 2 ; The magnetic field strength generated by the internal current of a PEMFC at a certain point in space can be decomposed into:

[0068] (5)

[0069] In the formula, To measure the magnitude of the x-axis component of the measurement point, To measure the magnitude of the y-component of the measurement point; Let be the counterclockwise angle between the direction of the magnetic field strength and the positive x-axis. Then, the magnetic field strength at 60 measurement points... and Represented as:

[0070] (6)

[0071] (7)

[0072] Rewritten in matrix form:

[0073] (8)

[0074] (9)

[0075] In the formula, , The coefficient matrix, Let be the current element matrix. The two equations can be combined as:

[0076] (10)

[0077] In the formula, ; This formula is also the part used to embed the training of the PINN network.

[0078] A training dataset containing "external magnetic field distribution" and "internal current density distribution" was constructed based on 192 operating conditions. The dataset was then min-max normalized and randomly divided into a training set (80%) and a test set (20%), with 25% of the training set used as a validation set. The min-max normalization was as follows:

[0079] (11)

[0080] In the formula: For the original sample under the current features, for The corresponding normalized sample data; It is the maximum value among all samples under the current feature; It is the minimum value among all samples under the current feature.

[0081] After acquiring the dataset, a Physical Information Neural Network (PINN) model was constructed. This model employs a multi-layer fully connected network structure. The input layer contains 120 features (i.e., the magnetic flux density components of 60 measurement points in the x and y directions), and the output layer contains 60 features (i.e., the current density distribution of 60 regions). The PINN network structure for this example is shown in Table 1.

[0082]

[0083] PINN input With output The equation between them is:

[0084] (12)

[0085] In the formula: This is the input matrix, representing the inputs to PINN; For PINN m The output matrix of the layer; It is the output matrix, representing the output of PINN; and They represent the PINN number mThe weights and biases of the layer parameters are the objects that the neural network needs to train; This is the non-linear activation function of neurons in PINN; in this example, the ReLU function is used:

[0086] (13)

[0087] A Dropout layer (with a dropout rate of 0.2) is introduced to prevent overfitting. The network's loss function... Data loss and physical loss Composed of two weighted parts,

[0088] (14)

[0089] (15)

[0090] In the formula, This represents the number of sampling points (current batch size) used to calculate the loss. In this example, ; The labels are matrices composed of the distribution of external magnetic fields in the sample. and The relationship shown in formula (1) above is satisfied.

[0091] In this example, the current weight factors are adaptively calculated by monitoring the training progress and the real-time data fit. Its function graph is Figure 4 As shown, the specific calculation process is as follows:

[0092] Normalize the number of training epochs to obtain the current number of training epochs. and the set total number of training rounds Calculate the normalized time Obtain the current real-time data loss item The value is set to 1. If the data loss value exceeds a preset threshold (e.g., the initial loss value), it is truncated to 1. This is then adjusted based on the real-time data loss. Calculate the dynamic decay rate factor . The value is linearly negatively correlated with the value of the data loss term, as shown in the above formula (3); in this embodiment, a fast decay constant is set. =40, slow decay constant =15. Calculate the dynamic weighting factor. The final weighting factor is calculated using the piecewise exponential decay model shown in formula (2). Among them, a data-driven saturation cutoff time is set. = 0.1, the steady-state lower limit of the weighting factor =0.4.

[0093] The PINN model is trained using the dynamic weights described above. The training process employs the Adam optimizer, with a total training cycle of [number missing]. The initial learning rate is set to 1×10⁻⁶, the batch size is 60, and the learning rate is 1×10⁻⁶. -4 The learning rate is set to decay to 0.5 times its original value every 100 epochs. The change in total loss during training is shown below. Figure 4 As shown, the model has converged. After training, the actual measured PEMFC surface scanning magnetic field data can be input into the model to quickly output the reconstructed internal current density distribution, enabling non-invasive detection of the fuel cell's operating status.

[0094] Example 2

[0095] This invention provides a method for monitoring the state of a proton exchange membrane fuel cell, including monitoring the internal current density distribution of the proton exchange membrane fuel cell, wherein the internal current density distribution of the proton exchange membrane fuel cell is obtained by the method for reconstructing the internal current density distribution of the proton exchange membrane fuel cell in the above embodiment 1.

[0096] The relevant technical solutions are the same as above, and will not be repeated here.

[0097] Example 3

[0098] This invention provides an electronic device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the methods in Embodiment 1, or Embodiment 2.

[0099] The relevant technical solutions are the same as above, and will not be repeated here.

[0100] Example 4

[0101] This invention provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the methods in Embodiment 1, or Embodiment 2.

[0102] Specifically, the memory may include high-speed random access memory, as well as non-volatile memory, such as hard disks, RAM, plug-in hard disks, smart media cards (SMC), secure digital (SD) cards, flash cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.

[0103] The relevant technical solutions are the same as above, and will not be repeated here.

[0104] Example 5

[0105] This invention provides a computer program product, including a computer program that, when run on a computer, causes the computer to perform the steps of the methods in Embodiment 1, or Embodiment 2.

[0106] The relevant technical solutions are the same as above, and will not be repeated here.

[0107] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for reconstructing the internal current density distribution of a proton exchange membrane fuel cell based on a physical information neural network, characterized in that, include: Training phase and application phase; The training phase includes: constructing an electromagnetic dataset, wherein the samples in the electromagnetic dataset include the internal current density distribution and the corresponding external magnetic field distribution of PEMFC under different operating conditions; The external magnetic field distribution in the sample is input into the physical information neural network model to obtain the predicted internal current density distribution of the PEMFC. The physical information neural network model is trained using a loss function. When the loss function converges, the trained physical information neural network model is obtained. The loss function is a weighted sum of a data loss term and a physical loss term. The data loss term is the error between the predicted internal current density distribution of the PEMFC and the internal current density distribution in the sample. The physical loss term is the error between the theoretical external magnetic field distribution calculated using the Biot-Savart law based on the predicted internal current density distribution of the PEMFC and the external magnetic field distribution in the input sample. The application phase includes: inputting the current external magnetic field distribution of the PEMFC into the trained physical information neural network model to obtain the reconstructed internal current density distribution.

2. The method for reconstructing the internal current density distribution of a proton exchange membrane fuel cell according to claim 1, characterized in that, The loss function for: in, As a dynamic weighting factor, For the current training process, For data loss items, For physical loss items, The saturation cutoff point dominated by the data loss term. For the total training cycle, This represents the steady-state lower limit of the weighting factor. For data loss items Normalized real-time data loss The dynamic decay rate factor of feedback control, and and They exhibit a linear negative correlation.

3. The method for reconstructing the internal current density distribution of a proton exchange membrane fuel cell according to claim 2, characterized in that, The dynamic decay rate factor for: in, For rapid decay constant, It is the slow decay constant. and The value of satisfies the condition within a total training cycle. Inside, It is a continuous function, and in Inside, exist It begins to decay in the neighborhood and in Decay within the neighborhood to ,exist Inside, exist Fluctuations within the neighborhood of for decay to The time point is taken from experience.

4. The method for reconstructing the internal current density distribution of a proton exchange membrane fuel cell according to any one of claims 1-3, characterized in that, The construction of the electro-magnetic dataset includes: The PEMFC is divided into n current element regions along its surface by rows and columns, and n magnetic field measurement points are set accordingly. The current density distribution of the n current element regions is measured under each operating condition, and the external magnetic field distribution of each measurement point under each operating condition is calculated according to the Biot-Savart law to obtain the constructed electro-magnetic dataset.

5. The method for reconstructing the internal current density distribution of a proton exchange membrane fuel cell according to claim 4, characterized in that, The data loss item and the physical loss term They are respectively: in, The batch size of the current training samples. The input sample matrix of the physical information neural network model is the matrix composed of the distribution of external magnetic fields in the samples. The output matrix predicted by the physical information neural network model is a matrix composed of the predicted internal current density distribution of the PEMFC. It is a matrix composed of the distribution of external magnetic fields in the sample; Let be the coefficient matrix, satisfying ;in, The current element matrix is ​​composed of the current density distribution in the electromagnetic dataset. For based on The matrix calculated using Biot-Savart's law, which consists of the theoretical external magnetic field distribution.

6. The method for reconstructing the internal current density distribution of a proton exchange membrane fuel cell according to claim 1, characterized in that, The physical information neural network model is a multi-layer fully connected neural network.

7. A method for monitoring the state of a proton exchange membrane fuel cell, characterized in that, The method includes monitoring the internal current density distribution of a proton exchange membrane fuel cell, wherein the internal current density distribution of the proton exchange membrane fuel cell is obtained using the internal current density distribution reconstruction method of the proton exchange membrane fuel cell as described in any one of claims 1-6.

8. An electronic device, characterized in that, Includes computer-readable storage media and processors; The computer-readable storage medium is used to store executable instructions; The processor is used to read executable instructions stored in the computer-readable storage medium to execute the method for reconstructing the internal current density distribution of a proton exchange membrane fuel cell based on a physical information neural network as described in any one of claims 1-6, or / and to execute the proton exchange membrane fuel cell state monitoring method as described in claim 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method for reconstructing the internal current density distribution of a proton exchange membrane fuel cell based on a physical information neural network as described in any one of claims 1-6, or / and implements the proton exchange membrane fuel cell state monitoring method as described in claim 7.

10. A computer program product, characterized in that, The method includes a computer program that, when run on a computer, causes the computer to execute the method for reconstructing the internal current density distribution of a proton exchange membrane fuel cell based on a physical information neural network as described in any one of claims 1-6, or / and to execute the method for monitoring the state of a proton exchange membrane fuel cell as described in claim 7.

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