A method and system for estimating water content in a fuel cell based on physical information neural network

Abstract

The present invention proposes a fuel cell water content estimation method and system based on a physical information neural network, which relates to the field of fuel cell technology. The method comprises: obtaining the original frequency domain impedance characteristics and the measurable variable time series of the battery to be estimated, eliminating the frequency domain redundant data in the original frequency domain impedance characteristics, obtaining the filtered frequency domain characteristics, performing equivalue mapping on the measurable variable time series to obtain an equivalue mapping sequence, and using a self-attention mechanism to process the filtered frequency domain characteristics to obtain a frequency domain self-attention feature, and performing feature connection on the equivalue mapping sequence and the frequency domain self-attention feature to obtain a spatiotemporal heterogeneous feature; the spatiotemporal heterogeneous feature is input into a trained fuel cell water content estimation model to obtain the multimodal water predicted content of the battery to be estimated output by the fuel cell water content estimation model. The present invention can not only accurately estimate the multimodal water content of the fuel cell, but also has low computational cost and strong interpretability.

Description

Technical Field

[0001] The present invention relates to the technical field of fuel cells, and in particular to a method and system for estimating water content in a fuel cell based on a physical information neural network. Background Art

[0002] Proton Exchange Membrane Fuel Cell (PEMFC) has high energy conversion efficiency and low operating temperature, and has become one of the most promising power generation systems. However, since PEMFC needs to ensure both low-level liquid water and high-level membrane water, fuel cell water management is still one of the key technical issues of PEMFC. In addition, the multimodal water inside PEMFC is not easy to measure, which increases the difficulty of implementing water management. Therefore, a corresponding high-precision and easy-to-implement multimodal water content estimation technology is needed.

[0003] At present, the methods for estimating the water content of fuel cells are mainly divided into two types: model-based and data-driven. Model-based methods include sliding mode observers, Kalman filter observers, Luenberger observers, etc. However, due to the limitations of the observer structure, these observer models are usually of low dimension and order, and are difficult to adapt to the complex operating conditions of fuel cells. The finite element calculation model will take into account the coupling of multiple physical fields inside the fuel cell, and can accurately characterize the water transport mechanisms such as two-phase flow and reverse diffusion inside the fuel cell, but its online solution process is too time-consuming and is generally only used for offline optimization design and parameter estimation. Data-driven methods usually need to first calibrate high-information input features, and then train them through architectures including reverse diffusion networks, long short-term memory networks, and Transformers, and finally output high-reliability water content prediction results, but the prediction accuracy of data-driven methods depends on input features and has poor interpretability.

[0004] Therefore, it is necessary to provide a fuel cell water content estimation method with high accuracy, low computational cost and strong interpretability. Summary of the invention

[0005] In view of this, the present invention proposes a fuel cell water content estimation method and system based on physical information neural network to solve the problem that the prediction accuracy of the current fuel cell water content estimation method depends on the input characteristics and has poor interpretability.

[0006] The technical solution of the present invention is achieved in this way:

[0007] According to a first aspect, an embodiment of the present invention provides a method for estimating water content in a fuel cell based on a physical information neural network, the method comprising:

[0008] Obtaining the original frequency domain impedance characteristics and the measurable variable time series of the battery to be estimated, eliminating the frequency domain redundant data in the original frequency domain impedance characteristics, obtaining the filtered frequency domain characteristics, performing equivalue mapping on the measurable variable time series to obtain an equivalue mapping sequence, and using the self-attention mechanism to process the filtered frequency domain characteristics to obtain frequency domain self-attention characteristics, and performing feature connection on the equivalue mapping sequence and the frequency domain self-attention characteristics to obtain spatiotemporal heterogeneous characteristics;

[0009] Inputting the spatiotemporal heterogeneous features into a trained fuel cell water content estimation model to obtain a multimodal predicted water content of the battery to be estimated output by the fuel cell water content estimation model;

[0010] The fuel cell water content estimation model uses a gradient descent method to update the weight of each hidden layer. The loss function of the fuel cell water content estimation model consists of data loss and physical information loss. The physical information loss includes a first physical information loss for characterizing information loss of voltage polarization impedance, a second physical information loss for characterizing information loss of mass transfer time impedance, and a third physical information loss for characterizing information loss of cathode charge impedance.

[0011] The fuel cell water content estimation model is trained by the following steps:

[0012] Obtaining the original frequency domain impedance characteristics of the sample, and eliminating the frequency domain redundant data in the original frequency domain impedance characteristics of the sample, to obtain the filtered sample frequency domain characteristics;

[0013] Obtaining a sample measurable variable time series, and performing equivalent mapping on the sample measurable variable time series to obtain a sample equivalent mapping sequence;

[0014] The frequency domain features of the filtered samples are processed using the self-attention mechanism to obtain the frequency domain self-attention features of the samples;

[0015] The sample equivalue mapping sequence and the sample frequency domain self-attention feature are feature-connected to obtain the sample time-frequency heterogeneous feature;

[0016] The sample time-frequency heterogeneous features are used as input data for training, and the neural network is trained using supervised learning to build a fuel cell water content estimation model.

[0017] The loss of the fuel cell water content estimation model is adjusted through an adaptive algorithm of local physical information error and a Bayesian optimization method to obtain a trained fuel cell water content estimation model.

[0018] In combination with the first aspect, in the first implementation of the first aspect, obtaining the original frequency domain impedance characteristics of the sample and eliminating the frequency domain redundant data in the original frequency domain impedance characteristics of the sample to obtain the filtered sample frequency domain characteristics specifically includes:

[0019] Obtain the original frequency domain impedance characteristics of the sample;

[0020] The original frequency domain impedance characteristics of the sample are amplified by using the Akima interpolation method to obtain the sample amplified frequency domain impedance characteristics; the sample amplified frequency domain impedance characteristics include the sample frequency domain impedance amplified data obtained after amplification and the sample multimodal water amplified data;

[0021] Obtain the Pearson correlation coefficient between the sample frequency domain impedance amplification data and the sample multimodal water amplification data;

[0022] According to the Pearson coefficient, the sensitivity of each frequency domain impedance in the sample amplification frequency domain impedance characteristics is determined;

[0023] According to the sensitivity calculation result, the frequency domain redundant data in the original frequency domain impedance characteristics of the sample are eliminated to obtain the filtered sample frequency domain characteristics; the frequency domain redundant data includes the sample frequency sequence in the original frequency domain impedance characteristics of the sample and the sample impedance sequence below the preset sensitivity.

[0024] In combination with the first embodiment of the first aspect, in the second embodiment of the first aspect, the calculation formula of the Pearson correlation coefficient is:

[0025]

[0026] in, Represents the frequency domain impedance characteristics of the sample amplification Middle Sensitivity of column frequency domain impedance; Indicates Column sample frequency domain impedance amplification data Multimodal water augmentation data with samples Pearson correlation coefficient between ; Indicates Column feature frequency amplification data Multimodal water augmentation data with samples The Pearson correlation coefficient between .

[0027] In combination with the second implementation of the first aspect, in the third implementation of the first aspect, the calculation formula of the sensitivity is:

[0028]

[0029] in, Represents the frequency domain impedance characteristics of the sample amplification Middle Sensitivity of column frequency domain impedance; Indicates Column sample frequency domain impedance amplification data Multimodal water augmentation data with samples Pearson correlation coefficient between ; Indicates Column feature frequency amplification data Multimodal water augmentation data with samples The Pearson correlation coefficient between .

[0030] In combination with the first aspect, in a fourth implementation of the first aspect, the method of using the self-attention mechanism to process the filtered sample frequency domain features to obtain the sample frequency domain self-attention features specifically includes:

[0031] Introducing position encoding into the self-attention mechanism based on SoftMax probability distribution;

[0032] The self-attention mechanism with position encoding is used to capture the internal correlation between the frequency domain features of the filtered samples, and the sample frequency domain self-attention features are obtained.

[0033] In combination with the first aspect, in a fifth implementation of the first aspect, the loss function of the fuel cell water content estimation model is:

[0034]

[0035] in, Indicates data loss; Represents the first loss weight, which is the data loss The corresponding loss weight; Indicates the first physical information loss; represents the second loss weight, which is the first physical information loss The corresponding loss weight; Indicates second physical information loss; Represents the third loss weight, which is the second physical information loss The corresponding loss weight; Indicates third physical information loss; Represents the fourth loss weight, which is the third physical information loss the corresponding loss weights; and .

[0036] In combination with the first aspect, in a sixth implementation of the first aspect, the physical information loss is obtained by the following steps:

[0037] Determine data loss based on the multimodal water true content and the multimodal water predicted content;

[0038] determining a first physical information loss according to the proton exchange membrane fuel cell voltage and the real voltage;

[0039] Determine the second physical information loss according to the equivalent diffusion time and the actual time;

[0040] The third physical information loss is determined based on the cathode charge transfer admittance and the cathode real charge.

[0041] According to a second aspect, an embodiment of the present invention further provides a fuel cell water content estimation system based on a physical information neural network, the system comprising:

[0042] A data acquisition module is used to obtain the original frequency domain impedance characteristics and the measurable variable time series of the battery to be estimated, eliminate the frequency domain redundant data in the original frequency domain impedance characteristics, obtain the filtered frequency domain characteristics, perform equivalue mapping on the measurable variable time series to obtain an equivalue mapping sequence, and use the self-attention mechanism to process the filtered frequency domain characteristics to obtain frequency domain self-attention characteristics, and perform feature connection on the equivalue mapping sequence and the frequency domain self-attention characteristics to obtain spatiotemporal heterogeneous characteristics;

[0043] A data prediction module, used for inputting the spatiotemporal heterogeneous features into a trained fuel cell water content estimation model to obtain a multimodal water prediction content of a battery to be estimated output by the fuel cell water content estimation model;

[0044] The fuel cell water content estimation model uses a gradient descent method to update the weight of each hidden layer. The loss function of the fuel cell water content estimation model consists of data loss and physical information loss. The physical information loss includes a first physical information loss for characterizing information loss of voltage polarization impedance, a second physical information loss for characterizing information loss of mass transfer time impedance, and a third physical information loss for characterizing information loss of cathode charge impedance.

[0045] The fuel cell water content estimation model is trained by the following steps:

[0046] Obtaining the original frequency domain impedance characteristics of the sample, and eliminating the frequency domain redundant data in the original frequency domain impedance characteristics of the sample, to obtain the filtered sample frequency domain characteristics;

[0047] Obtaining a sample measurable variable time series, and performing equivalent mapping on the sample measurable variable time series to obtain a sample equivalent mapping sequence;

[0048] The frequency domain features of the filtered samples are processed using the self-attention mechanism to obtain the frequency domain self-attention features of the samples;

[0049] The sample equivalue mapping sequence and the sample frequency domain self-attention feature are feature-connected to obtain the sample time-frequency heterogeneous feature;

[0050] The sample time-frequency heterogeneous features are used as input data for training, and the neural network is trained using supervised learning to build a fuel cell water content estimation model.

[0051] The loss of the fuel cell water content estimation model is adjusted through an adaptive algorithm of local physical information error and a Bayesian optimization method to obtain a trained fuel cell water content estimation model.

[0052] According to the third aspect, an embodiment of the present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of any of the above-mentioned methods for estimating the water content of a fuel cell based on a physical information neural network are implemented.

[0053] According to a fourth aspect, an embodiment of the present invention further provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of any of the above-described methods for estimating the water content of a fuel cell based on a physical information neural network.

[0054] According to a fifth aspect, an embodiment of the present invention further provides a computer program product, comprising a computer program, which, when executed by a processor, implements the steps of the fuel cell water content estimation method based on a physical information neural network as described in any one of the above items.

[0055] The fuel cell water content estimation method and system based on physical information neural network of the present invention has the following beneficial effects compared with the prior art:

[0056] By inputting the target image into the trained fuel cell water content estimation model, and by inputting the spatiotemporal heterogeneous features into the trained fuel cell water content estimation model, the multimodal water predicted content of the battery to be estimated output by the fuel cell water content estimation model is obtained, wherein the spatiotemporal heterogeneous features are obtained by equivalue mapping the time series of measurable variables and processing the frequency domain features of the filtered samples using the self-attention mechanism, and feature connecting the processed features. For the original frequency domain impedance features, the frequency domain redundant information is filtered out by global sensitivity analysis based on the Pearson correlation coefficient to obtain the filtered frequency domain features. Then, for the external measurable variable time series and the filtered frequency domain features, the equivalue mapping technology and the self-attention mechanism based on position encoding are used respectively and sequentially connected to obtain the spatiotemporal heterogeneous features. In this way, the multimodal water content of the battery to be estimated can be estimated with high precision and high interpretability at a low implementation cost, providing a reliable benchmark value for precise water management inside the fuel cell. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0058] Figure 1 It is a flow chart of a method for estimating water content in a fuel cell based on a physical information neural network of the present invention;

[0059] Figure 2 A schematic diagram of a flow chart of estimating multi-modal water content prediction using a fuel cell water content estimation method based on a physical information neural network according to the present invention;

[0060] Figure 3 It is a schematic diagram of the flow of training a fuel cell water content estimation model in the fuel cell water content estimation method based on physical information neural network of the present invention;

[0061] Figure 4 It is a structural schematic diagram of a PEMFC model used in training data in the method for estimating water content in a fuel cell based on a physical information neural network of the present invention;

[0062] Figure 5 It is a schematic diagram of the original frequency domain impedance characteristics of the sample in the fuel cell water content estimation method based on physical information neural network of the present invention;

[0063] Figure 6 The schematic diagram of the structure of the fuel cell water content estimation system based on the physical information neural network provided by the present invention is shown;

[0064] Figure 7 It is a schematic diagram of the hardware structure of the electronic device provided in the embodiment of the present application. DETAILED DESCRIPTION

[0065] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0066] PEMFC has high energy conversion efficiency and low operating temperature, and has become one of the most promising power generation systems. However, since PEMFC needs to ensure both low-level liquid water and higher-level membrane water, fuel cell water management is still one of the key technical issues of PEMFC. In addition, it is not easy to measure the multimodal water inside PEMFC, which increases the difficulty of implementing water management. Therefore, a corresponding high-precision and easy-to-implement multimodal water content estimation technology is needed.

[0067] At present, the methods for estimating the water content of fuel cells are mainly divided into two types: model-based and data-driven. Model-based methods include sliding mode observers, Kalman filter observers, Luenberger observers, etc. However, due to the limitations of the observer structure, these observer models are usually of low dimension and order, and are difficult to adapt to the complex operating conditions of fuel cells. The finite element calculation model will take into account the coupling of multiple physical fields inside the fuel cell, and can accurately characterize the water transport mechanisms such as two-phase flow and reverse diffusion inside the fuel cell, but its online solution process is too time-consuming and is generally only used for offline optimization design and parameter estimation. Data-driven methods usually need to first calibrate high-information input features, and then train them through architectures including reverse diffusion networks, long short-term memory networks, and Transformers, and finally output high-reliability water content prediction results, but the prediction accuracy of data-driven methods depends on input features and has poor interpretability.

[0068] In summary, how to provide a fuel cell water content estimation method with high accuracy, low computational cost and strong interpretability is an important issue that needs to be urgently addressed in the industry.

[0069] The method for estimating the water content of a fuel cell based on a physical information neural network provided in this specification can be applied to electronic devices with data processing capabilities. The electronic devices may include notebooks, desktop computers, smart phones, smart wearable devices (virtual reality glasses, smart watches, etc.), tablet computers, etc. Of course, the method for estimating the water content of a fuel cell based on a physical information neural network provided in this specification can also be applied to applications running in the above-mentioned electronic devices. For example, the method for estimating the water content of a fuel cell based on a physical information neural network can be applied to a browser with data processing capabilities, or it can be applied to processing software with data processing capabilities.

[0070] See also Figure 1 and Figure 2 , Figure 1 The flowchart of the method for estimating water content in a fuel cell based on a physical information neural network according to an embodiment of the present invention is shown. Figure 2 A schematic diagram of a process for estimating a multi-modal predicted water content in a fuel cell water content estimation method based on a physical information neural network according to an embodiment of the present invention is shown. The method may include the following steps:

[0071] S101. Obtain the original frequency domain impedance characteristics and the measurable variable time series of the battery to be estimated, eliminate the frequency domain redundant data in the original frequency domain impedance characteristics, obtain the filtered frequency domain characteristics, perform equivalue mapping on the measurable variable time series to obtain an equivalue mapping sequence, and use the self-attention mechanism to process the filtered frequency domain characteristics to obtain frequency domain self-attention characteristics, and perform feature connection on the equivalue mapping sequence and the frequency domain self-attention characteristics to obtain spatiotemporal heterogeneous characteristics.

[0072] S102, inputting the spatiotemporal heterogeneous features into a trained fuel cell water content estimation model to obtain a multimodal predicted water content of the battery to be estimated output by the fuel cell water content estimation model.

[0073] Among them, see Figure 3 , the training process of the fuel cell water content estimation model is:

[0074] S103, obtaining the original frequency domain impedance characteristics of the sample, and eliminating the frequency domain redundant data in the original frequency domain impedance characteristics of the sample, to obtain the filtered sample frequency domain characteristics.

[0075] The sample original frequency domain impedance features include sample frequency domain impedance original data and sample multimodal water original data. The sample frequency domain impedance original data and the sample multimodal water original data are used together as the sample original frequency domain impedance features, and the sample original frequency domain impedance features are used as one of the input data required for model training. Similarly, the sample frequency domain impedance original data and the sample multimodal water original data can be stored in the electronic device in advance, or they can be obtained by the electronic device from the outside. There is no restriction on the specific acquisition form of the sample frequency domain impedance original data and the sample multimodal water original data. It is only necessary to ensure that the electronic device can obtain the sample frequency domain impedance original data and the sample multimodal water original data.

[0076] Preferably, the sample DRT raw data obtained based on the DRT method is used as the sample frequency domain impedance raw data. Figure 4 As shown in the figure, the PEMFC model is obtained by coupling multiple physical fields such as gas diffusion, multimodal water transport, charge transfer and heat transfer. The PEMFC model is the source of multimodal water content and operating parameters. Typical operating conditions are designed in the PEMFC model and key time domain parameters of the model are extracted. The original frequency domain impedance data of the samples extracted by the Distribution of Relaxation Times (DRT) can be used for multimodal water content estimation of membrane water content and liquid water saturation.

[0077] In this way, a sample frequency domain impedance raw data set is obtained and a sample multimodal water data dataset ,in, Indicates Sample frequency domain raw data, Indicates Sample multimodal water data, represents the liquid water saturation in multimodal water, represents the membrane water content in multimodal water, represents the number of identifiable polarization processes, Represents the total number of sample data. Figure 5 As shown, the original frequency domain impedance characteristics of the sample exist A recognizable polarization process.

[0078] In order to eliminate redundant data in the frequency domain, in this embodiment, a global sensitivity analysis based on the Pearson correlation coefficient is used, focusing on the two main characteristic peak resistances of the DRT peak in the original frequency domain impedance characteristics of the sample. Frequency corresponding to peak resistance , in order to perform feature screening, that is, focus on ,in, represents the peak resistance, Indicates The frequency corresponding to the peak resistance. Accordingly, step S103 specifically includes:

[0079] S1031. Obtain original frequency domain impedance characteristics of the sample.

[0080] S1032: Amplify the original frequency domain impedance characteristics of the sample using the Akima interpolation method to obtain the sample amplified frequency domain impedance characteristics. The sample amplified frequency domain impedance characteristics include the sample frequency domain impedance amplified data obtained after amplification and the sample multimodal water amplified data.

[0081] For each operating condition data in the sample original frequency domain impedance characteristics First, the Akima interpolation method is used to convert the working condition data Amplification of frequency domain impedance characteristics for samples .in, represents the sample frequency domain impedance amplification data, represents the multimodal water amplification data of the sample, more specifically, , , .

[0082] S1033, obtaining the Pearson correlation coefficient between the sample frequency domain impedance amplification data and the sample multimodal water amplification data. Sample frequency domain impedance amplification data Multimodal water augmentation data with samples The Pearson correlation coefficient between can be expressed as:

[0083] (1)

[0084] In formula (1), Represents sample frequency domain impedance amplification data Multimodal water augmentation data with samples Pearson correlation coefficient between ; Represents sample frequency domain impedance amplification data The Column data; Represents sample multimodal water augmentation data The Column data; Represents sample frequency domain impedance amplification data The average value of Represents sample multimodal water augmentation data The average value of .

[0085] S1034. Determine the frequency domain impedance characteristics of the sample amplification according to the Pearson coefficient The sensitivity of each impedance in the frequency domain.

[0086] for Sequence number The sensitivity of the column frequency domain impedance can be expressed as:

[0087] (2)

[0088] In formula (2), Represents the frequency domain impedance characteristics of the sample amplification Middle Sensitivity of column frequency domain impedance; Indicates Column sample frequency domain impedance amplification data Multimodal water augmentation data with samples Pearson correlation coefficient between ; Indicates Column feature frequency amplification data Multimodal water augmentation data with samples The Pearson correlation coefficient between .

[0089] Preferably, and Respectively and Achieve maximum sensitivity.

[0090] S1035. According to the sensitivity calculation result, the frequency domain redundant data in the original frequency domain impedance characteristics of the sample are eliminated to obtain the filtered sample frequency domain characteristics. The frequency domain redundant data includes the sample frequency sequence in the original frequency domain impedance characteristics of the sample and the sample impedance sequence below the preset sensitivity. Since the multimodal water contains two variables, by calculating the maximum sensitivity optimum, two corresponding optimal values ​​will be obtained, namely:

[0091] (3)

[0092] In formula (3), Represents the frequency domain characteristics of the sample after screening; Indicates the highest peak impedance of liquid water sensitivity; Represents the highest peak impedance of membrane water sensitivity. After screening, the sample frequency domain characteristics finally include the two optimal values ​​of the highest peak impedance of liquid water sensitivity and the highest peak impedance of membrane water sensitivity.

[0093] S104. Obtaining sample measurable variable time series , and for the sample measurable variable time series Perform equal-value mapping to obtain a sample equal-value mapping sequence .

[0094] The sample measurable variable time series is also used as one of the input data required for model training. The sample measurable variable time series can be stored in the electronic device in advance, or it can be obtained by the electronic device from the outside. There is no restriction on the specific acquisition form of the sample measurable variable time series, as long as the electronic device can obtain the sample measurable variable time series.

[0095] In this embodiment, by comprehensively collecting the original frequency domain impedance characteristics of the samples and the time series of the measurable variables of the samples as sample data, a massive amount of data support is provided for the training of the model.

[0096] Specifically, , where Sample anode pressure data, represents the sample cathode pressure data, Represents the sample excess oxygen ratio data, represents the sample anode temperature data, represents the sample cathode temperature data, represents the sample anode humidity data, represents the sample cathode humidity data, Represents sample current data.

[0097] In this embodiment, the equivalent mapping technology is used to match the time-frequency feature dimension. The mapped time feature is the sample equivalent mapping sequence. It can be expressed as:

[0098] (4)

[0099] In formula (4), The weight matrix representing the equivalue map; represents the bias of the iso-map; Represents the sigmoid activation function.

[0100] S105. Use the self-attention mechanism to process the frequency domain features of the filtered samples Get the sample frequency domain self-attention feature .

[0101] In this embodiment, position encoding is introduced into the self-attention mechanism so that the self-attention mechanism can handle the distance between the characteristic frequencies of multimodal water contents.

[0102] Accordingly, step S105 specifically includes:

[0103] S1051. Introduce position encoding in the self-attention mechanism based on SoftMax probability distribution.

[0104] S1052. Use the self-attention mechanism introduced by position encoding to capture the frequency domain characteristics of the filtered samples The internal correlation between them is used to obtain the sample frequency domain self-attention feature .

[0105] According to the query matrix , key matrix and the value matrix , self-attention output based on SoftMax probability distribution It can be expressed as:

[0106] (5)

[0107] In formula (5), Represents the key matrix The transpose of represents the scaling factor, is the key matrix Dimension.

[0108] Self-attention mechanism can capture frequency sequences The internal correlation between them maps a query and a set of key-value pairs to an output matrix.

[0109] In the traditional self-attention output Position encoding is also introduced on the basis of , so that the self-attention mechanism can take into account the distance between the characteristic frequencies of multimodal water content, specifically:

[0110] (6)

[0111] In formula (6), Indicates The frequency corresponding to each peak resistance is normalized.

[0112] Sample frequency domain self-attention feature data set Can be expressed as .

[0113] S106, mapping the sample to a sequence And sample frequency domain self-attention features Perform feature connection to obtain sample time-frequency heterogeneous features .

[0114] In order to fuse the time-frequency heterogeneous features of samples, the sample equivalent mapping sequence And sample frequency domain self-attention features are directly connected sequentially as sample time-frequency heterogeneous features .

[0115] S107, sample time-frequency heterogeneous features As the input data for training, the neural network is trained using supervised learning to construct a weight matrix and the bias vector has Hidden Layers Physical Informed Neutral Network (PINN) is used to obtain a fuel cell water content estimation model, which is used to predict the multi-modal water content of the fuel cell to be estimated. :

[0116] (7)

[0117] In formula (7), , special .

[0118] The fuel cell water content estimation model uses the gradient descent method to update the weight of each hidden layer, where the first Hidden Layer Time weight matrix The update method is:

[0119] (8)

[0120] In formula (8), represents the learning rate; represents the loss function.

[0121] In this embodiment, the loss function Is caused by data loss and physical information loss , and Composition, among which, represents the first physical information loss, which is the information loss of voltage polarization impedance, represents the second physical information loss, which is the information loss of mass transfer time impedance, It represents the third physical information loss, which is the information loss of cathode charge impedance, specifically:

[0122] (9)

[0123] In formula (9), represents the first loss weight, which is The corresponding loss weight; represents the second loss weight, which is The corresponding loss weight; represents the third loss weight, which is The corresponding loss weight; represents the fourth loss weight, which is The corresponding loss weight. And satisfy .

[0124] More specifically, the data loss mentioned above , physical information loss , and It is calculated by:

[0125] Determine the data loss based on the multimodal water true content and the multimodal water predicted content:

[0126] (10)

[0127] In formula (10), Represents the true multimodal water content.

[0128] According to the PEMFC voltage and the real voltage, determine the first physical information loss:

[0129] (11)

[0130] In formula (11), Indicates the actual voltage.

[0131] Determine the second physical information loss based on the equivalent diffusion time and the actual time:

[0132] (12)

[0133] In formula (12), Indicates the actual time.

[0134] According to the cathode charge transfer admittance and the cathode real charge, the third physical information loss is determined:

[0135] (13)

[0136] In formula (13), Indicates the real charge of the cathode.

[0137] Among them, PEMFC voltage It can be obtained by:

[0138] (14)

[0139] In formula (14), represents the reversible voltage, ; represents the activation loss parameter; represents the Ohm loss parameter; represents the concentration loss parameter; Indicates The activity of the gas and the activity of the liquid are both 1; represents the gas constant; Indicates PEMFC temperature; represents the Faraday constant; Indicates the battery reference temperature; Indicates the liquid water saturation gradient calculation; represents the observed value of membrane water content obtained after being processed by the fuel cell water content estimation model; represents the observed value of liquid water saturation obtained after being processed by the fuel cell water content estimation model; represents the hydrogen observation value obtained after being processed by the fuel cell water content estimation model.

[0140] Superscript Represents physical information neural network observations.

[0141] Equivalent diffusion time It can be obtained in the following way.

[0142] (15)

[0143] In formula (15), represents the equivalent diffusion coefficient, , ; represents the minimum order that satisfies the accuracy requirement of formula (11); represents the error factor, i.e. ; Indicates the battery reference pressure; Indicates The coefficient of the correction term.

[0144] Current density in the BV equation for the cathode half reaction Find the cathode overpotential The partial derivative of the cathode charge transfer admittance is , the related expressions are:

[0145] (16)

[0146] In formula (16), Indicates the oxygen concentration in the catalyst layer; Indicates the reference oxygen concentration; It represents the cathode oxidation coefficient; represents the reduction charge transfer coefficient; Represents the observed value of oxygen concentration in the catalyst layer after being processed by the fuel cell water content estimation model.

[0147] S108. In order to improve the accuracy and prediction stability of the fuel cell water content estimation model, in this embodiment, the loss of the fuel cell water content estimation model is adjusted by an adaptive algorithm of local physical information error and a Bayesian optimization method. to , and obtain a trained fuel cell water content estimation model.

[0148] Adaptive coarse adjustment algorithm to determine initial weight value , , and :

[0149] (17)

[0150] In formula (17), express The initial value of loss.

[0151] Considering formula (8) as the mean The variance is Gaussian process, that is:

[0152] (18)

[0153] In formula (18), Represents Gaussian operation.

[0154] For working condition data , the maximum likelihood estimation of the objective function can be expressed as:

[0155] (19)

[0156] In formula (19), represents maximum likelihood.

[0157] Afterwards, the posterior distribution can be obtained using Bayes’ theorem, and the next sample point can be selected by maximizing the expected improvement strategy:

[0158] (20)

[0159] In formula (20), .

[0160] The fuel cell water content estimation method based on physical information neural network of the present invention obtains the multimodal water predicted content of the battery to be estimated output by the fuel cell water content estimation model by inputting spatiotemporal heterogeneous features into the trained fuel cell water content estimation model, wherein the spatiotemporal heterogeneous features are obtained by performing equivalue mapping on the time series of measurable variables and processing the frequency domain features of the filtered samples using a self-attention mechanism, and performing feature connection on the processed features. For the original frequency domain impedance features, the frequency domain redundant information is filtered by global sensitivity analysis based on the Pearson correlation coefficient to obtain the filtered frequency domain features. Then, for the external measurable variable time series and the filtered frequency domain features, the equivalue mapping technology and the self-attention mechanism based on position coding are respectively used and sequentially connected to obtain the spatiotemporal heterogeneous features. In this way, the multimodal water content estimation of the battery to be estimated with high precision and high interpretability can be achieved under the premise of low implementation cost, providing a reliable benchmark value for precise water management inside the fuel cell.

[0161] The following describes a system provided by an embodiment of the present invention. The system described below and the method described above can be referenced to each other.

[0162] See also Figure 6 , Figure 6 The structure diagram of the fuel cell water content estimation system based on physical information neural network according to an embodiment of the present invention is shown. The system may include:

[0163] The data acquisition module 10 is used to obtain the original frequency domain impedance characteristics and the measurable variable time series of the battery to be estimated, eliminate the frequency domain redundant data in the original frequency domain impedance characteristics, obtain the filtered frequency domain characteristics, perform equivalue mapping on the measurable variable time series to obtain an equivalue mapping sequence, and use the self-attention mechanism to process the filtered frequency domain characteristics to obtain frequency domain self-attention characteristics, and perform feature connection on the equivalue mapping sequence and the frequency domain self-attention characteristics to obtain spatiotemporal heterogeneous characteristics.

[0164] The data prediction module 20 is used to input the spatiotemporal heterogeneous features into the trained fuel cell water content estimation model to obtain the multimodal water content prediction of the battery to be estimated output by the fuel cell water content estimation model.

[0165] The fuel cell water content estimation system based on physical information neural network of the present invention obtains the multimodal water predicted content of the battery to be estimated output by the fuel cell water content estimation model by inputting spatiotemporal heterogeneous features into the trained fuel cell water content estimation model, wherein the spatiotemporal heterogeneous features are obtained by performing equivalue mapping on the time series of measurable variables and processing the frequency domain features of the filtered samples using a self-attention mechanism, and performing feature connection on the processed features. For the original frequency domain impedance features, the frequency domain redundant information is filtered by global sensitivity analysis based on the Pearson correlation coefficient to obtain the filtered frequency domain features. Then, for the external measurable variable time series and the filtered frequency domain features, the equivalue mapping technology and the self-attention mechanism based on position coding are respectively used and sequentially connected to obtain the spatiotemporal heterogeneous features. In this way, the multimodal water content estimation of the battery to be estimated with high precision and high interpretability can be achieved under the premise of low implementation cost, providing a reliable benchmark value for precise water management inside the fuel cell.

[0166] Figure 7 An example of a physical structure diagram of an electronic device is shown in FIG. Figure 7 As shown, the electronic device may include: a processor 710 (processor), a communication interface 720 (Communications Interface), a memory 730 (memory) and a communication bus 740, wherein the processor 710, the communication interface 720, and the memory 730 communicate with each other through the communication bus 740. The processor 710 may call the logic command in the memory 730 to execute the fuel cell water content estimation method based on the physical information neural network, and the method includes:

[0167] Obtaining the original frequency domain impedance characteristics and the measurable variable time series of the battery to be estimated, eliminating the frequency domain redundant data in the original frequency domain impedance characteristics, obtaining the filtered frequency domain characteristics, performing equivalue mapping on the measurable variable time series to obtain an equivalue mapping sequence, and using the self-attention mechanism to process the filtered frequency domain characteristics to obtain frequency domain self-attention characteristics, and performing feature connection on the equivalue mapping sequence and the frequency domain self-attention characteristics to obtain spatiotemporal heterogeneous characteristics;

[0168] Inputting the spatiotemporal heterogeneous features into a trained fuel cell water content estimation model to obtain a multimodal predicted water content of the battery to be estimated output by the fuel cell water content estimation model;

[0169] The fuel cell water content estimation model uses a gradient descent method to update the weight of each hidden layer. The loss function of the fuel cell water content estimation model consists of data loss and physical information loss. The physical information loss includes a first physical information loss for characterizing information loss of voltage polarization impedance, a second physical information loss for characterizing information loss of mass transfer time impedance, and a third physical information loss for characterizing information loss of cathode charge impedance.

[0170] The fuel cell water content estimation model is trained by the following steps:

[0171] Obtaining the original frequency domain impedance characteristics of the sample, and eliminating the frequency domain redundant data in the original frequency domain impedance characteristics of the sample, to obtain the filtered sample frequency domain characteristics;

[0172] Obtaining a sample measurable variable time series, and performing equivalent mapping on the sample measurable variable time series to obtain a sample equivalent mapping sequence;

[0173] The frequency domain features of the filtered samples are processed using the self-attention mechanism to obtain the frequency domain self-attention features of the samples;

[0174] The sample equivalue mapping sequence and the sample frequency domain self-attention feature are feature-connected to obtain the sample time-frequency heterogeneous feature;

[0175] The sample time-frequency heterogeneous features are used as input data for training, and the neural network is trained using supervised learning to build a fuel cell water content estimation model.

[0176] The loss of the fuel cell water content estimation model is adjusted through an adaptive algorithm of local physical information error and a Bayesian optimization method to obtain a trained fuel cell water content estimation model.

[0177] In addition, the logic instructions in the above-mentioned memory 730 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when it is sold or used as an independent product. Based on this understanding, the technical solution of the present invention can be essentially or partly embodied in the form of a software product that contributes to the prior art. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memor), random access memory (RAM, Random Access Memory), disk or optical disk, etc. Various media that can store program codes.

[0178] On the other hand, the present invention further provides a computer program product, the computer program product comprising a computer program stored on a non-transitory computer-readable storage medium, the computer program comprising program instructions, when the program instructions are executed by a computer, the computer can execute the fuel cell water content estimation method based on a physical information neural network provided by the above methods, the method comprising:

[0179] Obtaining the original frequency domain impedance characteristics and the measurable variable time series of the battery to be estimated, eliminating the frequency domain redundant data in the original frequency domain impedance characteristics, obtaining the filtered frequency domain characteristics, performing equivalue mapping on the measurable variable time series to obtain an equivalue mapping sequence, and using the self-attention mechanism to process the filtered frequency domain characteristics to obtain frequency domain self-attention characteristics, and performing feature connection on the equivalue mapping sequence and the frequency domain self-attention characteristics to obtain spatiotemporal heterogeneous characteristics;

[0180] Inputting the spatiotemporal heterogeneous features into a trained fuel cell water content estimation model to obtain a multimodal predicted water content of the battery to be estimated output by the fuel cell water content estimation model;

[0181] The fuel cell water content estimation model uses a gradient descent method to update the weight of each hidden layer. The loss function of the fuel cell water content estimation model consists of data loss and physical information loss. The physical information loss includes a first physical information loss for characterizing information loss of voltage polarization impedance, a second physical information loss for characterizing information loss of mass transfer time impedance, and a third physical information loss for characterizing information loss of cathode charge impedance.

[0182] The fuel cell water content estimation model is trained by the following steps:

[0183] Obtaining the original frequency domain impedance characteristics of the sample, and eliminating the frequency domain redundant data in the original frequency domain impedance characteristics of the sample, to obtain the filtered sample frequency domain characteristics;

[0184] Obtaining a sample measurable variable time series, and performing equivalent mapping on the sample measurable variable time series to obtain a sample equivalent mapping sequence;

[0185] The frequency domain features of the filtered samples are processed using the self-attention mechanism to obtain the frequency domain self-attention features of the samples;

[0186] The sample equivalue mapping sequence and the sample frequency domain self-attention feature are feature-connected to obtain the sample time-frequency heterogeneous feature;

[0187] The sample time-frequency heterogeneous features are used as input data for training, and the neural network is trained using supervised learning to build a fuel cell water content estimation model.

[0188] The loss of the fuel cell water content estimation model is adjusted through an adaptive algorithm of local physical information error and a Bayesian optimization method to obtain a trained fuel cell water content estimation model.

[0189] In another aspect, the present invention further provides a non-transitory computer-readable storage medium having a computer program stored thereon, which is implemented when the computer program is executed by a processor to perform the above-mentioned method for estimating the water content of a fuel cell based on a physical information neural network, the method comprising:

[0190] Obtaining the original frequency domain impedance characteristics and the measurable variable time series of the battery to be estimated, eliminating the frequency domain redundant data in the original frequency domain impedance characteristics, obtaining the filtered frequency domain characteristics, performing equivalue mapping on the measurable variable time series to obtain an equivalue mapping sequence, and using the self-attention mechanism to process the filtered frequency domain characteristics to obtain frequency domain self-attention characteristics, and performing feature connection on the equivalue mapping sequence and the frequency domain self-attention characteristics to obtain spatiotemporal heterogeneous characteristics;

[0191] Inputting the spatiotemporal heterogeneous features into a trained fuel cell water content estimation model to obtain a multimodal predicted water content of the battery to be estimated output by the fuel cell water content estimation model;

[0192] The fuel cell water content estimation model uses a gradient descent method to update the weight of each hidden layer. The loss function of the fuel cell water content estimation model consists of data loss and physical information loss. The physical information loss includes a first physical information loss for characterizing information loss of voltage polarization impedance, a second physical information loss for characterizing information loss of mass transfer time impedance, and a third physical information loss for characterizing information loss of cathode charge impedance.

[0193] The fuel cell water content estimation model is trained by the following steps:

[0194] Obtaining the original frequency domain impedance characteristics of the sample, and eliminating the frequency domain redundant data in the original frequency domain impedance characteristics of the sample, to obtain the filtered sample frequency domain characteristics;

[0195] Obtaining a sample measurable variable time series, and performing equivalent mapping on the sample measurable variable time series to obtain a sample equivalent mapping sequence;

[0196] The frequency domain features of the filtered samples are processed using the self-attention mechanism to obtain the frequency domain self-attention features of the samples;

[0197] The sample equivalue mapping sequence and the sample frequency domain self-attention feature are feature-connected to obtain the sample time-frequency heterogeneous feature;

[0198] The sample time-frequency heterogeneous features are used as input data for training, and the neural network is trained using supervised learning to build a fuel cell water content estimation model.

[0199] The loss of the fuel cell water content estimation model is adjusted through an adaptive algorithm of local physical information error and a Bayesian optimization method to obtain a trained fuel cell water content estimation model.

[0200] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0201] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for estimating water content in a fuel cell based on a physical information neural network, characterized in that: The method comprises: Obtaining the original frequency domain impedance characteristics and the measurable variable time series of the battery to be estimated, eliminating the frequency domain redundant data in the original frequency domain impedance characteristics, obtaining the filtered frequency domain characteristics, performing equivalue mapping on the measurable variable time series to obtain an equivalue mapping sequence, and using the self-attention mechanism to process the filtered frequency domain characteristics to obtain frequency domain self-attention characteristics, and performing feature connection on the equivalue mapping sequence and the frequency domain self-attention characteristics to obtain spatiotemporal heterogeneous characteristics; Inputting the spatiotemporal heterogeneous features into a trained fuel cell water content estimation model to obtain a multimodal predicted water content of the battery to be estimated output by the fuel cell water content estimation model; The fuel cell water content estimation model uses a gradient descent method to update the weight of each hidden layer. The loss function of the fuel cell water content estimation model consists of data loss and physical information loss. The physical information loss includes a first physical information loss for characterizing information loss of voltage polarization impedance, a second physical information loss for characterizing information loss of mass transfer time impedance, and a third physical information loss for characterizing information loss of cathode charge impedance. The fuel cell water content estimation model is trained by the following steps: Obtaining the original frequency domain impedance characteristics of the sample, and eliminating the frequency domain redundant data in the original frequency domain impedance characteristics of the sample, to obtain the filtered sample frequency domain characteristics; Obtaining a sample measurable variable time series, and performing equivalent mapping on the sample measurable variable time series to obtain a sample equivalent mapping sequence; The frequency domain features of the filtered samples are processed using the self-attention mechanism to obtain the frequency domain self-attention features of the samples; The sample equivalue mapping sequence and the sample frequency domain self-attention feature are feature-connected to obtain the sample time-frequency heterogeneous feature; The sample time-frequency heterogeneous features are used as input data for training, and the neural network is trained using supervised learning to build a fuel cell water content estimation model. The loss of the fuel cell water content estimation model is adjusted through an adaptive algorithm of local physical information error and a Bayesian optimization method to obtain a trained fuel cell water content estimation model.

2. The method for estimating water content in a fuel cell based on a physical information neural network according to claim 1, characterized in that: The method of obtaining the original frequency domain impedance characteristics of the sample and eliminating the frequency domain redundant data in the original frequency domain impedance characteristics of the sample to obtain the filtered sample frequency domain characteristics specifically includes: Obtain the original frequency domain impedance characteristics of the sample; The original frequency domain impedance characteristics of the sample are amplified by using the Akima interpolation method to obtain the sample amplified frequency domain impedance characteristics; the sample amplified frequency domain impedance characteristics include the sample frequency domain impedance amplified data obtained after amplification and the sample multimodal water amplified data; Obtain the Pearson correlation coefficient between the sample frequency domain impedance amplification data and the sample multimodal water amplification data; According to the Pearson coefficient, the sensitivity of each frequency domain impedance in the sample amplification frequency domain impedance characteristics is determined; According to the sensitivity calculation result, the frequency domain redundant data in the original frequency domain impedance characteristics of the sample are eliminated to obtain the filtered sample frequency domain characteristics; the frequency domain redundant data includes the sample frequency sequence in the original frequency domain impedance characteristics of the sample and the sample impedance sequence below the preset sensitivity.

3. The method for estimating water content in a fuel cell based on a physical information neural network according to claim 2, characterized in that: The calculation formula of the Pearson correlation coefficient is: ； in, represents the sample frequency domain impedance amplification data; Represents the sample multimodal water amplification data; Represents sample frequency domain impedance amplification data Multimodal water augmentation data with samples Pearson correlation coefficient between ; Represents sample frequency domain impedance amplification data The Column data; Represents sample multimodal water augmentation data The Column data; Represents sample frequency domain impedance amplification data The average value of Represents sample multimodal water augmentation data The average value of .

4. The method for estimating water content in a fuel cell based on a physical information neural network according to claim 3, characterized in that: The sensitivity is calculated as: ； in, Represents the frequency domain impedance characteristics of the sample amplification Middle Sensitivity of column frequency domain impedance; Indicates Column sample frequency domain impedance amplification data Multimodal water augmentation data with samples Pearson correlation coefficient between ; Indicates Column feature frequency amplification data Multimodal water augmentation data with samples The Pearson correlation coefficient between .

5. The method for estimating water content in a fuel cell based on a physical information neural network according to claim 1, characterized in that: The method of using the self-attention mechanism to process the filtered sample frequency domain features to obtain the sample frequency domain self-attention features specifically includes: Introducing position encoding into the self-attention mechanism based on SoftMax probability distribution; The self-attention mechanism with position encoding is used to capture the internal correlation between the frequency domain features of the filtered samples, and the sample frequency domain self-attention features are obtained.

6. The method for estimating water content in a fuel cell based on a physical information neural network according to claim 1, characterized in that: The loss function of the fuel cell water content estimation model is: ； in, Indicates data loss; Represents the first loss weight, which is the data loss The corresponding loss weight; Indicates the first physical information loss; represents the second loss weight, which is the first physical information loss The corresponding loss weight; Indicates the second physical information loss; Represents the third loss weight, which is the second physical information loss The corresponding loss weight; Indicates third physical information loss; Represents the fourth loss weight, which is the third physical information loss the corresponding loss weights; and .

7. The method for estimating water content in a fuel cell based on a physical information neural network according to claim 1, characterized in that: The physical information loss is obtained by the following steps: Determine data loss based on the multimodal water true content and the multimodal water predicted content; determining a first physical information loss according to the proton exchange membrane fuel cell voltage and the real voltage; Determine the second physical information loss according to the equivalent diffusion time and the actual time; The third physical information loss is determined based on the cathode charge transfer admittance and the cathode real charge.

8. A fuel cell water content estimation system based on physical information neural network, characterized in that: The system comprises: A data acquisition module is used to obtain the original frequency domain impedance characteristics and the measurable variable time series of the battery to be estimated, eliminate the frequency domain redundant data in the original frequency domain impedance characteristics, obtain the filtered frequency domain characteristics, perform equivalue mapping on the measurable variable time series to obtain an equivalue mapping sequence, and use the self-attention mechanism to process the filtered frequency domain characteristics to obtain frequency domain self-attention characteristics, and perform feature connection on the equivalue mapping sequence and the frequency domain self-attention characteristics to obtain spatiotemporal heterogeneous characteristics; A data prediction module, used for inputting the spatiotemporal heterogeneous features into a trained fuel cell water content estimation model to obtain a multimodal water prediction content of a battery to be estimated output by the fuel cell water content estimation model; The fuel cell water content estimation model uses a gradient descent method to update the weight of each hidden layer. The loss function of the fuel cell water content estimation model consists of data loss and physical information loss. The physical information loss includes a first physical information loss for characterizing information loss of voltage polarization impedance, a second physical information loss for characterizing information loss of mass transfer time impedance, and a third physical information loss for characterizing information loss of cathode charge impedance. The fuel cell water content estimation model is trained by the following steps: Obtaining the original frequency domain impedance characteristics of the sample, and eliminating the frequency domain redundant data in the original frequency domain impedance characteristics of the sample, to obtain the filtered sample frequency domain characteristics; Obtaining a sample measurable variable time series, and performing equivalent mapping on the sample measurable variable time series to obtain a sample equivalent mapping sequence; The frequency domain features of the filtered samples are processed using the self-attention mechanism to obtain the frequency domain self-attention features of the samples; The sample equivalue mapping sequence and the sample frequency domain self-attention feature are feature-connected to obtain the sample time-frequency heterogeneous feature; The sample time-frequency heterogeneous features are used as input data for training, and the neural network is trained using supervised learning to build a fuel cell water content estimation model. The loss of the fuel cell water content estimation model is adjusted through an adaptive algorithm of local physical information error and a Bayesian optimization method to obtain a trained fuel cell water content estimation model.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the fuel cell water content estimation method based on physical information neural network as described in any one of claims 1 to 7 are implemented.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for estimating the water content of a fuel cell based on a physical information neural network as claimed in any one of claims 1 to 7 are implemented.

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