Proton exchange membrane electrolyzer mechanism and data double-driven reduced modeling method, device and computer equipment

Abstract

The application relates to a mechanism and data double-driven reduced-order modeling method, device and computer equipment for a proton exchange membrane electrolyzer. The method comprises the following steps: performing spatial dimension reduction on a three-dimensional multi-physical field coupling model along the thickness direction of the polar plate of the electrolyzer to obtain a physical reduced-order model; inputting average physical response quantities of each lumped parameter node output by the physical reduced-order model into a preset time sequence convolutional neural network, superimposing the average physical response quantities and local extreme compensation quantities to obtain a mechanism and data double-driven reduced-order model; optimizing mechanism parameters to be identified in the physical reduced-order model according to the difference between a prediction value and a reference value corresponding to the reference data in a virtual reference data set to obtain target mechanism parameters; and configuring the mechanism and data double-driven reduced-order model according to the target mechanism parameters to obtain a target state observation model. The method can improve the accuracy of the prediction of the internal physical field state of the electrolyzer stack of the proton exchange membrane electrolyzer.

Description

Technical Field

[0001] This application relates to the field of hydrogen energy system modeling and equipment condition monitoring technology, and in particular to a proton exchange membrane electrolyzer mechanism and data-driven dual-drive reduced-order modeling method, device, computer equipment, computer-readable storage medium and computer program product. Background Technology

[0002] Hydrogen, as a high-energy-density, renewable, and pollution-free clean energy source, is considered a key support for the future transformation of the energy structure. Proton exchange membrane electrolyzers for hydrogen production through water electrolysis have significant advantages, including high current density, high electrolysis efficiency, fast dynamic response, and high hydrogen purity, making them highly promising for hydrogen production from fluctuating renewable energy sources such as wind and solar power.

[0003] In actual industrial production, to obtain hydrogen production power of megawatts or higher, it is usually necessary to stack dozens to hundreds of proton exchange membrane electrolyzer (PEMEC) cells in series and parallel to form a large electrolyzer stack. However, as the number of stacked cells increases, the spatial non-uniformity of fluid distribution, heat conduction, and electrochemical reaction rates within the stack increases dramatically. This inconsistency in the spatiotemporal distribution of the internal physical fields not only leads to performance fluctuations between core groups but also easily triggers serious safety accidents such as local thermal runaway or membrane perforation. Therefore, achieving real-time, high-precision online sensing of the complex multiphysics state within the stack is of decisive significance for equipment health management and control optimization.

[0004] While a single PEMEC cell has relatively low power output, in actual industrial production, multiple electrolytic cells are often stacked in series and parallel to form an electrolytic cell stack, thereby achieving greater electrolytic power. However, the complex structural design of the stack and the stacking arrangement of the internal unit electrolytic cells enhance the inconsistent distribution of component concentration fields, flow fields, thermal fields, and electrochemical fields within the stack. This leads to fluctuations in the electrical performance between cell groups within the stack, which is detrimental to the long-term safe and stable operation of the stack. As the number of cells increases, this inconsistency in the spatiotemporal distribution of state parameters within the stack and the performance differences between cell groups become even more pronounced.

[0005] Currently, obtaining the hidden state parameters inside a proton exchange membrane electrolyzer mainly relies on three-dimensional computational fluid dynamics (CFD) multiphysics simulation. However, the high-precision three-dimensional multiphysics simulation calculation process involves solving a set of highly nonlinear partial differential equations involving multiple coupled fields such as electrochemical dynamics and energy conservation. A single steady-state solution often takes several hours, which cannot meet the millisecond-level real-time monitoring and control requirements of industrial field controllers, resulting in low accuracy in predicting the physical field state inside the proton exchange membrane electrolyzer stack. Summary of the Invention

[0006] Based on this, it is necessary to provide a method, apparatus, computer equipment, computer-readable storage medium, and computer program product that can improve the accuracy of predicting the internal physical field state of a proton exchange membrane electrolyzer stack by providing a dual-driven reduced-order modeling method, apparatus, computer equipment, computer-readable storage medium, and computer program product that can address the above-mentioned technical problems.

[0007] Firstly, this application provides a dual-driven, data-driven method for reducing the order of proton exchange membrane electrolyzer modeling, including:

[0008] Based on the three-dimensional multiphysics coupling model corresponding to the proton exchange membrane electrolyzer stack, a virtual benchmark dataset of the stack is obtained; the virtual benchmark dataset includes the external characteristic parameters of the stack under various operating conditions and the local extreme state variables inside the stack.

[0009] The three-dimensional multiphysics coupling model is spatially reduced along the electrode thickness direction of the fuel cell stack to obtain a physical order-reduced model; the physical order-reduced model includes lumped parameter nodes corresponding to each electrolysis cell in the fuel cell stack;

[0010] The average physical response of each lumped parameter node output by the physical reduction model is input into a preset temporal convolutional neural network to obtain the local extremum compensation amount corresponding to the average physical response. The average physical response and the local extremum compensation amount are superimposed to obtain a mechanism- and data-driven reduction model. The local extremum compensation amount is predicted by the temporal convolutional neural network and is used to compensate for the local extrema lost by the physical reduction model due to spatial dimensionality reduction.

[0011] The predicted values ​​of the mechanism- and data-driven order reduction model under the corresponding operating conditions in the virtual benchmark dataset are obtained. Based on the difference between the predicted values ​​and the corresponding benchmark values ​​in the virtual benchmark dataset, the mechanism parameters to be identified in the physical order reduction model are optimized to obtain target mechanism parameters. The mechanism- and data-driven order reduction model is configured according to the target mechanism parameters to obtain a target state observation model. The target state observation model is used to determine the predicted results of the physical field state inside the fuel cell stack based on the external operating conditions parameters of the fuel cell stack.

[0012] In one embodiment, the step of spatially reducing the dimensionality of the three-dimensional multiphysics coupling model along the electrode thickness direction of the fuel cell stack to obtain a physically reduced-order model includes:

[0013] The three-dimensional multiphysics coupling model is spatially reduced along the electrode thickness direction of the electric stack to obtain the series topology structure composed of the lumped parameter nodes corresponding to each electrolysis cell in the electric stack.

[0014] The physical order reduction model is constructed based on the equivalent lumped heat capacity corresponding to each lumped parameter node in the series topology and the equivalent thermal resistance between adjacent lumped parameter nodes.

[0015] In one embodiment, the step of inputting the average physical response of each of the lumped parameter nodes output by the physical reduction model into a preset temporal convolutional neural network to obtain the local extremum compensation amount corresponding to the average physical response includes:

[0016] Extract the average physical response of each lumped parameter node output by the physical reduction model within a preset time window to determine the input feature sequence;

[0017] The input feature sequence is input into the temporal convolutional neural network, and long temporal dependency features in the input feature sequence are extracted through the dilated causal convolutional layer in the temporal convolutional neural network; the dilated causal convolutional layer is a convolutional structure used to expand the receptive field of the input feature sequence by introducing a dilation coefficient and to perform convolution operations on the input feature sequence.

[0018] The long temporal dependency features are nonlinearly mapped by the fully connected layer in the temporal convolutional neural network to obtain the local extremum compensation amount corresponding to the average physical response.

[0019] In one embodiment, optimizing the mechanistic parameters to be identified in the physical reduction model based on the difference between the predicted value and the corresponding benchmark value in the virtual benchmark dataset to obtain the target mechanistic parameters includes:

[0020] Extract the predicted terminal voltage value of the fuel cell stack and the predicted local maximum temperature inside the fuel cell stack from the predicted values; and extract the reference value of the terminal voltage value and the reference value of the local maximum temperature of the fuel cell stack from the corresponding reference values ​​in the virtual reference dataset.

[0021] The fitness function value is determined based on the error between the predicted terminal voltage value and the reference terminal voltage value, and the error between the predicted local maximum temperature value and the reference local maximum temperature value.

[0022] The target mechanism parameters are obtained by iteratively optimizing the mechanism parameters to be identified in the physical reduction model based on the fitness function value.

[0023] In one embodiment, the step of iteratively optimizing the mechanism parameters to be identified in the physical reduction model based on the fitness function value to obtain the target mechanism parameters includes:

[0024] An initial population is generated within a preset search boundary corresponding to the mechanism parameters to be identified in the physical reduction model by using chaotic mapping. Each individual in the initial population corresponds to a set of values ​​of the mechanism parameters to be identified. The chaotic mapping is used to make the individuals in the initial population traverse uniformly within the preset search boundary.

[0025] Based on the fitness function value, individuals in the initial population are divided into discoverers, followers, and vigilants;

[0026] During the iteration process, the discoverer performs a global search within the preset search boundary, the followers move closer to the individual with the smallest fitness function value in the initial population, and the watchdog applies a random perturbation to the current global best individual when the iteration process stalls, so as to obtain candidate individuals; the global search step size of the discoverer is adjusted by a weight factor that decreases with the number of iterations.

[0027] If the fitness function value of the candidate individual is less than the fitness function value of the current global best individual, the candidate individual is adopted as the updated current global best individual.

[0028] If the iteration process meets the iteration termination condition, the latest combination of values ​​corresponding to the current global optimal individual is taken as the target mechanism parameter.

[0029] In one embodiment, after configuring the mechanism-data dual-drive order reduction model according to the target mechanism parameters to obtain the target state observation model, the method further includes:

[0030] The external operating parameters of the fuel cell stack are input into the target state observation model; the external operating parameters include the electrolysis current, terminal voltage, anode inlet flow rate, and inlet and outlet operating temperatures of the fuel cell stack.

[0031] The target state observation model outputs the physical field state prediction results inside the stack, which include the local current density distribution of the plates inside the stack, the temperature field distribution of each electrolysis cell, and the extreme hotspot information inside the stack.

[0032] Secondly, this application also provides a dual-drive modeling device for proton exchange membrane electrolyzer mechanism and data-driven order reduction, comprising:

[0033] The simulation module is used to obtain a virtual reference dataset of the proton exchange membrane electrolyzer stack based on the three-dimensional multiphysics coupling model corresponding to the stack. The virtual reference dataset includes the external characteristic parameters of the stack under various operating conditions and the local extreme state variables inside the stack.

[0034] The order reduction module is used to spatially reduce the dimension of the three-dimensional multiphysics coupling model along the electrode thickness direction of the fuel cell stack to obtain a physical order reduction model; the physical order reduction model includes lumped parameter nodes corresponding to each electrolysis cell in the fuel cell stack;

[0035] The compensation module is used to input the average physical response of each lumped parameter node output by the physical reduction model into a preset temporal convolutional neural network to obtain the local extremum compensation amount corresponding to the average physical response. The average physical response and the local extremum compensation amount are superimposed to obtain a mechanism- and data-driven reduction model. The local extremum compensation amount is predicted by the temporal convolutional neural network and is used to compensate for the local extrema lost by the physical reduction model due to spatial dimensionality reduction.

[0036] The configuration module is used to obtain the predicted values ​​of the mechanism-data dual-driven reduction model under the corresponding operating conditions of the virtual benchmark dataset; optimize the mechanism parameters to be identified in the physical reduction model based on the difference between the predicted values ​​and the corresponding benchmark values ​​in the virtual benchmark dataset to obtain target mechanism parameters; configure the mechanism-data dual-driven reduction model based on the target mechanism parameters to obtain a target state observation model; the target state observation model is used to determine the predicted results of the physical field state inside the fuel cell stack based on the external operating conditions parameters of the fuel cell stack.

[0037] Thirdly, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the above-described method.

[0038] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.

[0039] Fifthly, this application also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the above-described method.

[0040] The aforementioned mechanism and data-driven dual-drive modeling method, apparatus, computer equipment, computer-readable storage medium, and computer program products for proton exchange membrane electrolyzers obtain a simulation dataset containing external characteristic parameters and local extremum state quantities through a three-dimensional multiphysics coupling model corresponding to the electrolyzer stack. This provides a comparative benchmark covering both the external and internal states of the electrolyzer stack for subsequent optimization of mechanism parameters in the mechanism and data-driven dual-drive modeling. By spatially reducing the three-dimensional multiphysics coupling model along the electrode thickness direction of the electrolyzer stack, a physical reduction model composed of lumped parameter nodes corresponding to each electrolysis cell is obtained. This transforms the multiphysics coupling solution process in three-dimensional space into a finite-dimensional solution process based on each lumped parameter node while preserving the physical interpretability of the electrolyzer stack, which helps reduce the computational load in the solution process of the electrolyzer stack's operating state. By inputting the average physical response output of the physical reduction model into a temporal convolutional neural network to obtain the corresponding local extremum compensation quantity, and then comparing the average physical response with the local extremum compensation quantity, the model can achieve the desired results. By superimposing the compensation values, a mechanism- and data-driven reduced-order model is obtained. This model can compensate for the local extremum features lost by the physical reduced-order model due to spatial dimensionality reduction using a temporal convolutional neural network, which is beneficial to improving the prediction ability of the reduced-order model for local extrema inside the fuel cell stack. By optimizing the mechanistic parameters to be identified in the physical reduced-order model based on the difference between the predicted values ​​and the baseline values ​​of the mechanism- and data-driven reduced-order model under the corresponding operating conditions in the simulation dataset, target mechanism parameters are obtained. Based on the target mechanism parameters, the mechanism- and data-driven reduced-order model is configured to obtain a target state observation model. This model can track the drift of mechanism parameters caused by equipment aging during dynamic load changes and long-term operation of the fuel cell stack, which is beneficial to maintaining good adaptability of the target state observation model under various operating conditions. This target state observation model can output the prediction results of the physical field state inside the fuel cell stack based on the easily measurable operating parameters outside the fuel cell stack, thereby improving the accuracy of predicting the physical field state inside the proton exchange membrane electrolyzer fuel cell stack. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the drawings used in the description of the embodiments of this application or related technologies will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 This is an application environment diagram of a dual-driven, data-driven, order-reduction modeling method for a proton exchange membrane electrolyzer, as shown in one embodiment.

[0043] Figure 2 This is a flowchart illustrating a dual-driven, data-driven modeling method for reducing the order of a proton exchange membrane electrolyzer, as described in one embodiment.

[0044] Figure 3 This is a schematic diagram of the structure of a physical order reduction model in one embodiment;

[0045] Figure 4 This is a schematic diagram of the structure of a temporal convolutional neural network in one embodiment;

[0046] Figure 5 This is a flowchart illustrating an improved sparrow search algorithm in one embodiment;

[0047] Figure 6 This is a structural block diagram of a proton exchange membrane electrolyzer mechanism and data-driven order reduction modeling device in one embodiment;

[0048] Figure 7 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0050] In related technologies, obtaining the hidden state parameters inside a proton exchange membrane electrolyzer mainly relies on three-dimensional computational fluid dynamics (CFD) multiphysics simulation. However, the high-precision three-dimensional multiphysics simulation calculation process involves solving a system of highly nonlinear partial differential equations involving multiple coupled fields such as electrochemical dynamics and energy conservation. A single steady-state solution often takes several hours, which is far from meeting the millisecond-level real-time monitoring and control requirements of industrial field controllers. To overcome the above computational bottleneck, pure data-driven machine learning methods or one-dimensional lumped parameter models are usually used to reduce the model order. However, existing reduction-order modeling methods have obvious theoretical flaws: First, when performing spatial dimensionality reduction and averaging on the physical field, one-dimensional physical reduction models inevitably lose the strict three-dimensional spatial inhomogeneity characteristics inside the electrolytic cell, leading to serious distortion in the model's prediction of microscopic local extrema. Second, purely data-driven reduction-order models treat the electrolytic cell as a "black box," completely detaching it from the rigid boundary constraints of the conservation laws of electrochemistry and thermodynamics, resulting in a lack of physical interpretability and easy divergence when faced with untrained abrupt operating conditions. Third, existing reduction-order methods are mostly based on fixed static physical parameter assumptions, failing to consider that core mechanism parameters such as membrane conductivity and contact thermal resistance will undergo nonlinear drift with equipment aging and complex operating conditions, resulting in extremely poor generalization ability of the model during long-term operation and difficulty in controlling prediction errors.

[0051] The proton exchange membrane electrolyzer mechanism and data-driven dual-drive order reduction modeling method provided in this application embodiment can be applied to, for example... Figure 1In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be integrated onto server 104, or it can be located in the cloud or on another network server.

[0052] In specific implementation, terminal 102 obtains a virtual reference dataset of the proton exchange membrane electrolyzer stack based on the three-dimensional multiphysics coupling model corresponding to the stack. The virtual reference dataset includes the external characteristic parameters of the stack under various operating conditions and the local extremum state quantities inside the stack. Terminal 102 performs spatial dimensionality reduction on the three-dimensional multiphysics coupling model along the electrode thickness direction of the stack to obtain a physical reduction model. The physical reduction model includes lumped parameter nodes corresponding to each electrolysis chamber in the stack. The average physical response of each lumped parameter node output by the physical reduction model is input into a preset temporal convolutional neural network to obtain the local extremum compensation quantity corresponding to the average physical response quantity. The average physical response quantity and the local extremum compensation quantity are then superimposed. The mechanism and data-driven order reduction model is obtained. The local extremum compensation amount is the compensation amount for the local extrema lost due to spatial dimensionality reduction of the average physical response predicted by the temporal convolutional neural network. The terminal 102 obtains the predicted value of the mechanism and data-driven order reduction model under the corresponding operating conditions in the virtual benchmark dataset. Based on the difference between the predicted value and the corresponding benchmark value in the virtual benchmark dataset, the mechanism parameters to be identified in the physical order reduction model are optimized to obtain the target mechanism parameters. The terminal 102 configures the mechanism and data-driven order reduction model according to the target mechanism parameters to obtain the target state observation model. The target state observation model is used to determine the predicted result of the physical field state inside the fuel cell based on the external operating conditions of the fuel cell.

[0053] The terminal 102 can be, but is not limited to, various personal computers, laptops, smartphones, tablets, IoT devices, etc. The server 104 can be a standalone physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server that provides cloud computing services.

[0054] In one exemplary embodiment, such as Figure 2 As shown, a dual-driven, data-driven method for reducing the order of proton exchange membrane electrolyzers is provided, which is then applied to... Figure 1 Taking terminal 102 as an example, the explanation includes:

[0055] Step S202: Obtain the virtual benchmark dataset of the proton exchange membrane electrolyzer stack based on the three-dimensional multiphysics coupling model corresponding to the stack.

[0056] Among them, a proton exchange membrane electrolyzer can refer to an electrochemical device that uses a proton exchange membrane as an electrolyte to electrolyze water to produce hydrogen and oxygen. An electrolysis stack can refer to an electrolysis assembly formed by stacking multiple proton exchange membrane electrolysis cells in series or parallel. An electrolysis cell can refer to an independent unit within the electrolysis stack used to realize the process of electrolyzing water to produce hydrogen and oxygen.

[0057] Among them, the three-dimensional multiphysics coupling model can refer to a numerical simulation model that solves the electrochemical field, thermal field, flow field and mass transfer field involved in the electrolysis process of the fuel cell stack in three-dimensional space.

[0058] The virtual benchmark dataset refers to a set of data obtained by simulating a three-dimensional multiphysics coupled model under different operating conditions, which reflects the operation process of the fuel cell stack. It is used to provide benchmark values ​​for the subsequent optimization process of mechanism parameters, so that the target state observation model can be constructed through the optimized target mechanism parameters.

[0059] The virtual benchmark dataset includes external characteristic parameters of the fuel cell stack under various operating conditions, as well as local extreme state variables within the stack. External characteristic parameters refer to operating parameters that can be directly measured by external sensors, such as terminal voltage, electrolytic current, anode inlet flow rate, and inlet / outlet operating temperatures. Local extreme state variables refer to state variables existing within the stack that are difficult to measure directly using external sensors, including local current density distribution on the electrodes, temperature field distribution in a single electrolytic cell, and the highest extreme hotspot temperature on the membrane surface and its corresponding spatial coordinates.

[0060] In practical implementation, a proportional three-dimensional geometric model can be established based on the actual structural dimensions of the proton exchange membrane electrolyzer stack. This model can be formed by stacking multiple PEMEC single cells in series at equal intervals. Each PEMEC single cell can refer to a proton exchange membrane electrolysis cell. Each electrolysis cell can spatially include an anode bipolar plate, an anode flow channel, an anode liquid-gas diffusion layer, an anode catalyst layer, a proton exchange membrane, a cathode catalyst layer, a cathode liquid-gas diffusion layer, a cathode flow channel, a coolant flow channel, and a cathode bipolar plate. Specifically, physicochemical parameters can be set in each computational domain based on the three-dimensional geometric model. These parameters can include the effective conductivity, thermal conductivity, constant-pressure heat capacity, and density of the electrodes.

[0061] Furthermore, based on the three-dimensional geometric model, a multi-physics field strongly coupled solution interface can be configured on each computational domain to characterize the evolution law between electricity, heat, and mass during the electrolysis of the fuel cell stack, thereby obtaining a three-dimensional multi-physics field coupled model.

[0062] In some embodiments, corresponding charge conservation control equations are configured for electron transport in the solid phase and proton transport in the electrolyte phase, respectively. The charge conservation control equations can be expressed as:

[0063] ;

[0064] ;

[0065] in, and Characterize electronic conductivity and proton conductivity, respectively; and Characterize the solid-state potential and the film potential, respectively; and Each represents a corresponding current source term.

[0066] In some embodiments, an electrochemical reaction module can be constructed based on the Butler-Volmer equation, which can be expressed as:

[0067] ;

[0068] Where i represents the operating current density; α is the charge transfer coefficient; is the exchange current density; n is the number of electrons transferred in the electrolysis reaction; The activation overpotential is given by F; F is the Faraday constant; T represents the temperature; and R represents the gas constant, also known as the universal gas constant, which has a value of 8.314 J / (mol·K).

[0069] In some embodiments, a mixture model and a concentrated mass transfer interface can be used to construct a multiphase flow and mass transport module. Specifically, the two-phase flow of liquid water and gaseous oxygen can be described on the anode side based on the mixture model, and the corresponding momentum conservation equation and phase volume fraction equation can be expressed as follows:

[0070] ;

[0071] ;

[0072] in, p is the velocity of the mixture; p is the pressure. ρ is the dynamic viscosity; ρ is the density of the mixture; g is the acceleration due to gravity; ρ l The density of the liquid phase; The degree of saturation of liquid water; u l The velocity in the liquid phase is s. lThis refers to the liquid phase mass source term. Specifically, the concentration transfer process of each component can be described on both the cathode and anode sides based on the concentrated mass transfer interface, and the corresponding mass transfer control equation can be expressed as:

[0073] ;

[0074] in, Components concentration, To characterize the effective diffusion coefficient after correction by the effective medium theory of porous media, This refers to the mass source term consumed or generated by electrochemical reactions.

[0075] In some embodiments, a heat transfer module can be constructed based on a solid-fluid heat transfer interface to describe the thermal effects inside the fuel cell stack caused by ohmic losses, entropy changes in electrochemical reactions, and irreversible activation. The corresponding energy conservation governing equation can be expressed as:

[0076] ;

[0077] in, For equivalent volumetric heat capacity, Effective thermal conductivity; The total heat source term can encompass irreversible heat of reaction, reversible entropy change heat, and ohmic heat generated by contact resistance and film resistance. It can be represented as:

[0078] .

[0079] After configuring the multiphysics control equations and boundary conditions for the three-dimensional ensemble model to obtain the three-dimensional multiphysics coupled model, different combinations of operating parameters can be set for the three-dimensional multiphysics coupled model to obtain simulation solution results under multiple operating conditions, thereby obtaining a virtual benchmark dataset. In some embodiments, the electrolysis current in the operating parameter combination can range from 20A to 100A, the anode water inlet flow velocity can range from 0.05m / s to 0.2m / s, and the operating temperature can range from 30℃ to 80℃. Specifically, a massively parallel sparse direct solver can be used to perform steady-state and transient joint solutions on the three-dimensional multiphysics coupled model, deriving full-field data including the grid node states, and removing numerical singularities with gradient anomalies in the solution results to obtain a virtual benchmark dataset characterizing the non-uniform state of the internal field.

[0080] Step S204: Spatial dimensionality reduction of the three-dimensional multiphysics coupling model along the electrode thickness direction of the fuel cell stack is performed to obtain a physical reduced-order model.

[0081] The physical reduction model refers to a simplified model obtained by spatially reducing the dimensionality of a three-dimensional multiphysics coupling model, which can solve the operation process of the fuel cell stack using ordinary differential equations of finite dimension. The physical reduction model includes lumped parameter nodes corresponding to each electrolytic cell in the fuel cell stack. A lumped parameter node can refer to a node unit that treats a single electrolytic cell in space as a node with a unified physical state. This node unit can describe the evolution of state variables such as temperature and voltage of the electrolytic cell using ordinary differential equations.

[0082] In practical implementation, the spatial dimension of the three-dimensional multiphysics coupling model along the electrode thickness direction of the fuel cell stack can be averaged to obtain a physically reduced-order model composed of multiple lumped parameter nodes. Specifically, the lumped parameter nodes can be boundary-coupled through the bipolar plate contact surface, and corresponding state evolution equations can be established for each lumped parameter node based on electrochemical polarization theory and the first law of thermodynamics, thereby obtaining a physically reduced-order model that can be solved in milliseconds.

[0083] Step S206: Input the average physical response of each lumped parameter node output by the physical reduction model into a preset temporal convolutional neural network to obtain the local extremum compensation amount corresponding to the average physical response amount. Then, superimpose the average physical response amount and the local extremum compensation amount to obtain the mechanism and data dual-driven reduction model.

[0084] The average physical response quantity can refer to the physical quantity output by the physical reduction model that characterizes the overall macroscopic state of a single electrolytic cell. The average physical response quantity can include the macroscopic average temperature, terminal voltage, and macroscopic current density of the electrolytic cell.

[0085] Among them, temporal convolutional neural networks can refer to neural networks that perform feature extraction and nonlinear mapping on time series data based on dilated causal convolutional structures.

[0086] Among them, the local extremum compensation amount is a physical quantity predicted by the temporal convolutional neural network and used to compensate for the local extrema lost by the physical reduction model due to spatial dimensionality reduction.

[0087] Among them, the mechanism and data dual-driven order reduction model can refer to the order reduction model that takes the superposition result of the average physical response and the local extremum compensation as the output. The average physical response in the mechanism and data dual-driven order reduction model is obtained by solving the physical order reduction model according to the physical mechanism, and the local extremum compensation in the mechanism and data dual-driven order reduction model is predicted by the temporal convolutional neural network according to the average physical response.

[0088] In specific implementation, the average physical response of each lumped parameter node output by the physical reduction model can be used as the input of a temporal convolutional neural network. The temporal convolutional neural network extracts temporal features and performs nonlinear mapping on the input average physical response to obtain the local extremum compensation amount. Then, the average physical response output by the physical reduction model can be superimposed with the local extremum compensation amount output by the temporal convolutional neural network. The superposition result is the output of the mechanism and data dual-driven reduction model. Thus, the mechanism and data dual-driven reduction model can compensate for the local extremum features lost due to spatial dimensionality reduction inside the fuel cell stack while retaining the physical interpretability of the physical reduction model.

[0089] Step S208: Obtain the predicted values ​​of the mechanism and data dual-driven order reduction model under the corresponding working conditions in the virtual benchmark dataset. Based on the difference between the predicted values ​​and the corresponding benchmark values ​​in the virtual benchmark dataset, optimize the mechanism parameters to be identified in the physical order reduction model to obtain the target mechanism parameters. Configure the mechanism and data dual-driven order reduction model according to the target mechanism parameters to obtain the target state observation model.

[0090] The predicted values ​​can include physical quantities obtained by inputting the operating parameters of each operating condition in the virtual benchmark dataset into the mechanism- and data-driven order reduction model, such as the external characteristic parameters of the fuel cell stack and the local extremum state quantities inside the fuel cell stack predicted by the mechanism- and data-driven order reduction model. The benchmark values ​​can refer to the physical quantities recorded in the virtual benchmark dataset that correspond to the predicted values, such as the external characteristic parameters of the fuel cell stack and the local extremum state quantities.

[0091] Among them, the mechanism parameters to be identified can refer to the parameters in the physical reduction model that characterize the physical properties of the fuel cell stack and undergo nonlinear drift with dynamic load changes or long-term aging of the fuel cell stack. The mechanism parameters to be identified can include equivalent film conductivity, reference exchange current density, charge transfer coefficient, equivalent contact thermal resistance, and equivalent mass transfer coefficient.

[0092] Among them, the target mechanism parameter can refer to the optimal parameter combination obtained after iterative optimization of the mechanism parameter to be identified.

[0093] The target state observation model refers to a model formed by solidifying the parameters of a mechanism- and data-driven reduced-order model based on target mechanism parameters, used for online observation of the internal state of the fuel cell stack. The target state observation model is used to determine the predicted physical field state of the fuel cell stack based on its external operating parameters.

[0094] In practical implementation, the predicted values ​​of the mechanism- and data-driven order reduction model under the corresponding working conditions in the virtual benchmark dataset can be compared with the corresponding benchmark values ​​in the virtual benchmark dataset. The difference between the predicted values ​​and the benchmark values ​​is used as the optimization objective to iteratively optimize the mechanism parameters to be identified in the physical order reduction model, thereby obtaining the target mechanism parameters. Then, the obtained target mechanism parameters can be substituted into the mechanism- and data-driven order reduction model to replace the mechanism parameters to be identified in the mechanism- and data-driven order reduction model, thus obtaining the target state observation model.

[0095] In the aforementioned mechanism- and data-driven modeling method for reducing the order of proton exchange membrane electrolyzers, a simulation dataset containing external characteristic parameters and local extremum state quantities is obtained through a three-dimensional multiphysics coupling model corresponding to the electrolyzer stack. This provides a comparative benchmark covering both the external and internal states of the electrolyzer stack for subsequent optimization of mechanism parameters in the mechanism- and data-driven modeling. By spatially reducing the three-dimensional multiphysics coupling model along the electrode thickness direction of the electrolyzer stack, a physical reduction model composed of lumped parameter nodes corresponding to each electrolysis cell is obtained. This transforms the multiphysics coupling solution process in three-dimensional space into a finite-dimensional solution process based on each lumped parameter node while preserving the physical interpretability of the electrolyzer stack, which helps reduce the computational load in the solution process of the electrolyzer stack's operating state. By inputting the average physical response quantity output by the physical reduction model into a temporal convolutional neural network to obtain the corresponding local extremum compensation quantity, the average physical response quantity and the local extremum compensation quantity are superimposed. The resulting mechanism- and data-driven reduced-order model can compensate for the local extremum features lost due to spatial dimensionality reduction in the physical reduced-order model using a temporal convolutional neural network, thus improving the model's ability to predict local extrema within the fuel cell stack. By optimizing the mechanistic parameters to be identified in the physical reduced-order model based on the difference between the predicted values ​​and baseline values ​​of the mechanism- and data-driven reduced-order model under the corresponding operating conditions in the simulation dataset, target mechanism parameters are obtained. Based on these target mechanism parameters, the mechanism- and data-driven reduced-order model is configured to obtain a target state observation model. This model can track the drift of mechanism parameters caused by equipment aging during dynamic load changes and long-term operation of the fuel cell stack, enabling the target state observation model to maintain good adaptability under various operating conditions. This target state observation model can output the predicted results of the internal physical field state of the fuel cell stack based on easily measurable external operating parameters, thereby improving the accuracy of the prediction of the internal physical field state of the fuel cell stack.

[0096] In another embodiment, the three-dimensional multiphysics coupling model is spatially reduced along the electrode thickness direction of the fuel cell stack to obtain a physical order reduction model. This includes: spatially reducing the three-dimensional multiphysics coupling model along the electrode thickness direction of the fuel cell stack to obtain a series topology structure composed of lumped parameter nodes corresponding to each electrolysis cell in the fuel cell stack; and constructing a physical order reduction model based on the equivalent lumped heat capacity corresponding to each lumped parameter node in the series topology structure and the equivalent thermal resistance between adjacent lumped parameter nodes.

[0097] Among them, the physical order reduction model can be constructed based on the law of conservation of mass and energy.

[0098] For the convenience of those skilled in the art, Figure 3 An exemplary schematic diagram of a physical order reduction model is provided.

[0099] In practical implementation, the spatial distribution of each electrolytic cell in the stack along the electrode thickness direction can be equivalent to a lumped parameter node, and the lumped parameter nodes are connected in series according to the physical arrangement of the electrolytic cells in the stack to form a series topology. Specifically, each lumped parameter node can be further divided into four functional sub-modules, which may include an anode sub-module, a cathode sub-module, a proton exchange membrane sub-module, and a voltage output sub-module. The functional sub-modules can be internally coupled through mass flow and heat flow, and adjacent lumped parameter nodes can be boundary coupled through the thermal resistance network corresponding to the bipolar plate contact surface.

[0100] The equivalent lumped heat capacity refers to the total heat capacity when all components in a single electrolytic cell are considered as a whole with a uniform temperature state. The equivalent lumped heat capacity characterizes the inertial characteristics of the electrolytic cell's temperature change with heat generation and dissipation. The equivalent thermal resistance refers to the thermal resistance between two adjacent electrolytic cells when heat is conducted through the bipolar plate contact surface.

[0101] In practical implementation, a voltage output submodule can be constructed based on electrochemical polarization theory, and the terminal voltage V of the electrolysis chamber can be... cell The terminal voltage V of the electrolytic cell can be obtained by linear superposition of the reversible open-circuit voltage, activation overpotential, ohmic overpotential, and concentration overpotential. cell It can be expressed as the following voltage equation:

[0102] ;

[0103] in, Since it is a reversible open-circuit voltage, it can be described using the Nernst equation; The activation overpotential can be obtained by the simplified derivation of the Butler-Folmer equations described above; This is the concentration overpotential; The ohmic overpotential, used to characterize the overpotential caused by factors including the ohmic impedance of the proton exchange membrane and the contact impedance between modules, can be expressed as:

[0104] ;

[0105] in, For local current density, The thickness of the proton exchange membrane. Equivalent membrane conductivity Equivalent contact resistance. Equivalent film conductivity. and equivalent contact resistance It can be used as a mechanism parameter to be identified and optimized through subsequent steps.

[0106] In some embodiments, an unsteady lumped energy conservation ordinary differential equation can be established for each lumped parameter node based on the first law of thermodynamics to characterize the physical boundary of the system's thermal evolution. The temperature T corresponding to the nth electrolytic cell... n The evolution equation can be expressed as the following energy conservation ordinary differential equation:

[0107] ;

[0108] in, The equivalent lumped heat capacity of a single electrolysis cell can be determined by the weighted sum of the mass and specific heat capacity of each component in the electrolysis cell. Each component may include bipolar plates, membrane electrodes, etc. For the total heat generation term of the nth electrolytic cell, it can cover the sum of entropy change heat, irreversible activation heat and ohmic heat generated by the electrochemical reaction; This is a convective heat transfer term used to describe the heat carried away by the circulating water on the anode side, and it can be proportional to the inlet flow rate and temperature difference. This is a thermal coupling term used to describe the thermal conduction effect between adjacent electrolysis cells. It can be represented as:

[0109] ;

[0110] in, The equivalent thermal resistance across the compartment can be obtained by fitting a virtual benchmark dataset.

[0111] Then, the voltage equation and the energy conservation ordinary differential equation are combined to construct a physical reduced-order model. Given an external current or terminal voltage as the input boundary condition, the physical reduced-order model can be quickly integrated and solved using an ordinary differential equation solver, outputting the macroscopic average temperature and terminal voltage of each electrolysis cell.

[0112] In another embodiment, the average physical response of each lumped parameter node output by the physical reduction model is input into a preset temporal convolutional neural network to obtain the local extremum compensation amount corresponding to the average physical response. This includes: extracting the average physical response of each lumped parameter node output by the physical reduction model within a preset time window to determine the input feature sequence; inputting the input feature sequence into the temporal convolutional neural network, and extracting long temporal dependency features from the input feature sequence through the dilated causal convolutional layer in the temporal convolutional neural network; the dilated causal convolutional layer is a convolutional structure used to expand the receptive field of the input feature sequence by introducing a dilation coefficient and to perform convolution operations on the input feature sequence; and performing nonlinear mapping on the long temporal dependency features through the fully connected layer in the temporal convolutional neural network to obtain the local extremum compensation amount corresponding to the average physical response.

[0113] In the specific implementation, firstly, the average physical response of each lumped parameter node output by the physical reduction model within a preset time window is extracted to determine the input feature sequence.

[0114] The preset time window can refer to the time period extracted by the terminal from the output sequence of the physical reduced-order model to reflect the historical operating state of the fuel cell stack. The input feature sequence can refer to the data sequence formed by arranging the average physical response quantities within the preset time window in chronological order.

[0115] In practice, the terminal voltage within a preset time window L, including the current time and the time before the current time, can be selected. Macroscopic current density And the macroscopic average temperature of each electrolysis cell, simultaneously calculated and output by the physical reduction model. As input feature variables, the input feature sequence corresponding to time step t It can be represented as:

[0116] ;

[0117] Where n is the dimension of the input feature.

[0118] Then, the input feature sequence is fed into a temporal convolutional neural network, and long temporal dependent features in the input feature sequence are extracted through the dilated causal convolutional layer in the temporal convolutional neural network.

[0119] For the convenience of those skilled in the art, Figure 4 An exemplary schematic diagram of a temporal convolutional neural network is provided.

[0120] Among them, the dilated causal convolutional layer is a convolutional structure used to expand the receptive field of the input feature sequence by introducing a dilation coefficient and to perform convolution operations on the input feature sequence. Long temporal dependency features can refer to features that can reflect the interdependencies between time intervals in the input feature sequence.

[0121] In specific implementation, for a one-dimensional input sequence The dilation convolution operation at sequence element s can be represented as:

[0122] ;

[0123] in, The coefficient of thermal expansion; The kernel size; It is used to characterize past directions. Specifically, by increasing the expansion coefficient d exponentially with the increase of the number of layers in the temporal convolutional neural network, the temporal convolutional neural network can obtain a larger receptive field without increasing the number of computational parameters, thereby capturing the long-period thermal inertia and mass transport hysteresis effect of the fuel cell stack under variable voltage conditions.

[0124] In some embodiments, the internal architecture of a temporal convolutional neural network can employ a residual connection architecture to avoid the vanishing gradient problem during deep network training. The output O of the residual block can be obtained by adding the dilated causal convolutional feature transform to the identity mapping, and the output O of the residual block can be expressed as:

[0125] ;

[0126] Where F(X) represents the dilated causal convolution feature transformation, and Activation represents the activation function.

[0127] For example, a fully connected layer can be connected to the end of the temporal convolutional neural network. This fully connected layer performs a nonlinear mapping on the extracted long-term temporal dependent features to obtain the local extremum compensation amount corresponding to the average physical response. In some embodiments, the local extremum compensation amount can be the residual compensation amount for the highest microscopic extremum temperature inside the electrolysis chamber. .

[0128] Then, the macroscopic average physical quantity output by the physical reduction model can be superimposed with the local extremum compensation quantity output by the temporal convolutional neural network to obtain a mechanism- and data-driven reduction model. The mechanism- and data-driven reduction model predicts the highest microscopic extremum temperature inside the electrolysis chamber. It can be represented as:

[0129] ;

[0130] in, Characterizes the macroscopic average temperature output by the physical reduced-order model; The amount of local extremum compensation in the output of a temporal convolutional neural network.

[0131] In another embodiment, the mechanism parameters to be identified in the physical reduction model are optimized based on the difference between the predicted values ​​and the corresponding benchmark values ​​in the virtual benchmark dataset to obtain the target mechanism parameters. This includes: extracting the predicted terminal voltage value and the predicted local maximum temperature value inside the fuel cell from the predicted values, and extracting the benchmark values ​​of the terminal voltage and the local maximum temperature from the corresponding benchmark values ​​in the virtual benchmark dataset; determining the fitness function value based on the error value between the predicted terminal voltage value and the benchmark value, and the error value between the predicted local maximum temperature value and the benchmark value; and iteratively optimizing the mechanism parameters to be identified in the physical reduction model based on the fitness function value to obtain the target mechanism parameters.

[0132] In practice, mechanistic parameters that significantly affect the model's output accuracy can be selected from the physical reduction model as the mechanistic parameters to be identified. Optionally, the equivalent membrane conductivity can be used. Reference exchange current density Charge transfer coefficient Equivalent contact thermal resistance and equivalent quality transmission coefficient As the mechanism parameters to be identified, the set of mechanism parameters to be identified, X=[ , , , , Then, the predicted terminal voltage of the fuel cell stack can be extracted from the predicted values ​​of the mechanism- and data-driven reduced-order model under the corresponding operating conditions in the virtual benchmark dataset. Predicted maximum local temperature inside the fuel cell stack And extract the stack terminal voltage reference value from the corresponding reference value in the virtual reference dataset. Compared with the local maximum temperature reference value .

[0133] In practice, the predicted terminal voltage value can be calculated. With terminal voltage reference value root mean square error between and the predicted local maximum temperature Compared with the local maximum temperature reference value root mean square error between Root mean square error With root mean square error It can be represented as:

[0134] ;

[0135] ;

[0136] Where N represents the number of samples involved in the error calculation.

[0137] To eliminate the influence of the dimensional difference between terminal voltage and temperature on the optimization process, the root mean square error can be normalized, and a joint fitness function can be constructed using a weighted approach. The joint fitness function, Fitness, can be expressed as:

[0138] ;

[0139] in, and Characterizing the weighting coefficients, and + =1; The maximum value of the terminal voltage reference value is characterized by... The maximum value representing the local highest temperature benchmark. Optionally, it can be adjusted according to the specific engineering focus. and Configure it so that, when electrical efficiency is a primary concern during fuel cell stack operation, it can be... The value is set to be greater than The value of ; when thermal safety is a greater concern in the operation of the fuel cell stack, it can be The value is set to be greater than The value of .

[0140] In practice, the set of mechanism parameters X to be identified can be used as the optimization variable, and the joint fitness function Fitness can be used as the optimization objective. The set of mechanism parameters X to be identified can be iteratively updated through an iterative optimization algorithm until the joint fitness function Fitness meets the preset convergence accuracy threshold or reaches the preset maximum number of iterations, thereby obtaining the target mechanism parameters.

[0141] In another embodiment, the target mechanism parameters are obtained by iteratively optimizing the mechanistic parameters to be identified in the physical reduction model based on the fitness function values. This includes: generating an initial population within a preset search boundary corresponding to the mechanistic parameters to be identified in the physical reduction model using chaotic mapping, where each individual in the initial population corresponds to a set of values ​​for the mechanistic parameters to be identified; the chaotic mapping is used to ensure that the individuals in the initial population traverse the preset search boundary uniformly; the individuals in the initial population are divided into discoverers, followers, and vigilants based on the fitness function values; during the iteration process, the discoverers are evaluated based on their movement within the preset search boundary. A global search is conducted within the boundary. Followers move towards the individual with the smallest fitness function value in the initial population. When the iteration process stalls, the watcher applies a random perturbation to the current global best individual to obtain candidate individuals. The global search step size of the discoverer is adjusted by a weight factor that decreases with the number of iterations. If the fitness function value of a candidate individual is less than that of the current global best individual, the candidate individual is adopted as the updated current global best individual. If the iteration process meets the iteration termination condition, the combination of values ​​corresponding to the latest current global best individual is used as the target mechanism parameter.

[0142] Here, a chaotic map can refer to a nonlinear map that enables individuals in the initial population to traverse uniformly within a preset search boundary. Optionally, a chaotic map can include a Tent chaotic map.

[0143] The preset search boundary can refer to the upper and lower limits set according to the physical meaning of the mechanism parameter to be identified, used to limit the range of values ​​of the mechanism parameter to be identified. For example, the preset search boundary can be... , This serves as a lower bound for the mechanistic parameters to be identified. This represents the upper bound of the mechanistic parameters to be identified.

[0144] In this context, each individual in the initial population corresponds to a set of combinations of mechanistic parameters to be identified. The initial population can refer to the set of candidate parameter combinations generated by the chaotic mapping for iterative optimization.

[0145] In practical implementation, an improved sparrow search algorithm can be used to iteratively optimize the mechanistic parameters to be identified, thereby obtaining the target mechanistic parameters. The Sparrow Search Algorithm (SSA) is a swarm intelligence optimization algorithm that simulates the foraging behavior and anti-predation mechanisms of a sparrow population to solve complex optimization problems. The improved sparrow search algorithm refers to an iterative optimization algorithm obtained by introducing improved strategies such as chaotic mapping initialization, nonlinear dynamically decreasing weight factors, and Gaussian random walk perturbations on the basis of the traditional sparrow search algorithm. In the improved sparrow search algorithm, the initial population can be represented as an initial sparrow population position matrix, and the individuals in the initial population can refer to sparrows in the sparrow population. The position of each sparrow in the solution space can correspond to a set of combinations of values ​​for the mechanistic parameters to be identified.

[0146] For the convenience of those skilled in the art, Figure 5 An exemplary flowchart of an improved sparrow search algorithm is provided.

[0147] In practice, physical search boundaries can be set for the mechanism parameters to be identified. And an initial sparrow population position matrix of size M is generated using Tent chaotic mapping:

[0148] ;

[0149] Among them, chaotic sequences can be Mapped to the actual physical parameter solution space:

[0150] ;

[0151] in, Let be the value of the j-th dimension of the i-th sparrow in the initial sparrow population position matrix.

[0152] The above mapping method enables individuals representing combinations of physical parameters to have high ergodicity and diversity in the nonlinear solution space, thereby providing a more uniformly distributed initial solution for the subsequent iterative optimization process.

[0153] In this context, discoverers, followers, and vigilants are three roles assigned to individuals in the initial population based on their fitness function values. Discoverers are individuals with relatively high fitness function values ​​in the initial population responsible for conducting a global search within a predefined search boundary to explore potential optimal parameter regions. Followers are all other individuals in the initial population besides discoverers; they can update their combinations of mechanistic parameters to be identified based on the location information provided by the discoverer. Vigilants are randomly selected individuals from the initial population used to apply random perturbations to the currently globally optimal individual when the iteration process stalls, triggering an anti-predator jump. An anti-predator jump refers to the vigilant's action of randomly perturbing the position corresponding to the currently globally optimal individual to escape the local optimum when it senses that the iterative optimization process has fallen into a local optimum.

[0154] In practice, the combination of the mechanistic parameters to be identified carried by each sparrow in the initial population can be used as the input boundary, substituted into the mechanism and data dual-driven order reduction model for solution, and the fitness function value corresponding to each individual can be calculated based on the joint fitness function mentioned above. Specifically, the individuals with the smallest fitness function value in the initial population can be classified as discoverers, who are used to perform a global search within a preset search boundary; the remaining individuals in the initial population can be classified as followers, who are used to move closer to the individual with the smallest fitness function value in the initial population; and a portion of individuals can be randomly selected from the initial population as vigilants, who are used to apply random perturbations to the current globally optimal individual when the iteration process stalls.

[0155] The global search step size of the discoverer is adjusted by a weight factor that decreases with the number of iterations. The current global best individual can be the individual with the smallest fitness function value in the initial population at the current iteration number. A candidate individual can be a new individual obtained by the watcher applying a random perturbation to the current global best individual.

[0156] In practice, the discoverer can perform a global search within a preset search boundary to explore potential regions of optimal electrochemical parameters. To balance the exploration and development capabilities of the iterative optimization algorithm, a nonlinear dynamically decreasing weight factor ω can be introduced during the discoverer's position update process. This nonlinear dynamically decreasing weight factor ω can be expressed as:

[0157] ;

[0158] in, and Let represent the upper and lower bounds of the nonlinear dynamically decreasing weight factor, respectively, and t represent the current iteration number. The maximum number of iterations is represented. Specifically, the search step size of the discoverer can be adjusted based on a nonlinear dynamically decreasing weight factor ω. In the early stage of iteration, a larger value of ω enables the discoverer to perform a large-scale search within the physical search boundary, thereby avoiding local optima; in the later stage of iteration, a smaller value of ω enables the discoverer to perform a fine search within the neighborhood of the optimal parameters, thereby improving convergence accuracy.

[0159] In practice, followers can update the combination of their mechanistic parameters to be identified based on the location information provided by the discoverer, thus moving closer to the individual with the smallest fitness function value in the initial population. If the fitness function value of a follower is greater than a preset threshold, it indicates that the combination of its mechanistic parameters to be identified deviates significantly from the true situation. In this case, the follower can make a large leap across regions towards the position of the current global best individual to obtain a better solution. If the fitness function value of a follower is less than or equal to the preset threshold, it indicates that the combination of its mechanistic parameters to be identified is relatively close to the true situation. In this case, the follower can perform a local search within the neighborhood of the current best discoverer to accelerate the convergence speed of the parameter cluster.

[0160] Considering the phenomenon of heteroparameters having the same effect as equivalent membrane conductivity and equivalent contact thermal resistance—that is, different combinations of values ​​for the mechanistic parameters to be identified may correspond to similar terminal voltage responses, which can easily cause stagnation in the improved sparrow search algorithm—a Gaussian random walk perturbation can be applied to the current globally optimal individual when the iteration process stalls after the follower update and anti-predation warning phases are completed, thereby obtaining candidate individuals. Candidate individuals It can be represented as:

[0161] ;

[0162] in, This represents the current globally optimal individual corresponding to the current iteration number t. Characterized by a mean of 0 and a variance of The Gaussian random distribution function is used. By employing the aforementioned random perturbation method, fine perturbations at the microscale can be introduced into the multidimensional parameter space, enabling local depth optimization of the current global optimum and avoiding iterative optimization algorithms from getting trapped in local optima.

[0163] In specific implementation, candidate individuals can be... The corresponding combinations of the mechanistic parameters to be identified are substituted into the mechanism and data-driven reduced-order model for solution, and candidate individuals are calculated. The corresponding fitness function value; then, the candidate individuals The corresponding fitness function value is compared with the fitness function value of the current global best individual, and in the candidate individual If the fitness function value of the candidate individual is less than the fitness function value of the current global best individual, then the candidate individual can be considered as a candidate individual. As the updated current global best individual; among candidate individuals If the fitness function value is greater than or equal to the fitness function value of the current global best individual, the current global best individual can remain unchanged.

[0164] Among them, the iteration termination condition can refer to the judgment condition used to determine whether the iterative optimization process has ended. The iteration termination condition may include the current iteration number reaching the maximum iteration number, or the global optimal fitness function value being lower than the preset convergence accuracy threshold for multiple consecutive iterations.

[0165] In practice, at the end of each iteration, it can be determined whether the current iteration number t has reached the maximum number of iterations. Alternatively, check if the global optimal fitness function value is continuously lower than the preset convergence accuracy threshold ε multiple times. If the iteration termination condition is not met, let t = t + 1, and re-substitute the updated combination of mechanistic parameters carried by the population into the mechanism and data-driven order reduction model to enter the next round of closed-loop calculation; if the iteration termination condition is met, stop the iterative optimization process, and take the latest combination of values ​​corresponding to the current global optimal individual as the target mechanistic parameter.

[0166] The technical solution of this application combines a one-dimensional reduced-order physical model with a temporal convolutional network and adopts a multi-strategy improved swarm intelligence algorithm to solve the problems of traditional reduced-order models lacking physical constraints, having poor generalization ability, and losing extreme value information.

[0167] In another embodiment, after configuring the mechanism and data dual-drive order reduction model according to the target mechanism parameters to obtain the target state observation model, the method further includes: inputting the external operating parameters of the fuel cell stack into the target state observation model; the external operating parameters include the electrolysis current, terminal voltage, anode inlet flow rate and inlet and outlet operating temperatures of the fuel cell stack; and outputting the physical field state prediction results inside the fuel cell stack through the target state observation model, the physical field state prediction results including the local current density distribution of the electrode plates inside the fuel cell stack, the temperature field distribution of each electrolysis cell, and the extreme hotspot information inside the fuel cell stack.

[0168] The external operating parameters include the electrolysis current, terminal voltage, anode inlet flow rate, and inlet and outlet operating temperatures of the fuel cell stack.

[0169] The physical field state prediction results include the local current density distribution of the electrodes inside the stack, the temperature field distribution of each electrolysis cell, and the extreme hotspot information inside the stack. The extreme hotspot information can include the highest extreme hotspot temperature on the membrane surface and its corresponding spatial coordinates.

[0170] In practical implementation, the target state observation model can be deployed in the monitoring terminal or controller corresponding to the physical proton exchange membrane electrolyzer system. During the actual operation of the stack, external operating parameters of the stack can be collected in real time by sensors installed outside the stack, and the time series data corresponding to the collected external operating parameters can be input into the target state observation model in real time. The physical reduction model and the temporal convolutional neural network in the target state observation model can be solved forward synchronously, and the macroscopic physical response output by the physical reduction model and the local extremum compensation output by the temporal convolutional neural network are superimposed in parallel to output the physical field state prediction result inside the stack, realizing high-fidelity, non-invasive online sensing of the complex state inside the electrolyzer.

[0171] The mechanism- and data-driven modeling method for proton exchange membrane electrolyzers in this application addresses the shortcomings of existing three-dimensional simulations, such as long computation time, easy loss of microscopic extreme value features in simple one-dimensional reduction, and lack of physical constraints in pure data models. First, a three-dimensional multiphysics coupled model of the electrolyzer stack is constructed to obtain a virtual benchmark dataset. Second, a physical reduction model is constructed based on the laws of mass and energy conservation to establish the rigid physical boundaries of system evolution. Then, a temporal convolutional network (TCN) is introduced to map microscopic spatial extreme values, constructing a mechanism-data dual-driven architecture. Next, an improved multi-strategy sparrow search algorithm (ISSA) is used to adaptively optimize the core mechanism parameters in a closed loop, generating a target state observation model. Finally, real-time macroscopic detection data is input into this model to achieve real-time online observation of the hidden three-dimensional state inside the electrolyzer stack. This method accurately compensates for the nonlinear feature loss caused by dimensionality reduction within a simplified architecture, balancing computational speed with high fidelity in microscopic state perception.

[0172] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0173] Based on the same inventive concept, this application also provides a proton exchange membrane electrolyzer mechanism and data dual-driven order reduction modeling device for implementing the above-mentioned proton exchange membrane electrolyzer mechanism and data dual-driven order reduction modeling method. The solution provided by this device is similar to the solution described in the above method. Therefore, the specific limitations of one or more proton exchange membrane electrolyzer mechanism and data dual-driven order reduction modeling device embodiments provided below can be found in the limitations of the proton exchange membrane electrolyzer mechanism and data dual-driven order reduction modeling method described above, and will not be repeated here.

[0174] In one exemplary embodiment, such as Figure 6 As shown, a dual-drive modeling device for proton exchange membrane electrolyzer mechanism and data-driven order reduction is provided, comprising:

[0175] The simulation module 610 is used to obtain a virtual reference dataset of the proton exchange membrane electrolyzer stack based on the three-dimensional multiphysics coupling model corresponding to the stack. The virtual reference dataset includes the external characteristic parameters of the stack under various operating conditions and the local extreme state variables inside the stack.

[0176] The reduction module 620 is used to spatially reduce the dimension of the three-dimensional multiphysics coupling model along the electrode thickness direction of the fuel cell stack to obtain a physical reduction model; the physical reduction model includes lumped parameter nodes corresponding to each electrolysis cell in the fuel cell stack.

[0177] The compensation module 630 is used to input the average physical response of each of the lumped parameter nodes output by the physical reduction model into a preset temporal convolutional neural network to obtain the local extremum compensation amount corresponding to the average physical response. The average physical response and the local extremum compensation amount are superimposed to obtain a mechanism and data dual-driven reduction model. The local extremum compensation amount is predicted by the temporal convolutional neural network and is used to compensate for the local extrema lost by the physical reduction model due to spatial dimensionality reduction.

[0178] The configuration module 640 is used to obtain the predicted value of the mechanism and data dual-driven reduction model under the corresponding operating conditions of the virtual benchmark dataset; optimize the mechanism parameters to be identified in the physical reduction model based on the difference between the predicted value and the corresponding benchmark value in the virtual benchmark dataset to obtain target mechanism parameters; configure the mechanism and data dual-driven reduction model according to the target mechanism parameters to obtain a target state observation model; the target state observation model is used to determine the predicted result of the physical field state inside the fuel cell stack based on the external operating conditions parameters of the fuel cell stack.

[0179] In one embodiment, the order reduction module 620 is specifically used to spatially reduce the dimension of the three-dimensional multiphysics coupling model along the electrode thickness direction of the fuel cell stack to obtain a series topology structure composed of lumped parameter nodes corresponding to each electrolysis cell in the fuel cell stack; and to construct the physical order reduction model based on the equivalent lumped heat capacity corresponding to each lumped parameter node in the series topology structure and the equivalent thermal resistance between adjacent lumped parameter nodes.

[0180] In one embodiment, the compensation module 630 is specifically used to extract the average physical response of each of the lumped parameter nodes output by the physical reduction model within a preset time window to determine the input feature sequence; input the input feature sequence into the temporal convolutional neural network, and extract long temporal dependency features in the input feature sequence through the dilated causal convolutional layer in the temporal convolutional neural network; the dilated causal convolutional layer is used to expand the receptive field of the input feature sequence by introducing a dilation coefficient, and is a convolutional structure for performing convolution operations on the input feature sequence; the long temporal dependency features are nonlinearly mapped through the fully connected layer in the temporal convolutional neural network to obtain the local extremum compensation amount corresponding to the average physical response.

[0181] In one embodiment, the configuration module 640 is specifically configured to extract the predicted terminal voltage value and the predicted local maximum temperature value inside the fuel cell stack from the predicted values, and to extract the reference value of the terminal voltage and the reference value of the local maximum temperature from the corresponding reference values ​​in the virtual reference dataset; determine the fitness function value based on the error value between the predicted terminal voltage value and the reference value, and the error value between the predicted local maximum temperature value and the reference value; and iteratively optimize the mechanism parameters to be identified in the physical reduction model based on the fitness function value to obtain the target mechanism parameters.

[0182] In one embodiment, the configuration module 640 is specifically used to generate an initial population within a preset search boundary corresponding to the mechanistic parameters to be identified in the physical reduction model through chaotic mapping. Each individual in the initial population corresponds to a set of values ​​for the mechanistic parameters to be identified. The chaotic mapping is used to ensure that the individuals in the initial population traverse the preset search boundary uniformly. The individuals in the initial population are divided into discoverers, followers, and vigilants according to the fitness function value. During the iteration process, the discoverers perform a global search within the preset search boundary, and the followers perform a global search. Individuals with the smallest fitness function value in the initial population are grouped together. When the iteration process stalls, the watcher applies a random perturbation to the current global best individual to obtain candidate individuals. The global search step size of the discoverer is adjusted by a weight factor that decreases with the number of iterations. If the fitness function value of a candidate individual is less than that of the current global best individual, the candidate individual is adopted as the updated current global best individual. If the iteration process meets the iteration termination condition, the combination of values ​​corresponding to the latest current global best individual is adopted as the target mechanism parameter.

[0183] In one embodiment, the proton exchange membrane electrolyzer mechanism and data dual-drive order reduction modeling device further includes a prediction module. The prediction module is used to input the external operating parameters of the electrolyzer stack into the target state observation model. The external operating parameters include the electrolysis current, terminal voltage, anode inlet flow rate, and inlet and outlet operating temperatures of the electrolyzer stack. The target state observation model outputs the physical field state prediction results inside the electrolyzer stack. The physical field state prediction results include the local current density distribution of the electrode plates inside the electrolyzer stack, the temperature field distribution of each electrolysis cell, and the extreme hotspot information inside the electrolyzer stack.

[0184] Each module in the aforementioned dual-drive modeling device for proton exchange membrane electrolyzer mechanism and data reduction can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the computer device's memory as software, so that the processor can call and execute the corresponding operations of each module.

[0185] In one exemplary embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 7As shown, the computer device includes a processor, memory, input / output interface, communication interface, display unit, and input device. The processor, memory, and input / output interface are connected via a system bus, and the communication interface, display unit, and input device are also connected to the system bus via the input / output interface. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The input / output interface is used for exchanging information between the processor and external devices. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, mobile cellular networks, Near Field Communication (NFC), or other technologies. When executed by the processor, the computer program implements a dual-driven, data-driven, order-reduction modeling method for proton exchange membrane electrolyzer mechanisms. The display unit is used to form a visually visible image and can be a display screen, projection device, or virtual reality imaging device. The display screen can be an LCD screen or an e-ink screen. The input device of the computer device can be a touch layer covering the display screen, or buttons, trackballs, or touchpads set on the casing of the computer device, or external keyboards, touchpads, or mice, etc.

[0186] Those skilled in the art will understand that Figure 7 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0187] In one exemplary embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0188] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps in the above method embodiments.

[0189] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above method embodiments.

[0190] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0191] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile memory and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, artificial intelligence (AI) processors, etc., and are not limited to these.

[0192] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this application.

[0193] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A dual-driven, data-driven method for reducing the order of proton exchange membrane electrolyzers, characterized in that, The method includes: Based on the three-dimensional multiphysics coupling model corresponding to the proton exchange membrane electrolyzer stack, a virtual benchmark dataset of the stack is obtained; the virtual benchmark dataset includes the external characteristic parameters of the stack under various operating conditions and the local extreme state variables inside the stack. The three-dimensional multiphysics coupling model is spatially reduced along the electrode thickness direction of the fuel cell stack to obtain a physical order-reduced model; the physical order-reduced model includes lumped parameter nodes corresponding to each electrolysis cell in the fuel cell stack; The average physical response of each lumped parameter node output by the physical reduction model is input into a preset temporal convolutional neural network to obtain the local extremum compensation amount corresponding to the average physical response. The average physical response and the local extremum compensation amount are superimposed to obtain a mechanism- and data-driven reduction model. The local extremum compensation amount is predicted by the temporal convolutional neural network and is used to compensate for the local extrema lost by the physical reduction model due to spatial dimensionality reduction. The predicted values ​​of the mechanism- and data-driven order reduction model under the corresponding operating conditions in the virtual benchmark dataset are obtained. Based on the difference between the predicted values ​​and the corresponding benchmark values ​​in the virtual benchmark dataset, the mechanism parameters to be identified in the physical order reduction model are optimized to obtain target mechanism parameters. The mechanism- and data-driven order reduction model is configured according to the target mechanism parameters to obtain a target state observation model. The target state observation model is used to determine the predicted results of the physical field state inside the fuel cell stack based on the external operating conditions parameters of the fuel cell stack.

2. The method according to claim 1, characterized in that, The step of spatially reducing the dimensionality of the three-dimensional multiphysics coupling model along the electrode thickness direction of the fuel cell stack to obtain a physically reduced-order model includes: The three-dimensional multiphysics coupling model is spatially reduced along the electrode thickness direction of the electric stack to obtain the series topology structure composed of the lumped parameter nodes corresponding to each electrolysis cell in the electric stack. The physical order reduction model is constructed based on the equivalent lumped heat capacity corresponding to each lumped parameter node in the series topology and the equivalent thermal resistance between adjacent lumped parameter nodes.

3. The method according to claim 1, characterized in that, The step of inputting the average physical response of each of the lumped parameter nodes output by the physical reduction model into a preset temporal convolutional neural network to obtain the local extremum compensation corresponding to the average physical response includes: Extract the average physical response of each lumped parameter node output by the physical reduction model within a preset time window to determine the input feature sequence; The input feature sequence is input into the temporal convolutional neural network, and long temporal dependency features in the input feature sequence are extracted through the dilated causal convolutional layer in the temporal convolutional neural network; the dilated causal convolutional layer is a convolutional structure used to expand the receptive field of the input feature sequence by introducing a dilation coefficient and to perform convolution operations on the input feature sequence. The long temporal dependency features are nonlinearly mapped by the fully connected layer in the temporal convolutional neural network to obtain the local extremum compensation amount corresponding to the average physical response.

4. The method according to claim 1, characterized in that, The step of optimizing the mechanistic parameters to be identified in the physical reduction model based on the difference between the predicted value and the corresponding benchmark value in the virtual benchmark dataset to obtain the target mechanistic parameters includes: Extract the predicted terminal voltage value of the fuel cell stack and the predicted local maximum temperature inside the fuel cell stack from the predicted values; and extract the reference value of the terminal voltage value and the reference value of the local maximum temperature of the fuel cell stack from the corresponding reference values ​​in the virtual reference dataset. The fitness function value is determined based on the error between the predicted terminal voltage value and the reference terminal voltage value, and the error between the predicted local maximum temperature value and the reference local maximum temperature value. The target mechanism parameters are obtained by iteratively optimizing the mechanism parameters to be identified in the physical reduction model based on the fitness function value.

5. The method according to claim 4, characterized in that, The step of iteratively optimizing the mechanistic parameters to be identified in the physical reduction model based on the fitness function value to obtain the target mechanistic parameters includes: An initial population is generated within a preset search boundary corresponding to the mechanism parameters to be identified in the physical reduction model by using chaotic mapping. Each individual in the initial population corresponds to a set of values ​​of the mechanism parameters to be identified. The chaotic mapping is used to make the individuals in the initial population traverse uniformly within the preset search boundary. Based on the fitness function value, individuals in the initial population are divided into discoverers, followers, and vigilants; During the iteration process, the discoverer performs a global search within the preset search boundary, the followers move closer to the individual with the smallest fitness function value in the initial population, and the watchdog applies a random perturbation to the current global best individual when the iteration process stalls, so as to obtain candidate individuals; the global search step size of the discoverer is adjusted by a weight factor that decreases with the number of iterations. If the fitness function value of the candidate individual is less than the fitness function value of the current global best individual, the candidate individual is adopted as the updated current global best individual. If the iteration process meets the iteration termination condition, the latest combination of values ​​corresponding to the current global optimal individual is taken as the target mechanism parameter.

6. The method according to claim 1, characterized in that, After configuring the mechanism-data dual-driven order reduction model according to the target mechanism parameters to obtain the target state observation model, the method further includes: The external operating parameters of the fuel cell stack are input into the target state observation model; the external operating parameters include the electrolysis current, terminal voltage, anode inlet flow rate, and inlet and outlet operating temperatures of the fuel cell stack. The target state observation model outputs the physical field state prediction results inside the stack, which include the local current density distribution of the plates inside the stack, the temperature field distribution of each electrolysis cell, and the extreme hotspot information inside the stack.

7. A dual-driven, data-driven modeling device for reducing the order of proton exchange membrane electrolyzers, characterized in that, The device includes: The simulation module is used to obtain a virtual reference dataset of the proton exchange membrane electrolyzer stack based on the three-dimensional multiphysics coupling model corresponding to the stack. The virtual reference dataset includes the external characteristic parameters of the stack under various operating conditions and the local extreme state variables inside the stack. The order reduction module is used to spatially reduce the dimension of the three-dimensional multiphysics coupling model along the electrode thickness direction of the fuel cell stack to obtain a physical order reduction model; the physical order reduction model includes lumped parameter nodes corresponding to each electrolysis cell in the fuel cell stack; The compensation module is used to input the average physical response of each lumped parameter node output by the physical reduction model into a preset temporal convolutional neural network to obtain the local extremum compensation amount corresponding to the average physical response. The average physical response and the local extremum compensation amount are superimposed to obtain a mechanism- and data-driven reduction model. The local extremum compensation amount is predicted by the temporal convolutional neural network and is used to compensate for the local extrema lost by the physical reduction model due to spatial dimensionality reduction. The configuration module is used to obtain the predicted values ​​of the mechanism-data dual-driven reduction model under the corresponding operating conditions of the virtual benchmark dataset; optimize the mechanism parameters to be identified in the physical reduction model based on the difference between the predicted values ​​and the corresponding benchmark values ​​in the virtual benchmark dataset to obtain target mechanism parameters; configure the mechanism-data dual-driven reduction model based on the target mechanism parameters to obtain a target state observation model; the target state observation model is used to determine the predicted results of the physical field state inside the fuel cell stack based on the external operating conditions parameters of the fuel cell stack.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

Images