Quantitative analysis method and device for membrane electrode parameter sensitivity of proton exchange membrane fuel cell, computer equipment, readable storage medium and program product

Abstract

The application relates to a method and device for quantitatively analyzing membrane electrode parameter sensitivity of a proton exchange membrane fuel cell, computer equipment, a computer readable storage medium and a computer program product, and relates to the technical field of fuel cells, and improves the optimization design process efficiency of a membrane electrode. The method comprises the following steps: determining a three-dimensional calculation domain and a one-dimensional calculation domain of the proton exchange membrane fuel cell based on physical operation behavior of the proton exchange membrane fuel cell; acquiring a data interaction interface between the calculation domains; determining a simulation model based on the three-dimensional calculation domain, the one-dimensional calculation domain and the data interaction interface; determining a relative transformation rate of a sensitivity parameter of the proton exchange membrane fuel cell after a preset transformation; determining a relative transformation rate of a target performance index of the proton exchange membrane fuel cell after the preset transformation based on the simulation model; and determining a quantitative sensitivity coefficient based on the relative transformation rate of the target performance index and the relative transformation rate of the sensitivity parameter.

Description

Technical Field

[0001] This application relates to the field of fuel cell technology, and in particular to a method, apparatus, computer equipment, computer-readable storage medium, and computer program product for quantitative analysis of the sensitivity of membrane electrode parameters in a proton exchange membrane fuel cell. Background Technology

[0002] With the increasing global demand for clean energy, proton exchange membrane fuel cells (PEMFCs) have become one of the key technologies for hydrogen energy utilization due to their advantages such as low operating temperature, fast response and high power density.

[0003] The performance and cost of proton exchange membrane fuel cells largely depend on the design of their core component, the membrane electrode assembly (MEA). In the relevant research and development process, researchers use experimental testing or computer simulations to analyze the impact of MEA design parameters on the cell's output performance.

[0004] However, most existing studies are limited to discussing the qualitative impact or trend of a single variable on battery performance, and fail to provide a method to accurately and quantitatively analyze the sensitivity of different design parameters to performance. This is not conducive to researchers quickly identifying key parameters, resulting in low efficiency in the optimization design process of membrane electrodes. Summary of the Invention

[0005] Therefore, it is necessary to provide a method, apparatus, computer equipment, computer-readable storage medium, and computer program product for quantitative analysis of the sensitivity of membrane electrode parameters in proton exchange membrane fuel cells, in order to address the above-mentioned technical problems.

[0006] In a first aspect, this application provides a method for quantitatively analyzing the sensitivity of membrane electrode parameters in a proton exchange membrane fuel cell, including:

[0007] Based on the physical operating behavior of the plates, flow channels, and gas diffusion layer of the proton exchange membrane fuel cell, the three-dimensional computational domain of the proton exchange membrane fuel cell is determined.

[0008] Based on the physical operating behavior of the microporous layer, catalyst layer, and proton exchange membrane of the proton exchange membrane fuel cell, a one-dimensional computational domain of the proton exchange membrane fuel cell is determined.

[0009] Obtain the data interaction interface between the three-dimensional computational domain and the one-dimensional computational domain;

[0010] Based on the three-dimensional computational domain, the one-dimensional computational domain, and the data interaction interface, a simulation model is determined.

[0011] The relative conversion rate of the sensitivity parameters of the proton exchange membrane fuel cell after a preset transformation is determined; the sensitivity parameters are the structural and physical property parameters of the membrane electrode of the proton exchange membrane fuel cell.

[0012] Based on the simulation model, the relative conversion rate of the target performance index of the proton exchange membrane fuel cell after the preset transformation is determined;

[0013] Based on the relative rate of change of the target performance index and the relative rate of change of the sensitivity parameter, the quantitative sensitivity coefficient of the sensitivity parameter to the target performance index is determined.

[0014] In one embodiment, the relative rate of change includes a relative rate of change and a combined relative rate of change; determining the relative rate of change of the sensitivity parameter of the proton exchange membrane fuel cell after a preset transformation includes:

[0015] When multiple sensitivity parameters change, determine the relative rates of change of each of the multiple sensitivity parameters after the preset transformation occurs;

[0016] Obtain multiple relative change vectors corresponding to each of the relative change rates, and aggregate the multiple relative change vectors to obtain a joint relative change rate that characterizes the overall degree of change of the multiple relative change rates;

[0017] The determination of the quantitative sensitivity coefficient of the sensitivity parameter to the target performance index based on the relative rate of change of the target performance index and the relative rate of change of the sensitivity parameter includes:

[0018] Based on the relative rate of change of the target performance index and the joint relative rate of change, the quantitative sensitivity coefficients of the plurality of sensitivity parameters to the target performance index are obtained.

[0019] In one embodiment, determining the relative transformation rate of the sensitivity parameter of the proton exchange membrane fuel cell after a preset transformation includes:

[0020] Obtain the reference sensitivity parameter value of the proton exchange membrane fuel cell under reference operating conditions, and the disturbance parameter value of the sensitivity parameter after a preset change based on the reference sensitivity parameter value;

[0021] Based on the baseline sensitivity parameter value and the disturbance parameter value, the relative rate of change of the sensitivity parameter is determined.

[0022] The step of determining the relative conversion rate of the target performance index of the proton exchange membrane fuel cell after the preset transformation based on the simulation model includes:

[0023] Based on the simulation model, the benchmark target performance index corresponding to the benchmark sensitivity parameter value is determined when the proton exchange membrane fuel cell is under the benchmark operating condition.

[0024] Based on the simulation model, the target performance index of the disturbance parameter value is determined under the target condition after the preset change of the baseline condition.

[0025] Based on the baseline target performance index and the disturbance target performance index, the relative rate of change of the target performance index is determined.

[0026] In one embodiment, determining the relative conversion rate of the target performance index of the proton exchange membrane fuel cell after the preset transformation based on the simulation model includes:

[0027] Determine the influence region corresponding to the benchmark sensitivity parameter value;

[0028] If the affected area indicates the three-dimensional computational domain, then based on the benchmark sensitivity parameter, the three-dimensional operating data is determined through the three-dimensional computational domain of the simulation model;

[0029] The three-dimensional operational data is input into the one-dimensional computational domain of the simulation model via a data interaction interface to determine the one-dimensional operational data.

[0030] If the three-dimensional running data and the one-dimensional running data meet the preset conditions, the benchmark target performance index is determined based on the three-dimensional running data and the one-dimensional running data.

[0031] In one embodiment, after determining the influence region corresponding to the benchmark sensitivity parameter value, the method further includes:

[0032] If the affected area indicates the one-dimensional computational domain, then based on the benchmark sensitivity parameter, the one-dimensional operating data is determined through the one-dimensional computational domain of the simulation model.

[0033] The one-dimensional operational data is input into the three-dimensional computational domain of the simulation model via the data interaction interface to determine the three-dimensional operational data;

[0034] If the three-dimensional running data and the one-dimensional running data meet the preset conditions, the benchmark target performance index is determined based on the three-dimensional running data and the one-dimensional running data.

[0035] In one embodiment, after determining the quantified sensitivity coefficient of the sensitivity parameter to the target performance index based on the relative rate of change of the target performance index and the relative rate of change of the sensitivity parameter, the method further includes:

[0036] Based on the quantized sensitivity coefficient and the preset error value, the range of sensitivity indicators affected by the preset error value is determined; the range of sensitivity indicators includes the maximum value and the minimum value of the sensitivity indicator.

[0037] For multiple different sensitivity parameters, determine the quantization sensitivity coefficients corresponding to each sensitivity parameter;

[0038] Based on the values ​​of the multiple quantized sensitivity coefficients, the multiple sensitivity parameters are sorted by sensitivity to obtain a sensitivity sorting result;

[0039] The range of the sensitivity indicators and the sensitivity ranking results are displayed.

[0040] Secondly, this application also provides a quantitative analysis device for the sensitivity of membrane electrode parameters in a proton exchange membrane fuel cell, comprising:

[0041] The three-dimensional computational domain determination module is used to determine the three-dimensional computational domain of the proton exchange membrane fuel cell based on the physical operating behavior of the plates, flow channels and gas diffusion layer of the proton exchange membrane fuel cell.

[0042] A one-dimensional computational domain determination module is used to determine the one-dimensional computational domain of the proton exchange membrane fuel cell based on the physical operating behavior of the microporous layer, catalyst layer and proton exchange membrane of the proton exchange membrane fuel cell.

[0043] A data interaction interface determination module is used to obtain the data interaction interface between the three-dimensional computing domain and the one-dimensional computing domain.

[0044] The simulation model determination module is used to determine the simulation model based on the three-dimensional computational domain, the one-dimensional computational domain, and the data interaction interface.

[0045] The sensitivity parameter change determination module is used to determine the relative change rate of the sensitivity parameters of the proton exchange membrane fuel cell after a preset change; the sensitivity parameters are the structural parameters and physical property parameters of the membrane electrode of the proton exchange membrane fuel cell.

[0046] The performance index change determination module is used to determine the relative change rate of the target performance index of the proton exchange membrane fuel cell after the preset change, based on the simulation model.

[0047] The sensitivity coefficient determination module is used to determine the quantitative sensitivity coefficient of the sensitivity parameter to the target performance index based on the relative change rate of the target performance index and the relative change rate of the sensitivity parameter.

[0048] 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 perform the following steps:

[0049] Based on the physical operating behavior of the plates, flow channels, and gas diffusion layer of the proton exchange membrane fuel cell, the three-dimensional computational domain of the proton exchange membrane fuel cell is determined.

[0050] Based on the physical operating behavior of the microporous layer, catalyst layer, and proton exchange membrane of the proton exchange membrane fuel cell, a one-dimensional computational domain of the proton exchange membrane fuel cell is determined.

[0051] Obtain the data interaction interface between the three-dimensional computational domain and the one-dimensional computational domain;

[0052] Based on the three-dimensional computational domain, the one-dimensional computational domain, and the data interaction interface, a simulation model is determined.

[0053] The relative conversion rate of the sensitivity parameters of the proton exchange membrane fuel cell after a preset transformation is determined; the sensitivity parameters are the structural and physical property parameters of the membrane electrode of the proton exchange membrane fuel cell.

[0054] Based on the simulation model, the relative conversion rate of the target performance index of the proton exchange membrane fuel cell after the preset transformation is determined;

[0055] Based on the relative rate of change of the target performance index and the relative rate of change of the sensitivity parameter, the quantitative sensitivity coefficient of the sensitivity parameter to the target performance index is determined.

[0056] In one embodiment, determining the relative transformation rate of the sensitivity parameter of the proton exchange membrane fuel cell after a preset transformation includes:

[0057] Obtain the reference sensitivity parameter value of the proton exchange membrane fuel cell under reference operating conditions, and the disturbance parameter value of the sensitivity parameter after a preset change based on the reference sensitivity parameter value;

[0058] Based on the baseline sensitivity parameter value and the disturbance parameter value, the relative rate of change of the sensitivity parameter is determined.

[0059] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the following steps:

[0060] Based on the physical operating behavior of the plates, flow channels, and gas diffusion layer of the proton exchange membrane fuel cell, the three-dimensional computational domain of the proton exchange membrane fuel cell is determined.

[0061] Based on the physical operating behavior of the microporous layer, catalyst layer, and proton exchange membrane of the proton exchange membrane fuel cell, a one-dimensional computational domain of the proton exchange membrane fuel cell is determined.

[0062] Obtain the data interaction interface between the three-dimensional computational domain and the one-dimensional computational domain;

[0063] Based on the three-dimensional computational domain, the one-dimensional computational domain, and the data interaction interface, a simulation model is determined.

[0064] The relative conversion rate of the sensitivity parameters of the proton exchange membrane fuel cell after a preset transformation is determined; the sensitivity parameters are the structural and physical property parameters of the membrane electrode of the proton exchange membrane fuel cell.

[0065] Based on the simulation model, the relative conversion rate of the target performance index of the proton exchange membrane fuel cell after the preset transformation is determined;

[0066] Based on the relative rate of change of the target performance index and the relative rate of change of the sensitivity parameter, the quantitative sensitivity coefficient of the sensitivity parameter to the target performance index is determined.

[0067] In one embodiment, determining the relative transformation rate of the sensitivity parameter of the proton exchange membrane fuel cell after a preset transformation includes:

[0068] Obtain the reference sensitivity parameter value of the proton exchange membrane fuel cell under reference operating conditions, and the disturbance parameter value of the sensitivity parameter after a preset change based on the reference sensitivity parameter value;

[0069] Based on the baseline sensitivity parameter value and the disturbance parameter value, the relative rate of change of the sensitivity parameter is determined.

[0070] Fifthly, this application also provides a computer program product, including a computer program that, when executed by a processor, performs the following steps:

[0071] Based on the physical operating behavior of the plates, flow channels, and gas diffusion layer of the proton exchange membrane fuel cell, the three-dimensional computational domain of the proton exchange membrane fuel cell is determined.

[0072] Based on the physical operating behavior of the microporous layer, catalyst layer, and proton exchange membrane of the proton exchange membrane fuel cell, a one-dimensional computational domain of the proton exchange membrane fuel cell is determined.

[0073] Obtain the data interaction interface between the three-dimensional computational domain and the one-dimensional computational domain;

[0074] Based on the three-dimensional computational domain, the one-dimensional computational domain, and the data interaction interface, a simulation model is determined.

[0075] The relative conversion rate of the sensitivity parameters of the proton exchange membrane fuel cell after a preset transformation is determined; the sensitivity parameters are the structural and physical property parameters of the membrane electrode of the proton exchange membrane fuel cell.

[0076] Based on the simulation model, the relative conversion rate of the target performance index of the proton exchange membrane fuel cell after the preset transformation is determined;

[0077] Based on the relative rate of change of the target performance index and the relative rate of change of the sensitivity parameter, the quantitative sensitivity coefficient of the sensitivity parameter to the target performance index is determined.

[0078] In one embodiment, determining the relative transformation rate of the sensitivity parameter of the proton exchange membrane fuel cell after a preset transformation includes:

[0079] Obtain the reference sensitivity parameter value of the proton exchange membrane fuel cell under reference operating conditions, and the disturbance parameter value of the sensitivity parameter after a preset change based on the reference sensitivity parameter value;

[0080] Based on the baseline sensitivity parameter value and the disturbance parameter value, the relative rate of change of the sensitivity parameter is determined.

[0081] The aforementioned quantitative analysis method, apparatus, computer equipment, computer-readable storage medium, and computer program product for the sensitivity of membrane electrode parameters in proton exchange membrane fuel cells (PEMFCs) determine the three-dimensional computational domain of the PEMFC based on the physical operating behavior of the electrode plates, flow channels, and gas diffusion layer; determine the one-dimensional computational domain based on the physical operating behavior of the microporous layer, catalyst layer, and proton exchange membrane; obtain the data interaction interface between the three-dimensional and one-dimensional computational domains; determine the simulation model based on the three-dimensional, one-dimensional, and data interaction interfaces; determine the relative transformation rate of the sensitivity parameters after a preset transformation of the PEMFC; the sensitivity parameters are the structural and physical property parameters of the membrane electrode assembly of the PEMFC; determine the relative transformation rate of the target performance index after a preset transformation of the PEMFC based on the simulation model; and determine the quantitative sensitivity coefficient of the sensitivity parameters to the target performance index based on the relative change rate of the target performance index and the relative change rate of the sensitivity parameters. By acquiring the parameters and performance indicators of a proton exchange membrane fuel cell under baseline operating conditions, as well as the perturbation parameter values ​​and corresponding perturbation performance indicators after preset parameter changes, the relative change rates of the sensitivity parameters and the target performance indicators were calculated. This application overcomes the problem of different physical parameters having different dimensions and being unable to be directly compared by using relative change rates. By calculating the ratio of these two relative change rates, a dimensionless quantitative sensitivity coefficient was determined, establishing a quantitative mapping relationship between parameter perturbations and performance output. This allows researchers to quickly identify and optimize parameters that significantly affect battery performance on a unified numerical scale based on this quantitative sensitivity coefficient, thereby improving the efficiency of the membrane electrode optimization design process. Attached Figure Description

[0082] 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.

[0083] Figure 1 This is a flowchart illustrating a method for quantitatively analyzing the sensitivity of membrane electrode parameters in a proton exchange membrane fuel cell in one embodiment.

[0084] Figure 2 This is a schematic diagram of a simulation model in one embodiment;

[0085] Figure 3 This is a schematic diagram of the simulation model in another embodiment;

[0086] Figure 4 This is a schematic diagram of the simulation process for executing a simulation model in one embodiment;

[0087] Figure 5 This is a schematic diagram illustrating the variation of fuel cell output voltage with platinum loading in the cathode catalyst layer in one embodiment.

[0088] Figure 6 This is a schematic diagram illustrating the loss variation within a fuel cell in one embodiment;

[0089] Figure 7 This is a schematic diagram illustrating the variation of fuel cell output voltage with cathode catalyst porosity in one embodiment;

[0090] Figure 8 Another embodiment is a schematic diagram of loss changes within the fuel cell;

[0091] Figure 9 This is a schematic diagram illustrating the change in fuel cell output voltage with gas diffusion layer porosity in one embodiment.

[0092] Figure 10 This is another schematic diagram illustrating the loss changes within the fuel cell in one embodiment;

[0093] Figure 11 This is a structural block diagram of a device for quantitatively analyzing the sensitivity of membrane electrode parameters in a proton exchange membrane fuel cell in one embodiment.

[0094] Figure 12 This is an internal structural diagram of a computer device in one embodiment;

[0095] Figure 13 This is a schematic diagram showing the results of a quantitative analysis method for the sensitivity of membrane electrode parameters of a proton exchange membrane fuel cell performed on a program product in one embodiment.

[0096] Figure 14 This is a schematic diagram illustrating the results of a quantitative analysis method for the sensitivity of membrane electrode parameters of a proton exchange membrane fuel cell performed on a program product in another embodiment. Detailed Implementation

[0097] 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.

[0098] It should be noted that the terms "first," "second," etc., used in this application can be used to describe various elements, but these elements are not limited by these terms. These terms are only used to distinguish the first element from the second element. The terms "comprising" and "having," and any variations thereof, used in this application, are intended to cover non-exclusive inclusion. The term "multiple" used in this application refers to two or more. The term "and / or" used in this application refers to one of the embodiments, or any combination of multiple embodiments.

[0099] In one embodiment, such as Figure 1 As shown, a quantitative analysis method for the sensitivity of membrane electrode parameters in a proton exchange membrane fuel cell is provided. This embodiment illustrates the application of this method to a terminal. It is understood that this method can also be applied to a server, and to a system including both a terminal and a server, and implemented through interaction between the terminal and the server. In this embodiment, the method includes the following steps:

[0100] Step S101: Based on the physical operating behavior of the plates, flow channels, and gas diffusion layer of the proton exchange membrane fuel cell, determine the three-dimensional computational domain of the proton exchange membrane fuel cell.

[0101] The three-dimensional computational domain can refer to a virtual geometric space constructed in a computer simulation environment to characterize the macroscopic mass transport behavior in a proton exchange membrane fuel cell. It includes, but is not limited to, components in the cell with significant three-dimensional fluid flow characteristics, such as bipolar plates (BP), channels (CH), and gas diffusion layers (GDL). This computational domain is a numerical computing carrier formed by discretizing (e.g., meshing) the actual physical dimensions and geometric topological relationships of the above components. It is used to carry and solve a set of three-dimensional partial differential equations describing physical processes such as fluid dynamics, multi-component diffusion, and heat conduction.

[0102] For example, the physical components in a proton exchange membrane fuel cell (PEMFC) where macroscopic fluid flow and mass transport mainly occur are identified, namely, the electrodes, channels, and gas diffusion layer. Given the significant three-dimensional spatial characteristics of the transport of reactant gases and reaction products within these components—such as convective transport along the channel direction and diffusion transport along the thickness and planar directions of the gas diffusion layer—the terminal extracts geometric characteristic parameters, such as channel width, depth, and ridge width, based on the physical operating behavior of these components. Subsequently, using a pre-defined mesh generation strategy, the geometric models of these components are discretized, thereby constructing a three-dimensional computational domain for the PEMFC. During this process, the distribution of fluid control equations within this three-dimensional space can also be defined to facilitate subsequent simulation of the macroscopic flow distribution of the gas.

[0103] Step S102: Based on the physical operating behavior of the microporous layer, catalyst layer and proton exchange membrane of the proton exchange membrane fuel cell, determine the one-dimensional computational domain of the proton exchange membrane fuel cell.

[0104] The one-dimensional computational domain can be a virtual physical space constructed based on computer simulation technology to simulate electrochemical reactions and transmembrane transport behavior at the microscale inside a fuel cell. It mainly covers components in the battery with thin geometric thickness and significant changes in physical field along the thickness direction, such as the membrane electrode (MEA) microporous layer (MPL), catalyst layer (CL), and proton exchange membrane (MEM). This computational domain is formed by simplifying and reducing the geometric structure of the above components in the planar dimension. For example, it is used to carry and solve a set of one-dimensional governing equations describing microscopic physical processes such as electrochemical reaction kinetics, proton conduction, and dissolved water diffusion.

[0105] For example, the main physical components involved in electrochemical reactions and proton transport in a proton exchange membrane fuel cell (PEMFC) are identified as the microporous layer, catalyst layer, and proton exchange membrane. Considering that these components are geometrically thin-layered, and that key physical quantities within them (such as reaction rate, overpotential, and membrane water content) undergo drastic gradient changes primarily along the thickness direction perpendicular to the membrane plane, while the changes along the planar direction are relatively gradual, the terminal model is dimensionality-reduced based on the physical behavior of these components, retaining only the geometric characteristic parameters along the thickness direction. Subsequently, a one-dimensional computational domain for the PEMFC is constructed, and corresponding electrochemical reaction source terms and transmembrane transport mechanisms are defined within this domain to simulate microscopic-scale physicochemical processes.

[0106] Step S103: Obtain the data interaction interface between the three-dimensional computational domain and the one-dimensional computational domain.

[0107] The data interaction interface can be a logical boundary or virtual medium connecting the three-dimensional computational domain and the one-dimensional computational domain. It is configured to transmit physical field information bidirectionally between computational domains of different dimensions. For example, it can transmit scalar field data (such as component concentration, pressure, temperature, etc.) in the three-dimensional domain to the one-dimensional domain and feed back source term data (such as reaction rate, mass flux, current density, etc.) calculated in the one-dimensional domain to the three-dimensional domain. In a specific implementation, this interface can be two special mesh layers (such as an extra layer (EL)) pre-set in the three-dimensional mesh for storing source term information, or it can be a data mapping function built based on an interpolation algorithm.

[0108] For example, to achieve the coupled solution of macroscopic fluid transport and microscopic electrochemical reactions, the terminal needs to establish a data flow bridge between the defined three-dimensional computational domain and the one-dimensional computational domain. The terminal can set one or more virtual meshes as extension layers at the boundary of the three-dimensional computational domain (e.g., the interface between the gas diffusion layer and the microporous layer). This extension layer does not directly participate in solving the three-dimensional fluid dynamics equations, but rather acts as a data container, used to read the physical parameters at the boundary of the three-dimensional computational domain in real time and input them as boundary conditions into the one-dimensional computational domain. Simultaneously, this extension layer also receives the electrochemical reaction results output from the one-dimensional computational domain and converts them into mass source terms, momentum source terms, or energy source terms in the three-dimensional computational domain. In this way, the terminal constructs a data interaction interface capable of exchanging data in real time, ensuring the accurate transmission of information between models of different dimensions.

[0109] Step S104: Determine the simulation model based on the three-dimensional computational domain, the one-dimensional computational domain, and the data interaction interface.

[0110] The simulation model can be a complete mathematical-physical description system based on the aforementioned computational domain and interface, constructed as a dimensionality-reduced coupled model (e.g., a "3+1 dimensional" model), such as... Figure 2 As shown, the model mathematically consists of a three-dimensional set of partial differential equations (such as the mass and momentum conservation equations) describing macroscopic fluid flow, a set of one-dimensional ordinary differential or algebraic equations (such as the Butler-Folmer equations and diffusion equations) describing microscopic electrochemical processes, and coupled boundary conditions connecting these two sets of equations. Outside of the mathematical-physical description system, its entity can be represented as follows: Figure 3 As shown, the activation area is 25 cm², and both the anode and cathode have serpentine flow fields. The specific parameters of the model are shown in Table 1.

[0111] Table 1. Model Specific Parameters

[0112]

[0113] For example, after defining the three-dimensional computational domain, the one-dimensional computational domain, and the data interaction interface between them, the terminal logically integrates these independent components to construct the final simulation model. In this process, the terminal sets fluid dynamics and mass transfer control equations for the three-dimensional computational domain and electrochemical reaction kinetics and transmembrane transport control equations for the one-dimensional computational domain. More importantly, the terminal uses the data interaction interface to define a coupling iteration mechanism between the two sets of control equations: setting the scalar fields (such as pressure and component concentration) calculated in the three-dimensional domain as the input boundary conditions for the one-dimensional domain, and simultaneously setting the fluxes or source terms (such as current density and water flux) calculated in the one-dimensional domain as the source term update basis for the three-dimensional domain equations. In this way, the terminal establishes a closed-loop solution system, enabling the model to simulate the entire process from macroscopic gas supply to microscopic reaction and product discharge.

[0114] Step S105: Determine the relative conversion rate of the sensitivity parameters of the proton exchange membrane fuel cell after the preset conversion. The sensitivity parameters are the structural and physical property parameters of the membrane electrode assembly (MEA) of the proton exchange membrane fuel cell.

[0115] The relative transformation rate of the sensitivity parameter can be a numerical index used to quantify the degree of change of the input variable. It is determined by calculating the ratio of the difference between the value of the sensitivity parameter (such as the structural or physical property parameters of the membrane electrode) after a preset transformation and the reference value to the reference value. This index aims to eliminate the differences in physical dimensions and orders of magnitude of different sensitivity parameters and provide normalized input data for subsequent standardized sensitivity analysis.

[0116] For example, the terminal determines a baseline sensitivity parameter value for the proton exchange membrane fuel cell under baseline operating conditions. This sensitivity parameter is selected from structural parameters (such as thickness and porosity) or physical property parameters (such as conductivity and permeability) of the membrane electrode. Subsequently, the terminal applies a preset perturbation to this sensitivity parameter, for example, increasing or decreasing the porosity of the cathode catalyst layer by a certain percentage, thereby obtaining a perturbation parameter value. Then, based on the aforementioned baseline value and perturbation value, the terminal calculates the relative proportion of the parameter change, i.e., determines the relative conversion rate of the sensitivity parameter. Specifically, the relative conversion rate of the sensitivity parameter can be expressed by formula (1).

[0117] (1)

[0118] Where ref represents the baseline value of each parameter, The change in the sensitivity parameter It is the relative transformation rate of the sensitivity parameter.

[0119] Step S106: Based on the simulation model, determine the relative conversion rate of the target performance index of the proton exchange membrane fuel cell after the preset conversion.

[0120] The relative transformation rate of the target performance index can be a numerical index used to quantify the degree of system output response. It can be determined by calculating the ratio of the difference between the performance value (such as output voltage and power density) of the proton exchange membrane fuel cell after the sensitivity parameters have undergone a preset transformation and the baseline performance value to the baseline performance value. This index aims to transform the absolute change in battery performance into a normalized relative change, thereby eliminating the influence of different performance index dimensions or baseline values ​​on the sensitivity analysis results.

[0121] For example, the terminal runs a simulation model under baseline operating conditions to calculate the baseline target performance index (e.g., baseline output voltage) of the proton exchange membrane fuel cell. Then, the terminal inputs the perturbation parameter values ​​determined in the above steps after a preset transformation into the simulation model, and runs the simulation calculation again while keeping other conditions unchanged, thereby obtaining the perturbed target performance index. Next, based on the difference between the perturbed value and the baseline value, the terminal calculates its percentage or ratio relative to the baseline value, thereby determining the relative transformation rate of the target performance index. Specifically, the relative transformation rate of the target performance index can be expressed by formula (2).

[0122] (2)

[0123] Where ref represents the baseline value of each parameter, It is the change in the target result; It is the relative change rate of the target performance index.

[0124] In one embodiment, the simulation process is as follows: Figure 4 As shown, specifically, this process mainly involves cyclical interaction between the three-dimensional solution domain and the one-dimensional solution domain through a data interaction interface (i.e., the connection nodes and extension layers in the diagram). Specifically, firstly, on the three-dimensional computational domain side, conservation equations (including mass, momentum, energy, and component transport equations) are solved using initial conditions or the results of the previous time step, thereby obtaining the macroscopic fluid physics field distribution. Subsequently, the terminal extracts key scalar field data from the extension layer, which serves as the data interaction interface. This data specifically includes parameters such as pressure, component concentration, and temperature at that location, and is then passed as boundary conditions to the one-dimensional computational domain.

[0125] Next, the terminal, based on the received scalar field data, calls upon electrochemical and transmembrane transport models within the one-dimensional computational domain to calculate one-dimensional analytical solutions, thereby determining microscopic physical quantities, specifically including the membrane water content, local overpotential, and electrochemical reaction rate. Based on these calculated one-dimensional microscopic parameters, the terminal further calculates the source terms (such as mass, heat, and current sources) fed back to the three-dimensional domain and updates the physical property parameters (such as the effective diffusion coefficient). Finally, these updated source terms and physical property parameters are fed back to the three-dimensional computational domain to correct the coefficients and source terms of the three-dimensional conservation equations. The terminal continuously repeats the above closed-loop iterative process until the data exchange between the three-dimensional and one-dimensional domains meets the preset convergence conditions, thereby achieving accurate simulation of the multiphysics coupling behavior of a proton exchange membrane fuel cell.

[0126] Step S107: Based on the relative rate of change of the target performance index and the relative rate of change of the sensitivity parameter, determine the quantitative sensitivity coefficient of the sensitivity parameter to the target performance index.

[0127] Among them, the quantification sensitivity coefficient can be a dimensionless evaluation index used to standardize the weight of the influence of input variables on the output response. It can be a value determined based on the ratio between the relative transformation rate of the target performance index and the relative transformation rate of the sensitivity parameter. This coefficient aims to shield the inherent differences in physical units and orders of magnitude of different sensitivity parameters (such as porosity, thickness, conductivity, etc.) and provide a unified scale that can horizontally compare the degree of influence of different design parameters on battery performance. The absolute value of the value is used to characterize the strength of the sensitivity.

[0128] For example, the terminal calls the two relative change data obtained from the above steps: the relative transformation rate of the sensitivity parameter and the relative transformation rate of the target performance index. Subsequently, the terminal performs a division operation or ratio calculation, dividing the relative transformation rate of the target performance index by the relative transformation rate of the sensitivity parameter, thereby obtaining the quantized sensitivity coefficient of the specific sensitivity parameter for the target performance index. Specifically, the quantized sensitivity coefficient can be represented by formula (3).

[0129] (3)

[0130] in, , is the quantification of parameters sensitivity coefficient.

[0131] Optionally, the terminal can repeat the above calculation process for multiple different sensitivity parameters to obtain a set of quantified sensitivity coefficients, and sort the parameters according to the magnitude of the coefficient values ​​to identify the key parameters that have the most significant impact on system performance.

[0132] In this embodiment, the problem of different physical parameters having different dimensions and being unable to be directly compared is overcome by using relative change rates. By calculating the ratio of these two relative change rates, a dimensionless quantitative sensitivity coefficient is determined, establishing a quantitative mapping relationship between parameter perturbations and performance output. This allows researchers to quickly identify and optimize parameters that significantly affect battery performance on a unified numerical scale based on this quantitative sensitivity coefficient, thereby improving the efficiency of the membrane electrode optimization design process.

[0133] In an exemplary embodiment, the relative change rate includes a joint relative change rate; determining the relative change rate of the sensitivity parameter of the proton exchange membrane fuel cell after a preset change includes:

[0134] When multiple sensitivity parameters change, determine multiple relative change rates of multiple sensitivity parameters after a preset transformation; obtain multiple relative change vectors corresponding to each relative change rate, and aggregate the multiple relative change vectors to obtain a joint relative change rate that characterizes the overall degree of change of multiple relative change rates;

[0135] Based on the relative rate of change of the target performance index and the relative rate of change of the sensitivity parameter, the quantitative sensitivity coefficient of the sensitivity parameter to the target performance index is determined, including:

[0136] Based on the relative rate of change and the joint relative rate of change of the target performance index, the quantitative sensitivity coefficients of multiple sensitivity parameters to the target performance index are obtained.

[0137] Among them, the joint relative change rate can be a scalar index used to characterize the intensity of the comprehensive disturbance generated when multiple sensitive parameters change simultaneously in a multidimensional parameter space. In essence, it is a dimensionality reduction or summation of multi-source input changes.

[0138] A relative change vector can refer to the rate of change of each discrete parameter as a vector component in a multidimensional space. Through specific mathematical operations (such as Euclidean norm calculation), these components can be combined into a value that represents the overall change magnitude.

[0139] In an exemplary embodiment, the terminal performs a sensitivity analysis step for a multivariate coupled scenario. Specifically, when the operating conditions of a proton exchange membrane fuel cell change, causing multiple sensitive parameters (such as operating temperature, inlet pressure, and relative humidity) to undergo preset changes simultaneously, the terminal first calculates the relative rate of change of each sensitive parameter before and after the change. Subsequently, the terminal obtains multiple relative change vectors corresponding to these relative rates of change and uses a preset aggregation algorithm (e.g., calculating the magnitude or root mean square of the vectors) to aggregate these vectors, thereby obtaining a joint relative rate of change (i.e., the comprehensive input change) that can characterize the overall degree of change of all parameters. Based on this, the terminal further calculates the relative rate of change of the target performance index (such as output voltage) during this process and performs a ratio calculation between the relative rate of change of this performance index and the joint relative rate of change obtained above. This ratio is determined as the quantitative sensitivity coefficient of these sensitive parameters as a whole to the target performance index.

[0140] For example, in a proton exchange membrane fuel cell system, cell performance is often affected by a variety of operating and structural parameters, including but not limited to operating temperature, inlet pressure, relative humidity, and stoichiometry. These parameters are independent of each other when they are set, but they usually change together in combination during actual operation, which has a significant coupled effect on the cell voltage.

[0141] In an exemplary embodiment, it is assumed that the results were obtained through experimental testing or multiphysics numerical simulation methods. Group The sample is run, and each set of samples corresponds to a set of sensitivity parameters and a target performance index (such as output voltage). Among them, the first... The sensitivity parameters of the group samples are shown in formula (4):

[0142] (4)

[0143] in, This indicates the number of sensitive parameters selected, such as operating temperature and intake pressure; the corresponding output voltage is denoted as... The values ​​of each input parameter are independent of each other, and any set of samples represents only one independent experimental or simulation condition.

[0144] Based on the theory of sample comparison, this paper analyzes the relationship between the joint changes in input parameters and the changes in output voltage under any two different operating conditions, thereby achieving an overall sensitivity analysis of the PEMFC system to simultaneous changes in multiple parameters. For any two different samples... and , defines the first The relative rate of change of each input parameter on this sample pair is shown in Equation (5):

[0145] (5)

[0146] This formula uses a sample For reference operating conditions, the description parameters are derived from the operating conditions. To working condition The relative change range. Employing dimensionless relative change eliminates differences in dimensions and orders of magnitude among different physical parameters, making it feasible to analyze different types of parameters within the same framework. When multiple variables change simultaneously, the relative rate of change of each parameter is considered as a... Vectors of dimension 1, combined using the Euclidean norm, define sample pairs. The relative change of the joint inputs As shown in formula (6):

[0147] (6)

[0148] In mathematics, it represents the magnitude of the relative change vector of parameters; in a physical sense, it can be understood as the magnitude of the PEMFC system's operating conditions in a multidimensional parameter space. arrive The intensity of the overall disturbance experienced. The larger the value, the more significant the combined change in multiple operating parameters. The corresponding PEMFC output voltage in the sample... and The relative rate of change between them As shown in formula (7):

[0149] (7)

[0150] Finally, quantitative sensitivity coefficients of multiple sensitivity parameters to the target performance index (output voltage) were constructed, which are also known as multivariate joint sensitivity indices. As shown in formula (8):

[0151] (8)

[0152] This metric represents the relative strength of the change in output performance caused by the relative changes in multiple sensitivity parameters in each group. When A larger value indicates that a small combined change in the input parameters can cause a significant change in the battery output voltage, indicating that the PEMFC system has high sensitivity in the direction of parameter change; conversely, a smaller value indicates that the system has poor sensitivity to the combined change of multiple parameters in this direction.

[0153] To obtain the overall multivariate sensitivity level of PEMFC across the entire sample space, the arithmetic mean of the joint sensitivity indices of sample pairs that meet the calculation conditions can be taken, and defined as the global joint sensitivity index. As shown in formula (9):

[0154] (9)

[0155] in, Denotes the set of all valid sample pairs. This represents the number of valid sample pairs. This global metric reflects the average response of PEMFC output performance to simultaneous changes in multiple parameters within the coverage of existing experimental or simulation conditions, and can serve as an important quantitative indicator for evaluating the overall parameter sensitivity level of the system.

[0156] In this embodiment, the above steps achieve a quantitative assessment of multi-parameter synergistic changes under operating conditions. This analysis method based on joint relative change rate breaks through the limitations of traditional univariate sensitivity analysis, effectively capturing the comprehensive impact of multiple parameters on battery performance due to coupling effects during actual operation. Through vector aggregation processing, complex multidimensional parameter fluctuations are simplified into a unified comprehensive disturbance intensity index. This allows designers to quickly identify which parameter combinations have a significant impact on system performance, directly based on experimental or simulation data, even in the absence of detailed electrochemical mechanism models. This provides a powerful mathematical tool for system stability assessment and control strategy optimization under complex operating conditions.

[0157] In an exemplary embodiment, determining the relative conversion rate of a sensitivity parameter of a proton exchange membrane fuel cell after a preset transformation includes:

[0158] Obtain the baseline sensitivity parameter value of the proton exchange membrane fuel cell under the baseline operating conditions, as well as the disturbance parameter value after the sensitivity parameter has undergone a preset change based on the baseline sensitivity parameter value; determine the relative change rate of the sensitivity parameter based on the baseline sensitivity parameter value and the disturbance parameter value.

[0159] The baseline operating condition can be the standard operating state or initial setting conditions of a proton exchange membrane fuel cell when it is not affected by parameter changes. It includes the baseline sensitivity parameter value as the basis for comparison. This value is the standard value in the design specification or the reference value in the existing experimental data. The disturbance parameter value refers to the parameter value obtained by applying a preset change amount through mathematical superposition or physical adjustment based on the above baseline sensitivity parameter value. It is used to simulate parameter fluctuations in actual manufacturing errors or design optimization processes. The difference between this value and the baseline value constitutes the arithmetic basis for calculating the relative rate of change.

[0160] Specifically, the terminal acquires the baseline sensitivity parameter value of the proton exchange membrane fuel cell under baseline operating conditions. For example, the baseline platinum loading of the cathode catalyst layer is set to 0.4 mg / cm². Then, according to preset analytical requirements, the terminal applies a small perturbation to this parameter (e.g., increasing or decreasing a certain value), thereby acquiring the perturbation parameter value (e.g., 0.3 mg / cm² or 0.5 mg / cm²) after the preset change. Next, the terminal calculates the difference between the perturbation parameter value and the baseline parameter value using a formula, and divides this difference by the absolute value of the baseline parameter value to obtain the relative rate of change of the sensitivity parameter.

[0161] In this embodiment, by calculating the relative rate of change based on the baseline value and the disturbance value, the parameter changes with different physical meanings are effectively transformed into dimensionless proportional values. This provides standardized input data for subsequent sensitivity analysis, ensuring that the analysis results can truly reflect the impact of the parameter's own variation on the system, without being disturbed by the initial value of the parameter.

[0162] In an exemplary embodiment, based on a simulation model, the relative conversion rate of the target performance index of the proton exchange membrane fuel cell after a preset conversion is determined, including:

[0163] Based on the simulation model, the baseline target performance index corresponding to the baseline sensitivity parameter value is determined under the baseline operating condition of the proton exchange membrane fuel cell; based on the simulation model, the perturbation target performance index corresponding to the perturbation parameter value is determined under the target operating condition after the baseline operating condition has undergone a preset change; based on the baseline target performance index and the perturbation target performance index, the relative rate of change of the target performance index is determined.

[0164] Among them, the baseline target performance index can be the battery performance output value calculated by the simulation model when the input sensitive parameters are in the baseline state, such as the baseline output voltage or power density, which represents the initial performance level of the system; the disturbance target performance index refers to the battery performance output value calculated by the simulation model after the input sensitive parameters are replaced with disturbance parameter values ​​(i.e., in the target operating condition), which represents the performance level of the system after responding to parameter changes. The difference between these two indices directly reflects the physical response amplitude of the system to disturbances of specific parameters.

[0165] Specifically, the terminal first invokes the simulation model and performs steady-state calculations with the input parameters being the baseline sensitivity parameter values ​​to determine the baseline target performance index of the proton exchange membrane fuel cell (e.g., a baseline voltage of 0.677V). Then, the terminal modifies the input conditions of the simulation model to the target operating condition after preset changes, i.e., inputting disturbance parameter values, and runs the simulation calculation again to determine the corresponding disturbance target performance index (e.g., when the platinum loading becomes 0.2 mg / cm², the voltage becomes 0.667V). Finally, the terminal calculates the difference between the disturbance target performance index and the baseline target performance index, and divides it by the baseline target performance index to obtain the relative rate of change of the target performance index.

[0166] In this embodiment, by comparing the changes in performance indicators before and after the disturbance, the dynamic response characteristics of battery performance to fluctuations in minute parameters can be accurately captured. Simultaneously, calculating the relative rate of change eliminates the influence of the absolute magnitude of performance indicators (such as high-voltage versus low-voltage conditions) on sensitivity evaluation, making the analysis results comparable across different operating ranges and providing an objective output basis for the final calculation of the quantified sensitivity coefficient.

[0167] In an exemplary embodiment, based on a simulation model, the relative conversion rate of the target performance index of the proton exchange membrane fuel cell after a preset conversion is determined, including:

[0168] Determine the influence area corresponding to the baseline sensitivity parameter value; if the influence area indicates a three-dimensional computational domain, then determine the three-dimensional operating data based on the baseline sensitivity parameter and the three-dimensional computational domain of the simulation model; input the three-dimensional operating data into the one-dimensional computational domain of the simulation model via the data interaction interface to determine the one-dimensional operating data; if the three-dimensional operating data and the one-dimensional operating data meet the preset conditions, determine the baseline target performance index based on the three-dimensional operating data and the one-dimensional operating data.

[0169] The influence region can refer to the computational space range to which the sensitive parameter belongs in terms of physical and geometric logic. It is used to indicate whether the change of the parameter first or mainly affects the macroscopic fluid transport process or the microscopic electrochemical reaction process, thus determining the data triggering point of the simulation calculation. The three-dimensional running data refers to the macroscopic physical field distribution information obtained by solving the fluid dynamics equations in the three-dimensional computational domain, such as the concentration field, pressure field and velocity field data of gas components, which constitute the boundary environmental conditions of the microscopic reaction region.

[0170] Specifically, the terminal first determines the influence region corresponding to the current baseline sensitivity parameter value. If the parameter is a macroscopic structural parameter (e.g., the porosity of the gas diffusion layer or the channel size), its influence region is determined to be a three-dimensional computational domain. At this point, based on the baseline sensitivity parameter, the terminal prioritizes solving the conservation equations through the three-dimensional computational domain of the simulation model to determine the three-dimensional operating data. Subsequently, the terminal inputs this three-dimensional operating data (e.g., reactant gas concentration) into the one-dimensional computational domain via a data interaction interface (e.g., an extended layer) as boundary conditions for the one-dimensional calculation. After completing the electrochemical calculations and determining the one-dimensional operating data (e.g., current density source terms) in the one-dimensional domain, if the preset convergence conditions are met, the terminal determines the final baseline target performance index based on the converged three-dimensional and one-dimensional operating data.

[0171] In this embodiment, for sensitive parameters belonging to the three-dimensional computational domain, the three-dimensional flow field data is updated first and then passed down to the micro-region. This computational strategy based on the influence region not only ensures the logical correctness of the simulation process, but also helps to improve the stability of the coupled iterative computation, ensuring that the final performance indicators can accurately reflect the comprehensive impact of changes in macroscopic structural parameters.

[0172] In an exemplary embodiment, after determining the influence region corresponding to the benchmark sensitivity parameter value, the method further includes:

[0173] If the affected area indicates a one-dimensional computational domain, then based on the benchmark sensitivity parameters, one-dimensional operating data is determined through the one-dimensional computational domain of the simulation model; the one-dimensional operating data is input into the three-dimensional computational domain of the simulation model via the data interaction interface to determine the three-dimensional operating data; if the three-dimensional operating data and the one-dimensional operating data meet the preset conditions, the benchmark target performance index is determined based on the three-dimensional operating data and the one-dimensional operating data.

[0174] Among them, one-dimensional operating data can be microscopic physical quantity information obtained by the simulation model in solving electrochemical kinetics and transmembrane transport equations in the one-dimensional computational domain, such as membrane water content, local overpotential, electrochemical reaction rate, and source terms data of mass, momentum or energy derived therefrom. These data reflect the activity level of the core reaction region inside the battery and are fed back to the macroscopic computational domain as source terms to correct the fluid state.

[0175] Specifically, if the terminal determines that the influence region corresponding to the baseline sensitivity parameter value indicates a one-dimensional computational domain (e.g., the sensitivity parameter is the platinum loading of the catalyst layer or the porosity of the microporous layer), then the solver of the one-dimensional computational domain is preferentially invoked based on this parameter. The terminal calculates and determines the one-dimensional operating data, especially the generated source term data. Subsequently, the terminal inputs this data, which contains information on reaction consumption and generation, into the three-dimensional computational domain via a data interaction interface, updating it as the source term of the three-dimensional governing equations. The three-dimensional computational domain then recalculates the macroscopic physical field (i.e., determines the three-dimensional operating data). When the interactive iteration between the three-dimensional and one-dimensional data reaches convergence equilibrium, i.e., when the preset conditions are met, the terminal determines the baseline target performance index based on the final operating data.

[0176] In this embodiment, for sensitivity parameters belonging to the one-dimensional computational domain, the microscopic reaction source terms are calculated first and fed back to the three-dimensional domain. This reverse data flow logic fully leverages the advantages of the coupled model, ensuring that the sensitivity analysis of parameters involving the core reaction region can capture the physical response across scales and improving the confidence of the analysis results.

[0177] In an exemplary embodiment, after determining the quantified sensitivity coefficient of the sensitivity parameter to the target performance index based on the relative rate of change of the target performance index and the relative rate of change of the sensitivity parameter, the method further includes:

[0178] Based on the quantified sensitivity coefficient and the preset error value, the range of sensitivity indicators affected by the preset error value is determined; the range of sensitivity indicators includes the maximum value and the minimum value of the sensitivity indicators; for multiple different sensitivity parameters, the quantified sensitivity coefficients corresponding to each sensitivity parameter are determined; based on the values ​​of the multiple quantified sensitivity coefficients, the multiple sensitivity parameters are ranked according to their sensitivity, and the sensitivity ranking results are obtained; the range of sensitivity indicators and the sensitivity ranking results are displayed.

[0179] The preset error value can be a value input by the user to characterize the accuracy error of the test bench, the confidence error of the model, or the measurement uncertainty of the parameters. It is used to correct the sensitivity calculation results under ideal conditions. The sensitivity index range refers to the range of values ​​in which the quantified sensitivity coefficient may fluctuate after considering the above-mentioned error effects, including the upper limit (maximum value) and the lower limit (minimum value), which is used to reflect the robustness of the analysis results. The sensitivity ranking result is an ordered list after arranging multiple parameters according to the magnitude of the quantified sensitivity coefficient, which is used to intuitively display the importance level of each parameter.

[0180] Specifically, after calculating the quantized sensitivity coefficient, the terminal obtains the preset error value input by the user. Based on this error value, the quantized sensitivity coefficient is corrected to determine the range of sensitivity indicators affected by the error, i.e., the maximum and minimum values ​​of the sensitivity indicators are calculated. Furthermore, the terminal calculates the quantized sensitivity coefficient for multiple different sensitivity parameters (such as cathode catalyst layer porosity, platinum loading, and gas diffusion layer porosity), and sorts these parameters according to the magnitude of the coefficient values ​​(e.g., from largest to smallest), generating a sensitivity ranking result. Finally, the terminal displays the calculated sensitivity indicator range and the sensitivity ranking result through a display interface.

[0181] In this embodiment, by introducing an error analysis mechanism, the quantification result is no longer a single ideal value, but a range containing a confidence interval. This allows the analysis results to better adapt to measurement errors and environmental interference present in actual engineering, improving the reference value of the data. Simultaneously, through automatic sorting and intuitive display, designers can readily identify the key parameters (such as catalyst layer porosity) that have the greatest impact on performance, thereby quickly focusing on optimization directions and greatly improving the decision-making efficiency of membrane electrode design and optimization.

[0182] In one embodiment, multiple sets of parameter sensitivity verifications and electrochemical mechanism analyses can be performed to quantify the nonlinear impact of different design parameters on battery performance. Specifically, this embodiment includes the following three targeted simulation experiments:

[0183] The first group of experiments involved the platinum loading of the cathode catalyst layer. For the sensitivity analysis, the terminal first set baseline conditions, keeping the platinum loading of the anode catalyst layer at 0.1 mg / cm² and other parameters constant. Then, the terminal simulated the change in platinum loading by adjusting the Pt / C ratio of the cathode catalyst (platinum-carbon catalyst), while keeping the catalyst layer thickness constant. The cathode catalyst layer parameters are shown in Table 2. Specifically, the terminal set a gradient of platinum loading in the cathode catalyst layer within the range of 0.05 mg / cm² to 0.5 mg / cm², with corresponding Pt / C ratios of 0.09, 0.166, 0.287, 0.379, 0.45, and 0.508, respectively. Based on these settings, the terminal calculated and output the results.

[0184] Table 2 Cathode Catalyst Layer Parameters

[0185]

[0186] The target performance indicator, the change in fuel cell output voltage with the platinum loading of the cathode catalyst layer, is as follows: Figure 5As shown, the output voltage of the fuel cell increases with increasing platinum loading in the cathode catalyst layer, but this increasing trend slows down when the platinum loading is high (e.g., exceeding 0.4 mg / cm²). Further analysis of the various losses within the battery yields the following results: Figure 6 The changes in various losses within the fuel cell shown indicate that the increase in fuel cell output voltage with increasing platinum loading is mainly due to the decrease in activation losses.

[0187] Based on this analysis, the conclusion is that increasing the platinum loading in the cathode catalyst layer has diminishing marginal returns on fuel cell performance. Therefore, cost factors should be comprehensively considered when designing the membrane electrode assembly to avoid blindly pursuing high platinum loading.

[0188] The second group of experiments showed the porosity of the cathode catalyst layer. Following sensitivity analysis, the terminal then investigated the effect of cathode catalyst layer porosity on gas-liquid transport and conductivity. While keeping the anode catalyst layer porosity and other parameters constant, the terminal simulated the change in cathode catalyst layer porosity by varying the Pt / C ratio (considering that porosity is affected by carbon type and coating process in actual preparation). The cathode catalyst layer parameters are shown in Table 3. Specifically, the terminal set the cathode catalyst layer porosity to 0.4, 0.5, 0.6, and 0.7, with corresponding Pt / C ratios of 0.371, 0.416, 0.473, and 0.548, respectively.

[0189] Table 3 Cathode Catalyst Layer Parameters

[0190]

[0191] After the terminal simulation is completed, the following can be obtained: Figure 7 The fuel cell output voltage variation with cathode catalyst porosity is shown; as cathode catalyst porosity increases, the output voltage generally decreases. Further analysis of various losses reveals... Figure 8 The study examined various losses within the fuel cell and determined that while increased porosity promotes gas-liquid transport, thereby reducing activation and mass transfer losses, it also reduces proton transport pathways, leading to a significant increase in ohmic losses. Since the negative impact of increased ohmic losses far outweighs the positive benefits of improved mass transfer, this ultimately results in performance degradation. Therefore, the study concluded that a lower catalyst layer porosity should be prioritized in the fabrication of the membrane electrode assembly (MEA) to promote proton transport.

[0192] The third group of experiments focused on the porosity of the gas diffusion layer. Sensitivity analysis was performed, and finally, simulation analysis was conducted on the porosity of the gas diffusion layer (GDL). The porosity value of the GDL was gradually increased, resulting in the following... Figure 9 The change in fuel cell output voltage with the porosity of the gas diffusion layer, as shown, indicates that the fuel cell output voltage first increases and then decreases.

[0193] Further terminal access such as Figure 10 The diagram illustrates the changes in various losses within the fuel cell: Increased porosity of the gas diffusion layer has a dual impact on performance. On one hand, increased porosity facilitates the transport of reactant gases to the catalyst layer, significantly reducing mass transfer losses. On the other hand, increased porosity reduces electron transport paths, leading to a significant increase in ohmic losses. In the lower porosity range, the voltage increase resulting from improved mass transfer dominates; while in the higher porosity range, the increase in ohmic losses dominates. Therefore, it is determined that a suitable gas diffusion layer porosity should be selected during the design phase to balance the effects of both factors.

[0194] In one embodiment, after completing the above electrochemical analysis, a simulation model is used to perform simulation. By controlling variables, the effects of single changes in the cathode catalyst platinum loading, cathode catalyst porosity, and cathode gas diffusion layer porosity on the output voltage are obtained, as shown in Table 4, which presents the baseline operating conditions and the effects of adding disturbances to single variables on the output voltage.

[0195] Table 4. Effects of Baseline Operating Conditions and the Influence of Adding Disturbance to a Single Variable on Output Voltage

[0196]

[0197] Specifically, the sensitivity quantization coefficients of each parameter are calculated, and the calculation results and quantization ranking are as follows:

[0198]

[0199] By ranking the sensitivity results of key MEA parameters, it can be seen that the porosity of the cathode catalyst layer has the greatest impact on the output voltage, followed by the porosity of the cathode gas diffusion layer, while the platinum loading of the cathode catalyst layer has the least impact on the output voltage. This is consistent with the results obtained through electrochemical analysis, proving the effectiveness of the method. Furthermore, this method allows for direct analysis of numerical results, eliminating the need for complex electrochemical mechanism analysis and providing support for subsequent optimization of key MEA parameters.

[0200] It should be understood that although the steps in the flowcharts of the above embodiments 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 above embodiments 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 in other steps. It is understood that the steps in different embodiments can be freely combined as needed, and all non-contradictory solutions formed by such combinations are within the scope of protection of this application.

[0201] Based on the same inventive concept, this application also provides a device for quantitatively analyzing the membrane electrode parameter sensitivity of a proton exchange membrane fuel cell, which is used to implement the above-described method for quantitatively analyzing the sensitivity of membrane electrode parameters of a proton exchange membrane fuel cell. The solution provided by this device is similar to the solution described in the above method. Therefore, the specific limitations of one or more embodiments of the device for quantitatively analyzing the sensitivity of membrane electrode parameters of a proton exchange membrane fuel cell provided below can be found in the limitations of the above-described method for quantitatively analyzing the sensitivity of membrane electrode parameters of a proton exchange membrane fuel cell, and will not be repeated here.

[0202] In one exemplary embodiment, such as Figure 11 As shown, a quantitative analysis device for the sensitivity of membrane electrode parameters in a proton exchange membrane fuel cell is provided, comprising: a three-dimensional computational domain determination module 1101, a one-dimensional computational domain determination module 1102, a data interaction interface determination module 1103, a simulation model determination module 1104, a sensitivity parameter change determination module 1105, a performance index change determination module 1106, and a sensitivity coefficient determination module 1107, wherein:

[0203] The three-dimensional computational domain determination module 1101 is used to determine the three-dimensional computational domain of the proton exchange membrane fuel cell based on the physical operating behavior of the plates, flow channels and gas diffusion layer of the proton exchange membrane fuel cell.

[0204] The one-dimensional computational domain determination module 1102 is used to determine the one-dimensional computational domain of the proton exchange membrane fuel cell based on the physical operating behavior of the microporous layer, catalyst layer and proton exchange membrane of the proton exchange membrane fuel cell.

[0205] The data interaction interface determination module 1103 is used to obtain the data interaction interface between the three-dimensional computing domain and the one-dimensional computing domain.

[0206] The simulation model determination module 1104 is used to determine the simulation model based on the three-dimensional computing domain, the one-dimensional computing domain, and the data interaction interface;

[0207] The sensitivity parameter change determination module 1105 is used to determine the relative change rate of the sensitivity parameters of the proton exchange membrane fuel cell after a preset change; the sensitivity parameters are the structural parameters and physical property parameters of the membrane electrode of the proton exchange membrane fuel cell.

[0208] The performance index change determination module 1106 is used to determine the relative change rate of the target performance index of the proton exchange membrane fuel cell after the preset change, based on the simulation model.

[0209] The sensitivity coefficient determination module 1107 is used to determine the quantitative sensitivity coefficient of the sensitivity parameter to the target performance index based on the relative change rate of the target performance index and the relative change rate of the sensitivity parameter.

[0210] In one embodiment, the relative rate of change includes a relative rate of change and a joint relative rate of change; the sensitivity parameter change determination module 1105 is further configured to determine, in the case of multiple sensitivity parameter changes, multiple relative rates of change of each of the multiple sensitivity parameters after the preset transformation occurs;

[0211] Obtain multiple relative change vectors corresponding to each of the relative change rates, and aggregate the multiple relative change vectors to obtain a joint relative change rate that characterizes the overall degree of change of the multiple relative change rates;

[0212] In one embodiment, the performance index change determination module 1106 is further configured to obtain the quantitative sensitivity coefficients of the plurality of sensitivity parameters to the target performance index based on the relative change rate of the target performance index and the joint relative change rate.

[0213] In one embodiment, the sensitivity parameter change determination module 1105 is further configured to obtain the reference sensitivity parameter value of the proton exchange membrane fuel cell under reference operating conditions, and the disturbance parameter value of the sensitivity parameter after a preset change based on the reference sensitivity parameter value;

[0214] Based on the baseline sensitivity parameter value and the disturbance parameter value, the relative rate of change of the sensitivity parameter is determined.

[0215] In one embodiment, the performance index change determination module 1106 is further configured to determine, based on the simulation model, the benchmark target performance index corresponding to the benchmark sensitivity parameter value when the proton exchange membrane fuel cell is under the benchmark operating condition;

[0216] Based on the simulation model, the target performance index of the disturbance parameter value is determined under the target condition after the preset change of the baseline condition.

[0217] Based on the baseline target performance index and the disturbance target performance index, the relative rate of change of the target performance index is determined.

[0218] In one embodiment, the performance index change determination module 1106 is further configured to determine the influence region corresponding to the benchmark sensitivity parameter value;

[0219] If the affected area indicates the three-dimensional computational domain, then based on the benchmark sensitivity parameter, the three-dimensional operating data is determined through the three-dimensional computational domain of the simulation model;

[0220] The three-dimensional operational data is input into the one-dimensional computational domain of the simulation model via a data interaction interface to determine the one-dimensional operational data.

[0221] If the three-dimensional running data and the one-dimensional running data meet the preset conditions, the benchmark target performance index is determined based on the three-dimensional running data and the one-dimensional running data.

[0222] In one embodiment, the performance index change determination module 1106 is further configured to determine one-dimensional operating data based on the benchmark sensitivity parameter and through the one-dimensional computing domain of the simulation model if the affected area indicates the one-dimensional computing domain;

[0223] The one-dimensional operational data is input into the three-dimensional computational domain of the simulation model via the data interaction interface to determine the three-dimensional operational data;

[0224] If the three-dimensional running data and the one-dimensional running data meet the preset conditions, the benchmark target performance index is determined based on the three-dimensional running data and the one-dimensional running data.

[0225] In one embodiment, the sensitivity coefficient determination module 1107 is further configured to determine the range of sensitivity indicators affected by the preset error value based on the quantized sensitivity coefficient and the preset error value; the range of sensitivity indicators includes the maximum value of the sensitivity indicator and the minimum value of the sensitivity indicator;

[0226] For multiple different sensitivity parameters, determine the quantization sensitivity coefficients corresponding to each sensitivity parameter;

[0227] Based on the values ​​of the multiple quantized sensitivity coefficients, the multiple sensitivity parameters are sorted by sensitivity to obtain a sensitivity sorting result;

[0228] The range of the sensitivity indicators and the sensitivity ranking results are displayed.

[0229] Each module in the aforementioned quantitative analysis device for the sensitivity of membrane electrode parameters in a proton exchange membrane fuel cell 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 memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0230] In one exemplary embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 12 As 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 computational and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. 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 the computer program is executed by the processor, it implements a quantitative analysis method for the sensitivity of membrane electrode parameters in a proton exchange membrane fuel cell.

[0231] Those skilled in the art will understand that Figure 12 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.

[0232] 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.

[0233] 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.

[0234] In an exemplary embodiment, the terminal runs a parameter sensitivity quantification calculation tool written in a programming language (such as Python) and packaged as a standalone executable file (.exe) to provide a convenient and efficient analysis environment. The specific operation process is as follows: First, the terminal displays the calculator's input interface and receives the change values ​​of the sensitivity parameters entered by the user in a specific order. After receiving the user's confirmation instruction (such as pressing the Enter key), the terminal prompts and receives the target parameter values ​​entered by the user, each corresponding to one of the aforementioned change values. Based on these two sets of input data, the terminal executes the steps of the above-described method embodiments to quickly calculate the sensitivity quantification coefficient of the sensitivity parameter to the target performance index, and intuitively outputs the calculation results on the interface (e.g., ...). Figure 13 (As shown).

[0235] In another embodiment, to extend this sensitivity quantization method to the application of experimental results, it is necessary to avoid the influence of test bench precision errors on the sensitivity quantization results. Adding the error value as input to the calculator yields a range of sensitivity quantization results, such as... Figure 14 As shown, the maximum and minimum values ​​of the sensitivity index under the influence of error can be obtained, as well as the original values ​​when the error is 0, to improve the universality and practicality of the calculator.

[0236] 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.

[0237] 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.

[0238] 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.

[0239] 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 method for quantitative analysis of the sensitivity of membrane electrode parameters in a proton exchange membrane fuel cell, characterized in that, The method includes: Based on the physical operating behavior of the plates, flow channels, and gas diffusion layer of the proton exchange membrane fuel cell, the three-dimensional computational domain of the proton exchange membrane fuel cell is determined. Based on the physical operating behavior of the microporous layer, catalyst layer, and proton exchange membrane of the proton exchange membrane fuel cell, a one-dimensional computational domain of the proton exchange membrane fuel cell is determined. Obtain the data interaction interface between the three-dimensional computational domain and the one-dimensional computational domain; Based on the three-dimensional computational domain, the one-dimensional computational domain, and the data interaction interface, a simulation model is determined. The relative conversion rate of the sensitivity parameters of the proton exchange membrane fuel cell after a preset transformation is determined; the sensitivity parameters are the structural and physical property parameters of the membrane electrode of the proton exchange membrane fuel cell. Based on the simulation model, the relative conversion rate of the target performance index of the proton exchange membrane fuel cell after the preset transformation is determined; Based on the relative rate of change of the target performance index and the relative rate of change of the sensitivity parameter, the quantitative sensitivity coefficient of the sensitivity parameter to the target performance index is determined.

2. The method according to claim 1, characterized in that, The relative change rate includes the relative change rate and the combined relative change rate; the relative change rate for determining the sensitivity parameter of the proton exchange membrane fuel cell after a preset change includes: When multiple sensitivity parameters change, determine the relative rates of change of each of the multiple sensitivity parameters after the preset transformation occurs; Obtain multiple relative change vectors corresponding to each of the relative change rates, and aggregate the multiple relative change vectors to obtain a joint relative change rate that characterizes the overall degree of change of the multiple relative change rates; The determination of the quantitative sensitivity coefficient of the sensitivity parameter to the target performance index based on the relative rate of change of the target performance index and the relative rate of change of the sensitivity parameter includes: Based on the relative rate of change of the target performance index and the joint relative rate of change, the quantitative sensitivity coefficients of the plurality of sensitivity parameters to the target performance index are obtained.

3. The method according to claim 1, characterized in that, The determination of the relative transformation rate of the sensitivity parameters of the proton exchange membrane fuel cell after a preset transformation includes: Obtain the reference sensitivity parameter value of the proton exchange membrane fuel cell under reference operating conditions, and the disturbance parameter value of the sensitivity parameter after a preset change based on the reference sensitivity parameter value; Based on the baseline sensitivity parameter value and the disturbance parameter value, the relative rate of change of the sensitivity parameter is determined; The step of determining the relative conversion rate of the target performance index of the proton exchange membrane fuel cell after the preset transformation based on the simulation model includes: Based on the simulation model, the benchmark target performance index corresponding to the benchmark sensitivity parameter value is determined when the proton exchange membrane fuel cell is under the benchmark operating condition. Based on the simulation model, the target performance index of the disturbance parameter value is determined under the target condition after the preset change of the baseline condition. Based on the baseline target performance index and the disturbance target performance index, the relative rate of change of the target performance index is determined.

4. The method according to claim 3, characterized in that, The step of determining the relative conversion rate of the target performance index of the proton exchange membrane fuel cell after the preset transformation based on the simulation model includes: Determine the influence region corresponding to the benchmark sensitivity parameter value; If the affected area indicates the three-dimensional computational domain, then based on the benchmark sensitivity parameter, the three-dimensional operating data is determined through the three-dimensional computational domain of the simulation model; The three-dimensional operational data is input into the one-dimensional computational domain of the simulation model via a data interaction interface to determine the one-dimensional operational data. If the three-dimensional running data and the one-dimensional running data meet the preset conditions, the benchmark target performance index is determined based on the three-dimensional running data and the one-dimensional running data.

5. The method according to claim 4, characterized in that, After determining the influence region corresponding to the benchmark sensitivity parameter value, the method further includes: If the affected area indicates the one-dimensional computational domain, then based on the benchmark sensitivity parameter, the one-dimensional operating data is determined through the one-dimensional computational domain of the simulation model. The one-dimensional operational data is input into the three-dimensional computational domain of the simulation model via the data interaction interface to determine the three-dimensional operational data; If the three-dimensional running data and the one-dimensional running data meet the preset conditions, the benchmark target performance index is determined based on the three-dimensional running data and the one-dimensional running data.

6. The method according to any one of claims 1 to 5, characterized in that, After determining the quantified sensitivity coefficient of the sensitivity parameter to the target performance index based on the relative change rate of the target performance index and the relative change rate of the sensitivity parameter, the method further includes: Based on the quantized sensitivity coefficient and the preset error value, the range of sensitivity indicators affected by the preset error value is determined; the range of sensitivity indicators includes the maximum value and the minimum value of the sensitivity indicator. For multiple different sensitivity parameters, determine the quantization sensitivity coefficients corresponding to each sensitivity parameter; Based on the values ​​of the multiple quantized sensitivity coefficients, the multiple sensitivity parameters are sorted by sensitivity to obtain a sensitivity sorting result; The range of the sensitivity indicators and the sensitivity ranking results are displayed.

7. A quantitative analysis device for the sensitivity of membrane electrode parameters in a proton exchange membrane fuel cell, characterized in that, The device includes: The three-dimensional computational domain determination module is used to determine the three-dimensional computational domain of the proton exchange membrane fuel cell based on the physical operating behavior of the plates, flow channels and gas diffusion layer of the proton exchange membrane fuel cell. A one-dimensional computational domain determination module is used to determine the one-dimensional computational domain of the proton exchange membrane fuel cell based on the physical operating behavior of the microporous layer, catalyst layer and proton exchange membrane of the proton exchange membrane fuel cell. A data interaction interface determination module is used to obtain the data interaction interface between the three-dimensional computing domain and the one-dimensional computing domain. The simulation model determination module is used to determine the simulation model based on the three-dimensional computational domain, the one-dimensional computational domain, and the data interaction interface. The sensitivity parameter change determination module is used to determine the relative change rate of the sensitivity parameters of the proton exchange membrane fuel cell after a preset change; the sensitivity parameters are the structural parameters and physical property parameters of the membrane electrode of the proton exchange membrane fuel cell. The performance index change determination module is used to determine the relative change rate of the target performance index of the proton exchange membrane fuel cell after the preset change, based on the simulation model. The sensitivity coefficient determination module is used to determine the quantitative sensitivity coefficient of the sensitivity parameter to the target performance index based on the relative change rate of the target performance index and the relative change rate of the sensitivity parameter.

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.

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