A gradient solid oxide fuel cell design method and device

Abstract

The present application is applicable to the field of solid oxide fuel cell technology and provides a gradient solid oxide fuel cell design method and device, the method comprising: utilizing a numerical simulation method for electrode microstructure evolution combining a discrete element method (DEM) and a kinetic Monte Carlo (KMC) method to simulate the microstructure evolution process during the sintering preparation process of a functionally gradient electrode to generate a microstructure with a gradient structure; based on the microstructure, utilizing a preset microscale multi-field coupling model to evaluate the electrochemical and mechanical properties of the functionally gradient electrode to obtain an evaluation result; inputting the evaluation result into a machine learning prediction model to output the electrochemical and mechanical properties under a preset gradient design parameter combination; utilizing a multi-objective optimization algorithm to optimize the gradient design parameter combination based on the electrochemical and mechanical properties to determine a target gradient design parameter combination. The method enables efficient and accurate design of gradient solid oxide fuel cells.

Description

Technical Field

[0001] The present application belongs to the field of solid oxide fuel cell technology, and in particular relates to a gradient solid oxide fuel cell design method and device. Background Art

[0002] Currently, the design of solid oxide fuel cells (SOFCs) primarily relies on experimental trial-and-error methods and numerical simulation. Trial-and-error methods are costly and time-consuming. While numerical simulation can reduce the number of experiments to a certain extent, existing methods are typically based on simplified models, such as the percolation theory micromodel of particle stacking and the macroscopic layered model. These models have limitations in describing electrode microstructures and cannot accurately account for true microstructural (also known as microstructural) parameters such as specific surface area, three-phase line density, pore size, and tortuosity factor. Consequently, existing numerical simulation methods exhibit certain errors in predicting cell performance, resulting in inaccurate SOFC designs and difficulties in achieving optimal performance. Summary of the Invention

[0003] The embodiments of the present application provide a gradient solid oxide fuel cell design method and device, which can solve the technical problems of high cost, long cycle and inaccurate design of existing solid oxide fuel cell design methods.

[0004] In a first aspect, an embodiment of the present application provides a gradient solid oxide fuel cell design method, comprising:

[0005] The numerical simulation method of electrode microstructure evolution, which combines discrete element method (DEM) and dynamic Monte Carlo (KMC), is used to simulate the microstructure evolution process of functionally gradient electrodes during sintering and generate microstructures with gradient structures.

[0006] Based on the microstructure, the electrochemical and mechanical properties of the functionally gradient electrode are evaluated using a preset microscale multi-field coupling model to obtain an evaluation result;

[0007] Inputting the evaluation results into a machine learning prediction model to output the electrochemical and mechanical properties under a preset gradient design parameter combination;

[0008] According to the electrochemical properties and the mechanical properties, a multi-objective optimization algorithm is used to optimize the gradient design parameter combination to determine a target gradient design parameter combination.

[0009] In a second aspect, an embodiment of the present application provides a gradient solid oxide fuel cell design device, comprising:

[0010] The simulation module is used to simulate the microstructure evolution process of the functionally gradient electrode during sintering by using the numerical simulation method of electrode microstructure evolution that combines the discrete element method (DEM) and the dynamic Monte Carlo (KMC) method to generate a microstructure with a gradient structure.

[0011] An evaluation module, configured to evaluate the electrochemical and mechanical properties of the functionally gradient electrode based on the microstructure using a preset microscale multi-field coupling model to obtain an evaluation result;

[0012] A performance output module, configured to input the evaluation results into a machine learning prediction model and output the electrochemical and mechanical properties under a preset gradient design parameter combination;

[0013] An optimization module is used to optimize the gradient design parameter combination according to the electrochemical performance and the mechanical performance using a multi-objective optimization algorithm to determine a target gradient design parameter combination.

[0014] Compared with the prior art, the embodiments of the present application have the following beneficial effects:

[0015] A numerical simulation method for electrode microstructure evolution, combining the discrete element method (DEM) and kinetic Monte Carlo (KMC), is used to simulate the microstructural evolution of a functionally gradient electrode during sintering, generating a microstructure with a gradient structure. Based on this microstructure, the electrochemical and mechanical properties of the functionally gradient electrode are evaluated using a pre-defined microscale multi-field coupling model to obtain evaluation results. These evaluation results are input into a machine learning prediction model to output the electrochemical and mechanical properties for a pre-defined gradient design parameter combination. Based on these electrochemical and mechanical properties, a multi-objective optimization algorithm is used to optimize the gradient design parameter combination to determine a target gradient design parameter combination. The combination of DEM and KMC accurately simulates the microstructural evolution of the electrode during sintering, generating a realistic gradient microstructure. Compared to traditional simulation methods based on simplified assumptions, this method more accurately reflects the actual electrode microstructure, providing a more reliable basis for subsequent performance evaluation. This precise microstructural simulation helps improve the accuracy of battery performance predictions and reduce errors caused by model simplification. Furthermore, by precisely simulating the evolution of electrode microstructures, comprehensively evaluating electrochemical and mechanical properties, leveraging machine learning for performance prediction, and employing multi-objective optimization algorithms for parameter optimization, efficient, accurate, and optimized solid oxide fuel cell design is achieved. This significantly improves the accuracy of battery performance predictions, reduces development costs and cycle times, and simultaneously optimizes the overall performance of the battery, resulting in improved performance and reliability in practical applications. This comprehensive technical approach provides a new and efficient approach to solid oxide fuel cell design. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the embodiments or descriptions of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0017] Figure 1 This is a schematic flow chart of a gradient solid oxide fuel cell design method provided in one embodiment of the present application;

[0018] Figure 2 This is a schematic diagram of the neural network architecture of the machine learning prediction model provided in one embodiment of the present application;

[0019] Figure 3 This is a schematic structural diagram of a gradient solid oxide fuel cell design device provided in an embodiment of the present application;

[0020] Figure 4 It is a structural diagram of the computer device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0021] In the following description, specific details such as specific system structures and techniques are provided for purposes of illustration rather than limitation to facilitate a thorough understanding of the embodiments of the present application. However, it will be apparent to those skilled in the art that the present application may be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to avoid obscuring the description of the present application with unnecessary detail.

[0022] It should be understood that when used in the present specification and the appended claims, the term "comprising" indicates the presence of the described features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or their collections. It should also be understood that the term "and / or" used in the present specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes these combinations.

[0023] As used in this specification and the appended claims, the term "if" can be interpreted as "when" or "upon" or "in response to determining" or "in response to detecting," depending on the context. Similarly, the phrase "if it is determined" or "if [described condition or event] is detected" can be interpreted as meaning "upon determination" or "in response to determining" or "upon detection of [described condition or event]" or "in response to detecting [described condition or event]," depending on the context.

[0024] In addition, in the description of the present application specification and the appended claims, the terms "first", "second", "third", etc. are only used to distinguish the descriptions and cannot be understood as indicating or implying relative importance.

[0025] References to "one embodiment" or "some embodiments" in this specification mean that a particular feature, structure, or characteristic described in conjunction with that embodiment is included in one or more embodiments of the present application. Thus, phrases such as "in one embodiment," "in some embodiments," "in other embodiments," and "in other embodiments" appearing in various places in this specification do not necessarily refer to the same embodiment, but rather mean "one or more but not all embodiments," unless otherwise specifically emphasized. The terms "including," "comprising," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0026] Solid oxide fuel cells have become a clean energy technology with development potential due to their high efficiency, wide fuel adaptability, low pollution emissions and the absence of precious metal catalysts. In the process of promoting the commercial application of SOFC, electrochemical performance, durability, etc. are the core factors that determine its market competitiveness. Among them, the electrochemical performance of SOFC is closely related to the electrode microstructure. Theoretical and experimental studies have shown that introducing the functional gradient design concept into the electrode microstructure design of SOFC can effectively improve its electrochemical performance. At the same time, functional gradient design can alleviate the problem of interface material property mismatch between different components of SOFC. However, the currently disclosed functional gradient solid oxide fuel cell related schemes mainly focus on the protection of the preparation process, and there has been no disclosure and protection of the design method of functional gradient solid oxide fuel cells.

[0027] Currently, SOFC design methods primarily rely on experimental trial-and-error methods and numerical simulations. Experimental trial-and-error methods are costly and time-consuming. Numerical simulations primarily rely on microscopic percolation theory models of particle packing and macroscopic layered models. However, real SOFC electrodes are formed by sintering irregularly shaped powder particles, forming sintering necks between particles. The actual electrode microstructure and corresponding microstructural parameters (specific surface area, three-phase line density, pore size, tortuosity, and other microstructural parameters) differ significantly from the output of microscopic percolation theory models. Furthermore, macroscopic layered models generally assume that the physical properties of the electrode material gradually vary across the thickness, while the material properties are isotropic within the same plane perpendicular to the thickness. However, in reality, SOFC electrodes can exhibit local variations in particle packing, resulting in anisotropy in the electrode's physical and electrochemical properties. Gradient structures designed based on these numerical simulation methods are often the microstructures of the sintered material.

[0028] In addition, most existing gradient SOFC design schemes only involve single gradient designs (such as composition gradient, porosity gradient, or particle size distribution gradient). These single gradient designs have limited effects on improving battery performance and cannot fully utilize the advantages of functional gradient designs.

[0029] Figure 1 A schematic flow chart of a gradient solid oxide fuel cell design method provided in one embodiment of the present application is shown.

[0030] S101 uses a numerical simulation method for electrode microstructure evolution that combines the Discrete Element Method (DEM) and Kinetic Monte Carlo (KMC) to simulate the microstructure evolution process during the sintering preparation process of functionally gradient electrodes and generate a microstructure with a gradient structure.

[0031] DEM is a numerical simulation technique based on interparticle interaction forces. It tracks the motion and contact behavior of individual particles to simulate the dynamic evolution of a particle system. Its core lies in establishing a mechanical model of the particles (e.g., contact forces, friction, and damping forces), calculating the displacement and rotation of particles under load, and reconstructing the macroscopic mechanical response of the particle system. In electrode microstructure simulation, DEM is used to generate the initial particle packing structure, accurately characterizing the particle size distribution, spatial arrangement, and pore formation mechanism, providing a realistic microscopic initial state for subsequent sintering evolution.

[0032] KMC is a probability-based numerical simulation method that simulates the dynamic evolution of physical processes by randomly selecting events and calculating their probability of occurrence. KMC introduces the concept of a time step, prioritizing the simulation of events with lower energy or faster rates, thereby efficiently reproducing the time-dependent changes in microstructure. In electrode sintering simulations, KMC is used to simulate mechanisms such as grain growth, pore migration, and vacancy densification, driving microstructural optimization and stabilization through energy minimization principles (such as surface energy and grain boundary energy).

[0033] Among them, the numerical simulation method of electrode microstructure evolution is a multi-scale, multi-physical field coupled computational framework. By integrating DEM and KMC, the dynamic changes of the electrode microstructure from the initial accumulation of particles to sintering molding can be reproduced throughout the entire process. It can replace experimental trial and error and achieve accurate prediction of electrode performance and global optimization of process parameters.

[0034] Among them, simulating the microstructure evolution process during the sintering preparation process of the functional gradient electrode refers to simulating the sintering preparation process of the functional gradient anode or cathode to reproduce the full-cycle dynamic evolution process of the microstructure from the initial accumulation of particles to high-temperature sintering molding.

[0035] Herein, generating a microstructure with a gradient structure refers to generating a porous anode or cathode microstructure with a gradient structure.

[0036] In an optional embodiment, S101 utilizes a numerical simulation method for electrode microstructure evolution that combines a discrete element method (DEM) and a kinetic Monte Carlo (KMC) method to simulate the microstructure evolution process during the sintering preparation process of the functionally gradient electrode, thereby generating a microstructure with a gradient structure, including:

[0037] Step a1: using the discrete element method (DEM) to simulate the initial stacking structure of the electrode particles according to a preset particle size distribution.

[0038] The simulated initial stacking structure of electrode particles specifically refers to the simulated initial stacking structure of electrode particles of the anode or cathode.

[0039] In this embodiment, a three-dimensional computational domain is constructed to define the spatial extent along the electrode thickness. Subsequently, a particle set is generated based on a target particle size distribution (e.g., normal or lognormal). For example, the anode Ni particle size is set to 1-5 μm, and the cathode LSCF particle size is set to 0.5-3 μm. A random number algorithm is used to assign each particle a size value that matches the distribution characteristics. Next, the particles are gradually introduced into the computational domain under the influence of a gravity field. The normal elastic force and tangential friction between the particles are calculated using the Hertz-Mindlin contact model, simulating the collision, sliding, and rotational behavior experienced in a real packing process until the particle system reaches dynamic equilibrium and forms a densely packed initial structure. During this process, the packing density can be controlled by adjusting the particle friction coefficient and wall boundary conditions (e.g., rigid constraints). The spatial distribution of pore-forming agent particles is also introduced, laying the foundation for subsequent porosity gradient design. This step accurately replicates the spatial arrangement of electrode particles at the micron scale, capturing the characteristics of interparticle contact points and pore distribution, providing realistic and reliable initial conditions for subsequent KMC sintering simulations.

[0040] Step a2: Introducing pore-forming agent particles into the initial stacking structure to simulate the distribution of pores. After the electrode particles are stacked, the pore-forming agent particles are removed to form an electrode with a gradient structure. The gradient structure is formed by stacking different sublayers. The electrode particles in each sublayer are uniformly distributed across the sublayer space.

[0041] In the present embodiment, within the initial electrode particle stacking structure obtained through DEM simulation, pore-forming agent particles (such as carbon powder and polymer microspheres) are introduced into different sublayers based on the gradient design objectives to simulate the spatial distribution of pores. The electrode is first divided into N sublayers (e.g., N = 3-5 layers) along the thickness direction, with each sublayer corresponding to independent pore-forming agent content and particle size parameters. For example, in the anode gradient structure, the surface sublayer (fuel side) has a higher pore-forming agent volume fraction (e.g., 30%-40%) and is matched with larger pore-forming agent particles (e.g., 2-4 μm) to form a high-porosity region to promote fuel diffusion. The inner sublayer (electrolyte side) has a lower pore-forming agent content of 10%-20% and uses smaller particles (e.g., 0.5-1 μm) to balance porosity and mechanical strength. During the particle stacking process, the pore-forming agent particles and electrode particles (e.g., Ni and YSZ) participate in dynamic stacking using a discrete element method. Their position and distribution are constrained by the sublayer spatial boundaries to ensure a clear gradient interface. Once the stacking is complete and the system reaches mechanical equilibrium, program instructions automatically remove all pore-forming agent particles, converting the space they occupied into pores, forming a composite structure of "electrode particle skeleton + gradient porosity." This process, through sub-layer division and differentiated pore-forming agent parameter settings, achieves a gradient of porosity along the thickness of the electrode (e.g., decreasing from 40% in the surface layer to 25% in the inner layer), while maintaining effective contact between particles to maintain the continuity of the conductive network. This approach overcomes the limitations of traditional uniform pore design and provides a physical vehicle for the subsequent coordinated optimization of the triple gradient (composition, particle size, and porosity).

[0042] In step a3, for each sublayer, gradient parameters are controlled based on the gradient control equation to obtain the target stacking structure. The gradient parameters include composition gradient parameters, porosity gradient parameters, and particle size distribution gradient parameters. The gradient control equations include: a composition gradient parameter control equation for controlling the composition gradient parameters in each sublayer; a porosity gradient parameter control equation for controlling the porosity gradient parameters in each sublayer; and a particle size distribution gradient parameter control equation for controlling the particle size distribution gradient parameters in each sublayer.

[0043] In an embodiment of the present application, for each sublayer divided in the thickness direction of the electrode, the three types of gradient parameters, namely composition, porosity and particle size distribution, are precisely controlled through the gradient control equation to generate the target stacking structure.

[0044] Among them, for the composition gradient control, according to the sub-layer position, the composition gradient parameter control equation is: (Equation 1), the proportion of each phase is adjusted layer by layer. For example, in a certain cathode sublayer, the volume fraction of LSCF (electronic phase) increases from 60% in the surface layer to The index decreases to 40% in the inner layer, while GDC (ionic phase) increases from 40% to 60% accordingly, forming a composition gradient interface.

[0045] in, Indicates the layer Volume fraction of express Minimum volume fraction; express The maximum volume fraction of Ion-conducting phase , electronic conductive phase or pore phase ion conducting phase Can include YSZ, LSCF, GDC, etc.; electronic conductive phase It can include Ni, LSCF, etc. is the number of sub-layers; is the total number of layers; is the gradient index.

[0046] For porosity gradient control, the porosity gradient parameter control equation is used by correlating the pore former content with the sublayer position. (Equation 2) controls the volume fraction of the porous phase. For example, the porosity of the anode surface layer is set to 40%, and that of the inner layer is set to 25%. A gradient transition is achieved by adjusting the remaining space after removing the pore-forming agent from each sublayer.

[0047] Wherein, Equation 2 represents the Ion-conducting phase The volume fraction, electronically conductive phase of the layer The volume fraction and Porous phase The sum of the volume fractions is 1.

[0048] For the particle size distribution gradient control, the particle size distribution gradient parameter control equation is adopted:

[0049] (Equation 3) makes the average particle size change layer by layer along the thickness direction. For example, the particle size of the anode particles changes from 5 μm on the surface to It decreases linearly to 2μm in the inner layer, enhancing the structural strength of the inner layer while reducing the gas diffusion resistance.

[0050] in, Indicates the Average particle size of the layer; Indicates the minimum particle size; Indicates the maximum particle size of the particles; is the gradient index.

[0051] Through the coordinated regulation of three types of gradient parameters, each sublayer forms differentiated microstructural characteristics, which are finally superimposed into a target stacking structure with a triple gradient of composition, particle size and porosity, providing a parameterized basis for the multi-physical field coupling simulation of the subsequent sintering process.

[0052] Step a4: voxelize the target stacking structure to generate a three-dimensional voxelized model.

[0053] In an embodiment of the present application, for the target stacking structure obtained by gradient parameter regulation, a voxelization algorithm is used to discretize the continuous particle stacking space into three-dimensional grid units (voxels), generating a digital structure that can be recognized by the dynamic Monte Carlo KMC model.

[0054] First, based on the particle coordinates and size data output by the DEM simulation, a computational domain is defined in three-dimensional space (e.g., 100×100×50μm³) and a voxel resolution is set (e.g., 10nm / voxel). The resolution must be less than 1 / 5 of the minimum particle size to ensure geometric feature preservation. Subsequently, all voxels within the computational domain are traversed using a thresholding method or a scanning line algorithm. Voxels intersecting with electrode particles (e.g., Ni, YSZ) are labeled as "solid phase," and spaces unoccupied by particles (including pores after the pore-forming agent is removed) are labeled as "pore phase." This creates a three-dimensional grayscale image composed of discrete voxel units—where the attribute value of each voxel corresponds to the phase type (e.g., 0 for pores, 1 for ion-conducting phases, 2 for electronic-conducting phases).

[0055] The voxelization process requires geometric repair to eliminate interparticle penetration or gaps, ensuring the continuity of the solid phase and the topological authenticity of the pore phase. The resulting 3D voxelized model can be further visualized and statistically analyzed to obtain microstructural parameters such as initial porosity and particle contact density, which serve as the initial crystal site matrix for KMC sintering simulations. This step transitions from continuous particle stacking to a discretized microstructure, providing a numerical framework for subsequent lattice-based simulations of sintering mechanisms (such as grain growth and pore migration) and laying the foundation for meshing in multi-field coupled analyses.

[0056] Step a5: Using the three-dimensional voxelized model as the initial crystal site matrix, the kinetic Monte Carlo (KMC) method is used to simulate the microstructure evolution, thereby generating a microstructure of a porous anode or cathode having a gradient structure.

[0057] In the embodiment of this application, a three-dimensional voxelized model is used as the initial crystal site matrix (each voxel corresponds to a site in the KMC simulation, and the site state is defined as a porous phase, an ion conductive phase, or an electronic conductive phase). The Metropolis Monte Carlo algorithm is used to drive the microstructure evolution and simulate the physical and chemical changes of the electrode during high-temperature sintering. First, the KMC simulation parameters are set, including the sintering temperature (through the Boltzmann constant Associated dimensionless temperature ), the frequency of attempts of each mechanism (such as the grain growth frequency ), pore migration frequency ), and define the system energy (Equation 4), where For the site and sites The interaction energy between them corresponds to the surface energy on the pore-grain interface Grain boundary energy and grain-grain boundary interaction ; is the total number of voxel sites; is the Kronecker function, which determines whether the phase states of the sites are the same. hour , hour .

[0058] The evolution process is achieved through the following mechanisms:

[0059] 1) Grain growth: Randomly exchange the phase states of adjacent sites (such as ion-conducting phase and electronic-conducting phase) and calculate the energy change ,like Then accept the exchange; if , then with probability (Equation 5) determines whether to accept the simulation of grain merging caused by short-range atomic diffusion. Indicates the simulated sintering temperature.

[0060] 2) Pore migration: Pore sites are randomly exchanged with adjacent non-pore sites. Energy evaluation and Metropolis probability are used to determine whether migration is retained, reflecting changes in pore position caused by long-range surface diffusion. This is done using Equation 4 and re-evaluating the probability using Equation 5 to determine whether the pore migration attempt is accepted.

[0061] 3) Vacancy Formation and Disappearance: Vacancies are generated by exchanging pore and grain sites. If isolated vacancies are formed, they are attempted to migrate to the surface and disappear, simulating the densification behavior during sintering. If isolated vacancies are formed after the exchange, Equations 4 and 5 are used to determine whether the exchange is accepted. After vacancy formation, disappearance is simulated by moving the vacancy site to the sample surface.

[0062] 4) Interface exchange: For composite phases (such as Ni / YSZ), different phase points are allowed to exchange states to maintain mass conservation and suppress stress concentration caused by interface unevenness.

[0063] Among them, the parameters controlling the KMC simulation are mainly the simulated sintering temperature and attempt frequency : Including grain growth ( and ), pore migration ( and ), vacancy formation and disappearance ( and ) and interface exchange ( and ) Four mechanisms.

[0064] in, represents the simulation temperature applied in the grain growth algorithm; represents the trial frequency applied in the grain growth algorithm; represents the simulation temperature to which the pore migration algorithm is applied; represents the frequency of attempts to apply the pore migration algorithm; represents the simulation temperature to which the grain boundary vacancy formation algorithm is applied; represents the frequency of attempts to apply the grain boundary vacancy formation algorithm; represents the simulated temperature applied in the interface exchange algorithm; Indicates the frequency of attempts applied in the interface switching algorithm;

[0065] Under the constraints of the gradient structure, each sublayer exhibits different evolution rates due to differences in composition, particle size, and porosity: pore shrinkage dominates in the surface high-porosity region, while grain coarsening dominates in the inner low-porosity region, ultimately resulting in a porous structure with gradient characteristics (e.g., surface pore diameters of 200-300 nm, inner pore diameters of 50-100 nm). After the simulation, microstructural parameters (such as specific surface area, three-phase line density, and tortuosity factor) are extracted to provide realistic geometric input for subsequent multi-field coupling performance evaluation. This step replicates the microscopic mechanisms of the sintering process through dynamic simulation, transcending the static assumptions of traditional percolation theory and enabling modeling of the dynamic evolution from initial accumulation to a functionally gradient microstructure.

[0066] In addition to using the KMC method to simulate the sintering of electrode microstructures, the phase-field method can also be used to simulate the microstructural evolution during electrode sintering. The phase-field method describes the internal microstructural state of the material by introducing continuous phase-field variables. Based on diffusion equations and thermodynamic theory, it simulates sintering phenomena such as grain growth, interface evolution, and pore migration. This method can intuitively demonstrate the dynamic changes in the electrode microstructure from initial particle accumulation to densification, providing an effective means for analyzing the effects of sintering process parameters (such as temperature and time) on microstructural characteristics (such as grain size and porosity distribution).

[0067] Among them, multi-physics field coupling simulation, in addition to the above methods, can also be solved with the help of the lattice Boltzmann (LBM) method. By simulating the migration and collision behavior of particles in a discrete lattice space, this method can effectively characterize the material transport (such as gas diffusion, ion conduction), electrochemical reaction heat generation and heat conduction processes within the porous electrode, thereby realizing cross-scale coupled analysis of the potential distribution, temperature field, and concentration field. Its advantages lie in its strong adaptability to complex pore structures and its efficient collaborative computing capabilities of multiple physical fields. It can accurately reveal the interaction mechanism of electrochemical reactions and transport processes at the microscale, providing key support for the performance prediction and optimized design of functional gradient electrodes.

[0068] S102, based on the microstructure, using a preset microscale multi-field coupling model to evaluate the electrochemical properties and mechanical properties of the functional gradient electrode to obtain an evaluation result.

[0069] Among them, the microscale multi-field coupling model includes: a charge transport model, which is used to calculate the potential distribution of electrons and ions; an electrochemical reaction model, which is used to calculate the current density and overpotential at the three-phase junction; a material transport model, which is used to calculate the transport process of gas materials in the electrode; a heat conduction model, which is used to calculate the temperature distribution in the electrode; and a mechanical property model, which is used to calculate the thermal stress and failure probability of the electrode.

[0070] Electrochemical and mechanical properties are evaluated, including:

[0071] Calculate the total overpotential; plot the output voltage versus current density curve; calculate the maximum power density; calculate the maximum thermal stress; and perform Weibull failure probability analysis.

[0072] The charge transport model is used to solve the potential distribution in electronically conductive phases (such as Ni and LSCF) and ionically conductive phases (such as YSZ and GDC), revealing the effectiveness of the electrical conduction path. The following is an introduction to the charge transport model.

[0073] Electronic phase: (Equation 6);

[0074] Ionic phase: (Equation 7);

[0075] Where, and are the potentials in the electronic and ionic conducting phases, respectively, and are the electronic and ionic conductivities, is the exchange current density at the three-phase or two-phase interface.

[0076] The ionic conductivity of YSZ and the electronic conductivity of Ni in the composite anode are calculated as follows:

[0077] (Equation 8);

[0078] (Equation 9);

[0079] in, Indicates the material temperature.

[0080] The conductivity of the LSCF in the composite cathode is defined by the temperature and oxygen partial pressure dependence formula:

[0081] (Equation 10);

[0082] (Equation 11);

[0083] (Equation 12);

[0084] (Equation 13);

[0085] in, ~ is the preset temperature-dependent empirical coefficient; is the molar volume of LSCF; is the partial pressure of oxygen in the solid; is the partial pressure of oxygen in atmospheric pressure; is the chemical diffusion coefficient; δ is the oxygen nonstoichiometry; is the Faraday constant; is a constant used for molar scale and energy conversion.

[0086] The temperature-dependent ionic conductivity in GDC is calculated as follows:

[0087] (Equation 14);

[0088] in, is the electron volt; is the Boltzmann constant.

[0089] Electrochemical reaction models focus on simulating electrochemical reactions at the three-phase interface (TPB, solid-ion-gas) and the two-phase interface (DPB, electron-ion) in solid oxide fuel cell (SOFC) electrodes. Their core goal is to quantify reaction kinetics and reveal performance bottlenecks. The following describes electrochemical reaction models.

[0090] The electrochemical reaction occurs only at the active interface in the electrode microstructure (such as the TPB of anode fuel gas / nickel / yttria-stabilized zirconia (YSZ), or the DPB of cathode composite oxide / electrolyte). The model is based on the Butler-Volmer (BV) equation to describe the relationship between the reaction rate and the overpotential, which is:

[0091] (Equation 15);

[0092] in, is the volume current density generated by the electrochemical reaction; is the TPB density at the electrode reaction; is the exchange current density per unit volume of TPB, in (A / m); and are the forward and backward reaction coefficients, respectively, at the anode TPB and Take 1 and 0.5 respectively, take 1 at cathode TPB, and take 0.6 and 0.5 respectively at cathode DPB; is the gas constant; is the Faraday constant; is the number of electrons released in the reaction; is the activation overpotential.

[0093] Among them, Equation 15 is a formula common to both cathode and anode.

[0094] The exchange current density is:

[0095] (Equation 16);

[0096] (Equation 17);

[0097] (Equation 18);

[0098] in, is the exchange current density per unit length of anode TPB; is the hydrogen partial pressure is the water vapor partial pressure; is the exchange current density per unit length of cathode TPB; is the partial pressure of oxygen; is the exchange current density per unit length of cathode DPB.

[0099] Among them, Equation 15 is the common formula for cathode and anode, so the anode activation overpotential is and cathodic activation overpotential is defined as follows:

[0100] (Equation 19);

[0101] (Equation 20);

[0102] in, is the anode activation overpotential, is the activation overpotential of the cathode, calculated as follows:

[0103] (Equation 21);

[0104] (Equation 22);

[0105] in, is set as a constant in the boundary conditions Gas partial pressure; is set as a constant in the boundary conditions Gas partial pressure; is set as a constant in the boundary conditions Gas partial pressure; is the interfacial partial pressure of hydrogen; is the interfacial partial pressure of oxygen; is the interfacial partial pressure of water vapor.

[0106] Among them, the relevant introduction to the material transfer model is as follows.

[0107] In the porous structure of the electrode, gas transport is dominated by both molecular diffusion (collisions between gas molecules) and Knudsen diffusion (collisions between gas molecules and pore walls), depending on the relative relationship between pore size and the mean free path of the gas. The model describes the species transport process through the species conservation equation:

[0108] (Equation 23);

[0109] in, For components The quality score of is the density of the mixture; For components The effective diffusion coefficient of is the mass source term.

[0110] Since the reaction only occurs at TPB, the consumption and production of components are also at TPB. Calculated by the following formula: (Equation 24);

[0111] in, For components The quality score of For components and components The binary diffusion coefficient of For components The Knudsen diffusion coefficient.

[0112] Knudsen diffusion coefficient is calculated as: (Equation 25);

[0113] in, is the average pore diameter; For components The molar mass of .

[0114] The binary diffusion coefficient is calculated using the Fuller–Schettler–Giddings model:

[0115] (Equation 26); where and The components are and The diffusion volume; and Components and molecular weight.

[0116] The mass source term in Equation 23 is calculated as follows:

[0117] (Equation 27);

[0118] (Equation 28);

[0119] (Equation 29).

[0120] in, is the mass source term of hydrogen; is the mass source term of water vapor; is the mass source term of oxygen; is the volume current density.

[0121] The heat conduction model focuses on the heat transfer process within solid oxide fuel cell (SOFC) electrodes. It aims to reveal the dynamic balance between electrochemical reaction heat release, ohmic loss heat generation, and heat conduction, and to assess the impact of temperature distribution on battery performance and reliability. Based on the thermophysical properties of microscale porous media and incorporating a multi-field coupling mechanism, the model enables the coordinated calculation of temperature and stress fields. The following describes the heat conduction model.

[0122] During SOFC operation, heat is primarily generated by electrochemical reaction heat (activation heat, entropy change heat) and ohmic resistance heat, which is conducted through the solid skeleton (electrode particles) and pore gas. The model describes the temperature field distribution using the heat conduction equation:

[0123] (Equation 30);

[0124] in, is the specific heat capacity, is the thermal conductivity, is the heat source term, which is calculated as follows:

[0125] (Equation 31);

[0126] Wherein, / in the above text means or. Wherein, is the heat source term; is the volume current density; is the electron potential gradient norm; is the electronic conductivity; is the ionic potential gradient model; is the ionic conductivity; For entropy change.

[0127] The boundary conditions are as follows:

[0128]

[0129] in, For components The quality score of is the mass fraction of the component given as a constant; is the total overpotential; is the temperature given as a constant.

[0130] Based on the above formulas and boundary conditions, the distribution of electron and ion electrochemical potentials and the total overpotential are calculated; the output voltage versus current density curve VI and the maximum power density are calculated and plotted; the temperature field results of the simulation results are used as the initial conditions for the thermal stress simulation, and a finite element program (such as Abaqus) is used for meshing and thermal stress simulation to calculate the maximum thermal stress; and a Weibull failure probability analysis is performed.

[0131] Among them, the relevant introduction of the mechanical performance model is as follows.

[0132] Taking into account the displacement and stress caused by thermal expansion mismatch, the force balance equation of the solid element in differential form is: (Equation 32);

[0133] in, is the displacement vector, is the density, It's physical strength. is the stress tensor.

[0134] Among them, the strain tensor Defined as: (Equation 33);

[0135] According to Hooke's law, the relationship between the stress tensor and the strain tensor is:

[0136] (Equation 34);

[0137] in, is the transpose of the strain tensor, is the unit tensor, and is the Lame constant, which is related to Young's modulus and Poisson's ratio The relationship is:

[0138] (Equation 35);

[0139] (Equation 36);

[0140] For the stress tensor with temperature load, its tensor form expression is:

[0141] (Equation 37);

[0142] Where α is the coefficient of thermal expansion; is the strain tensor; is the initial temperature.

[0143] According to equations 32 to 34, the equilibrium equation can be rewritten as:

[0144] (Equation 38).

[0145] Among them, the relevant introduction of Weibull failure probability analysis is as follows.

[0146] In order to quantify the mechanical strength of the microstructure, the Weibull method for brittle material failure analysis was applied to estimate the mechanical failure probability of all samples. The mechanical failure probability is defined as:

[0147] (Equation 39);

[0148] is the Weibull strength of the material, the constant =8 is the Weibull modulus, Suitable for measurement The material reference volume, The total probability is calculated by calculating the three principal stresses It is calculated by multiplying the survival probabilities of Represents the three principal stress directions within the material.

[0149] S103, inputting the evaluation results into a machine learning prediction model, and outputting the electrochemical properties and mechanical properties under a preset gradient design parameter combination.

[0150] Among them, the training process of the machine learning prediction model includes: obtaining the electrochemical properties and mechanical properties under different gradient design parameter combinations; using the gradient design parameter combination as the input of the initial artificial neural network, and the electrochemical properties and mechanical properties as the output of the initial artificial neural network, training the initial artificial neural network to obtain the machine learning prediction model.

[0151] like Figure 2 The figure below shows a schematic diagram of the neural network architecture of the machine learning prediction model. This machine learning prediction model is based on the initial artificial neural network training. The neural network architecture of the machine learning prediction model includes an input layer, a hidden layer, and an output layer. The input parameters of the input layer are: .in, is the number of sublayers, is the gradient index, is the thickness of the transition layer, is the porosity, is the particle size. Output electrochemical and mechanical properties.

[0152] In the embodiment of the present application, the generation of gradient design parameter combinations follows the experimental design (DoE) method, and parameterized design is performed through the DEM-KMC model. The specific steps are as follows:

[0153] Parameter space definition:

[0154] Core parameter: number of sublayers , gradient index , transition layer thickness , porosity , particle size .

[0155] DoE sampling strategy: Use Latin hypercube sampling (LHS) or orthogonal array design to uniformly generate sample points in the parameter space to ensure coverage of linear and nonlinear gradient scenarios. For example, generate 200 sets of parameter combinations, each corresponding to a functionally gradient electrode microstructure.

[0156] Performance evaluation: For each set of parameters, the microstructure was generated through DEM-KMC simulation, and the electrochemical and mechanical properties were calculated using a multi-field coupling model.

[0157] After that, data preprocessing is performed. Input features (gradient parameters), including , where N is an integer discrete variable and the rest are continuous variables. Continuous variables are normalized using Min-Max normalization, while discrete variables are converted to continuous values using one-hot encoding or label encoding.

[0158] Output labels (performance indicators), including: electrochemical properties (such as total overpotential, maximum power density) and mechanical properties (such as maximum thermal stress and Weibull failure probability).

[0159] Among them, the architecture design of the initial artificial neural network is as follows:

[0160] Input layer: 5 neurons, corresponding to 5-dimensional gradient parameters (normalized values).

[0161] Hidden layers, including the number of layers and nodes and activation functions.

[0162] Number of layers and nodes: The number of hidden layers and nodes is a hyperparameter determined by cross-validation. Example configuration: 2 hidden layers, 32 nodes in the first layer, and 16 nodes in the second layer (satisfying the requirement that the number of hidden layers and nodes is determined during training).

[0163] Activation function: ReLU function (solves the gradient disappearance problem).

[0164] Output layer: 4 neurons, corresponding to 4-dimensional performance indicators (normalized values), and the activation function is a linear function (suitable for regression tasks).

[0165] During model training, the dataset is divided into a training set (80%) and a validation set (20%). Gradient parameters are input and prediction performance indicators are calculated. The gradient of the loss function with respect to the weights of each layer is calculated and the parameters are updated. The validation set loss is calculated after each epoch. If the validation loss does not decrease after 10 consecutive epochs, the early stopping mechanism is triggered to prevent overfitting.

[0166] Optionally, when new experimental or simulation data is obtained, it is input into the model as a new sample, and the model parameters are updated through online learning or incremental training to achieve iteration.

[0167] In the embodiments of the present application, the process of inputting the evaluation results into the machine learning prediction model requires first normalizing the electrochemical properties (such as polarization curves, total overvoltage, and maximum power density) and mechanical properties (maximum thermal stress and Weibull failure probability) output by the multi-field coupling model to eliminate dimensional differences. Subsequently, these evaluation results are combined with the corresponding gradient design parameter combinations (number of sublayers, gradient index, transition layer thickness, porosity, and particle size) to form a training dataset, which is input into the artificial neural network model. When the preset gradient design parameter combination is input, the model outputs a normalized performance prediction value through forward propagation, which is then restored to the actual physical dimension through denormalization. This provides fast and accurate performance prediction support for subsequent multi-objective genetic algorithm optimization, significantly improving the efficiency of gradient electrode design.

[0168] S104 , optimizing the gradient design parameter combination according to the electrochemical performance and the mechanical performance using a multi-objective optimization algorithm to determine a target gradient design parameter combination.

[0169] In this embodiment, a multi-objective optimization algorithm (such as NSGA-II) was used to globally optimize the gradient design parameter combinations (number of sublayers N, gradient exponent P, transition layer thickness t, porosity ε, and particle size d) based on the electrochemical performance (such as maximum power density and total overvoltage) and mechanical properties (maximum thermal stress and Weibull failure probability) of the gradient design parameter combinations output by a machine learning prediction model. The optimization objective (such as maximizing power density and minimizing thermal stress and failure probability) and parameter constraints (such as N being an integer between 2 and 6 and porosity between 15% and 45%) were first set. Then, through an iterative process involving population initialization, fitness evaluation, and genetic operations (selection, crossover, and mutation), a Pareto-optimal solution set was searched in the parameter space. A compromise between performance and reliability (such as prioritizing power density or emphasizing durability) was selected from the solution set based on the design requirements. The selected parameter combinations were then simulated and verified using a multi-field coupling model to ensure that the predicted performance and actual results remained within an acceptable error range. The final target gradient design parameter combination can directly guide the optimization of the preparation process of the electrode microstructure, achieve a synergistic improvement of the electrochemical and mechanical properties, avoid the inefficiency of the traditional trial and error method, and significantly shorten the fuel cell R&D cycle.

[0170] Optionally, S104 optimizes the gradient design parameter combination according to the electrochemical performance and the mechanical performance using a multi-objective optimization algorithm to determine a target gradient design parameter combination, including:

[0171] Step b1, defining a multi-objective optimization objective function based on the electrochemical properties and the mechanical properties; wherein the objective function includes minimizing the total overpotential, maximizing the maximum power density, minimizing the maximum thermal stress, and minimizing the Weibull failure probability.

[0172] In the embodiments of the present application, when defining the objective function of multi-objective optimization, it is necessary to comprehensively consider the balance between electrochemical performance and mechanical properties, and construct the following objective function system: first, the total overpotential to be minimized is clarified, which covers activation overpotential, ohmic overpotential and concentration overpotential, which directly affects the energy conversion efficiency of the battery. A lower total overpotential means less energy loss and higher voltage output; secondly, the maximum power density is maximized, which characterizes the power generation capacity of the battery per unit area and is one of the core indicators for measuring battery performance. By optimizing the electrode microstructure, the reaction interface area and material transfer efficiency can be increased, thereby improving this indicator; the third goal is to minimize the maximum thermal stress, which is derived from the temperature gradient during battery operation and the difference in thermal expansion coefficient of the material. Excessive thermal stress can cause electrode cracks or even structural failure, and thermal stress concentration needs to be reduced through gradient design; finally, the Weibull failure probability is minimized, which is calculated based on the internal defect distribution and stress state of the material, reflecting the reliability of the electrode under actual working conditions. Reducing this probability can significantly extend the battery life. These four objective functions are interrelated and may conflict with each other. For example, increasing power density may increase thermal stress. Therefore, it is necessary to seek a Pareto optimal solution in multi-objective optimization to achieve a coordinated improvement in performance and reliability.

[0173] Step b2: setting the optimization parameter range and constraints.

[0174] In the embodiment of the present application, the value range of each gradient design parameter combination is determined during the optimization process, and corresponding constraints are set to ensure the feasibility of the optimization results.

[0175] Step b3: constructing a multi-objective optimization model based on the objective function and the constraints.

[0176] A multi-objective optimization model was constructed based on the objective functions (minimizing total overpotential, maximizing maximum power density, minimizing maximum thermal stress, and minimizing Weibull failure probability) and constraints (parameter range, physical compatibility, and performance threshold). The optimization parameters (number of sublayers, gradient index, transition layer thickness, porosity, and particle size) were first mapped into continuous variables using real-number encoding. The discrete parameter N was then constrained by an integer. NSGA-II (non-dominated sorting genetic algorithm) was then introduced as the optimization engine, and the model was constructed using the following process:

[0177] Initialize the population: Randomly generate an initial population (e.g., 100 individuals) within the parameter range. Each individual corresponds to a set of parameter combinations, and its electrochemical and mechanical performance indicators are obtained through a machine learning prediction model.

[0178] Non-dominated sorting: The individuals in the population are stratified according to the objective function. The solution in which no objective function is better than other individuals is defined as the first layer of the Pareto front (optimal solution). The remaining individuals are sorted in sequence to form a multi-level non-dominated solution set.

[0179] Crowding degree calculation: For individuals in the same non-dominated layer, the Euclidean distance of each objective function value is calculated as the crowding degree to ensure the uniformity of the solution distribution and avoid the population converging to a local area.

[0180] Genetic operations: Generate offspring populations through selection (retaining high-ranking individuals), simulated binary crossover, and polynomial mutation.

[0181] Iteration termination: When there is no significant update on the Pareto front for 10 consecutive generations or the preset number of iterations (such as 200 generations) is reached, the optimization is terminated and a Pareto solution set containing multiple trade-off solutions is output.

[0182] Step b4: determining a corresponding multi-objective optimization algorithm based on the multi-objective optimization model.

[0183] In this embodiment, a suitable multi-objective optimization algorithm was selected based on the high-dimensional parameter space (five-dimensional parameters such as the number of sublayers and gradient index), the nonlinear objective function (the conflict between power density and thermal stress), and the need to search for Pareto optimal solutions in a multi-objective optimization model. NSGA-II (non-dominated sorting genetic algorithm) was preferred. It handles multi-objective conflicts hierarchically through non-dominated sorting, maintains solution diversity through crowding calculation, and efficiently searches the parameter space by combining real-number encoding with genetic operations (crossover and mutation). It is particularly suitable for medium-scale optimization problems with five-dimensional parameters. If the objective function is decomposable, MOEA / D (decomposition-based multi-objective evolutionary algorithm) can be considered. This algorithm breaks down complex problems into single-objective subproblems and solves them in parallel. Furthermore, MOPSO (multi-objective particle swarm optimization algorithm) is suitable for real-time optimization scenarios due to its fast convergence speed and small number of parameters. Considering both model characteristics and engineering efficiency, NSGA-II was ultimately selected as the core algorithm. Through approximately 200 iterations, it searches for a Pareto optimal solution set that balances electrochemical performance and mechanical reliability within parameter constraints, providing systematic support for gradient parameter optimization.

[0184] Step b5: Iteratively optimize the gradient design parameter combination using the multi-objective optimization algorithm to generate the target gradient design parameter combination.

[0185] In an embodiment of the present application, the multi-objective optimization algorithm is used to iteratively optimize the gradient design parameter combination to generate a current iteratively optimized gradient design parameter combination; based on the current iteratively optimized gradient design parameter combination, a microstructure with a gradient structure is regenerated, and the electrochemical and mechanical properties are evaluated until the preset performance target is achieved. The current iteratively optimized gradient design parameter combination corresponding to the preset performance target is used as the target gradient design parameter combination.

[0186] The optimization parameter ranges include: the number of sublayers, the gradient index, the transition layer thickness, the porosity, and the particle size. Constraints include: the number of sublayers is an integer, the gradient index is a positive number, the transition layer thickness is less than the total electrode thickness, the porosity is within the material's physical property limits, and the particle size is within the material's sintering process parameter range. Constraints may also include electrochemical performance within the battery's operating range and mechanical properties less than the material's yield strength.

[0187] First, the population is initialized and performance prediction is performed: Initial parameter combinations (e.g., 100 combinations) are randomly generated within parameter constraints (e.g., number of sublayers 2-6, porosity 15%-45%). Each parameter combination corresponds to a gradient electrode structure (e.g., 3-layer linear gradient, porosity 30%). A machine learning prediction model is used to rapidly obtain the electrochemical performance (e.g., maximum power density, total overpotential) and mechanical properties (e.g., maximum thermal stress, Weibull failure probability) for each parameter combination. An iterative optimization cycle then begins. After a certain number of iterations (e.g., 20 generations), multiple (e.g., 5) high-performing parameter combinations are selected from the current Pareto solution set. The corresponding gradient microstructures (e.g., gradient porosity from 40% in the surface layer to 25% in the inner layer) are generated using the DEM-KMC model. A multi-field coupling model is then used to accurately evaluate the electrochemical and mechanical properties (not the predicted values).

[0188] Optimization terminates when the Pareto solution set fails to improve significantly over multiple generations (e.g., 10 generations), or when a particular combination meets the preset performance targets (e.g., power density ≥ 300mW / cm², failure probability ≤ 3%) for the first time. The final selected target parameter combination undergoes multiple rounds of microstructure generation and field measurement verification to ensure reliability. The final target gradient design parameter combination, determined through multi-field coupling evaluation, can directly guide the electrode fabrication process (e.g., setting layered sintering parameters).

[0189] In the examples of this application, a machine learning model combined with a multi-objective optimization algorithm enables intelligent screening of gradient parameters, avoiding the material waste and time loss associated with repeated experiments, significantly reducing trial-and-error costs, and shortening the development cycle. This application introduces more realistic simulation methods for electrode microstructure evolution (such as the DEM-KMC model) and combines them with microscale multi-physics field coupling analysis (co-calculation of heat conduction, electrochemical reactions, and mechanical stresses) to more accurately characterize the complex physical processes within the electrode and achieve high-precision predictions of electrochemical performance. Compared to existing single functionally graded SOFC designs, this application incorporates the concept of a triple functionally graded design based on composition, particle size, and porosity, maximizing battery performance. With the assistance of artificial intelligence (AI) tools (such as the NSGA-II multi-objective optimization algorithm and an artificial neural network prediction model), it is possible to rapidly search for Pareto optimal solutions within the global parameter space, avoiding local optima and significantly improving design efficiency.

[0190] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0191] Corresponding to the gradient solid oxide fuel cell design method described in the above embodiment, Figure 3 A structural block diagram of a gradient solid oxide fuel cell design device provided in an embodiment of the present application is shown. For ease of explanation, only the parts related to the embodiment of the present application are shown.

[0192] Reference Figure 3 , the gradient solid oxide fuel cell design device includes:

[0193] The simulation module is used to simulate the microstructure evolution process of the functionally gradient electrode during sintering by using the numerical simulation method of electrode microstructure evolution that combines the discrete element method (DEM) and the dynamic Monte Carlo (KMC) method to generate a microstructure with a gradient structure.

[0194] An evaluation module, configured to evaluate the electrochemical and mechanical properties of the functionally gradient electrode based on the microstructure using a preset microscale multi-field coupling model to obtain an evaluation result;

[0195] A performance output module, configured to input the evaluation results into a machine learning prediction model and output the electrochemical and mechanical properties under a preset gradient design parameter combination;

[0196] An optimization module is used to optimize the gradient design parameter combination according to the electrochemical performance and the mechanical performance using a multi-objective optimization algorithm to determine a target gradient design parameter combination.

[0197] It should be noted that the information interaction, execution process and other contents between the above modules are based on the same concept as the method embodiment of this application. Their specific functions and technical effects can be found in the method embodiment part and will not be repeated here.

[0198] Those skilled in the art can clearly understand that, for the convenience and brevity of description, only the division of the above-mentioned functional units and modules is used as an example for illustration. In actual applications, the above-mentioned functions can be distributed and completed by different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiment can be integrated into one processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of software functional units. In addition, the specific names of the functional units and modules are only for the convenience of distinguishing each other, and are not used to limit the scope of protection of this application. The specific working process of the units and modules in the above-mentioned system can refer to the corresponding process in the aforementioned method embodiment, and will not be repeated here.

[0199] An embodiment of the present application also provides a computer device, which includes: at least one processor, a memory, and a computer program stored in the memory and executable on the at least one processor, wherein the processor implements the steps of any of the above-mentioned method embodiments when executing the computer program.

[0200] An embodiment of the present application further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps in the above-mentioned various method embodiments can be implemented.

[0201] An embodiment of the present application provides a computer program product. When the computer program product is run on a computer device, the computer device can implement the steps in the above-mentioned method embodiments when executing the computer program product.

[0202] Figure 4 This is a schematic diagram of the structure of a computer device provided in one embodiment of the present application. Figure 4 As shown, the computer device of this embodiment includes: at least one processor 20 ( Figure 4 Only one is shown), a memory 21 and a computer program 22 stored in the memory 21 and executable on the at least one processor 20, wherein the processor 20 implements the steps of any of the above-mentioned embodiments of the gradient solid oxide fuel cell design method when executing the computer program 22.

[0203] The computer device may include, but is not limited to, a processor 20 and a memory 21. Those skilled in the art will understand that Figure 4 The computer device is merely an example and does not constitute a limitation on the computer device. The computer device may include more or fewer components than shown in the figure, or a combination of certain components, or different components. For example, the computer device may also include input and output devices, network access devices, etc.

[0204] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present application implements all or part of the processes in the above-mentioned embodiment method by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, it can implement the steps of each of the above-mentioned method embodiments.

[0205] In the above embodiments, the description of each embodiment has its own focus. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant description of other embodiments.

[0206] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0207] The above-described embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. A gradient solid oxide fuel cell design method, characterized in that: include: The numerical simulation method of electrode microstructure evolution, which combines discrete element method (DEM) and dynamic Monte Carlo (KMC), is used to simulate the microstructure evolution process of functionally gradient electrodes during sintering and generate microstructures with gradient structures. Based on the microstructure, the electrochemical and mechanical properties of the functionally gradient electrode are evaluated using a preset microscale multi-field coupling model to obtain an evaluation result; Inputting the evaluation results into a machine learning prediction model to output the electrochemical and mechanical properties under a preset gradient design parameter combination; According to the electrochemical properties and the mechanical properties, a multi-objective optimization algorithm is used to optimize the gradient design parameter combination to determine a target gradient design parameter combination; Among them, the numerical simulation method of electrode microstructure evolution using a combination of discrete element method DEM and dynamic Monte Carlo KMC simulates the microstructure evolution process during the sintering preparation process of the functional gradient electrode to generate a microstructure with a gradient structure, including: using the discrete element method DEM to simulate the initial stacking structure of the electrode particles according to a preset particle size distribution; introducing pore-forming agent particles into the initial stacking structure to simulate the distribution of pores, and after the electrode particles are stacked, deleting the pore-forming agent particles to form an electrode with a gradient structure; wherein the gradient structure is formed by stacking different sublayers; for each sublayer, the gradient parameters are controlled based on the gradient control equation to obtain a target stacking structure; the target stacking structure is voxelized to generate a three-dimensional voxelized model; using the three-dimensional voxelized model as the initial crystal site matrix, the dynamic Monte Carlo KMC is used to simulate the microstructure evolution to generate a microstructure of a porous anode or cathode with a gradient structure; Among them, the gradient control equation includes: a composition gradient parameter control equation, which is used to control the composition gradient parameters in each sublayer; a porosity gradient parameter control equation, which is used to control the porosity gradient parameters of each sublayer; and a particle size distribution gradient parameter control equation, which is used to control the particle size distribution gradient parameters of each sublayer.

2. The gradient solid oxide fuel cell design method according to claim 1, characterized in that: The microscale multi-field coupling model includes: Charge transport models, used to calculate the potential distribution of electrons and ions; Electrochemical reaction model, used to calculate the current density and overpotential at the three-phase junction; Material transport model, used to calculate the transport process of gaseous substances in the electrode; Heat conduction model, used to calculate the temperature distribution within the electrode; Mechanical property models are used to calculate the thermal stress and failure probability of electrodes.

3. The gradient solid oxide fuel cell design method according to claim 1, wherein: Electrochemical and mechanical properties are evaluated, including: Calculate the total overpotential; Draw the curve of output voltage versus current density; Calculate the maximum power density; Calculate the maximum thermal stress; Perform Weibull failure probability analysis.

4. The gradient solid oxide fuel cell design method according to claim 1, wherein: The method further comprises: Obtain electrochemical and mechanical properties under different gradient design parameter combinations; The gradient design parameter combination is used as the input of an initial artificial neural network, the electrochemical properties and mechanical properties are used as the output of the initial artificial neural network, and the initial artificial neural network is trained to obtain the machine learning prediction model.

5. The gradient solid oxide fuel cell design method according to claim 1, wherein: The step of optimizing the gradient design parameter combination based on the electrochemical performance and the mechanical performance using a multi-objective optimization algorithm to determine a target gradient design parameter combination includes: Defining a multi-objective optimization objective function based on the electrochemical properties and the mechanical properties; wherein the objective function includes minimizing total overpotential, maximizing maximum power density, minimizing maximum thermal stress, and minimizing Weibull failure probability; Set optimization parameter ranges and constraints; Constructing a multi-objective optimization model based on the objective function and the constraints; Determining a corresponding multi-objective optimization algorithm based on the multi-objective optimization model; The multi-objective optimization algorithm is used to iteratively optimize the gradient design parameter combination to generate the target gradient design parameter combination.

6. The gradient solid oxide fuel cell design method according to claim 5, characterized in that: The optimization parameter ranges include: sub-layer number range, gradient index range, transition layer thickness range, porosity range, and particle size range; The constraints include: the number of sublayers is an integer, the gradient index is a positive number, the thickness of the transition layer is less than the total thickness of the electrode, the porosity is within the physical property limit range of the material, and the particle size is within the sintering process parameter range of the material.

7. The gradient solid oxide fuel cell design method according to claim 5, characterized in that: The iterative optimization of the gradient design parameter combination using the multi-objective optimization algorithm to generate the target gradient design parameter combination includes: Iteratively optimizing the gradient design parameter combination using the multi-objective optimization algorithm to generate a current iteratively optimized gradient design parameter combination; Based on the current iteratively optimized gradient design parameter combination, a microstructure with a gradient structure is regenerated, and the electrochemical and mechanical properties are evaluated until the preset performance target is achieved. The current iteratively optimized gradient design parameter combination corresponding to the preset performance target is used as the target gradient design parameter combination.

8. A gradient solid oxide fuel cell design device, characterized in that: include: The simulation module is used to simulate the microstructure evolution process of the functionally gradient electrode during sintering by using the numerical simulation method of electrode microstructure evolution that combines the discrete element method (DEM) and the dynamic Monte Carlo (KMC) method to generate a microstructure with a gradient structure. An evaluation module, configured to evaluate the electrochemical and mechanical properties of the functionally gradient electrode based on the microstructure using a preset microscale multi-field coupling model to obtain an evaluation result; A performance output module, configured to input the evaluation results into a machine learning prediction model and output the electrochemical and mechanical properties under a preset gradient design parameter combination; an optimization module, configured to optimize the gradient design parameter combination according to the electrochemical performance and the mechanical performance using a multi-objective optimization algorithm to determine a target gradient design parameter combination; Among them, the numerical simulation method of electrode microstructure evolution using a combination of discrete element method DEM and dynamic Monte Carlo KMC simulates the microstructure evolution process during the sintering preparation process of the functional gradient electrode to generate a microstructure with a gradient structure, including: using the discrete element method DEM to simulate the initial stacking structure of the electrode particles according to a preset particle size distribution; introducing pore-forming agent particles into the initial stacking structure to simulate the distribution of pores, and after the electrode particles are stacked, deleting the pore-forming agent particles to form an electrode with a gradient structure; wherein the gradient structure is formed by stacking different sublayers; for each sublayer, the gradient parameters are controlled based on the gradient control equation to obtain a target stacking structure; the target stacking structure is voxelized to generate a three-dimensional voxelized model; using the three-dimensional voxelized model as the initial crystal site matrix, the dynamic Monte Carlo KMC is used to simulate the microstructure evolution to generate a microstructure of a porous anode or cathode with a gradient structure; Among them, the gradient control equation includes: a composition gradient parameter control equation, which is used to control the composition gradient parameters in each sublayer; a porosity gradient parameter control equation, which is used to control the porosity gradient parameters of each sublayer; and a particle size distribution gradient parameter control equation, which is used to control the particle size distribution gradient parameters of each sublayer.

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