Gradient solid oxide fuel cell design method and device

Abstract

The invention is suitable for the technical field of solid oxide fuel cells, and provides a gradient solid oxide fuel cell design method and device, and the method comprises the steps: employing a discrete element method DEM and dynamics Monte Carlo KMC combined electrode microstructure evolution numerical simulation method, simulating a microstructure evolution process in a sintering preparation process of the functional gradient electrode to generate a microstructure with a gradient structure; based on the microstructure, utilizing a preset micro-scale multi-field coupling model to evaluate the electrochemical performance and the mechanical performance of the functionally gradient electrode to obtain an evaluation result; inputting the evaluation result into a machine learning prediction model, and outputting electrochemical performance and mechanical performance under a preset gradient design parameter combination; and according to the electrochemical performance and the mechanical performance, a multi-objective optimization algorithm is adopted to optimize the gradient design parameter combination, and a target gradient design parameter combination is determined. And the gradient solid oxide fuel cell can be designed efficiently and accurately.

Description

Technical Field

[0001] This application belongs to the technical field of solid oxide fuel cells, and particularly relates to a design method and device for a gradient solid oxide fuel cell. Background Art

[0002] Currently, the design methods of solid oxide fuel cells (SOFCs) mainly rely on experimental trial-and-error methods and numerical simulation methods. Among them, the experimental trial-and-error method has high costs and a long cycle. Although the numerical simulation method can reduce the number of experiments to a certain extent, the existing numerical simulation methods are usually based on simplified models, such as the percolation theory microscopic model of particle packing and the macroscopic layered model. These models have limitations in describing the electrode microstructure and cannot accurately account for real microstructure (also known as microscopic structure) parameters, such as specific surface area, triple-phase line density, pore size, tortuosity factor, etc. Therefore, there are certain errors in the prediction of battery performance by the existing numerical simulation methods, resulting in inaccurate design of solid oxide fuel cells and difficulty in achieving the best performance. Summary of the Invention

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

[0004] In a first aspect, the embodiments of this application provide a design method for a gradient solid oxide fuel cell, including: Using a numerical simulation method for electrode microstructure evolution that combines the discrete element method (DEM) and the kinetic Monte Carlo (KMC) method to simulate the microstructure evolution process during the sintering preparation process of a functional gradient electrode, and generating a microstructure with a gradient structure; Based on the microstructure, using a preset microscale multi-field coupling model to evaluate the electrochemical performance and mechanical performance of the functional gradient electrode, and obtaining an evaluation result; Inputting the evaluation result into a machine learning prediction model, and outputting the electrochemical performance and mechanical performance under a preset gradient design parameter combination; According to the electrochemical performance and the mechanical performance, using a multi-objective optimization algorithm to optimize the gradient design parameter combination, and determining the target gradient design parameter combination.

[0005] In a second aspect, the embodiments of this application provide a design device for a gradient solid oxide fuel cell, including: A simulation module, which is used to simulate the microstructure evolution process in the sintering preparation process of a functional gradient electrode by using a numerical simulation method for electrode microstructure evolution that combines the discrete element method (DEM) and the kinetic Monte Carlo (KMC), and generate a microstructure with a gradient structure; An evaluation module, which is used to evaluate the electrochemical performance and mechanical performance of the functional gradient electrode based on the microstructure by using a preset microscale multi-field coupling model, and obtain an evaluation result; A performance output module, which is used to input the evaluation result into a machine learning prediction model and output the electrochemical performance and mechanical performance under a preset gradient design parameter combination; An optimization module, which is used to optimize the gradient design parameter combination by using a multi-objective optimization algorithm according to the electrochemical performance and the mechanical performance, and determine the target gradient design parameter combination.

[0006] The beneficial effects of the embodiments of the present application compared with the prior art are as follows: By using a numerical simulation method for electrode microstructure evolution that combines the discrete element method (DEM) and the kinetic Monte Carlo (KMC), the microstructure evolution process in the sintering preparation process of a functional gradient electrode is simulated, and a microstructure with a gradient structure is generated; based on the microstructure, the electrochemical performance and mechanical performance of the functional gradient electrode are evaluated by using a preset microscale multi-field coupling model, and an evaluation result is obtained; the evaluation result is input into a machine learning prediction model, and the electrochemical performance and mechanical performance under a preset gradient design parameter combination are output; according to the electrochemical performance and the mechanical performance, the gradient design parameter combination is optimized by using a multi-objective optimization algorithm, and the target gradient design parameter combination is determined. Among them, through the combination of DEM and KMC, the microstructure evolution of the electrode during the sintering process can be accurately simulated, and a real gradient structure microstructure can be generated. Compared with the traditional simulation method based on simplified assumptions, it can more accurately reflect the actual microstructure of the electrode, thereby providing a more reliable basis for subsequent performance evaluation. This accurate microstructure simulation helps to improve the accuracy of battery performance prediction and reduce the errors caused by model simplification. In addition, by accurately simulating the electrode microstructure evolution, comprehensively evaluating the electrochemical and mechanical performance, using machine learning for performance prediction, and using a multi-objective optimization algorithm for parameter optimization, the efficient, accurate and optimized design of solid oxide fuel cells is realized. It can significantly improve the accuracy of battery performance prediction, reduce the development cost and cycle, and at the same time optimize the comprehensive performance of the battery, making it have better performance and reliability in practical applications. This comprehensive technical solution provides a new and efficient method for the design of solid oxide fuel cells. Description of the Drawings

[0007] To more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the accompanying drawings required for use in the embodiments or the description of the prior art. Obviously, the accompanying drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can also be obtained based on these drawings.

[0008] Figure 1 is a schematic flowchart of a design method for a gradient solid oxide fuel cell provided by an embodiment of the present application; Figure 2 is a schematic diagram of the neural network architecture of a machine learning prediction model provided by an embodiment of the present application; Figure 3 is a schematic structural diagram of a gradient solid oxide fuel cell design device provided by an embodiment of the present application; Figure 4 is a schematic structural diagram of a computer device provided by an embodiment of the present application. Detailed implementation manners

[0009] In the following description, for the purpose of illustration rather than limitation, specific details such as specific system structures and technologies are presented to thoroughly understand the embodiments of the present application. However, those skilled in the art should clearly understand that the present application can also 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 unnecessary details from interfering with the description of the present application.

[0010] It should be understood that when used in the specification and the appended claims of the present application, the term "comprising" indicates the presence of the described features, wholes, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components, and / or their combinations. It should also be understood that the term "and / or" used in the specification and the appended claims of the present application refers to any combination and all possible combinations of one or more of the associated listed items, and includes these combinations.

[0011] As used in the specification and the appended claims of the present application, the term "if" can be interpreted as "when", "once", "in response to determining", or "in response to detecting" according to the context. Similarly, the phrase "if determined" or "if detecting [the described condition or event]" can be interpreted as meaning "once determined", "in response to determining", "once detecting [the described condition or event]", or "in response to detecting [the described condition or event]" according to the context.

[0012] In addition, in the description of the specification and the appended claims of the present application, the terms "first", "second", "third", etc. are only used for distinguishing descriptions and cannot be construed as indicating or implying relative importance.

[0013] The reference to "one embodiment" or "some embodiments" described in the specification of the present application means that a specific feature, structure, or characteristic described in connection with the embodiment is included in one or more embodiments of the present application. Thus, the statements "in one embodiment", "in some embodiments", "in other some embodiments", "in still other embodiments", etc. that appear in different places in this specification do not necessarily refer to the same embodiment, but mean "one or more but not all embodiments", unless otherwise specifically emphasized. The terms "comprising", "including", "having", and their variants all mean "including but not limited to", unless otherwise specifically emphasized.

[0014] Solid oxide fuel cells have become a clean energy technology with development potential due to characteristics such as high efficiency, wide fuel adaptability, low pollution emissions, and the absence of the need for noble metal catalysts. In promoting the commercial application process of SOFCs, electrochemical performance, durability, etc. are the core elements determining their market competitiveness. Among them, the electrochemical performance of SOFCs is closely related to the electrode microstructure. Theoretical and experimental studies have shown that introducing the concept of functional gradient design into the electrode microstructure design of SOFCs can effectively improve their electrochemical performance. At the same time, through functional gradient design, the problem of mismatch in the interfacial material properties between different components of SOFCs can be alleviated. However, the currently disclosed related solutions for functional gradient solid oxide fuel cells mainly focus on the protection of the preparation process, and there is no disclosure and protection regarding the design method of functional gradient solid oxide fuel cells.

[0015] Currently, the design methods of SOFCs mainly rely on experimental trial-and-error methods and numerical simulation methods. Among them, the experimental trial-and-error method has high costs and a long cycle. The numerical simulation method mainly relies on the percolation theory microscopic model of particle packing and the macroscopic layered model. However, the electrodes of real SOFCs are sintered from powder particles with irregular morphologies, and sintering necks are formed between the particles. There are significant differences between the real electrode microstructure and the output results of the percolation theory microscopic model in terms of corresponding microstructure parameters (microstructure parameters such as specific surface area, triple-phase line density, pore size, tortuosity factor, etc.). In addition, the macroscopic layered model generally assumes that the physical properties of the electrode material gradually change in the thickness direction, and the material properties are isotropic in the same plane perpendicular to the thickness direction. However, in actual situations, there are differences in the local particle packing of SOFC electrodes, resulting in anisotropy in the physical and electrochemical properties of the electrodes. The gradient structure designed based on the above numerical simulation method is often the microstructure after sintering preparation.

[0016] In addition, most of the existing design schemes for gradient SOFCs 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.

[0017] Figure 1 Fig. 4 shows a schematic flow chart of a gradient solid oxide fuel cell design method provided by an embodiment of the present application.

[0018] S101, using a numerical simulation method for electrode microstructure evolution that combines the Discrete Element Method (DEM) and Kinetic Monte Carlo (KMC), simulate the microstructure evolution process during the sintering preparation of a functional gradient electrode to generate a microstructure with a gradient structure.

[0019] Among them, DEM is a numerical simulation technology based on the interaction forces between particles. By tracking the motion and contact behavior of individual particles, it simulates the dynamic evolution process of the particle system. Its core lies in establishing the mechanical model of particles (such as contact force, friction force, damping force), calculating the displacement and rotation of particles under the action of forces, and then reconstructing the macroscopic mechanical response of the particle system. In the simulation of electrode microstructure, DEM is used to generate the initial particle packing structure, accurately depict the particle size distribution, spatial arrangement, and pore formation mechanism of particles, and provide a real microscopic initial state for subsequent sintering evolution.

[0020] Among them, KMC is a probability-based numerical simulation method. By randomly selecting events and calculating their occurrence probabilities, it simulates the dynamic evolution of physical processes. KMC introduces the concept of time step, preferentially simulating events with lower energy or faster rates, so as to efficiently restore the time-dependent changes of the microscopic structure. In the simulation of electrode sintering, KMC is used to simulate mechanisms such as grain growth, pore migration, and vacancy densification, and drives the optimization and stabilization of the microscopic structure through the principle of energy minimization (such as surface energy, grain boundary energy).

[0021] Among them, the numerical simulation method for electrode microstructure evolution is a multi-scale and multi-physical-field coupling calculation framework. By integrating DEM and KMC, it reproduces the dynamic changes of the microscopic structure of the electrode from the initial particle packing to the sintering forming process in the whole process, can replace experimental trial and error, and achieve accurate prediction of electrode performance and global optimization of process parameters.

[0022] Among them, simulating the microstructure evolution process during the sintering preparation of a functional gradient electrode means simulating the full-cycle dynamic evolution process of the microstructure from the initial particle packing to the high-temperature sintering forming process during the sintering preparation of a functional gradient anode or cathode.

[0023] Among them, generating a microstructure with a gradient structure refers to generating a porous anode or cathode microstructure with a gradient structure.

[0024] In an alternative embodiment, 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 of a functionally graded electrode, and generate a microstructure with a gradient structure, including: Step a1, using the Discrete Element Method (DEM), simulate the initial packing structure of electrode particles according to a preset particle size distribution.

[0025] Among them, simulating the initial packing structure of electrode particles specifically refers to simulating the initial packing structure of anode or cathode electrode particles.

[0026] In the embodiments of the present application, a three-dimensional computational domain is built to define the spatial range in the electrode thickness direction. Subsequently, a particle assembly is generated according to the target particle size distribution (such as normal distribution, lognormal distribution). For example, the particle size of anode Ni particles is set to 1 - 5 μm, and the particle size of cathode LSCF particles is set to 0.5 - 3 μm. Each particle is given a particle size value that conforms to the distribution characteristics through a random number algorithm. Then, the particles are gradually dropped into the computational domain under the action of gravity. The normal elastic force and tangential frictional force between the particles are calculated through the Hertz-Mindlin contact model to simulate the collision, sliding, and rotation behaviors in real packing until the particle system reaches a dynamic equilibrium state, forming a closely packed initial structure. During the process, the packing density can be controlled by adjusting the particle friction coefficient and wall boundary conditions (such as rigid constraints), and the spatial distribution of pore-forming agent particles is introduced to lay the foundation for subsequent porosity gradient design. This step can accurately reproduce the spatial arrangement of electrode particles at the micron scale, capture the contact points between particles and the pore distribution characteristics, and provide a real and reliable initial condition for subsequent KMC sintering simulation.

[0027] Step a2, introduce pore-forming agent particles into the initial packing structure to simulate the pore distribution, and after the electrode particle packing is completed, delete the pore-forming agent particles to form an electrode with a gradient structure; among them, the gradient structure is composed of different sub-layer packings. Among them, the electrode particles in each sub-layer are uniformly distributed in the sub-layer space.

[0028] In the embodiments of the present application, in the initial packing structure of electrode particles obtained by DEM simulation, according to the gradient design target, pore-forming agent particles (such as carbon powder, polymer microspheres, etc.) are introduced into different sub-layers to simulate the spatial distribution of pores. First, the electrode is divided into N sub-layers along the thickness direction (e.g., N = 3 - 5 layers), and each sub-layer corresponds to independent pore-forming agent content and particle size parameters. For example, in the anode gradient structure, a higher pore-forming agent volume fraction (e.g., 30% - 40%) is set in the surface sub-layer (fuel side), and pore-forming agent particles with a larger particle size (e.g., 2 - 4 μm) are matched to form a high-porosity region to promote fuel diffusion; in the inner sub-layer (electrolyte side), the pore-forming agent content is reduced to 10% - 20%, and smaller particle size particles (e.g., 0.5 - 1 μm) are used to balance the porosity and mechanical strength. During the particle packing process, the pore-forming agent particles and the electrode particles (such as Ni, YSZ) jointly participate in the dynamic packing through the discrete element algorithm, and their positions and distributions are restricted by the spatial boundaries of the sub-layers to ensure a clear gradient interface. When the packing is completed and the system reaches mechanical equilibrium, all pore-forming agent particles are automatically deleted through program instructions, and the space they occupy is transformed into pores, forming a composite structure of "electrode particle skeleton + gradient pores". This process realizes the gradient change of porosity along the electrode thickness direction (e.g., decreasing from 40% on the surface layer to 25% on the inner layer) through sub-layer division and differential setting of pore-forming agent parameters, while retaining the effective contact between particles to maintain the continuity of the conductive network. This method breaks through the limitations of traditional uniform pore design and provides a physical carrier for the subsequent coordinated optimization of triple gradients (composition, particle size, porosity).

[0029] Step a3, for each sub-layer, control the gradient parameters based on the gradient control equation to obtain the target packing structure. Among them, the gradient parameters include the composition gradient parameter, the porosity gradient parameter, and the particle size distribution gradient parameter. Among them, the gradient control equation includes: the composition gradient parameter control equation, which is used to control the composition gradient parameter in each sub-layer; the porosity gradient parameter control equation, which is used to control the porosity gradient parameter in each sub-layer; and the particle size distribution gradient parameter control equation, which is used to control the particle size distribution gradient parameter in each sub-layer.

[0030] In the embodiments of the present application, for each sub-layer divided along the electrode thickness direction, the three types of gradient parameters of composition, porosity, and particle size distribution are accurately regulated through the gradient control equation to generate the target packing structure.

[0031] Among them, for the composition gradient control, according to the sub-layer position, through the composition gradient parameter control equation: (Equation 1), adjust the proportion of each phase layer by layer. For example, in a certain sub-layer of the cathode, the volume fraction of LSCF (electronic phase) decreases exponentially from 60% on the surface layer along the thickness direction at to 40% on the inner layer, and GDC (ionic phase) correspondingly increases from 40% to 60%, forming a composition gradient interface.

[0032] Among them, represents the volume fraction of the layer; represents the minimum volume fraction of ; represents the maximum volume fraction of represents the ion conductive phase , the electron conductive phase or the pore phase ; the ion conductive phase may include YSZ, LSCF, GDC, etc.; the electron conductive phase may include Ni, LSCF, etc.; is the number of sub-layers; is the total number of layers; is the gradient index.

[0033] For the control of the porosity gradient, by correlating the pore former content with the sub-layer position, the volume fraction of the pore phase is controlled using the porosity gradient parameter control equation (Equation 2). For example, the porosity of the anode surface layer is set to 40% and the inner layer is set to 25%, and the gradient transition is achieved by adjusting the remaining space after removing the pore former in each sub-layer.

[0034] Among them, Equation 2 represents the sum of the volume fraction of the ion conductive phase in the layer, the volume fraction of the electron conductive phase in the layer, and the volume fraction of the pore phase in the layer is 1.

[0035] For the control of the particle size distribution gradient, the particle size distribution gradient parameter control equation is adopted: (Equation 3), so that the average particle size of the particles changes layer by layer along the thickness direction. For example, the particle size of the anode particles decreases linearly from 5 μm on the surface layer to 2 μm on the inner layer, reducing the gas diffusion resistance while enhancing the inner layer structure strength.

[0036] Among them, represents the average particle size of the layer; represents the minimum particle size of the particles; represents the maximum particle size of the particles; is the gradient index.

[0037] Through the collaborative regulation of three types of gradient parameters, each sub-layer forms differentiated microstructural features, which are finally superimposed into a target stacking structure with triple gradients of composition-particle size-porosity, providing a parametric basis for the multi-physical field coupling simulation of the subsequent sintering process.

[0038] Step a4: Voxelize the target stacking structure to generate a three-dimensional voxel model.

[0039] In the 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 cells (voxels), generating a digital structure that can be recognized by the kinetic Monte Carlo (KMC) model.

[0040] First, based on the particle coordinates and particle size data output by the DEM simulation, the calculation domain range (such as 100×100×50 μm³) is delimited in three-dimensional space, and the voxel resolution (such as 10 nm / voxel) is set. The resolution needs to be less than 1 / 5 of the minimum particle size to ensure the retention of geometric features. Subsequently, all voxels within the calculation domain are traversed through the threshold method or the scan line algorithm. The voxels intersecting with the electrode particles (such as Ni, YSZ) are marked as "solid phase", and the spaces not occupied by particles (including the pores after the removal of pore formers) are marked as "pore phase", forming a three-dimensional grayscale image composed of discrete voxel units - where the attribute value of each voxel corresponds to the phase type (such as 0 representing pores, 1 representing ion-conducting phase, 2 representing electron-conducting phase).

[0041] During the voxelization process, geometric repair is required to eliminate the penetration or gaps between particles, ensuring the continuity of the solid phase and the topological authenticity of the pore phase. The generated three-dimensional voxel model can be further visualized and statistically analyzed to obtain microstructural parameters such as the initial porosity and particle contact density, serving as the initial crystal site lattice for the KMC sintering simulation. This step realizes the conversion from continuous particle stacking to discretized microstructures, providing a numerical carrier for subsequent lattice-based sintering mechanism simulations (such as grain growth, pore migration), and laying a foundation for mesh generation in multi-field coupling analysis.

[0042] Step a5: Using the three-dimensional voxel model as the initial crystal site lattice, perform microstructural evolution simulation using the kinetic Monte Carlo (KMC) to generate the microstructures of porous anodes or cathodes with gradient structures.

[0043] In the embodiment of the present application, taking the three-dimensional voxel model as the initial crystal site lattice (each voxel corresponds to a site in the KMC simulation, and the site state is defined as pore phase, ion-conducting phase, or electron-conducting phase), the microstructural evolution is driven based on the Metropolis Monte Carlo algorithm to simulate the physical and chemical changes of the electrode during the high-temperature sintering process. First, set the KMC simulation parameters, including the sintering temperature (through the Boltzmann constant Associated dimensionless temperature ), the attempt frequency of each mechanism (such as the grain growth frequency ), the pore migration frequency ), and define the system energy (Equation 4), where is the site and the site The interaction energy between them corresponds to the surface energy on the pore-grain interface and the grain boundary energy of the grain-grain grain boundary interaction ; is the total number of voxel sites; is the Kronecker function, which judges whether the phase states of the sites are the same. When When , When .

[0044] Among them, the evolution process is achieved through the following mechanisms: 1) Grain growth: Randomly exchange the phase states of adjacent sites (such as the ion-conducting phase and the electron-conducting phase), and calculate the energy change . If Then accept the exchange; if , then with probability (Equation 5) to decide whether to accept, simulating the grain coalescence caused by short-range atomic diffusion. Among them, represents the simulated sintering temperature.

[0045] 2) Pore migration: Randomly exchange the pore sites with adjacent non-pore sites, and judge whether to retain the migration through energy evaluation and Metropolis probability, reflecting the change of pore position caused by long-range surface diffusion. That is, use Equation 4 to evaluate and Equation 5 to re-evaluate the probability to judge whether to accept the pore migration attempt.

[0046] 3) Vacancy formation and disappearance: Generate vacancies by exchanging pore and grain sites. If isolated vacancies are formed, try to migrate them to the surface to disappear, simulating the densification behavior during sintering. If isolated vacancies are formed after the exchange, use Equation 4 and Equation 5 to determine whether to accept this exchange. After the vacancies are formed, simulate their disappearance by moving the vacancy positions to the sample surface.

[0047] 4) Interface exchange: For composite phases (such as Ni / YSZ), allow different phase sites to exchange states to maintain mass conservation and suppress stress concentration caused by interface unevenness.

[0048] Among them, the parameters controlling the KMC simulation are mainly the simulated sintering temperature and the attempt frequency : including four mechanisms: grain growth ( and ), pore migration ( and ), vacancy formation and disappearance ( and ), and interface exchange ( and ).

[0049] Among them, represents the simulated temperature applied in the grain growth algorithm; represents the attempt frequency applied in the grain growth algorithm; represents the simulated temperature applied in the pore migration algorithm; represents the attempt frequency applied in the pore migration algorithm; represents the simulated temperature applied in the grain boundary vacancy formation algorithm; represents the attempt frequency applied in the grain boundary vacancy formation algorithm; represents the simulated temperature applied in the interface exchange algorithm; represents the attempt frequency applied in the interface exchange algorithm; Under the gradient structure constraint, each sub-layer shows different evolution rates due to differences in composition, particle size, and porosity: the high-porosity region on the surface is mainly characterized by pore shrinkage, while the low-porosity region in the inner layer is mainly characterized by grain coarsening, and finally a porous structure with gradient characteristics is generated (such as the pore size on the surface is 200 - 300 nm, and the pore size in the inner layer is 50 - 100 nm). After the simulation is completed, microstructure parameters (such as specific surface area, triple-phase line density, tortuosity factor) are extracted to provide real geometric input for the subsequent multi-field coupling performance evaluation. This step reproduces the microscopic mechanism of the sintering process through kinetic simulation, breaks through the static assumption of the traditional percolation theory, and realizes the dynamic evolution modeling from the initial packing to the functionally graded microstructure.

[0050] Among them, in addition to using the KMC method to simulate the sintering of the electrode microstructure, the phase field method can also be used to realize the simulation of the microstructure evolution during the electrode sintering process. The phase field method describes the microscopic structure state inside the material by introducing continuous phase field variables. Based on the diffusion equation and thermodynamics theory, it simulates sintering phenomena such as grain growth, interface evolution, and pore migration, and can intuitively show the dynamic changes of the electrode microstructure from the initial particle packing to the densification process, providing an effective means for analyzing the influence of sintering process parameters (such as temperature, time) on microstructure characteristics (such as grain size, porosity distribution).

[0051] Among them, for multi-physics field coupling simulation, in addition to the above methods, the lattice Boltzmann method (LBM) can also be used to solve the problem. By simulating the migration and collision behavior of particles in a discrete lattice space, this method can effectively describe the mass transfer in porous electrodes (such as gas diffusion and ion conduction), the heat generation of electrochemical reactions, and the heat conduction process, and then realize the cross-scale coupling analysis of the potential distribution, temperature field, and concentration field. Its advantages lie in its strong adaptability to complex pore structures and its high-efficiency collaborative calculation ability for multi-physics fields, which can accurately reveal the interaction mechanism between electrochemical reactions and transport processes at the microscale and provide key support for the performance prediction and optimal design of functional gradient electrodes.

[0052] S102, based on the microstructure, use a preset microscale multi-field coupling model to evaluate the electrochemical performance and mechanical performance of the functional gradient electrode, and obtain an evaluation result.

[0053] Among them, the microscale multi-field coupling model includes: a charge transport model for calculating the potential distribution of electrons and ions; an electrochemical reaction model for calculating the current density and overpotential at the three-phase junction; a mass transfer model for calculating the transport process of gas substances in the electrode; a heat conduction model for calculating the temperature distribution in the electrode; and a mechanical performance model for calculating the thermal stress and failure probability of the electrode.

[0054] Evaluating the electrochemical performance and mechanical performance includes: Calculating the total overpotential; plotting the curve of output voltage versus current density; calculating the maximum power density; calculating the maximum thermal stress; and performing Weibull failure probability analysis.

[0055] Among them, based on the charge transport model, the potential distributions in the electronic conductive phase (such as Ni, LSCF) and the ionic conductive phase (such as YSZ, GDC) are solved to reveal the effectiveness of the electrical conduction path. The relevant introduction to the charge transport model is as follows.

[0056] Electronic phase: (Equation 6); Ionic phase: (Equation 7); In the formula, and are the potentials in the electronic and ionic conductive phases respectively, and are the electrical conductivities of electrons and ions respectively, is the exchange current density at the three-phase or two-phase interface.

[0057] The ionic conductivity of YSZ and the electronic conductivity of Ni in the composite anode are calculated as follows: (Equation 8); (Equation 9); wherein, represents the material temperature.

[0058] The LSCF conductivity in the composite cathode is defined by the temperature and oxygen partial pressure dependence formula: (Equation 10); (Equation 11); (Equation 12); (Equation 13); wherein, ~ is a preset temperature-dependent empirical coefficient; is the molar volume of LSCF; is the oxygen partial pressure in the solid; is the oxygen partial pressure in the atmospheric pressure; is the chemical diffusion coefficient; δ is the oxygen non-stoichiometry; is the Faraday constant; is a constant for converting molar scale and energy.

[0059] The temperature-dependent ionic conductivity in GDC is calculated as follows: (Equation 14); wherein, is the electron volt; is the Boltzmann constant.

[0060] Among them, the electrochemical reaction model focuses on simulating the electrochemical reaction process at the triple-phase boundary (TPB, solid phase - ionic phase - gas phase) and the double-phase boundary (DPB, electronic phase - ionic phase) in the electrodes of solid oxide fuel cells (SOFCs). The core goal is to quantify the reaction kinetic parameters and reveal the performance bottlenecks. The relevant introduction to the electrochemical reaction model is as follows.

[0061] The electrochemical reaction only occurs at the active interfaces 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 describes the relationship between the reaction rate and the overpotential based on the Butler-Volmer (BV) equation, and the formula is: (Equation 15); wherein, is the volumetric 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, with the unit of (A / m); and are the forward and backward reaction coefficients, respectively, at the anodic TPB and take 1 and 0.5 respectively, both take 1 at the cathodic TPB, and take 0.6 and 0.5 respectively at the cathodic DPB; is the gas constant; is the Faraday constant; is the number of electrons released in the reaction; is the activation overpotential.

[0062] Among them, Equation 15 is a formula common to both the cathode and the anode.

[0063] The exchange current density is: (Equation 16); (Equation 17); (Equation 18); Among them, is the exchange current density per unit length of the anodic TPB; is the partial pressure of hydrogen is the partial pressure of water vapor; is the exchange current density per unit length of the cathodic TPB; is the partial pressure of oxygen; is the exchange current density per unit length of the cathodic DPB.

[0064] Among them, Equation 15 is a formula common to both the cathode and the anode, then the anodic activation overpotential and the cathodic activation overpotential are defined as follows: (Equation 19); (Equation 20); Among them, is the anodic activation overpotential, is the cathodic activation overpotential, and the calculation is as follows: (Equation 21); (Equation 22); Among them, is the partial pressure of the gas set as a constant in the boundary condition; is the partial pressure of the gas set as a constant in the boundary condition; is the partial pressure of the gas set as a constant in the boundary condition; is the interfacial partial pressure of hydrogen; is the partial pressure of oxygen at the interface; is the partial pressure of water vapor at the interface.

[0065] Among them, the relevant introduction to the mass transfer model is as follows.

[0066] In the porous structure of the electrode, gas transport is simultaneously dominated by molecular diffusion (collisions between gas molecules) and Knudsen diffusion (collisions between gas molecules and pore walls), specifically depending on the relative relationship between the pore size and the mean free path of the gas. The model describes the mass transfer process through the component conservation equation: (Equation 23); Among them, is the mass fraction of component ; is the density of the mixture; is the effective diffusion coefficient of component ; is the mass source term.

[0067] Since the reaction only occurs at the TPB, the consumption and generation of components also occur at the TPB. The effective diffusion coefficient is calculated by the following formula: (Equation 24); Among them, is the mass fraction of component ; is the binary diffusion coefficient of component and component ; is the Knudsen diffusion coefficient of component .

[0068] The Knudsen diffusion coefficient is calculated as: (Equation 25); Among them, is the average pore diameter; is the molar mass of component .

[0069] The binary diffusion coefficient is calculated using the Fuller–Schettler–Giddings model: (Equation 26); In the formula, and are the diffusion volumes of components and respectively; and are the molecular weights of components and respectively.

[0070] The mass source term in Equation 23 is calculated as follows: (Equation 27); (Equation 28); (Equation 29).

[0071] Among them, 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.

[0072] Among them, the heat conduction model focuses on the heat transfer process inside the electrodes of a solid oxide fuel cell (SOFC), aiming to reveal the dynamic balance among the heat release of electrochemical reactions, the heat generation of ohmic losses, and heat conduction, and to evaluate the influence of temperature distribution on the performance and reliability of the cell. The model is based on the thermophysical properties of microscale porous media and combines multi-field coupling mechanisms to achieve the collaborative calculation of the temperature field and stress field. The relevant introduction to the heat conduction model is as follows.

[0073] During the operation of the SOFC, the heat mainly comes from the heat release of electrochemical reactions (activation heat, entropy change heat) and the heat generation of ohmic resistance, and is conducted through the solid skeleton (electrode particles) and pore gas. The model describes the temperature field distribution through the heat conduction equation: (Equation 30); Among them, is the specific heat capacity, is the thermal conductivity, is the heat source term, and the heat source term is calculated as follows: (Equation 31); Among them, the / in the above text means "or". Among them, is the heat source term; is the volume current density; is the square of the modulus of the electron potential gradient; is the electron conductivity; is the square of the modulus of the ion potential gradient; is the ion conductivity; is the entropy change.

[0074] Among them, the boundary conditions are as follows:

[0075] Among them, is the mass fraction of component ; is the mass fraction of the component given as a constant; is the total overpotential; is the temperature given as a constant.

[0076] Based on the above formulas and boundary conditions, the electrochemical potential distributions of electrons and ions are calculated, and the total overpotential is calculated; the curve of output voltage versus current density V-I and the maximum power density are calculated and plotted; the temperature field result of the simulation result is used as the initial condition for the thermal stress simulation, and the finite element program (such as Abaqus) is used for mesh generation and thermal stress simulation to calculate the maximum thermal stress; and the Weibull failure probability analysis is carried out.

[0077] Among them, the relevant introduction of the mechanical property model is as follows.

[0078] Considering the displacements and stresses caused by the thermal expansion mismatch, the force balance equation of the solid element in differential form is: (Equation 32); Among them, is the displacement vector, is the density, is the body force, is the stress tensor.

[0079] Among them, the strain tensor is defined as: (Equation 33); According to Hooke's law, the relationship between the stress tensor and the strain tensor is: (Equation 34); Among them, is the transpose of the strain tensor, is the unit tensor, and are the Lamé constants, and their relationship with the Young's modulus and the Poisson's ratio is: (Equation 35); (Equation 36); For the stress tensor with temperature load, its tensor form expression is: (Equation 37); Among them, α is the thermal expansion coefficient; is the strain tensor; is the initial temperature.

[0080] According to Equations 32 to 34, the equilibrium equation can be rewritten as: (Equation 38).

[0081] Among them, the relevant introduction to Weibull failure probability analysis is as follows.

[0082] To quantify the mechanical strength of the microstructure, the Weibull method for brittle material failure analysis is applied to estimate the mechanical failure probability of all samples. The mechanical failure probability is defined as: (Equation 39); is the Weibull strength of the material, and the constant = 8 is the Weibull modulus, applicable to measuring the reference volume of the material, is the volume of the conductive phase calculated. The total probability is calculated by multiplying the survival probabilities of the three principal stresses ; represents the directions of the three principal stresses inside the material.

[0083] S103, input the evaluation result into the machine learning prediction model, and output the electrochemical performance and mechanical performance under the preset gradient design parameter combination.

[0084] Among them, the training process of the machine learning prediction model includes: obtaining the electrochemical performance and mechanical performance under different gradient design parameter combinations; using the gradient design parameter combination as the input of the initial artificial neural network, and the electrochemical performance and mechanical performance as the output of the initial artificial neural network, and training the initial artificial neural network to obtain the machine learning prediction model.

[0085] As Figure 2 shown, it is a schematic diagram of the neural network architecture of the machine learning prediction model. This machine learning prediction model is obtained by training based on the initial artificial neural network. 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: . Among them, is the number of sub-layers, is the gradient index, is the thickness of the transition layer, is the porosity, is the particle size. The electrochemical performance and mechanical performance are output.

[0086] In the embodiments of the present application, the generation of the gradient design parameter combination follows the experimental design (DoE) method and is parametrically designed through the DEM-KMC model. The specific steps are as follows: Parameter space definition: Core parameters: number of sub-layers , gradient index , thickness of the transition layer , Porosity , Particle size .

[0087] DoE Sampling Strategy: Use Latin Hypercube Sampling (LHS) or Orthogonal Array Design to uniformly generate sample points within the parameter space, ensuring coverage of linear and non-linear gradient scenarios. For example, generate 200 sets of parameter combinations, each corresponding to a functionally graded electrode microstructure.

[0088] Performance Evaluation: For each set of parameters, generate the microstructure through DEM-KMC simulation, and then calculate the electrochemical and mechanical properties using the multi-field coupling model.

[0089] After that, perform data preprocessing. The input features (gradient parameters) include , where N is an integer discrete variable, and the rest are continuous variables. Use Min-Max normalization for continuous variables and one-hot encoding or label encoding for discrete variables to convert them into continuous numerical values.

[0090] The output labels (performance metrics) include: electrochemical properties (such as total overpotential, maximum power density) and mechanical properties (such as maximum thermal stress and Weibull failure probability).

[0091] Among them, the architecture design of the initial artificial neural network is as follows: Input layer: 5 neurons, corresponding to 5-dimensional gradient parameters (normalized values).

[0092] Hidden layer, including the number of layers, number of nodes, and activation function.

[0093] Number of layers and nodes: The number of hidden layers and nodes are hyperparameters determined through cross-validation. Example configuration: 2 hidden layers, 32 nodes in the first layer, and 16 nodes in the second layer (meeting the requirement that "the number of hidden layers and nodes are determined during training").

[0094] Activation function: ReLU function (to solve the vanishing gradient problem).

[0095] Output layer: 4 neurons, corresponding to 4-dimensional performance metrics (normalized values), and the activation function is a linear function (suitable for regression tasks).

[0096] Among them, during model training, the dataset is divided into a training set (80%) and a validation set (20%); input the gradient parameters, calculate the predicted performance metrics; calculate the gradients of the loss function with respect to the weights of each layer, and update the parameters; calculate the validation set loss after each epoch. If the validation loss does not decrease for 10 consecutive epochs, trigger the early stopping mechanism to prevent overfitting.

[0097] Optionally, when new experimental or simulation data is obtained, it is input into the model as new samples, and the model parameters are updated through online learning or incremental training to achieve iteration.

[0098] In the embodiment of the present application, in the process of inputting the evaluation results into the machine learning prediction model, it is necessary to first normalize the electrochemical performance (such as polarization curve, total overvoltage, maximum power density) and mechanical performance (maximum thermal stress, Weibull failure probability) data output by the multi-field coupling model to eliminate the dimension difference. Subsequently, these evaluation results and the corresponding gradient design parameter combinations (number of sub-layers, gradient index, thickness of the transition layer, porosity, particle size) are formed into a training data set and input into the artificial neural network model. When a preset gradient design parameter combination is input, the model outputs a normalized performance prediction value through forward propagation, and then restores it to the actual physical dimension through denormalization, providing fast and accurate performance prediction support for the subsequent multi-objective genetic algorithm optimization, and significantly improving the gradient electrode design efficiency.

[0099] S104, according to the electrochemical performance and the mechanical performance, optimize the gradient design parameter combination by using a multi-objective optimization algorithm to determine the target gradient design parameter combination.

[0100] In the embodiment of the present application, according to the electrochemical performance (such as maximum power density, total overvoltage) and mechanical performance (maximum thermal stress, Weibull failure probability) under the gradient design parameter combination output by the machine learning prediction model, a multi-objective optimization algorithm (such as NSGA-II) is used to globally optimize the gradient design parameter combination (number of sub-layers N, gradient index P, thickness of the transition layer t, porosity ε, particle size d). First, set the optimization objectives (such as maximizing the power density, minimizing the thermal stress and failure probability) and the parameter constraint range (such as N is an integer from 2 to 6, porosity is 15% - 45%), and then through iterative processes such as initializing the population, fitness evaluation, and genetic operations (selection, crossover, mutation), search for the Pareto optimal solution set in the parameter space. According to the design requirements, select a trade-off solution that takes into account both performance and reliability from the solution set (such as preferentially improving the power density or focusing on durability), and verify the preferred parameter combination through the multi-field coupling model to ensure that the error between the predicted performance and the actual result is within an acceptable range. The finally determined target gradient design parameter combination can directly guide the optimization of the electrode microstructure preparation process, realize the coordinated improvement of electrochemical and mechanical performance, avoid the inefficiency of the traditional trial-and-error method, and significantly shorten the fuel cell R & D cycle.

[0101] Optionally, S104 according to the electrochemical performance and the mechanical performance, optimize the gradient design parameter combination by using a multi-objective optimization algorithm to determine the target gradient design parameter combination, including: Step b1: Define the objective function for multi-objective optimization based on the electrochemical performance and the mechanical performance. The objective function includes minimizing the total overpotential, maximizing the maximum power density, minimizing the maximum thermal stress, and minimizing the Weibull failure probability.

[0102] In the embodiments of the present application, when defining the objective function for multi-objective optimization, it is necessary to comprehensively consider the balance between electrochemical performance and mechanical performance, and construct the following objective function system: First, clarify the total overpotential to be minimized, which includes activation overpotential, ohmic overpotential, and concentration overpotential, and directly affects the energy conversion efficiency of the battery. A lower total overpotential means less energy loss and higher voltage output. Secondly, maximize the maximum power density, which characterizes the power generation capacity per unit area of the battery and is one of the core indicators for measuring battery performance. By optimizing the electrode microstructure, the reaction interface area and mass transfer efficiency can be improved, thereby increasing this indicator. The third objective is to minimize the maximum thermal stress, which results from the temperature gradient during battery operation and the difference in the thermal expansion coefficients of materials. Excessive thermal stress can lead to electrode cracking and even structural failure, and gradient design is required to reduce the concentration of thermal stress. Finally, minimize the Weibull failure probability, which is calculated based on the internal defect distribution and stress state of the material and reflects the reliability of the electrode under actual working conditions. Reducing this probability can significantly extend the service life of the battery. These four objective functions are interrelated and may conflict with each other. For example, increasing the power density may increase the thermal stress. Therefore, it is necessary to seek the Pareto optimal solution in multi-objective optimization to achieve the coordinated improvement of performance and reliability.

[0103] Step b2: Set the range of optimization parameters and the constraint conditions.

[0104] In the embodiments of the present application, determine the value range of each gradient design parameter combination during the optimization process, and set the corresponding constraint conditions to ensure the feasibility of the optimization results, etc.

[0105] Step b3: Construct a multi-objective optimization model based on the objective function and the constraint conditions.

[0106] Among them, based on the objective function (minimizing the total overpotential, maximizing the maximum power density, minimizing the maximum thermal stress, minimizing the Weibull failure probability) and the constraint conditions (parameter range, physical compatibility, performance threshold), construct a multi-objective optimization model. First, use the real number coding method to map the optimization parameters (number of sub-layers, gradient index, thickness of the transition layer, porosity, particle size) to continuous variables, and the discrete parameter N is processed through integer constraints. Subsequently, introduce NSGA-II (Non-dominated Sorting Genetic Algorithm) as the optimization engine, and realize the model construction through the following process: 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.

[0107] Non-dominated sorting: Stratify the individuals in the population according to the objective function. The solutions that are not dominated by any objective function are defined as the first layer of the Pareto front (optimal solutions), and the remaining individuals are sorted in turn to form a multi-level non-dominated solution set.

[0108] Crowding degree calculation: For individuals within the same non-dominated layer, calculate the Euclidean distance of each objective function value as the crowding degree to ensure the uniformity of the solution distribution and avoid the population converging to a local area.

[0109] Genetic operations: Generate an offspring population through selection (retaining high-level individuals), simulated binary crossover, and polynomial mutation.

[0110] Iteration termination: When there is no significant update to the Pareto front for 10 consecutive generations or the preset number of iterations (e.g., 200 generations) is reached, terminate the optimization and output a Pareto solution set containing multiple trade-off solutions.

[0111] Step b4, determine the corresponding multi-objective optimization algorithm based on the multi-objective optimization model.

[0112] In the embodiments of the present application, according to the high-dimensional parameter space (5D parameters such as the number of sub-layers, gradient index, etc.), non-linear objective function (conflict between power density and thermal stress), and the search requirements for Pareto optimal solutions in the multi-objective optimization model, a suitable multi-objective optimization algorithm is selected. NSGA-II (Non-dominated Sorting Genetic Algorithm) is preferred. It hierarchically processes multi-objective conflicts through non-dominated sorting, maintains the diversity of solutions by calculating the crowding degree, and combines real-number coding with genetic operations (crossover, mutation) to achieve efficient search in the parameter space, especially suitable for medium-scale optimization problems with 5D parameters. If there are characteristics of decomposable objective functions, MOEA / D (Multi-Objective Evolutionary Algorithm Based on Decomposition) can be considered to decompose complex problems into single-objective sub-problems for parallel solution. In addition, MOPSO (Multi-Objective Particle Swarm Optimization Algorithm) is suitable for real-time optimization scenarios due to its advantages of fast convergence speed and few parameters. Considering the model characteristics and engineering efficiency, NSGA-II is finally determined as the core algorithm. Through about 200 generations of iteration, a Pareto optimal solution set that takes into account both electrochemical performance and mechanical reliability is searched within the parameter constraint range, providing systematic support for gradient parameter optimization.

[0113] Step b5, use the multi-objective optimization algorithm to iteratively optimize the gradient design parameter combinations to generate the target gradient design parameter combinations.

[0114] In the embodiments of the present application, the multi-objective optimization algorithm is used to iteratively optimize the gradient design parameter combination to generate the gradient design parameter combination of the current iterative optimization; based on the gradient design parameter combination of the current iterative optimization, a microstructure with a gradient structure is regenerated, and the electrochemical performance and mechanical performance are evaluated until a preset performance target is reached, and the gradient design parameter combination of the current iterative optimization corresponding to reaching the preset performance target is used as the target gradient design parameter combination.

[0115] Among them, the optimization parameter range includes: the range of the number of sub-layers, the range of the gradient index, the range of the thickness of the transition layer, the range of the porosity, and the range of the particle size; the constraint conditions include: the number of sub-layers 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. The constraint conditions may also include that the electrochemical performance is within the battery operation range and the mechanical performance is less than the yield strength of the material.

[0116] First, initialize the population and performance prediction: randomly generate initial parameter combinations (such as 100 groups) within the parameter constraint range (such as the number of sub-layers 2 - 6, porosity 15% - 45%), and each group of parameters corresponds to a gradient electrode structure (such as a 3-layer linear gradient, porosity 30%). Quickly obtain the electrochemical performance (such as the maximum power density, total overpotential) and mechanical performance (maximum thermal stress, Weibull failure probability) of each group of parameters through the machine learning prediction model. Then, enter the iterative optimization loop. After every certain number of iterations (such as 20 generations), select multiple groups (such as 5 groups) of excellent parameter combinations from the current Pareto solution set, generate the corresponding gradient microstructure (such as the gradient porosity gradually changing from 40% on the surface layer to 25% on the inner layer) through the DEM-KMC model, and call the multi-field coupling model to accurately evaluate the electrochemical and mechanical performance (non-predicted values).

[0117] When the Pareto solution set has not been significantly improved for multiple consecutive generations (such as 10 generations), or when the performance of a certain combination first meets the preset target (such as power density ≥ 300 mW / cm², failure probability ≤ 3%), terminate the optimization. The finally selected target parameter combination needs to go through multiple rounds of microstructure generation and actual measurement verification to ensure reliability. Determine the final target gradient design parameter combination through multi-field coupling evaluation, which can directly guide the preparation process of the electrode (such as the setting of the layer-by-layer sintering parameters).

[0118] In the embodiments of the present application, through the combination of a machine learning model and a multi-objective optimization algorithm, the intelligent screening of gradient parameters is achieved, avoiding material waste and time loss caused by repeated experiments, significantly reducing the trial-and-error cost and shortening the development cycle. The present application introduces a more realistic simulation method for the evolution of the electrode microstructure (such as the DEM-KMC model), and combines the microscale multi-physics field coupling analysis (cooperative calculation of heat conduction, electrochemical reaction, and mechanical stress) to more accurately depict the complex physical processes inside the electrode and achieve high-precision prediction of electrochemical performance. Compared with the existing single-functional gradient SOFC design scheme, the present application has the concept of triple-functional gradient design of composition, particle size, and porosity, which can maximize the improvement of battery performance. With the aid of artificial intelligence-assisted means (such as the NSGA-II multi-objective optimization algorithm and the artificial neural network prediction model), it is possible to quickly search for Pareto optimal solutions in the global parameter space, avoid falling into local optima, and significantly improve the design efficiency.

[0119] It should be understood that the magnitudes of the sequence numbers of the steps in the above embodiments do not imply the order of execution, and the execution order of each process should be determined according to its function and internal logic, and should not constitute any limitation to the implementation process of the embodiments of the present application.

[0120] Corresponding to the gradient solid oxide fuel cell design method described in the above embodiments, Figure 3 The structural block diagram of the gradient solid oxide fuel cell design device provided by the embodiments of the present application is shown. For the sake of convenience of description, only the parts related to the embodiments of the present application are shown.

[0121] Referring to Figure 3 This gradient solid oxide fuel cell design device includes: A simulation module, which is used to simulate the microstructure evolution process during the sintering preparation process of the functional gradient electrode by using a numerical simulation method for the evolution of the electrode microstructure that combines the discrete element method DEM and the kinetic Monte Carlo KMC, and generate a microstructure with a gradient structure; An evaluation module, which is used to evaluate the electrochemical performance and mechanical performance of the functional gradient electrode based on the microstructure by using a preset microscale multi-field coupling model to obtain an evaluation result; A performance output module, which is used to input the evaluation result into a machine learning prediction model and output the electrochemical performance and mechanical performance under a preset gradient design parameter combination; An optimization module, which is used to optimize the gradient design parameter combination by using a multi-objective optimization algorithm according to the electrochemical performance and the mechanical performance, and determine the target gradient design parameter combination.

[0122] It should be noted that for the content such as information interaction and execution process among the above modules, since it is based on the same concept as the method embodiments of the present application, for its specific functions and the technical effects brought, reference can be specifically made to the method embodiment part, and details will not be elaborated here.

[0123] Those skilled in the art can clearly understand that for the convenience and conciseness of description, only the above division of each functional unit and module is used as an example for illustration. In actual applications, the above functions can be allocated to different functional units and modules according to needs, that is, the internal structure of the device is divided into different functional units or modules to complete all or part of the functions described above. Each functional unit and module in the embodiment can be integrated in a processing unit, or each unit can exist physically alone, or two or more units can be integrated in one unit. The above integrated unit can be implemented in the form of hardware or in the form of a software functional unit. In addition, the specific names of each functional unit and module are only for the convenience of mutual distinction and do not limit the protection scope of the present application. The specific working processes of the units and modules in the above system can refer to the corresponding processes in the foregoing method embodiments and will not be elaborated here.

[0124] The 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. When the processor executes the computer program, the steps in any of the above method embodiments are implemented.

[0125] The embodiment of the present application also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the steps in the above method embodiments can be implemented.

[0126] The embodiment of the present application provides a computer program product. When the computer program product runs on a computer device, it enables the computer device to implement the steps in the above method embodiments when executed.

[0127] Figure 4 It is a schematic structural diagram of a computer device provided by an embodiment of the present application. As Figure 4 shown, the computer device in this embodiment includes: at least one processor 20 ( Figure 4 only one is shown here), a memory 21, and a computer program 22 stored in the memory 21 and executable on the at least one processor 20. When the processor 20 executes the computer program 22, the steps in any of the above method embodiments of the gradient solid oxide fuel cell design method are implemented.

[0128] The computer device may include, but is not limited to, a processor 20 and a memory 21. Those skilled in the art can understand that Figure 4 merely examples of computer devices, which do not constitute a limitation on computer devices. It may include more or fewer components than those shown in the figure, or combine certain components, or different components. For example, it may also include input / output devices, network access devices, etc.

[0129] 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, to implement all or part of the processes in the above-described embodiment methods of this application, a computer program can be used to instruct relevant hardware to complete. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, the steps of the above-described method embodiments can be implemented.

[0130] In the above embodiments, the descriptions of the various embodiments each have their own focuses. For parts not described in detail or recorded in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0131] Those of ordinary skill in the art can realize that the units and algorithm steps of the examples described in conjunction with the embodiments disclosed in this document can be implemented by electronic hardware, or by a combination of computer software and electronic hardware. Whether these functions are executed in a hardware or software manner depends on the specific application and design constraints of the technical solution. Professional technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered to exceed the scope of this application.

[0132] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features. These modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A design method for a gradient solid oxide fuel cell, characterized in that, Including: An electrode microstructure evolution numerical simulation method that combines the discrete element method (DEM) and the kinetic Monte Carlo (KMC) to simulate the microstructure evolution process during the sintering preparation of a functionally graded electrode, and generate a microstructure with a gradient structure; Based on the microstructure, use a preset microscale multi-field coupling model to evaluate the electrochemical and mechanical properties of the functionally graded electrode, and obtain an evaluation result; Input the evaluation result into a machine learning prediction model, and output the electrochemical and mechanical properties under a preset gradient design parameter combination; According to the electrochemical and mechanical properties, use a multi-objective optimization algorithm to optimize the gradient design parameter combination, and determine the target gradient design parameter combination.

2. The gradient solid oxide fuel cell design method according to claim 1, characterized in that The electrode microstructure evolution numerical simulation method that combines the discrete element method (DEM) and the kinetic Monte Carlo (KMC) to simulate the microstructure evolution process during the sintering preparation of a functionally graded electrode, and generate a microstructure with a gradient structure, includes: Use the discrete element method (DEM) to simulate the initial packing structure of electrode particles according to a preset particle size distribution; Introduce pore-forming agent particles into the initial packing structure to simulate the pore distribution, and after the electrode particles are packed, delete the pore-forming agent particles to form an electrode with a gradient structure; wherein, the gradient structure is composed of different sub-layer packings; For each sub-layer, control the gradient parameter based on the gradient control equation to obtain the target packing structure; Perform voxelization on the target packing structure to generate a three-dimensional voxelization model; Use the three-dimensional voxelization model as the initial crystal site lattice, and use the kinetic Monte Carlo (KMC) to perform microstructure evolution simulation to generate the microstructure of a porous anode or cathode with a gradient structure.

3. The gradient solid oxide fuel cell design method according to claim 2, characterized in that, The gradient control equation includes: A composition gradient parameter control equation for controlling the composition gradient parameter in each sub-layer; A porosity gradient parameter control equation for controlling the porosity gradient parameter in each sub-layer; A particle size distribution gradient parameter control equation for controlling the particle size distribution gradient parameter in each sub-layer.

4. The gradient solid oxide fuel cell design method according to claim 1, characterized in that The microscale multi-field coupling model includes: A charge transport model for calculating the potential distribution of electrons and ions; An electrochemical reaction model for calculating the current density and overpotential at the three-phase boundary; A mass transport model for calculating the transport process of gas substances in the electrode; A heat conduction model for calculating the temperature distribution in the electrode; A mechanical property model for calculating the thermal stress and failure probability of the electrode.

5. The gradient solid oxide fuel cell design method according to claim 1, characterized in that Evaluating the electrochemical and mechanical properties includes: Calculating the total overpotential; Plotting the curve of output voltage versus current density; Calculating the maximum power density; Calculating the maximum thermal stress; Performing Weibull failure probability analysis.

6. The gradient solid oxide fuel cell design method according to claim 1, wherein, The method further includes: Obtaining the electrochemical and mechanical properties under different gradient design parameter combinations; Taking the gradient design parameter combination as the input of the initial artificial neural network, and the electrochemical and mechanical properties as the output of the initial artificial neural network, and training the initial artificial neural network to obtain the machine learning prediction model.

7. The design method of the gradient solid oxide fuel cell according to claim 1, characterized in that According to the electrochemical performance and the mechanical performance, a multi-objective optimization algorithm is used to optimize the gradient design parameter combination to determine the target gradient design parameter combination, including: Define the objective function for multi-objective optimization according to the electrochemical performance and the mechanical performance; 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; Set the optimization parameter range and constraint conditions; Based on the objective function and the constraint conditions, construct a multi-objective optimization model; Determine the corresponding multi-objective optimization algorithm based on the multi-objective optimization model; Use the multi-objective optimization algorithm to iteratively optimize the gradient design parameter combination to generate the target gradient design parameter combination.

8. The gradient solid oxide fuel cell design method according to claim 7, characterized in that, The optimization parameter range includes: the range of the number of sub-layers, the range of the gradient index, the range of the transition layer thickness, the range of the porosity, and the range of the particle size; The constraint conditions include: the number of sub-layers 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 physical property limit range of the material, and the particle size is within the sintering process parameter range of the material.

9. The gradient solid oxide fuel cell design method according to claim 7, wherein The use of the multi-objective optimization algorithm to iteratively optimize the gradient design parameter combination to generate the target gradient design parameter combination includes: Use the multi-objective optimization algorithm to iteratively optimize the gradient design parameter combination to generate the gradient design parameter combination of the current iterative optimization; Based on the gradient design parameter combination of the current iterative optimization, regenerate the microstructure with a gradient structure, and evaluate the electrochemical performance and the mechanical performance until the preset performance target is reached. The gradient design parameter combination of the current iterative optimization corresponding to reaching the preset performance target is used as the target gradient design parameter combination.

10. A gradient solid oxide fuel cell design device, characterized in that, Including: A simulation module for simulating the microstructure evolution process during the sintering preparation process of the functionally graded electrode by using a numerical simulation method for electrode microstructure evolution that combines the discrete element method (DEM) and the kinetic Monte Carlo (KMC) method to generate a microstructure with a gradient structure; An evaluation module for evaluating the electrochemical performance and the mechanical performance of the functionally graded electrode based on the microstructure by using a preset microscale multi-field coupling model to obtain an evaluation result; A performance output module for inputting the evaluation result into a machine learning prediction model and outputting the electrochemical performance and the mechanical performance under the preset gradient design parameter combination; An optimization module for optimizing the gradient design parameter combination by using a multi-objective optimization algorithm according to the electrochemical performance and the mechanical performance to determine the target gradient design parameter combination.

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