A method, device and storage medium for optimizing a thermal barrier coating pore structure

Abstract

The application discloses a kind of thermal barrier coating pore structure optimization method, device and storage medium, the method includes the following steps: numerical simulation is carried out to the pore structure of thermal barrier coating, and corresponding pore structure numerical model is generated;The pore structure numerical model is simulated calculation, and the initial thermal radiation characteristic parameter value of the pore structure is determined;Establish the optimization model of the thermal radiation characteristic parameter;Based on the optimization model, the pore structure of optimal thermal radiation characteristic is determined.The application can predict and optimize coating pore structure according to actual working condition, and accurately assess the influence of pore structure on coating thermal radiation performance, provide reliable basis for the optimization result of optimization model, finally realize the prediction and optimization of thermal barrier coating pore structure in combination with optimization model.

Description

Technical Field

[0001] This invention relates to the field of porous media technology, specifically to a method, apparatus, and storage medium for optimizing the pore structure of a thermal barrier coating. Background Technology

[0002] Aero-engines and gas turbines, as core power systems, are among the most important guarantees for the development of aerospace and marine technologies, as well as energy and power, meeting major national needs. Due to their excellent properties such as low thermal conductivity, corrosion resistance, and good high-temperature phase stability, the development of thermal barrier coatings (TBCs) has effectively promoted the advancement of power equipment such as gas turbines and aero-engines. A TBC is a low-porosity, anisotropic porous material, typically composed of a ceramic top layer, an anti-oxidation bonding layer, and a superalloy substrate, with the ceramic top layer providing the primary thermal insulation. Current research on the thermal insulation properties of the coating top layer microstructure mainly focuses on heat conduction. However, in high-temperature environments, radiative heat transfer is also a crucial mechanism for heat transfer in TBCs. Research on the radiative properties of TBC microstructures is relatively limited, urgently requiring further research to comprehensively understand the heat transfer characteristics of TBCs. Due to the high cost of experimental radiative property studies, numerical simulation methods have become an important tool for studying the radiative performance of TBCs in recent years, thanks to the rapid development of computer technology. Some scholars have used ray tracing, finite element simulation software, and discrete dipole algorithm to calculate and analyze the radiation characteristics of coating pore structure under specific working conditions. However, the parameter settings of the pore structure are based on the assumptions of experimental observation, and it is impossible to reverse-engineer the pore structure of the coating according to the actual working conditions. Therefore, this study provides some reference value for coating preparation.

[0003] Existing patent CN114218826A discloses a method for modeling a two-dimensional physical model of a coating with random multiphase phases. This method includes the following steps: constructing a two-dimensional multi-scale random medium for the coating; using a threshold truncation method, extracting the coordinates of the lubricating phase and pore positions from the total nodes on the two-dimensional multi-scale random medium; using the remaining nodes as the matrix position coordinates to obtain a two-dimensional physical model of the coating with random multiphase phases. Furthermore, a method for evaluating coating performance is provided, including: constructing a two-dimensional physical model of the coating with random multiphase phases using the above-described modeling method; performing numerical simulation using the finite element method based on the two-dimensional physical model of the coating to obtain coating performance parameters; and evaluating the coating performance.

[0004] Existing patent CN118395779A discloses a finite element modeling method for thermal barrier coatings based on real structures, including the following steps: S1: preparing thermal barrier coating system samples; S2: processing thermal barrier coating system samples to obtain a vector diagram of the microstructure of the thermal barrier coating system samples that marks defects, pores and impurities in the thermal barrier coating system samples; S3: importing and setting the vector diagram of the microstructure of the thermal barrier coating system to obtain a finite element model of the microstructure of the thermal barrier coating system samples that marks defects, pores and impurities.

[0005] In summary, neither of the two existing patents mentioned above addresses the problem that existing technologies mostly rely on experimental observations and assumptions for simulation, making it impossible to predict and optimize the pore structure of the coating based on actual working conditions, and thus failing to meet the precise requirements of coating preparation. Summary of the Invention

[0006] Based on the above-mentioned technical problems, this invention proposes a method and apparatus for optimizing the pore structure of thermal barrier coatings, which solves the problem that most existing technologies are based on experimental observations and assumptions, making it impossible to predict and optimize the pore structure of coatings according to actual working conditions, and thus failing to meet the precise requirements of coating preparation.

[0007] To achieve the above objectives, this invention proposes a method for optimizing the pore structure of thermal barrier coatings.

[0008] A method for optimizing the pore structure of a thermal barrier coating includes:

[0009] Numerical simulation of the pore structure of thermal barrier coatings was performed, and corresponding numerical models of the pore structure were generated.

[0010] The numerical model of the pore structure is simulated to determine the initial thermal radiation characteristic parameter values ​​of the pore structure;

[0011] Establish an optimization model for the aforementioned thermal radiation characteristic parameters;

[0012] Based on the optimization model, the pore structure with optimal thermal radiation characteristics is determined.

[0013] Furthermore, the pore structure of the thermal barrier coating is numerically simulated, and a corresponding numerical model of the pore structure is generated, including:

[0014] The pore structure of thermal barrier coatings was simulated using a four-parameter random growth method, and the corresponding numerical model of the pore structure was generated.

[0015] Furthermore, the pore structure of the thermal barrier coating is simulated using a four-parameter random growth method, and a corresponding numerical model of the pore structure is generated, including:

[0016] The simulation region for the pore structure is set;

[0017] The grid points and pore structure parameters within the simulation area are initialized. The pore structure parameters include the growth probability of the nucleation center of the growth phase, the growth probability of the nuclei in each direction, and the preset volume fraction of the growth phase.

[0018] The nucleation centers of the first growth phase are randomly arranged according to the growth probability of the nucleation centers of the growth phase;

[0019] The nucleation center of the first growth phase grows in the i-th direction according to the growth probability of the nuclei in each direction until the volume fraction of the growth phase reaches the preset volume fraction.

[0020] Furthermore, numerical simulations were performed on the pore structure model to determine the thermal radiation characteristic parameters of the pore structure, including:

[0021] Based on the numerical model of the pore structure, the thermal radiation process of the pore structure is simulated using simulation methods to determine the thermal radiation characteristic parameters of the pore structure. The thermal radiation characteristic parameters include one or more of reflectivity, transmittance, and absorptivity.

[0022] Furthermore, based on the numerical model of the pore structure, the thermal radiation process of the pore structure is simulated using simulation methods to determine the thermal radiation characteristic parameters of the pore structure, including:

[0023] The Maxwell curl equation is discretized using the finite-time difference method to determine the expressions for the changes of electric and magnetic field components with time.

[0024] The electric field intensity vector and the magnetic field intensity vector are determined by using the expressions for the changes of the electric field component and the magnetic field component with time.

[0025] Calculate the Poynting vector based on the electric field intensity vector and the magnetic field intensity vector;

[0026] The thermal radiation characteristic parameters of the pore structure are determined based on the Poynting vector.

[0027] Furthermore, based on the electric field intensity vector and the magnetic field intensity vector, the Poynting vector is calculated, including:

[0028] The Poynting vector is calculated using Formula 1 based on the electric field intensity vector and the magnetic field intensity vector. Formula 1 is: ,in, Represents the Poyinting vector. The period of an electromagnetic wave, Let be the electric field intensity vector. is the magnetic field strength vector.

[0029] Furthermore, the thermal radiation characteristic parameters of the pore structure are determined based on the Poynting vector, including:

[0030] Based on the Poynting vector, the radiation intensity of the pore structure is determined using Formula 2, which is: ,in, Represents the Poyinting vector. Radiation intensity;

[0031] The reflectivity and / or transmittance and / or absorptivity of the pore structure are determined based on the radiation intensity.

[0032] Furthermore, an optimization model for the aforementioned thermal radiation characteristic parameters is established, including:

[0033] An optimization model is established using the LM optimization algorithm, and an objective function for the optimization model is established based on the thermal radiation characteristic parameters. The objective function is: ,in, This indicates the number of sampling points for thermal radiation characteristic parameters within the semi-transparent band. , This indicates that at a wavelength of Simulated values ​​of a certain thermal radiation characteristic parameter of the pore structure. For parameters to be optimized, This indicates that at a wavelength of The theoretical value of a certain thermal radiation characteristic parameter of the pore structure.

[0034] Furthermore, based on the optimization model, the pore structure with optimal thermal radiation characteristics is determined, including:

[0035] The objective function of the optimization model is iteratively optimized by invoking the four-parameter random growth method and the finite-time difference method using the optimization model until the objective function reaches convergence.

[0036] The objective function of the optimization model is iteratively optimized using the four-parameter random growth method and the finite-time difference method, until the objective function reaches convergence, including:

[0037] Using the optimization model, the four-parameter random growth method and the finite-time difference method are invoked to determine the array of changes in pore structure parameters and the changes in the objective function value.

[0038] Determine whether the array of changes in pore structure parameters converges;

[0039] If the array of changes in pore structure parameters converges, then determine whether the change in the objective function value converges.

[0040] If the change in the objective function value converges, the iteration stops, and the pore structure corresponding to the current pore structure parameters is taken as the pore structure with the best thermal radiation characteristics.

[0041] If the change in the objective function value diverges, the pore structure parameters are updated based on the array of changes in the pore structure parameters, and the objective function is iteratively optimized again.

[0042] Furthermore, before invoking the four-parameter stochastic growth method and the finite-time difference method using the optimization model, the following steps are also included:

[0043] The parameters of the optimization model are initialized, including the number of convergences, the convergence threshold, the difference factor, and the damping coefficient vector.

[0044] Furthermore, determine the amount of change in the objective function value, including:

[0045] The pore structure parameters are differentially derived based on the differential multiple.

[0046] The four-parameter random growth method and the finite-time difference method are used to determine the corresponding thermal radiation characteristic parameters based on the pore structure parameters after the difference.

[0047] The change in the objective function value is determined based on the thermal radiation characteristic parameters before and after the difference.

[0048] Furthermore, the array of variations in pore structure parameters is determined, including:

[0049] Determine the Jacobian matrix based on the pore structure parameters after differentiation;

[0050] Based on the Jacobian matrix, the variation array of pore structure parameters is solved using Formula 4. Formula 4 is... ,in, for The transpose of the Jacobian matrix, for Jacobian matrix, Here is the damping matrix. Let I represent the damping coefficient vector corresponding to each parameter, and let I be a positive definite diagonal identity matrix. This is an array of changes in pore structure parameters.

[0051] Furthermore, determining whether the array of changes in pore structure parameters converges includes:

[0052] Compare the array of changes in pore structure parameters corresponding to the k-th convergence. The array of changes in pore structure parameters corresponding to the (k-1)th convergence ;

[0053] If the change array There exists an element whose absolute value is greater than 1. The absolute value of the corresponding element, or the array of changes. There exists a symbol of a certain element and The array of changes in pore structure parameters is determined by the different signs of the corresponding elements. The array of changes relative to pore structure parameters Divergence;

[0054] Conversely, if the change array The absolute value of each element in the array is less than or equal to 1. The absolute value of the corresponding element in the array, and the change amount. The symbol of each element in the middle and If all corresponding elements in the array have the same sign, then the array of changes in pore structure parameters represents the change in pore structure parameters. The array of changes relative to pore structure parameters convergence.

[0055] Furthermore, if the array of variations in pore structure parameters exhibits a divergent trend, then let the damping coefficient vector... And recalculate the array of changes in pore structure parameters according to Formula 4.

[0056] Furthermore, determining whether the array of changes in the objective function value converges includes:

[0057] Determine the objective function value corresponding to the k-th convergence. The objective function value corresponding to the (k-1)th convergence Is the absolute value of the difference less than the convergence threshold?

[0058] if If the change in the objective function value is less than the convergence threshold, then the array of changes in the objective function value converges.

[0059] Furthermore, it also includes:

[0060] If the array of changes in pore structure parameters converges, then determine the value of the array of changes. Check whether the absolute value of each element is less than the corresponding convergence threshold;

[0061] If the change array If the absolute value of each element is less than the corresponding convergence threshold, the iteration stops, and the pore structure corresponding to the current pore structure parameters is taken as the pore structure with the best thermal radiation characteristics.

[0062] To achieve the above objectives, the present invention proposes an optimization device for the pore structure of thermal barrier coatings.

[0063] An optimization device for the pore structure of a thermal barrier coating, the device comprising:

[0064] The numerical simulation module is used to perform numerical simulation of the pore structure of thermal barrier coatings and generate corresponding numerical models of the pore structure.

[0065] The calculation module is used to simulate and calculate the numerical model of the pore structure to determine the thermal radiation characteristic parameters of the pore structure.

[0066] Establish a module for building an optimization model of thermal radiation characteristic parameters;

[0067] The determination module is used to determine the pore structure with optimal thermal radiation characteristics based on the optimization model.

[0068] A computer-readable storage medium comprising a stored computer program, wherein the computer program can be executed by an electronic device to perform the above-described method.

[0069] A computer program product includes a computer program that, when executed by a processor, implements the steps of the method.

[0070] An electronic device includes a memory and a processor, wherein the memory stores a computer program and the processor is configured to perform the above-described method via the computer program.

[0071] Based on the above technical solution, the present invention has at least the following beneficial effects:

[0072] 1. This invention generates a numerical model of the pore structure based on numerical simulation, and performs simulation calculations on the numerical model of the pore structure. On the basis of high-precision simulation of the pore structure of the thermal barrier layer, it accurately evaluates the influence of the pore structure on the thermal radiation performance of the coating, provides a reliable basis for the optimization results of the optimization model, and finally determines the pore structure with the best thermal radiation characteristics by combining the optimization model, thereby realizing the prediction and optimization of the pore structure of the thermal barrier coating.

[0073] 2. This invention utilizes the LM optimization algorithm to establish an optimization model. Within the optimization model, the four-parameter random growth method and the finite-time difference method are repeatedly called to determine the array of changes in pore structure parameters and the change in the objective function value. By sequentially judging whether the array of changes in pore structure parameters and the change in the objective function value converge, iterative optimization of the objective function and updating of the pore structure parameters are achieved, ultimately determining the pore structure with the optimal thermal radiation characteristics.

[0074] 3. This invention proposes to determine the Jacobian matrix based on the differential pore structure parameters, and solve the array of changes in pore structure parameters based on the Jacobian matrix. This method can efficiently capture the influence of changes in pore structure parameters on thermal radiation characteristics, thereby significantly improving the optimization accuracy and efficiency of the pore structure of thermal barrier coatings.

[0075] 4. This invention generates a numerical model of the pore structure of thermal barrier coatings using a four-parameter random growth method. This method can flexibly control the shape, size, and distribution of pores, thereby simulating a pore structure similar to that of actual thermal barrier coatings, providing accurate input for subsequent radiation characteristic analysis. Attached Figure Description

[0076] The accompanying drawings, which form part of this specification, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0077] Figure 1 This is a flowchart of a method for optimizing the pore structure of a thermal barrier coating according to an embodiment of the present invention;

[0078] Figure 2 In one embodiment of the present invention, a four-parameter random growth method is used to simulate 26 directions in three-dimensional space when pore structure is simulated;

[0079] Figure 3 This is a parameter control interface for generating a coating pore structure model using a four-parameter random growth method in one embodiment of the present invention;

[0080] Figure 4 This is a schematic diagram of the xz-axis structural cross-section of a thermal barrier coating lamellar porous structure model in one embodiment of the present invention;

[0081] Figure 5 This is a schematic diagram of a model and boundary conditions for calculating radiation characteristics using FDTD Solutions software in one embodiment of the present invention;

[0082] Figure 6 The spectral reflectance of layered and columnar porous coatings calculated using the FDTD method in one embodiment of the present invention is shown below.

[0083] Figure 7 The transmittance of layered and columnar porous coatings calculated using the FDTD method in one embodiment of the present invention is shown.

[0084] Figure 8 This is a flowchart illustrating the process of determining the optimal pore structure for thermal radiation characteristics using an optimization model in one embodiment of the present invention.

[0085] Figure 9 This is a schematic diagram of an optimization device for the pore structure of a thermal barrier coating according to an embodiment of the present invention;

[0086] Figure 10 This is a block diagram of a computer system architecture for implementing an electronic device according to embodiments of the present invention;

[0087] Figure 11 This is a schematic diagram of an electronic device for optimizing the pore structure of a thermal barrier coating, according to an embodiment of the present invention. Detailed Implementation

[0088] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0089] The present invention will be further described in detail below with reference to specific embodiments, which should not be construed as limiting the scope of protection claimed by the present invention.

[0090] Example

[0091] To address the problem that most existing technologies rely on experimental observations and assumptions for simulation, which cannot predict and optimize the pore structure of coatings based on actual working conditions and thus fail to meet the precision requirements of coating preparation, this invention proposes a method, apparatus, and storage medium for optimizing the pore structure of thermal barrier coatings.

[0092] To achieve the above objectives, this invention proposes a method for optimizing the pore structure of thermal barrier coatings.

[0093] like Figure 1 The diagram shows a flowchart of a method for optimizing the pore structure of a thermal barrier coating according to an embodiment of the present invention. The method includes the following steps:

[0094] S1, numerical simulation of the pore structure of the thermal barrier coating is performed, and the corresponding numerical model of the pore structure is generated.

[0095] In this embodiment, a four-parameter random growth method (QSGS) is used to simulate the pore structure of thermal barrier coatings and generate a corresponding numerical model of the pore structure. The QSGS algorithm uses one phase in a multiphase material system as the growth phase and randomly constructs nucleation centers for the growth phase. By controlling the growth probability of the nucleation centers and the growth probability of nuclei in various directions, pores of different shapes, sizes, and distributions are generated, thereby simulating the pore microstructure of real thermal barrier coatings. This method has good repeatability and can be used for multiple simulations and analyses, which is beneficial for statistical and comparative studies. For a typical two-phase (gas-solid) structure of a thermal barrier coating, simulating the pore structure of the thermal barrier coating using the four-parameter random growth method and generating a corresponding numerical model of the pore structure includes the following sub-steps:

[0096] S101, set the simulation region for the pore structure.

[0097] For example, the simulation region of the pore structure can be set to two-dimensional or three-dimensional.

[0098] S102 initializes the grid points and pore structure parameters within the simulation area.

[0099] In this embodiment, all grid points within the simulation region are set to 0. The pore structure parameters include the growth probability of the nucleation center of the growth phase, the growth probability of nuclei in each direction, and the volume fraction of the growth phase. When initializing the growth probability of the nucleation center of the growth phase, its value should be less than the preset volume fraction.

[0100] S103, the nucleation centers of the first growth phase are randomly arranged according to the growth probability of the nucleation centers of the growth phase.

[0101] After initializing the growth probability of the nucleation center of the growth phase and the growth probability of nuclei in each direction, the nucleation centers of the first growth phase are randomly arranged according to the initialized growth probability. After arrangement, the value of the nucleation center changes from 0 to 1.

[0102] S104, the nucleation center of the first growth phase grows in the i-th direction according to the growth probability of the nuclei in each direction, until the volume fraction of the growth phase reaches the preset volume fraction.

[0103] The nucleation centers of the first growth phase, randomly arranged in step S103, are traversed, and each pore node is randomly grown in 26 directions in three-dimensional space according to the growth probability of the growth nucleus in each direction. For example... Figure 2 As shown, the nucleation center of the growth phase grows in the i-th direction according to the set growth probability and achieves binary transformation. The grid point that is transformed into 1 will become the new growth nucleation center and continue to grow in each of the set growth probabilities.

[0104] Growth stops when the volume fraction of the growth phase reaches a preset volume fraction, generating the corresponding numerical model of the pore structure. Figure 3 Taking the QSGS model parameter settings as an example, within a computational domain size of 1mm × 0.25mm × 0.25mm, the grid number is set to 400 × 100 × 100, the growth probability of the growth phase nucleus center is 5%, and the growth probability of the growth nucleus in each direction is... P i(i=1~6) for P i(i=1,3) =500、 P i(i=2,4~6) =1, porosity 15%, a numerical model of the lamellar pore structure of the thermal barrier coating was generated, such as Figure 4 This is a cross-sectional view of the pore structure along the xz axis.

[0105] S2, simulate and calculate the numerical model of the pore structure to determine the thermal radiation characteristic parameters of the pore structure.

[0106] In this embodiment, the numerical model of the pore structure determined in step S1 is imported into simulation software. The simulation software is used to simulate the thermal radiation process of the pore structure and determine the thermal radiation characteristic parameters of the pore structure. The thermal radiation characteristic parameters include one or more of reflectivity, transmittance, and absorptivity.

[0107] Specifically, this embodiment uses FDTD Solutions software for simulation. After importing the numerical model of the pore structure into the simulation software, the thermal radiation process of the pore structure is simulated using FDTD Solutions. It should be understood that different simulation software can be selected for simulation calculations depending on the application scenario.

[0108] Furthermore, the FDTD simulation region is larger than the coating physical model, with its sides set as periodic boundaries and perfect matched layers (PMLs) at the top and bottom, such as... Figure 5 The model diagram is shown below. The working principle of FDTDSolutions software is as follows: A plane wave source is used to simulate the radiation beam on the outer surface, which is incident vertically from above the region; a reflectivity power monitor is set between the plane wave source and the upper boundary of the PML to receive all reflected beams; a transmittance power monitor is set between the lower surface of the TBC coating physical model and the lower boundary of the PML to receive all radiation beams that pass through the coating, thereby simulating and calculating the multi-band radiation characteristics of different thermal barrier coating microstructures, such as reflectivity and transmittance.

[0109] Furthermore, the thermal radiation process of the pore structure is simulated using FDTD Solutions software to determine the thermal radiation characteristic parameters of the pore structure, specifically including steps S201 to S204.

[0110] S201 uses the finite-time difference method to discretize Maxwell's curl equation and determine the expressions for the changes of electric and magnetic field components with time.

[0111] The finite-time difference method has become a mature numerical method for solving Maxwell's equations. Its main idea is to discretize Maxwell's curl equations, replace partial differentials with central differences, and solve for the thermal radiation process of the coating. The Maxwell's curl Maxwell equations can be expressed in the following form:

[0112]

[0113]

[0114] After processing the partial differentials of Maxwell's equations in time and space, the electric field components are determined using a central difference scheme.E and magnetic field components H An expression that changes over time.

[0115] S202, using the expressions for the changes of electric field components and magnetic field components with time, determine the electric field intensity vector and the magnetic field intensity vector.

[0116] S203, calculate the Poynting vector based on the electric field intensity vector and the magnetic field intensity vector.

[0117] Energy transfer in electromagnetic fields is achieved using the Poynting vector. S The magnitude of this energy flux density represents the energy density of the electromagnetic wave, which is the energy passing through a unit area per unit time, and is measured in W / m². 2 In thermal radiation calculations, the direction of the Poynting vector represents the direction of electromagnetic wave energy transmission. It is perpendicular to the directions of the electric and magnetic fields and conforms to the right-hand rule.

[0118] In this embodiment, the Poynting vector is calculated using Formula 1 based on the electric field intensity vector and the magnetic field intensity vector. Formula 1 is... ,in, Represents the Poyinting vector. The period of an electromagnetic wave, Let be the electric field intensity vector. is the magnetic field strength vector.

[0119] S204, the thermal radiation characteristic parameters of the pore structure are determined based on the Poynting vector.

[0120] Based on the Poynting vector, the radiation intensity of the pore structure is determined using Formula 2, which is: ,in, Represents the Poyinting vector. The radiation intensity is used to determine the reflectivity and / or transmittance and / or absorptivity of the porous structure. Specifically, the radiation intensity obtained through the reflectivity and transmittance power receivers are respectively... , reflectivity transmittance Because of absorption rate +reflectivity +transmittance If the value is 1, then the corresponding absorption rate can be obtained according to the above parameters and formula.

[0121] In this embodiment, the reflectivity, transmittance, and absorptivity of the porous structure were determined using the method described above. For example... Figure 6 The spectral reflectance of coatings with layered and columnar porous structures, calculated using the FDTD model, is shown below; Figure 7The transmittance of layered and columnar porous coatings calculated using the FDTD model is shown.

[0122] S3. Establish an optimization model for thermal radiation characteristic parameters.

[0123] In this embodiment, the LM optimization algorithm is used to establish an optimization model, and the objective function of the optimization model is established based on the thermal radiation characteristic parameters. The LM optimization algorithm is an optimization algorithm that combines the Gauss-Newton method and the gradient descent method, and it is easier to converge than the Gauss-Newton method and gradient descent method alone. The LM optimization algorithm has certain requirements on the form of the objective function S, which is written in the form of the sum of squares of the differences between the simulated values ​​and the theoretical values ​​at each point. In combination with the technical problem to be solved by this invention, the objective function of the optimization model is established as follows: ,in, This indicates the number of sampling points for thermal radiation characteristic parameters within the semi-transparent band. , This indicates that at a wavelength of Simulated values ​​of a certain thermal radiation characteristic parameter of the pore structure. For parameters to be optimized, This indicates that at a wavelength of The theoretical value of a certain thermal radiation characteristic parameter of the pore structure. Further, this embodiment will use the theoretical value... The objective function F is set to 0 for optimization, aiming to achieve either maximum reflectivity or minimum transmittance, i.e., the optimal coating pore structure for heat radiation protection. gradient It can be represented as ,in, , , m represents the number of sampling points for radiation characteristic parameters (such as reflectivity, transmittance, etc.) in the semi-transparent band. It can be further expressed as ,in for The transpose of the Jacobi matrix, The Jacobi matrix is .

[0124] Furthermore, the second-order partial derivative matrix of the objective function, i.e., the Hessian matrix, can be represented by the following matrix elements:

[0125]

[0126] Define a new matrix as O ,matrix O The elements are represented as: The iterative formula for Newton's method is: Combining formulas five and six, the Hessian matrix...H It can be represented as: Formula five is Formula six is... This indicates the change in parameters during the next iteration, when the matrix is ​​ignored. O At that time, the iterative formulas for Gauss-Newton's method were formed, such as Formula 7. This reduces the difficulty of the optimization algorithm from finding the Hessian matrix of the function to finding the Jacobi matrix of the function. To improve convergence, a damping matrix is ​​introduced. μI , μ This represents the damping coefficient vector corresponding to each parameter. I Given a positive definite diagonal identity matrix, the iterative formula for the LM optimization algorithm is formed, as shown in Formula 4. .

[0127] S4. Based on the optimization model, determine the pore structure with the optimal thermal radiation characteristics.

[0128] In this embodiment, the optimization model is used to call the four-parameter random growth method and the finite-time difference method to iteratively optimize the objective function of the optimization model until the objective function reaches a convergent state.

[0129] like Figure 8 The flowchart shown illustrates the process of determining the optimal pore structure for thermal radiation characteristics using an optimization model. This process mainly includes the following sub-steps:

[0130] S401 uses the optimization model to call the four-parameter random growth method and the finite-time difference method to determine the array of changes in pore structure parameters and the changes in the objective function value.

[0131] In this embodiment, before calling the four-parameter random growth method and the finite-time difference method using the optimization model, the method further includes: S406, initializing the parameters of the optimization model. The parameters of the optimization model include the number of convergences, the convergence threshold, the difference factor, and the damping coefficient vector. In this embodiment, the number of convergences is defined as k and initialized to 0. The initial pore structure parameter array is as follows: The convergence threshold is defined as σ The difference multiple is defined as ε The initial damping coefficient vector is defined as Based on the initial array of pore structure parameters, the corresponding numerical model of the pore structure is generated by using the four-parameter random growth method with the optimization model, and the initial thermal radiation characteristic parameter values ​​of the coating can be determined by calling the finite-time difference method.

[0132] Determining the change in the objective function value includes the following sub-steps:

[0133] S4011, differentially analyzes pore structure parameters based on differential multiples.

[0134] Taking the first iteration as an example, the initial pore structure parameters can be differentially differentiated sequentially according to the initial differential multiple.

[0135] S4012 calls the four-parameter random growth method and the finite-time difference method to determine the corresponding thermal radiation characteristic parameter values ​​based on the pore structure parameters after difference.

[0136] S4013. Determine the change in the objective function value based on the thermal radiation characteristic parameter values ​​before and after the difference.

[0137] Specifically, this can be achieved by using the thermal radiation characteristic parameter values ​​before and after the difference, through the objective function formula. The corresponding objective function values ​​are determined, and then the change in the objective function values ​​is determined.

[0138] The process of determining the array of changes in the pore structure parameters is as follows: First, the Jacobian matrix is ​​determined based on the differencing pore structure parameters; then, based on the Jacobian matrix, the array of changes in the pore structure parameters is solved using Formula 4, which is: ,in, for The transpose of the Jacobian matrix, for Jacobian matrix, Here is the damping matrix. Let I represent the damping coefficient vector corresponding to each parameter, and let I be a positive definite diagonal identity matrix. This is an array of changes in pore structure parameters.

[0139] Specifically, the Jacobian matrix is ​​represented as In this embodiment, each element of the Jacobi matrix is ​​approximated by forward differencing. For example, the elements in the matrix... Substituting the obtained Jacobian matrix and other parameters into Formula 4, the variation array of pore structure parameters can be solved. .

[0140] S402, determine whether the array of changes in pore structure parameters converges.

[0141] Furthermore, the process for determining whether the array of changes in pore structure parameters converges is as follows:

[0142] S4021, Compare the array of changes in pore structure parameters corresponding to the k-th convergence. The array of changes in pore structure parameters corresponding to the (k-1)th convergence .

[0143] S4022, if the change array There exists an element whose absolute value is greater than 1. The absolute value of the corresponding element, or the array of changes. There exists a symbol of a certain element and The array of changes in pore structure parameters is determined by the different signs of the corresponding elements. The array of changes relative to pore structure parameters Divergent.

[0144] S4023, conversely, if the change array The absolute value of each element in the array is less than or equal to 1. The absolute value of the corresponding element in the array, and the change amount. The symbol of each element in the middle and If all corresponding elements in the array have the same sign, then the array of changes in pore structure parameters represents the change in pore structure parameters. The array of changes relative to pore structure parameters convergence.

[0145] Furthermore, if the array of variations in pore structure parameters exhibits a divergent trend, then let the damping coefficient vector... The Jacobian matrix is ​​redefined and the array of changes in pore structure parameters is recalculated according to Formula 4.

[0146] S403, if the array of changes in pore structure parameters converges, then determine whether the change in the objective function value converges.

[0147] Furthermore, the process of determining whether the array of changes in the objective function value converges is as follows:

[0148] S4031, Determine the objective function value corresponding to the k-th convergence. The objective function value corresponding to the (k-1)th convergence Is the absolute value of the difference less than the convergence threshold?

[0149] S4032, if If the change in the objective function value is less than the convergence threshold, then the array of changes in the objective function value converges.

[0150] S404. If the change in the objective function value converges, the iteration stops, and the pore structure corresponding to the current pore structure parameters is taken as the pore structure with the best thermal radiation characteristics.

[0151] S405, if the change in the objective function value diverges, then update the pore structure parameters according to the array of changes in pore structure parameters, and iterate and optimize the objective function again.

[0152] In another embodiment of the invention, the change array Each element in the algorithm has a corresponding convergence threshold. Steps S406 and S407 determine whether the array of changes in the objective function value has converged. Specifically...

[0153] S406, if the array of changes in pore structure parameters converges, then determine the value of the array of changes. Check whether the absolute value of each element is less than the corresponding convergence threshold.

[0154] S407, if the change array If the absolute value of each element is less than the corresponding convergence threshold, the iteration stops, and the pore structure corresponding to the current pore structure parameters is taken as the pore structure with the best thermal radiation characteristics.

[0155] Understandably, when the array of changes in pore structure parameters is found to be converged, it can be determined whether further iterations are needed by judging the convergence of the objective function or by judging the convergence of each parameter in the array of changes in pore structure parameters.

[0156] If further iterations are needed, then let , The pore structure parameters and the number of iterations are updated respectively, and the iteration is performed based on the updated parameters.

[0157] To achieve the above objectives, the present invention proposes an optimization device for the pore structure of thermal barrier coatings.

[0158] like Figure 9 The diagram shows a schematic of an optimization device for the pore structure of a thermal barrier coating according to an embodiment of the present invention. The optimization device implements the above-described optimization method and includes: a numerical simulation module 101, a calculation module 102, a setup module 103, and a determination module 104. The functions of each module will be described in detail below.

[0159] The numerical simulation module 101 is used to perform numerical simulation of the pore structure of the thermal barrier coating and generate the corresponding numerical model of the pore structure.

[0160] The calculation module 102 is used to perform simulation calculations on the numerical model of the pore structure to determine the thermal radiation characteristic parameters of the pore structure.

[0161] Module 103 is established to create an optimization model for thermal radiation characteristic parameters.

[0162] The determination module 104 is used to determine the pore structure with optimal thermal radiation characteristics based on the optimization model.

[0163] Furthermore, the pore structure of the thermal barrier coating is numerically simulated, and a corresponding numerical model of the pore structure is generated, including:

[0164] The pore structure of thermal barrier coatings was simulated using a four-parameter random growth method, and the corresponding numerical model of the pore structure was generated.

[0165] As an optional solution, the above-mentioned device is also used to simulate the pore structure of the thermal barrier coating using a four-parameter random growth method, and generate a corresponding numerical model of the pore structure, including:

[0166] The simulation region for the pore structure is set;

[0167] The grid points and pore structure parameters within the simulation area are initialized. The pore structure parameters include the growth probability of the nucleation center of the growth phase, the growth probability of the nuclei in each direction, and the preset volume fraction of the growth phase.

[0168] The nucleation centers of the first growth phase are randomly arranged according to the growth probability of the nucleation centers of the growth phase;

[0169] The nucleation center of the first growth phase grows in the i-th direction according to the growth probability of the nuclei in each direction until the volume fraction of the growth phase reaches the preset volume fraction.

[0170] As an optional solution, the above-mentioned device is also used to simulate and calculate the numerical model of the pore structure to determine the thermal radiation characteristic parameters of the pore structure, including:

[0171] Based on the numerical model of the pore structure, the thermal radiation process of the pore structure is simulated using simulation methods to determine the thermal radiation characteristic parameters of the pore structure. The thermal radiation characteristic parameters include one or more of reflectivity, transmittance, and absorptivity.

[0172] As an optional solution, the above-mentioned device is further used to simulate the thermal radiation process of the pore structure based on the numerical model of the pore structure using simulation methods, and determine the thermal radiation characteristic parameters of the pore structure, including:

[0173] The Maxwell curl equation is discretized using the finite-time difference method to determine the expressions for the changes of electric and magnetic field components with time.

[0174] The electric field intensity vector and the magnetic field intensity vector are determined by using the expressions for the changes of the electric field component and the magnetic field component with time.

[0175] Calculate the Poynting vector based on the electric field intensity vector and the magnetic field intensity vector;

[0176] The thermal radiation characteristic parameters of the pore structure are determined based on the Poynting vector.

[0177] As an optional embodiment, the above-mentioned device is also used to calculate the Poynting vector based on the electric field intensity vector and the magnetic field intensity vector, including:

[0178] The Poynting vector is calculated using Formula 1 based on the electric field intensity vector and the magnetic field intensity vector. Formula 1 is: ,in, Represents the Poyinting vector. The period of an electromagnetic wave, Let be the electric field intensity vector. is the magnetic field strength vector.

[0179] As an optional solution, the above-mentioned device is also used to determine the thermal radiation characteristic parameters of the pore structure based on the Poynting vector, including:

[0180] Based on the Poynting vector, the radiation intensity of the pore structure is determined using Formula 2, which is: ,in, Represents the Poyinting vector. Radiation intensity;

[0181] The reflectivity and / or transmittance and / or absorptivity of the pore structure are determined based on the radiation intensity.

[0182] As an optional solution, the above-mentioned device is also used to establish an optimization model for the thermal radiation characteristic parameters, including:

[0183] An optimization model is established using the LM optimization algorithm, and an objective function for the optimization model is established based on the thermal radiation characteristic parameters. The objective function is: ,in, This indicates the number of sampling points for thermal radiation characteristic parameters within the semi-transparent band. , This indicates that at a wavelength of Simulated values ​​of a certain thermal radiation characteristic parameter of the pore structure. For parameters to be optimized, This indicates that at a wavelength of The theoretical value of a certain thermal radiation characteristic parameter of the pore structure.

[0184] As an optional solution, the above-mentioned device is also used to determine the pore structure with optimal thermal radiation characteristics based on the optimization model, including:

[0185] The objective function of the optimization model is iteratively optimized by invoking the four-parameter random growth method and the finite-time difference method using the optimization model until the objective function reaches convergence.

[0186] The objective function of the optimization model is iteratively optimized using the four-parameter random growth method and the finite-time difference method, until the objective function reaches convergence, including:

[0187] Using the optimization model, the four-parameter random growth method and the finite-time difference method are invoked to determine the array of changes in pore structure parameters and the changes in the objective function value.

[0188] Determine whether the array of changes in pore structure parameters converges;

[0189] If the array of changes in pore structure parameters converges, then determine whether the change in the objective function value converges.

[0190] If the change in the objective function value converges, the iteration stops, and the pore structure corresponding to the current pore structure parameters is taken as the pore structure with the best thermal radiation characteristics.

[0191] If the change in the objective function value diverges, the pore structure parameters are updated based on the array of changes in the pore structure parameters, and the objective function is iteratively optimized again.

[0192] As an optional solution, the above-mentioned apparatus is further used to, before iteratively optimizing the objective function of the optimization model, include:

[0193] The parameters of the optimization model are initialized, including the number of convergences, the convergence threshold, the difference factor, and the damping coefficient vector.

[0194] As an optional solution, the above-mentioned apparatus is also used to determine the change in the objective function value, including:

[0195] The pore structure parameters are differentially derived based on the differential multiple.

[0196] The four-parameter random growth method and the finite-time difference method are used to determine the corresponding thermal radiation characteristic parameters based on the pore structure parameters after the difference.

[0197] The change in the objective function value is determined based on the thermal radiation characteristic parameters before and after the difference.

[0198] As an optional solution, the above-mentioned apparatus is also used to determine an array of variations in pore structure parameters, including:

[0199] Determine the Jacobian matrix based on the pore structure parameters after differentiation;

[0200] Based on the Jacobian matrix, the variation array of pore structure parameters is solved using Formula 4. Formula 4 is... ,in, for The transpose of the Jacobian matrix, for Jacobian matrix, Here is the damping matrix. Let I represent the damping coefficient vector corresponding to each parameter, and let I be a positive definite diagonal identity matrix. This is an array of changes in pore structure parameters.

[0201] As an optional solution, the above-mentioned device is also used to determine whether the array of changes in pore structure parameters converges, including:

[0202] Compare the array of changes in pore structure parameters corresponding to the k-th convergence. The array of changes in pore structure parameters corresponding to the (k-1)th convergence ;

[0203] If the change array There exists an element whose absolute value is greater than 1. The absolute value of the corresponding element, or the array of changes. There exists a symbol of a certain element and The array of changes in pore structure parameters is determined by the different signs of the corresponding elements. The array of changes relative to pore structure parameters Divergence;

[0204] Conversely, if the change array The absolute value of each element in the array is less than or equal to 1. The absolute value of the corresponding element in the array, and the change amount. The symbol of each element in the middle and If all corresponding elements in the array have the same sign, then the array of changes in pore structure parameters represents the change in pore structure parameters. The array of changes relative to pore structure parameters convergence.

[0205] As an alternative, the aforementioned device is also used to, if the array of changes in pore structure parameters exhibits a divergent trend, then set the damping coefficient vector... And recalculate the array of changes in pore structure parameters according to Formula 4.

[0206] As an optional solution, the above-mentioned device is also used to determine whether the array of changes in the objective function values ​​has converged, including:

[0207] Determine the objective function value corresponding to the k-th convergence. The objective function value corresponding to the (k-1)th convergence Is the absolute value of the difference less than the convergence threshold?

[0208] if If the change in the objective function value is less than the convergence threshold, then the array of changes in the objective function value converges.

[0209] As an optional solution, the above-mentioned device is also used to further include:

[0210] If the array of changes in pore structure parameters converges, then determine the value of the array of changes. Check whether the absolute value of each element is less than the corresponding convergence threshold;

[0211] If the change array If the absolute value of each element is less than the corresponding convergence threshold, the iteration stops, and the pore structure corresponding to the current pore structure parameters is taken as the pore structure with the best thermal radiation characteristics.

[0212] In this application embodiment, the terms "module" or "unit" refer to a computer program or part of a computer program that has a predetermined function and works with other related parts to achieve a predetermined goal, and can be implemented wholly or partially using software, hardware (such as processing circuitry or memory), or a combination thereof. Similarly, a processor (or multiple processors or memory) can be used to implement one or more modules or units. Furthermore, each module or unit can be part of an overall module or unit that includes the functionality of that module or unit.

[0213] Regarding the apparatus in the above embodiments, the specific manner in which each module performs its operation has been described in detail in the embodiments related to the method, and will not be elaborated upon here.

[0214] According to one aspect of this application, a computer program product is provided, the computer program product comprising a computer program.

[0215] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0216] Figure 10 A schematic block diagram of a computer system architecture for implementing an electronic device according to embodiments of the present application is shown.

[0217] It should be noted that, Figure 10 The computer system 1100 of the electronic device shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments of this application.

[0218] like Figure 10As shown, the computer system 1100 includes a central processing unit (CPU) 1101, which can perform various appropriate actions and processes based on programs stored in read-only memory (ROM) 1102 or programs loaded from storage section 1108 into random access memory (RAM). The RAM 1103 also stores various programs and data required for system operation. The CPU 1101, ROM 1102, and RAM 1103 are interconnected via a bus 1104. An input / output interface 1105 (I / O interface) is also connected to the bus 1104.

[0219] The following components are connected to the input / output interface 1105: an input section 1106 including a keyboard, mouse, etc.; an output section 1107 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and speakers, etc.; a storage section 1108 including a hard disk, etc.; and a communication section 1109 including a network interface card such as a local area network card, modem, etc. The communication section 1109 performs communication processing via a network such as the Internet. A drive 1110 is also connected to the input / output interface 1105 as needed. Removable media 1111, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., are installed on the drive 1110 as needed so that computer programs read from them can be installed into the storage section 1108 as needed.

[0220] Specifically, according to embodiments of this application, the processes described in the various method flowcharts can be implemented as computer software programs. For example, embodiments of this application include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via communication section 1109, and / or installed from removable medium 1111. When the computer program is executed by central processing unit 1101, it performs various functions defined in the system of this application.

[0221] In such an embodiment, the computer program can be downloaded and installed from a network via communication section 1109, and / or installed from removable media 1111. When the computer program is executed by central processing unit 1101, it performs various functions provided in the embodiments of this application.

[0222] According to another aspect of the embodiments of this application, an electronic device for optimizing the pore structure of thermal barrier coatings is also provided. This embodiment uses this electronic device as an example of a terminal device for illustration. Figure 11 As shown, the electronic device includes a memory 1202 and a processor 1204. The memory 1202 stores a computer program, and the processor 1204 is configured to execute the steps of any of the above method embodiments through the computer program.

[0223] Optionally, in this embodiment, the aforementioned electronic device may be located in at least one of a plurality of network devices in a computer network.

[0224] Optionally, in this embodiment, the processor may be configured to execute the methods in the embodiments of this application via a computer program.

[0225] Alternatively, as those skilled in the art will understand, Figure 11 The structure shown is for illustrative purposes only. Figure 11 This does not limit the structure of the aforementioned electronic devices. For example, the electronic device may also include components that are more... Figure 11 The more or fewer components shown (such as network interfaces, etc.), or having the same Figure 11 The different configurations shown.

[0226] The memory 1202 can be used to store software programs and modules, such as the program instructions / modules corresponding to the optimization method and apparatus for the pore structure of the thermal barrier coating in this embodiment. The processor 1204 executes various functional applications and data processing by running the software programs and modules stored in the memory 1202, thereby realizing the above-mentioned optimization method for the pore structure of the thermal barrier coating. The memory 1202 may include high-speed random access memory, and may also include non-volatile memory, such as one or more magnetic storage devices, flash memory, or other non-volatile solid-state memory. In some instances, the memory 1202 may further include memory remotely located relative to the processor 1204, and these remote memories can be connected to the terminal via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof. Specifically, the memory 1202 may be used, but is not limited to, to store pore structure parameter data information. As an example, such as Figure 11 As shown, the memory 1202 may include, but is not limited to, the numerical simulation module 101, calculation module 102, establishment module 103, and determination module 104 in the optimization device for the thermal barrier coating pore structure. Furthermore, it may include, but is not limited to, other module units in the aforementioned device, which will not be elaborated upon in this example.

[0227] Optionally, the transmission device 1206 described above is used to receive or send data via a network. Specific examples of the network described above may include wired networks and wireless networks. In one example, the transmission device 1206 includes a Network Interface Controller (NIC), which can be connected to other network devices and a router via a network cable to communicate with the Internet or a local area network. In another example, the transmission device 1206 is a radio frequency (RF) module, used for wireless communication with the Internet.

[0228] In addition, the above-mentioned electronic device also includes: a display 1208 for displaying the above-mentioned thermal radiation characteristic data; and a connection bus 1210 for connecting the various module components in the above-mentioned electronic device.

[0229] In other embodiments, the aforementioned terminal device or server can be a node in a distributed system, wherein the distributed system can be a blockchain system, which is a distributed system formed by connecting multiple nodes through network communication. The nodes can form a peer-to-peer network, and any form of computing device, such as a server, terminal, or other electronic device, can become a node in the blockchain system by joining this peer-to-peer network.

[0230] According to one aspect of this application, a computer-readable storage medium is provided, wherein a processor of an electronic device reads computer instructions from the computer-readable storage medium, and executes the computer instructions, causing the electronic device to perform the optimization method for the thermal barrier coating pore structure provided in the various alternative implementations described above.

[0231] Optionally, in this embodiment, the computer-readable storage medium described above may be configured to store methods for performing the embodiments of this application.

[0232] Optionally, in this embodiment, those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be implemented by a program instructing the hardware related to the terminal device. The program can be stored in a computer-readable storage medium, which may include: flash drive, read-only memory (ROM), random access memory (RAM), disk or optical disk, etc.

[0233] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0234] If the integrated units in the above embodiments are implemented as software functional units and sold or used as independent products, they can be stored in the aforementioned computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause one or more electronic devices to execute all or part of the steps of the methods described in the various embodiments of this application.

[0235] In the above embodiments of this application, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0236] In the several embodiments provided in this application, it should be understood that the disclosed application can be implemented in other ways. The device embodiments described above are merely illustrative; for example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual couplings, direct couplings, or communication connections may be through some interfaces; indirect couplings or communication connections between units or modules may be electrical or other forms.

[0237] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0238] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0239] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0240] In summary, as can be seen from the above description, the embodiments of the present invention achieve the following technical effects:

[0241] 1. This invention generates a numerical model of the pore structure based on numerical simulation, and performs simulation calculations on the numerical model of the pore structure. On the basis of high-precision simulation of the pore structure of the thermal barrier layer, it accurately evaluates the influence of the pore structure on the thermal radiation performance of the coating, provides a reliable basis for the optimization results of the optimization model, and finally determines the pore structure with the best thermal radiation characteristics by combining the optimization model, thereby realizing the prediction and optimization of the pore structure of the thermal barrier coating.

[0242] 2. This invention utilizes the LM optimization algorithm to establish an optimization model. Within the optimization model, the four-parameter random growth method and the finite-time difference method are repeatedly called to determine the array of changes in pore structure parameters and the change in the objective function value. By sequentially judging whether the array of changes in pore structure parameters and the change in the objective function value converge, iterative optimization of the objective function and updating of the pore structure parameters are achieved, ultimately determining the pore structure with the optimal thermal radiation characteristics.

[0243] 3. This invention proposes to determine the Jacobian matrix based on the differential pore structure parameters, and solve the array of changes in pore structure parameters based on the Jacobian matrix. This method can efficiently capture the influence of changes in pore structure parameters on thermal radiation characteristics, thereby significantly improving the optimization accuracy and efficiency of the pore structure of thermal barrier coatings.

[0244] 4. This invention generates a numerical model of the pore structure of thermal barrier coatings using a four-parameter random growth method. This method can flexibly control the shape, size, and distribution of pores, thereby simulating a pore structure similar to that of actual thermal barrier coatings, providing accurate input for subsequent radiation characteristic analysis.

[0245] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.

[0246] It should be noted that, in the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

Claims

1. A method for optimizing the pore structure of a thermal barrier coating, characterized in that, include: Numerical simulation of the pore structure of the thermal barrier coating and generation of the corresponding pore structure numerical model include: simulating the pore structure of the thermal barrier coating using a four-parameter random growth method and generating the corresponding pore structure numerical model. The numerical model of the pore structure is simulated to determine the thermal radiation characteristic parameters of the pore structure. This includes: simulating the thermal radiation process of the pore structure using simulation methods based on the numerical model, determining the thermal radiation characteristic parameters of the pore structure; discretizing Maxwell's curl equation using the finite-time difference method to determine the expressions for the electric and magnetic field components as a function of time; determining the electric and magnetic field intensity vectors using the expressions for the electric and magnetic field components as a function of time; calculating the Poynting vector based on the electric and magnetic field intensity vectors; and determining the thermal radiation characteristic parameters of the pore structure based on the Poynting vector. The thermal radiation characteristic parameters include one or more of reflectivity, transmittance, and absorptivity. Establishing an optimization model for the aforementioned thermal radiation characteristic parameters includes: establishing an optimization model using the LM optimization algorithm, and establishing an objective function for the optimization model based on the aforementioned thermal radiation characteristic parameters, wherein the objective function is... ,in, This indicates the number of sampling points for thermal radiation characteristic parameters within the semi-transparent band. , Indicates at wavelength of Simulated values ​​of a certain thermal radiation characteristic parameter of the pore structure. For parameters to be optimized, Indicates at wavelength of The theoretical value of a certain thermal radiation characteristic parameter of the pore structure; Based on the optimization model, the pore structure with optimal thermal radiation characteristics is determined, including using the optimization model to call the four-parameter random growth method and the finite-time difference method to iteratively optimize the objective function of the optimization model until the objective function reaches a convergent state.

2. The method according to claim 1, characterized in that, The pore structure of the thermal barrier coating is simulated using a four-parameter random growth method, and a corresponding numerical model of the pore structure is generated, including: The simulated region of the pore structure is set; The grid points and pore structure parameters in the simulation area are initialized. The pore structure parameters include the growth probability of the nucleation center of the growth phase, the growth probability of the nuclei in each direction, and the preset volume fraction of the growth phase. The nucleation centers of the first growth phase are randomly arranged according to the growth probability of the nucleation centers of the growth phase; The nucleation center of the first growth phase grows in the i-th direction according to the growth probability of each direction, until the volume fraction of the growth phase reaches the preset volume fraction.

3. The method according to claim 1, characterized in that, The Poynting vector is calculated based on the electric field intensity vector and the magnetic field intensity vector, including: The Poynting vector is calculated using Formula 1 based on the electric field intensity vector and the magnetic field intensity vector. Formula 1 is... ,in, Represents the Poyinting vector. The period of an electromagnetic wave, Let be the electric field intensity vector. is the magnetic field strength vector.

4. The method according to claim 1, characterized in that, The thermal radiation characteristic parameters of the pore structure are determined based on the Poynting vector, including: Based on the Poynting vector, the radiation intensity of the pore structure is determined using Formula 2, where Formula 2 is: ,in, Represents the Poyinting vector. Radiation intensity; The reflectivity and / or transmittance and / or absorptivity of the pore structure are determined based on the radiation intensity.

5. The method according to claim 2, characterized in that, The objective function of the optimization model is iteratively optimized using the four-parameter random growth method and the finite-time difference method, until the objective function reaches convergence, including: Using the optimization model, the four-parameter random growth method and the finite-time difference method are invoked to determine the array of changes in the pore structure parameters and the change in the objective function value; Determine whether the array of changes in the pore structure parameters converges; If the array of changes in the pore structure parameters converges, then determine whether the change in the objective function value converges. If the change in the objective function value converges, the iteration stops, and the pore structure corresponding to the current pore structure parameters is taken as the pore structure with the best thermal radiation characteristics. If the change in the objective function value diverges, the pore structure parameters are updated based on the array of changes in the pore structure parameters, and the objective function is iteratively optimized again.

6. The method according to claim 5, characterized in that, Before invoking the four-parameter random growth method and the finite-time difference method using the optimization model, the following steps are also included: The parameters of the optimization model are initialized, including the number of convergences, the convergence threshold, the difference factor, and the damping coefficient vector.

7. The method according to claim 6, characterized in that, Determining the change in the objective function value includes: The pore structure parameters are differentially divided according to the differential multiple; The four-parameter random growth method and the finite-time domain difference method are invoked to determine the corresponding thermal radiation characteristic parameters based on the pore structure parameters after the difference. The change in the objective function value is determined based on the thermal radiation characteristic parameters before and after the difference.

8. The method according to claim 7, characterized in that, Determining the array of changes in the pore structure parameters includes: The Jacobian matrix is ​​determined based on the differentiald pore structure parameters. Based on the Jacobian matrix, the variation array of the pore structure parameters is solved using Formula 4, where Formula 4 is... ,in, for The transpose of the Jacobian matrix, for Jacobian matrix, Here is the damping matrix. Let I represent the damping coefficient vector corresponding to each parameter, and let I be a positive definite diagonal identity matrix. This is an array of changes in pore structure parameters.

9. The method according to claim 8, characterized in that, Determining whether the array of changes in the pore structure parameters converges includes: Compare the array of changes in pore structure parameters corresponding to the k-th convergence. The array of changes in pore structure parameters corresponding to the (k-1)th convergence ; If the change array There exists an element whose absolute value is greater than 1. The absolute value of the corresponding element, or the array of changes. There exists a symbol of a certain element and If the signs of the corresponding elements are different, then the change in the pore structure parameters is represented by an array. The array of changes relative to the pore structure parameters Divergence; Conversely, if the array of changes The absolute value of each element in the array is less than or equal to 1. The absolute value of the corresponding element in the array of changes. The symbol of each element in the middle and If the corresponding elements in the array all have the same sign, then the array of changes in the pore structure parameters... The array of changes relative to the pore structure parameters convergence.

10. The method according to claim 9, characterized in that, If the array of changes in the pore structure parameters shows a divergent trend, then let the damping coefficient vector... And recalculate the array of changes in pore structure parameters according to Formula 4.

11. The method according to claim 6, characterized in that, Determining whether the array of changes in the objective function value converges includes: Determine the objective function value corresponding to the k-th convergence. The objective function value corresponding to the (k-1)th convergence Whether the absolute value of the difference is less than the convergence threshold; if If the change in the objective function value is less than the convergence threshold, then the array of changes in the objective function value converges.

12. The method according to claim 9, characterized in that, Also includes: If the array of changes in the pore structure parameters converges, then the array of changes is determined to be convergent. Check whether the absolute value of each element is less than the corresponding convergence threshold; If the change array If the absolute value of each element is less than the corresponding convergence threshold, the iteration stops, and the pore structure corresponding to the current pore structure parameters is taken as the pore structure with the best thermal radiation characteristics.

13. An apparatus for optimizing the pore structure of a thermal barrier coating, used to implement the method for optimizing the pore structure of a thermal barrier coating as described in claim 1, characterized in that, include: The numerical simulation module is used to perform numerical simulation of the pore structure of thermal barrier coatings and generate corresponding numerical models of the pore structure. The calculation module is used to perform simulation calculations on the numerical model of the pore structure to determine the thermal radiation characteristic parameters of the pore structure. A module is established to create an optimization model for the aforementioned thermal radiation characteristic parameters; The determination module is used to determine the pore structure with optimal thermal radiation characteristics based on the optimization model.

14. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored computer program, wherein the computer program, when executed by an electronic device, performs the method according to any one of claims 1 to 12.

15. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1 to 12.

16. An electronic device comprising a memory and a processor, characterized in that, The memory stores a computer program, and the processor is configured to execute the method according to any one of claims 1 to 12 through the computer program.

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