Optimization design method and device of multi-dimensional functionally graded material, equipment and medium

Abstract

The application provides a multi-dimensional functionally graded material optimization design method, device, equipment and medium, and belongs to the technical field of functionally graded material design, which comprises the following steps: constructing a multi-dimensional functionally graded material based on a non-uniform rational B-spline basis function; the multi-dimensional functionally graded material comprises a plurality of control points; a sample set is constructed, and an initial material prediction model is trained based on the sample set to obtain a trained material performance prediction model; a multi-objective optimization function is constructed with the minimum total mass and the maximum free vibration fundamental frequency as the target, the multi-objective optimization function is iteratively solved, and the control point optimized material volume fraction and optimized thickness are obtained; wherein the predicted performance required in the multi-objective optimization function iterative solving process is determined based on the material performance prediction model. The application reduces the data amount in the multi-objective optimization algorithm, and thus can realize the rapid and reliable optimization design of the multi-dimensional functionally graded material with high design dimension and many design variables.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of functional gradient material design, and particularly relates to a multi-dimensional functional gradient material optimization design method, device, equipment and medium. BACKGROUND

[0002] Functional gradient material (FGM) is a new type of non-uniform composite material, which is usually composed of two or more materials, and the material composition gradually changes in space, with locally customized performance. It is widely used in aerospace, automotive, biomedical and military applications. In many complex service environments, one-dimensional FGM (1D-FGM) is often difficult to meet the service requirements. For example, the propulsion system and fuselage of modern aerospace aircraft usually operate in a high-temperature environment that changes in three directions, and the one-way change of material and performance of traditional 1D-FGM is difficult to meet these harsh service environments. In order to solve this problem, multi-dimensional functional gradient material (3D-FGM) is proposed, which has a smooth change in material performance in the pre-defined direction of the structure space, and by specifying the material composition at a specific location within the structure domain, a specific performance can be achieved.

[0003] In order to better design multi-dimensional functional gradient materials and obtain the best material and shape distribution according to application requirements, using an optimization algorithm is an effective method. Multi-objective meta-heuristic optimization algorithms have recently been considered as a robust and reliable method to solve various complex optimization problems, such as non-dominated sorting genetic algorithm (NSGA-II, NSGA-III), multi-objective particle swarm optimization (MOPSO), multi-objective evolutionary algorithm (MOEA) and multi-objective artificial bee colony algorithm (MOABC), etc. Due to their superior performance, these algorithms have begun to be gradually applied to the multi-objective optimization of MFGM. However, with the increasing complexity of multi-field coupling performance analysis of multi-dimensional functional gradient materials and the increasing requirement for numerical solution accuracy, the required amount of calculation and the length of calculation time significantly increase, which seriously limits the multi-objective optimization work of multi-dimensional functional gradient materials. Specifically, a large number of performance calculations need to be performed in the optimization algorithm, which will result in a very long optimization time, making it difficult to run in practice. Therefore, the multi-objective optimization algorithm in the prior art can only be used for optimization design of functional gradient materials with low design dimension and few design variables, and cannot effectively optimize multi-dimensional functional gradient materials.

[0004] Therefore, there is an urgent need to provide a multi-dimensional functional gradient material optimization design method, device, equipment and medium, which reduces the amount of calculation and the length of calculation time required for performance calculation in the optimization algorithm, and realizes rapid and accurate optimization design of multi-dimensional functional gradient materials. SUMMARY

[0005] Therefore, it is necessary to provide a multi-dimensional functionally graded material optimization design method, device, equipment and medium to solve the technical problems that the multi-dimensional functionally graded material cannot be effectively optimized or the optimization design efficiency is too low due to the large amount of calculation in the multi-objective optimization algorithm in the prior art.

[0006] In one aspect, to solve the above technical problems, the present application provides a multi-dimensional functionally graded material optimization design method, comprising:

[0007] Constructing a multi-dimensional functionally graded material based on a non-uniform rational B-spline basis function; the multi-dimensional functionally graded material includes a plurality of control points;

[0008] Constructing a sample set and training an initial material prediction model based on the sample set to obtain a trained material performance prediction model;

[0009] Constructing a multi-objective optimization function with the minimum total mass and the maximum free vibration fundamental frequency as the target, iteratively solving the multi-objective optimization function to obtain the optimized material volume fraction and the optimized thickness of the control points;

[0010] Wherein, the predicted performance required in the multi-objective optimization function iterative solving process is determined based on the material performance prediction model.

[0011] In one possible implementation, the multi-dimensional functionally graded material is a composite material of metal phase material and ceramic phase material; the multi-objective optimization function is:

[0012]

[0013]

[0014] In the formula, is the total mass; is the material volume fraction of the ceramic phase material of the jth control point; is the thickness of the jth control point; is the ceramic phase material volume fraction at any point in space; is the density of the ceramic phase material; is the mass density of the metal phase material at room temperature; is the total volume of the multi-dimensional functionally graded material, which is related to the thickness; is the dimensionless free vibration fundamental frequency; is the first order natural frequency of free vibration; is the side length of the square multi-dimensional functionally graded material; is the elastic modulus of the metal phase material at room temperature; is the Poisson's ratio of the metal phase material at room temperature; is an initial thickness of the square multi-dimensional functionally graded material; is a non-uniform rational B-spline basis function; n x m x l is a total number of control points.

[0015] In a possible implementation, the constraint condition of the multi-objective optimization function is:

[0016]

[0017] wherein, is a total material volume fraction of the ceramic phase material; is a unit stiffness matrix; is a temperature-dependent unit thermal stiffness matrix; is a unit mass matrix; is a unit displacement vector.

[0018] In a possible implementation, the multi-dimensional functionally graded material includes a target sub-region and at least one mirror sub-region symmetrical to the target sub-region; the multi-objective optimization function is a function corresponding to the target sub-region, and the method comprises:

[0019] determining a target material volume fraction and a target thickness of each control point in the target sub-region based on the multi-objective optimization function and the material performance prediction model;

[0020] mirror-symmetry processing the target material volume fraction and the target thickness to obtain a mirror material volume fraction and a target thickness of each control point in the mirror sub-region.

[0021] In a possible implementation, the sample set includes a plurality of sample data, and the sample data includes a material volume fraction, a thickness, a total mass reference value, and a free vibration fundamental frequency reference value;

[0022] The constructing the sample set comprises:

[0023] randomly initializing a material distribution and a geometric model to obtain a material volume fraction and a thickness of each control point;

[0024] determining a spatial thermal field of the multi-dimensional functionally graded material based on high-throughput parallel finite element analysis;

[0025] determining a total mass reference value and a free vibration fundamental frequency reference value of the multi-dimensional functionally graded material based on the spatial thermal field.

[0026] In a possible implementation, the training the initial material prediction model based on the sample set to obtain a trained material performance prediction model comprises:

[0027] The sample set is divided into a training set and a verification set in a preset proportion;

[0028] The initial material performance prediction model is trained based on the training set to obtain a to-be-verified performance prediction model;

[0029] The to-be-verified performance prediction model is verified based on the verification set, and when the verification is passed, the to-be-verified performance prediction model is the material performance prediction model.

[0030] In a possible implementation, the material performance prediction model comprises a first three-dimensional convolution module, a first pooling layer, a plurality of second three-dimensional convolution modules, a flattening layer and a full connection layer connected in sequence, and each of the first three-dimensional convolution module and the second three-dimensional convolution modules comprises a three-dimensional convolution layer, a batch normalization layer and an activation function layer.

[0031] In another aspect, the present application also provides an optimization design device for a multi-dimensional functionally graded material, comprising:

[0032] A multi-dimensional functionally graded material construction unit is configured to construct a multi-dimensional functionally graded material based on a non-uniform rational B-spline basis function, and the multi-dimensional functionally graded material comprises a plurality of control points.

[0033] A material performance prediction model training unit is configured to construct a sample set and train an initial material prediction model based on the sample set to obtain a trained material performance prediction model.

[0034] A material parameter optimization design unit is configured to construct a multi-objective optimization function with the minimum total mass and the maximum free vibration fundamental frequency as targets, iteratively solve the multi-objective optimization function, and obtain the optimized material volume fraction and the optimized thickness of the control points.

[0035] In the process of iteratively solving the multi-objective optimization function, the predicted performance required is determined based on the material performance prediction model.

[0036] In another aspect, the present application also provides an optimization design device, comprising a memory and a processor, wherein,

[0037] The memory is configured to store a program.

[0038] The processor is coupled to the memory and is configured to execute the program stored in the memory to implement the steps in the optimization design method for a multi-dimensional functionally graded material in any of the possible implementation manners.

[0039] In another aspect, the present application also provides a computer readable storage medium for storing computer readable programs or instructions, which can realize the steps of the optimization design method of the multi-dimensional functionally graded material when executed by a processor.

[0040] The present application has the following beneficial effects: the optimization design method of the multi-dimensional functionally graded material provided by the present application applies the trained material performance prediction model to the solution process of the multi-objective function, without the need for numerical calculation of the total mass and the free vibration fundamental frequency by the multi-objective optimization algorithm, thereby improving the determination efficiency of the total mass and the free vibration fundamental frequency, reducing the data volume in the multi-objective optimization algorithm, accelerating the multi-objective optimization process, and further realizing the fast and reliable optimization design of the multi-dimensional functionally graded material with high design dimension and many design variables, solving the shortcomings of slow performance prediction speed, low design dimension, small design freedom, and performance limitation of the current FGM, and ensuring that the multi-dimensional functionally graded material meets the application requirements in the fields of aerospace, automobile machinery, military defense, and the like. BRIEF DESCRIPTION OF DRAWINGS

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0042] Figure 1 An embodiment flowchart of the optimization design method of the multi-dimensional functionally graded material provided by the present application is shown in the figure.

[0043] Figure 2 An embodiment structure diagram of the multi-dimensional functionally graded material provided by the present application is shown in the figure.

[0044] Figure 3 Another embodiment flowchart of the optimization design method of the multi-dimensional functionally graded material provided by the present application is shown in the figure.

[0045] Figure 4 An embodiment flowchart of the construction of the sample set provided by the present application is shown in the figure.

[0046] Figure 5 An embodiment flowchart of the construction of the sample set provided by the present application is shown in the figure.

[0047] Figure 6 An embodiment structure diagram of the material performance prediction model training and verification process provided by the present application is shown in the figure.

[0048] Figure 7 An embodiment simulation result diagram of the optimization design structure provided by the present application is shown in the figure.

[0049] Figure 8 An embodiment structure diagram of the optimization design device for the multi-dimensional functionally graded material provided by the present application is shown in the figure.

[0050] Figure 9 An embodiment structure diagram of the optimization design device provided by the present application is shown in the figure. DETAILED DESCRIPTION

[0051] The technical solutions in the embodiments of the present application will be clearly and completely described in connection with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by a person skilled in the art without creative work fall within the protection scope of the present application.

[0052] It should be understood that the schematic drawings are not drawn to scale. The flowcharts used in the present application show the operations implemented according to some embodiments of the present application. It should be understood that the operations of the flowcharts can be implemented in no order, the steps without logical context relationship can be reversed in order or implemented simultaneously. In addition, a person skilled in the art can add one or more other operations to the flowcharts or remove one or more operations from the flowcharts under the guidance of the content of the present application. Some block diagrams shown in the drawings are functional entities, which do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in the form of software, or in one or more hardware modules or integrated circuits, or in different network and / or processor systems and / or microcontroller systems.

[0053] In this document, reference to“an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the application. The appearances of the phrase in various places in the specification are not necessarily all referring to the same embodiment, nor are they necessarily mutually exclusive of other embodiments. A person skilled in the art will understand explicitly and implicitly that the embodiments described herein can be combined with other embodiments.

[0054] The present application provides an optimization design method, device, equipment and medium for a multi-dimensional functionally graded material, which are described respectively as follows.

[0055] Figure 1 An embodiment flowchart of the optimization design method for the multi-dimensional functionally graded material provided by the present application is shown in the figure, which includes the following steps. Figure 1

[0056] ​S101, constructing a multi-dimensional functionally graded material based on a non-uniform rational B-spline (NURBS) basis function; the multi-dimensional functionally graded material comprises a plurality of control points;

[0057] S102, constructing a sample set and training an initial material performance prediction model based on the sample set to obtain a trained material performance prediction model;

[0058] S103, constructing a multi-objective optimization function with the minimum total mass and the maximum free vibration fundamental frequency as the target, iteratively solving the multi-objective optimization function to obtain the optimized material volume fraction and the optimized thickness of the control points;

[0059] In the process of iteratively solving the multi-objective optimization function, the predicted performance is determined based on the material performance prediction model.

[0060] Based on the high-order continuity of the NURBS basis function, the continuous gradient distribution of the material in the domain can be smoothly represented, thereby enabling the construction of the multi-dimensional functionally graded material.

[0061] In specific embodiments of the present application, the multi-dimensional functionally graded material includes three spatial directions, i.e., the length direction, the width direction, and the height direction, and the NURBS basis function is:

[0062]

[0063] In the formula, is a non-uniform rational B-spline basis function; p is the order of the basis function in the length direction; n is the number of control points in the length direction; q is the order of the basis function in the width direction; m is the number of control points in the width direction; r is the order of the basis function in the height direction; l is the number of control points in the height direction; is the B-spline basis function in the length direction; is the B-spline basis function in the width direction; is the B-spline basis function in the height direction; is the weight of the (i, j, k) control point.

[0064] For a one-dimensional B-spline basis function, it is usually composed of a node vector , wherein , and and are usually repeated p+1 times. p is the interpolation basis function order; n is the number of control points and basis functions. The B-spline basis function is defined by the Cox-de-Boor recursive formula:

[0065] ;

[0066] .

[0067] In the premise of one-dimensional B-spline basis function, the weight value is introduced to obtain one-dimensional NURBS basis function, and the NURBS basis function in the embodiment of the application is a three-dimensional basis function, which can be constructed by tensor product of one-dimensional NURBS basis function.

[0068] Compared with the prior art, the multi-dimensional functionally graded material optimization design method provided in the embodiment of the application applies the trained complete material performance prediction model to the solving process of the multi-objective function, does not need the multi-objective optimization algorithm to perform numerical calculation on the total mass and the free vibration base frequency, improves the determination efficiency of the total mass and the free vibration base frequency, reduces the data amount in the multi-objective optimization algorithm, speeds up the multi-objective optimization process, and then can realize the fast and reliable optimization design of the multi-dimensional functionally graded material with high design dimension and many design variables, solves the shortcomings of slow performance prediction speed, low design dimension, small design freedom, and performance limitation of the current FGM, and ensures that the multi-dimensional functionally graded material meets the application requirements in the fields of aerospace, automobile machinery, military defense and the like.

[0069] In some embodiments of the application, the multi-dimensional functionally graded material is composed of two materials, specifically, the multi-dimensional functionally graded material is composed of a metal phase material and a ceramic phase material, and the multi-objective optimization function is:

[0070]

[0071]

[0072] In the formula, is the total mass; is the material volume fraction of the ceramic phase material at the jth control point; is the thickness of the jth control point; is the volume fraction of the ceramic phase material at any point in space; is the density of the ceramic phase material; is the mass density of the metal phase material at room temperature; is the total volume of the multi-dimensional functionally graded material, which is related to the thickness; is the dimensionless free vibration base frequency; is the first order natural frequency of free vibration; is the side length of the square multi-dimensional functionally graded material; is the elastic modulus of the metal phase material at room temperature; is the Poisson's ratio of the metal phase material at room temperature; is the initial thickness of the square multidimensional functionally gradient material; is the non-uniform rational B-spline basis function; n x m x l is the total number of control points.

[0073] It should be noted that: , is the volume fraction of the metallic phase material at any point in space.

[0074] Specifically, the material volume fraction can be obtained by interpolation of NURBS basis functions.

[0075] In a specific embodiment of the present invention, the multi-dimensional functional gradient material is constructed based on the NURBS basis function. L = 1m square plate, the initial thickness of the plate h 0 is =0.1m, such as Figure 2 (a) and Figure 2 (b) shown.

[0076] In order to further improve the optimization efficiency of the multi-objective optimization function and the accuracy of the determined optimization parameters, in some embodiments of the present invention, at least one constraint condition is set to constrain the optimization process of the multi-objective optimization function. Specifically, the constraint condition of the multi-objective optimization function is:

[0077]

[0078] Where, is the total material volume fraction of the ceramic phase material; is the element stiffness matrix; is the element thermal stiffness matrix related to temperature; is the unit mass matrix; is the unit displacement vector.

[0079] In a specific embodiment of the present invention, the multi-objective optimization algorithm of the multi-objective optimization function is NSGA-III.

[0080] In some embodiments of the present invention, the multidimensional functionally gradient material is a centrally symmetrical pattern, and the boundary conditions applied to the multidimensional functionally gradient material are also centrally symmetrical, such as Figure 2 (a) and 2(b), the multidimensional functionally gradient material is a square plate. The boundary conditions are that the four sides of the plate are fixed, and a uniform temperature is applied to the upper surface of the plate, while the lower surface is at a uniform room temperature. That is, the optimized material volume fraction and optimized thickness are also symmetric about the center.

[0081] Then Figure 2 As shown in (c), the multidimensional functional gradient material can be divided into a target sub-region (Design Area) and three mirror sub-regions symmetrical to the target sub-region.

[0082] In this premise, in order to further reduce the amount of calculation and improve the efficiency of the optimization design of the multi-dimensional functionally graded material, in some embodiments of the present application, the multi-objective optimization function is a function corresponding to the target sub-region, as shown in Figure 3 The optimization design method of the multi-dimensional functionally graded material comprises the following steps:

[0083] S301, determining the target material volume fraction and the target thickness of each control point in the target sub-region based on the multi-objective optimization function and the material performance prediction model;

[0084] S302, performing mirror symmetry processing on the target material volume fraction and the target thickness to obtain the mirror material volume fraction and the target thickness of each control point in the mirror sub-region.

[0085] The embodiments of the present application can reduce the calculation amount by one fourth or even one eighth in the optimization process by only optimizing the target sub-region, and the mirror material volume fraction and the target thickness of the other three mirror sub-regions through the three mirror symmetry activities, thereby greatly reducing the calculation amount and further improving the optimization design efficiency.

[0086] As can be seen from the above description, the input of the material performance prediction model is the material volume fraction and the thickness of each control point, and the output is the total mass and the free vibration fundamental frequency, therefore, the sample set includes a plurality of sample data, and the sample data includes the material volume fraction, the thickness, the total mass reference value and the free vibration fundamental frequency reference value; in some embodiments of the present application, as shown in Figure 4 The step S102 of constructing the sample set comprises the following steps:

[0087] S401, randomly initializing the material distribution and the geometric model to obtain the material volume fraction and the thickness of each control point;

[0088] S402, determining the spatial thermal field of the multi-dimensional functionally graded material based on high-throughput parallel geometric analysis;

[0089] S403, determining the total mass reference value and the free vibration fundamental frequency reference value of the multi-dimensional functionally graded material based on the spatial thermal field.

[0090] In the step S402 of determining the spatial thermal field, the equivalent material properties of the multi-dimensional functionally graded material are required, and the specific equivalent material properties include but are not limited to the elastic modulus, the Poisson's ratio, the thermal conductivity and the thermal expansion coefficient, and specifically:

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101]

[0102]

[0103] E, v, k, a, p, E , v , k , a, p, are the elastic modulus, Poisson's ratio, thermal conductivity, thermal expansion coefficient and mass density of the multi-dimensional functionally graded material, respectively; is the bulk modulus; is the shear modulus; and are the bulk modulus of the metallic phase material and the ceramic phase, respectively; and are the bulk modulus of the metallic phase material and the ceramic phase, respectively; and are the elastic modulus of the metallic phase material and the ceramic phase, respectively; and are the thermal conductivity of the metallic phase material and the ceramic phase, respectively; and are the thermal expansion coefficient of the metallic phase material and the ceramic phase, respectively; and are the mass density of the metallic phase material and the ceramic phase, respectively.

[0104] It should be noted that each of the above equivalent material properties is related to temperature, and the relationship between any equivalent material property and temperature is as follows:

[0105]

[0106] wherein, represents any of the above equivalent material properties. T is the temperature in Kelvin scale. is a constant determined by the cubic fitting of material properties and temperature. , ,​ 、 is , , , a constant.

[0107] In a specific embodiment of the present application, the ceramic phase material is ZrO2, the metal phase material is SUS304, and the above-mentioned five temperature-related constants are shown in Table 1:

[0108] Table 1 Material and temperature-related constants

[0109]

[0110] wherein the determination process of the spatial thermal field is specifically as follows:

[0111] The steady-state thermal field equation is as follows:

[0112] ;

[0113] The constitutive equation of the three-dimensional elastic theory isotropic material considering thermal coupling can be written as:

[0114] ；

[0115] wherein and represent the stress and strain tensors, is the effective thermal expansion coefficient, ∆T is the temperature change, is the Kronecker operator, is the elastic constant matrix.

[0116] The strain can be represented as follows by using the displacement of the material point:

[0117] ；

[0118] For the bending problem of the multi-dimensional functionally graded material in the thermal environment, according to the virtual work principle, the control equation can be written as:

[0119] ；

[0120] Further represented in the matrix form:

[0121] ;

[0122] wherein, C is the elastic constant matrix, is the stress vector due to temperature change, t is the boundary traction, is the volume domain; is the boundary.

[0123] where the stress , strain , displacement , stress vector due to temperature change , C is calculated as follows:

[0124] , , ,

[0125] .

[0126] For the free vibration problem in thermal environment, it is assumed that the temperature of each location of the multi-dimensional functionally graded material in the initial state is 300 K. The temperature boundary condition is applied, and the heat transfer process will be carried out until equilibrium is reached. The rise in temperature will cause the multi-dimensional functionally graded material to produce thermal expansion and initial internal stress, and the strain energy caused by the initial thermal stress can be written as:

[0127] ;

[0128] In the formula, and are the stress and strain under the initial thermal stress, respectively.

[0129] The final matrix form of the control equation of free vibration can be written as:

[0130]

[0131] In the formula, is the strain vector due to temperature change.

[0132] The control equation derived by discretization using the isogeometric analysis numerical technique is solved to obtain the free vibration under the thermal-mechanical coupling condition.

[0133] Specifically, the temperature vector and the displacement vector are obtained by interpolation through the NURBS basis function:

[0134]

[0135]

[0136] wherein, and are the temperature vector and the displacement vector at the control point.

[0137] The weak form governing equation of steady heat transfer in a multi-dimensional functionally graded material can be written as:

[0138]

[0139]

[0140]

[0141]

[0142] where, is the temperature vector of each control point in the multi-dimensional functionally graded material unit .

[0143] It is worth noting that the thermal conductivity in this equation is also a function of temperature, and the change in temperature will lead to the change in thermal conductivity . Therefore, an iterative method is needed to solve this equation.

[0144] The iterative process mainly includes: first, initialize the temperature field, then use the temperature field to calculate the thermal conductivity of the material , and solve the temperature field according to the governing equation. Iterative calculation is carried out until the convergence evaluation criterion of the temperature vector and is less than the set tolerance, and the final temperature field vector is obtained, that is, the temperature thermal field distribution.

[0145] After obtaining the temperature thermal field distribution, the governing equation of free vibration in the unit can be written as:

[0146] ; ;

[0147] ;

[0148] ;

[0149] ;

[0150] ; ;

[0151]

[0152]

[0153]

[0154] In the formula, is a unit external force load vector; is a unit thermal load vector; is a non-uniform rational B-spline basis function.

[0155] In the formula, is a volume domain is obtained after the volume domain is divided into a plurality of units.

[0156] Solving the above equation can obtain the free vibration fundamental frequency and the total mass.

[0157] By changing the material volume fraction and the plate thickness at the control points, the boundary conditions, the initial temperature field, and the shape of the geometric model, the above process is cycled until a required number of training samples are obtained to generate the sample set.

[0158] In specific embodiments of the present application, the sample set includes 20,000 groups of data.

[0159] To further ensure the model performance of the material performance prediction model, in some embodiments of the present application, as shown in Figure 5 the determination process of the material performance prediction model in step S102 is as follows:

[0160] S501, divide the sample set into a training set and a validation set at a preset ratio;

[0161] S502, train the initial material performance prediction model based on the training set to obtain a performance prediction model to be verified;

[0162] S503, verify the performance prediction model to be verified based on the validation set, and when the verification is passed, the performance prediction model to be verified is the material performance prediction model.

[0163] In the training process of the initial material performance prediction model, the loss function used is the mean square error (MSE) function.

[0164] Specifically, the preset ratio is 8:2.

[0165] It should be noted that the index used in the verification process is the coefficient of determination R 2 . The expression is specifically as follows:

[0166]

[0167] In the formula, is the predicted value of the material performance prediction model, and the predicted value is the total mass and the free vibration fundamental frequency; is the reference value in the sample set, and the reference value is the total mass reference value and the free vibration fundamental frequency reference value; is the total number of data in the validation set.

[0168] It should be understood that: R 2 The closer to 1, the higher the prediction accuracy of the material performance prediction model.

[0169] In specific embodiments of the present application, as Figure 6 shown, the material performance prediction model comprises a first three-dimensional convolution module, a first pooling layer, a plurality of second three-dimensional convolution modules, a flattening layer and a full connection layer connected in turn, and the first three-dimensional convolution module and each second three-dimensional convolution module all comprise a three-dimensional convolution layer, a batch normalization layer and an activation function layer.

[0170] Among them, the activation function of the activation function layer is the RELU function.

[0171] In specific embodiments of the present application, step S103 obtains the Pareto frontier, so that the representative elite solutions in the Pareto frontier can be uniformly selected for result visualization. From the drawn material distribution cloud map and the sample geometric model structure, the characteristics of the optimization results under different optimization objectives, constraint conditions, boundary conditions, initial temperature field, load conditions and other factors are extracted, and the influence law of the material distribution mode and the sample geometric model on the 3D-FGM macroscopic performance is analyzed.

[0172] Specifically, taking a square plate with fixed boundary conditions on all sides and a uniform temperature of 500K applied to the upper surface as an example, the material volume fraction and thickness distribution visualization results of the ceramic phase material on the representative elite are shown in Figure 7 , there are 8 representative elites, Figure 7 (a) is the material volume fraction and thickness of the ceramic phase material corresponding to the dimensionless free vibration base frequency of 5.1080 and the total mass of 524.86kg, Figure 7 (b) is the material volume fraction and thickness of the ceramic phase material corresponding to the dimensionless free vibration base frequency of 4.9901 and the total mass of 491.96kg, Figure 7 (c) is the material volume fraction and thickness of the ceramic phase material corresponding to the dimensionless free vibration base frequency of 4.8921 and the total mass of 470.95kg, Figure 7 (d) is the material volume fraction and thickness of the ceramic phase material corresponding to the dimensionless free vibration base frequency of 4.7942 and the total mass of 460.16kg, Figure 7 (e) is the material volume fraction and thickness of the ceramic phase material corresponding to the dimensionless free vibration base frequency of 4.7304 and the total mass of 451.97kg, Figure 7 (f) is the material volume fraction and thickness of the ceramic phase material corresponding to the dimensionless free vibration base frequency of 4.6062 and the total mass of 440.25kg, Figure 7 (g) is the material volume fraction and thickness of the ceramic phase material corresponding to the dimensionless free vibration base frequency of 4.5345 and the total mass of 434.41kg,Figure 7 (h) the material volume fraction and thickness of the ceramic phase material corresponding to a dimensionless free vibration fundamental frequency of 4.3768 and a total mass of 424.26 kg, Figure 7 The color from black to white represents the gradually decreasing thickness and the gradually decreasing material volume fraction of the ceramic phase. The color from white to black represents the gradually increasing thickness and the gradually increasing material volume fraction of the ceramic phase. Figure 8 It can be seen that the ceramic phase material is mainly located in the inner region of the plate, and there are some regions of the metal phase in the inner region. For the plate thickness distribution, the plate is thicker in the middle of the four sides and the center position, and thinner in other regions. In addition, with the decrease of the mass and the fundamental frequency, it is observed that the plate thickness is significantly reduced.

[0173] In summary, the optimization design method of the multi-dimensional functionally graded material proposed in the embodiment of the application establishes a material performance prediction model of the multi-dimensional functionally graded material, improves the determination efficiency of the total mass and the automatic vibration fundamental frequency of the multi-dimensional functionally graded material required in the iterative solving process of the multi-objective optimization function, and improves the optimization design efficiency. At the same time, the best optimized material volume fraction and optimized thickness are obtained by combining the multi-objective optimization algorithm, which significantly improves the macro-mechanical properties of the multi-dimensional functionally graded material and reduces the overall mass of the sample. The current FGM performance prediction speed is slow, the design dimension is low, the design freedom is small, and the performance is limited. The method solves the shortcomings such as performance limitation. It has important significance for the development of multi-dimensional functionally graded materials in the fields of aerospace, automobiles, biomedicine and military applications.

[0174] In order to better implement the optimization design method of the multi-dimensional functionally graded material in the embodiment of the application, on the basis of the optimization design method of the multi-dimensional functionally graded material, the embodiment of the application also provides an optimization design device for the multi-dimensional functionally graded material, as shown in Figure 9 The optimization design device 800 for the multi-dimensional functionally graded material includes:

[0175] The multi-dimensional functionally graded material construction unit 801 is configured to construct the multi-dimensional functionally graded material based on the non-uniform rational B-spline basis function; the multi-dimensional functionally graded material includes a plurality of control points.

[0176] The material performance prediction model training unit 802 is configured to construct a sample set and train an initial material performance prediction model based on the sample set to obtain a trained material performance prediction model.

[0177] The material parameter optimization design unit 803 is configured to construct a multi-objective optimization function with the minimum total mass and the maximum free vibration fundamental frequency as the target, iteratively solve the multi-objective optimization function, and obtain the optimized material volume fraction and the optimized thickness of the control points.

[0178] In the iterative solving process of the multi-objective optimization function, the predicted performance is determined based on the material performance prediction model.

[0179] The multi-dimensional functionally graded material optimization design apparatus 800 provided by the above embodiments can implement the technical solutions described in the multi-dimensional functionally graded material optimization design method embodiments, and the principles of implementation of the above modules or units can refer to the corresponding content in the multi-dimensional functionally graded material optimization design method embodiments, which will not be repeated here.

[0180] As shown in Figure 9 The present application also provides an optimization design device 900. The optimization design device 900 includes a processor 901, a memory 902, and a display 903. ​ Only part of the components of the optimization design device 900 are shown, but it should be understood that all the shown components are not required to be implemented, and more or less components can be alternatively implemented.

[0181] The processor 901 can be a central processing unit (CPU), a microprocessor, or other data processing chip in some embodiments, used to run the program code or process data stored in the memory 902, such as the multi-dimensional functionally graded material optimization design method in the present application.

[0182] In some embodiments of the present application, the processor 901 can be a single server or a server group. The server group can be centralized or distributed. In some embodiments, the processor 901 can be local or remote. In some embodiments, the processor 901 can be implemented in a cloud platform. In an embodiment, the cloud platform can include a private cloud, a public cloud, a hybrid cloud, a community cloud, a distributed cloud, an internal cloud, a multi-cloud, etc., or any combination thereof.

[0183] The memory 902 can be an internal storage unit of the optimization design device 900 in some embodiments, such as a hard disk or a memory of the optimization design device 900. The memory 902 can also be an external storage device of the optimization design device 900 in other embodiments, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc. equipped on the optimization design device 900.

[0184] Further, the memory 902 can include both the internal storage unit and the external storage device of the optimization design device 900. The memory 902 is used to store application software and various data installed on the optimization design device 900.

[0185] The display 903 may, in some embodiments, be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, an OLED (Organic Light-Emitting Diode) toucher, and the like. The display 903 is used to display information of the optimization design device 900 and to display a visualized user interface. The components 901-903 of the optimization design device 900 communicate with each other through a system bus.

[0186] In some embodiments of the present application, when the processor 901 executes the optimization design program of the multi-dimensional functionally graded material in the memory 902, the following steps can be implemented:

[0187] The multi-dimensional functionally graded material is constructed based on a non-uniform rational B-spline basis function; the multi-dimensional functionally graded material includes a plurality of control points;

[0188] A sample set is constructed, and an initial material prediction model is trained based on the sample set to obtain a trained material performance prediction model;

[0189] A multi-objective optimization function is constructed with the minimum total mass and the maximum free vibration fundamental frequency as the target, the multi-objective optimization function is iteratively solved, and the optimized material volume fraction and the optimized thickness of the control points are obtained;

[0190] In the iterative solving process of the multi-objective optimization function, the required predicted performance is determined based on the material performance prediction model.

[0191] It should be understood that, in addition to the above functions, the processor 901 can also implement other functions when executing the optimization design program of the multi-dimensional functionally graded material in the memory 902, which can be referred to the description of the corresponding method embodiments.

[0192] Further, the type of the optimization design device 900 referred to in the embodiments of the present application is not specifically limited, and the optimization design device 900 can be a portable optimization design device such as a mobile phone, a tablet computer, a personal digital assistant (PDA), a wearable device, a laptop, and the like. Exemplary embodiments of the portable optimization design device include, but are not limited to, a portable optimization design device running an IOS, an Android, a Microsoft, or other operating system. The above-mentioned portable optimization design device can also be other portable optimization design devices, and it should also be understood that, in some other embodiments of the present application, the optimization design device 900 can also not be a portable optimization design device, but a desktop computer with a touch-sensitive surface (such as a touch panel).

[0193] Correspondingly, the embodiment of the present application further provides a computer readable storage medium for storing computer readable programs or instructions, which can realize the steps or functions in the optimization design method of the multi-dimensional functionally graded material when executed by a processor.

[0194] Those skilled in the art can understand that all or part of the processes of the above-mentioned embodiment methods can be completed by a computer program instructing relevant hardware (such as a processor, a controller, etc.) to complete, and the computer program can be stored in a computer readable storage medium. The computer readable storage medium is a disk, an optical disk, a read-only memory or a random access memory, etc.

[0195] The above describes in detail the optimization design method, device, equipment and medium of the multi-dimensional functionally graded material provided by the present application. The principle and implementation mode of the present application are described by applying specific examples. The above embodiment is only used to help understand the method and core idea of the present application. Meanwhile, for those skilled in the art, according to the idea of the present application, the specific implementation mode and application range can be changed. In summary, the content of the specification should not be understood as a limitation of the present application.

Claims

1. A method for the optimal design of a multi-dimensional functionally graded material, characterized by, The method comprises the following steps: a multi-dimensional functionally graded material is constructed based on a non-uniform rational B-spline basis function; the multi-dimensional functionally graded material comprises a plurality of control points; a sample set is constructed, and an initial material prediction model is trained based on the sample set to obtain a trained material performance prediction model; a multi-objective optimization function is constructed with the minimum total mass and the maximum free vibration fundamental frequency as the objectives, and the multi-objective optimization function is iteratively solved to obtain the optimized material volume fraction and thickness of the control points; wherein the predicted performance required in the iterative solving process of the multi-objective optimization function is determined based on the material performance prediction model; the multi-dimensional functionally graded material is a composite material of a metal phase material and a ceramic phase material; and the multi-objective optimization function is: wherein, is the total mass; is the material volume fraction of the ceramic phase material at the jth control point; is the thickness at the jth control point; is the volume fraction of the ceramic phase material at any point in space; is the density of the ceramic phase material; is the mass density of the metallic phase material at room temperature; is the total volume of the multi-dimensional functionally graded material, related to the thickness; is the dimensionless free vibration fundamental frequency; is the first order natural frequency of free vibration; is the side length of the square multi-dimensional functionally graded material; is the elastic modulus of the metallic phase material at room temperature; is the Poisson's ratio of the metallic phase material at room temperature; is the initial thickness of the square multi-dimensional functionally graded material; is the non-uniform rational B-spline basis function; n×m×l is the total number of control points; The multi-dimensional functionally graded material comprises three spatial directions, i.e., a length direction, a width direction, and a height direction, and the NURBS basis function is: wherein p is the number of basis functions in the length direction; n is the number of control points in the length direction; q is the number of basis functions in the width direction; m is the number of control points in the width direction; r is the number of basis functions in the height direction; l is the number of control points in the height direction; is the B-spline basis function in the length direction; is the B-spline basis function in the width direction; is the B-spline basis function in the height direction; is the weight of the (i,j,k) control point; The constraint condition of the multi-objective optimization function is: wherein is the total material volume fraction of ceramic phase material; is the element stiffness matrix; is the temperature dependent element thermal stiffness matrix; is the element mass matrix; is the element displacement vector; The multi-dimensional functionally graded material comprises a target sub-region and at least one mirror sub-region symmetrical to the target sub-region; the multi-objective optimization function is a function corresponding to the target sub-region; and the method comprises: determining the target material volume fraction and the target thickness of each control point in the target sub-region based on the multi-objective optimization function and the material performance prediction model; mirror-symmetrical processing the target material volume fraction and the target thickness to obtain the mirror material volume fraction and the target thickness of each control point in the mirror sub-region; The sample set comprises a plurality of sample data, and the sample data comprises a material volume fraction, a thickness, a total mass reference value, and a free vibration fundamental frequency reference value; The construction of the sample set comprises: randomly initializing a material distribution and a geometric model to obtain the material volume fraction and the thickness of each control point; determining a spatial thermal field of the multi-dimensional functionally graded material based on high-throughput parallel geometric analysis; determining a total mass reference value and a free vibration fundamental frequency reference value of the multi-dimensional functionally graded material based on the spatial thermal field.

2. The method of optimal design of multi-dimensional functionally graded materials according to claim 1, wherein, The training of the initial material prediction model based on the sample set to obtain the trained material performance prediction model comprises: dividing the sample set into a training set and a verification set at a preset ratio; training the initial material performance prediction model based on the training set to obtain a performance prediction model to be verified; verifying the performance prediction model to be verified based on the verification set, and when the verification is passed, the performance prediction model to be verified is the material performance prediction model.

3. The method of optimal design of multi-dimensional functionally graded materials according to claim 1, wherein, The material performance prediction model comprises a first three-dimensional convolution module, a first pooling layer, a plurality of second three-dimensional convolution modules, a flattening layer, and a full connection layer connected in sequence, and each of the first three-dimensional convolution module and the second three-dimensional convolution modules comprises a three-dimensional convolution layer, a batch normalization layer, and an activation function layer.

4. An apparatus for optimal design of a multi-dimensional functionally graded material, characterized by, The device is suitable for the optimization design method of the multi-dimensional functionally graded material, and the device comprises: a multi-dimensional functionally graded material construction unit configured to construct a multi-dimensional functionally graded material based on a non-uniform rational B-spline basis function; the multi-dimensional functionally graded material comprises a plurality of control points; The material performance prediction model training unit is configured to construct a sample set and train an initial material performance prediction model based on the sample set to obtain a trained material performance prediction model; The material parameter optimization design unit is configured to construct a multi-objective optimization function with the minimum total mass and the maximum free vibration fundamental frequency as targets, and iteratively solve the multi-objective optimization function to obtain the optimized material volume fraction and the optimized thickness of the control point. In the process of iteratively solving the multi-objective optimization function, the predicted performance is determined based on the material performance prediction model.

5. An optimization design apparatus characterized by comprising: The memory is configured to store a program. The processor is coupled to the memory and configured to execute the program stored in the memory to implement the steps of the optimization design method of the multi-dimensional functionally graded material according to any one of claims 1 to 3. The memory is configured to store a program or instructions readable by a computer, which can implement the steps of the optimization design method of the multi-dimensional functionally graded material according to any one of claims 1 to 3 when executed by a processor.

6. A computer-readable storage medium, characterized in that, ​

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