Dot matrix metamaterial design method based on rapid restart intelligent algorithm

Abstract

The invention relates to a dot matrix metamaterial design method based on a rapid restart intelligent algorithm, provides an improved ESPSO algorithm based on a rapid restart strategy, and realizes efficient solution of dot matrix metamaterial multi-dimensional design variables. The optimization process of the algorithm is periodically refreshed by adopting a quick restart strategy, so that the risk that the algorithm is caught in local convergence is avoided, the algorithm can be ensured to explore a design space in detail and fully to obtain a globally optimal solution, and the solution obtained by improving the ESPSO algorithm can be better on the premise of ensuring the same operation times. Aiming at dot matrix metamaterial design under complex service conditions, the improved ESPSO intelligent algorithm is adopted to realize independent design of diameters of all rod pieces in unit cells of the dot matrix metamaterial, the dot matrix rod pieces are allowed to be deleted and increased, the design flexibility of the dot matrix metamaterial is remarkably improved, the design space of the dot matrix metamaterial is fully expanded, and the design cost of the dot matrix metamaterial is reduced. And the mechanical property of the dot matrix metamaterial is improved.

Description

Technical Field

[0001] The invention relates to a lattice metamaterial design method, and in particular to a lattice metamaterial design method based on a fast restart intelligent algorithm. Background Art

[0002] Lattice metamaterial is a high-porosity material composed of unit cells composed of rods arranged periodically and repeatedly in space. It has superior mechanical advantages such as light weight, high specific strength / specific stiffness, high impact energy absorption rate, and excellent multifunctional properties such as heat insulation, sound insulation and vibration reduction, and biocompatibility. It has extremely important application value in many fields such as aviation, aerospace, navigation, vehicles, national defense, and biomedicine. At present, the configuration design of lattice metamaterials is mostly based on experiments or empirical improvements, and it is difficult to obtain innovative lattice configurations. The research on the mechanical properties of lattice metamaterials mainly focuses on the research of their inherent mechanical properties, and less consideration is given to the optimization of the mechanical properties of lattice metamaterials under complex service conditions, resulting in the failure to fully utilize the design space of lattice metamaterials, which seriously restricts the improvement of the mechanical properties of lattice metamaterials. The intelligent optimization algorithm has the advantages of simple principle, convenient implementation, and easy convergence to the global optimal solution. It has a wide range of applications in complex optimization problems (minimization) and is very suitable for free configuration optimization of lattice metamaterials under complex service conditions.

[0003] Regarding the optimization design of lattice metamaterials, relevant technicians in this field have done some relevant research, such as document 1: "S. Wang, Y. Ma, Z. Deng, Stretching-dominated truss lattice materials: Elastic anisotropy evaluation, control, and design, Composite Structures, 2022, 298: 116004." An analytical homogenization formula that takes lattice geometric parameters, matrix material properties, and load direction as independent variables was proposed to achieve anisotropic design of stretch-dominated lattice materials. However, this method did not further carry out the configuration optimization of lattice materials to fully explore the design space of lattice materials and give full play to the potential of materials. Reference 2: "L.Bai C.Gong X.ChenJ.Zheng J.Yang K.Li Y.Sun Heterogeneous compressive responses of additively manufactured Ti-6Al-4V lattice structures by varying geometric parameters of cells, International Journal of Mechanical Sciences, 2022, 214: 106922." Lattice materials with different morphologies and relative densities were designed by adjusting the geometric parameters of the lattice unit cells to obtain customized mechanical properties. However, this method does not consider the lattice material configuration design under actual service conditions, and cannot give full play to the material potential and improve the mechanical properties of the structure. Reference 3: "Maurizi M, Gao C, Berto F. Inverse design of truss lattice materials with superior buckling resistance. npj Computational Materials, 2022, 8 (1): 247." A method for designing assembled lattice materials based on deep learning and genetic algorithms was proposed. Lattice materials with excellent anti-buckling properties were obtained by assembling lattice unit cells of different configurations. However, this method does not consider the unit cell configuration optimization of the lattice material, and the diameters of all rods in the lattice unit cell are equal, which limits the design space of the lattice material and cannot fully improve the mechanical properties of the structure.

[0004] Aiming at the design problem of high-performance lattice metamaterials under complex service conditions, the present invention proposes a lattice metamaterial intelligent optimization design method with free configuration based on the particle swarm intelligent optimization algorithm (ESPSO) assisted by an approximate model. The method takes the mechanical properties of lattice materials under complex service conditions as the design target, independently optimizes the geometric parameters of each component rod of the lattice metamaterial, and deletes the lattice rods with low load-bearing efficiency in the optimization process, so as to fully explore the lattice design space and obtain the innovative design of the lattice metamaterial configuration, so as to maximize the mechanical properties of the lattice metamaterial. At the same time, in view of the risk that the ESPSO algorithm is very easy to fall into local convergence, the present invention adopts a fast restart strategy to regularly refresh the optimization process of the intelligent algorithm, and proposes an improved ESPSO algorithm to ensure that the algorithm can explore the design space more thoroughly and fully to obtain the global optimal solution, while ensuring the stability and efficiency of the algorithm iteration convergence process. Summary of the invention

[0005] In view of the above problems, the present invention provides a lattice metamaterial design method based on a fast restart intelligent algorithm.

[0006] The present invention adopts the following technical solutions:

[0007] A lattice metamaterial design method based on a fast restart intelligent algorithm comprises the following steps:

[0008] Step 1. The lattice structure is composed of periodically repeated lattice metamaterial cells, and the lattice metamaterial cell is taken as the object to be optimized. The lattice metamaterial cell to be optimized is composed of rods connecting predefined nodes. The lattice rod is composed of a cylinder and two spheres at its two ends. The geometric shapes of the cylinder and the sphere are described by an explicit topological function based on the level set to achieve an explicit geometric description of the lattice rod; the rods are used to connect the predefined nodes to form the initial design of the lattice metamaterial cell;

[0009] The explicit topological description model of the lattice member based on the level set is:

[0010]

[0011] in

[0012] φ(x)=max(φ c (x,y,z),φ s1 (x,y,z),φ s2 (x,y,z)),

[0013] φ c (x,y,z)=min(φ c1 (x,y,z),φ c2 (x,y,z)),

[0014] φ c1 (x,y,z)=(L / 2) 2 -(cosθ·L d ) 2 ,φ c2 (x,y,z)=(t / 2) 2 -(sinθ·L d ) 2 ,

[0015]

[0016]

[0017]

[0018] φ s1 (x,y,z)=(t / 2) 2 -(x-x1) 2 +(y-y1) 2 +(z-z1) 2 ,

[0019] φ s2 (x,y,z)=(t / 2) 2 -(x-x2) 2 +(y-y2) 2 +(z-z2) 2

[0020] In the formula, represents the spatial design domain of the lattice metamaterial, Ω represents the solid area where the rod part is located, is the boundary of the rod structure. The lattice rod consists of a cylinder and two spheres, and their level set functions are φ c (x,y,z),φ c1 (x,y,z),φ c2 (x, y, z); the centers of the ends of the cylinder are (x1, y1, z1) and (x2, y2, z2), which are also the centers of the two spheres, that is, the diameter of the cylinder t is equal to the diameter of the two spheres. (x0, y0, z0) and L are the coordinates of the center point of the cylinder and the length of the rod, respectively.

[0021] Step 2: Taking the minimum overall flexibility of the lattice structure under complex service conditions as the optimization goal, a mathematical optimization model with the diameters of each rod of the lattice metamaterial unit cell as the design variables is established:

[0022] Find:t=(t1,t2,...,t j ),j=1,2,...,D

[0023] Minimize:C(t)=F T U=U T KU

[0024] Subjectto:G(t)=V(t)-fV0≤0,

[0025] F=KU,

[0026] 0≤t min ≤t j ≤t max .

[0027] where t1, t2, ..., t j is the diameter of the different rods to be determined, D is the total number of rods, C represents the overall flexibility of the lattice structure, F is the total load matrix, U is the total displacement matrix generated under the load, K is the overall stiffness matrix of the lattice structure, G represents the volume rate constraint of the lattice structure, V(t) and V0 represent the material area volume and design domain volume of the lattice unit cell respectively, f is the given material volume rate, t min and t max are the upper and lower limits of the rod diameter;

[0028] Step 3: Use the improved ESPSO algorithm to obtain the optimal diameter of each rod. The specific steps are as follows:

[0029] Step 3.1, generate an initial population. Each particle in the population has D dimensions. The position of the particle in each dimension represents the possible diameter of a rod. A total of D dimensions represent the possible diameters of all rods.

[0030] Step 3.2, using radial basis function (RBF) to establish the global and local approximate models in the particle swarm optimization algorithm, where the global approximate model is constructed in the entire design space based on all evaluated particle points, and the local approximate model is constructed in the neighborhood of the particle;

[0031] Step 3.3: Use the following strategy to update the particle speed and position to obtain the optimal position of the particle, and delete the particles whose rod diameter is smaller than the preset threshold in the optimization process to obtain the optimal position of the particle in this iteration;

[0032]

[0033] xid (t+1)= xid (t)+ vid (t+1)

[0034] in

[0035]

[0036] d represents the dth dimension of the optimization problem, v i (t) = [v i1 (t),v i2 (t),...,v id (t)] and x i (t) = [x i1 (t),x i2 (t),...,x id (t)] are the velocity and position of the ith particle at the tth iteration, respectively. i (t) = [p i1 (t),p i2 (t),...,p id (t)] is the historical optimal position reached by the individual i-th particle. g (t) = [p g1 (t),p g2 (t),...,p gd (t)] is the global optimal position of all particles. is the predicted response value of the global RBF model constructed by all particles in the design space; X Gbest It is the optimal value point in the entire design space, that is, the global optimal position. is the particle p i (t) The predicted response value of the local RBF model composed of particles in the neighborhood; X Nbest is the optimal value point in the neighborhood, that is, the local optimal position. i (t) Update the position by tracking these two optimal values. r1 and r2 are two random numbers uniformly distributed in the range [0,1]; c1 and c2 are acceleration factors, which are usually greater than zero. Where φ = c1 + c2. Usually φ is greater than 4, so c1 and c2 are 2.05 respectively. k is a constant in the range [0,1], usually 0.729;

[0037] Step 3.4: Determine whether the maximum number of iterations has been reached. If yes, go to the next step. Otherwise, use the optimal particle position obtained in this iteration to update the population and proceed to step 3.1 again.

[0038] Step 3.5: Output the optimal position of the particle obtained in the last iteration, and obtain the optimal diameter value of each rod corresponding to the optimal particle.

[0039] Furthermore, in step 3.1, for the global approximate model, the number of sample points is consistent with the number of particle groups determined in advance, and is generally set to 30; for the local approximate model, the number of sample points is generally set to be greater than 5D.

[0040] Furthermore, in step 3.4, the maximum number of iterations is more than 3 times.

[0041] After adopting the above technical solution, the present invention has the following advantages compared with the prior art:

[0042] 1. Compared with the existing lattice metamaterial design method, the technical solution provided by the present invention proposes a new free-configuration lattice metamaterial design method. Specifically, the independent design of the diameters of all rods in the lattice unit cell is realized, and the rods with low load-bearing efficiency in the lattice unit cell are allowed to be deleted, which improves the design flexibility of the lattice metamaterial and expands the design space of the lattice metamaterial, so as to fully improve the mechanical properties of the lattice metamaterial.

[0043] 2. The present invention adopts an explicit topological geometric description function based on a level set, thereby achieving explicit description and precise control of the geometric configuration of the lattice metamaterial and ensuring smoothness and clarity of the geometric structure boundary of the lattice metamaterial.

[0044] 3. The present invention proposes an improved ESPSO algorithm based on a fast restart strategy, which realizes the efficient solution of multi-dimensional design variables of lattice metamaterials. Under the premise of ensuring the same number of operations, the new operation mode can obtain a better solution. In other words, to obtain the same optimal solution, the new method requires fewer iterations; since the optimization process of the algorithm is regularly refreshed by the fast restart strategy, the risk of the intelligent optimization algorithm falling into local convergence is avoided, ensuring that the algorithm can explore the design space more thoroughly and fully to obtain the global optimal solution, while ensuring the stability and efficiency of the iterative convergence process.

[0045] 4. The present invention provides a free-configuration lattice metamaterial design method based on a fast restart intelligent algorithm, which not only optimizes the geometric parameters of each rod in the lattice metamaterial, but also allows the deletion and addition of lattice rods, thus realizing the free design of lattice metamaterial configurations under complex service conditions. Compared with traditional lattice material design, it greatly expands the lattice material design space, gives full play to the material potential, and can effectively improve the mechanical properties of the lattice material and reduce the weight of the structure.

[0046] The present invention is described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 (a) is a schematic diagram of the design domain of the four-point support structure, and (b) is a schematic diagram of the initial design configuration of the lattice unit cell;

[0048] Figure 2 (a) is a schematic diagram of the initial design of the lattice unit cell, and (b) is a diagram of the optimal design structure;

[0049] Figure 3(a) shows the initial design of the lattice unit cell and its elastic modulus surface diagram; (b) shows the optimal design of the lattice unit cell and its elastic modulus surface diagram;

[0050] Figure 4 Schematic diagram of the optimal design lattice unit cell 3×3×3 periodic arrangement;

[0051] Figure 5 Schematic diagram of the optimal design lattice unit cell 3×3×3 periodic arrangement;

[0052] Figure 6 Schematic diagram of the final lattice design of the four-point support structure;

[0053] Figure 7 The figure is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0054] The principles and features of the present invention are described below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0055] The principles and features of the present invention are described below in conjunction with the accompanying drawings. The implementation scheme is illustrated by a four-point support structure example. The example is only used to explain the present invention and is not used to limit the scope of the present invention.

[0056] To achieve the above object, according to the present invention, a free-configuration lattice metamaterial design method based on a fast restart intelligent algorithm is provided, and the method comprises the following steps:

[0057] (a) The lattice metamaterial unit cell to be optimized is formed by connecting predefined nodes with rods. The rods are composed of a cylinder and spheres at both ends. The spheres can ensure that the two rods are perfectly connected at the nodes. The geometric shapes of the cylinder and the two spheres are described by explicit geometric topological functions based on level sets. First, the design domain of the three-dimensional lattice unit cell to be optimized is discretized into a finite element grid. The node coordinates of the finite element grid represent the position of the node in space. A four-dimensional level set function is formed by defining level set values ​​on the nodes in the three-dimensional lattice design domain. The level set values ​​represent the minimum distance from the node to the structural boundary. The zero isosurface of the four-dimensional level set function is the structural boundary of the three-dimensional lattice. Different from the traditional method of defining the level set function by using free functions or radial basis functions, the present invention defines the level set function by using the mathematical relationship between the sphere and the cylinder with explicit mathematical relationships, so as to achieve the explicit description of the structural geometric boundary of the three-dimensional lattice and achieve the purpose of accurately controlling the structural geometric characteristics by regulating the level set function parameters. Subsequently, the predefined nodes are connected using the described bars to form an initial design of the three-dimensional lattice unit cell.

[0058] (b) Taking the lattice structure under complex service conditions as the object to be optimized, the lattice structure is discretized into several periodic lattice cells. First, the equivalent elastic tensor of the three-dimensional lattice cell is calculated by the homogenization method, and the unit stiffness matrix of the lattice cell is further calculated; then, the global stiffness matrix of the entire lattice structure is obtained by assembling the unit stiffness matrix of the lattice cell, and the finite element analysis of the lattice structure is carried out to obtain the overall flexibility of the entire lattice structure; then, with the material volume rate given by the lattice cell as the constraint condition and the minimum overall flexibility of the lattice structure under complex service conditions as the optimization goal, a mathematical optimization model with the diameter of each rod of the lattice cell as the design variable is established.

[0059] (c) The improved ESPSO algorithm is used to efficiently solve the mathematical optimization model in step (b), and the global optimal particle is the optimal solution of the model. First, the initial particle swarm number of the ESPSO algorithm is set, which is generally five times the number of design variables, and the fitness of each particle is evaluated, and the deletion threshold of the design variables is set;

[0060] Secondly, the optimal solution information of the global and local approximate models is used to update the velocity and position of the particles. Particles with a velocity less than the deletion threshold are assigned a value of 0. Then, the volume fraction of the lattice structure is calculated based on the optimal particle searched by the algorithm to see if it meets the volume rate constraint. If so, the flexibility of the lattice structure is calculated through the optimization model. If not, a better particle is searched again.

[0061] Finally, the algorithm optimization process is refreshed periodically through a restart strategy, so that the optimal particle at the end of the previous optimization becomes the initial particle for the next optimization, ensuring a more detailed exploration of the design space to obtain the global optimal solution, and finally obtaining a multi-parameter lattice structure with optimized performance.

[0062] As a further preferred embodiment, in step (a), taking a three-dimensional lattice unit cell as an example, the lattice rod explicit topology description model based on the level set is:

[0063]

[0064] in

[0065] φ(x)=max(φ c (x,y,z),φ s1 (x,y,z),φ s2 (x,y,z)),

[0066] φ c (x,y,z)=min(φ c1 (x,y,z),φ c2 (x,y,z)),

[0067] φ c1(x,y,z)=(L / 2) 2 -(cosθ·L d ) 2 ,φ c2 (x,y,z)=(t / 2) 2 -(sinθ·L d ) 2 ,

[0068]

[0069] φ s1 (x,y,z)=(t / 2) 2 -(x-x1) 2 +(y-y1) 2 +(z-z1) 2 ,

[0070] φ s2 (x,y,z)=(t / 2) 2 -(x-x2) 2 +(y-y2) 2 +(z-z2) 2

[0071] In the formula, represents the spatial design domain of the lattice metamaterial, Ω represents the solid area where the rod part is located, is the boundary of the rod structure. The lattice rod consists of a cylinder and two spheres, and their level set functions are φ c (x,y,z),φ c1 (x,y,z),φ c2 (x,y,z); the centers of the ends of the cylinder are (x1,y1,z1) and (x2,y2,z2), which are also the centers of the two spheres, that is, the diameter of the cylinder t is equal to the diameter of the two spheres. (x0, y0, z0) and L are the coordinates of the center point of the cylinder and the length of the rod respectively.

[0072] As a further preferred embodiment, in step (b), the formula for calculating the equivalent elastic tensor of the lattice unit cell using the homogenization method can be expressed as:

[0073]

[0074] Among them, |Y| represents the volume of the lattice unit cell, i,j,k,l=1,2,3,...,d is the spatial dimension of the design problem, represents the initial unit test strain, which contains six independent unit strains in a three-dimensional problem, namely (1,0,0,0,0,0) T 、(0,1,0,0,0,0) T、(0,0,1,0,0,0) T 、(0,0,0,1,0,0) T 、(0,0,0,0,1,0) T 、(0,0,0,0,0,1) T . Represents the unknown strain field, which is generated in the lattice unit cell after the initial unit test strain field is applied, and can be obtained by solving the following linear elastic equilibrium equation:

[0075]

[0076] Where, ν i is the virtual displacement field, Represents the kinematically permissible displacement space under periodic boundary conditions.

[0077] After obtaining the equivalent elastic tensor of the unit cell, the unit stiffness matrix k of the lattice unit cell is e The following formula can be used for calculation:

[0078]

[0079] Among them, Ω m is the domain of the mth finite element, Ne is the total number of finite elements, and B is the strain-displacement matrix.

[0080] The global stiffness matrix K of the lattice structure can be obtained by assembling the unit stiffness matrix, as shown in the following formula:

[0081]

[0082] After obtaining the overall stiffness matrix, the displacement field of the lattice structure can be obtained by solving the equilibrium equation of the lattice structure, and the overall flexibility value of the lattice structure can be further calculated:

[0083] F=KU

[0084] C=F T U=U T KU

[0085] As a further preferred embodiment, in step (b), the geometric description parameters of the lattice unit cell are used as design variables, the given material usage is used as a constraint condition, and the minimization of the overall flexibility of the lattice structure is used as an objective function. The optimization mathematical model is constructed as shown in the following formula:

[0086] Find:t=(t1,t2,...,t j ),j=1,2,...,D

[0087] Minimize:C(t)=F T U=U TKU

[0088] Subjectto:G(t)=V(t)-fV0≤0,

[0089] F=KU,

[0090] 0≤t min ≤t j ≤t max .

[0091] where t1, t2, ..., t j is the diameter of the different rods to be determined, D is the total number of rods, C represents the overall flexibility of the lattice structure, F is the total load matrix, U is the total displacement matrix generated under the load, K is the overall stiffness matrix of the lattice structure, G represents the volume rate constraint of the lattice structure, V(t) and V0 represent the material area volume and design domain volume of the lattice unit cell respectively, f is the given material volume rate, t min and t max are the upper and lower limits of the rod diameter;

[0092] As a further preferred embodiment, in step (c), the ESPSO algorithm is used to find the optimal diameter value of each rod of the three-dimensional lattice unit cell. By introducing the BRF approximation model, the global and local approximation models in the particle swarm optimization algorithm are established, wherein the global approximation model is constructed in the entire design space based on all evaluated particle points, and the local approximation model is constructed in the neighborhood of the particle. The RBF model used in the present invention is defined as follows: Assuming there are n sample points x1, x2, ..., x n ∈R D , their responses are f(x1),f(x2),…f(x n ), then the RBF approximate model established by these n sample points can be expressed as:

[0093]

[0094] where Φ i (·) is the i-th basis function, ||·|| is the Euclidean norm, λ i is the weight coefficient of the i-th basis function. This paper adopts the cubic basis function: φ(r) = r 3 , in addition, p(x) is a first-order polynomial: b T x+a. In order to establish an accurate global and local approximate model, for the global approximate model, the number of sample points is consistent with the number of particle groups determined in advance, generally set to 30; for the local approximate model, the number of sample points is generally set to be greater than 5D, where D is the number of design variables.

[0095] In order to further improve the optimization efficiency of the approximate model collaborative PSO algorithm, a new strategy is adopted in the ESPSO algorithm to update the particle speed. The update method is as follows:

[0096]

[0097] xid (t+1)= xid (t)+ vid (t+1)

[0098] in

[0099]

[0100] d is the dth dimension of the optimization problem, v i (t) = [v i1 (t),v i2 (t),...,v id (t)] and x i (t) = [x i1 (t),x i2 (t),...,x id (t)] are the velocity and position of the ith particle at the tth iteration, respectively. i (t) = [p i1 (t),p i2 (t),...,p id (t)] is the historical optimal position reached by the individual i-th particle. g (t) = [p g1 (t),p g2 (t),...,p gd (t)] is the global optimal position of all particles. is the predicted response value of the global RBF model constructed by all particles in the design space; X Gbest It is the optimal value point in the entire design space, that is, the global optimal position. is the particle p i (t) The predicted response value of the local RBF model composed of particles in the neighborhood; X Nbest is the optimal value point in the neighborhood, that is, the local optimal position. i (t) Update the position by tracking these two optimal values. r1 and r2 are two random numbers uniformly distributed in the range [0,1]; c1 and c2 are acceleration factors, which are usually greater than zero. Where φ = c1 + c2. Usually φ is greater than 4, so c1 and c2 are 2.05 respectively. k is a constant in the range [0,1], usually 0.729.

[0101] In order to further expand the design space of lattice unit cells and give full play to the potential of materials, lattice rods with low load-bearing efficiency are allowed to be deleted during the optimization process of the ESPSO algorithm to improve the mechanical properties of the lattice structure. At the same time, in view of the risk that the ESPSO algorithm is very likely to fall into local convergence, the present invention adopts a fast restart strategy to regularly refresh the optimization process of the intelligent algorithm, ensuring that multiple cycles of the optimization algorithm are iterated at the same computational cost, ensuring that the algorithm explores the design space more thoroughly to obtain the global optimal solution.

[0102] 1) Deletion strategy: As the optimization process progresses, the main force-bearing rods will gradually become thicker, while the secondary force-bearing rods will gradually become thinner. If the force on the rod is too small, that is, the load-bearing efficiency is too low, then the value of its diameter t should be 0, which means that the rod is deleted to improve material utilization and enhance the mechanical properties of the lattice. Specifically, during the optimization process, when t is less than the set threshold, that is, t n <t min (delete threshold), then t n The diameter of is assigned to 0, that is, the nth member is deleted. Deletion threshold t min It is usually set to the minimum structure size allowed in the manufacturing process or the minimum mesh size for accurate FEA.

[0103] 2) Restart strategy: The particle swarm optimization algorithm assisted by the proxy model changes the entire population from disordered evolution to ordered evolution by sharing particle information, but it is easy to fall into local convergence due to the transition of the optimal solution. If there is no suitable mechanism, it is impossible to jump out of the local trap, resulting in a lack of diversity in the results and even a lack of high-quality solutions. To this end, the present invention proposes an improved algorithm based on a restart strategy based on the auxiliary particle swarm optimization algorithm assisted by the proxy model to avoid the algorithm from falling into local convergence. Once the population falls into local convergence, the restart mechanism begins to redistribute the population particles in space and guide the particles to find a better solution in the global area based on the previously found optimal solution.

[0104] The above is an example of the best implementation of the present invention, and the parts not described in detail are common knowledge of ordinary technicians in the field. The protection scope of the present invention shall be based on the content of the claims, and any equivalent transformation based on the technical enlightenment of the present invention is also within the protection scope of the present invention.

Claims

1. A lattice metamaterial design method based on a fast restart intelligent algorithm, characterized in that: The following steps are involved: Step 1, establish a lattice structure model, the lattice structure is composed of periodically repeated lattice metamaterial unit cells, take the lattice metamaterial unit cell as the object to be optimized, the lattice metamaterial unit cell to be optimized is a lattice rod composed of pre-defined nodes connected by rods, the lattice rod is composed of a cylinder and two spheres at both ends thereof, and the geometric shapes of the cylinder and the sphere are described by an explicit topological function based on a level set to realize the geometric explicit description of the lattice rod; the rods are used to connect the pre-defined nodes to form an initial design of the lattice metamaterial unit cell; The explicit topological description model of the lattice rod based on the level set is: in φ(x)=max(φ c (x,y,z),φ s1 (x,y,z),φ s2 (x,y,z)), φ c (x,y,z)=min(φ c1 (x,y,z),φ c2 (x,y,z)), φ c1 (x,y,z)=(L / 2) 2 -(cosθ·L d ) 2 ,φ c2 (x,y,z)=(t / 2) 2 -(sinθ·L d ) 2 , d x2 =x2-x0,d y2 =y2-y0,d z2 =z2-z0,d x =x-x0,d y =y-y0,d z =z-z0, φ s1 (x,y,z)=(t / 2) 2 -(x-x1) 2 +(y-y1) 2 +(z-z1) 2 , φ s2 (x,y,z)=(t / 2) 2 -(x-x2) 2 +(y-y2) 2 +(z-z2) 2 In the formula, represents the spatial design domain of the lattice metamaterial, Ω represents the solid area where the rod part is located, is the boundary of the rod structure; the lattice rod consists of a cylinder and two spheres, and their level set functions are φ c (x,y,z),φ c1 (x,y,z),φ c2 (x, y, z); the centers of the ends of the cylinder are (x1, y1, z1) and (x2, y2, z2), which are also the centers of the two spheres, that is, the diameter t of the cylinder is equal to the diameters of the two spheres; (x0, y0, z0) and L are the coordinates of the center point of the cylinder and the length of the rod respectively; Step 2: Taking the minimum overall flexibility of the lattice structure under complex service conditions as the optimization goal, a mathematical optimization model with the diameters of each rod of the lattice metamaterial unit cell as the design variables is established: Find:t=(t1,t2,...,t j ),j=1,2,...,D Minimize:C(t)=F T U=U T KU Subjectto:G(t)=V(t)-fV0≤0, F=KU, 0≤t min ≤t j ≤t max . where t1, t2, ..., t j is the diameter of the different rods to be determined, D is the total number of rods, C represents the overall flexibility of the lattice structure, F is the total load matrix, U is the total displacement matrix generated under the load, K is the overall stiffness matrix of the lattice structure, G represents the volume rate constraint of the lattice structure, V(t) and V0 represent the material area volume and design domain volume of the lattice unit cell respectively, f is the given material volume rate, t min and t max are the upper and lower limits of the rod diameter; Step 3: Use the improved ESPSO algorithm to obtain the optimal diameter of each rod. The specific steps are as follows: Step 3.1, generate an initial population. Each particle in the population has D dimensions. The position of the particle in each dimension represents the possible diameter of a rod. A total of D dimensions represent the possible diameters of all rods. Step 3.2, using radial basis function to establish the global RBF model and local RBF model in the particle swarm optimization algorithm, where the global RBF model is constructed in the entire design space based on all evaluated particle points, and the local RBF model is constructed in the neighborhood of the particle; Step 3.3: Use the following strategy to update the particle speed and position to obtain the optimal position of the particle, and delete the particles whose rod diameter is smaller than the preset threshold in the optimization process to obtain the optimal position of the particle in this iteration; xid (t+1)= xid (t)+ vid (t+1) in d represents the dth dimension of the optimization problem, v i (t) = [v i1 (t),v i2 (t),...,v id (t)] and x i (t) = [x i1 (t),x i2 (t),...,x id (t)] are the velocity and position of the ith particle at the tth iteration; p i (t) = [p i1 (t),p i2 (t),...,p id (t)] is the historical optimal position reached by the i-th particle; p g (t) = [p g1 (t),p g2 (t),...,p gd (t)] is the global optimal position of all particles; is the predicted response value of the global RBF model constructed by all particles in the design space; X Gbest is its optimal value point in the entire design space, that is, the global optimal position; is the particle p i (t) The predicted response value of the local RBF model composed of particles in the neighborhood; X Nbest is the optimal value point in the neighborhood, that is, the local optimal position; particle p i (t) Update the position by tracking these two optimal values; r1 and r2 are two random numbers uniformly distributed in the range [0,1]; c1 and c2 are acceleration factors; where φ = c1 + c2; Step 3.4: Determine whether the maximum number of iterations has been reached. If yes, go to the next step. Otherwise, use the optimal particle position obtained in this iteration to update the population and proceed to step 3.1 again. Step 3.5: Output the optimal position of the particle obtained in the last iteration, and obtain the optimal diameter value of each rod corresponding to the optimal particle.

2. The lattice metamaterial design method based on the fast restart intelligent algorithm according to claim 1, characterized in that: In step 3.1, for the global approximate model, the number of sample points is consistent with the number of particle groups determined in advance; for the local approximate model, the number of sample points is generally set to be greater than 5D.

3. The lattice metamaterial design method based on the fast restart intelligent algorithm according to claim 1, characterized in that: In step 3.4, the maximum number of restarts is more than 3 times.

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