Optical bench structure cross-scale optimization design method and device considering mirror surface shape

Abstract

The application discloses a mirror shape preserving optical bench structure cross-scale optimization design method and device, and relates to the technical field of optical engineering. The method comprises the following steps: in the offline stage, parameterized point array modeling and equivalent performance prediction are carried out, and a prediction model is established. In the online stage, the optical bench structure is selected, the design domain is determined and the finite element is discretized, then the entity and point array areas are divided, the load and boundary conditions are applied, and the design variables are defined. The prediction model is called to obtain the point array mechanical performance to calculate the structure strain energy, the mirror node displacement is extracted, and the mirror surface shape information is obtained by fitting. An optimization model is established with the minimum structure strain energy as the objective function and the mirror surface shape information as the constraint, and optimization iteration is carried out with the aid of sensitivity information. If the optimization model does not converge, the design variables are adjusted, the constraints are redefined, and the iteration is continued. If the optimization model converges, the optical bench cross-scale shape preserving optimization result is obtained. The method solves the problem that the traditional design method cannot meet the demand of a new generation of optical mechanical system in terms of light weight, stiffness and mirror shape preservation.

Description

Technical Field

[0001] This application relates to the field of optical engineering technology, and in particular to a method and apparatus for cross-scale optimization design of optical bench structures considering mirror conformal properties. Background Technology

[0002] With the rapid development of deep space exploration, high-resolution satellite observation, and laser communication, the next generation of space optomechanical systems is evolving towards larger apertures, lighter weight, and higher precision. As the core framework of the optomechanical system, the structural design of the optical bench is crucial for maintaining the spatial relative stability of optical components.

[0003] Existing optical bench structures primarily employ traditional machining methods, and optimization designs are often limited to a single macroscopic scale, failing to fully utilize the designability of microstructures to achieve optimal performance matching. Furthermore, current optical bench structure design optimization targets mainly focus on the overall mechanical properties of the structure, neglecting the impact of local conformal characteristics on optical performance, thus failing to maximize the load-bearing potential of the structure and materials.

[0004] Therefore, traditional optical bench structure design methods are insufficient to meet the requirements of next-generation optical engine systems in terms of lightweighting, rigidity, and mirror conformal preservation. Summary of the Invention

[0005] In this embodiment, a cross-scale optimization design method for optical bench structures that considers mirror conformal properties is provided, which solves the problem that traditional optical bench structure design methods are difficult to meet the requirements of next-generation optomechanical systems in terms of lightweighting, stiffness, and mirror conformal properties.

[0006] In a first aspect, embodiments of this application provide a cross-scale optimization design method for an optical bench structure considering mirror conformal properties. This method includes: in an offline stage, modeling and predicting the equivalent performance of a parametric lattice, establishing an equivalent performance prediction model for the lattice structure; in an online stage, selecting the optical bench structure, determining the design domain and non-design domain based on design requirements and the assembly environment, and performing finite element discretization on the entire structure; based on the discretized design domain and non-design domain, determining the solid region and lattice region, applying loads and boundary conditions, and defining design variables requiring topology optimization; wherein the design variables include the pseudo-density of the solid region and the pseudo-density and lattice parameters of the lattice region; calling the equivalent performance prediction model for the lattice structure established in the offline stage, inputting the lattice parameters of each element in the lattice region into the equivalent performance prediction model, and based on the current design... The mechanical properties of the lattice structure are obtained from variables. These properties are used to calculate the stiffness matrix of the structure, thereby obtaining the strain energy and deformation information of the overall structure. The normal displacement of the mirror nodes in the non-design domain is extracted, and the mirror surface shape information is obtained through Zernike polynomial fitting. The objective function is designed with the goal of minimizing the structural strain energy, and the mirror surface shape information is used as the conformal constraint. An optimization model is established based on the objective function and the conformal constraint, and the sensitivity is derived to carry out optimization design. The optimization model is then solved. Here, the sensitivity is the partial derivative of the objective function or constraint function with respect to the design variables. The convergence of the optimization model is determined. If it does not converge, the values ​​of the design variables are adjusted according to the sensitivity, and the conformal constraint is redefined according to the current mirror surface shape information. Iterative optimization continues. If it converges, the cross-scale conformal optimization result of the optical bench structure is obtained.

[0007] In one possible implementation, during the offline phase, modeling and equivalent performance prediction of the parameterized dot matrix are performed, and an equivalent performance prediction model of the dot matrix structure is established, including: introducing dot matrix parameters. Control lattice configuration; among which, Density parameter, describing the proportion of material used in a single cell. For configuration parameters, Used to control the amount of material used for vertical rods Used to control the amount of material used for horizontal bars. Material usage for diagonal braces is controlled; a BCC lattice structure with an outer frame is selected as the object, and the braces are divided into three types according to the additive manufacturing printing direction: vertical braces parallel to the printing direction, horizontal braces perpendicular to the printing direction, and diagonal braces; lattice parameters are then used to control the material usage of the diagonal braces. Converted into material usage ratio parameters Satisfying the constraints The actual diameter of each member is determined through numerical calculations, generating a parameterized lattice structure with variable configuration for modeling the parameterized lattice; among which, They are respectively The corresponding proportions; employing a numerical homogenization method, the equivalent elastic matrix is ​​calculated for a parameterized lattice structure with variable configuration. Specifically, this includes: obtaining the equivalent elastic tensor through integration based on the relationship between macroscopic material elastic properties and locally varying strain fields, in order to calculate the equivalent elastic matrix; establishing lattice parameters... The mapping relationship with the equivalent elasticity matrix is ​​established using a BP neural network to generate a surrogate model. The specific process includes: the input layer is a lattice parameter vector, and the output layer is the independent component vector of the equivalent elasticity tensor; a three-layer BP neural network is constructed, resulting in a complete BP network. : .in, The parameter vector represents the equivalent elasticity matrix of the output lattice structure. The input is a vector of point matrix parameters. The weights from the input layer to the hidden layer. This represents the weights from the hidden layer to the output layer. This is the bias vector of the hidden layer. This represents the bias vector of the output layer. is the activation function, and is the sigmoid function; the network weights and biases are iteratively optimized to minimize the loss function, thereby obtaining an equivalent performance prediction model for the lattice structure.

[0008] In one possible implementation, the process of determining the solid region and lattice region based on the finite element discretization of the design domain and non-design domain, applying loads and boundary conditions, and defining design variables requiring topology optimization includes: further dividing the finite element discretization of the design domain to determine the solid region and lattice region; discretizing the lattice region elements using hexahedral elements; performing tetrahedral discretization based on shared nodes in the solid and lattice regions; applying loads and boundary conditions; extracting the design domain element numbers; defining that each element in the solid region has only one pseudo-density design variable, and each element in the lattice region has five design variables, namely the pseudo-density... With lattice parameters The expression for each element in the solid region having only one pseudo-density design variable is: ;in, This represents a pseudo-density design variable in the solid region. The pseudo density of the first cell in the solid region. The pseudo density of the second unit in the solid region. For the first in the entity region The pseudo density of each unit This represents the total number of elements in the solid region; the expression for the design variable of each element in the lattice region is: ;in, The first dot in the dot matrix region Design variables for each unit, For the first point region Units, For the first point region The pseudo density of each unit For the first point region The unit cell density parameter describes the proportion of material used in each unit cell. For the first lattice region Configuration parameters of each unit, Used to control the amount of material used for vertical rods Used to control the amount of material used for horizontal bars. Used to control the amount of material used for diagonal bracing.

[0009] In one possible implementation, extracting the normal displacement of the mirror nodes in the non-design domain and obtaining the mirror surface shape information through Zernike polynomial fitting includes: extracting the normal displacement of the mirror nodes in the non-design domain. The extracted normal displacement is obtained using Zernike polynomials. Decomposed into linear combinations of Zernike polynomials of various orders as the basis and their corresponding coefficients, the macroscopic normal displacement is... The Zernike polynomial coefficients are obtained by summing Zernike displacements of various orders. Least squares fitting is then used to solve for these coefficients, treating the process as solving for the error between the actual surface shape and the fitted surface shape. Taking the smallest problem, the error The expression is: ;in, This represents the total number of mirror nodes. For the first The weight of each node, For the first Normal displacement at each node For Zernike order, For the first The coefficients of the Zernike polynomial of order 1 For the first Zernike polynomial of order 1 The value at each node Polar radius, Let the polar angle be ; let the error be . right coefficients of the order Zernike polynomial The partial derivatives are 0, so the problem can be expressed as a system of linear equations. The problem to be solved; among which, The incidence matrix is ​​determined by the Zernike basis functions and weights. Let Zernike polynomials be the coefficient vectors. Let be a constant vector, composed of basis functions and normal displacement. A joint decision.

[0010] In one possible implementation, the objective function is designed with minimizing structural strain energy as the goal, and the mirror surface shape information is used as the conformal constraint. An optimization model is established based on the objective function and the conformal constraint, sensitivity is derived for optimization design, and the optimization model is solved. The objective function is: ;in, It is a displacement vector. For transpose operation, Here is the stiffness matrix. Design variables for pseudo-density in the solid region. To optimize the lattice region in the model, design variables; the conformal constraint is: , ;in, To preserve form constraints, For the preset threshold, Before solving The correlation matrix corresponding to the Zernike coefficients of order Zernike. The coefficient vector of the Zernike polynomial in the conformal constraint. For normal displacement, The total number of mirror nodes; the pseudo-density design variable in the solid region of the optimization model is: The design variables in the lattice region of the optimization model are: Y ;in, For the first lattice region The pseudo density of each unit For the first lattice region Density parameters of each unit For the first lattice region Configuration parameters of each unit, The number of elements in the lattice region; the optimized model satisfies the following constraints: , , , ;in, Here is the stiffness matrix. It is a displacement vector. For loads related to design variables, For loads independent of design variables, , The total number of units, The number of units in the lattice region. The total number of entity elements in the design domain. For the first Volume of each unit For the total volume, The upper limit of volume is given; the objective function and conformal constraint conditions for the pseudo-density design variables in the pseudo-solid region are derived respectively. Design variables in the dot matrix area The sensitivity information is obtained; where sensitivity is the partial derivative of the objective function or constraint function with respect to the design variables. The finite element adjoint method is used to efficiently solve the sensitivity of the objective function with respect to the design variables. When solving the sensitivity information of the design variables of the lattice structure, the analytical expression of the neural network is used to solve the sensitivity relationship between each level through the chain rule. Based on the GCMMA algorithm, the obtained sensitivity information is used to optimize the optimization model iteratively.

[0011] In one possible implementation, if the relative rate of change of the objective function between two adjacent iterations is less than or equal to 0.2%, or the maximum change in the design variables is less than 0.01, or the maximum number of iterations does not exceed 300 steps, then the optimization model is considered to have converged. Based on the design variables, the cross-scale conformal optimization design of the optical bench structure is completed. The design variables are read, the actual lattice rod diameter is calculated through the lattice parameters, the optimization results are plotted, and the conformal effect diagram of the mirror is given. The optimization results are converted into an STL file for additive manufacturing.

[0012] Secondly, embodiments of this application provide a cross-scale optimization design device for an optical bench structure considering mirror conformal properties. This device includes: a modeling module, used in the offline stage to model and predict the equivalent performance of a parametric lattice, establishing an equivalent performance prediction model for the lattice structure; a selection module, used in the online stage to select the optical bench structure, determine the design domain and non-design domain based on design requirements and assembly environment, and perform finite element discretization on the entire structure; a determination module, used to determine the solid region and lattice region based on the finite element discretized design domain and non-design domain, apply loads and boundary conditions, and define design variables requiring topology optimization; wherein the design variables include the pseudo-density of the solid region and the pseudo-density and lattice parameters of the lattice region; and an acquisition module, used to call the equivalent performance prediction model of the lattice structure established in the offline stage, input the lattice parameters of each element in the lattice region into the equivalent performance prediction model of the lattice structure, and based on the current... The design variables are used to obtain the mechanical properties of the lattice structure. These mechanical properties are used to calculate the stiffness matrix of the structure, thereby obtaining the overall structural strain energy and deformation information. A fitting module is used to extract the normal displacement of the mirror nodes in the non-design domain and obtain the mirror surface shape information through Zernike polynomial fitting. A solution module is used to design an objective function with the goal of minimizing structural strain energy, using the mirror surface shape information as a conformal constraint. An optimization model is established based on the objective function and conformal constraint, and the sensitivity is derived to carry out optimization design and solve the optimization model. The sensitivity is the partial derivative of the objective function or constraint function with respect to the design variables. A judgment module is used to determine whether the optimization model has converged. If it has not converged, the values ​​of the design variables are adjusted according to the sensitivity, and the conformal constraint conditions are redefined based on the current mirror surface shape information, continuing iterative optimization. If it has converged, the cross-scale conformal optimization result of the optical bench structure is obtained.

[0013] Thirdly, embodiments of this application provide a cross-scale optimization design server for optical bench structures considering mirror conformal design, including a memory and a processor; the memory is used to store computer-executable instructions; the processor is used to execute the computer-executable instructions to implement the method described in the first aspect or any possible implementation of the first aspect.

[0014] Fourthly, embodiments of this application provide a computer-readable storage medium storing executable instructions, which, when executed by a computer, enable the method described in the first aspect or any possible implementation thereof.

[0015] The one or more technical solutions provided in this application have at least the following technical effects: This application provides a cross-scale optimization design method for optical bench structures considering mirror conformal design. By introducing lattice structures into the optical bench structure design, a bridge is successfully built from the force transmission path of macroscopic solid structures to the lattice configuration at the microscopic scale, achieving integrated material and structural design. This innovative breakthrough effectively enhances the "cross-scale" design capability of optical bench structures, opening up new ideas and directions for structural design. This application deeply integrates conformal design principles into the optical bench structure design, using the RMS value (root mean square value) of the optical element mirror surface as a key conformal constraint, realizing multi-disciplinary collaborative optimization design of structural mechanical properties and system optical properties. This greatly improves the efficiency of optimization design, strongly supports the development of next-generation optomechanical systems, and accelerates the development process of optomechanical systems. This application fully leverages the potential of topology optimization design, simultaneously improving the global stiffness, surface shape control of key local areas, and optical performance while achieving structural lightweighting. This ensures that the optical bench, while reducing weight, possesses superior comprehensive performance, meeting the high-precision requirements under complex working conditions. This application provides solid technical support for the structural design of next-generation optomechanical systems, possessing excellent scalability and adaptability. In the future, it can be smoothly extended to the structural design of optomechanical systems with multiple components, complex operating conditions, and complex applications, continuously providing innovative design solutions and scientific guidance for the iterative updates of complex optomechanical systems, and driving the continuous advancement of optomechanical system technology. It solves the problem that traditional optical bench structure design methods are insufficient in terms of lightweighting, stiffness, and mirror conformal preservation to meet the needs of next-generation optomechanical systems. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments of this application or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 A flowchart illustrating a cross-scale optimization design method for an optical bench structure considering mirror conformal properties, provided in an embodiment of this application.

[0018] Figure 2 This is a schematic diagram of the parameterized lattice configuration provided in the embodiments of this application.

[0019] Figure 3 A reference diagram showing the parameterized lattice configuration provided in the embodiments of this application.

[0020] Figure 4 This is a schematic diagram illustrating the validity verification of the proxy model provided in an embodiment of this application.

[0021] Figure 5 This is a schematic diagram of the finite element mesh generation for the optical bench structure provided in an embodiment of this application.

[0022] Figure 6 A comparison diagram of non-conformal design and conformal design optimization provided for embodiments of this application.

[0023] Figure 7 A schematic diagram showing the complete optimized design results of the optical bench structure provided in the embodiments of this application.

[0024] Figure 8 This is a schematic diagram of a cross-scale optimization design device for an optical bench structure that considers mirror conformal design, provided as an embodiment of this application.

[0025] Figure 9 This is a schematic diagram of a server with cross-scale optimization design of an optical bench structure considering mirror conformal properties, provided as an embodiment of this application. Detailed Implementation

[0026] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0027] The following description of some technologies involved in the embodiments of this application is provided to aid understanding and should be considered merely exemplary. Therefore, those skilled in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. Similarly, for clarity and brevity, some descriptions of well-known functions and structures are omitted in the following description.

[0028] This application provides a cross-scale optimization design method for optical bench structures that considers mirror conformal properties, such as... Figure 1 As shown, the method includes steps S101 to S107. Wherein, Figure 1 This is merely one execution order shown in the embodiments of this application and does not represent the only execution order for a cross-scale optimization design method for optical bench structures that considers mirror conformal properties. The execution order can be adjusted to achieve the desired final result. Figure 1 The steps shown can be performed in parallel or in reverse order.

[0029] S101: During the offline phase, perform modeling and equivalent performance prediction of the parameterized lattice, and establish an equivalent performance prediction model for the lattice structure.

[0030] During the offline phase, parameterized lattice modeling and equivalent performance prediction are performed, and an equivalent performance prediction model for the lattice structure is established, including the following:

[0031] Figure 2 This is a schematic diagram of the parameterized lattice configuration provided in the embodiments of this application. It shows a BCC lattice structure (body-centered cubic lattice structure) with an outer frame and its three different rod diameters, including vertical rods parallel to the printing direction (red rod direction). ), a horizontal bar perpendicular to the printing direction ( ) and a diagonal bar at a certain angle to the printing direction ( ).

[0032] Figure 3 This is a reference diagram illustrating the parametric lattice configurations provided in the embodiments of this application. It shows various parametric lattice structures generated under different lattice parameters, including a lattice structure with only horizontal and vertical rods, a lattice structure with only diagonal rods, and a standard lattice structure containing three types of rods.

[0033] Introducing lattice parameters Control lattice configuration. Among them, Density parameter, describing the proportion of material used in a single cell. For configuration parameters, Used to control the amount of material used for vertical rods Used to control the amount of material used for horizontal bars. Used to control the amount of material used for diagonal bracing.

[0034] The BCC dot matrix structure with an outer frame was selected as the object, and the rod diameters were divided into three categories according to the additive manufacturing printing direction: vertical rods parallel to the printing direction, horizontal rods perpendicular to the printing direction, and diagonal rods.

[0035] lattice parameters Converted into material usage ratio parameters Satisfying the constraints The actual diameter of each member is determined through numerical calculations, generating a parameterized lattice structure with variable configuration for modeling the parameterized lattice. They are respectively The corresponding proportion.

[0036] Specifically, such as Figure 3 As shown, by adjusting the values ​​of the lattice parameters, a series of parameterized lattice structures with different configurations can be generated.

[0037] A numerical homogenization method is used to calculate the equivalent elastic matrix for a parameterized lattice structure with variable configuration. Specifically, the equivalent elastic tensor is obtained by integral operation based on the relationship between macroscopic material elastic properties and local strain field variation, so as to calculate the equivalent elastic matrix.

[0038] Numerical homogenization methods are widely used to solve for the properties of various non-homogeneous materials such as composite materials and lattice structures. The principle is to replace the non-homogeneous material with a homogeneous equivalent material, thereby ensuring that the macroscopic mechanical behavior remains consistent before and after equivalence. Theoretically, the equivalent elastic constant tensor of a lattice structure can be calculated using a specific formula: ;in, Let be the equivalent elastic constant tensor of the lattice structure. The volume of the overall outer envelope of the lattice structure. For the elastic tensor of macroscopic solid material (the lattice material itself), The strain field is measured in units to simplify numerical calculations. This refers to the local variation of the strain field in a lattice unit cell after applying a unit test strain field. , The displacement field of the actual structure can be solved using the finite element method. For actual displacement The resulting strain field in the p and q directions (in three-dimensional space, p and q can take values ​​of 1, 2, and 3, corresponding to the three directions x, y, and z. x, y, and z satisfy the Cartesian coordinate system, with the horizontal to the right, the horizontal forward, and the vertical upward as positive directions, respectively). For displacement field exist The direction is correct Partial derivatives in direction, For displacement field exist The direction is correct Partial derivatives in direction.

[0039] Given the symmetry of the fourth-order elasticity tensor, to facilitate numerical calculations and engineering applications, the Voigt notation method is introduced to represent the fourth-order equivalent elasticity tensor. Mapped to a 6×6 equivalent elasticity matrix The relationship between tensor subscript indices and matrix indices is as follows: .

[0040] Based on this, the equivalent elastic matrix of the three-dimensional lattice structure can be solved using the finite element method based on energy equivalence, and is expressed as: .in, The finite element form of the equivalent elastic matrix of the lattice structure is given. The total number of finite element elements after discretization. The volume of the finite element when homogenized. For the first The unit in the first Total displacement under unit strain conditions No. The unit in the first Total displacement under unit strain conditions , For the first Displacement of each element The macroscopic linear displacement generated by the unit test strain field. This represents the periodic fluctuating displacement corresponding to the locally changing strain field. For the first Stiffness matrix of each element This is a transpose operation.

[0041] Establish lattice parameters The mapping relationship with the equivalent elasticity matrix is ​​established by generating a proxy model using a BP neural network. The specific process includes the following:

[0042] Although numerical homogenization methods can obtain the equivalent elasticity matrix of lattice structures, they require iterative calls to a large number of homogenization analyses during cross-scale structural optimization design, resulting in extremely high computational costs and severely restricting the efficiency of lattice structure design. Therefore, a BP neural network is used to generate a surrogate model.

[0043] The input layer consists of a lattice parameter vector, and the output layer consists of independent component vectors of the equivalent elastic tensor. The activation function in the network is the sigmoid function. A three-layer backpropagation (BP) neural network is constructed, forming the complete BP network. : .in, The parameter vector represents the equivalent elasticity matrix of the output lattice structure. The input is a vector of point matrix parameters. The weights from the input layer to the hidden layer. This represents the weights from the hidden layer to the output layer. This is the bias vector of the hidden layer. This represents the bias vector of the output layer. `x` is the activation function, and `y` is the sigmoid function. The network weights and biases are iteratively optimized to minimize the loss function, resulting in an equivalent performance prediction model for the lattice structure.

[0044] To improve the prediction accuracy of the grid, it is necessary to minimize the value of the loss function. Therefore, with the goal of minimizing the loss function, the network weights and biases are iteratively optimized to obtain an equivalent performance prediction model for the lattice structure.

[0045] Specifically, after 5083 iterations, the final goal was achieved: 10. -7 The design requirements were met, thus successfully establishing the mapping relationship between lattice parameters and the equivalent elastic matrix, and obtaining a prediction model for the equivalent performance of the lattice structure.

[0046] Figure 4 This diagram illustrates the validity verification of the surrogate model provided in this application embodiment. To verify the accuracy of the surrogate model, actual homogenization results are selected as sample points, and the surface is described by the prediction points of the lattice structure equivalent performance prediction model. The horizontal coordinates in the diagram are... The two lattice control parameters (representing the proportion of material used in the unit cell and the proportion of material used in the horizontal bar, respectively) have vertical coordinates that represent the equivalent elastic parameters of the nine-point lattice structure. As can be observed from the figure, the surface passes through each sample point well and is relatively smooth as the parameters change, which fully demonstrates that the established surrogate model can accurately predict the equivalent performance of the lattice structure.

[0047] S102: During the online phase, the optical bench structure is selected, the design domain and non-design domain are determined based on design requirements and assembly environment, and the entire structure is discretized using finite element methods.

[0048] S103: Based on the design and non-design domains after finite element discretization, determine the solid region and lattice region, apply loads and boundary conditions, and define the design variables requiring topology optimization. The design variables include the pseudo-density of the solid region and the pseudo-density and lattice parameters of the lattice region.

[0049] Based on the specific design requirements of the optical bench and its assembly environment, the design domain and non-design domain in the structure are clearly defined, and finite element discretization is performed on the entire optical bench structure, while the design domain and non-design domain are also divided. In this process, the mirror area, as a key non-design area, requires special attention during the discretization operation to ensure that all node information of the mirror surface can be successfully extracted subsequently.

[0050] Figure 5 This is a schematic diagram of the finite element mesh generation for an optical bench structure provided in an embodiment of this application. Taking a certain type of optical mirror mount as a representative example, this application performs finite element discretization on this model. The design domain is shown in blue, containing 32,564 tetrahedral elements and 5,028 hexahedral elements; the bottom flange, elliptical frame, and mirror are defined as non-design domains. Specifically, all nodes on the mirror's outer surface (located at the mirror text markers in the figure), totaling 843 nodes, need to be extracted. This node information will be used for subsequent extraction of mirror deformation-related data.

[0051] Based on the design domain and non-design domain after finite element discretization, the solid region and lattice region are determined, loads and boundary conditions are applied, and design variables requiring topology optimization are defined, including the following:

[0052] The design domain after finite element discretization is further divided to determine the solid region and the lattice region. The lattice region is discretized using hexahedral elements. The solid region and the lattice region are discretized using tetrahedral elements based on the common nodes of the solid region and the lattice region. Loads and boundary conditions are then applied.

[0053] Extract the design domain element numbers, define each element in the solid region as having only one pseudo-density design variable, and each element in the lattice region as having five design variables, namely the pseudo-density. With lattice parameters .

[0054] The expression for having only one pseudo-density design variable per element in the solid region is: .in, This represents a pseudo-density design variable in the solid region. The pseudo density of the first cell in the solid region. The pseudo density of the second unit in the solid region. For the first in the entity region The pseudo density of each unit This represents the total number of units in the physical region. In this application, It can be 32564.

[0055] The expression for the design variable of each element in the lattice region is: .in, The first dot in the dot matrix region Design variables for each unit, For the first lattice region Units, For the first lattice region The pseudo density of each unit For the first lattice region The unit cell density parameter describes the proportion of material used in each unit cell. For the first lattice region Configuration parameters of each unit, Used to control the amount of material used for vertical rods Used to control the amount of material used for horizontal bars. Used to control the amount of material used for the diagonal brace. In this application, The value of can be 1, 2, ..., 5028.

[0056] S104: Invoke the equivalent performance prediction model of the lattice structure established in the offline stage, input the lattice parameters of each element in the lattice region into the equivalent performance prediction model of the lattice structure, and obtain the mechanical properties of the lattice structure based on the current design variables. Among them, the mechanical properties of the lattice structure are used to calculate the stiffness matrix of the structure, thereby obtaining the strain energy and deformation information of the overall structure.

[0057] Specifically, by using the equivalent solution proxy model obtained in the offline stage, the equivalent elastic performance of each element is quickly obtained, and then the corresponding elastic matrix parameters are obtained. These parameters are then assigned to each element to assemble the overall stiffness matrix of the structure and obtain the mechanical performance of the lattice structure.

[0058] In the example finite element model, to simulate actual working conditions, the boundary conditions and loads are set as follows: all degrees of freedom of one flange of the optical bench structure are fixed, a vertically downward concentrated force load is applied to the other flange, and a 10-gram overload (this is the design-related load) is applied to the entire structure, thus completing the application of boundary conditions and loads. For the material properties in the model, except for the reflector, the remaining parts are made of INVAR alloy, with an elastic modulus of 122 GPa and a Poisson's ratio of 0.25; the reflector material is microcrystalline, with an elastic modulus of 68 GPa and a Poisson's ratio of 0.17. The performance of the lattice element is quickly solved using a proxy model. In the first step of the optimization iteration, initial optimization values ​​are given in advance: the pseudo-density is 0.3, and all lattice parameters are 0.5. After inputting the lattice parameters into the proxy model, the elastic parameters are obtained, completing the assembly of the lattice structure stiffness matrix. For each lattice element, only a new material parameter needs to be established, and the equivalent elastic matrix obtained through the proxy model is input into the material parameter to achieve the same effect as the above process. The obtained mechanical properties of the lattice structure will be used to calculate the structural strain energy, providing key data support for the optimized design of the optical bench structure.

[0059] S105: Extract the normal displacement of the mirror nodes in the non-design domain and obtain the mirror surface shape information by Zernike polynomial fitting.

[0060] Extract the normal displacement of the mirror nodes in the non-design domain, and obtain the mirror surface shape information by Zernike polynomial fitting, including the following:

[0061] Specifically, since this application example emphasizes the normal deformation of the mirror and ignores the horizontal displacement, it is necessary to extract the normal displacement at all nodes on the outer surface of the optical reflecting surface (mirror). In the example case, this means extracting a total of 843 nodes from the surface of the mirror. The displacement in the normal direction serves as a direct evaluation index of the mirror's deformation, providing fundamental data for subsequent assessments of optical aberrations.

[0062] Extracting the normal displacement of mirror nodes in the non-design domain .

[0063] The extracted normal displacement is obtained using Zernike polynomials. Decomposed into linear combinations of Zernike polynomials of various orders as the basis and their corresponding coefficients, the macroscopic normal displacement is... The Zernike polynomial coefficients are obtained by summing the Zernike displacements of each order.

[0064] The expression for the Zernike polynomial is: .in, For a point on the mirror surface The deformation value, Polar radius, Polar angle, The coefficient of the constant term, , These are the corresponding Zernike coefficients, and their subscripts are respectively. c , d These represent the radial order and the azimuth order, respectively. This is a radial polynomial in the Zernike polynomial, which depends only on the polar radius r. To be compatible with only polar diameters Zernike polynomial terms The corresponding coefficients.

[0065] In the actual solution of polynomial coefficients, the least squares fitting method is used.

[0066] The Zernike polynomial coefficients are solved using least squares fitting, and the process of solving the Zernike coefficients is regarded as solving for the error between the actual surface shape and the fitted surface shape. Taking the smallest problem, the error The expression is: .in, This represents the total number of mirror nodes. For the first The weight of each node, For the first Normal displacement at each node Let Zernike be the order of the polynomial. For the first The coefficients of the Zernike polynomial of order 1 For the first Zernike polynomial of order 1 The value at each node Polar radius, It is the polar angle.

[0067] Let the error right The partial derivatives are 0: .

[0068] Let the error For the first coefficients of the order Zernike polynomial The partial derivatives are 0, so the problem can be expressed as a system of linear equations. The problem to be solved. Among them, The incidence matrix is ​​determined by the Zernike basis functions and weights, where the nth element of the incidence matrix is... Line number element It can be written as: ,in, For the first Zernike polynomial of order 1 The value at each node Polar radius, Polar angle, For the first The weight of each node, For the first Zernike polynomial of order 1 The values ​​at each node are similar. For the first Zernike polynomial of order 1 The values ​​at each node. The linear equations that need to be solved are: The coefficient vector of the Zernike polynomial is written as: , for Chinese elements, The total number of elements. Let be a constant vector, composed of basis functions and normal displacement. A joint decision, its first element Can be written as: . For the first Normal displacement at each node.

[0069] S106: The objective function is designed to minimize the structural strain energy. Mirror surface shape information is used as the conformal constraint. An optimization model is established based on the objective function and the conformal constraint. The sensitivity is derived to carry out the optimization design, and the optimization model is solved. Here, sensitivity is the partial derivative of the objective function or constraint function with respect to the design variables.

[0070] The objective function is designed with the goal of minimizing structural strain energy, and the mirror surface shape information is used as the conformal constraint. An optimization model is established based on the objective function and the conformal constraint, the sensitivity is derived to carry out optimization design, and the optimization model is solved, including the following contents.

[0071] The objective function is: , representing the strain energy of the structure. It is a displacement vector. For transpose operation, Here is the stiffness matrix. Design variables for pseudo-density in pseudo-entity regions. Variables are designed to optimize the lattice regions in the model.

[0072] The conformal constraint conditions are: , Its meaning is: the residual surface shape error after subtracting the first k orders of deformation from the mirror surface. Wherein, To preserve form constraints, The preset threshold for conformal constraint is 1 nm in this example. Before solving The correlation matrix corresponding to the Zernike coefficients of order Zernike. The coefficient vector of the Zernike polynomial in the conformal constraint. For normal displacement, This represents the total number of mirror nodes.

[0073] Specifically, in engineering The value is typically set to 3, meaning that the displacements corresponding to the first three Zernike coefficients can be eliminated through simple optical manipulation, while the remaining higher-order displacements... These high-order deformations are often impossible to limit through simple control methods. Therefore, the optimization model uses the RMS value (root mean square value) of these high-order deformations as a constraint, thereby reducing the high-order deformations of the mirror as much as possible through cross-scale conformal design, thus reducing the aberrations of the system.

[0074] Specifically, conformal constraints aim to limit the deformation of local areas of the mirror and ensure the optical performance of the optical elements supported by the optical bench.

[0075] The two types of design variables in the optimization model can be written as follows: The pseudo-density design variable in the solid region of the optimization model is: .

[0076] The design variables in the lattice region of the optimization model are: Y .

[0077] in, For the first lattice region The pseudo density of each unit For the first lattice region Density parameters of each unit For the first lattice region Configuration parameters of each unit, This represents the number of units in the lattice region.

[0078] The optimized model satisfies the following constraints: , , , .in, Here is the stiffness matrix. It is a displacement vector. For loads related to design variables, For loads independent of design variables, , The total number of units, The number of units in the lattice region. The total number of entity elements in the design domain. For the first Volume of each unit For the total volume, This represents the upper limit of the volume.

[0079] Derive the objective function and conformal constraints for the pseudo-density design variables in the pseudo-solid region. Design variables in the dot matrix area The sensitivity information is as follows: Sensitivity is the partial derivative of the objective function or constraint function with respect to the design variables.

[0080] The finite element adjoint method is used to efficiently solve for the sensitivity of the objective function to the design variables. When solving for the sensitivity information of the design variables of the lattice structure, it is necessary to obtain the derivative of the equivalent elasticity matrix with respect to the lattice parameters. This is achieved by using the analytical expression of a neural network (a complete BP network). The sensitivity relationship between different levels can be solved using the chain rule.

[0081] Based on the GCMMA algorithm, the sensitivity information obtained from the solution is used to perform iterative optimization of the optimization model.

[0082] Specifically, sensitivity is the partial derivative of the objective function or constraint function with respect to design variables, used to quantify the impact of small changes in design variables on the objective or constraint. It is necessary to derive the sensitivity information of the objective function, conformal constraints, and design variables in the pseudo-density region and lattice region, respectively. Specifically, the finite element adjoint method is used to efficiently solve for the sensitivity of the objective function with respect to design variables; when solving for the sensitivity information of the lattice structure design variables, the analytical expression of a neural network is used, and the chain rule is employed to solve for the sensitivity relationships between different levels.

[0083] Specifically, based on the GCMMA (Global Moving Asymptote Method) algorithm, the sensitivity information obtained from the solution is used to iteratively optimize the model. During the optimization process, if the objective function is sensitive to a certain design variable, the algorithm tends to increase that design variable to improve the objective; if the conformal constraint is sensitive to a certain design variable, the algorithm needs to suppress the adjustment of that design variable to avoid constraint violation. By continuously iterating, the algorithm seeks the optimal solution that satisfies all constraints and minimizes the objective function value, thus achieving the optimization design goal of improving the load-bearing capacity and optical performance of the optical bench structure while reducing its weight.

[0084] S107: Determine if the optimization model has converged. If it has not converged, adjust the values ​​of the design variables according to the sensitivity and redefine the conformal constraints based on the current mirror surface shape information, and continue iterative optimization. If it has converged, the cross-scale conformal optimization result of the optical bench structure is obtained.

[0085] Specifically, if convergence is not achieved, it is necessary to continue iterating based on the sensitivity information, further adjust the design variables and sensitivity information through three-field density filtering, dynamically adjust the conformal constraint conditions, and return to S104 to continue iterative optimization.

[0086] If the relative rate of change of the objective function between two adjacent iterations is less than or equal to 0.2%, or the maximum change in the design variables is less than 0.01, or the maximum number of iterations does not exceed 300 steps, then the optimization model is considered to have converged.

[0087] Based on the design variables, the cross-scale conformal optimization design of the optical bench structure is completed. The design variables are read, the actual lattice rod diameter is calculated through the lattice parameters, the optimization results are plotted, and the conformal effect diagram of the mirror is given.

[0088] The optimization results are converted into STL files for additive manufacturing.

[0089] Figure 6 A comparison diagram of non-conformal design and conformal design optimization provided for embodiments of this application. Figure 6 (a) in the diagram is a non-conformal design drawing. Figure 6 (b) in the diagram is a conformal design drawing. Figure 6 This demonstrates the application of conformal constraints in the optimization of typical optical bench structures. 1) Comparison with no conformal constraint. The figure clearly shows a significant difference in lattice distribution between the conformal design and the non-conformal design. The conformal design results in a more dispersed lattice structure with richer force transmission paths, effectively reducing higher-order deformations of the mirror surface. Surface shape analysis shows that the conformal design significantly reduces the mirror's RMS value (root mean square value) from 21.49 nm to 1 nm, a reduction of over 95%, while the overall stiffness only slightly decreases by 2% (from 21.03 to 21.46), fully validating the effectiveness of the conformal design.

[0090] Figure 7 This diagram illustrates the complete optimized design results of the optical bench structure provided in this embodiment. Since the parametric lattice modeling process can be implemented using a simple programming language, the results can be easily exported as an STL file. Based on... Figure 7 The optimized results can be directly tested for manufacturability and, after simple processing, can be used for 3D printing. This technological advantage allows subsequent complex structures, after the addition of manufacturability constraints, to be directly used in additive manufacturing, quickly entering the principle testing and verification stage, thereby improving the efficiency of optimization design and testing verification, and promoting the design and iteration of next-generation optomechanical systems.

[0091] This application also provides a cross-scale optimization design device 800 for optical bench structures that considers mirror conformal design, such as... Figure 8 As shown, the device includes: a setup module 801, a selection module 802, a determination module 803, an acquisition module 804, a fitting module 805, a solution module 806, and a judgment module 807.

[0092] Module 801 is used for offline phases to model and predict the equivalent performance of parameterized lattices, and to establish a lattice structure equivalent performance prediction model.

[0093] When selecting module 802 for the online phase, the optical bench structure is selected, the design domain and non-design domain are determined based on design requirements and assembly environment, and the entire structure is discretized using finite element methods.

[0094] The determination module 803 is used to determine the solid region and lattice region based on the design domain and non-design domain after finite element discretization, apply loads and boundary conditions, and define the design variables that require topology optimization. These design variables include the pseudo-density of the solid region and the pseudo-density and lattice parameters of the lattice region.

[0095] The acquisition module 804 is used to call the equivalent performance prediction model of the lattice structure established in the offline stage. It inputs the lattice parameters of each element in the lattice region into the model and obtains the mechanical properties of the lattice structure based on the current design variables. The mechanical properties of the lattice structure are used to calculate the stiffness matrix of the structure, thereby obtaining the strain energy and deformation information of the overall structure.

[0096] The fitting module 805 is used to extract the normal displacement of the mirror nodes in the non-design domain and obtain the mirror surface shape information through Zernike polynomial fitting.

[0097] The solver module 806 is used to design an objective function with the goal of minimizing structural strain energy, using mirror surface shape information as conformal constraints, establishing an optimization model based on the objective function and conformal constraints, deriving sensitivity to perform optimization design, and solving the optimization model. Sensitivity is the partial derivative of the objective function or constraint function with respect to the design variables.

[0098] The judgment module 807 is used to determine whether the optimization model has converged. If it has not converged, the values ​​of the design variables are adjusted according to the sensitivity, and the conformal constraints are redefined according to the current mirror surface shape information, and the iterative optimization continues. If it has converged, the cross-scale conformal optimization result of the optical bench structure is obtained.

[0099] Some modules in the apparatus described in this application can be described in the general context of computer-executable instructions that are executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, classes, etc., that perform a specific task or implement a specific abstract data type. This application can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0100] The apparatus or module described in the above embodiments can be implemented by a computer chip or physical entity, or by a product with a certain function. For ease of description, the above apparatus is described by dividing it into various modules according to their functions. When implementing the embodiments of this application, the functions of each module can be implemented in one or more software and / or hardware. Of course, a module that implements a certain function can also be implemented by combining multiple sub-modules or sub-units.

[0101] The methods, apparatus, or modules described in this application can be implemented in a computer-readable program code manner. The controller can be implemented in any suitable manner, for example, as a microprocessor or processor and a computer-readable medium storing computer-readable program code (e.g., software or firmware) executable by the (micro)processor, logic gates, switches, application-specific integrated circuits (ASICs), programmable logic controllers, and embedded microcontrollers. Examples of controllers include, but are not limited to, the following microcontrollers: ARC 625D, Atmel AT91SAM, Microchip PIC18F26K20, and Silicon Labs C8051F320. A memory controller can also be implemented as part of the control logic of a memory. Those skilled in the art will also recognize that, in addition to implementing the controller in purely computer-readable program code manner, the same functionality can be achieved by logically programming the method steps to make the controller take the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, such a controller can be considered a hardware component, and the means included within it for implementing various functions can also be considered as structures within the hardware component. Alternatively, the device used to implement various functions can be viewed as either a software module implementing the method or a structure within a hardware component.

[0102] like Figure 9 As shown in the figure, this application embodiment also provides a cross-scale optimization design server for an optical bench structure considering mirror conformal design, including a memory 901 and a processor 902; the memory 901 is used to store computer-executable instructions; the processor 902 is used to execute computer-executable instructions to implement the cross-scale optimization design method for an optical bench structure considering mirror conformal design described above in this application embodiment.

[0103] This application also provides a computer-readable storage medium storing executable instructions. When a computer executes the executable instructions, it can implement the cross-scale optimization design method for optical bench structures considering mirror conformal properties described above in this application.

[0104] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented by means of software plus necessary hardware. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product, or it can be embodied in the process of data migration. The computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, mobile terminal, server, or network device, etc.) to execute the methods described in the embodiments of this application.

[0105] The various embodiments described in this specification are presented in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. All or part of this application can be used in numerous general-purpose or special-purpose computer system environments or configurations.

[0106] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit this application. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of this application.

Claims

1. A method for cross-scale optimization design of optical bench structures considering mirror conformal properties, characterized in that, include: During the offline phase, parameterized lattice modeling and equivalent performance prediction are performed, and an equivalent performance prediction model for the lattice structure is established. During the online phase, an optical bench structure is selected, and the design domain and non-design domain are determined based on design requirements and assembly environment. The entire structure is then discretized using finite element methods. Based on the design domain and non-design domain after finite element discretization, the solid region and lattice region are determined, loads and boundary conditions are applied, and design variables that require topology optimization are defined; among them, the design variables include the pseudo density of the solid region and the pseudo density and lattice parameters of the lattice region. The equivalent performance prediction model of the lattice structure established in the offline stage is invoked. The lattice parameters of each element in the lattice region are input into the equivalent performance prediction model of the lattice structure, and the mechanical performance of the lattice structure is obtained based on the current design variables. The mechanical performance of the lattice structure is used to calculate the stiffness matrix of the structure, thereby obtaining the strain energy and deformation information of the overall structure. Extract the normal displacement of the mirror nodes in the non-design domain, and obtain the mirror surface shape information by Zernike polynomial fitting; The objective function is designed with the goal of minimizing structural strain energy, and the mirror surface shape information is used as the conformal constraint. An optimization model is established based on the objective function and the conformal constraint, and the sensitivity is derived to carry out the optimization design. The optimization model is then solved. Here, the sensitivity is the partial derivative of the objective function or constraint function with respect to the design variables. Determine whether the optimization model has converged. If it has not converged, adjust the values ​​of the design variables according to the sensitivity and redefine the conformal constraints according to the current mirror surface shape information, and continue iterative optimization. If it has converged, obtain the cross-scale conformal optimization results of the optical bench structure.

2. The cross-scale optimization design method for optical bench structures considering mirror conformal properties according to claim 1, characterized in that, During the offline phase, parameterized lattice modeling and equivalent performance prediction are performed, establishing a lattice structure equivalent performance prediction model, including: Introducing lattice parameters Control lattice configuration; among which, Density parameter, describing the proportion of material used in a single cell. For configuration parameters, Used to control the amount of material used for vertical rods Used to control the amount of material used for horizontal bars. Used to control the amount of material used for diagonal braces; The BCC dot matrix structure with an outer frame is selected as the object, and it is divided into three types of rod diameters according to the additive manufacturing printing direction, including vertical rods parallel to the printing direction, horizontal rods perpendicular to the printing direction, and diagonal rods. lattice parameters Converted into material usage ratio parameters The constraints are satisfied. The actual diameter of each member is determined through numerical calculations, generating a parameterized lattice structure with variable configuration for modeling the parameterized lattice; among which, They are respectively The corresponding proportion; A numerical homogenization method is used to calculate the equivalent elastic matrix for a parameterized lattice structure with variable configuration. Specifically, it includes obtaining the equivalent elastic tensor through integral operation based on the relationship between macroscopic material elastic properties and local strain field variation, in order to calculate the equivalent elastic matrix. Establish lattice parameters The mapping relationship with the equivalent elasticity matrix is ​​established using a BP neural network to generate a surrogate model. The specific process includes: The input layer is a vector of lattice parameters, and the output layer is a vector of independent components of the equivalent elastic tensor. The activation function is Sigmoid, and a three-layer backpropagation (BP) neural network is constructed. The complete BP network is as follows: ； in, The parameter vector represents the equivalent elasticity matrix of the output lattice structure. The input is a vector of point matrix parameters. The weights from the input layer to the hidden layer. This represents the weights from the hidden layer to the output layer. This is the bias vector of the hidden layer. This represents the bias vector of the output layer. Here, is the activation function, and is the Sigmoid function; The network weights and biases are iteratively optimized to minimize the loss function, thereby obtaining an equivalent performance prediction model for the lattice structure.

3. The cross-scale optimization design method for optical bench structures considering mirror conformal properties according to claim 2, characterized in that, Based on the design domain and non-design domain after finite element discretization, the solid region and lattice region are determined, loads and boundary conditions are applied, and design variables requiring topology optimization are defined, including: The design domain after finite element discretization is further divided to determine the solid region and the lattice region. The lattice region is discretized using hexahedral elements. The solid region and the lattice region are discretized using tetrahedral elements based on the common nodes of the solid region and the lattice region. Loads and boundary conditions are then applied. Extract the design domain element numbers, define each element in the solid region as having only one pseudo-density design variable, and each element in the lattice region as having five design variables, namely the pseudo-density. With lattice parameters ; The expression for having only one pseudo-density design variable per element in the solid region is: ;in, This represents a pseudo-density design variable in the solid region. The pseudo density of the first cell in the solid region. The pseudo density of the second unit in the solid region. For the first in the entity region The pseudo density of each unit This represents the total number of entity units in the design domain; The expression for the design variable of each element in the lattice region is: ;in, The first dot in the dot matrix region Design variables for each unit, For the first point region Units, For the first point region The pseudo density of each unit For the first point region The unit cell density parameter describes the proportion of material used in each unit cell. For the first point region Configuration parameters of each unit, Used to control the amount of material used for vertical rods Used to control the amount of material used for horizontal bars. Used to control the amount of material used for diagonal bracing.

4. The cross-scale optimization design method for optical bench structures considering mirror conformal properties according to claim 3, characterized in that, The extraction of the normal displacement of mirror nodes in the non-design domain and the acquisition of mirror surface shape information through Zernike polynomial fitting include: Extracting the normal displacement of mirror nodes in the non-design domain ; The extracted normal displacement is obtained using Zernike polynomials. Decomposed into linear combinations of Zernike polynomials of various orders as the basis and their corresponding coefficients, the macroscopic normal displacement is... The Zernike polynomial coefficients are obtained by summing the Zernike displacements of each order. The Zernike polynomial coefficients are solved using least squares fitting, and the process of solving the Zernike coefficients is regarded as solving for the error between the actual surface shape and the fitted surface shape. Taking the smallest problem, the error The expression is: ;in, This represents the total number of mirror nodes. For the first The weight of each node, For the first Normal displacement at each node For Zernike order, For the first The coefficients of the Zernike polynomial of order 1 For the first Zernike polynomial of order 1 The value at each node Polar radius, Polar angle; Let the error For the coefficients of the order Zernike polynomial The partial derivatives are 0, so the problem can be expressed as a system of linear equations. The problem to be solved; among which, The incidence matrix is ​​determined by the Zernike basis functions and weights. Let Zernike polynomials be the coefficient vectors. Let be a constant vector, composed of basis functions and normal displacement. A joint decision.

5. The cross-scale optimization design method for optical bench structures considering mirror conformal properties according to claim 4, characterized in that, The objective function is designed to minimize structural strain energy, and mirror surface shape information is used as a conformal constraint. An optimization model is established based on the objective function and conformal constraint, sensitivity is derived for optimization design, and the optimization model is solved, including: The objective function is: ;in, For displacement vectors, For transpose operation, Here is the stiffness matrix. Design variables for pseudo-density in the solid region. To design variables in the lattice region of the optimization model; The conformal constraint conditions are: , ;in, To preserve form constraints, For the preset threshold, Before solving The correlation matrix corresponding to the Zernike coefficients of order Zernike. The coefficient vector of the Zernike polynomial in the conformal constraint. For normal displacement, This represents the total number of mirror nodes; The pseudo-density design variable in the solid region of the optimization model is: ; The design variables in the lattice region of the optimization model are: Y ; in, For the first point region The pseudo density of each unit For the first point region Density parameters of each unit For the first point region Configuration parameters of each unit, The number of units in the lattice region; The optimized model satisfies the following constraints: , , , ;in, Here is the stiffness matrix. For displacement vectors, For loads related to design variables, For loads independent of design variables, , The total number of units, The number of units in the lattice region. The total number of entity elements in the design domain. For the first Volume of each unit For the total volume, This is the upper limit of the volume; Derive the objective function and conformal constraints for the pseudo-density design variables in the pseudo-solid region. Design variables in the dot matrix area The sensitivity information; where sensitivity is the partial derivative of the objective function or constraint function with respect to the design variables; The finite element adjoint method is used to efficiently solve the sensitivity of the objective function to the design variables. When solving the sensitivity information of the design variables of the lattice structure, the analytical expression of the neural network is used to solve the sensitivity relationship between each level through the chain rule. Based on the GCMMA algorithm, the sensitivity information obtained from the solution is used to perform iterative optimization of the optimization model.

6. The cross-scale optimization design method for optical bench structures considering mirror conformal properties according to claim 5, characterized in that, If the relative rate of change of the objective function between two adjacent rounds is less than or equal to 0.2%, or the maximum change in the design variables is less than 0.01, or the maximum number of iterations does not exceed 300 steps, then the optimization model is considered to have converged. Based on the design variables, the cross-scale conformal optimization design of the optical bench structure is completed. The design variables are read, the actual lattice rod diameter is calculated through the lattice parameters, the optimization results are plotted, and the conformal effect diagram of the mirror is given. The optimization results are converted into STL files for additive manufacturing.

7. A cross-scale optimization design device for an optical bench structure considering mirror conformal properties, characterized in that, The device performs the method as described in any one of claims 1 to 6, including: A module is established for modeling and predicting the equivalent performance of parameterized lattices during the offline phase, and an equivalent performance prediction model for lattice structures is established. When selecting a module for the online phase, the optical bench structure is selected, and the design domain and non-design domain are determined based on design requirements and assembly environment. The entire structure is then discretized using finite element methods. The determination module is used to determine the solid region and lattice region based on the design domain and non-design domain after finite element discretization, apply loads and boundary conditions, and define the design variables that need topology optimization; among them, the design variables include the pseudo density of the solid region and the pseudo density and lattice parameters of the lattice region. The acquisition module is used to call the equivalent performance prediction model of the lattice structure established in the offline stage. The lattice parameters of each element in the lattice region are input into the equivalent performance prediction model of the lattice structure, and the mechanical performance of the lattice structure is obtained based on the current design variables. The mechanical performance of the lattice structure is used to calculate the stiffness matrix of the structure, thereby obtaining the strain energy and deformation information of the overall structure. The fitting module is used to extract the normal displacement of the mirror nodes in the non-design domain and obtain the mirror surface shape information through Zernike polynomial fitting. The solution module is used to design an objective function with the goal of minimizing structural strain energy, using mirror surface shape information as conformal constraints, establishing an optimization model based on the objective function and conformal constraints, deriving sensitivity to carry out optimization design, and solving the optimization model; where sensitivity is the partial derivative of the objective function or constraint function with respect to the design variables; The judgment module is used to determine whether the optimization model has converged. If it has not converged, the values ​​of the design variables are adjusted according to the sensitivity, and the conformal constraints are redefined according to the current mirror surface shape information, and the iterative optimization continues. If it has converged, the cross-scale conformal optimization results of the optical bench structure are obtained.

8. A server with cross-scale optimization design of optical bench structure considering mirror conformal properties, characterized in that, Including memory and processor; The memory is used to store computer-executable instructions; The processor is configured to execute the computer-executable instructions to implement the method according to any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores executable instructions, which, when executed by a computer, enable the implementation of the method as described in any one of claims 1-6.

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