A multi-objective optimization solution method for structural topology optimization software

Abstract

This invention discloses a multi-objective optimization solution method for structural topology optimization software, relating to the field of structural topology optimization technology. The method includes importing the geometric model of the engineering structure into the topology optimization software; discretizing the geometric model using adaptive mesh refinement technology; solving the constructed multi-objective optimization model using an efficient finite element solver to obtain stress distribution data and displacement distribution data; performing optimization using a multi-swarm optimization algorithm with parallel computing to obtain a Pareto optimal solution set; conducting multi-criteria decision analysis on the Pareto optimal solution set using the analytic hierarchy process (AHP) to determine the topology scheme; and feeding the topology scheme back to the structural topology optimization software to complete the multi-objective optimization solution. Through the above steps, this invention achieves objective identification and scientific selection of the optimal topology scheme, and improves the practicality and engineering feasibility of the optimization results by feeding the optimal solution back to the topology optimization software through a feedback mechanism.

Description

Technical Field

[0001] This invention relates to the field of structural topology optimization technology, and in particular to a multi-objective optimization solution method for structural topology optimization software. Background Technology

[0002] Currently, structural topology optimization technology still faces significant technical bottlenecks in the field of multi-objective optimization. Traditional optimization methods typically employ single-objective optimization frameworks or fixed-weight multi-objective optimization strategies, making it difficult to effectively balance the collaborative optimization of multiple conflicting objectives. For example, iterative solutions based on the Variable Density Method (SIMP) and Optimization Criterion (OC) are highly sensitive to convergence conditions, potentially leading to local optima instead of achieving the globally optimal topology. Furthermore, existing methods still fall short in terms of computational efficiency, interpretability of optimization results, and engineering applicability, especially when dealing with optimization problems involving complex structures and multiple operating conditions, often failing to simultaneously meet the requirements of multiple performance indicators such as stiffness, strength, and lightweighting. Therefore, there is an urgent need for a multi-objective optimization solution method that integrates efficient numerical computation, intelligent optimization algorithms, and scientific decision analysis to improve the accuracy, efficiency, and engineering applicability of structural topology optimization.

[0003] CN115062510B discloses a multi-objective topology optimization method for result approximation. By combining a multi-material filling strategy and polynomial interpolation techniques, it expands the feasible result domain and employs an improved optimization criterion (OC) to enhance convergence efficiency. However, this method still relies on empirical weight allocation during multi-objective optimization and has limited adaptability to high-dimensional non-convex optimization problems, potentially leading to optimization results that deviate from actual engineering requirements. Furthermore, its inverse solution process may face numerical instability issues in complex structure optimization, affecting optimization accuracy.

[0004] CN115879232A proposes a multi-objective topology optimization method for mechanical structures based on fuzzy theory. By introducing membership functions and fuzzy weight coefficients, it optimizes the weight allocation strategy of the multi-objective optimization model, improving the reliability of the optimization results. However, the adaptability of this method under dynamic working conditions is still limited by the setting of fuzzy rules, and it does not incorporate efficient parallel computing technology, resulting in low computational efficiency for large-scale optimization problems. Furthermore, the decision-making process for the optimization results still relies on human experience, lacks a scientific multi-criteria evaluation system, and is difficult to automate and intelligently select optimization schemes. Summary of the Invention

[0005] In view of the fact that existing structural topology optimization software suffers from heavy computational burden and is prone to getting trapped in local optima when dealing with multi-objective optimization problems of engineering structures, this invention is proposed.

[0006] Therefore, the problem to be solved by this invention is how to achieve accurate and automated solving of multiple objectives in structural topology optimization by integrating a high-efficiency finite element solver, adaptive mesh refinement technology, multi-swarm particle swarm optimization algorithm and hierarchical analysis decision mechanism, so as to improve the comprehensive performance of structural optimization and its practical engineering application value.

[0007] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0008] Firstly, the present invention provides a multi-objective optimization solution method for structural topology optimization software.

[0009] It includes,

[0010] The geometric model of the engineering structure is imported into topology optimization software, and the geometric model is discretized using adaptive mesh refinement technology.

[0011] Based on the discretized geometric model, an efficient finite element solver is used to solve the constructed multi-objective optimization model to obtain stress distribution data and displacement distribution data;

[0012] Based on the stress distribution data and the displacement distribution data, the Pareto optimal solution set is obtained by optimizing the solution using a multi-swarm particle swarm algorithm with parallel computing.

[0013] The analytic hierarchy process (AHP) is used to perform multi-criteria decision analysis on the Pareto optimal solution set to determine the topology scheme. The topology scheme is then fed back to the topology optimization software to complete the multi-objective optimization solution.

[0014] As a preferred embodiment of the multi-objective optimization solution method of the structural topology optimization software of the present invention, the method includes: using the analytic hierarchy process (AHP) to perform multi-criteria decision analysis on the Pareto optimal solution set to determine the topology scheme, and feeding the topology scheme back to the structural topology optimization software to complete the multi-objective optimization solution, including:

[0015] The analytic hierarchy process is used to set evaluation indicators for the Pareto optimal solution set and construct a judgment matrix. The evaluation indicators include structural quality, stress level and displacement response.

[0016] The consistency of the judgment matrix is ​​checked, the weight coefficients of each evaluation index are calculated, and a comprehensive evaluation function is generated.

[0017] The Pareto optimal solution set is input into the comprehensive evaluation function, and the Pareto optimal solution set is sorted in descending order of score.

[0018] The solution with the highest comprehensive score is selected as the topology scheme, and the cell density distribution data of the topology scheme is extracted.

[0019] The unit density distribution data is imported into the structural topology optimization software, and an optimization result report is output, wherein the optimization result report includes the stress distribution, displacement distribution and iteration history data of the topology scheme.

[0020] As a preferred embodiment of the multi-objective optimization solution method of the structural topology optimization software of the present invention, the consistency check of the judgment matrix includes:

[0021] Calculate the largest eigenvalue of the judgment matrix, and solve the characteristic equation using the power iteration method to obtain the largest eigenvalue of the judgment matrix;

[0022] Based on the largest eigenvalue, calculate the consistency index (CI) of the judgment matrix;

[0023] Find the corresponding random consistency index value RI based on the consistency index CI, and calculate the consistency ratio CR of the judgment matrix.

[0024] When the consistency ratio CR is less than the second preset threshold, the judgment matrix is ​​determined to have passed the consistency test; when the consistency ratio CR is greater than the second preset threshold, the judgment matrix is ​​reconstructed.

[0025] For the judgment matrix that has passed the consistency test, the weight coefficient of each evaluation index is calculated using the arithmetic mean method.

[0026] As a preferred embodiment of the multi-objective optimization solution method of the structural topology optimization software described in this invention, the method for constructing the comprehensive evaluation function is as follows:

[0027] The evaluation indexes set for the Pareto optimal solution set are normalized, and the range standardization method is used to map the index values ​​to the [0,1] interval to construct a weighted summation type comprehensive evaluation function;

[0028] The monotonicity of the comprehensive evaluation function is tested, and the effectiveness of the tested comprehensive evaluation function is verified through test examples, thus completing the construction of the comprehensive evaluation function.

[0029] As a preferred embodiment of the multi-objective optimization solution method of the structural topology optimization software described in this invention, the method for obtaining the Pareto optimal solution set is as follows:

[0030] A multi-objective fitness evaluation function was constructed, and stress distribution data and displacement distribution data were used as fitness evaluation indicators to establish a population evaluation criterion.

[0031] The fitness values ​​of the particle swarm are calculated according to the population evaluation criteria, and the particle swarm is grouped using a subpopulation partitioning strategy. Search spaces are allocated to the subpopulations, and the fitness values ​​are exchanged between the subpopulations through an information exchange mechanism.

[0032] Set velocity update parameters and position update parameters for the subpopulation, wherein the subpopulation searches for particles according to a preset iteration rule, and performs non-dominated sorting on the searched particles to calculate the crowding value;

[0033] Based on the results of the non-dominated sorting and the crowding value, non-dominated solutions are selected, and the Pareto front is constructed.

[0034] According to a preset iteration cycle, non-dominated solutions are exchanged among subpopulations to update the Pareto front and generate a Pareto optimal solution set.

[0035] As a preferred embodiment of the multi-objective optimization solution method of the structural topology optimization software described in this invention, the method for obtaining the stress distribution data and displacement distribution data is as follows:

[0036] Apply boundary conditions and load conditions to the discretized geometric model;

[0037] Based on the boundary conditions and load conditions, define the objective function and constraints for topology optimization, and construct a multi-objective optimization model;

[0038] A high-efficiency finite element solver is established using multi-threaded parallel computing technology. The high-efficiency finite element solver includes a sparse matrix storage module and a conjugate gradient iterative solution module.

[0039] The high-efficiency finite element solver reads the element stiffness matrix of the multi-objective optimization model and generates the global stiffness matrix using a set method.

[0040] Based on the global stiffness matrix, the stress field is calculated using the conjugate gradient iterative solution module to obtain stress distribution data;

[0041] Based on the stress distribution data, the displacement field is calculated using the conjugate gradient iterative solution module to obtain the displacement distribution data;

[0042] Simultaneously, the stress distribution data and the displacement distribution data are stored in the sparse matrix storage module.

[0043] As a preferred embodiment of the multi-objective optimization solution method of the structural topology optimization software of the present invention, the objective function includes a first objective function and a second objective function; the first objective function is the global compliance minimization objective function; and the second objective function is the material consumption minimization objective function.

[0044] As a preferred embodiment of the multi-objective optimization solution method of the structural topology optimization software described in this invention, the discretization method of the geometric model is as follows:

[0045] The geometric model of the engineering structure is imported into the topology optimization software in STL format, a three-dimensional coordinate system is established, and the boundary information of the geometric model is obtained. The boundary information includes vertex coordinates, patch topology, and boundary normal vectors.

[0046] Based on the boundary information, tetrahedral meshing elements are used to perform initial meshing on the geometric model to construct a three-dimensional mesh model.

[0047] Finite element static analysis is performed on the mesh model to solve the stress distribution field under given load and constraint conditions, and the equivalent stress value inside each tetrahedral element is calculated.

[0048] The stress gradient distribution is calculated based on the rate of change of equivalent stress values ​​among tetrahedral elements.

[0049] When the stress value of a stress gradient distribution element is greater than the overall average stress ratio, and the stress elements form a continuously distributed region in space, this region is determined to be a high-stress region.

[0050] Adaptive mesh refinement is applied to the high-stress region, wherein the mesh size of the high-stress region is reduced by a preset ratio to form a locally refined mesh;

[0051] The localized encrypted mesh is subjected to mesh quality detection, and mesh quality indicators are calculated;

[0052] When the mesh quality index of all units is less than or equal to the first preset threshold, the discretization of the geometric model is completed.

[0053] In a second aspect, the present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, wherein: when the computer program instructions are executed by the processor, they implement the steps of the multi-objective optimization solution method of the structural topology optimization software as described in the first aspect of the present invention.

[0054] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein: when the computer program instructions are executed by a processor, they implement the steps of the multi-objective optimization solution method of the structural topology optimization software as described in the first aspect of the present invention.

[0055] The beneficial effects of this invention are:

[0056] 1. The geometric model of the engineering structure is imported into the topology optimization software. The geometric model is discretized by adaptive mesh refinement technology, which realizes high-fidelity finite element modeling of complex engineering structures. Through stress-driven adaptive mesh refinement strategy, the mesh is made more refined in the high stress concentration area. Under the premise of ensuring overall computational efficiency, the stress response of the structural model in the key area is refined and modeled, which improves the physical reliability and convergence stability of the subsequent finite element solution and optimization results.

[0057] 2. A multi-threaded finite element solver containing a sparse matrix storage module and a conjugate gradient iteration module was introduced, enabling fast solving in large-scale 3D structural scenes;

[0058] 3. A multi-group parallel particle swarm optimization algorithm was introduced, and combined with non-dominated sorting and fitness evaluation mechanism, an evolutionary strategy suitable for multi-objective function collaborative optimization was constructed. This breaks through the limitation of a single particle swarm being prone to getting trapped in local optima in complex objective spaces, and achieves a balance between maintaining the diversity of solution sets and fast convergence.

[0059] 4. The Analytic Hierarchy Process (AHP) is used to perform multi-criteria decision analysis on the Pareto optimal solution set to determine the topology scheme. The topology scheme is then fed back to the topology optimization software to complete the multi-objective optimization solution, avoiding the uncertainty and subjectivity of relying on manual judgment in traditional methods. Attached Figure Description

[0060] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0061] Figure 1 This is a flowchart of the multi-objective optimization solution method of the structural topology optimization software in Example 1. Detailed Implementation

[0062] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0063] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0064] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0065] Embodiments of the present invention

[0066] Reference Figure 1 This embodiment provides a multi-objective optimization solution method for structural topology optimization software, including:

[0067] S1: Import the geometric model of the engineering structure into the topology optimization software, and discretize the geometric model using adaptive mesh refinement technology;

[0068] S2: Based on the discretized geometric model, an efficient finite element solver is used to solve the constructed multi-objective optimization model to obtain stress distribution data and displacement distribution data;

[0069] S3: Based on stress distribution data and displacement distribution data, a Pareto optimal solution set is obtained by optimizing the solution using a multi-swarm particle swarm algorithm with parallel computing.

[0070] S4: The analytic hierarchy process (AHP) is used to perform multi-criteria decision analysis on the Pareto optimal solution set to determine the topology scheme. The topology scheme is then fed back to the topology optimization software to complete the multi-objective optimization solution.

[0071] In this embodiment of the application, step S1 includes:

[0072] S1.1: Import the geometric model of the engineering structure into the topology optimization software according to the STL format, establish a three-dimensional coordinate system, and obtain the boundary information of the geometric model, including vertex coordinates, patch topology, and boundary normal vectors;

[0073] S1.2: Based on boundary information, tetrahedral meshing elements are used to perform initial meshing of the geometric model, and a three-dimensional mesh model is constructed.

[0074] In an optional implementation, the mesh model is constructed as follows: Initial mesh generation is performed using the Delaunay triangulation algorithm based on tetrahedral elements. This process includes extracting the boundary vertices of the geometric model as the initial node set, constructing a convex hull containing the initial node set, reconstructing the model surface using boundary restoration techniques, and then inserting internal nodes inside the convex hull to generate the initial tetrahedral mesh. The initial tetrahedral mesh is then optimized by calculating the quality parameters of each tetrahedral element, deleting inferior tetrahedral elements, adjusting node positions to optimize element shapes, merging adjacent small tetrahedral elements, and regenerating the local mesh. Mesh refinement is performed based on stress gradients, specifically by calculating the stress gradient value of each element, marking high-stress-gradient regions and subdividing them, while inserting transition elements at subdivision boundaries to ensure mesh continuity. Mesh smoothing is then performed by calculating the topological relationships of each node, using the Laplace smoothing algorithm to adjust node positions, optimizing element volume ratios, and eliminating mesh distortion. Finally, mesh quality is evaluated, including calculating the element aspect ratio, checking element angles, evaluating node distribution uniformity, verifying mesh connectivity, and outputting a quality evaluation report, thus completing the mesh model construction process.

[0075] S1.3: Perform finite element static analysis on the mesh model to solve the stress distribution field under given load and constraint conditions, and calculate the equivalent stress value inside each tetrahedral element;

[0076] In an optional implementation, a finite element static analysis is performed on the mesh model, including: starting by calculating the shape function and its derivative of each tetrahedral element, calculating the element stiffness matrix using Gaussian integrals, converting the local coordinate system to a global coordinate system using isoparametric element technology, and establishing the strain matrix and stress-strain relationship matrix; assembling elements based on the nodal degrees of freedom of the elements, determining the correspondence of degrees of freedom using node numbering rules, and assembling the element stiffness matrix into a global stiffness matrix; introducing load conditions, converting concentrated forces into equivalent nodal forces, converting distributed forces into nodal force vectors through shape function interpolation, and simultaneously handling the influence of volumetric forces such as gravity; for constraint conditions, applying fixed constraints and elastic supports using the displacement method, and modifying the corresponding rows and columns of the global stiffness matrix.

[0077] In the solution phase, an improved conjugate gradient method is used to solve the large-scale sparse linear equation system, and the nodal displacement field is obtained through iterative calculation. Based on the nodal displacement field, the strain field of each element is calculated, and the stress field is solved using Hooke's law.

[0078] It should be noted that the von Mises equivalent stress criterion is used to calculate the equivalent stress value of each tetrahedral element. The specific formula is as follows:

[0079]

[0080] Where, σ eff σ is the equivalent stress value of the element. x Let σ be the normal stress component in the x-direction. y σ is the normal stress component in the y-direction. z τ is the normal stress component in the z-direction. xy Let τ be the shear stress component in the xy plane. yz Let τ be the shear stress component in the yz plane. zx Let α be the shear stress component in the zx plane. e ε is the element geometry correction factor. v ε is the volumetric strain, and ε0 is the reference strain value.

[0081] S1.4: Calculate the stress gradient distribution based on the rate of change of equivalent stress values ​​between tetrahedral elements;

[0082] It should be noted that the relevant formulas for stress gradient distribution are as follows:

[0083]

[0084] Among them, G σ ω represents the stress gradient value, n is the number of adjacent elements, and ω is the stress gradient value. e σ is the unit weight coefficient (determined by the number of shared nodes in the unit). eff x is the equivalent stress value of the element. e y e z e V represents the local coordinates of the element. e V is the unit volume. ref The reference volume value is λ (the average volume of the grid), where λ is the sensitivity coefficient (ranging from 1 to 10), and Q is the reference volume value. e This refers to the unit quality index.

[0085] S1.5: When the stress value of the element in the stress gradient distribution is greater than the overall average stress ratio, and the stress elements form a continuously distributed region in space, this region is determined to be a high-stress region.

[0086] As illustrated in the example, when the equivalent stress value of a certain element is 1.5 to 2 times greater than the global average stress value, this element will be marked as a high-stress element and requires densification. Simultaneously, these high-stress elements need to form a continuously distributed region in space, typically requiring a certain number of adjacent high-stress elements to be identified as a high-stress region requiring densification.

[0087] S1.6: Adaptive mesh refinement is applied to high-stress areas, where the mesh size in high-stress areas is reduced by a preset ratio to form a locally refined mesh;

[0088] In an optional implementation, the encryption method includes: refining the tetrahedral elements into eight subdivisions (i.e., subdividing each element into multiple tetrahedral elements according to its centroid and midpoint), and ensuring boundary continuity and mesh compatibility; reducing the mesh size in high-stress areas by a preset ratio (e.g., 1 / 2 of the original element side length).

[0089] S1.7: Perform mesh quality inspection on locally refined meshes and calculate mesh quality indicators;

[0090] It should be noted that the specific formula for the grid quality index is as follows:

[0091]

[0092] Among them, Q m Here, V represents the mesh quality index, and l represents the volume of a tetrahedral element. max θ is the length of the longest side of the element. max θ is the largest dihedral angle of the element. min It is the smallest dihedral angle of the unit.

[0093] As illustrated in the example, this formula calculates the result Q. m The value range is [0,1], where 0 represents a severely distorted element and 1 represents a perfectly regular equilateral tetrahedral element; when the mesh quality index Q m A value greater than 0.3 indicates that the unit quality is acceptable.

[0094] S1.8: When the mesh quality index of all elements is less than or equal to the first preset threshold, the discretization of the geometric model is completed.

[0095] In an optional implementation, when the mesh quality index of a cell is greater than a first preset threshold, it is processed according to the following priority:

[0096] 1) Laplacian smoothing: Moves the node positions of inferior units to optimize shape quality;

[0097] 2) Local re-meshing: For elements that cannot be repaired by smoothing, locally regenerate Delaunay tetrahedral meshes around them;

[0098] 3) Relax the densification ratio: If the mesh quality index of the cell is still greater than the first preset threshold, the densification ratio will be relaxed (gradually relaxed from 0.3 to 0.5) to reduce the subdivision intensity.

[0099] It should be noted that the first preset threshold is determined based on a multi-dimensional comprehensive analysis that balances the requirements for finite element calculation accuracy, industry standard compatibility, encryption process stability, physical field characterization needs, and engineering efficiency.

[0100] In this embodiment of the application, step S2 includes:

[0101] S2.1: Apply boundary conditions and load conditions to the discretized geometric model;

[0102] In an optional implementation, boundary nodes on the discretized geometric model are selected as fixed support areas, and boundary constraint information is set; based on engineering design requirements, load conditions are applied in high-stress areas, wherein the load includes nodal force vectors and directions of action.

[0103] S2.2: Based on boundary conditions and load conditions, define the objective function and constraints for topology optimization, and construct a multi-objective optimization model;

[0104] In an optional implementation, the objective function includes a first objective function and a second objective function; the first objective function is the objective function for minimizing global compliance; the second objective function is the objective function for minimizing material usage; and the constraints include volume constraints, displacement constraints, and stress constraints.

[0105] In an optional implementation, the relevant formulas for the first objective function and the second objective function are as follows:

[0106]

[0107] Where f1 is the volume objective function, f2 is the stress uniformity objective function, N is the total number of mesh elements, and ρ i V represents the density of the i-th cell (values ​​0-1). i Let Vi be the volume of the i-th element, V0 be the total volume of the initial design domain, and σi be the volume of the i-th element. i Let σ be the equivalent stress of the i-th element. avg σ is the average equivalent stress value of all elements. max This represents the maximum allowable stress.

[0108] As illustrated in the example, the range of f2 is [0,1], where 0 indicates that the material is completely removed and 1 indicates that the initial volume is maintained; the range of f_2 is [0,1], where 0 indicates that the stress is completely uniformly distributed and 1 indicates that the stress distribution is extremely non-uniform.

[0109] In an optional implementation, the relevant formulas for the constraints are as follows:

[0110]

[0111] Where g1(ρ) is the volume constraint function, g2(u) is the displacement constraint function, g3(σ) is the stress constraint function, N is the total number of mesh elements, and ρ i Let V be the density of the i-th cell. i Let Vi be the volume of the i-th element, V0 be the total volume of the initial design domain, and δ be the volume constraint coefficient (usually taken as 0.3-0.7).max For the maximum displacement value, u allow To allow the maximum displacement, σ avg σ is the average equivalent stress value of all elements. yield β is the yield strength of the material, and β is the stress safety factor (usually taken as 0.8-0.9).

[0112] S2.3: A high-efficiency finite element solver is established using multi-threaded parallel computing technology. The high-efficiency finite element solver includes a sparse matrix storage module and a conjugate gradient iterative solution module.

[0113] In an optional implementation, the establishment of an efficient finite element solver includes: dividing the computation into multiple threads based on the OpenMP parallel programming framework, implementing dynamic resource allocation through a thread pool management mechanism, and setting up a data synchronization strategy between threads to ensure consistency; constructing a sparse matrix storage module, using a compressed row storage format (CSR) to store the stiffness matrix, and establishing row pointer arrays and column index arrays to record the positions of non-zero elements; constructing a conjugate gradient iterative solution module, decomposing matrix-vector multiplication operations into subtasks and implementing parallel processing, and setting up a conjugate vector update synchronization mechanism; establishing an inter-thread communication mechanism, using a shared memory model for data exchange, and setting up critical section protection to avoid conflicts; reducing memory access latency through cache alignment technology, balancing the load through a dynamic scheduling strategy, and establishing a performance monitoring module to evaluate computational efficiency, thereby achieving the construction of an efficient parallel solver.

[0114] S2.4: The element stiffness matrix of the multi-objective optimization model is read through an efficient finite element solver, and the global stiffness matrix is ​​generated by grouping.

[0115] In an optional implementation, the specific formula for the global stiffness matrix is ​​as follows:

[0116]

[0117] Where [K] is the global stiffness matrix, N is the total number of mesh elements, ρ_e is the element density, and B e The strain matrix, Let be the transpose of the strain matrix, and D be the element stiffness matrix. The specific formula is as follows:

[0118]

[0119] Where E is the elastic modulus and v is Poisson's ratio.

[0120] S2.5: Based on the global stiffness matrix, the stress field is calculated using the conjugate gradient iterative solution module to obtain stress distribution data;

[0121] S2.6: Based on stress distribution data, the displacement field is calculated using the conjugate gradient iterative solution module to obtain displacement distribution data;

[0122] S2.7: Simultaneously, the stress distribution data and displacement distribution data are stored in a sparse matrix storage module.

[0123] In this embodiment of the application, step S3 includes:

[0124] S3.1: Construct a multi-objective fitness evaluation function, and use stress distribution data and displacement distribution data as fitness evaluation indicators to establish a population evaluation criterion;

[0125] In an optional implementation, a population evaluation criterion is established based on the Pareto dominance principle, including:

[0126] First-level evaluation rule: Compare the fitness values ​​of any two particles. If all fitness values ​​of the first particle are not greater than the corresponding fitness value of the second particle, and there is at least one fitness value less than the second particle, then the first particle dominates the second particle. Record the number of times each particle is dominated by other particles, and the set of other particles dominated by that particle.

[0127] Second-level evaluation rule: Particles with a dominance count of zero are assigned to the first frontier; these particles are removed from the first frontier in turn, and the dominance count of the remaining particles is updated; the above process is repeated to determine the second frontier and the third frontier, etc., until all particles are assigned to the corresponding frontier.

[0128] The third-level evaluation rule is as follows: calculate the distance between each particle and its neighboring particles within the same frontal plane; assess the particle distribution density based on the distance values; prioritize retaining particles with lower distribution densities to maintain population diversity;

[0129] Fourth-level evaluation rules: Sort particles by primary and secondary order according to the frontier level; within the same frontier, sort particles by distribution density; generate a particle sorting sequence.

[0130] S3.2: Calculate the fitness value of the particle swarm according to the population evaluation criteria, and use the subpopulation partitioning strategy to group the particle swarm and allocate search space to the subpopulations. The subpopulations exchange fitness values ​​through an information exchange mechanism.

[0131] It should be noted that the subpopulation consists of several particles; each particle includes topological density variables, velocity variables, and individual optimal position information.

[0132] In an optional implementation, the specific formula for the fitness value is as follows:

[0133]

[0134] Wherein: F i F represents the fitness value of individual i. max F represents the maximum fitness value in the population. min This represents the minimum fitness value in the population.

[0135] S3.3: Set velocity update parameters and position update parameters for the subpopulation. The subpopulation searches for particles according to a preset iteration rule, performs non-dominated sorting on the searched particles, and calculates the crowding value. The specific formula is as follows:

[0136]

[0137] Among them, C i Let i be the crowding level value for individual i. Let j be the value of the individual adjacent to the right of the target. Let j be the value of the individual adjacent to the left of the target. To maximize the target j Let j be the minimum value of the objective.

[0138] S3.4: Based on the results of the non-dominated ordination and the crowding value, filter the non-dominated solutions and construct the Pareto front.

[0139] In an optional implementation, the dominance level and crowding value of each particle are obtained based on the results of the non-dominance sorting. The particles are sorted in ascending order of dominance level. For particles with the same dominance level, the particles are sorted in descending order of crowding value. A preset number of particles with the highest sorting values ​​are selected to enter the elite archive set.

[0140] During the update process of the elite archive set, the dominance relationships between newly generated particles and existing particles in the archive set are compared. If a new particle is dominated by any particle in the archive set, the new particle is discarded. If a new particle dominates some particles in the archive set, these dominated particles are deleted. If a new particle and particles in the archive set do not dominate each other, the new particle is added to the archive set. Simultaneously, to maintain the size of the archive set, when the size exceeds a preset limit, a pruning mechanism is activated. This mechanism calculates the crowding value of all particles in the archive set, retains particles with higher crowding values ​​to maintain diversity, and deletes particles with lower crowding values ​​until the size requirement is met.

[0141] During the dynamic update of the Pareto front, non-dominated solutions provided by each subpopulation are collected, dominance relationships are determined for all non-dominated solutions, and solutions that are not mutually dominant are retained to form the global Pareto front. The changes in the front in each iteration are recorded.

[0142] In an optional implementation, to determine whether the optimization process has converged, the degree of change of the frontier surface in multiple consecutive iterations is calculated; when the degree of change is less than a preset threshold, convergence is determined, or when the calculation is terminated when the number of iterations reaches the upper limit, a non-dominated solution set is output; otherwise, the process returns to step S3.4 to continue iterative optimization.

[0143] S3.4: Exchange non-dominated solutions among subpopulations according to the preset iteration cycle, update the Pareto front, and generate the Pareto optimal solution set.

[0144] In this embodiment of the application, step S4 includes:

[0145] S4.1: The analytic hierarchy process (AHP) is used to set evaluation indicators for the Pareto optimal solution set and construct a judgment matrix. The evaluation indicators include structural quality, stress level and displacement response.

[0146] S4.2: Perform a consistency check on the judgment matrix, calculate the weight coefficients of each evaluation index, and generate a comprehensive evaluation function;

[0147] S4.2.1: Perform a consistency check on the judgment matrix;

[0148] Specifically, it includes:

[0149] S4.2.1.1: Calculate the largest eigenvalue of the judgment matrix, solve the characteristic equation using the power iteration method, and obtain the largest eigenvalue of the judgment matrix;

[0150] S4.2.1.2: Based on the largest eigenvalue, calculate the consistency index (CI) of the judgment matrix. The specific formula is as follows:

[0151]

[0152] Where CI is the consistency index, and λ max is the largest eigenvalue, and m is the order of the judgment matrix.

[0153] S4.2.1.3: Based on the consistency index CI, find the corresponding order of random consistency index value RI, and calculate the consistency ratio CR of the judgment matrix. The specific formula is as follows:

[0154]

[0155] S4.2.1.4: When the consistency ratio CR is less than the second preset threshold, the judgment matrix is ​​determined to pass the consistency test; when the consistency ratio CR is greater than the second preset threshold, the judgment matrix is ​​reconstructed.

[0156] It should be noted that the second preset threshold is determined based on the theoretical foundation of the Analytic Hierarchy Process (AHP) and engineering practice experience, and is usually set to 0.1.

[0157] S4.2.1.5: For the judgment matrix that passes the consistency test, the weight coefficient of each evaluation index is calculated using the arithmetic mean method.

[0158] S4.2.2: Construction of the comprehensive evaluation function;

[0159] Specifically, it includes:

[0160] S4.2.2.1: The evaluation indices set for the Pareto optimal solution set are normalized, and the range standardization method is used to map the values ​​of each index to the [0,1] interval, constructing a weighted summation type comprehensive evaluation function. The specific formula is as follows:

[0161]

[0162] Where S is the comprehensive evaluation score, w i Let x be the weight of the i-th indicator. i Let be the standardized value of the i-th indicator, and n be the number of evaluation indicators.

[0163] S4.2.2.2: Perform a monotonicity test on the comprehensive evaluation function, and verify the effectiveness of the tested comprehensive evaluation function through test examples, thus completing the construction of the comprehensive evaluation function.

[0164] S4.3: Input the Pareto optimal solution set into the comprehensive evaluation function and sort the Pareto optimal solution set according to the score from high to low;

[0165] S4.4: Select the solution with the highest comprehensive score as the topology scheme and extract the cell density distribution data of the topology scheme;

[0166] S4.5: Import the element density distribution data into the structural topology optimization software and output the optimization result report, which includes the stress distribution, displacement distribution and iteration history data of the topology scheme.

[0167] In summary, this invention introduces adaptive mesh refinement technology to discretize the geometric model, enabling localized mesh refinement of high-stress areas while maintaining overall structural computational efficiency. This achieves high-precision modeling of key structural components, thereby improving the accuracy and stability of the overall finite element analysis. By employing an efficient finite element solver to solve the discretized model, accurate stress and displacement distribution data can be quickly obtained, effectively supporting the computational needs of subsequent multi-objective optimization models and improving the overall response speed and resource utilization efficiency of the solution process. Utilizing a multi-swarm particle swarm optimization algorithm with parallel computing, the Pareto optimal solution set is efficiently searched in the multi-objective space. The diversity and global optimality of solutions are improved through sub-swarm collaborative search and solution exchange mechanisms, enhancing the global exploration capability and robustness of structural topology optimization results. By introducing the analytic hierarchy process (AHP) for multi-criteria decision analysis of the Pareto optimal solution set, and combining the comprehensive weight evaluation of multiple indicators such as structural quality, stress level, and displacement response, objective identification and scientific selection of the optimal topological structure scheme are achieved. Furthermore, the optimal solution is fed back to the topology optimization software through a feedback mechanism, improving the practicality and engineering feasibility of the optimization results.

[0168] This embodiment also provides an electronic device, which includes a processor, a memory, a communication interface, a display screen, and an input device connected via a system bus. The processor of this computer device provides computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The communication interface of the computer device is used for wired or wireless communication with external terminals. Wireless communication can be achieved through Wi-Fi, carrier networks, NFC (Near Field Communication), or other technologies. When the computer program is executed by the processor, it implements a multi-task edge computing resource scheduling method. The display screen of the computer device can be a liquid crystal display screen or an e-ink display screen. The input device of the computer device can be a touch layer covering the display screen, or buttons, a trackball, or a touchpad located on the casing of the computer device, or an external keyboard, touchpad, or mouse, etc.

[0169] This embodiment also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method proposed in the above embodiments.

[0170] The storage medium proposed in this embodiment belongs to the same inventive concept as the method proposed in the above embodiments. Technical details not described in detail in this embodiment can be found in the above embodiments, and this embodiment has the same beneficial effects as the above embodiments.

[0171] Based on the above description of the implementation methods, those skilled in the art can clearly understand that the present invention can be implemented using software and necessary general-purpose hardware, and of course, it can also be implemented using hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as a computer floppy disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk, or optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the method of the embodiments of the present invention.

[0172] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

[0173] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented using various computer languages.

[0174] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0175] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0176] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0177] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0178] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A multi-objective optimization solution method for structural topology optimization software, characterized in that: include, The geometric model of the engineering structure is imported into topology optimization software, and the geometric model is discretized using adaptive mesh refinement technology. Based on the discretized geometric model, an efficient finite element solver is used to solve the constructed multi-objective optimization model to obtain stress distribution data and displacement distribution data; Based on the stress distribution data and the displacement distribution data, the Pareto optimal solution set is obtained by optimizing the solution using a multi-swarm particle swarm algorithm with parallel computing. The analytic hierarchy process (AHP) is used to perform multi-criteria decision analysis on the Pareto optimal solution set to determine the topology scheme. The topology scheme is then fed back to the topology optimization software to complete the multi-objective optimization solution. The analytic hierarchy process is used to set evaluation indicators for the Pareto optimal solution set and construct a judgment matrix. The evaluation indicators include structural quality, stress level and displacement response. The consistency of the judgment matrix is ​​checked, the weight coefficients of each evaluation index are calculated, and a comprehensive evaluation function is generated. The Pareto optimal solution set is input into the comprehensive evaluation function, and the Pareto optimal solution set is sorted in descending order of score. The solution with the highest comprehensive score is selected as the topology scheme, and the cell density distribution data of the topology scheme is extracted. The unit density distribution data is imported into the structural topology optimization software, and an optimization result report is output, wherein the optimization result report includes the stress distribution, displacement distribution and iteration history data of the topology scheme; The method for obtaining the Pareto optimal solution set is as follows: A multi-objective fitness evaluation function was constructed, and stress distribution data and displacement distribution data were used as fitness evaluation indicators to establish a population evaluation criterion. The fitness values ​​of the particle swarm are calculated according to the population evaluation criteria, and the particle swarm is grouped using a subpopulation partitioning strategy. Search spaces are allocated to the subpopulations, and the fitness values ​​are exchanged between the subpopulations through an information exchange mechanism. Set velocity update parameters and position update parameters for the subpopulation, wherein the subpopulation searches for particles according to a preset iteration rule, and performs non-dominated sorting on the searched particles to calculate the crowding value; Based on the results of the non-dominated sorting and the crowding value, non-dominated solutions are selected, and the Pareto front is constructed. According to a preset iteration cycle, non-dominated solutions are exchanged among subpopulations to update the Pareto front and generate a Pareto optimal solution set. The method for obtaining the stress distribution data and displacement distribution data is as follows: Apply boundary conditions and load conditions to the discretized geometric model; Based on the boundary conditions and load conditions, define the objective function and constraints for topology optimization, and construct a multi-objective optimization model; A high-efficiency finite element solver is established using multi-threaded parallel computing technology. The high-efficiency finite element solver includes a sparse matrix storage module and a conjugate gradient iterative solution module. The high-efficiency finite element solver reads the element stiffness matrix of the multi-objective optimization model and generates the global stiffness matrix using a set method. Based on the global stiffness matrix, the stress field is calculated using the conjugate gradient iterative solution module to obtain stress distribution data; Based on the stress distribution data, the displacement field is calculated using the conjugate gradient iterative solution module to obtain the displacement distribution data; Simultaneously, the stress distribution data and the displacement distribution data are stored in the sparse matrix storage module; The discretization method for the geometric model is as follows: The geometric model of the engineering structure is imported into the topology optimization software in STL format, a three-dimensional coordinate system is established, and the boundary information of the geometric model is obtained. The boundary information includes vertex coordinates, patch topology, and boundary normal vectors. Based on the boundary information, tetrahedral meshing elements are used to perform initial meshing on the geometric model to construct a three-dimensional mesh model. Finite element static analysis is performed on the mesh model to solve the stress distribution field under given load and constraint conditions, and the equivalent stress value inside each tetrahedral element is calculated. The stress gradient distribution is calculated based on the rate of change of equivalent stress values ​​among tetrahedral elements. When the stress value of a stress gradient distribution element is greater than the overall average stress ratio, and the stress elements form a continuously distributed region in space, this region is determined to be a high-stress region. Adaptive mesh refinement is applied to the high-stress region, wherein the mesh size of the high-stress region is reduced by a preset ratio to form a locally refined mesh; The localized encrypted mesh is subjected to mesh quality detection, and mesh quality indicators are calculated; When the mesh quality index of all units is less than or equal to the first preset threshold, the discretization of the geometric model is completed.

2. The multi-objective optimization solution method of structural topology optimization software according to claim 1, wherein: Perform a consistency check on the judgment matrix, including: Calculate the largest eigenvalue of the judgment matrix, and solve the characteristic equation using the power iteration method to obtain the largest eigenvalue of the judgment matrix; Based on the largest eigenvalue, calculate the consistency index (CI) of the judgment matrix; Find the corresponding random consistency index value RI based on the consistency index CI, and calculate the consistency ratio CR of the judgment matrix. When the consistency ratio CR is less than the second preset threshold, the judgment matrix is ​​determined to have passed the consistency test; when the consistency ratio CR is greater than the second preset threshold, the judgment matrix is ​​reconstructed. For the judgment matrix that has passed the consistency test, the weight coefficient of each evaluation index is calculated using the arithmetic mean method.

3. The multi-objective optimization solution method of structural topology optimization software according to claim 2, characterized in that: The method for constructing the comprehensive evaluation function is as follows: The evaluation indexes set for the Pareto optimal solution set are normalized, and the range standardization method is used to map the index values ​​to the [0,1] interval to construct a weighted summation type comprehensive evaluation function; The monotonicity of the comprehensive evaluation function is tested, and the effectiveness of the tested comprehensive evaluation function is verified through test examples, thus completing the construction of the comprehensive evaluation function.

4. The multi-objective optimization solution method for structural topology optimization software as described in claim 1, characterized in that: The objective function includes a first objective function and a second objective function; the first objective function is the objective function for minimizing global compliance; the second objective function is the objective function for minimizing material usage.

5. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that: When the processor executes the computer program, it implements the steps of the multi-objective optimization solution method of the structural topology optimization software according to any one of claims 1 to 4.

6. A computer readable storage medium having stored thereon a computer program, characterized in that: When the computer program is executed by the processor, it implements the steps of the multi-objective optimization solution method of the structural topology optimization software according to any one of claims 1 to 4.

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