Multi-objective optimization solution method for structural topology optimization software

Abstract

The invention discloses a multi-objective optimization solution method for structural topological optimization software, which relates to the technical field of structural topological optimization, and comprises the following steps of: importing a geometric model of an engineering structure into topological optimization software, discretizing the geometric model through a self-adaptive mesh refinement technology, and solving the discretized geometric model; solving the constructed multi-objective optimization model by adopting an efficient finite element solver to obtain stress distribution data and displacement distribution data, and carrying out optimization solution through a parallel computing multi-population particle swarm algorithm to obtain a Pareto optimal solution set; and performing multi-criterion decision analysis on the Pareto optimal solution set by adopting an analytic hierarchy process, determining a topological structure scheme, and feeding back the topological structure scheme to the structure topological optimization software to complete multi-objective optimization solution. Through the above steps, objective discrimination and scientific screening of the optimal topological structure scheme are realized, the optimal solution is transmitted back to topological optimization software through a feedback mechanism, and the practicability of the optimization result and the engineering implementability are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of structural topology optimization, in particular to a multi-objective optimization solution method for structural topology optimization software. Background Art

[0002] At present, structural topology optimization technology still has significant technical bottlenecks in the field of multi-objective optimization. Traditional optimization methods usually adopt a single-objective optimization framework or a multi-objective optimization strategy with fixed weights, which makes it difficult to effectively balance the collaborative optimization of multiple conflicting objectives. For example, the iterative solution process based on the variable density method (SIMP) and the optimization criterion (OC) is sensitive to convergence conditions, which may lead to local optimal solutions and fail to obtain the globally optimal topological structure. In addition, the existing methods still have shortcomings in computational efficiency, interpretability of optimization results, and engineering applicability, especially when dealing with optimization problems under complex structures and multiple working conditions. It is often difficult to simultaneously meet the requirements of multiple performance indicators such as stiffness, strength, and lightweight. Therefore, there is an urgent need for a multi-objective optimization solution method that integrates efficient numerical calculation, intelligent optimization algorithm, 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 with approximate results. By combining a multi-material filling strategy and polynomial interpolation technology, the range of feasible result domains is expanded, and an improved optimization criterion (OC) is used to improve convergence efficiency. However, this method still relies on empirical weight allocation during the multi-objective optimization process and has limited adaptability to high-dimensional non-convex optimization problems, which may cause the optimization results to deviate from actual engineering requirements. In addition, its inverse solution process may face numerical instability problems in complex structural optimization, affecting the 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, this method optimizes the weight distribution strategy of the multi-objective optimization model and improves 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 its optimization results still relies on manual experience and lacks a scientific multi-criteria evaluation system, making it difficult to achieve automated and intelligent optimization solution selection. Summary of the Invention

[0005] In view of the fact that the traditional optimization algorithm of the existing structural topology optimization software has a heavy computational burden and is prone to falling into local optimality when dealing with multi-objective optimization problems of engineering structures, the present invention is proposed.

[0006] Therefore, the problem to be solved by the present invention is how to achieve accurate and automated solution of multiple objectives in structural topology optimization by integrating efficient finite element solvers, adaptive mesh refinement technology, multi-population 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] In order to solve the above technical problems, the present invention provides the following technical solutions:

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

[0009] These include,

[0010] Importing the geometric model of the engineering structure into the topology optimization software and discretizing the geometric model 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, an optimization solution is performed by a multi-swarm particle swarm algorithm using parallel computing to obtain a Pareto optimal solution set;

[0013] A hierarchical analysis method is used to perform a multi-criteria decision analysis on the Pareto optimal solution set to determine a topology structure scheme, and the topology structure scheme is fed back to the structural topology optimization software to complete the multi-objective optimization solution.

[0014] As a preferred solution of the multi-objective optimization solution method of the structural topology optimization software of the present invention, wherein: a multi-criteria decision analysis is performed on the Pareto optimal solution set using the hierarchical analysis method to determine a topology structure solution, and the topology structure solution is fed 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, wherein the evaluation indicators include structural quality, stress level and displacement response;

[0016] Performing consistency check on the judgment matrix, calculating the weight coefficient of each evaluation index, and generating a comprehensive evaluation function;

[0017] Inputting the Pareto optimal solution set into the comprehensive evaluation function, and sorting the Pareto optimal solution set in descending order of scores;

[0018] Selecting the solution with the highest comprehensive score as the topology solution, and extracting the unit density distribution data of the topology solution;

[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 stress distribution, displacement distribution and iteration history data of the topology structure scheme.

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

[0021] Calculating the maximum eigenvalue of the judgment matrix, solving the characteristic equation using the power iteration method, and obtaining the maximum eigenvalue of the judgment matrix;

[0022] Calculating the consistency index CI of the judgment matrix based on the maximum eigenvalue;

[0023] According to the consistency index CI, the random consistency index value RI of the corresponding order is found, and the consistency ratio CR of the judgment matrix is calculated;

[0024] When the consistency ratio CR is less than a second preset threshold, it is determined that the judgment matrix passes 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 passes the consistency test, the weight coefficient of each evaluation index is calculated using the arithmetic mean method.

[0026] As a preferred solution of the multi-objective optimization solution method of the structural topology optimization software of the present invention, the method for constructing the comprehensive evaluation function is:

[0027] The evaluation indicators of the Pareto optimal solution set are normalized, and the range normalization method is used to map the values of each indicator to the interval [0,1] to construct a weighted sum comprehensive evaluation function;

[0028] The monotonicity test of the comprehensive evaluation function is performed, and the effectiveness of the comprehensive evaluation function after the test is verified through a test example, thereby completing the construction of the comprehensive evaluation function.

[0029] As a preferred solution of the multi-objective optimization solution method of the structural topology optimization software of the present invention, the method for obtaining the Pareto optimal solution set is:

[0030] Construct a multi-objective fitness evaluation function, use stress distribution data and displacement distribution data as fitness evaluation indicators, and establish a population evaluation criterion;

[0031] Calculating the fitness value of the particle swarm according to the population evaluation criterion, and grouping the particle swarm using a sub-population partitioning strategy, allocating a search space for the sub-populations, wherein the sub-populations exchange the fitness values through an information exchange mechanism;

[0032] Setting a speed update parameter and a position update parameter for the subpopulation, wherein the subpopulation searches for particles according to a preset iterative rule, performs non-dominated sorting on the searched particles, and calculates a congestion value;

[0033] Based on the result of the non-dominated sorting and the congestion value, non-dominated solutions are screened and a Pareto front is constructed;

[0034] The non-dominated solutions are exchanged between the subpopulations according to a preset iteration period, the Pareto frontier is updated, and a Pareto optimal solution set is generated.

[0035] As a preferred solution of the multi-objective optimization solution method of the structural topology optimization software of the present invention, wherein: the method for obtaining the stress distribution data and the displacement distribution data is:

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

[0037] Based on the boundary conditions and the load conditions, defining the objective function and constraint conditions of topology optimization, and constructing a multi-objective optimization model;

[0038] An efficient finite element solver is established by using multi-threaded parallel computing technology, wherein the efficient finite element solver includes a sparse matrix storage module and a conjugate gradient iterative solution module;

[0039] Reading the unit stiffness matrix of the multi-objective optimization model through the efficient finite element solver, and generating a global stiffness matrix in a grouping manner;

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

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

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

[0043] As a preferred solution of the multi-objective optimization solution method of the structural topology optimization software described in the present invention, the objective function includes a first objective function and a second objective function; the first objective function is a global flexibility minimum objective function; and the second objective function is a material usage minimum objective function.

[0044] As a preferred solution of the multi-objective optimization solution method of the structural topology optimization software of the present invention, the discretization method of the geometric model is:

[0045] Importing the geometric model of the engineering structure into the topology optimization software in STL format, establishing a three-dimensional coordinate system, and obtaining the boundary information of the geometric model, wherein the boundary information includes vertex coordinates, facet topology structure, and boundary normal vector;

[0046] Based on the boundary information, the geometric model is initially meshed using tetrahedral meshing units to construct a mesh model of a three-dimensional structure;

[0047] Performing finite element static analysis on the mesh model to solve the stress distribution field under given load and constraint conditions, and calculating the equivalent stress value inside each tetrahedral unit;

[0048] Calculate the stress gradient distribution based on the rate of change of equivalent stress values between tetrahedral elements;

[0049] 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 continuous distribution area in space, this area is determined as a high stress area;

[0050] Adaptively encrypting the mesh in the high stress area, wherein the mesh size in the high stress area is reduced according to a preset ratio to form a locally encrypted mesh;

[0051] Performing a grid quality test on the local encrypted grid and calculating a grid quality index;

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

[0053] In a second aspect, the present invention provides a computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: when the computer program instructions are executed by the processor, 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 are implemented.

[0054] In a third aspect, 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, 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 are implemented.

[0055] The beneficial effects of the present invention are:

[0056] 1. The geometric model of the engineering structure is imported into the topology optimization software and discretized using adaptive mesh refinement technology, enabling high-fidelity finite element modeling of complex engineering structures. Furthermore, a stress-driven adaptive mesh encryption strategy refines the meshing in areas of high stress concentration. This allows for detailed analysis and modeling of the stress response of the structural model in key areas while ensuring overall computational efficiency, thereby improving the physical credibility and convergence stability of subsequent finite element solutions and optimization results.

[0057] 2. A multi-threaded finite element solver with a sparse matrix storage module and a conjugate gradient iteration module has been introduced, enabling fast solutions in large-scale three-dimensional structural scenarios.

[0058] 3. We introduced a multi-swarm parallel particle swarm optimization algorithm and combined it with a non-dominated sorting and fitness evaluation mechanism to construct an evolutionary strategy suitable for the collaborative optimization of multi-objective functions. This strategy overcomes the limitation of a single particle swarm that is prone to falling into local optimality in complex objective spaces and achieves a balance between maintaining the diversity of the solution set and rapid convergence.

[0059] 4. A hierarchical analysis method is used to perform a multi-criteria decision analysis on the Pareto optimal solution set to determine the topology structure scheme, and the topology structure scheme is fed back to the structural topology optimization software to complete the multi-objective optimization solution, avoiding the uncertainty and subjectivity of the traditional method that relies on manual judgment to select solutions. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] To more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. Those skilled in the art can also derive other drawings based on these drawings without inventive effort. Among them:

[0061] Figure 1 This is a flow chart of the multi-objective optimization solution method of the structural topology optimization software in Example 1. DETAILED DESCRIPTION

[0062] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0063] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0064] Secondly, the term "one embodiment" or "embodiment" 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 various places throughout this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive of 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 multi-swarm particle swarm algorithm with parallel computing is used to optimize and solve the problem, obtaining the Pareto optimal solution set.

[0070] S4: Use the hierarchical analysis method to perform multi-criteria decision analysis on the Pareto optimal solution set, determine the topology structure scheme, and feed the topology structure scheme back to the structural topology optimization software to complete the multi-objective optimization solution.

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

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

[0073] S1.2: Based on the boundary information, the geometric model is initially meshed using tetrahedral meshing elements to construct a mesh model of the three-dimensional structure.

[0074] In an optional embodiment, the method for constructing a mesh model is to perform initial mesh division based on the Delaunay triangulation algorithm of 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, and reconstructing the model surface through boundary recovery technology, and then inserting internal nodes inside the convex hull to generate an initial tetrahedral mesh; optimizing the initial tetrahedral mesh by calculating the quality parameters of each tetrahedral element, deleting inferior tetrahedral elements, adjusting the node position to optimize the element shape, and merging adjacent small tetrahedral elements to regenerate the local mesh; performing mesh encryption based on stress gradient, specifically including calculating the stress gradient value of each element, marking the high stress gradient area elements and subdividing them, and inserting transition elements at the subdivision boundary to ensure mesh continuity; performing mesh smoothing, by calculating the topological relationship of each node, using the Laplace smoothing algorithm to adjust the node position, optimize the volume ratio of the element, and eliminate mesh distortion; performing mesh quality assessment, including calculating the aspect ratio of the element, checking the angle of the element, evaluating the uniformity of the node distribution, verifying the mesh connectivity, and outputting a quality assessment report, thereby 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 embodiment, a finite element static analysis is performed on the mesh model, including: starting by calculating the shape function and its derivatives of each tetrahedral unit, using Gaussian integral to calculate the unit stiffness matrix, using isoparametric unit technology to convert the local coordinate system into a global coordinate system, and establishing a strain matrix and a stress-strain relationship matrix; assembling units based on the unit's nodal degrees of freedom, using node numbering rules to determine the degree of freedom correspondence, and assembling the unit stiffness matrix into a global stiffness matrix; introducing load conditions, converting concentrated forces into equivalent nodal forces, and converting distributed forces into nodal force vectors through shape function interpolation, while dealing with the influence of volume forces such as gravity; for constraint conditions, using the displacement method to impose fixed constraints and elastic supports, and modifying the corresponding rows and columns of the global stiffness matrix.

[0077] During the solution stage, the improved conjugate gradient method is used to solve the large-scale sparse linear equations, and the nodal displacement field is obtained through iterative calculation; based on the nodal displacement field, the strain field of each unit is calculated, and Hooke's law is used to solve the stress field.

[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] Among them, σ eff is the equivalent stress value of the unit, σ x is the normal stress component in the x direction, σ y is the normal stress component in the y direction, σ z is the normal stress component in the z direction, τ xy is the shear stress component in the xy plane, τ yz is the shear stress component in the yz plane, τ zx is the shear stress component in the zx plane, α e is the element geometry correction factor, ε v is the volume strain, and ε0 is the reference strain value.

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

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

[0083]

[0084] Among them, G σ is the stress gradient value, n is the number of adjacent elements, ω e is the unit weight coefficient (determined by the number of unit shared nodes), σ eff is the equivalent stress value of the unit, x e 、y e 、z e is the local coordinate of the unit, V e is the unit volume, V ref is the reference volume value (taking the average volume of the grid), λ is the sensitivity coefficient (range 1-10), Q e is the unit quality indicator.

[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 continuous distribution area in space, this area is determined to be a high stress area;

[0086] For example, when the equivalent stress value of a cell is greater than 1.5 to 2 times the global average stress value, the cell will be marked as a high-stress cell and require infill. At the same time, these high-stress cells need to form a continuous area in space, usually requiring a certain number of adjacent high-stress cells to be identified as a high-stress area requiring infill.

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

[0088] In an optional embodiment, the encryption method includes: octanting the tetrahedral units (i.e., subdividing each unit into multiple tetrahedral units according to its center of gravity and midpoint of the face), and ensuring boundary continuity and mesh compatibility; the mesh size in the high stress area is reduced by a preset ratio (such as 1 / 2 of the original unit side length).

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

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

[0091]

[0092] Among them, Q m is the mesh quality index, V is the volume of the tetrahedron unit, l max is the longest side length of the unit, θ max is the maximum dihedral angle of the element, θ min is the minimum dihedral angle of the element.

[0093] For example, this formula calculates the result Q m The value range is [0,1], where 0 represents a severely distorted unit and 1 represents a completely regular equilateral tetrahedron unit; when the mesh quality index Q m When >0.3, it means the unit quality is acceptable.

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

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

[0096] 1) Laplacian smoothing: Move the node positions of poor-quality elements to optimize shape quality;

[0097] 2) Local re-meshing: For cells that cannot be repaired by smoothing, Delaunay tetrahedron meshes are regenerated locally around them;

[0098] 3) Relaxing the encryption ratio: If the grid quality index of the unit is still greater than the first preset threshold, the encryption ratio will be relaxed (gradually 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 of finite element calculation accuracy requirements, industry standard compatibility, encryption process stability, physical field characterization requirements and engineering efficiency balance.

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

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

[0102] In an optional embodiment, 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 to high stress areas, where the load includes a node force vector and a direction of action.

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

[0104] In an optional embodiment, the objective function includes a first objective function and a second objective function; the first objective function is a global flexibility minimum objective function; the second objective function is a material usage minimum objective function; and the constraints include volume constraints, displacement constraints, and stress constraints.

[0105] In an optional embodiment, the related formulas of 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 grid elements, and ρ i is the density of the i-th unit (value ranges from 0 to 1), V i is the volume of the i-th unit, V0 is the total volume of the initial design domain, σ i is the equivalent stress of the i-th unit, σ avg is the average equivalent stress value of all elements, σ max is the maximum allowable stress.

[0108] For example, the range of f2 is [0,1], where 0 means that the material is completely removed and 1 means that the initial volume is maintained; the range of f_2 is [0,1], where 0 means that the stress is completely uniformly distributed and 1 means that the stress distribution is extremely uneven.

[0109] In an optional embodiment, the relevant formulas of the constraint conditions are as follows:

[0110]

[0111] Among them, 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 grid elements, ρ i is the density of the i-th unit, V i is the volume of the i-th unit, V0 is the total volume of the initial design domain, δ is the volume constraint coefficient (usually 0.3-0.7), umax is the maximum displacement value, u allow is the maximum allowable displacement, σ avg is the average equivalent stress value of all elements, σ yield is the material yield strength, and β is the stress safety factor (usually 0.8-0.9).

[0112] S2.3: Use multi-threaded parallel computing technology to establish an efficient finite element solver, where the efficient finite element solver includes a sparse matrix storage module and a conjugate gradient iterative solution module;

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

[0114] S2.4: Read the element stiffness matrix of the multi-objective optimization model through an efficient finite element solver and generate the global stiffness matrix using a grouping method;

[0115] In an optional embodiment, the specific formula of 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 is the strain matrix, is the transposed matrix of the strain matrix, D is the element stiffness matrix, and 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 conjugate gradient iterative solution module is used to calculate the stress field and obtain stress distribution data;

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

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

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

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

[0125] In an optional embodiment, 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 values of the second particle, and at least one fitness value is smaller than the second particle, then the first particle is determined to dominate the second particle. Record the number of times each particle is dominated by other particles, as well as the set of other particles dominated by the particle.

[0127] Second-level evaluation rule: Particles with zero dominance counts are assigned to the first frontier. These particles are removed from the first frontier in turn, and the dominance counts of the remaining particles are updated. The above process is repeated to determine the second and third frontiers, and so on, until all particles are assigned to the corresponding frontiers.

[0128] The third-level evaluation rule is to calculate the distance between each particle and its adjacent particles within the same frontier; evaluate the distribution density of particles based on the distance value; and give priority to retaining particles with smaller distribution density to maintain population diversity.

[0129] The fourth level evaluation rules are: sort the particles according to the frontier surface level; sort the particles according to the distribution density within the same frontier surface; and 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 sub-population division strategy to group the particle swarm and allocate search space for the sub-populations. The sub-populations exchange fitness values through the information exchange mechanism.

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

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

[0133]

[0134] Among them: F i is the fitness value of individual i, F max is the maximum fitness value in the population, F min is the minimum fitness value in the population.

[0135] S3.3: Set the speed update parameters and position update parameters for the sub-population. The sub-population searches for particles according to the preset iterative rules, performs non-dominated sorting on the searched particles, and calculates the congestion value. The specific formula is as follows:

[0136]

[0137] Among them, C i is the crowding value of individual i, is the value of target j in the adjacent right individual, is the value of target j in the adjacent left individual, is the maximum value of target j, is the minimum value of target j.

[0138] S3.4: Based on the results of non-dominated sorting and the congestion value, screen non-dominated solutions and construct the Pareto front;

[0139] In an optional embodiment, the dominance level and crowding value of each particle are obtained according to the result of non-dominated sorting, and a primary sorting is performed from low to high according to the dominance level. For particles with the same dominance level, a secondary sorting is performed from large to small according to the crowding value, and a preset number of particles with the highest ranking are selected to enter the elite archive set.

[0140] During the update process of the elite archive set, the dominance relationship between newly generated particles and existing particles in the archive set is compared. If a new particle is dominated by any particle in the archive set, it is discarded. If a new particle dominates some particles in the archive set, these dominated particles are deleted. If the new particle and the particles in the archive set do not dominate each other, the new particle is added to the archive set. At the same time, to maintain the size of the archive set, when the archive set size exceeds a preset upper limit, a pruning mechanism is activated. The crowding values of all particles in the archive set are calculated, and particles with higher crowding values are retained to maintain diversity, while particles with lower crowding values are deleted until the size requirement is met.

[0141] During the dynamic update process of the Pareto front, the non-dominated solutions provided by each sub-population are collected, the dominance relationship of all non-dominated solutions is judged, the mutually non-dominated solutions are retained to form the global Pareto front, and the changes in the front of each iteration are recorded.

[0142] In an optional embodiment, in order to determine whether the optimization process has converged, the degree of change of the frontier surface for 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 an upper limit, the non-dominated solution set is output, otherwise return to step S3.4 to continue iterative optimization.

[0143] S3.4: Exchange non-dominated solutions between subpopulations according to the preset iteration period, update the Pareto frontier, and generate a Pareto optimal solution set.

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

[0145] S4.1: Use the analytic hierarchy process to set evaluation indicators for the Pareto optimal solution set and construct a judgment matrix, where the evaluation indicators include structural quality, stress level and displacement response;

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

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

[0148] Specifically include:

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

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

[0151]

[0152] Among them, CI is the consistency index, λ max is the maximum eigenvalue, and m is the order of the judgment matrix.

[0153] S4.2.1.3: Find the random consistency index value RI of the corresponding order based on the consistency index CI 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 have passed 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 basis of the hierarchical analysis method 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 arithmetic mean method is used to calculate the weight coefficient of each evaluation indicator.

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

[0159] Specifically include:

[0160] S4.2.2.1: Normalize the evaluation indicators set for the Pareto optimal solution set and use the range normalization method to map the values of each indicator to the interval [0,1] to construct a weighted summation type comprehensive evaluation function. The specific formula is as follows:

[0161]

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

[0163] S4.2.2.2: Perform a monotonicity test on the comprehensive evaluation function, verify the effectiveness of the tested comprehensive evaluation function through test cases, and complete 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 from high to low according to the score;

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

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

[0167] In summary, the present invention discretizes the geometric model by introducing adaptive mesh refinement technology. While retaining the overall structural calculation efficiency, it can perform local encryption processing on high stress areas, achieve high-precision modeling of key parts of the structure, and thus improve the accuracy and stability of the overall finite element analysis. By using an efficient finite element solver to solve the discretized model, not only can accurate stress and displacement distribution data be quickly obtained, but it also effectively supports the calculation requirements of the subsequent multi-objective optimization model, improving the overall response speed and resource utilization efficiency of the solution process. With the help of a multi-population 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 the solution are improved through sub-population collaborative search and solution exchange mechanism, thereby enhancing the global exploration capability and robustness of the structural topology optimization results. By introducing the hierarchical analysis method to perform multi-criteria decision analysis on the Pareto optimal solution set, combined with the comprehensive weight evaluation of multiple indicators such as structural quality, stress level and displacement response, the objective identification and scientific screening of the optimal topological structure scheme are achieved, and 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, memory, a communication interface, a display screen, and an input device connected via a system bus. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The communication interface of the computer device is used to communicate with an external terminal in a wired or wireless manner. The wireless manner can be achieved through WIFI, an operator network, NFC (near field communication) or other technologies. When the computer program is executed by the processor, a multi-task edge computing resource scheduling method is implemented. The display screen of the computer device can be a liquid crystal display or an electronic ink display screen. The input device of the computer device can be a touch layer covering the display screen, or a button, trackball or touchpad provided on the computer device housing, or an external keyboard, touchpad or mouse.

[0169] This embodiment further provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the method proposed in the above embodiment is implemented.

[0170] The storage medium proposed in this embodiment and the method proposed in the above embodiment belong to the same inventive concept. For technical details not fully described in this embodiment, please refer to the above embodiment, and this embodiment has the same beneficial effects as the above embodiment.

[0171] Through the above description of the implementation methods, those skilled in the art can clearly understand that the present invention can be implemented with the help of software and necessary general-purpose hardware, and of course it can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the 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 (FLASH), hard disk or optical disk, etc., including a number of instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute the method of the embodiment 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 the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

[0173] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the application can adopt 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.) that contain computer-usable program code. The scheme in the embodiment of the present application can be implemented in various computer languages.

[0174] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0175] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0176] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0177] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present application.

[0178] Obviously, those skilled in the art may make various changes and modifications to this application without departing from the spirit and scope of this application. Thus, if these modifications and variations of this application fall within the scope of the claims of this application and their equivalents, this application is intended to include these modifications and variations.

Claims

1. A multi-objective optimization solution method for structural topology optimization software, characterized by: include, Importing the geometric model of the engineering structure into the topology optimization software and discretizing the geometric model 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, an optimization solution is performed by a multi-swarm particle swarm algorithm using parallel computing to obtain a Pareto optimal solution set; A hierarchical analysis method is used to perform a multi-criteria decision analysis on the Pareto optimal solution set to determine a topology structure scheme, and the topology structure scheme is fed back to the structural topology optimization software to complete the multi-objective optimization solution.

2. The multi-objective optimization solution method of structural topology optimization software according to claim 1, characterized in that: A multi-criteria decision analysis is performed on the Pareto optimal solution set using the analytic hierarchy process to determine a topology solution. The topology solution is then fed back to the structural topology optimization software to complete a multi-objective optimization solution, including: The analytic hierarchy process is used to set evaluation indicators for the Pareto optimal solution set and construct a judgment matrix, wherein the evaluation indicators include structural quality, stress level and displacement response; Performing consistency check on the judgment matrix, calculating the weight coefficient of each evaluation index, and generating a comprehensive evaluation function; Inputting the Pareto optimal solution set into the comprehensive evaluation function, and sorting the Pareto optimal solution set in descending order of scores; Selecting the solution with the highest comprehensive score as the topology solution, and extracting the unit density distribution data of the topology solution; 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 stress distribution, displacement distribution and iteration history data of the topology structure scheme.

3. The multi-objective optimization solution method of structural topology optimization software according to claim 2, characterized in that: Performing a consistency check on the judgment matrix includes: Calculating the maximum eigenvalue of the judgment matrix, solving the characteristic equation using the power iteration method, and obtaining the maximum eigenvalue of the judgment matrix; Calculating the consistency index CI of the judgment matrix based on the maximum eigenvalue; According to the consistency index CI, the random consistency index value RI of the corresponding order is found, and the consistency ratio CR of the judgment matrix is calculated; When the consistency ratio CR is less than a second preset threshold, it is determined that the judgment matrix passes 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 passes the consistency test, the weight coefficient of each evaluation index is calculated using the arithmetic mean method.

4. 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: The evaluation indicators of the Pareto optimal solution set are normalized, and the range normalization method is used to map the values of each indicator to the interval [0,1] to construct a weighted sum comprehensive evaluation function; The monotonicity test of the comprehensive evaluation function is performed, and the effectiveness of the comprehensive evaluation function after the test is verified through a test example, thereby completing the construction of the comprehensive evaluation function.

5. The multi-objective optimization solution method of structural topology optimization software according to claim 4, characterized in that: The method for obtaining the Pareto optimal solution set is: Construct a multi-objective fitness evaluation function, use stress distribution data and displacement distribution data as fitness evaluation indicators, and establish a population evaluation criterion; Calculating the fitness value of the particle swarm according to the population evaluation criterion, and grouping the particle swarm using a sub-population partitioning strategy, allocating a search space for the sub-populations, wherein the sub-populations exchange the fitness values through an information exchange mechanism; Setting a speed update parameter and a position update parameter for the subpopulation, wherein the subpopulation searches for particles according to a preset iterative rule, performs non-dominated sorting on the searched particles, and calculates a congestion value; Based on the result of non-dominated sorting and the congestion value, non-dominated solutions are screened and a Pareto front is constructed; The non-dominated solutions are exchanged between the subpopulations according to a preset iteration period, the Pareto frontier is updated, and a Pareto optimal solution set is generated.

6. The multi-objective optimization solution method of structural topology optimization software according to claim 5, characterized in that: The method for obtaining the stress distribution data and displacement distribution data is: Apply boundary conditions and load conditions to the discretized geometric model; Based on the boundary conditions and the load conditions, defining the objective function and constraint conditions of topology optimization, and constructing a multi-objective optimization model; An efficient finite element solver is established by using multi-threaded parallel computing technology, wherein the efficient finite element solver includes a sparse matrix storage module and a conjugate gradient iterative solution module; Reading the unit stiffness matrix of the multi-objective optimization model through the efficient finite element solver, and generating a global stiffness matrix in a grouping manner; Based on the global stiffness matrix, the conjugate gradient iterative solution module is used to perform stress field calculation to obtain stress distribution data; Based on the stress distribution data, the conjugate gradient iterative solution module is used to calculate the displacement field to obtain displacement distribution data; At the same time, the stress distribution data and the displacement distribution data are stored in the sparse matrix storage module.

7. The multi-objective optimization solution method of structural topology optimization software according to claim 6, characterized in that: The objective function includes a first objective function and a second objective function; the first objective function is a global flexibility minimum objective function; the second objective function is a material usage minimum objective function.

8. The multi-objective optimization solution method of structural topology optimization software according to claim 6, characterized in that: The discretization method of the geometric model is: Importing the geometric model of the engineering structure into the topology optimization software in STL format, establishing a three-dimensional coordinate system, and obtaining the boundary information of the geometric model, wherein the boundary information includes vertex coordinates, facet topology structure, and boundary normal vector; Based on the boundary information, the geometric model is initially meshed using tetrahedral meshing units to construct a mesh model of a three-dimensional structure; Performing finite element static analysis on the mesh model to solve the stress distribution field under given load and constraint conditions, and calculating the equivalent stress value inside each tetrahedral unit; Calculate the stress gradient distribution based on the rate of change of equivalent stress values between tetrahedral elements; 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 continuous distribution area in space, this area is determined to be a high stress area; Adaptively encrypting the mesh in the high stress area, wherein the mesh size in the high stress area is reduced according to a preset ratio to form a locally encrypted mesh; Performing a grid quality test on the local encrypted grid and calculating a grid quality index; When the mesh quality indexes of all cells are less than or equal to a first preset threshold, the discretization of the geometric model is completed.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the multi-objective optimization solution method of the structural topology optimization software according to any one of claims 1 to 8 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the multi-objective optimization solution method of the structural topology optimization software according to any one of claims 1 to 8 are implemented.

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