CN-122020873-A - Mechanical structure topology optimization method based on whale optimization algorithm

Abstract

The invention provides a mechanical structure topology optimization method based on a whale optimization algorithm, which comprises the following steps of 1, establishing a material density set M, 2, setting a target of minimizing the sum of flexibility values, optimizing the material density by using the whale optimization algorithm to generate an optimal material density configuration, and 3, applying the optimal material density configuration to a mechanical structure. The invention effectively avoids the common checkerboard phenomenon in the traditional topology optimization algorithm, thereby ensuring that the structure topology is clearer and more stable.

Inventors

• LI YAXUAN
• DENG WENXIN
• LUO RUI
• ZHANG XINYANG
• Zang Shang
• Wei Sichuang
• ZENG QIANYU
• LI CHENXUE

Assignees

• 上海理工大学

Dates

Publication Date

20260512

Application Date

20251218

Claims (4)

1. 1. The mechanical structure topology optimization method based on whale optimization algorithm is characterized by comprising the following steps of: Step 1, establishing a material density set M= (M 1 ,m 2 ,...,m n ); Wherein the elements in the material density set M are the material densities of all the components in the mechanical structure; m n -the material density of the nth member; Step 2, setting the aim of minimizing the sum of the flexibility values, and optimizing the material density by using a whale optimization algorithm to generate an optimal material density configuration; And 3, applying the optimal material density configuration to a mechanical structure.
2. 2. The mechanical structure topology optimization method based on whale optimization algorithm according to claim 1, wherein the step 2 specifically comprises the following steps: step 2A, inputting a material density set M as a variable to be optimized into a whale optimization algorithm model; step 2B, setting an optimization objective function as follows: C(u)=min u T Ku Wherein C (u) -optimizes the objective function; u-global compliance matrix, wherein the elements are compliance values of the component; K-global rigidity matrix, wherein elements are rigidity values of the components; u T -transpose of the global compliance matrix; Step 2C, initializing the number N w of whale population individuals, and randomly generating an initial parameter vector X i (1)＝(m 1i (1),m 2i (1),...,m ni (1));i∈1～N w for each individual; step 2D, in each generation of iterative process, parameter updating is carried out according to a position updating formula of a whale optimizing algorithm, and spiral bubble predation behaviors, shrinkage surrounding behaviors and random hunting behaviors are simulated; step 2E, outputting an optimal parameter solution when the maximum iteration number or the error convergence condition is met
3. 3. The method of claim 2, wherein the updating rule used in step 2D comprises: spiral bubble predation behavior: X(t+1)=D′·e bl ·cos(2πl)+X * (t)D′=|X*(t)-X(t)| shrink wrapping behavior: X(t+1)=X * (t)-A·D D=|C·X * (t)-X(t)| Random search for hunting behavior: X(t+1)=X rand -A·D rand D rand ＝|C·X rand -X(t)| wherein c=2·r; a=2a· r-a; x (t+1) -position of next step whale; D' -spiral bubble predation, distance of current whale from prey; e bl -spiral equation, b-spiral convergence rate; l-a random number between (-1, 1); x (t) -the position of the current optimal solution; x (t) -current whale position; d-distance of current whale from prey while contracting surrounding behavior; x rand -a randomly selected position; d rand -distance between current whale and random solution; r-a random number between (0, 1); The a-convergence factor decreases linearly from 2 to 0.
4. 4. The method for topology optimization of a mechanical structure based on whale optimization algorithm of claim 1, wherein the mechanical structure is a robotic arm.

Description

Mechanical structure topology optimization method based on whale optimization algorithm Technical Field The invention belongs to the technical field of mechanical structure optimization, and particularly relates to a mechanical structure topology optimization method based on a whale optimization algorithm. Background Topology optimization is used as an advanced structural design method, and the optimal performance is realized under the constraint condition by optimizing material distribution. In mechanical structural design, optimizing design indexes is a key for improving structural performance. Common optimization criteria include structural stiffness, compliance, mass, strength, etc., where minimizing structural compliance is often the objective of optimization, as it is directly related to structural stability and performance. The deformation of the structure under the action of external force can be effectively reduced by minimizing the flexibility, and the durability and bearing capacity of the whole structure are improved. Therefore, how to improve the performance of the mechanical structure by optimizing the flexibility of the design structure becomes an important research direction in the design of the mechanical structure. Currently, common solving methods for optimizing the structural flexibility mainly comprise methods based on traditional optimizing algorithms (such as gradient descent methods, genetic algorithms, particle swarm optimization and the like). These approaches approach the optimal solution step by continuously adjusting design parameters such as material distribution, topology, etc. For example, genetic algorithms perform a balance of global and local searches by modeling the natural selection process, while particle swarm optimization algorithms mimic the foraging behavior of a bird swarm, looking for an optimal solution. While these methods can give somewhat better optimization results, they often suffer from drawbacks such as being prone to falling into locally optimal solutions when faced with complex constraints, and the computational resource consumption in high-dimensional problems is enormous. For example, BESO (bidirectional evolutionary structural optimization) and genetic algorithm are easy to fall into a local optimal solution in practical application, and the computational complexity is high, so that the performance of the method in high-dimensional problems is affected. In recent years, the academy has also proposed improved optimization methods. For example, the Whale Optimization Algorithm (WOA) has received increasing attention from students as a meta-heuristic based on population intelligence. The algorithm is used as a bionic algorithm, is inspired by the bubble net feeding behavior of the whale, and can perform global search in a large-scale search space by simulating the whale feeding behavior, so that the problem of local optimization is effectively avoided. Compared with the traditional algorithm, the whale optimization algorithm has stronger adaptability and superiority when dealing with complex nonlinear problems. The WOA algorithm has a simple structure and strong global searching capability, and can remarkably improve the optimization efficiency and the result quality by combining the WOA algorithm with topology optimization. However, whale optimization algorithms still face challenges in practical applications, for example, as the number of iterations increases, the algorithm may converge prematurely to a locally optimal solution or lack convergence speed, which affects the final optimization result. Therefore, although the existing solving methods can optimize indexes such as flexibility of a mechanical structure to a certain extent, there are some limitations on solving high-dimensional and multi-constraint problems, and further improvement and innovation are needed to improve the overall optimization effect. Disclosure of Invention The invention provides a mechanical structure topology optimization method based on a whale optimization algorithm, which aims to overcome the limitation of the traditional algorithm on global search, thereby finding a better design. The method simulates the spiral predation behavior of whales, considers the volume limitation of materials in the optimization process, and forms a high-efficiency and stable design optimization model. The whale optimizing algorithm simulates predation behavior of whales with the whales being mainly colonised, the bubble net feeding method is a inspiration source of the algorithm. The spiral rising and double-ring actions in the predation behavior have high strategic and cooperative properties, and provide a biological model foundation for algorithm design. The method realizes the global optimal solution under the complex constraint condition by simulating the spiral rising and double-ring predation behaviors of the whales and combining a topological optimization model. In the "spiral-up" mode,