Lightweight optimization design method for components based on a new multi-objective particle swarm optimization algorithm

Abstract

This invention discloses a lightweight component optimization design method based on a novel multi-objective particle swarm algorithm. This method belongs to the technical field of lightweight component optimization design. The key technical solutions include four steps: finite element modeling and analysis; mathematical model establishment; solving the problem using an improved multi-objective particle swarm algorithm; and comparing and verifying the optimization results. This lightweight component optimization design method based on a novel multi-objective particle swarm algorithm improves upon the basic multi-objective particle swarm algorithm to overcome its shortcomings, such as its inability to emphasize the varying importance of different objective functions, poor robustness of the inertia weight factor, and difficulty in global optimization.

Description

Technical Field

[0001] The present invention relates to the technical field of component lightweight optimization design, and in particular to a component lightweight optimization design method based on a novel multi-objective particle swarm algorithm. Background Art

[0002] In recent years, with the increasing severity of energy shortages and environmental crises, lightweighting vehicles has become an inevitable trend in automotive development. The foundation of lightweighting the entire vehicle is the lightweighting of components. The forward development of lightweight component technologies has become a hot research area for scholars at home and abroad. Currently, many scholars at home and abroad have conducted in-depth research on the optimized design, fatigue life prediction, and reliable durability of lightweight components. However, there are still many theoretical deficiencies. The core of current research is how to determine the component design scheme, component function and structural parameters, so that the components have the highest strength and the lowest mass while meeting various performance indicators.

[0003] Particle swarm optimization (PSO) is a swarm intelligence optimization algorithm in the field of computational intelligence, alongside ant colony algorithms and fish swarm algorithms. It was first proposed by Kennedy and Eberhart in 1995, stemming from their research on bird predation. Subsequently, scholars and experts have applied this algorithm to practical engineering applications.

[0004] The PSO algorithm treats each individual in a swarm as a particle solution, without volume or mass, but only with position and velocity. Each particle flies through space at a constant speed, which is dynamically adjusted based on its own flight experience and the experience of its companions. It assumes that each particle knows its current best position and the best position found by all particles in the swarm. In other words, all particles have a fitness value determined by the function being optimized. The problem-solving process can be compared to a flock of birds collaboratively foraging for food, with the location of the food being the optimal solution.

[0005] The mathematical expression of the particle swarm algorithm is (see Figure 1 ):

[0006] Assume that the population of N particles in D-dimensional space is X = (x1, x2, ... xN), and the state attributes of particle i at time t are set as follows:

[0007] 1) Position: Xit = (xi1, xi2, ...xiN)T, where xid∈[Lid, Uid], (Lid, Uid are the upper and lower limits of the search space respectively) d∈[1, 2, ...D]

[0008] 2) Speed: Vit = (vi1, vi2, ... viN)T, where vidt∈[vmin.d, vmax,d], where vmin.d, vmax,d are the maximum and minimum values of the speed, determined by the upper and lower limits of the search space.

[0009] 3) Individual extreme value: the position where each particle Xi has the best adaptability;

[0010] 4) Group extreme value: the best position experienced by all particles in the group - the global optimal fitness value.

[0011] 5) Iteration: The velocity and position of the particle at time t+1 are updated using the following formula:

[0012] Among them, c1 and c2 are constants, which become acceleration factors; r1 and r2 are random numbers on (0, 1). The first formula consists of three parts: (1) is the initial velocity of the particle, indicating the current state of the particle; the second part is the "individual cognition" of the particle, which plays a role in indicating the global search ability of the particle itself; the third part is the "social cognition" of the particle, which indicates the information exchange and mutual cooperation between particles. The three parts together constitute the group search ability of the particle in space.

[0013] The multi-objective particle swarm optimization algorithm makes the following three improvements based on the single-objective particle swarm optimization algorithm:

[0014] (1) Add archiving mechanism:

[0015] (2) Global Optimal Selection Mechanism

[0016] (3) Scale management of archival documents

[0017] However, it is now found that the multi-objective particle swarm optimization algorithm still has the following problems:

[0018] (1) Although the current multi-swarm particle swarm optimization algorithm realizes information interaction between populations, during optimization, the amount of information of the corresponding populations is different due to the different importance of each objective function. Traditional algorithms cannot solve this problem.

[0019] (2) The selection of global extrema is very important in the multi-objective particle swarm algorithm. It is directly related to the update of particles and more directly affects the convergence speed of the algorithm and the distribution of the solution set. Most of the methods currently used only consider the distribution of the non-inferior solution set, without considering the quality of the selected global extrema. How to properly select the global extrema, which can not only improve the distribution of the non-inferior solution set but also improve the quality of the global extrema, is the key to improving the performance of the algorithm.

[0020] (3) The inertia weight of the particle swarm algorithm affects the balance between the global contraction and local search capabilities of the algorithm. When it is larger, the global search capability is stronger, and when it is smaller, the local search capability is stronger. The methods proposed so far mainly include linear attenuation weight, which improves the performance of the algorithm to a certain extent, but the actual search process is often nonlinear. Fuzzy inertia weight, but the selection of membership function and the implementation process of fuzzy inference rules are very complicated and difficult to generalize. Therefore, how to propose a reasonable inertia weight change strategy is the key to balancing the local search and global search of the algorithm. Summary of the Invention

[0021] The purpose of the present invention is to provide a lightweight optimization design method for components based on a novel multi-objective particle swarm algorithm to solve the problems mentioned in the background technology.

[0022] The above technical objectives of the present invention are achieved through the following technical solutions: a lightweight optimization design method for components based on a novel multi-objective particle swarm algorithm, comprising the following steps:

[0023] S1: Finite element modeling and analysis: Using the finite element analysis method, the static calculation and analysis of the components to be optimized are carried out. By simulating stress, the stress concentration points or the maximum stress points of the structure during the stress process are calculated, and the relevant technical parameters are extracted.

[0024] S2: Mathematical model building, using mathematical logic methods and mathematical language to construct scientific or engineering models, including the following steps:

[0025] a. Model preparation;

[0026] b. Model assumptions;

[0027] c. Model composition;

[0028] d. Model solution;

[0029] e. Model analysis;

[0030] f. Model testing and conclusion;

[0031] S3: Improve the solution of multi-objective particle swarm optimization algorithm, use the improved MOPSO algorithm to optimize the objective function of each attribute, and optimize the attributes or design parameters involved in the established model;

[0032] S4: Comparison and verification of optimization results, comparative analysis and verification of the optimized results.

[0033] In some embodiments, in step S1, the finite element analysis includes the following steps:

[0034] a. Divide the grid;

[0035] b. How to establish a connection;

[0036] c. Import materials and characteristic parameters;

[0037] d. Establish boundary conditions and constraints;

[0038] e. Simulate force balance.

[0039] In some embodiments, in step S2, model preparation includes first understanding the actual background of the problem, clarifying the purpose of modeling, collecting necessary information, and clarifying the characteristics of the object.

[0040] In some embodiments, in step S2, model assumptions include simplifying the problem and making assumptions based on the characteristics of the object and the purpose of modeling.

[0041] In some embodiments, in step S2, model construction includes analyzing the cause-effect relationship of the object based on the assumptions made, and constructing the equation relationship or mathematical structure between various quantities using the inherent laws of the object and mathematical tools.

[0042] In some embodiments, in step S2, the method of solving the model includes solving equations, drawing graphs, proving theorems, logical operations and numerical operations, and also includes solving using computer technology.

[0043] In some embodiments, in step S2 , the model analysis includes performing a mathematical analysis on the model solution.

[0044] In summary, the present invention has the following beneficial effects:

[0045] This lightweight component optimization design method, based on a novel multi-objective particle swarm algorithm, improves upon the basic multi-objective particle swarm algorithm to overcome its shortcomings, such as its inability to prioritize the varying importance of different objective functions, poor robustness of its inertia weight factor, and difficulty finding a global optimal solution. By introducing an improved inertia weight factor and transforming the weight coefficients of the objective functions, along with innovatively incorporating the concept of natural science variation and evolution, the algorithm effectively enhances its optimization and computational capabilities, resulting in superior results and significantly improved algorithm efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a calculation flow chart of the basic particle swarm algorithm of the present invention;

[0047] Figure 2 is a graph showing a change in the weight of the inertia factor of the present invention;

[0048] Figure 3 The algorithm flow chart after the introduction of the variation evolution idea of the present invention;

[0049] Figure 4This is a simulated force cloud diagram of a leaf spring in an embodiment of the present invention under a vertical 2.4g working condition;

[0050] Figure 5 This is a simulated force cloud diagram of the leaf spring in the embodiment of the present invention under the longitudinal working condition of 0.8g;

[0051] Figure 6 This is a simulated force cloud diagram of the leaf spring in an embodiment of the present invention under a 0.4g lateral working condition;

[0052] Figure 7 Schematic diagram of thickness attribute classification of leaf springs in an embodiment of the present invention;

[0053] Figure 8 This is a screenshot of the program of the multi-objective particle swarm algorithm of the present invention during initialization;

[0054] Figure 9 This is a screenshot of the multi-objective particle swarm algorithm of the present invention when the group position is updated;

[0055] Figure 10 This is a diagram of the iterative optimization process of the particle swarm optimal individual stiffness attribute of the present invention;

[0056] Figure 11 It is a diagram of the iterative optimization process of the particle swarm optimal individual strength attribute of the present invention;

[0057] Figure 12 This is a diagram of the iterative optimization process for the optimal individual strength and weight attributes of a particle swarm according to the present invention;

[0058] Figure 13 This is a simulated force cloud diagram of the leaf spring in the embodiment of the present invention after optimization under the vertical 2.4g working condition;

[0059] Figure 14 This is a simulated force cloud diagram of the leaf spring in the embodiment of the present invention after optimization under the longitudinal 0.8g working condition;

[0060] Figure 15 This is a simulated force cloud diagram of the leaf spring after optimization under the 0.4g lateral working condition in an embodiment of the present invention. DETAILED DESCRIPTION

[0061] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0062] This example uses the rear leaf spring of a light commercial vehicle as the research object. By improving the inertia weight factor and transforming the weight coefficients of the objective function in a standard particle swarm algorithm (PSO), and by innovatively incorporating the concept of evolutionary variation from natural science, a standard multi-objective PSO algorithm is improved. This improved PSO algorithm achieves multi-objective optimization of the rear leaf spring, enhancing its strength and stiffness without increasing its mass. This approach provides a reference for similar engineering problems.

[0063] Inertia factor improvements:

[0064] In order to improve the convergence performance of the basic multi-objective particle swarm optimization algorithm, the inertia weight factor in the particle swarm velocity update formula is improved.

[0065] The inertia weight factor ω is used to describe the degree of influence of historical speed on current speed. The basic particle swarm algorithm is a special case with an inertia weight of 1. When ω is large, the particle's global search capability is strong and its local search capability is weak, and vice versa. Therefore, choosing a suitable ω value can effectively improve the algorithm's search and convergence capabilities. The currently commonly used linear decrease strategy for inertia weight has a certain improvement in algorithm performance, but there are still problems such as weak local search capability in the early iteration stage and slow convergence calculation speed. To this end, this patent proposes an adaptive inertia weight oscillation decrease strategy.

[0066] The inertia weight factor ω describes the influence of a particle's historical velocity on its current velocity. The value of ω can adjust the algorithm's global and local search capabilities. A large ω value strengthens the particle's global search capability and weakens its local search capability. Conversely, a small ω value strengthens its local search capability and weakens its global search capability. Therefore, choosing an appropriate weight value can balance global and local search capabilities and improve the algorithm's efficiency.

[0067] like Figure 2 As shown in the figure, in the early stage of iterative optimization, the inertia weight factor is large and the local search ability is strong; in the later stage of iterative optimization, the inertia weight factor is weakened while ensuring a certain local search ability.

[0068] Introduction of the idea of mutation evolution:

[0069] This invention introduces the crossover and mutation ideas in the genetic algorithm into the particle swarm algorithm. When updating, individual particles cross and mutate with the individual optimal and group optimal particles in turn, which can effectively avoid the problem of the basic PSO algorithm falling into the local optimal state too early. In summary, the flow chart of the hybrid multi-objective adaptive oscillating particle swarm algorithm is as follows: Figure 3 shown.

[0070] See also Figure 1-15 , a lightweight optimization design method for components based on a new multi-objective particle swarm algorithm includes the following steps:

[0071] S1: Finite element modeling and analysis. Using the finite element analysis method, the static calculation and analysis of the entire optimized component is carried out. By simulating stress, the stress concentration point or the maximum stress point of the structure during the stress process is calculated, and the relevant technical parameters are extracted. The finite element analysis includes the following steps:

[0072] a. Divide the grid;

[0073] b. How to establish a connection;

[0074] c. Import materials and characteristic parameters;

[0075] d. Establish boundary conditions and constraints;

[0076] e. Simulate force balance;

[0077] S2: Mathematical model building, using mathematical logic methods and mathematical language to construct scientific or engineering models, including the following steps:

[0078] a. Model preparation, including first understanding the actual background of the problem, clarifying the modeling purpose, collecting necessary information, and clarifying the characteristics of the object;

[0079] b. Model assumptions, including simplifying the problem and making assumptions based on the characteristics of the object and the purpose of modeling;

[0080] c. Model construction, including analyzing the cause-effect relationship of the object based on the assumptions made, and constructing the equation relationship or mathematical structure between various quantities by using the inherent laws of the object and mathematical tools;

[0081] d. Model solving. Model solving methods include solving equations, drawing graphs, proving theorems, logical operations, numerical operations, and using computer technology to solve problems.

[0082] e. Model analysis, including mathematical analysis of model solutions;

[0083] f. Model testing and conclusion;

[0084] S3: Improve the solution of multi-objective particle swarm optimization algorithm, use the improved MOPSO algorithm to optimize the objective function of each attribute, and optimize the attributes or design parameters involved in the established model;

[0085] S4: Comparison and verification of optimization results, comparative analysis and verification of the optimized results.

[0086] This lightweight component optimization design method, based on a novel multi-objective particle swarm algorithm, improves upon the basic multi-objective particle swarm algorithm to overcome its shortcomings, such as its inability to prioritize the varying importance of different objective functions, poor robustness of its inertia weight factor, and difficulty finding a global optimal solution. By introducing an improved inertia weight factor and transforming the weight coefficients of the objective functions, along with innovatively incorporating the concept of natural science variation and evolution, the algorithm effectively enhances its optimization and computational capabilities, resulting in superior results and significantly improved algorithm efficiency.

[0087] When performing lightweight optimization design on leaf springs using the above technical solution, the steps are as follows:

[0088] S1: Finite element modeling of leaf spring. Finite element modeling of leaf spring is performed. The mid-surface of the original leaf spring geometric model is extracted and simulated using shell elements. Since the leaf spring is a symmetrical model, half of the mesh is divided and then symmetrically copied. After dividing the mesh, three working conditions are used for simulation. The simulated force cloud diagram is as follows Figure 4 、 5 , 6, the finite element strength analysis results are shown in the following table:

[0089]

[0090] S2: Establishing a multi-objective optimization model. The design stiffness requirement for the leaf spring is 224.81 N / mm. Taking into account actual project conditions and production consistency tolerances, the optimized stiffness range is set at 200-240 N / mm. Furthermore, the leaf spring's vertical ultimate load is 16.1 kN. Based on this, the optimization design adopts a 70% safety margin, setting the leaf spring's strength target to withstand a load of 27 kN without failure.

[0091] According to the characteristics of the leaf spring structure, the central symmetry plane of the leaf spring is divided into 13 different attributes on each side, and the other side is a symmetrical structure. The division method is as follows Figure 7 As shown, there is an attribute interval between every two white lines.

[0092] The thickness and width of each attribute layer are used as design variables. The relevant design variables and constraints are shown in the following table:

[0093]

[0094] S3: Objective function is established. In the optimization design of glass fiber leaf springs, there are three important problems that need to be solved: (1) How to maximize the strength while minimizing the mass of the leaf spring while meeting the stiffness design standard. (2) How to optimize the stiffness while minimizing the mass of the leaf spring while meeting the strength requirements. (3) How much can the minimum mass be achieved under the premise that both stiffness and strength meet the design standards. Based on these three problems, the relationship between the stiffness, strength and mass of glass fiber leaf springs is explored, which can effectively provide guidance for the laying and design of glass fiber leaf springs. Based on this, this paper establishes the objective function of the three sub-goals of stiffness, strength and mass. The formula is as follows:

[0095]

[0096] Where |K-224.81| is the stiffness attribute of the individual population, representing the difference between the leaf spring's stiffness and the design value of 224.81 N / mm. σ is the strength attribute of the leaf spring, representing the difference between the strength of the fiberglass leaf spring and the target value of 27. n is the number of attributes, with a total of 13 attributes. is the ply length of each attribute in the individual population. b is the spring width. is the material density.

[0097] Using the improved multi-objective particle swarm algorithm, the program screenshot is as follows Figure 8 and Figure 9 shown.

[0098] S4: Optimization results and analysis, based on the objective function, the improved particle swarm algorithm is used for optimization iteration, giving priority to making the stiffness or strength reach the ideal value. The optimization results are as follows Figure 10 、 11 and 12.

[0099] Through comparative analysis of data from each generation, an adjustment and optimization plan is established. The data from each generation are shown in the following table:

[0100]

[0101] S5: Result analysis and test verification, e.g. Figure 13 、 14 As shown in Figure 15, the optimized leaf spring was modeled and subjected to finite element analysis under the same operating conditions. It was found that after optimization, the stress values experienced by the same leaf spring under the same operating conditions were reduced. This is beneficial for improving durability and reliability. The results of the finite element strength analysis are shown in the following table:

[0102]

[0103] S6: Leaf spring bench test verification. In order to verify the optimization effect of the leaf spring multi-objective optimization, a bench test was carried out. The test found that compared with the original design of the leaf spring, the number of fatigue cycles of the improved leaf spring increased by more than 15%.

[0104] This specific embodiment is merely an explanation of the present invention and is not intended to limit the present invention. After reading this specification, those skilled in the art may make non-creative modifications to this embodiment as needed. However, as long as such modifications are within the scope of the claims of the present invention, they are protected by patent law.

Claims

1. A lightweight optimization design method for components based on a new multi-objective particle swarm algorithm, characterized by: The following steps are involved: S1: Finite element modeling and analysis: Using the finite element analysis method, the static calculation and analysis of the components to be optimized are carried out. By simulating stress, the stress concentration points or the maximum stress points of the structure during the stress process are calculated, and the relevant technical parameters are extracted. S2: Mathematical model building, using mathematical logic methods and mathematical language to construct scientific or engineering models, including the following steps: a. Model preparation; b. Model assumptions; c. Model composition; d. Model solution; e. Model analysis; f. Model testing and conclusions; S3: Improve the solution of multi-objective particle swarm optimization algorithm, use the improved MOPSO algorithm to optimize the objective function of each attribute, and optimize the attributes or design parameters involved in the established model; The optimization of each attribute objective function by using the improved MOPSO algorithm specifically includes: introducing the inertia weight factor improvement, wherein the inertia weight +0.1, where t is the number of iterations; The crossover and mutation ideas in the genetic algorithm are introduced into the particle swarm algorithm, so that individual particles can cross and mutate with the individual optimal and group optimal in turn when updating; S4: Comparison and verification of optimization results, comparative analysis and verification of the optimized results.

2. The lightweight optimization design method for components based on a novel multi-objective particle swarm algorithm according to claim 1 is characterized in that: In step S1, the finite element analysis includes the following steps: a. Divide the grid; b. How to establish a connection; c. Import materials and characteristic parameters; d. Establish boundary conditions and constraints; e. Simulate force balance.

3. The lightweight optimization design method for components based on a novel multi-objective particle swarm algorithm according to claim 1 is characterized in that: In step S2, model preparation includes first understanding the actual background of the problem, clarifying the purpose of modeling, collecting necessary information, and clarifying the characteristics of the object.

4. The lightweight optimization design method for components based on a novel multi-objective particle swarm algorithm according to claim 1 is characterized in that: In step S2, model assumptions include simplifying the problem and making assumptions based on the characteristics of the object and the purpose of modeling.

5. The lightweight optimization design method for components based on a novel multi-objective particle swarm algorithm according to claim 1 is characterized in that: In step S2, model construction includes analyzing the cause-effect relationship of the object based on the assumptions made, and constructing the equation relationship or mathematical structure between various quantities using the inherent laws of the object and mathematical tools.

6. The lightweight optimization design method for components based on a novel multi-objective particle swarm algorithm according to claim 1 is characterized in that: In step S2, the method of solving the model includes solving equations, drawing graphs, proving theorems, logical operations and numerical operations, and also includes solving using computer technology.

7. The lightweight optimization design method for components based on a novel multi-objective particle swarm algorithm according to claim 1 is characterized in that: In step S2, the model analysis includes performing a mathematical analysis on the model solution.

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