Mechanical structure optimization design method based on mixed point adding strategy

Abstract

The invention discloses a mechanical structure optimization design method based on a mixed point adding strategy, and the method comprises the steps: generating sample points through Latin hypercube design, and calculating a response value through a real model; constructing an approximate optimization problem by using a proper agent model, and solving an optimal value through a (GA) genetic algorithm; dividing an initial sample space by adopting a Voronoi graph method, calculating a global sparsity value GSI of a sample, and generating a global point according to a sample point of a sample Voronoi subspace corresponding to the GSI; then generating local points based on the Voronoi sample points of the potential optimal parameters; and finally, screening a newly added point set through the minimum Euclidean distance, adding qualified points into the sample space and updating the model, and if the point set is unqualified, continuously optimizing the point set by using the hybrid strategy until the requirement is met. According to the method, the precision of the output solution is improved, any agent model and optimization algorithm can be combined, meanwhile, the characteristic has wide universality, and extremely high application value is shown in the field of mechanical structure optimization design.

Description

Technical Field

[0001] The present invention relates to the field of mechanical mechanism optimization design, and in particular to an optimization design method for finding an optimal solution using a mixed point addition strategy. Background Art

[0002] The optimization design problem of complex mechanical structures is an important part of modern engineering. However, as the complexity of the optimization design problem of complex mechanical structures increases, the mapping relationship between design variables and real responses is highly nonlinear, which makes it difficult to ensure the accuracy of the proxy model and obtain a satisfactory optimal solution. Although the existing methods for improving the accuracy of the proxy model have a certain effect, they have low versatility, cumbersome processes, and difficulty in reproduction. Therefore, it is of extremely important research significance to effectively improve the accuracy of the proxy model and ensure that the obtained optimal solution meets the design requirements.

[0003] When searching for the optimal solution for surrogate models, existing optimization design methods have the following problems:

[0004] 1. Existing optimization design methods for complex mechanical structures, some of which are based on traditional mechanical knowledge, such as the patent "A Wing Stiffness Constrained Optimization Design Method" with publication number CN118607329A, can only optimize the design of a certain mechanical structure and cannot be applied to the optimization of other complex mechanical structures. Therefore, a general method for multiple complex mechanical structures needs to be further studied.

[0005] 2. Most of the existing optimization design methods for complex mechanical structures are optimization designs of multi-objective functions of complex mechanical structures, such as the patent "Integrated optimization of tool and process parameters and energy-saving prediction method in side milling" with publication number CN118466223A. However, many problems in the multi-objective function design process of complex mechanical structures are usually composed of multiple conflicting objectives, and there are conflicts in the improvements in these design objectives. Therefore, there is still room for improvement in the multi-objective function optimization design methods for complex mechanical structures, which needs further research and improvement.

[0006] 3. Existing optimization design methods for mechanical structures are based on finite element analysis, such as the patent "A three-dimensional solid structure optimization design method, device and storage medium" with publication number CN118657035A. However, when using traditional optimization methods for complex structures with multiple objective functions, it often takes a very long time and the analysis situation is complicated. Therefore, the efficiency is low when analyzing complex models with multiple objective functions.

[0007] 4. Existing optimization design methods for complex mechanical structures based on proxy models often use an unsuitable point-adding method without considering both local development and global exploration. They also do not discuss the selection of multi-faceted point sets. Therefore, the accuracy of proxy models for complex mechanical structures needs to be further improved.

[0008] In summary, ensuring the high precision of the optimal solution of the proxy model of complex mechanical structures and reducing the number of samples required to deal with such complex engineering problems in order to improve computational efficiency are the key to current research on the optimization design of complex mechanical structures. Currently, the multi-purpose optimization design methods for complex mechanical structures have not yet considered the problem of the optimal solution obtained by adding points that affects the proxy model. Therefore, the development of a mechanical structure optimization design method based on a hybrid addition strategy can optimize the structural performance of complex machinery and play a significant role in improving the efficiency of the complex machinery design process. Summary of the Invention

[0009] The purpose of the present invention is to solve the above problems existing in the existing multi-objective optimization design method for complex mechanical structures and to propose a mechanical structure optimization design method based on a hybrid point addition strategy.

[0010] The technical solution adopted by the present invention to solve the technical problem is: a mechanical structure optimization design method based on a mixed point addition strategy, characterized in that it includes the following steps:

[0011] Step 1: Establish a real model or simulation model of the mechanical structure, and determine the design variables, constraint functions, and objective functions based on the characteristics of the proxy model, thereby establishing a multi-objective optimization problem. The specific expression is formula (1):

[0012] minf(X) formula (1) sth i (X)=0 i=1,…,a g j (X)≤0 j=1,…,b X=(X1,X2,…,X d ) T

[0013] In the above formula, f(X) is the objective function of optimization, h i (X) is the equality constraint function, g j (X) is the inequality constraint function, X is the design variable, a is the number of equality constraints, b is the number of inequality constraints, and d is the dimension of the design variable;

[0014] Step 2: Experimental design uses the OLHD method to obtain the initial sample X={X1,X2,...,X N}, set the tolerance ε and the number of cycles k = 0;

[0015] Step 3: Use the real model of the mechanical structure or numerical simulation analysis to calculate the real response value f corresponding to the initial sample (k) (X), and

[0016] Step 4: Select the appropriate type of surrogate model and use the initial sample information to construct the surrogate model of the objective and constraint functions to obtain the approximate optimization problem as shown in formula (2):

[0017] minf(X) formula (2) X=(X1,X2,…,X d ) T

[0018] In the above formula, Approximate functions for their respective surrogate models;

[0019] Step 5: Solve the approximate optimization problem formula (2) through the GA algorithm to obtain the potential optimal parameter X * and potential optimal solution and the approximate constraint function value and

[0020] Step 6: Calculate the potential optimal parameters X through a real model or numerical simulation analysis of the mechanical structure * The corresponding true value f (k) (X * ), and And calculate the maximum error Δ max The value of is as shown in formula (3):

[0021]

[0022] In the above formula, X * is the potential optimal parameter, f (k) (X * ), and is the optimal parameter X * The corresponding true response value, is the potential optimal solution, are the approximate constraint function values ​​of their respective surrogate models;

[0023] Step 7: If Δ max If the error is less than the allowable error ε, the loop stops and the optimal solution {X * ,f (k) (X * )}, otherwise jump to step (8);

[0024] Step 8: Use the Voronoi method to divide the sample space and calculate the global sparsity value GSI (X i );

[0025] Step 9: Use the maximum global sparsity value to find the corresponding sample Voronoi subspace P i,max , in P i,max Generate a global point

[0026] x global =argmax(||X random -X i ||),X random ,X i ∈P i,max Formula (4)

[0027] In the above formula, arg represents the input parameter corresponding to the maximum value of the current model, X random ,X i P i,max Random points and central sample points within;

[0028] Step 10: Use the local point addition method to find the local optimal point

[0029] Step 11: Use the minimum Euclidean distance criterion to filter the newly added point set like If the requirements of the guidelines are met, Add to the sample space, set k=k+1 and go to step 3, If it does not meet the criteria, skip to step 12;

[0030] Step 12: In the Voronoi subspace P i,max and P * Reselect global points and local points and add them to In the , use the minimum Euclidean distance criterion to filter again Until the requirements are met;

[0031] Step 13: Update the Add it to the sample space, set k=k+1 and go to step 3 to repeat the cycle.

[0032] The beneficial effects of the present invention are:

[0033] 1. In response to the first point raised in the background technology, the present invention uses proxy model technology to construct an approximate optimization framework for complex mechanical structures, aiming to fundamentally improve computational efficiency while supporting the setting of multiple constraints to ensure that the functionality of multiple structures is comprehensively considered.

[0034] 2. Regarding the second point of background technology, the present invention adopts a genetic algorithm (GA) to simulate natural selection and genetic mechanisms, and can obtain corresponding potential optimal parameters and potential optimal solutions when solving optimization problems of complex mechanical structures, thereby making the obtained solution more accurate.

[0035] 3. Regarding the third point raised in the background technology, the present invention constructs a proxy model by globally adding points and locally adding points to obtain relatively accurate samples, and then uses the minimum Euclidean distance criterion to screen the sample points to obtain a more accurate structure, thereby obtaining a proxy model with higher efficiency.

[0036] 4. Regarding point 4 of the background technology, the present invention conducts a global exploration of the optimal solution that affects the accuracy of the proxy model, seeks a more detailed and universal solution set, can take into account both local development and global exploration, and screens the point set through the maximum and minimum distance criteria to obtain a more accurate optimal solution, thereby improving the accuracy of the model.

[0037] Note: The above designs are not listed in any particular order, and each one makes the present invention distinctive and significantly advanced compared to the prior art. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The present invention will be further described below with reference to the accompanying drawings and examples.

[0039] Figure 1 It is a flow chart of the mechanical structure optimization method based on the hybrid point addition strategy of the present invention;

[0040] Figure 2 This is the finite element model diagram of the bucket wheel excavator; DETAILED DESCRIPTION

[0041] The general method of the present invention is described below with reference to the accompanying drawings:

[0042] like Figure 1 As shown, a mechanical structure optimization method based on a hybrid point addition strategy is characterized by comprising the following steps:

[0043] Step 1: Establish a numerical simulation model of the upper structure of the bucket wheel machine, and determine the design variables, constraint functions and objective functions based on the structural characteristics of the machine, thereby establishing a multi-objective optimization design problem. The specific expression is formula (1):

[0044] minf(X) formula (1) sthi (X)=0 i=1,…,a g j (X)≤0j=1,…,b X=(X1,X2,…,X d ) T

[0045] In the above formula, f(X) is the objective function of optimization, h i (X) is the equality constraint function, g j (X) is the inequality constraint function, X is the design variable, a is the number of equality constraints, b is the number of inequality constraints, and d is the dimension of the design variable;

[0046] Step 2: Experimental design uses the OLHD method to obtain the initial sample X={X1,X2,...,X N}, set the tolerance ε and the number of cycles k = 0;

[0047] Step 3: Use the real model of the mechanical structure or numerical simulation analysis to calculate the real response value f corresponding to the initial sample (k) (X), and

[0048] Step 4: Select the appropriate type of surrogate model and use the initial sample information to construct the surrogate model of the objective and constraint functions to obtain the approximate optimization problem as shown in formula (2):

[0049] minf(X) formula (2) X=(X1,X2,…,X d ) T

[0050] In the above formula, Approximate functions for their respective surrogate models;

[0051] Step 5: Solve the approximate optimization problem formula (2) through the GA algorithm to obtain the potential optimal parameter X * and potential optimal solution and the approximate constraint function value and

[0052] Step 6: Calculate the potential optimal parameters X through a real model or numerical simulation analysis of the mechanical structure * The corresponding true value f (k) (X * ), and And calculate the maximum error Δ max The value of is as shown in formula (3):

[0053]

[0054] In the above formula, X * is the potential optimal parameter, f (k) (X * ), and is the optimal parameter X * The corresponding true response value, is the potential optimal solution, are the approximate constraint function values ​​of their respective surrogate models;

[0055] Step 7: If Δ max If the error is less than the allowable error ε, the loop stops and the optimal solution {X * ,f (k) (X * )}, otherwise jump to step (8);

[0056] Step 8: Use the Voronoi method to divide the sample space and calculate the global sparsity value GSI (X i );

[0057] Step 9: Use the maximum global sparsity value to find the corresponding sample Voronoi subspace P i,max , in P i,max Generate a global point

[0058] x global =argmax(||X random -X i ||),X random ,X i ∈P i,max Formula (4)

[0059] In the above formula, arg represents the input parameter corresponding to the maximum value of the current model, X random ,X i P i,max Random points and central sample points within;

[0060] Step 10: Use the local point addition method to find the local optimal point

[0061] Step 11: Use the minimum Euclidean distance criterion to filter the newly added point set like If the requirements of the guidelines are met, Add to the sample space, set k=k+1 and go to step 3, If it does not meet the criteria, skip to step 12;

[0062] Step 12: In the Voronoi subspace P i,max and P * Reselect global points and local points and add them to In the , use the minimum Euclidean distance criterion to filter again Until the requirements are met;

[0063] Step 13: Update the Add it to the sample space, set k=k+1 and go to step 3 to repeat the cycle.

[0064] In order to further explain the present invention in detail, the solution of the present invention is described below in conjunction with a specific embodiment. This embodiment takes the optimized design of the bucket wheel machine structure as an embodiment, and is implemented under the premise of the technical solution of the present invention. A detailed implementation method and specific operation process are given, but the protection scope of the present invention is not limited to the following embodiments.

[0065] like Figure 2 As shown in FIG, it is the finite element model diagram of the upper structure of the bucket wheel machine targeted by the method of the present invention. Figure 1 A mechanical structure optimization design method based on a mixed point strategy is implemented for Figure 2 The upper structure of the bucket wheel machine shown in the figure has the following specific steps:

[0066] Step 1: Establish a numerical simulation model of the upper structure of the bucket wheel machine, and according to the characteristics of the upper part of the bucket wheel machine, select the weight M(X) of the upper structure of the bucket wheel machine as the optimization target; the overall maximum deformation D(X) and the maximum stress P(X) borne are used as constraints to construct the optimization problem, where the overall maximum deformation D(X) ≤ 20 mm, the maximum stress P(X) borne ≤ 200 MPa, select X1 as the front tie rod diameter (mm), X2 as the rear tie rod diameter (mm); X3 as the column structure thickness (mm); X4 as the balance frame thickness (mm) as design variables, thereby establishing the optimization design problem for the upper structure of the bucket wheel machine, and the specific expression is formula (5):

[0067] minM(X)=f1(X) Formula (5) X=(X1,X2,X3,X4) T 100≤X1≤200 100≤X2≤200 9≤X3≤15 9≤X4≤15

[0068] In formula (5), f1(X) is the objective function, which represents the selection of the axle housing mass M(X) as the optimization design target, X is the design variable, X1 is the front tie rod diameter, X2 is the rear tie rod diameter, X3 is the column structure thickness, and X4 is the balance frame thickness;

[0069] Step 2: Use Latin hypercube experimental design method to design domain space The sample points are sampled within , where the initial sample points of the objective function f1(X) are 5, and the allowable error e is set max =10%, set the number of iterations k = 0;

[0070] Step 3: Import the sample points into the numerical simulation model of the upper structure of the bucket wheel machine for calculation, thereby obtaining the sample of the objective function f1(X);

[0071] Step 4: Construct the Kriging model and use the initial sample information to construct the proxy model of the objective and constraint functions to obtain the approximate optimization problem as shown in formula (6):

[0072] minf(X) formula (6) X=(X1,X2,…,X d ) T

[0073] In the above formula, Approximate functions for their respective surrogate models;

[0074] Step 5: Solve the approximate optimization problem formula (6) through the GA algorithm to obtain the potential optimal parameter X * and potential optimal solution and the approximate constraint function value and

[0075] Step 6: Calculate the potential optimal parameters X through a real model or numerical simulation analysis of the mechanical structure * The corresponding true value f (k) (X * ), and And calculate the maximum error Δ max The value of is as shown in formula (7):

[0076]

[0077] In the above formula, X * is the potential optimal parameter, f (k) (X * ), and is the optimal parameter X * The corresponding true response value, is the potential optimal solution, are the approximate constraint function values ​​of their respective surrogate models;

[0078] Step 7: If Δ max If the error is less than the allowable error ε, the loop stops and the optimal solution {X * ,f (k) (X * )}, otherwise jump to step (8);

[0079] Step 8: Use the Voronoi method to divide the sample space and calculate the global sparsity value GSI (X i );

[0080] Step 9: Use the maximum global sparsity value to find the corresponding sample Voronoi subspace P i,max , in P i,max Generate a global point

[0081] x global =argmax(||X random -X i ||),X random ,X i ∈P i,max Formula (8)

[0082] In the above formula, arg represents the input parameter X corresponding to the maximum value of the current model. random ,X i P i,max Random points and central sample points within;

[0083] Step 10: Use the local point addition method to find the local optimal point

[0084] Step 11: Use the minimum Euclidean distance criterion to filter the newly added point set like If the requirements of the guidelines are met, Add to the sample space, set k=k+1 and go to step 3, If it does not meet the criteria, skip to step 12;

[0085] Step 12: In the Voronoi subspace P i,max and P * Reselect global points and local points and add them to In the , use the minimum Euclidean distance criterion to filter again Until the requirements are met;

[0086] Step 13: Update the Add it to the sample space, set k=k+1 and go to step 3 to repeat the cycle.

[0087] Table 1 The number of iterations and maximum error of the hybrid point addition strategy method

[0088]

[0089] Table 2 Optimization results in iterative step 2 based on the hybrid point addition strategy method

[0090]

[0091] The above detailed description is a specific description of a feasible embodiment of the present invention. The embodiment is not intended to limit the patent scope of the present invention. Any equivalent implementation or modification that does not depart from the present invention should be included in the patent scope of this case.

Claims

1. A mechanical structure optimization design method based on a mixed point addition strategy, characterized in that: The steps include: Step 1: Establish a real model or simulation model of the mechanical structure, and determine the design variables, constraint functions, and objective functions based on the characteristics of the proxy model, thereby establishing a multi-objective optimization problem. The specific expression is formula (1): minf(X) formula (1) s.t.h i (X)=0i=1,…,a g j (X)≤0j=1,…,b X=(X1,X2,…,X d ) T In the above formula, f(X) is the objective function of optimization, h i (X) is the equality constraint function, g j (X) is the inequality constraint function, X is the design variable, a is the number of equality constraints, b is the number of inequality constraints, and d is the dimension of the design variable; Step 2: Experimental design uses the OLHD method to obtain the initial sample X={X1,X2,…,X N }, set the tolerance ε and the number of cycles k = 0; Step 3: Use the real model of the mechanical structure or numerical simulation analysis to calculate the real response value f corresponding to the initial sample (k) (X), and Step 4: Select the appropriate type of surrogate model and use the initial sample information to construct the surrogate model of the objective and constraint functions to obtain the approximate optimization problem as shown in formula (2): X=(X1,X2,…,X d ) T In the above formula, Approximate functions for their respective surrogate models; Step 5: Solve the approximate optimization problem formula (2) through the GA algorithm to obtain the potential optimal parameter X * and potential optimal solution and the approximate constraint function value and Step 6: Calculate the potential optimal parameters X through a real model or numerical simulation analysis of the mechanical structure * The corresponding true value f (k) (X * ), and And calculate the maximum error Δ max The value of is as shown in formula (3): In the above formula, X * is the potential optimal parameter, f (k) (X * ), and is the optimal parameter X * The corresponding true response value, is the potential optimal solution, are the approximate constraint function values ​​of their respective surrogate models; Step 7: If Δ max If the error is less than the allowable error ε, the loop stops and the optimal solution {X * ,f (k) (X * )}, otherwise jump to step (8); Step 8: Use the Voronoi method to divide the sample space and calculate the global sparsity value GSI (X i ); Step 9: Use the maximum global sparsity value to find the corresponding sample Voronoi subspace P i,max , in P i,max Generate a global point x global =argmax(||X random -X i ||),X random ,X i ∈P i,max Formula (4) In the above formula, arg represents the input parameter corresponding to the maximum value of the current model, X random ,X i P i,max Random points and central sample points within; Step 10: Use the local point addition method to find the local optimal point Step 11: Use the minimum Euclidean distance criterion to filter the newly added point set like If the requirements of the guidelines are met, Add to the sample space, set k=k+1 and go to step 3, If it does not meet the criteria, skip to step 12; Step 12: In the Voronoi subspace P i,max and P * Reselect global points and local points and add them to In the , use the minimum Euclidean distance criterion to filter again Until the requirements are met; Step 13: Update the Add it to the sample space, set k=k+1 and go to step 3 to repeat the cycle.

2. The mechanical structure optimization design method based on the hybrid point addition strategy according to claim 1 is characterized in that: Step 8 uses the Voronoi method to divide the sample space and calculate the global sparsity value GSI (X i ) includes the following steps: Use the Voronoi diagram method to divide the initial sample space p i i=1,...,N: P i ={X∈R d |||XX i ||≤||XX j ||},j=(1,2,…,N),i≠j Formula (6) In the above formula, N is the number of initial sample points, X is a random vector point in the design space R, and ||·|| represents the Euclidean distance between two points; The global sparsity index is used to calculate the global sparsity value GSI (X i ): In the above formula, M is the sample point X i The Voronoi subspace P to which it belongs i The number of random points on the boundary depends on the number of initial sample points. In this paper, the empirical value M=5 is used. is the sample point X i The Voronoi subspace P to which it belongs i Random points on the boundary, i=1,…,N,F max is the potential optimal parameter X among f(X), h(X) and g(X) * The function type corresponding to the maximum relative error at F max The proxy model not only helps to find the areas that need to be added, but also facilitates the generation of new sample points.

3. The design method of a mechanical structure based on a hybrid point addition strategy according to claim 1, characterized in that: The step 10 uses the local point addition method to generate the local optimal point The steps include: Use efficient intelligent optimization algorithms to solve the potential optimal parameters X in each optimization iteration * ; Using local encryption technology, X * Add to the sample space; Find X * The Voronoi subspace P * , and according to the maximum and minimum distance criterion in P * Generate a local point x local , the specific expression is as follows: x local =argmax(||X random -X j ||),X random ,X j ∈P * Formula (8) In the above formula, arg represents the input parameter corresponding to the maximum value of the current model, X random ,X j P * Random sample points and central sample points within the image are added, so that the accuracy of the added points is higher.

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