A data-driven non-intrusive shape-topology collaborative optimization method and system

Abstract

The data-driven non-intrusive shape-topology collaborative optimization method and system disclosed by the present invention relate to the field of structural optimization. First, the present invention uses mesh deformation technology to perform parametric modeling on the structure, and uses shape equations to constrain the displacements of the structure control points, ensuring the regular and smooth shape of the structure after mesh deformation; secondly, the present invention uses a variety of solvers to perform topology optimization on models of different shapes to obtain multi-source topology optimization response data; finally, the present invention establishes a non-intrusive surrogate model between the shape design variables and the topology optimization response data, and obtains a shape-topology collaborative optimization scheme based on the non-intrusive surrogate model. The present invention takes into account the interaction between shape optimization and topology optimization, helps to expand the design space, has higher optimization efficiency and optimization ability compared with other shape-topology optimization methods, and does not require complex sensitivity formula derivation, facilitating its application to practical engineering.

Description

Technical Field

[0001] The present invention relates to the technical field of structural optimization, and in particular to a data-driven non-invasive shape-topology collaborative optimization method and system. Background Art

[0002] Traditional structural optimization methods often rely on engineering experience, which can easily lead to conservative design results. Obtaining the optimal design through topology optimization and shape optimization is an important measure to achieve structural lightweighting. Since structural equipment often faces harsh load conditions in complex service environments, there is often a contradiction between the demand for high reliability and the demand for extreme lightweighting. At present, the shape and topology of the structure are often designed separately, making it difficult for the originally compactly designed structure to obtain the optimal structural performance. At the same time, the intrusive solution method of shape and topology optimization faces cumbersome sensitivity formula derivation and analysis, which brings challenges to shape-topology collaborative optimization.

[0003] Existing shape-topology collaborative optimization methods are mainly aimed at structures with simple shapes and small scales. They usually adopt intrusive methods to couple and solve shape and topology optimization design variables, which often requires cumbersome sensitivity formula derivation and analysis processes. For large and complex structures, it is difficult to derive sensitivity formulas. For example, Chinese patent CN113515824A discloses a topology optimization design method for rib layout and substrate shape collaboration. At the same time, in the existing methods, the shape optimization design variables are the control point displacements of the substrate, and the node coordinates are obtained by interpolation based on the control point coordinates. For large and complex structures, when the number of control points is insufficient, the accuracy of the structural boundary interpolation is difficult to guarantee, which in turn affects the overall performance of the structure. The increase in the number of control points means an increase in shape design variables, which brings about problems such as low optimization efficiency and poor convergence, making the final shape irregular and difficult to meet real needs. Therefore, there is a lack of non-invasive shape-topology collaborative optimization methods for large and complex structures, and it is impossible to use fewer design variables to characterize the shape of complex structures, resulting in difficulty in obtaining a relatively smooth and regular optimization solution for the optimization of complex structure shapes. Furthermore, for large and complex structures, due to the complexity of the optimization problem, the optimization time is often long, and the traditional optimization algorithm is very likely to fall into the local optimal solution. Therefore, for large and complex structures, more advanced optimization methods need to be used to optimize and improve the optimization efficiency and optimization ability. Summary of the invention

[0004] The purpose of the present invention is to provide a data-driven non-intrusive shape-topology collaborative optimization method and system, which can realize non-intrusive shape-topology collaborative optimization while realizing the decoupling of shape and topology design variables, so as to ensure the optimization efficiency and optimization ability and realize the lightweight design of the structure.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A data-driven non-intrusive shape-topology collaborative optimization method, comprising:

[0007] Construct a finite element model of the structure to be optimized, and select control points within the design domain;

[0008] Construct a shape equation that constrains the displacements of the control points, and perform parametric modeling using the parameters in the shape equation and mesh deformation technology to obtain a parametric model;

[0009] Use multiple solvers to perform topology optimization on the parametric models of different shapes to obtain multi-source topology optimization response data;

[0010] Based on the multi-source topology optimization response data and historical data, establish a non-intrusive surrogate model between the shape variables and the topology optimization response;

[0011] Adopt a point-adding strategy to improve the accuracy of the non-intrusive surrogate model until the accuracy requirements of the non-intrusive surrogate model are met;

[0012] Adopt an intelligent optimization algorithm to carry out optimal design on the non-intrusive surrogate model to obtain a shape-topology collaborative design scheme.

[0013] Preferably, the shape equation that constrains the displacements of the control points includes: super-ellipse equation, rotational surface equation, and quadratic surface equation.

[0014] Preferably, the point-adding strategy includes: Thiessen polygon adaptive point-adding method and active learning point-adding method.

[0015] Preferably, the intelligent optimization algorithm includes: genetic algorithm, ant colony algorithm, particle swarm algorithm, and covariance matrix adaptation evolution algorithm.

[0016] Preferably, the training method of the non-intrusive surrogate model includes: radial basis function, Gaussian process, deep neural network, and artificial neural network.

[0017] Preferably, assign the finite element models corresponding to the shapes of the shape design variables to different topology optimization solvers for topology optimization to obtain multi-source topology optimization response data.

[0018] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0019] First, the present invention uses grid deformation technology to parametrically model the structure and uses shape equations to constrain the displacements of the structure's control points, ensuring the regular and smooth shape of the structure after grid deformation. Secondly, the present invention uses multiple solvers to perform topology optimization on models of different shapes to obtain multi-source topology optimization response data. Finally, the present invention establishes a non-intrusive surrogate model between the shape design variables and the topology optimization response data and obtains a shape-topology collaborative optimization scheme based on the non-intrusive surrogate model. The present invention considers the interaction between shape optimization and topology optimization, helps to expand the design space, has higher optimization efficiency and optimization ability compared with other shape-topology optimization methods, and does not require complex sensitivity formula derivation, making it easy to be applied to practical engineering.

[0020] Corresponding to the above-provided data-driven non-intrusive shape-topology collaborative optimization method, the present invention also provides a data-driven non-intrusive shape-topology collaborative optimization system, which includes:

[0021] A control point selection module, configured to construct a finite element model of the structure to be optimized and select control points within the design domain;

[0022] A parametric model construction module, configured to construct a shape equation that constrains the displacements of the control points, and perform parametric modeling using the parameters in the shape equation and grid deformation technology to obtain a parametric model;

[0023] A topology optimization module, configured to perform topology optimization on the parametric models of different shapes using multiple solvers to obtain multi-source topology optimization response data;

[0024] A non-intrusive surrogate model construction module, configured to establish a non-intrusive surrogate model between the shape variables and the topology optimization response based on the multi-source topology optimization response data and historical data;

[0025] An accuracy improvement module, configured to use a point addition strategy to improve the accuracy of the non-intrusive surrogate model until the accuracy requirements of the non-intrusive surrogate model are met;

[0026] An optimal design module, configured to perform optimal design on the non-intrusive surrogate model using an intelligent optimization algorithm to obtain a shape-topology collaborative design scheme.

[0027] Since the technical effects achieved by the data-driven non-intrusive shape-topology collaborative optimization system provided by the present invention are the same as those achieved by the above-provided data-driven non-intrusive shape-topology collaborative optimization method, they will not be elaborated here. Description of the Drawings

[0028] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0029] Figure 1 Flowchart of the data-driven non-intrusive shape-topology collaborative optimization method provided by the present invention;

[0030] Figure 2 Schematic diagram of dividing the shape design domain and selecting control points for the finite element model provided by the embodiment of the present invention; among them, Figure 2 Part (a) is a schematic diagram of the established finite element model; Figure 2 Part (b) is a schematic diagram of the selected control points;

[0031] Figure 3 Schematic diagram of obtaining multi-source topology optimization response data using multiple solvers provided by the embodiment of the present invention;

[0032] Figure 4 Schematic diagram of the surrogate model structure between non-intrusive shape variables and topology optimization responses provided by the embodiment of the present invention;

[0033] Figure 5 Schematic diagram of the non-intrusive shape-topology collaborative optimization result provided by the embodiment of the present invention; among them, Figure 5 Part (a) is a schematic diagram of the optimized shape; Figure 5 Part (b) is a schematic diagram of the optimal topology configuration;

[0034] Figure 6 Schematic diagram of the structure of the data-driven non-intrusive shape-topology collaborative optimization system provided by the present invention. Detailed implementation manners

[0035] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0036] The purpose of the present invention is to provide a data-driven non-intrusive shape-topology collaborative optimization method and system, which can decouple the shape and topology design variables while realizing non-intrusive shape-topology collaborative optimization to ensure the optimization efficiency and optimization ability and achieve the lightweight design of the structure.

[0037] To make the above objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0038] As Figure 1 shown, the data-driven non-intrusive shape-topology collaborative optimization method provided by the present invention includes:

[0039] Step 100: Construct a finite element model of the structure to be optimized, and select control points within the design domain. In this step, parameters such as load boundaries and material properties of the model are set, and the mesh is divided. Some mesh nodes are uniformly selected as control points for mesh deformation within the design domain of shape optimization.

[0040] Step 101: Construct a shape equation that constrains the displacement of the control points, and use the parameters in the shape equation and mesh deformation technology to perform parametric modeling to obtain a parametric model. Specifically, according to the shape of the structure to be optimized, a suitable shape equation is selected to constrain the displacement of the control points, and a small number of parameters in the shape equation are used to drive the mesh deformation. Among them, the shape equation includes, but is not limited to, super-elliptical equations, rotational surface equations, quadratic surface equations, etc.

[0041] Step 102: Use multiple solvers to perform topology optimization on parametric models of different shapes to obtain multi-source topology optimization response data. Specifically, the finite element models of different shapes obtained in the above steps are assigned to different topology optimization solvers for topology optimization to obtain multi-source topology optimization response data. Among them, the topology optimization solvers include, but are not limited to, Tosca, Optistruct, self-developed programs, etc.

[0042] Step 103: Based on the multi-source topology optimization response data and historical data, establish a non-intrusive surrogate model between the shape variables and the topology optimization response. Among them, the non-intrusive surrogate models include, but are not limited to, Radial Basis Function (RBF), Gaussian Process (GP), Deep Neural Network (DNN), etc.

[0043] Step 104: Adopt a point addition strategy to improve the accuracy of the non-intrusive surrogate model until the accuracy requirement of the non-intrusive surrogate model is met. Specifically, use the obtained non-intrusive surrogate model to perform leave-one-out validation on the data set, and adopt a non-intrusive surrogate model point addition method near the sample point with the largest prediction error to update the non-intrusive surrogate model and improve the accuracy of the non-intrusive surrogate model until the accuracy requirement is met, such as the accuracy evaluation index is greater than 98%. Among them, the point addition methods of the non-intrusive surrogate model include, but are not limited to, Thiessen polygon point addition method, active learning point addition method, etc.

[0044] Step 105: Use an intelligent optimization algorithm to rapidly and efficiently optimize the non-intrusive surrogate model to obtain a shape-topology collaborative design scheme. Specifically, use the intelligent optimization algorithm to perform point addition optimization on the non-intrusive surrogate model until the convergence requirement is met. Among them, the intelligent optimization algorithm includes but is not limited to genetic algorithm, ant colony algorithm, particle swarm algorithm, covariance matrix adaptation evolution algorithm, etc. The convergence requirement includes but is not limited to reaching the maximum number of iterations, etc. For example, when reaching the maximum number of iterations, the prediction and real error do not exceed 1%, the absolute error between the model prediction and the real value is less than the specified value, and the optimization results have not improved in m rounds, etc.

[0045] The following further details the data-driven non-intrusive shape-topology collaborative optimization method provided by the present invention in combination with an example of shape-topology collaborative optimization design of a certain hatch structure. It can be understood that the specific examples described herein are only used to explain the present invention and are not intended to limit the present invention.

[0046] First step, establish a finite element model of the hatch structure to be optimized and select control points. The specific process is as Figure 2 shown. First, establish a finite element model of the hatch structure, and correctly set the material properties, loads, and boundary conditions. Then, perform mesh division on the hatch structure, and uniformly select several mesh nodes on the surface of the shape design domain of the finite element model as control points.

[0047] Second step, according to the shape of the hatch structure to be optimized, construct the following shape equation. The semi-axis length c (unit: mm) and the degree n (used to characterize the shape of the equation) in the shape equation are used as shape optimization design parameters, and are used to drive mesh deformation to achieve rapid modeling. The expression constructed in this example is:

[0048]

[0049] Among them, x, y, and z are the three coordinate components of the control point, and 530 is the radius of this example, with the unit of mm. Calculate the coordinates of the control point after deformation according to the semi-axis length c and the degree n. Then train the mapping relationship between the coordinates of the control point before and after deformation, and use this mapping relationship to achieve mesh deformation. Parametric modeling is realized based on the shape parameters c and n and the mesh deformation technology.

[0050] Third step, use multiple solvers to perform topology optimization on parametric models of different shapes to obtain multi-source topology optimization response data. First, as Figure 3 shown, sample in the shape design space and perform parametric modeling using mesh deformation. Assign hatch models of different shapes to different solvers to carry out topology optimization design to obtain multi-source topology optimization response data. Among them, the topology optimization objectives and constraints of different solvers should be kept consistent. Then, as Figure 4As shown, a non-intrusive surrogate model is established for the shape design variables and the multi-source topology optimization response. Among them, the parameters to be optimized in the shape equation are the inputs, and the responses after topology optimization (including but not limited to stress, strain, strain energy, displacement, fundamental frequency, etc.) are the outputs.

[0051] In the fourth step, leave-one-out validation is performed using the obtained non-intrusive surrogate model to determine whether the accuracy of the non-intrusive surrogate model meets the requirements. If the requirements are not met, points are added near the sample point with the largest prediction error in the leave-one-out validation using the non-intrusive surrogate model point addition method, and the non-intrusive surrogate model is updated until the accuracy requirements are met. The accuracy requirement indicators include but are not limited to R 2 > 0.98, RRMSE <0.02, etc. The non-intrusive surrogate model point addition methods include but are not limited to the Thiessen polygon point addition method, the active learning point addition method, etc.

[0052] In the fifth step, rapid optimization of the non-intrusive surrogate model is carried out based on the high-precision non-intrusive surrogate model and the intelligent optimization algorithm obtained in the above steps. As Figure 5 shown, after optimization, an optimized shape-topology collaborative optimization scheme for the hatch structure is obtained. Among them, the intelligent optimization algorithms include but are not limited to genetic algorithms, ant colony algorithms, particle swarm algorithms, covariance matrix adaptation evolution algorithms, etc.

[0053] Based on the above description, compared with the prior art, the present invention also has the following advantages:

[0054] 1. Aiming at the problem that it is difficult to perform sensitivity analysis on complex structures using traditional intrusive shape-topology optimization coupling solution methods, the present invention adopts a data-driven method to decouple the shape design variables and topology optimization variables, and establishes a non-intrusive shape-topology collaborative optimization method, which can effectively reduce the difficulty of collaborative optimization and avoid the derivation of complex sensitivity formulas for shape design variables.

[0055] 2. Aiming at the problems that the traditional method using control point displacement as the shape design variable is prone to insufficient interpolation accuracy of the boundary shape, too many design variables, difficult convergence, and it is difficult to ensure that the final converged shape meets the actual requirements in large complex structures, the present invention replaces the control point displacement with a small number of parameters in the shape equation. While reducing the number of design variables, grid deformation technology is used for modeling, which further improves the modeling accuracy and ensures that the complex structure has a regular shape and meets the actual requirements.

[0056] 3. Aiming at the problems faced in the shape-topology collaborative optimization of large and complex structures in engineering, such as the complexity of the problem, the limited optimization ability of gradient-based algorithms that are prone to falling into local optimal solutions, and the high computational cost and long time consumption of intelligent optimization algorithms, the present invention uses a data-driven method to establish a non-intrusive surrogate model between shape variables and topology optimization responses, replacing the real calculation process in the intelligent optimization algorithm, accelerating the optimization process, and effectively reducing the computational cost in optimization. To ensure the accuracy of the non-intrusive surrogate model, a non-intrusive surrogate model point addition method is adopted to improve the accuracy of the non-intrusive surrogate model, further ensuring the optimization ability of the present method.

[0057] 4. The present invention can select a suitable non-intrusive surrogate model and hyperparameter setting optimization method according to the actual problem to ensure that the non-intrusive surrogate model has high accuracy.

[0058] In addition, corresponding to the above-provided data-driven non-intrusive shape-topology collaborative optimization method, the present invention also provides a data-driven non-intrusive shape-topology collaborative optimization system, as Figure 6 shown, the system includes:

[0059] A control point selection module 600, configured to construct a finite element model of the structure to be optimized and select control points within the design domain.

[0060] A parametric model construction module 601, configured to construct a shape equation that constrains the displacements of the control points, and perform parametric modeling using the parameters in the shape equation and mesh deformation technology to obtain a parametric model.

[0061] A topology optimization module 602, configured to perform topology optimization on parametric models of different shapes using multiple solvers to obtain multi-source topology optimization response data.

[0062] A non-intrusive surrogate model construction module 603, configured to establish a non-intrusive surrogate model between shape variables and topology optimization responses based on the multi-source topology optimization response data and historical data.

[0063] An accuracy improvement module 604, configured to adopt a point addition strategy to improve the accuracy of the non-intrusive surrogate model until the accuracy requirements of the non-intrusive surrogate model are met.

[0064] An optimal design module 605, configured to perform optimal design on the non-intrusive surrogate model using an intelligent optimization algorithm to obtain a shape-topology collaborative design scheme.

[0065] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. For the same or similar parts among the various embodiments, reference can be made to each other. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple. For the relevant parts, reference can be made to the description in the method section.

[0066] Specific examples are used in this article to elaborate on the principles and implementation manners of the present invention. The descriptions of the above embodiments are only used to help understand the method of the present invention and its core idea. At the same time, for those of ordinary skill in the art, based on the idea of the present invention, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation on the present invention.

Claims

1. A data-driven non-intrusive shape-topology collaborative optimization method, characterized in that Including: Construct a finite element model of the structure to be optimized and select control points within the design domain; Construct a shape equation that constrains the displacements of the control points, and perform parametric modeling using the parameters in the shape equation and mesh deformation technology to obtain a parametric model; Use multiple solvers to perform topology optimization on the parametric models of different shapes to obtain multi-source topology optimization response data; Take the parameters to be optimized in the shape equation as the input and the multi-source topology optimization response data as the output to establish a non-intrusive surrogate model between the shape variables and the topology optimization response; the parameters to be optimized in the shape equation are shape design variables; Adopt a point addition strategy to improve the accuracy of the non-intrusive surrogate model until the accuracy requirements of the non-intrusive surrogate model are met; Adopt an intelligent optimization algorithm to carry out optimization design on the non-intrusive surrogate model to obtain a shape-topology collaborative design scheme.

2. The data-driven non-intrusive shape-topology collaborative optimization method according to claim 1, characterized in that The shape equation that constrains the displacements of the control points includes: super-ellipse equation, rotational surface equation or quadratic surface equation.

3. The data-driven non-intrusive shape-topology collaborative optimization method according to claim 1, wherein The point addition strategy includes: Thiessen polygon adaptive point addition method or active learning point addition method.

4. The data-driven non-intrusive shape-topology collaborative optimization method according to claim 3, characterized in that The intelligent optimization algorithm includes: genetic algorithm, ant colony algorithm, particle swarm algorithm or covariance matrix adaptation evolution algorithm.

5. The data-driven non-intrusive shape-topology collaborative optimization method according to claim 1, characterized in that The training method of the non-intrusive surrogate model includes: radial basis function, Gaussian process or neural network.

6. The data-driven non-invasive shape-topology collaborative optimization method according to claim 1, characterized in that Assign the finite element models corresponding to the shapes of the shape design variables to different topology optimization solvers for topology optimization to obtain multi-source topology optimization response data.

7. A data-driven non-invasive shape-topology collaborative optimization system, characterized in that, Including: A control point selection module, which is used to construct a finite element model of the structure to be optimized and select control points within the design domain; A parametric model construction module, which is used to construct a shape equation that constrains the displacements of the control points, and perform parametric modeling using the parameters in the shape equation and mesh deformation technology to obtain a parametric model; A topology optimization module, which is used to use multiple solvers to perform topology optimization on the parametric models of different shapes to obtain multi-source topology optimization response data; A non-intrusive surrogate model construction module, which is used to take the parameters to be optimized in the shape equation as the input and the multi-source topology optimization response data as the output to establish a non-intrusive surrogate model between the shape variables and the topology optimization response; the parameters to be optimized in the shape equation are shape design variables; An accuracy improvement module, which is used to adopt a point addition strategy to improve the accuracy of the non-intrusive surrogate model until the accuracy requirements of the non-intrusive surrogate model are met; An optimization design module, which is used to adopt an intelligent optimization algorithm to carry out optimization design on the non-intrusive surrogate model to obtain a shape-topology collaborative design scheme.

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