Efficient, high-resolution topology optimization method based on convolutional neural networks

doi:10.1007/s11465-020-0614-2

Front. Mech. Eng.

2021, Vol. 16

Issue (1) : 80-96 https://doi.org/10.1007/s11465-020-0614-2

RESEARCH ARTICLE

Efficient, high-resolution topology optimization method based on convolutional neural networks

Liang XUE^1,², Jie LIU², Guilin WEN^1,²(

), Hongxin WANG¹

¹. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China
². Center for Research on Leading Technology of Special Equipment, School of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, China

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Abstract

Topology optimization is a pioneer design method that can provide various candidates with high mechanical properties. However, high resolution is desired for optimum structures, but it normally leads to a computationally intractable puzzle, especially for the solid isotropic material with penalization (SIMP) method. In this study, an efficient, high-resolution topology optimization method is developed based on the super-resolution convolutional neural network (SRCNN) technique in the framework of SIMP. SRCNN involves four processes, namely, refinement, path extraction and representation, nonlinear mapping, and image reconstruction. High computational efficiency is achieved with a pooling strategy that can balance the number of finite element analyses and the output mesh in the optimization process. A combined treatment method that uses 2D SRCNN is built as another speed-up strategy to reduce the high computational cost and memory requirements for 3D topology optimization problems. Typical examples show that the high-resolution topology optimization method using SRCNN demonstrates excellent applicability and high efficiency when used for 2D and 3D problems with arbitrary boundary conditions, any design domain shape, and varied load.

Keywords topology optimization convolutional neural network high resolution density-based

Corresponding Author(s): Guilin WEN

Just Accepted Date: 15 January 2021 Online First Date: 11 February 2021 Issue Date: 11 March 2021

Cite this article:

Liang XUE,Jie LIU,Guilin WEN, et al. Efficient, high-resolution topology optimization method based on convolutional neural networks[J]. Front. Mech. Eng., 2021, 16(1): 80-96.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-020-0614-2
https://academic.hep.com.cn/fme/EN/Y2021/V16/I1/80

Fig.1 Relative position and connection state of SRCNN operations. SRCNN: Super-resolution convolutional neural network.

Fig.2 Presentation of several training samples. This illustration shows 4 types of classical topological optimization models: (a) Cantilever beam, (b) L-bracket, (c) T-bracket, and (d) MBB beam.

Tab.1 Model data of different high-resolution transformations

Fig.3 Filter region and filtered elements of different high-resolution transformations.

Fig.4 Pooling strategy with corner mean sampling.

Fig.5 High-resolution topology optimization method.

Fig.6 Combination treatment of 3D models using 2D SRCNN.

Fig.7 Design domain and boundary conditions of two 2D examples: (a) A barrier structure with a hole and (b) a sandwich structure with symmetrical boundary conditions.

Fig.8 High-resolution images of the barrier structure under various strategies. Results obtained by traditional methods: (a) Low-resolution, 210×210, r_min= 4, c_obj= 91.495; (b) high-precision, 840×840, r_min = 19, c_obj= 97.613; (c) large-scale, 840×840, r_min = 4, c_obj= 84.179. (d) Result post-processed by SRCNN, 840×840, r_min = 4, c_obj= 1.2×10⁸. Results obtained by HRTO: (e) High-precision, 840×840, r_min = 4, c_obj= 81.168; (f) large-scale, 840×840, r_min = 0.25, c_obj= 83.348. r_minand c_obj represent the filter radius and the objective function, respectively.

Fig.9 High-resolution images of the sandwich structure under various strategies. Results obtained by traditional methods: (a) Low-resolution, 200×140, r_min = 4, c_obj= 2.0214; (b) high-precision, 800×560, r_min = 19, c_obj= 2.0715; (c) large-scale, 800×560, r_min = 4, c_obj= 1.9335. (d) Result post-processed by SRCNN, 800×560, r_min = 4, c_obj= 2.1632. Results obtained by HRTO: (e) High-precision, 800×560, r_min = 4, c_obj= 1.8352; (f) large-scale, 800×560, r_min = 0.25, c_obj= 1.9201. r_min and c_obj indicate the filtering radius and objective function, respectively.

Fig.10 MBB beam basic model.

Tab.2 Alternative optimization parameters

Fig.11 The influence of each optimization parameter of 2D designs on the objective. The influence of (a) number of elements, (b) volume fraction, (c) filter radius, and (d) upscaling factor on the objective under the high-precision situation. The influence of (e) number of elements, (f) volume fraction, (g) filter radius, (h) upscaling factor on the objective under the large-scale situation.

Fig.12 MBB beam convergence history of the conventional method and HRTO method.

Tab.3 MBB beam efficiency of the conventional method and HRTO method

Tab.4 Efficiency data reduction ratio of the conventional method and HRTO method

Tab.5 Efficiencies of the HRTO method at different resolutions

Fig.13 Design domain and HRTO topology solution of a 3D cantilever beam.

Tab.6 Comparison of acceleration ratios of three algorithms

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