基于变尺度混沌算法的曲面品质优化

徐翔宇; 闫光荣; 雷毅

doi:10.13700/j.bh.1001-5965.2022.0070

基于变尺度混沌算法的曲面品质优化

doi: 10.13700/j.bh.1001-5965.2022.0070

1.
北京航空航天大学机械工程及自动化学院，北京 100191
2.
北京数码大方科技股份有限公司，北京 100094

基金项目: 国家重点研发计划(2020YFB1709102)

详细信息

通讯作者:
E-mail：yangr@buaa.edu.cn

中图分类号: TP391.7
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- 被引次数: 0
出版历程
- 收稿日期: 2022-02-14
- 录用日期: 2022-08-07
- 网络出版日期: 2022-08-12
- 整期出版日期: 2023-12-29

Surface quality optimization based on mutative scale chaos algorithm

1.
School of Mechanical Engineering，Beihang University，Beijing 100191，China
2.
CAXA Technology Co., Ltd.，Beijing 100094，China

Funds: National Key R & D Program of China(2020YFB1709102)

More Information

Corresponding author: E-mail：yangr@buaa.edu.cn

摘要

摘要:
曲面品质优化是曲面重构中的常见问题，在航空航天和汽车等高端产品设计中，如果要求重构的曲面间具有高阶连续性，往往需要进行大量的优化工作。为了便捷地得到光滑的高品质曲面，提出一种基于变尺度混沌算法的曲面品质优化方法。引入可调参数，在与邻接面NURBS曲面片一阶连续条件下，可以灵活调整多个参数值对目标面进行变形操作；建立变尺度混沌优化的数学模型，计算出可调参数组的最优解，得到相对原曲面变形量最小的高品质曲面。通过案例分析验证了所提方法的鲁棒性和实用性。对优化后的曲面进行光影分析，结果表明：所提方法可以在保证曲面品质的同时，提高曲面重构的效率。
- 曲面重构 /
- 高品质曲面 /
- 混沌优化 /
- 变尺度 /
- 光影分析
Abstract:
Surface quality optimization is a common problem in surface reconstruction. In the design of high-end products such as aerospace and automobile, if the reconstructed surfaces are required to have high-order continuity, a lot of optimization work is often needed. In order to obtain smooth and high-quality surfaces conveniently, an optimization method of surface quality based on a mutative scale chaos algorithm is proposed. Adjustable parameters are introduced. The target surface can be deformed by flexibly adjusting a number of parameters under the G¹ continuity constraint between neighboring NURBS patches. A mathematical model of mutative scale chaos optimization is established, and the optimal solution of the adjustable parameters is calculated to obtain a high-quality surface with the smallest deformation compared with the original surface. The robustness and practicability of this method are verified by case analysis. The isolux analysis of the optimized surface is carried out. The outcomes demonstrate that the mutative scale chaotic algorithm-based surface quality optimization technique may guarantee the surface's quality and enhance the effectiveness of surface reconstruction.
- surface reconstruction /
- high-quality surface /
- chaos optimization /
- mutative scale /
- diagnostic shade

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图 1 曲面整形过程

Figure 1. Surface reshaping process

下载: 全尺寸图片幻灯片

图 2 关键控制点坐标及权重的计算流程

Figure 2. Calculation process of key control vertex and weight information

下载: 全尺寸图片幻灯片

图 3 曲面整形前后的网格图

Figure 3. Control mesh of two surfaces before and after reshaping

下载: 全尺寸图片幻灯片

图 4 曲面整形前后的等照度图

Figure 4. Isolux diagram before and after surface reshaping

下载: 全尺寸图片幻灯片

表 1 变尺度混沌优化算法中的参数值

Table 1. Parameter values in mutative scale chaos optimization algorithm

可调参数	初始值	迭代次数	最优值	曲面误差(加权和)
$ {x_1} $	0.017	12237	0.0144	86.3432
$ {x_2} $	−0.43	12237	−2.374	86.3432
$ {x_3} $	0.36	12237	0.0094	86.3432
$ {x_4} $	0.33	12237	0.2314	86.3432

可调参数	初始值	迭代次数	最优值	曲面误差(加权和)
$ {x_1} $	0.04	162728	0.0056	94.4156
$ {x_2} $	−0.23	162728	−0.9779	94.4156
$ {x_3} $	0.41	162728	0.0137	94.4156
$ {x_4} $	1.26	162728	0.5321	94.4156

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表 2 邻公共边第1排控制顶点信息

Table 2. The first row control vertex information adjacent to common edge

控制顶点	原始控制顶点及权重				优化后控制顶点及权重
控制顶点	$ {x_1} $	$ {y_1} $	${{\textit{z}}_1}$	$ {\omega _1} $	$ {x_2} $	$ {y_2} $	${{\textit{z}}_2}$	$ {\omega _2} $
${P}_{1,1}$	12.34	−15.57	−2.68	1	23.45	−15.57	−1.83	3.44
${P}_{1,2}$	18.42	−33.57	−7.86	1	20.38	−37.57	−2.39	5.03
${P}_{1,3}$	26.51	−57.98	−12.26	1	16.34	−57.57	−5.62	2.18
${P}_{1,4}$	35.06	−74.73	−8.82	1	34.62	−76.45	−2.81	1.03
${P}_{1,5}$	42.02	−55.97	−5. 32	1	35.66	−57.57	−4.38	0.63
${P}_{1,6}$	53.31	−52.91	−5.12	1	45.68	−53.51	−5.32	0.32
${P}_{1,7}$	62.02	−58.94	−6. 26	1	65.28	−57.77	−6.38	7.74

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