带襟翼导轨翼肋后缘尺寸-拓扑综合优化的摄动神经网络代理模型法

谢川; 徐超; 周丹发; 姚卫星

doi:10.21656/1000-0887.440033

带襟翼导轨翼肋后缘尺寸-拓扑综合优化的摄动神经网络代理模型法

doi: 10.21656/1000-0887.440033

谢川^1,,
徐超¹,
周丹发²,
姚卫星^{1, 3, ,}

1.
南京航空航天大学航空航天结构力学及控制全国重点实验室，南京 210016
2.
上海机电工程研究所，上海 201109
3.
南京航空航天大学飞行器先进设计技术国防重点学科实验室，南京 210016

详细信息

作者简介:
谢川(1992—)，男，博士生(E-mail: xcshovelm@nuaa.edu.cn)

通讯作者:
姚卫星(1957—)，男，教授，博士，博士生导师(通讯作者. E-mail: wxyao@nuaa.edu.cn)

中图分类号: O342
计量
- 文章访问数: 126
- HTML全文浏览量: 48
- PDF下载量: 43
- 被引次数: 0
出版历程
- 收稿日期: 2023-02-13
- 修回日期: 2023-03-15
- 刊出日期: 2024-01-01

The Perturbation Neural Network Surrogate Model Method for Size-Topology Synthetical Optimization of Wing Rib Trailing Edges With Flap Tracks

XIE Chuan^1
,,
XU Chao¹,
ZHOU Danfa²,
YAO Weixing^{1, 3
, ,}

1.
State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R.China
2.
Shanghai Electro-Mechanical Engineering Institute, Shanghai 201109, P.R.China
3.
Key Laboratory of Fundamental Science for National Defense-Advanced Design Technology of Flight Vehicle, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R.China

摘要

摘要: 带襟翼导轨的翼肋后缘设计需要确定肋缘条、腹板的尺寸和肋腹板的拓扑形状，对此提出了一种针对尺寸-拓扑综合优化的摄动神经网络(perturbation neural network, PNN)代理模型法. 其基本思想是基于拓扑优化对参数的敏感性，引入了对试验设计(design of experiments, DOE)样本点的摄动，通过过滤手段捕获拓扑突变点，并降低数值噪声，极大地提高了代理模型的预测精度，将拓扑优化过程作为黑盒，直接建立起尺寸变量与拓扑优化后结构响应的代理模型. 最后在代理模型上进行优化，得到了结构尺寸与拓扑形状的最优组合. 该文完成了一个翼肋后缘优化典型算例，证明了该方法的有效性和优越性.
- 摄动神经网络 /
- 尺寸优化 /
- 拓扑优化 /
- 代理模型 /
- 翼肋
Abstract: The design of wing rib trailing edges with flap tracks requires the determination of sizes of the rib edge strips, the webs and the topological shapes of the rib webs. Therefore, a perturbation neural network surrogate model method was proposed for the size-topology synthetical optimization. The basic idea is that, based on the sensitivity of topology optimization to parameters, the perturbation is introduced in the DOE samples to capture the topological mutation points by means of the filtering measure, and reduce the numerical noise, which greatly improves the prediction accuracy of the surrogate model. With the topology optimization process viewed as a black box, the surrogate model for the size variables and topology optimized structural responses was directly built up. Finally, optimization was carried out on the surrogate model to obtain the optimal combination of structural sizes and topological shapes. A typical calculation example of wing rib trailing edge optimization demonstrates the validity and superiority of the proposed method.
- perturbation neural network /
- size optimization /
- topology optimization /
- surrogate model /
- wing rib

HTML全文

图 1 带襟翼导轨的翼肋后缘结构初始模型

Figure 1. The initial model for the trailing edge of the wing rib with a flap track

下载: 全尺寸图片幻灯片

图 2 翼肋后缘结构基本尺寸与变量定义

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 2. Dimensions of trailing edge of wing rib structure and definition of design variables

下载: 全尺寸图片幻灯片

图 3 ANN与PNN构成对比

Figure 3. Comparison between ANN and PNN

下载: 全尺寸图片幻灯片

图 4 优化流程

Figure 4. Optimization flow chart

下载: 全尺寸图片幻灯片

图 5 尺寸优化后模型应力分布

Figure 5. Model stress distributions after size optimization

下载: 全尺寸图片幻灯片

图 6 翼肋形状设计过程

Figure 6. The wing rib shape design process

下载: 全尺寸图片幻灯片

图 7 拓扑重量关于尺寸变量的归一化灵敏度箱型图

Figure 7. The normalized sensitivity box diagram of the topological weight with respect to size variables

下载: 全尺寸图片幻灯片

图 8 基于PNN的尺寸-拓扑综合优化结果

Figure 8. Results of the size-topology synthetical optimization based on PNN

下载: 全尺寸图片幻灯片

表 1 代理模型预测精度及特点^[21]

Table 1. Prediction accuracy and characteristics of the surrogate model^[21]

surrogate model	prediction accuracy	characteristic
PRS	low	high efficiency
Kriging	high	sensitivity to digital noise
RBF	medium	the best effect in general

下载: 导出CSV

表 2 变量说明及取值范围

Table 2. Variable description and range

variable name	symbol	range
upper edge strip thickness	t₁/mm	3.0~8.0
middle edge strip thickness	t₂/mm	3.0~8.0
lower edge strip thickness	t₃/mm	3.0~8.0
lower web thickness	t₄/mm	3.0~8.0
upper web thickness	t₅/mm	1.0~4.0

下载: 导出CSV

表 3 传统优化中变量与响应各阶段结果

Table 3. Variable and response results at each stage in traditional optimization

variable or response	initial value	1st size optimization	final result
t₁/mm	3.00	3.26	3.00
t₂/mm	3.00	3.00	3.00
t₃/mm	3.00	3.00	3.00
t₄/mm	3.00	3.70	4.54
t₅/mm	1.00	1.49	1.56
δ_max/mm	10.72	9.57	10.90
σ_max/MPa	394.60	299.99	299.94
w/kg	1.842	2.12	2.06

下载: 导出CSV

表 4 基于PNN的优化结果

Table 4. Optimization results based on PNN

variable or response	t₁/mm	t₂/mm	t₃/mm	t₄/mm	t₅/mm	δ/mm	σ/MPa	w/kg
result	3.00	3.00	3.00	3.71	1.72	7.44	300.15	1.90

下载: 导出CSV

表 5 代理模型精度对比

Table 5. Surrogate model accuracy comparison

criterion	Kriging with PNN	PRS with PNN	RBF with PNN	Kriging without PNN
R²	0.915	0.536	0.897	0.782
R_RMSE	0.105	0.254	0.112	0.197

下载: 导出CSV

参考文献(21)

[1]	张广圣, 王其祚. 机械结构多级优化的问题与对策[J]. 合肥工业大学学报(自然科学版), 1990, 13(1): 52-58. ZHANG Guangsheng, WANG Qizuo. Multilevel mechanical structure optimization difficulties and strategis[J]. Journal of Hefei University of Technology (Natural Science), 1990, 13(1): 52-58. (in Chinese)
[2]	谢浩然, 贺媛媛, 陶志坚. 扑旋翼飞行器气动特性分析及机翼拓扑优化设计[J]. 南京航空航天大学学报, 2020, 52(2): 280-287. XIE Haoran, HE Yuanyuan, TAO Zhijian. Aerodynamic characteristics analysis and topology optimization design of wing of flapping rotorcraft[J]. Journal of Nanjing University of Aeronautics & Astronautics, 2020, 52(2): 280-287. (in Chinese)
[3]	KUTYŁOWSKI R, SZWECHŁOWICZ M. Application of topology optimization to thighbone and thighbone/implant structure modelling[J]. Archives of Civil and Mechanical Engineering, 2019, 19(4): 1006-1019. doi: 10.1016/j.acme.2019.05.007
[4]	BRIOT S, GOLDSZTEJN A. Topology optimization of industrial robots: application to a five-bar mechanism[J]. Mechanism and Machine Theory, 2018, 120: 30-56. doi: 10.1016/j.mechmachtheory.2017.09.011
[5]	GAO X, MA H. Topology optimization of continuum structures under buckling constraints[J]. Computers & Structures, 2015, 157: 142-152.
[6]	张东东, 栾福强, 赵礼辉, 等. 基于变体积约束的阻尼材料微结构拓扑优化研究[J]. 应用数学和力学, 2022, 43(6): 648-659. doi: 10.21656/1000-0887.420206 ZHANG Dongdong, LUAN Fuqiang, ZHAO Lihui, et al. Research on topology optimization of damping material microstructures with varied volume constraints[J]. Applied Mathematics and Mechanics, 2022, 43(6): 648-659. (in Chinese) doi: 10.21656/1000-0887.420206
[7]	LÓPEZ J, ANITESCU C, RABCZUK T. Isogeometric structural shape optimization using automatic sensitivity analysis[J]. Applied Mathematical Modelling, 2021, 89(2): 1004-1024.
[8]	GHOMMEM M, COLLIER N, NIEMI A H, et al. On the shape optimization of flapping wings and their performance analysis[J]. Aerospace Science and Technology, 2014, 32(1): 274-292. doi: 10.1016/j.ast.2013.10.010
[9]	刘宏亮, 祝雪峰, 杨迪雄. 基于等几何分析的结构优化设计研究进展[J]. 固体力学学报, 2018, 39(3): 248-267. LIU Hongliang, ZHU Xuefeng, YANG Dixiong. Research advances in isogeometric analysis-based optimum design of structure[J]. Chinese Journal of Solid Mechanics, 2018, 39(3): 248-267. (in Chinese)
[10]	荣见华, 姜节胜, 胡德文, 等. 基于应力及其灵敏度的结构拓扑渐进优化方法[J]. 力学学报, 2003, 35(5): 584-591. doi: 10.3321/j.issn:0459-1879.2003.05.010 RONG Jianhua, JIANG Jiesheng, HU Dewen, et al. A structural topology evolutionary optimization method based on stresses and their sensitivity[J]. Chinese Journal of Theoretical and Applied Mechanics, 2003, 35(5): 584-591. (in Chinese) doi: 10.3321/j.issn:0459-1879.2003.05.010
[11]	BENNACEUR M, XU Y, LAYACHI H. Wing rib stress analysis and design optimization using constrained natural element method[J]. IOP Conference Series: Materials Science and Engineering, 2017, 234(3): 12-18.
[12]	AZID I A, KWAN A S K, SEETHARAMU K N. An evolutionary approach for layout optimization of a three-dimensional truss[J]. Structural and Multidisciplinary Optimization, 2002, 24(4): 333-337. doi: 10.1007/s00158-002-0244-9
[13]	RAJAN S D. Sizing, shape, and topology design optimization of trusses using genetic algorithm[J]. Journal of Structural Engineering, 1995, 121(10): 1480-1487. doi: 10.1061/(ASCE)0733-9445(1995)121:10(1480)
[14]	DUAN B Y, YE S H. A mixed method for shape optimization of skeletal structures[J]. Engineering Optimization, 1986, 10(3): 183-197. doi: 10.1080/03052158608902536
[15]	隋允康, 高峰, 龙连春, 等. 基于层次分解方法的桁架结构形状优化[J]. 计算力学学报, 2006, 23(1): 46-51. SUI Yunkang, GAO Feng, LONG Lianchun, et al. Shape optimization of truss structure based on hierarchical decomposition method[J]. Chinese Journal of Computational Mechanics, 2006, 23(1): 46-51. (in Chinese)
[16]	FLAGER F, ADYA A, HAYMAKER J, et al. A bi-level hierarchical method for shape and member sizing optimization of steel truss structures[J]. Computers & Structures, 2014, 131: 1-11.
[17]	石连栓, 王跃方, 孙焕纯. 具有动应力、位移和稳定性约束的离散变量桁架结构布局优化设计算法[J]. 应用数学和力学, 2006, 27(5): 527-532. doi: 10.3321/j.issn:1000-0887.2006.05.004 SHI Lianshuan, WANG Yuefang, SUN Huanchun. Approach for layout optimization of truss structures with discrete variables under dynamic stress, displacement and stability constraints[J]. Applied Mathematics and Mechanics, 2006, 27(5): 527-532. (in Chinese) doi: 10.3321/j.issn:1000-0887.2006.05.004
[18]	高普阳, 赵子桐, 杨扬. 基于卷积神经网络模型数值求解双曲型偏微分方程的研究[J]. 应用数学和力学, 2021, 42(9): 932-947. doi: 10.21656/1000-0887.420050 GAO Puyang, ZHAO Zitong, YANG Yang. Study on numerical solutions to hyperbolic partial differential equations based on the convolutional neural network model[J]. Applied Mathematics and Mechanics, 2021, 42(9): 932-947. (in Chinese) doi: 10.21656/1000-0887.420050
[19]	吴雨程, 殷红, 彭珍瑞. 基于Kriging模型和提升小波变换的随机模型修正[J]. 应用数学和力学, 2022, 43(7): 761. doi: 10.21656/1000-0887.420128 WU Yucheng, YIN Hong, PENG Zhenrui. Stochastic model updating based on Kriging model and lifting wavelet transform[J]. Applied Mathematics and Mechanics, 2022, 43(7): 761. (in Chinese) doi: 10.21656/1000-0887.420128
[20]	陶然, 周焕林, 孟增, 等. 基于响应面法和改进算术优化算法的抱杆优化设计[J]. 应用数学和力学, 2022, 43(10): 1113. doi: 10.21656/1000-0887.420318 TAO Ran, ZHOU Huanlin, MENG Zeng, et al. Optimization design of holding poles based on the response surface methodology and the improved arithmetic optimization algorithm[J]. Applied Mathematics and Mechanics, 2022, 43(10): 1113. (in Chinese) doi: 10.21656/1000-0887.420318
[21]	穆雪峰, 姚卫星, 余雄庆, 等. 多学科设计优化中常用代理模型的研究[J]. 计算力学学报, 2005, 22(5): 608-612. MU Xuefeng, YAO Weixing, YU Xiongqing, et al. A survey of surrogate models used in mdo[J]. Chinese Journal of Computational Mechanics, 2005, 22(5): 608-612. (in Chinese)