Robust optimization of uncertain structures based on interval closeness coefficients and the 3D violation vectors of interval constraints

作     者：Cheng, Jin Liu, Zhenyu Qian, Yangming Wu, Di Zhou, Zhendong Gao, Wei Zhang, Jia Tan, Jianrong 

作者机构：Zhejiang Univ State Key Lab Fluid Power & Mechatron Syst Hangzhou 310027 Zhejiang Peoples R China Harbin Inst Technol Minist Educ Key Lab Microsyst & Microstruct Mfg Harbin 150080 Heilongjiang Peoples R China Univ New South Wales Sch Civil & Environm Engn Sydney NSW 2052 Australia 

出 版 物：《STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION》 (结构和多学科最佳设计)

年 卷 期：2019年第60卷第1期

页      面：17-33页

核心收录：

学科分类：08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 0801[工学-力学（可授工学、理学学位）] 080102[工学-固体力学] 

基　　金：National Natural Science Foundation of China Science Fund for Creative Research Groups of National Natural Science Foundation of China Key Laboratory of Micro-systems and Micro-structures Manufacturing of Ministry of Education, Harbin Institute of Technology [2015KM001] Fundamental Research Funds for the Central Universities 

主　　题：Robust optimization Uncertain structure Interval closeness coefficient 3D violation vector of interval constraint Kriging technique Nested genetic algorithm 

摘      要：In this paper, a novel direct interval robust optimization approach is proposed so that the robust optimal design vectors for structures with interval uncertainties can be achieved. A new concept of interval closeness coefficient is proposed to describe the relative positional relationship between the boundaries of two intervals. Subsequently, the explicit formulae for calculating the four interval closeness coefficients between the boundaries of an interval constraint mechanical performance index and those of its corresponding given interval constant are put forward. Consequently, the 3D violation vectors of different interval constraints can be calculated, and the feasibility of a design vector can be evaluated by its total 3D violation vector of all interval constraints. Finally, various design vectors are directly ranked according to the preferential guidelines considering the robustness of all the mechanical performance indices of uncertain structures, which is realized by integrating the Kriging technique and nested genetic algorithm. Unlike the traditional robust optimization of structures involving interval uncertainties, the proposed method can avoid the complicated model transformation process and ensure the robustness of all the mechanical performance indices of the optimal solution. Two examples are thoroughly investigated, the results of which demonstrate the applicability and advantages of the proposed approach.