Multiobjective reliability-based design optimization approach using the gray system and evidence theory

Aimed at the subjectivity of selecting the weight of each objective function in the process of multiobjective reliability-based design optimization (MRBDO), this study proposed a multiobjective weight quantitative analysis method by combining the gray incidence analysis method and evidence theory. This method derived the weight of each objective function from the uncertainty information of design variables, and effectively avoided the subjectivity of weight selection. First, the ideal attribute interval number and the interval number matrix of uncertain design variables were defined based on the gray system theory. On the basis of the definition of the information structure sequence, the gray incidence coefficient (GIC) matrix of measures with ideal attribute deviations was derived. Second, the basic probability assignment of each objective function and model under uncertainty variables was derived based on the Dempster-Shafer evidence theory. The Dempster-Shafer evidence synthesis rule was used to fuse the multisource evidence information to obtain the weight of each objective function. Then, an MRBDO problem was converted into a single-objective reliability-based design optimization (SRBDO) problem, which is relatively easier to address. Third, the performance measurement analysis (PMA) method was used to transform the reliability constraint into an optimized iterative process, and the MRBDO solution was obtained based on the MATLAB Optimization Toolbox and Symbol Toolbox. Finally, the accuracy and efficiency of the proposed method were verified through a numerical example and a small aeroengine gear reduction system.