Dimensional synchronous modeling-based enhanced Kriging algorithm and adaptive Copula method for multi-objective synthetical reliability analyses

To accomplish the reliability analyses of the correlation of multi-analytical objectives, an innovative framework of Dimensional Synchronous Modeling (DSM) and correlation analysis is developed based on the stepwise modeling strategy, cell array operation principle, and Copula theory. Under this framework, we propose a DSM-based Enhanced Kriging (DSMEK) algorithm to synchronously derive the modeling of multi-objective, and explore an adaptive Copula function approach to analyze the correlation among multiple objectives and to assess the synthetical reliability level. In the proposed DSMEK and adaptive Copula methods, the Kriging model is treated as the basis function of DSMEK model, the Multi-Objective Snake Optimizer (MOSO) algorithm is used to search the optimal values of hyperparameters of basis functions, the cell array operation principle is adopted to establish a whole model of multiple objectives, the goodness of fit is utilized to determine the forms of Copula functions, and the determined Copula functions are employed to perform the reliability analyses of the correlation of multi-analytical objectives. Furthermore, three examples, including multi-objective complex function approximation, aeroengine turbine bladed-disc multi-failure mode reliability analyses and aircraft landing gear system brake temperature reliability analyses, are performed to verify the effectiveness of the proposed methods, from the viewpoints of mathematics and engineering. The results show that the DSMEK and adaptive Copula approaches hold obvious advantages in terms of modeling features and simulation performance. The efforts of this work provide a useful way for the modeling of multi-analytical objectives and synthetical reliability analyses of complex structure/system with multi-output responses.