Sequential mixture of Gaussian processes and saddlepoint approximation for reliability-based design optimization of structures

This paper presents an efficient optimization procedure for solving the reliability-based design (RBDO) problem of structures under aleatory uncertainty in material properties and external loads. To reduce number structural analysis calls during process, mixture models Gaussian processes (MGPs) are constructed prediction responses. The MGP is used to expand application process model (GPM) large training sets well covering input variable space, significantly reducing time, improving overall accuracy regression models. A set variables associated responses first generated split into independent subsets similar samples using clustering method. GPM each subset then developed produce a GPMs that together define as their weighted average. weight vector computed specified contains probability belongs projection onto space. calculate failure probabilities inverse values required RBDO problem, novel saddlepoint approximation proposed based on three cumulants random variables. original replaced by sequential deterministic (SDO) which MGPs serve surrogates limit-state functions probabilistic constraints problem. SDO strategically solved exploring promising region may contain optimal solution, region, producing reliable solution. Two examples truss steel frame demonstrate efficiency procedure.