A sequential optimization framework for simultaneous design variables optimization and probability uncertainty allocation

In engineering design, the performance of the system and the budget of design uncertainty should be balanced, which means that it is best to optimize design variables and allocate the manufacturing uncertainty simultaneously. This work formulates this problem as an uncertainty optimization problem, where the input uncertainty is modeled by the probability method and both the design variables and the uncertainty magnitude are included in the optimization variables. A sequence optimization framework is proposed to solve the optimization problem. The Taylor-based first-order method is used to translate the probability constraint into a deterministic constraint. A correction coefficient is calculated by the dimensional adaptive polynomial chaos expansion method to improve the accuracy of the uncertainty analysis. The constraint translation and the correction coefficient calculation are executed sequentially. The accuracy and effectiveness of the proposed framework are validated by three benchmark problems, including a mathematical problem, a cantilever I-beam, and a ten-bar truss case.