Polynomial Chaos Expansion for Probabilistic Uncertainty Propagation

Uncertainty propagation (UP) methods are of great importance to design optimization under uncertainty. As a well-known and rigorous probabilistic UP approach, the polynomial chaos expansion (PCE) technique has been widely studied and applied. However, there is a lack of comprehensive overviews and studies of the latest advances of the PCE methods, and there is still a large gap between the academic research and engineering application for PCE due to its high computational cost. In this chapter, latest advances of the PCE theory and method are elaborated, in which the newly developed data-driven PCE method that does not depend on the complete information of input probabilistic distribution as the common PCE approaches is introduced and improved. Meanwhile, the least angle regression technique and the trust region scenario are, respectively, extended to reduce the computational cost of data-driven PCE to accommodate it to practical engineering design applications. In addition, comprehensive comparisons are made to explore the relative merits of the most commonly used PCE approaches in the literature to help designers to choose more suitable PCE techniques in probabilistic design optimization.