MPP-based dimension reduction method for accurate prediction of the probability of failure of a performance function

A hybrid reliability analysis method is proposed to yield very accurate failure rate calculation of a performance function when dealing with highly nonlinear electromagnetic systems in the presence of uncertainties. To achieve this goal, the first-order reliability method called reliability index approach is first conducted for searching a most probable failure point (MPP) at a given design. However, its result may have significant errors especially for nonlinear or multi-dimensional performance functions. To overcome the drawback, the univariate dimension reduction method is additionally executed at the obtained MPP, and then the probability of failure of a performance function is recalculated through additively decomposing an n-dimensional function into n 1-D functions. A mathematical example and TEAM workshop problem 22 are provided to demonstrate numerical efficiency and accuracy of the proposed method by comparison with the existing reliability methods.