A Most Probable Point Based Method for Uncertainty Analysis

Uncertainty is inevitable at every stage of the life cycle development of a product. To make use of probabilistic information and to make reliable decisions by incorporating decision maker’s risk attitude under uncertainty, methods for propagating the effect of uncertainty are therefore needed. When designing complex systems, the efficiency of methods for uncertainty analysis becomes critical. In this paper, a most probable point (MPP) based uncertainty analysis (MPPUA) method is proposed. The concept of the MPP is utilized to generate the cumulative distribution function (CDF) of a system output by evaluating the probability estimates at a serial of limit states. To improve the efficiency of locating the MPP, a novel MPP search algorithm is presented that employs a set of searching strategies, including evaluating derivatives to direct a search, tracing the MPP locus, and predicting the initial point for MPP search. A mathematical example and the Pratt & Whitney (PW) engine design are used to verify the effectiveness of the proposed method. With the MPPUA method, the probabilistic distribution of a system output can be generated across the whole range of its performance.