Piecewise point classification for uncertainty propagation with nonlinear limit states

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Department of Mechanical Engineering-Engineering Mechanics


Reliability measures the probability that engineered systems successfully perform the intended functionalities under various sources of uncertainties. A piecewise point classification (PPC) method is proposed in this work for effectively propagating uncertainty with nonlinear limit states and approximating the probability of failure accurately. The idea is to efficiently identify a set of points near the critical region, and thus enable capturing the nonlinearity of limit states by constructing piecewise linear approximations. In PPC, the first-order reliability method (FORM) is initially employed to search the most probable point. To handle the nonlinearity of failure surfaces, a sampling-based limit state learning algorithm is then developed to search critical points near the failure surface. With all the points evaluated during the search process, a distance-based piecewise point classification method is developed as a classifier to predict failure events. Monte Carlo simulation (MCS) is finally utilized to propagate uncertainties and approximate the probability of failure, in which a large size of sample points is generated randomly and classified by the developed piecewise point classifier. Three case studies are used to demonstrate the efficacy of the developed approach.

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Structural and Multidisciplinary Optimization