Failure Probability Estimation of Linear Time Varying Systems by Progressive Refinement of Reduced Order Models

Agnimitra Dasgupta, Debraj Ghosh

Abstract: Estimation of failure probabilities is computationally expensive, and the usage of reduced order models (ROM) holds a promise in reducing this cost. However, such an attempt also requires development of new algorithms to minimize the error due to approximation by ROMs. In this work, a novel iterative algorithm is proposed for estimating failure probabilities of parametrically uncertain linear dynamical systems using ROMs. The key idea in this algorithm is to progressively localize the training domain of the ROM in the domain of random parameters. While the algorithm is generic in nature, particularly a proper orthogonal decomposition based ROM is used here and found to be very effective. Through a detailed numerical study implementing the proposed algorithm, two variants of the ROM—global and local—are explored and a considerable cost gain over a full-scale model is observed. The algorithm also performed well in estimating a low probability of failure. Being dependent on a statistical simulation, this algorithm has inherent potential to be easily and efficiently parallelized.