Reliability estimation for dynamical systems subject to stochastic excitation using subset simulation with splitting |
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| Affiliation: | 1. Department of Construction Engineering, National Taiwan University of Science and Technology, Tapei 106, Taiwan, ROC;2. School of Civil and Environmental Engineering, Nanyang Technology University, Singapore 639798;3. Applied Mechanics and Civil Engineering, Mail Code 104-44, California Institute of Technology, Pasadena, CA 91125, USA;1. Key Laboratory of Fundamental Science for National Defense-Advanced Design Technology of Flight Vehicles, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;2. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China;1. State Key Laboratory of Water Resources and Hydropower Engineering Science, Institute of Engineering Risk and Disaster Prevention, Wuhan University, 8 Donghu South Road, Wuhan 430072, PR China;2. Department of Architecture and Civil Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong 999077, PR China;3. State Key Laboratory of Ocean Engineering, Department of Civil Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road 200030, Shanghai, PR China;1. Institute for Risk and Uncertainty and Centre for Engineering Dynamics, University of Liverpool, UK;2. Chair of Uncertainty, Reliability and Risk, University of Liverpool, UK;3. University of Exeter, UK;1. University of Liverpool, United Kingdom;2. California Institute of Technology, United States |
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| Abstract: | A new subset simulation approach is proposed for reliability estimation for dynamical systems subject to stochastic excitation. The basic idea of subset simulation is to factor a small failure probability into a product of larger failure probabilities conditional on intermediate failure events. The new method proposed in this work does not require Markov Chain Monte Carlo simulation, in contrast to the original method, to estimate the conditional probabilities; instead, only direct Monte Carlo simulation is needed. The method employs splitting of a trajectory that reaches an intermediate failure level into multiple trajectories subsequent to the corresponding first passage time. The new approach still enjoys most of the advantages of the original subset simulation, e.g. it is applicable to general causal dynamical systems and it is robust with respect to the dimension of the uncertain input variables. The statistical properties of the failure probability estimators are presented, where it is shown that they are unbiased and formulas are derived to assess the error of estimation, including the coefficient of variation. We also discuss the selection of intermediate failure events and the number of samples for each failure level. The resulting algorithm is simple and easy to implement. Two examples are presented to demonstrate the effectiveness of the new approach, and the results are compared with the original subset simulation and with direct Monte Carlo simulation. |
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