UBC Theses and Dissertations
Estimating resilience for hydrotechnical systems Li, Yi
With the cycle of natural conditions (hydrological or meteorological), a repairable hydrotechnical system may have a recovery capacity after a system failure. Resilience is a probabilistic performance indicator that measures such a recovery capacity. It is also one of performance indicators that can be used to measure the sustainability of a water resources project. In nature, resilience is a conditional probability that, given a system failure at an earlier time moment, the system can resume functioning at a later time moment. The conditional probability is a close derivative of two-state transition probabilities in a stochastic process. The current estimating techniques for the two-state lag-I transition probabilities may require a high computational cost, or a complex implementation procedure. This thesis explores practical approximation methods for estimating the two-state lag-1 transition probabilities in discrete processes, and the resultant resilience. Two methods are proposed herein. By developing a concise and straightforward approximation for the lag-1 autocorrelation coefficient of system performance functions at two consecutive moments on the basis of the first-order reliability method, one method improves the conventional approaches that estimate the transition probabilities based on a bivanate normal distribution of the system performance functions. The other employs a linear stochastic prediction of the performance function based on the mean point of failure or safety domain. The mean points are one of the fundamental properties of reliability problem. The thesis mathematically defines the mean points, and develops a practical approach for approximating them based on the first-order reliability method. The mean points-based method improves the conventional approaches that estimate the transition probabilities based on a linear stochastic prediction of performance function. The two methods developed herein are demonstrated in a typical river hydrology example for estimating seasonal lag-1 resilience. The proposed approximation methods for estimating the transition probabilities in discrete processes can be also applicable to other civil engineering problems, such as marine/offshore steel structure fatigue analysis, river navigability study, or concrete reinforcement corrosion prediction.
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