Novel simulation methods for calculating the reliability of structural dynamical systems subjected to stochastic loads

The current trend towards Performance Based Design (PBD) requiresthe development of methodologies for assessing whether a given structural design satisfies specified engineering performance objectives. Assessment of the performance of structures subjected to random dynamic loadings such as earthquake, ocean wave or wind, is one of the most challenging problems in structural engineering. The parameters used to describe the structural model and loading conditions are inherently random in nature. Thus it is both rational and scientific to assess the performance of a structure by evaluating its reliability at different performance levels. Here the violation of any one of the performance objectives is considered as structural "failure". In PBD, the structure is designed so that its failure probability does not exceed a certain specified value (typically a very small value, such as 10-7) within a specific time period or its service life. The complexity in solving the reliability problem roots from three aspects namely the high dimensionality (the number of random variables involved is of the order of hundreds and thousands), non-linearity and the large number of limit state functions involved. Most existing methods fail to provide satisfactory solutions to the aforementioned high-dimensional reliability problems. During the whole course of MPHIL study, several novel efficient simulation methods have been developed, only four of which will be presented in this Thesis. These methods have been shown to be robust, accurate and efficient, outperforming MCS by a computational saving at least of an order of 3500, 0.24 and 17.5 million times (for the linear problems) with failure probabilities of an order of 10-3, 10-5 and 10-7 respectively. When considering nonlinear problems, the computational saving is at least of an order of 30, 200 and 1500 times when estimating failure probabilities of an order of 10-3, 10-5 and 10-6 respectively. The proposed methodology offers drastic improvement over current methodologies and will be able to serve as a basic tool for seismic analysis and design of structures. It must be emphasized though our focus is in structural engineering reliability problem, the proposed methodology can be applied to other fields wherever solving reliability problems is provoked. It is the ultimate goal that this state-of-the-art rational approach be eventually incorporated into seismic PBD codes