| System reliability has been an active area of research for the past two decades, but its application to realistic structures have been limited. The primary reason for this lack of application is that the analytical methods developed so far are handicapped by their idealized assumptions and tedious computations, and often provide wide approximate bounds of the reliability estimate. Unlike the analytical methods, Monte Carlo simulation is a robust and easy-to-use technique for system reliability estimation. The only drawback of a simple Monte Carlo simulation strategy is its inability to converge to the failure probability estimate quickly, for high reliability problems. Therefore, the central idea of this dissertation is to develop an efficient simulation methodology, based on adaptive importance sampling, for system reliability estimation.; The proposed method is developed for solving problems both in the time-independent as well as in the time-dependent domain. The application of this method covers ductile and brittle structural elements. The details of the proposed method are outlined as follows. The proposed method starts out as a branch and bound method, which is used to identify the first failure sequence of a structure. This serves as the initial failure domain for starting the adaptive importance sampling technique. As further simulations are performed, information about the other important failure sequences is incorporated to arrive at a unique estimate of the failure probability. In the proposed method, instead of performing the simulation in the total variable space, a conditional sampling strategy is pursued in which the sampling is performed in the resistance space only. This makes the selection of the sampling density function more efficient. In the resistance space, different failure sequences are represented as different regions in the resistance plane. Therefore, a multimodal sampling density function is constructed to accurately map the sampling domain according to the relative importance of the failure sequences. In the time-dependent domain, the proposed method is able to handle important concepts like resistance degradation, multiple load-overlapping and periodic repair. The proposed method is modular and can easily be added to the structural analysis routine. |
