| Recent natural disasters, such as the earthquakes at Northridge, California and Kobe, Japan and hurricanes Hugo and Andrew, have inflicted enormous economic losses on the public and the insurance industry. These losses and resulting impacts have led to renewed interest in development and implementation of performance-based design (PBD). The performance levels in typical PBD recommendations are mapped to measurable structural responses and limit states. To facilitate this development, an efficient procedure to assess system reliabilities of realistic structures accurately is needed. This dissertation is dedicated to developing such a procedure.; Analysis of the reliability of complex structural systems requires an efficient simulation procedure coupled with finite element analysis. Directional simulation (DS) is among the most efficient methods for system reliability analysis in the sense that every direction can yield information about system failure. However, the randomly generated directions may not represent the underlying probability distributions very well when the number of directions is limited. Various point sets, which are collectively named deterministic point sets (DPS) herein and have been developed in different domains of science and engineering, have high fidelity in representing the distribution and can reduce simulation error. DPS from the uniform distribution are emphasized herein, since the uniform distribution is commonly used in DS. DPS include spherical t-designs, Fekete points, GLP points, spiral points, and advanced hyperspace division method (AHDM) points. Extensive tests on the efficiency and accuracy of these point sets in system reliability analysis are conducted. Fekete point sets are shown to have some particularly attractive features in terms of accuracy.; Two types of neural networks, namely the feed-forward back-propagation network and the radial basis network, are utilized to further improve the efficiency in a two-phase point refinement scheme based on the Fekete method. The neural network works as a parallel concept to importance sampling in identifying the regions in hyperspace that contribute significantly to the failure probability. The Fekete point method and neural network technique form the essential statistical module denoted “FeketeNN” used to perform system reliability analyses in this dissertation.; Load space formulation has been shown to be particularly useful in limiting the number of calls to the finite element programs in system reliability analysis. These techniques are demonstrated using several realistic plane steel structures. With the help of the load space formulation, the FeketeNN method can achieve accurate estimates of the system failure probabilities efficiently. |
