Uncertainty is inherent in the control of all engineering structures. This uncertainty can arise from control hardware malfunctions, neglected system dynamics and other inadequacies of the mathematical model, errors in identifying parameters, model reduction, degradation of the structure over time, etc. If the uncertainties are not properly considered in the design of a control strategy, the performance of the controlled structure may be severely degraded, and an otherwise stable nominal structure may even become unstable due to actuator control forces. While the modeling assumptions have become more elaborate and accurate over the years, the reliability analysis of stochastic structural systems still remains a challenging problem. Therefore the reliability analysis of uncertain structural systems subjected to dynamic loads is of great engineering interest and poses a challenging computational problem. Because of the uncertainty inherent in engineering structures, consistent probabilistic stability/performance measures are essential to accurately assessing and comparing the robustness of structural control systems. Several reliability estimation methods, procedures and algorithms with various capabilities, accuracy and efficiency have been suggested in the past. A quantitative comparison of these approaches is considered to be most instrumental and useful for the engineering community. In this article, a simulation approach, called “Subset Simulation”, is used to compute small failure probabilities encountered in reliability analysis of engineering systems. In part I, several illustrative examples are presented to demonstrate the efficiency of the used simulation and compare its results to those of other methods. In part II, several examples of SDOF and MDOF seismically excited structures with active protective systems are applied to compare their results to each other. The results of two part show that “Subset Simulation” method is robust and efficient in estimating the probability of failure of structural systems with complex failure regions, large numbers of random variables, and small probabilities of failure.

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