Subset Simulation Method in Active Structural Control

When designing new civil, mechanical or aerospace systems that will experience dynamic excitation in their operating environment, it is desirable to quantify the predicted performance of a proposed design in terms of the reliability that it will achieve the specified design objectives. In view of the uncertainties about the modeling of systems and about the future dynamic excitation the system will experience, the design team can specify a set of possible dynamic inputs and a set of possible models of the system and then choose probability distributions over these sets to model the uncertainties. One can then evaluate the ‘failure probability’ of the design that measures how likely the system will achieve the desired performance over its operational lifetime, based on available information and the probability models chosen to represent the missing information. 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. An approach is presented herein for calculating such probabilistic measures for a controlled structure. Subset Simulation method is shown to be appropriate for the required calculations. The original version of Subset Simulation, SubSim/MCMC, employs a Markov chain Monte Carlo (MCMC) method to simulate samples conditional on intermediate failure events it is a general method that is applicable to all the benchmark problems. The concepts are illustrated through several examples of seismically excited structures with active protective systems. The results show that the original version of Subset Simulation based on the Metropolis–Hasting algorithm 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.and applicable to all problems.