Pseudo Analytical Method for Nonlinear Structural Reliability

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In random vibration, probability of an event that system performance function becomes negative during the time duration is a means to discuss the system safety. This probability is well known as first excursion probability. Presently, how to develop the evaluation method for nonlinear systems has been a major concern among many researchers.The most powerful tool available for the analysis of the response of nonlinear systems to random loading is the Markovian vector approach. In this case the joint probability density of the state vector components is governed by Fokker-Plank equation. Unfortunately, only very few closed-form solutions are known. Even for the SDOF case only some stationary solutions are available. This means that for more general cases approximated methods such as equivalent linearization have to be utilized.In this context, this research also proposes a method to evaluate the probability for nonlinear SDOF systems under a class of stochastic excitations. The method is a hybrid analytical procedure with the help of numerically simulated response data, namely Pseudo Analytical. This method is a class of linearization approaches that linearize approximately a nonlinear state vector equation to a discrete Gaussian and Markovian state vector equation, and the optimal state vector and covariances at times k and k+1 are estimated by the Kalman Filter algorithm with a set of numerically obtained response data. In this way, the probability of performance may be evaluated. Finally, a numerical example of a nonlinear structural system is demonstrated in order to examine the efficiency of the method.