Multiobjective non-linear random vibration analysis for performance-based earthquake engineering

A new multiobjective linearization method for nonlinear random vibration analysis is presented. The strategy employs the Tail-Equivalent Linearization Method (TELM) which is a non-parametric linearization algorithm for multi-DOFs nonlinear systems. Due to the definition of conditioned probability, the joint tail probability of a multi-response structural system can be written as the product of a first marginal probability and some lower order conditioned tail probabilities. The algorithm decomposes the joint probability into a conveient form so that the conditioned probabilities are arranged consequently. In this case, each probability but the first is conditioned to previously computed responses. Then, TELM is recursively applied in order to define a set of interconnected linearized systems, each one defined in terms of its impulse response function. The definition of the base excitation by its cross-covariance or its power spectral density leads to the first marginal tail probability and to the power spectral density of the corresponding response. Afterwards, the interconnected linearized system is used to compute the tail probability and the power spectral density of each response in function of the previously analyzed responses' statistics. The computed joint probability can be used in random vibration analysis in order to get various statistics of the nonlinear response, such as the mean level-crossing rate and the joint first-passage probability. This work analyzes a series system, however, the procedure can be easily extended to the general case. Also, numerical applications illustrate the features of the method and comparison with results obtained by Monte Carlo simulations demonstrate its accuracy, in particular for high response thresholds. © 2010 Taylor & Francis Group, London.