Plenary Speaker Armen Der Kiureghian

Professor Armen Der Kiureghian

Professor Armen Der Kiureghian

University of California, Berkeley

Tail-Equivalent Linearization in Nonlinear Stochastic Dynamics

Nonlinearity and stochasticity are essential considerations when assessing the reliability of structural and mechanical systems under extreme loads. Other than simulation methods, equivalent linearization is perhaps the only available practical method to address this class of problems for general systems. On the other hand, the traditional equivalent linearization method, which aims at minimizing the variance in the error of linearization, is a poor predictor of small tail probabilities that are of interest in reliability studies. Tail-equivalent linearization is a recent alternative that provides better accuracy in the tail probabilities. It is based on the idea of defining the equivalent linear system by equating its tail probability to a first-order approximation of the tail probability of the nonlinear system response. The approach is non-parametric in the sense that it does not require consideration of a parameterized equivalent linear model. Instead, the equivalent linear system is determined numerically, in terms of its impulse- or frequency-response function. This lecture will provide a review of this method, its advantages and limitations, and describe its potential for further development. Applications involving earthquake and wave loading will be presented.

Keynote References