Stochastic Fragility Analysis of MDOF Systems using Gaussian Mixture-Based Equivalent Linearization Method (GM-ELM)

Abstract

This research improves the recently developed Gaussian mixture based equivalent linearization method (GM-ELM) to promote its applications to the seismic fragility analysis. GM-ELM is a stochastic linearization method, which defines the equivalent linear system by a set of linear oscillators. This linear system is identified from Gaussian mixture distribution-based decomposition of the instantaneous response probability distribution function (PDF). The method has merits in terms of the applicability to general multi-degree of freedom (MDOF) systems. However, the method may suffer from limitations of stationary assumption and excitation-intensity-dependency of ELS. As a further development to facilitate earthquake engineering applications, we extended GM-ELM to nonstationary responses by proposing to use the temporal average of response PDF. Furthermore, the concept of universal ELS which is invariant to the scaling of excitation is established by utilizing intensity-augmented PDF. Numerical experiments demonstrate viability of the proposed approach on general MDOF systems and nonstationary excitations.