Stochastic Estimates of Seismic Response and Damage of Building Structures

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In this study an analytical procedure of stochastic estimates is presented for the structural responses and damage states of hysteretic structural systems under intense earthquakes from noisy and partial observations of seismic structural responses. Based on experimental and theoretical results of structural members and frames, hysteretic constitutive laws and damage measures of hysteretic structural systems have been modeled and expressed by nonlinear differential equations. By making use of these differential representations and stochastic seismic excitation models, the basic equations of estimates, namely, the system and observation equations are formulated in the form of the Ito stochastic differential equations. With recourse of appropriate conditional probability density functions given observations, the time-dependent conditional statistics and conditional probability density functions concerning structural seismic damages as well as the responses are determined.