• Earthquakes and Structures
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• v.5 no.3
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• pp.359-378
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• 2013

The problem of identification of multi-component and (or) spatially varying earthquake support motions based on measured responses in instrumented structures is considered. The governing equations of motion are cast in the state space form and a time domain solution to the input identification problem is developed based on the Kalman and particle filtering methods. The method allows for noise in measured responses, imperfections in mathematical model for the structure, and possible nonlinear behavior of the structure. The unknown support motions are treated as hypothetical additional system states and a prior model for these motions are taken to be given in terms of white noise processes. For linear systems, the solution is developed within the Kalman filtering framework while, for nonlinear systems, the Monte Carlo simulation based particle filtering tools are employed. In the latter case, the question of controlling sampling variance based on the idea of Rao-Blackwellization is also explored. Illustrative examples include identification of multi-component and spatially varying support motions in linear/nonlinear structures.

• Earthquakes and Structures
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• v.9 no.5
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• pp.1115-1132
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• 2015

The study considers earthquake shake table testing of bending-torsion coupled structures under multi-component stationary random earthquake excitations. An experimental procedure to arrive at the optimal excitation cross-power spectral density (psd) functions which maximize/minimize the steady state variance of a chosen response variable is proposed. These optimal functions are shown to be derivable in terms of a set of system frequency response functions which could be measured experimentally without necessitating an idealized mathematical model to be postulated for the structure under study. The relationship between these optimized cross-psd functions to the most favourable/least favourable angle of incidence of seismic waves on the structure is noted. The optimal functions are also shown to be system dependent, mathematically the sharpest, and correspond to neither fully correlated motions nor independent motions. The proposed experimental procedure is demonstrated through shake table studies on two laboratory scale building frame models.