Schemes For Reconstructing the Seismic Response of Instrumented Buildings

by Dionisio Bernal, Arash Nasseri

Dionisio Bernal, Arash Nasseri (2009). Schemes For Reconstructing the Seismic Response of Instrumented Buildings SMIP09 Seminar on Utilization of Strong-Motion Data, p. 23 - 38.

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Methodology for reconstructing the seismic response of buildings from measured accelerations is examined. The popular cubic spline (CS) interpolation is shown to be equivalent to fitting the measured response on a basis whose dimension is equal to the number of sensors and whose span is determined by the sensor positions. The basis fitting perspective makes clear that a necessary condition for accuracy is that the number of sensors be no less than the number of modes that contribute substantially to the estimated quantity. It is shown that low pass filtering of the measured response, using a cutoff frequency in the proximity of the frequency of mode (m-1), where m is the number of sensors, is advisable. Reconstruction by blending the measurements with a nominal model is examined using the Kalman Filter, the RTS Smoother and a new approach designated as the Minimum Norm Response Corrector (MIRC). Results obtained using 3 nonlinear building models and an ensemble of 30 bi-directional earthquake motions suggest that, for the conditions that prevail in practice, (i.e., relatively poor nominal models and possible nonlinearity in the measured response) the MIRC estimator is the most accurate. The gains in accuracy offered by MIRC over the CS are modest for inter-story drift but are significant in story shears. Specifically, the mean of predictions normalized to the true result (based on 1560 story shear histories) proved to be 1.48 for the CS and 1.00 for MIRC.