Optimal location of sensors for reconstruction of seismic responses through spline function interpolation

In this paper, a criterion is proposed for the choice of the optimal location of a limited number of recording sensors for reconstruction of seismic responses of multistorey frames. Reconstruction of unknown responses is performed by modelling through a spline shape function the evolution of the relative acceleration along the height of the building. The coefficients of the spline function are determined by interpolating available responses in terms of absolute accelerations taking into account boundary conditions. The optimal location for a given number of recording sensors is defined as the one corresponding to the minimum value of the global error evaluated on the whole set of reconstructed responses. The criterion has been verified by using simulated responses of numerical models of multistorey frames and responses recorded on real buildings during the Northridge earthquake. A physical characterization of the location of available sensors leading to the minimum global error between calculated and real responses is proposed in terms of effective modal participation factors relevant to the principal modes of the structure. This characterization allows for frames of known modal characteristics the definition of a criterion for the choice of the location of a limited number of sensors for monitoring or vibration control purposes. Copyright © 2003 John Wiley & Sons, Ltd.