Adaptive mode selection integrating Kalman filter for dynamic response reconstruction

Abstract

Direct application of the Kalman filter algorithm to state estimation of civil structures presents a computational challenge due to their high dimensions and complexity. Rewriting dynamic equations using modal coordinates can be an alternative solution to this problem because high modes with minimal contributions to structural responses can be truncated. Although the mode selection is important in accurately estimating the state of civil structures, studies on determining the remaining mode number are limited. Hence, the mode selection method in the Kalman filter for the optimal reconstruction of structural responses is investigated in this study. A modal signal-to-noise ratio (MSNR) is defined as the ratio of the estimated modal response variance to the corresponding estimation error variance. Only modes with MSNR values higher than an analytically derived threshold are selected. A beam structure is numerically investigated to examine effects of excitation amplitude and frequency, measurement noise, and number of sensors on the adaptive mode selection for optimal response reconstruction. Experimental studies using a simply supported overhanging beam also confirm the efficacy of the proposed approach in response reconstruction using multiple types of sensors (including strain gauges, displacement sensors and accelerometers). Both the numerical and experimental results reveal that using all vibration modes or a complete numerical model with all degrees of freedom will reduce the accuracy of response reconstruction.