Optimal sensor placement for joint reconstruction of multiscale responses and unknown inputs using modal Kalman filter

SummaryMany optimal sensor placement (OSP) techniques have been developed basing on known external loads. However, it is often difficult to obtain excitation measurements. Therefore, the development of OSP under unknown inputs (OSP‐UI) is desirable. In this paper, based on modal Kalman filter (MKF), an OSP‐UI approach (MKF‐OSP‐UI) is proposed for optimally determining the number and locations of multitype sensors with the aim of minimizing the reconstructed responses errors. An MKF‐based approach previously developed by the authors is first employed for estimating multiscale structural responses and unknown loads. Then, an error covariance matrix is defined as a measure of the differences between the reconstructed responses and the corresponding actual ones. By using the covariance matrix of measurement noise for normalization, the ill‐conditioning problem caused by data fusion of multiscale responses is avoided. The sensors that have few contributions to the reconstructed responses are removed from the candidate set during iteration procedure. The sensor placement is finally determined when the estimation errors are below the preset level. Numerical results show that the sensor configuration determined by the proposed approach has a better performance on the joint estimation of multiscale responses and unknown inputs, as compared with that determined by experience.