Optimal multi-type sensor placement for response and excitation reconstruction

The need to perform dynamic response reconstruction always arises as the measurement of structural response is often limited to a few locations, especially for a large civil structure. Besides, it is usually very difficult, if not impossible, to measure external excitations under the operation condition of a structure. This study presents an algorithm for optimal placement of multi-type sensors, including strain gauges, displacement transducers and accelerometers, for the best reconstruction of responses of key structural components where there are no sensors installed and the best estimation of external excitations acting on the structure at the same time. The algorithm is developed in the framework of Kalman filter with unknown excitation, in which minimum-variance unbiased estimates of the generalized state of the structure and the external excitations are obtained by virtue of limited sensor measurements. The structural responses of key locations without sensors can then be reconstructed with the estimated generalized state and excitation. The asymptotic stability feature of the filter is utilized for optimal sensor placement. The number and spatial location of the multi-type sensors are determined by adding the optimal sensor which gains the maximal reduction of the estimation error of reconstructed responses. For the given mode number in response reconstruction and the given locations of external excitations, the optimal multi-sensor placement achieved by the proposed method is independent of the type and time evolution of external excitation. A simply-supported overhanging steel beam under multiple types of excitation is numerically studied to demonstrate the feasibility and superiority of the proposed method, and the experimental work is then carried out to testify the effectiveness of the proposed method.