On Optimal Sensor Placement for Structural Health Monitoring by Subspace Approximation

A novel sensor placement method is proposed for structural health monitoring. The aim of the method is to select sensor locations from a set of possible candidate positions for achieving the best identification of modal frequencies and mode shapes. The proposed method depends on both the characteristics and the actual loading situations of a structure. It selects the sensor positions with the best subspace approximation of the vibration responses from the linear space spanned by the mode shapes. We search the best subspace approximation with a relative small subset through our recently proposed representative least squares method to approximate the original least squares estimator with the whole data set. The selected data subset is required to be representative and sufficiently approaching to portrait the scenario defined by the original full data set. The basic ideas of the representative least squares method are illustrated by a simple linear regression example. The algorithm for finding the representative subset for subspace approximation is described, and is applied to the I-40 Bridge.