OPTIMAL SENSOR PLACEMENT FOR MODAL PARAMETER IDENTIFICATION USING SIGNAL SUBSPACE CORRELATION TECHNIQUES

Abstract

Placing vibration sensors at appropriate locations plays an important role in experimental modal analysis. It is known that maximising the determinant of Fisher information matrix (FIM) can result in an optimal configuration of sensors from a set of candidate locations. Some methods have already been proposed in the literature, such as maximising the determinant of the diagonal elements of mode shape correlation matrix, ranking the sensor contributions by Hankel singular values (HSVs), and using perturbation theory to achieve minimum variance of estimation, etc. The objectives of this work were to systematically analyse existing methods and to propose methods that either improve their performance or accelerate the searching process for modal parameter identification. The approach used in this article is based on the analytical formulation of singular value decomposition (SVD) for a candidate-blocked Hankel matrix using signal subspace correlation (SSC) techniques developed earlier by the author. The SSC accounts for factors that contribute to the estimated results, such as mode shapes, damping ratios, sampling rate and matrix size (or number of data used). With the aid of SSC, it will be shown that using information of mode shapes and that of singular values are equivalent under certain conditions. The results of this work are not only consistent with those of existing methods, but also demonstrate a more general viewpoint to the optimisation problem. Consequently, the insight of the sensor placement problem is clearly interpreted. Finally, two modified methods that inherit the merits of existing methods are proposed, and their effectiveness is demonstrated by numerical examples.