Optimal sensor placement for modal parameter identification using signal subspace correlation techniques

Placing vibration sensors at appropriate locations plays an important role in experimental modal analysis, in order to ultimately describe the system under considerations. To this end, maximizing the determinant of Fisher information Matrix has been shown to provide optimal solutions. Some methods have been proposed in the literature, such as maximizing 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 estimate variance, etc. The objectives of this work were to systematically analyze existing methods and to propose methods that improve their performance or accelerate the searching process. The approach used in this paper is based on the analytical formulation of 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 in this article that using information of mode shapes and singular values are equivalent under certain conditions. The results of this work not only consist with those of existing methods, but also demonstrate a more general viewpoint to the optimization problem. Consequently, the insight of the sensor placement problem is clearly unfolded. A modified method that treats targeted modes equally is then proposed. Finally, a hybrid method that possesses advantages of existing methods is also proposed and believed to be efficient and effective.