Separation of Physical from Mathematical Poles in Operational Modal Analysis Using Reduced, Reassembled Covariance Matrices

Abstract

Modal analysis is one of the elementary tools for the analysis of structural dynamics. In context of vibration-based damage diagnosis and continuous monitoring of modal quantities, different variants of Operational Modal Analysis (OMA) were developed. In most cases, the results of the analysis (modal data) are improved by post-processing methods, e.g., by clustering of stable poles in stability diagrams. The aim of this paper is to facilitate the automatic interpretability of the computational results by preprocessing techniques. The method presented in this paper is used to distinguish between the physical poles and the unwanted mathematical poles to determine the natural frequencies more accurately. This is necessary because for the monitoring of complex real structures, high model orders are required, leading to the occurrence of mathematical poles. To enable a reliable separation, the spectral signal components are analyzed regarding their information content and their energy level in a specific frequency band. For this purpose, the widespread assumption is used that the largest singular values of the system response are related to the highest signal energy and that the lower singular values are caused by noise. With the use of different narrow frequency bands (e.g., by using bandpass filters), the estimation of an accurate threshold between noise and eigenfrequencies can be well established for each band. This technique is applied on the Covariance-Driven Stochastic Subspace Identification algorithm (SSI-COV) for OMA. In context of SSI-COV the Singular Value Decomposition (SVD) and the estimated threshold is used to build reduced and reassembled Hankel matrices from partial sum matrices for each frequency band separately. The advantage of the reduced matrices is that only physical poles have plausible modal damping values, and these can be well separate from mathematical poles. The effectiveness of the method is first demonstrated on simulated data and then successfully tested on a laboratory structure. The results, the advantages, and limitations of the method as well as the need for further improvements are discussed.