An Alternating Least Squares (ALS) based Blind Source Separation Algorithm for Operational Modal Analysis

Abstract

In a former paper (“Second Order Blind Identification (SOBI) and its relation to Stochastic Subspace Identification (SSI) algorithm”, 28th IMAC, 2010), the authors established the link between the popular SSI algorithm used in output-only modal analysis and the Second Order Blind Identification (SOBI) algorithm developed for blind source separation in the field of signal processing. It was concluded that the two algorithms, although seemingly very different, are actually jointly diagonalizing the same covariance matrix over a range of time-lags. This is explicit in SOBI and implicit in SSI. One main difference, however, is that SOBI focuses on estimating the (real) modal matrix as a joint diagonalizer, but without taking advantage of the specific structure of the covariance matrix formed by the Markov coefficients and by incorrectly assuming no-damping or very low damping. On the other hand, SSI specifically exploits the covariance matrix structure so as to estimate complex modes, but puts less emphasis on the “joint diagonalizing” property of the modal matrix. The aim of this communication is to introduce a new algorithm based on Alternating Least Squares (ALS) approach that combines advantages of both SOBI and SSI in order to return improved estimates of modal parameters. It is shown in this work that this algorithm is capable of identifying complex modes, closely spaced modes and heavily damped and can also be expanded to deal with the cases where there are less number of sensors available than the number modes to be estimated. The suggested approach therefore is a step towards expanding the applicability of BSS based approaches to Operational Modal Analysis applications.