Using the unified matrix polynomial approach (UMPA) for the development of the stochastic subspace identification (SSI) algorithm

Abstract

The unified matrix polynomial approach (UMPA) was developed in order to understand and derive various experimental modal analysis algorithms (which have been developed in isolation) using a common mathematical formulation. Various commercially available algorithms – such as the polyreference time domain, least squares complex exponential, and eigensystem realization algorithm etc. – can be explained using UMPA methodology, which makes it easier to understand both the advantages and limitations of such algorithms. In view of this fundamental characteristic of the UMPA, this paper aims at using the approach to understand, explain and develop the stochastic subspace identification (SSI) algorithm - a popular time domain operational modal analysis (OMA) algorithm. The roots of SSI algorithm lie in the identification of linear dynamic systems, traditionally a communications and controls engineering area. By means of the UMPA, the SSI algorithm’s similarity to a high order time domain OMA algorithm can be shown. It can also be shown that state transition matrices identified using the SSI algorithm and UMPA formulation are related to each other through a similarity transformation, thus characterizing the same system.