Fast online implementation of covariance-driven stochastic subspace identification

Abstract

Fast online system identification is critical for the timeliness of downstream applications such anomaly detection, condition assessment and decision making. Although some very efficient algorithms, such as the fast Fourier transform (FFT), exist, they are unable to identify damping ratios or mode shapes. The stochastic subspace identification (SSI) method is currently a widely used system identification algorithm. However, its time-consuming operation prevents downstream applications from running online in (near) real time. This paper aims to develop a fast online implementation of covariance-driven SSI (COV-SSI). Time complexity is utilized to analyze the computational cost of COV-SSI. Two steps of COV-SSI are determined to be time-consuming and are accelerated. They are (i) the computation of the covariance matrix (accelerated through incremental aggregation in the dataflow model) and (ii) the singular value decomposition (SVD) of the Toeplitz matrix (accelerated through a fast truncated SVD approach). These strategies do not require any additional parameters; the error between the proposed method and the original COV-SSI method is negligible, but the method is significantly accelerated. Finally, some numerical examples are used to validate the speed and accuracy of the fast online strategies.