AOSID: An analytical solution to the output-only system identification problem to estimate physical parameters and unknown input simultaneously

Abstract

This paper studies an analytical solution for the identification problem of linear systems, where inputs are unknown and only output data are accessible. A linear output-only model (LOM) is developed and employed along with physical constraints in state space to simultaneously identify two subspace models, one of which represents the physical system and the other describes the behavior of the unknown input by reconstructing its history. Inputs are assumed to be an arbitrary combination of harmonic signals with constant or time varying exponential amplitudes with non-overlapping frequency ranges with natural frequencies of the physical system. The identification is first performed by a zero-input eigensystem realization algorithm in time domain that estimates the LOM in a generic form; we call it unfixed form, which contains both physical system model and input model in a coupled configuration. By transforming the LOM into a canonical form and utilizing the physical constraints, an analytical approach is developed to decouple the physical model from the input dynamics. The proposed method of analytical output-only system identification (AOSID) is evaluated through simulation of a set of scenarios to demonstrate its capabilities. To this end, we study the effects of type of sensor models, level of measurement noise, and complexity level of the problem on the estimation error. The accuracy of the identified LOM demonstrates that the AOSID method is capable of simultaneous identification of physical model and unknown inputs in the presence of measurement noise with a considerable accuracy at a modest computational expense. Furthermore, AOSID method demonstrates a considerable robustness against nonlinear inputs and white noise disturbances which challenge the assumptions initially made in the theoretical development of the model.