Fast multi-order computation of system matrices in subspace-based system identification

Abstract

Subspace methods have proven to be efficient for the identification of linear time-invariant systems, especially applied to mechanical, civil or aeronautical structures in operation conditions. Therein, system identification results are needed at multiple (over-specified) model orders in order to distinguish the true structural modes from spurious modes using the so-called stabilization diagrams. In this paper, new efficient algorithms are derived for this multi-order system identification with subspace-based identification algorithms and the closely related Eigensystem Realization Algorithm. It is shown that the new algorithms are significantly faster than the conventional algorithms in use. They are demonstrated on the system identification of a large-scale civil structure.

Tangential interpolation-based eigensystem realization algorithm for MIMO systems

“…The field of subspace-based system identification (SI) provides powerful tools for fitting a linear time-invariant (LTI) system to given input-output responses of the measured system. Applications of subspace-based SI arise in many engineering disciplines, such as in aircraft wing flutter assessment [1,2], vibration analysis for bridges [3], structural health analysis for buildings [4], modelling of indoor-air behaviour of energy efficient buildings [5], flow control [6][7][8], seismic imaging [9] and many more. In all applications, the identification of LTI systems was crucial for analysis and control of the plant.…”

Operational modal analysis with uncertainty quantification for SDDLV-based damage localization

“…In the first step, we identify estimates A d and C d of the system matrices and subsequently the modal parameters at different model orders from the measurements using covariance-driven subspace identification [15,16]. In the resulting stabilization diagram, at most r mode pairs are selected in the second step, such that the condition 2r ≥ n is fulfilled.…”

Structural health monitoring with statistical methods during progressive damage test of S101 Bridge

“…Based on the observation that physical modes remain quite constant when estimated at different over-specified model orders, while spurious modes vary, they can be distinguished using so-called stabilization diagrams. The system is identified truncating in (9) at multiple model orders, and frequencies from this multi-order system identification are plotted against the model order [16,17]. From the modes common to many models and using further stabilization criteria, such as threshold on damping values, low variation between modes and mode shapes of successive orders etc., the final estimated model is obtained.…”

“…Our contribution to these methods concerns their applicability: Being elaborate methods but lacking some feasibility in practice, both methods were recently enhanced with a strongly decreased computational burden, feasibility of high model orders and a more numerically robust computation [17,19,23]. The results are fast algorithms that can be applied easily to vibration data from civil, mechanical or aeronautical structures.…”

“…In this paper two subspace-based methods for vibration monitoring are considered that take the statistical uncertainties into account. First, we use the covariance-driven subspace-based system identification [16,17] together with their confidence interval estimation [18,19] for the operational modal analysis. Thanks to this uncertainty quantification, the significance of the modal parameters and their changes during the monitoring period can be evaluated.…”