Efficient multi-order uncertainty computation for stochastic subspace identification

Abstract

Stochastic Subspace Identification methods have been extensively used for the modal analysis of mechanical, civil or aeronautical structures for the last ten years. So-called stabilization diagrams are used, where modal parameters are estimated at successive model orders, leading to a graphical procedure where the physical modes of the system are extracted and separated from spurious modes. Recently an uncertainty computation scheme has been derived allowing the computation of uncertainty bounds for modal parameters at some given model order. In this paper, two problems are addressed. Firstly, a fast computation scheme is proposed reducing the computational burden of the uncertainty computation scheme by an order of magnitude in the model order compared to a direct implementation. Secondly, a new algorithm is proposed to derive efficiently the uncertainty bounds for the estimated modes at all model orders in the stabilization diagram. It is shown that this new algorithm is both computationally and memory efficient, reducing the computational burden by two orders of magnitude in the model order.

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

“…The identification of these matrices is subject to uncertainties due to the unknown excitation (being modeled as white noise), measurement noise and finite data length. Methods for the uncertainty quantification of the estimates from stochastic subspace identification are given in [11,12]. With these methods, the empirical covariance of the measurement data is computed from subsets of the available data and propagated to the modal parameters by an analytical sensitivity analysis, resulting in an automated algorithm.…”

“…We have chosen the values s 1 = 0, s 2 = 1 + 40i, s 3 = 1 + 140i, s 4 = 1 + 250i, s 5 = 1 + 400i and s 6 = 1 + 800i. Then, the real and imaginary parts of the stress vector S(s i ) containing these moments and their joint covariance in (12) is computed for these Laplace variables.…”

“…The estimated modal parameters from the output-only measurements that are used for damage localization are naturally subject to variance errors [10][11][12]. Taking into account these uncertainties proves to be important for structural damage diagnosis.…”

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

“…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.…”

“…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.…”