Uncertainty quantification for modal parameters from stochastic subspace identification on multi-setup measurements

Abstract

a b s t r a c tIn operational modal analysis, the modal parameters (natural frequencies, damping ratios and mode shapes), obtained with stochastic subspace identification from ambient vibration measurements of structures, are subject to statistical uncertainty. It is hence necessary to evaluate the uncertainty bounds of the obtained results, which can be done by a first-order perturbation analysis. To obtain vibration measurements at many coordinates of a structure with only a few sensors, it is common practice to use multiple sensor setups for the measurements. Recently, a multi-setup subspace identification algorithm has been proposed that merges the data from different setups prior to the identification step to obtain one set of global modal parameters, taking the possibly different ambient excitation characteristics between the measurements into account. In this paper, an algorithm is proposed that efficiently estimates the covariances on modal parameters obtained from this multi-setup subspace identification. The new algorithm is validated on multi-setup ambient vibration data of the Z24 Bridge, benchmark of the COST F3 European network.

Uncertainty quantification in operational modal analysis with stochastic subspace identification: Validation and applications

“…This sensitivity analysis, the related covariance expressions, and a numerical verification have been presented in [1]. An implementation of the covariance expressions that is optimized in terms of computational efficiency was presented in [19], and an extension towards the joint analysis of multi-setup measurements was presented in [20].…”

Stochastic Subspace Method for Experimental Modal Analysis

“…The natural frequency from finite element analysis [11][12][13] is as follows ( The mode shape from finite element analysis is as follows:…”

“…3 Stochastic state subspace parameter identification theory [2][3][4] the procedure is divided into several steps. In order to unify each measuring step, the reference measuring points are important and must be selected previously.…”

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

“…for (theoretical) first-order perturbations of the frequencies f i , damping ratios ξ i and mode shapes ϕ i , where J denotes their sensitivity with respect to the stacked Hankel matrix vec H, as detailed in [18,19,20]. The uncertainty of the stacked Hankel matrix is quantified by its covariance Σ H , which can be easily evaluated by splitting the available sensor data into blocks on which instances of the Hankel matrix are obtained.…”