Finally, we apply the proposed uncertainty quantification method to a scaled three-story frame structure to demonstrate its practicability. The simulation example also indicates that we can expect to identify structural parameters with higher reliability if the input force to the structure is measured, and the identified modal scaling and corresponding flexibility matrix undergo more uncertainty than those of the modal parameters. The accuracies of the derived expressions are verified by a numerical example through the comparison of variance values estimated from Monte Carlo simulations. Finally, the predicted displacements and their uncertainty intervals are used to implement the reliability analysis in terms of the structural displacement serviceability limit state (SLS). Then, the mode scaling factors and integrated modal flexibility are subsequently derived and quantified. First, a novel procedure for variance estimations of the complete system matrix of the state-space model is derived based on first-order perturbation theory. In contrast to the traditional uncertainty quantification of the modal parameters identified from the output-only measurement data, this study develops an uncertainty propagation and quantification method for structural flexibility identified from input–output measurement data and then uses the derived flexibility matrix for structural reliability analysis.
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