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Structural health monitoring of complex structures is often limited by restricted accessibility to locations of interest within the structure and availability of operational loads. In this work, a novel output-only virtual sensing scheme is proposed. This scheme involves the implementation of the modal expansion in an augmented Kalman filter. Performance of the proposed scheme is compared with two existing methods. Method 1 relies on a finite element model updating, batch data processing, and modal expansion (MUME) procedure. Method 2 employs a recursive sequential estimation algorithm, which feeds a substructure model of the instrumented system into an Augmented Kalman Filter (AKF). The new scheme referred to as Method 3 (ME-AKF), implements strain estimates generated via Modal Expansion into an AKF as virtual measurements. To demonstrate the applicability of the aforementioned methods, a rollercoaster connection was instrumented with accelerometers, strain rosettes, and an optical sensor. A comparison of estimated dynamic strain response at unmeasured locations using three alternative schemes is presented. Although acceleration measurements are used indirectly for model updating, the response-only methods presented in this research use only measurements from strain rosettes for strain history predictions and require no prior knowledge of input forces. Predicted strains using all methods are shownmore »to sufficiently predict the measured strain time histories from a control location and lie within a 95% confidence interval calculated based on modal expansion equations. In addition, the proposed ME-AKF method shows improvement in strain predictions at unmeasured locations without the necessity of batch data processing. The proposed scheme shows high potential for real-time dynamic estimation of the strain and stress state of complex structures at unmeasured locations.« less

Mechanics-based dynamic models are commonly used in the design and performance assessment of structural systems, and their accuracy can be improved by integrating models with measured data. This paper provides an overview of hierarchical Bayesian model updating which has been recently developed for probabilistic integration of models with measured data, while accounting for different sources of uncertainties and modeling errors. The proposed hierarchical Bayesian framework allows one to explicitly account for pertinent sources of variability such as ambient temperatures and/or excitation amplitudes, as well as modeling errors, and therefore yields more realistic predictions. The paper reports observations from applications of hierarchical approach to three full-scale civil structural systems, namely (1) a footbridge, (2) a 10-story reinforced concrete (RC) building, and (3) a damaged 2-story RC building. The first application highlights the capability of accounting for temperature effects within the hierarchical framework, while the second application underlines the effects of considering bias for prediction error. Finally, the third application considers the effects of excitation amplitude on structural response. The findings underline the importance and capabilities of the hierarchical Bayesian framework for structural identification. Discussions of its advantages and performance over classical deterministic and Bayesian model updating methods are provided.