This Bayesian filtering-technique proposed for the reconstruction of the state and input forces can next be employed in the emerging fatigue prognosis frameworks. Contrary to the present methods that produce significant low-frequency drifts while using noisy acceleration response-only measurements, the proposed method offers drift-free perfect predictions. It is observed that the proposed method achieves decent accuracy for estimating the state, input forces, and noise covariance matrices when compared to the actual values. Numerical and experimental examples are used to examine and demonstrate the efficacy of the method. Moreover, the method is outlined in a computational algorithm offering real-time estimations of the state and input forces. This prior distribution aims to eliminate low-frequency drifts from estimations of the state and input. The proposed method avoids the direct transmission of the input into predictions of the state using a zero-mean Gaussian distribution for the input. An appealing feature of the proposed method is the promise it delivers for updating the covariance matrices of the process and measurement noise in a real-time fashion using asymptotic approximations. The problem of joint estimation of the state and input in linear time-invariant dynamical systems is revisited proposing novel sequential Bayesian formulations. As shown in the application section, this methodology is able to increase the accuracy of the estimated quantities against the use of conventional numerical processing methods.

The tools employed involve a multi-rate Kalman Filter scheme, as presented in (Smyth & Wu 2007) and an artificial white noise (WN) observation technique necessary for eradicating the displacement drift issue which stems from the integration process. The overall goal is to successfully fuse the heterogeneous measurements, obtained on-line while sampled at different frequencies. In this study, a method of combining displacement and acceleration data for the purpose of structural health monitoring is demonstrated and the example of a new innovative high-rise structure in China, featuring a fully functional on-line monitoring system is conceived as a test-case. This work outlines a procedure for the effective fusion of different types of sensor data, namely acceleration and displacement records, aiming at the successful simulation and monitoring of the behavior of large structures under dynamic loading.

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