A dynamic force reconstruction method based on modified Kalman filter using acceleration responses under multi-source uncertain samples

Abstract

A novel method for dynamic force reconstruction is developed in this paper to identify the time history of uncertain force for the linear time-invariant system, which combines the modified Kalman filter and non-probabilistic uncertainty analysis. For the force reconstruction issue, some acceleration responses are regarded as the observation information. The optimal estimation of the system state vector and unknown input force vector are deduced recursively on the basis of minimum variance unbiased estimate, along with the covariance matrices updating of force reconstruction error and state estimation error under the framework of modified Kalman filter. Considering multi-source uncertainties in inherent characteristics and external environment, the multidimensional interval model, which is transformed by the principal component analysis (PCA) method, is involved to envelope experiential samples of uncertain parameters. To enhance the accuracy and efficiency of uncertainty propagation, the Chebyshev orthogonal polynomial is adopted to approximate the unknown force and to obtain the force interval boundaries. Eventually, the validity and feasibility of the proposed methodology are clarified by three numerical examples: a spring-oscillator, a plane truss and an equivalent rudder structure. The results indicate that the proposed method can be utilized to reconstruct the uncertain force interval with the interference of system uncertainties and measurement noise.