A frequency-domain sequential Bayesian filter for sparse and broadband force estimation problems

This paper presents a novel method for estimating the external sources acting on a mechanical structure in the frequency domain. Under the assumption of spatially sparse and broadband sources, a sequential Bayesian filter is derived. Its general structure follows that of a sequential Kalman-like filter, which is commonly used for input-state estimation problems in the time domain. This paper also includes an original Bayesian method for computing the noise variances of each measurement channel, which is a key element for the proper tuning of the proposed filtering algorithm. The proposed method is validated by a numerical experiment and an experimental application. The numerical experiment considers a simply supported beam subjected to a broadband point force under different operating conditions, while the experimental application deals with the identification of a point force acting on a simply supported plate. The comparison made with approaches available in the literature shows that the proposed strategy is able to estimate the external forces acting on a mechanical structure with the best trade-off between computational time/resources and accuracy. • A sequential Bayesian filter in the frequency domain is proposed. • A novel procedure for estimating the noise covariance matrix is developed. • The method is validated numerically and experimentally and benchmarked. • The proposed method offers the best trade-off accuracy/computational cost.