Minimum variance unbiased Bayesian smoothing for input and state estimation of systems without direct Feedthrough: Mitigating Ill-Posedness of online load identification

In this paper, the problem of moving load identification using pure displacement measurements is addressed. It is known that when no assumptions are made on the statistics of the unknown loads and a minimum variance unbiased (MVU) estimation approach is adopted, the existing methods in the literature suffer from a very elevated load estimation uncertainty. This elevated uncertainty is due to ill-posedness of the problem. In this paper a new method is proposed that addresses this issue via an MVU smoothing approach. To alleviate this problem, a MVU smoothing algorithm is proposed in this study, via modification of a MVU smoothing Bayesian estimator proposed by some of the co-authors of this paper hence referred to as MSBE, which leads to substantial decrease in the moving load estimation uncertainties using pure displacement measurements. The efficacy of the MSBE is studied through a simulated experiment corresponding to a numerical model of an operating steel railway bridge with riveted connections and a multi-axle load. The selection of the hyperparameters of the smoothing and filtering techniques are discussed, and the optimal values are presented. The parametric studies show that the proposed method can yield highly accurate results, and substantially outperforms a celebrated MVU filter proposed by Gillijns and De Moor.