Robust estimation of excitation in mechanical systems under model uncertainties

The identification of excitation in mechanical systems is one of the most common practical problems in the field of Applied Mechanics. Among all of the possible methods used for solving this problem, model-based methods are often employed along with the least square estimation. However, it is well known in the literature that results obtained in this way might not be precise, if the following are true: (i) the model of the system is not adequate or is characterised by uncertainties or (ii) the experimental data are corrupted or affected by noise. The authors have already analysed the problem of the accuracy of excitation identification in mechanical systems using model-based methods by introducing the application M-estimators in this specific field. In this paper, the performance of other estimation techniques is tested and evaluated against the classical least squares method and M-estimators. High breakdown-point (HBP) and bounded influence (BI) estimators are thus employed for the assessment of the displacement that excites a simple lumped-parameter vibrating test-rig. To the best of the authors’ knowledge, HBP and BI have never been used for the identification of excitation in mechanical systems. The performances of the different classes of estimators are evaluated by considering the uncertainties and approximations of the model. Relevant theoretical developments are presented along with the experimental case study.