Robust estimation of excitations in mechanical systems using M-estimators –Experimental applications

This second part of the study presents some experimentalapplications to mechanicalsystems in which the results of excitationestimation, obtained using traditional least squares and M-estimate, are compared. The first case presented is a single input–multiple outputs system: a simple test-rig for the study of the vibrations of a two-degrees of freedom system is employed to identify the constraint displacement that causes the measured mass vibrations in presence of heavy noise. The second case is a multiple inputs–multiple outputs system: a rotor test-rig is used to identify the positions, the amplitudes and the phases of two unbalances using the vibrations measured in the bearings. In this case, also an additional theoretical part is introduced about the basics of model-based identification in the frequency domain applied to rotor dynamics. The last case is again a single input–multiple outputs system, but in an industrial application: experimental vibrations of a 320 MW steam turbo-generator are used to identify position and amount of a known balancing mass in an on-field real case. Moreover, whilst in the numerical examples presented in the first part the knowledge of the system was perfect, in these cases some uncertainties are present also in the system model. Finally, the paper introduces the use of the M-estimate technique to evaluate the adequacy the model of the system, by means of the analysis of the weights attributed to the measures as a function of the frequency of the excitation.