Operational-modal-analysis-based processing of no-next engineering applications datasets: A generalized power spectral density modal model formulation

Operational Modal Analysis, OMA, even referred to as Output-only Modal Analysis, as opposed to the Input-Output technique, is a powerful technique used to identify the dynamic properties of a vibration system in steady working conditions. Starting from the only measured output signals, OMA allows achieving the estimation of resonance frequencies, damping ratios, and modes, i.e. the modal parameters. The main drawback of OMA approach consists in the NExT assumptions of uncorrelated white noises excitations. These hypotheses, in fact, are violated in all those cases in which the exerted environmental loads cannot be described as white noises, as in the cases of systems having rotating parts (machine tools, engines or wind turbines) or characterized by speed and/or time correlated inputs (road and rail vehicles). In this paper, we derive an OMA formulation not based on the NExT assumptions but incorporating the relationship between outputs, inputs, and modal parameters in a suitable way. Specifically, the proposed OMA technique requires some knowledge about the inputs acting on the system and, thus, it is applicable to systems for which something about the inputs is somehow known. We show the existence of a modal model of the output Power Spectral Densities, PSDs, which contain the dependence not only by the modal parameters, but also by the input PSDs. This model is referred to as the generalized PSD modal model. Examples of the usage of this approach are illustrated in the case of the identification of a lumped parameter system in the presence of both stochastic and harmonic excitations and in that of the rigid body modes of a road/railway vehicle from numerical data.