Propagation of uncertainty in measurements applied to frequency-domain identification of mass, stiffness and damping matrices for mechanical systems

Abstract

In the parameter identification of mechanical systems, the accuracy on the parameter estimates is limited since they are obtained by processing the excitation and response system measurements which are inherently linked to experimental errors. A general formulation to estimate the uncertainty on the estimated mass, stiffness and damping matrices for linear mechanical systems is presented in this article. Pursuing applicability, the proposed methodology is formulated as an extension of the accepted practice to determine uncertainty propagation for multidimensional measurand. The approach can be applied to identification of linear mechanical systems in frequency domain, independently of the algorithm considered for estimating the system parameters. The limitations of the proposed formulation are also discussed and an experimental example is provided to illustrate the suggested methodology by means of two identification methods: ordinary least squares and instrumental variable methods. The comparison of parameters' variability, obtained from the propagation of random uncertainties, with the one generated by direct computation, i.e. from a sample of estimates of parameters, reveals the matching orders of magnitude for most of the uncertainties of the parameter estimates, confirming the consistency of the formulation in order to propagate random and systematic measurement uncertainties in the identification of the system parameters.