Measurement uncertainty propagation in parameter identification of mechanical systems in frequency domain

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. The estimated errors on those measurements are usually categorized as random or precision uncertainties, as they are based on processing statistically repeated observations, while estimates for bias error contributions are referred as systematic uncertainties. A formulation to estimate the uncertainty on the estimated mass, stiffness and damping matrices for linear mechanical systems is presented in this article. General expressions to determine the parameter uncertainties and the corresponding confidence regions for the estimates are derived. Pursuing applicability, the proposed methodology is formulated as an extension of the accepted (standardized) practice to determine uncertainty propagation for one-dimensional 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.