Application of multivariate uncertainty analysis to frequency response function estimates

A systematic uncertainty analysis for liner impedance eduction technology

“…Under these assumptions obtaining the normalized impedance is straightforward using the axial wavenumber from the transmission coefficient (Eqs. (25) and (26)), the Ingard-Myers boundary condition Eq. (6) plus the wave dispersion relationship Eq.…”

“…In order to get the 95 percent confidence interval results for complex-valued variables, the normal confidence interval should be extended to a confidence area for its possible correlated real and imaginary parts. For a normally distributed complex variable with a real part x R and an imaginary part x I , the confidence region is given by [24,25] x…”

“…Unfortunately these efforts did not provide a systematic method for the propagation from component uncertainties to the overall uncertainty in the identified impedance results. In contrast to the Monte Carlo method, the purpose of this paper is to provide a multivariate uncertainty analysis method [24,25], which makes it possible to track the multiple, possible correlated components. In order to avoid numerical uncertainty in this study, a straightforward single mode analysis is used.…”

A covariance based framework for the propagation of uncertainty through inverse problems with an application to force identification

“…Their suggestion of using a bivariate description of complex uncertainty was further elaborated in [34]. In the field of structural dynamics, Schultz et al [35] adopted the same complex bivariate description for FRFs acquired using a random noise excitation, and further investigated the propagation of uncertainty from real and imaginary components onto magnitude and phase descriptors. Similarly, Kim and Schmitz [36] used a complex bivariate description in the analysis of measured tool-holder-spindle-machine assembly FRFs.…”

Frequency-Domain Analysis for Nonlinear Systems With Time-Domain Model Parameter Uncertainty

“…This method can hence offer a more flexible and accurate description because it can represent the uncertainty as an ellipse rather than a circle (compared to the complex statistics method). Multivariate uncertainty propagation has been applied to quantifying the measurement uncertainty in experimentally gathered data [15], [16] and to finite-element models [17].…”