MPUQ-b: Bootstrapping Based Modal Parameter Uncertainty Quantification—Fundamental Principles

Abstract

It is well known that modal parameters play a key role towards understanding the dynamics of a structure. Their estimation, by means of experiments, forms the crux of modal analysis. Modal parameters not only help in characterizing the dynamics of the structure but are also used for several other purposes including, finite element model updating, design optimization, sensitivity analysis, etc. It is therefore important to estimate them accurately and several modal parameter estimation techniques have been developed over the years for this purpose. Despite advance methods, estimation of modal parameters is always accompanied with certain uncertainty, which can be attributed to several factors including, noisy measurements, complexities inherent in the structure, modeling errors etc. Remarkably, the usual practice is to provide the estimated modal parameters as they are, without providing any means to validate the accuracy of these estimates. In other words, the estimation procedure often does not include, or overlooks, the measures for quantifying the uncertainty associated with estimated modal parameters.

In this work, a methodology to quantify uncertainty associated with the modal parameters estimated using Experimental Modal Analysis techniques is developed. This methodology is termed as Bootstrapping based Modal Parameter Uncertainty Quantification (MPUQ-b). The proposed methodology utilizes the technique of Bootstrapping, which is a computer intensive method for statistical inference. In this first paper, the fundamentals of this methodology are laid out. The paper focuses on illustrating the characteristics of Bootstrapping and its effectiveness for the intended use of modal parameter uncertainty quantification. By means of studies conducted on a simple single degree of freedom system, it is shown how Bootstrapping can be employed for quantifying the uncertainty associated with estimated modal parameters by providing such measures of accuracy as variance, confidence intervals, bias etc. Incorporation of bootstrapping in modal parameter estimation procedure forms the essence of MPUQ-b and is detailed in a subsequent paper.