Chapter5 Uncertainty propagation in Experimental Modal Analysis Bart Peeters, Mahmoud El-Kafafy, Patrick Guillaume, and Herman Van der Auweraer Abstract As all experimental procedures, Experimental Modal Analysis (EMA) is subject to a wide range of potential testing and processing errors. The modal identification methods are sensitive to these errors, yielding modal results which are uncertain up to certain error bounds. The question hence is what these error bounds on test data and modal parameters are. In this paper, the studied source of uncertainty is related to the variance (noise) on the Frequency Response Function (FRF) measurements. Under the H1 assumptions and in single-input cases, the FRF variances can be computed from the coherences and the FRFs. In multiple-input cases, some more measurement functions are required. Advanced system identification methods like the Maximum Likelihood Estimator (MLE) and PolyMAX Plus have the possibility to take the uncertainty on the measurement data into account and to propagate the data uncertainty to (modal) parameter uncertainty. This paper will review FRF variance estimation techniques, including some pragmatic approaches. The basic concepts of Maximum Likelihood Estimation and the calculation of confidence bounds will be discussed. Some typical structural testing and modal analysis cases will be used as illustration of the discussed concepts. Keywords PolyMAX Plus • Uncertainty propagation • Maximum Likelihood Estimation • Experimental Modal Analysis 5.1 Introduction The usefulness of structural dynamics test and analysis results for solving noise and vibration problems or for performing a design assessment or a design optimisation, depends largely on the confidence that one can have in these results. In other words, the results must be characteristic for the actual problem (and not be the result of testing artefacts) and the models must be representative for the actual behaviour of the investigated structure(s). Essentially, two types of problems are distinguished: (1) the test and modelling data are subject to experimentation and analysis errors and (2) the tested (or modelled) structure is not representative for the actual structure. A third (and often neglected) potential problem with the significance of the analysis results can originate from a violation of the assumptions used to model the structure. One of the most prominent examples is the effect of nonlinear structural behaviour on a linear (e.g. modal) model identification process. The first problem is this of experimentation and analysis uncertainty. The “true” test result can in principle never be achieved. The level of the uncertainty associated with the test result is however not easy to quantify. A multitude of totally different causes may be at the origin of major bias and/or variance errors in the analysis. Adequate testing and analysis procedures may reduce (at least some of) these errors significantly, but a proper overall uncertainty quantification is hard to issue. Also in building numerical simulation models (e.g. based on the Finite Element approach), uncertainty is introduced by discretization effects, through imperfectly known material, geometry or loading parameters, or through uncertainty in the applicable model formulations. The second problem is this of product variability, introducing changes in the structural dynamics characteristics because of differences in material, geometric, manufacturing or even operational use (loading, temperature: : : ) parameters when B. Peeters ( ) • H. Van der Auweraer LMS International, Interleuvenlaan 68, 3001 Leuven, Belgium e-mail: bart.peeters@lmsintl.com M. El-Kafafy • P. Guillaume Vrije Universiteit Brussel (VUB), Pleinlaan 2, 1050 Brussel, Belgium H.S. Atamturktur et al. (eds.), Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-04552-8__5, © The Society for Experimental Mechanics, Inc. 2014 41
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