Reliable Identification of Modal Parameters in Vibratory Mechanical Structures under Uncertainty

• Applicant: Professor Dr.-Ing. Michael Hanss
• Subject Area: Mechanics ; Applied Mechanics, Statics and Dynamics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 514188140

Modern standards require vibratory mechanical structures in engineering to remain durable, whereas cost and efficiency trends necessitate those to become lighter. These demands frequently result in a strong sensitivity of the structures to undesirable vibrations and call for a thorough analysis of their vibrational characteristics, not least in order to robustify and optimize them. Modal analysis is an engineering discipline aimed at studying, predicting and identifying these characteristics, which generally include eigenfrequencies, mode shapes and modal damping ratios. A common shortcoming of modal analysis, however, is the disregard of uncertainties that may occur in its process. But so-called polymorphic uncertainty, i.e. incomplete knowledge of aleatory and epistemic nature, is present in most engineering systems. And existing techniques for the quantification of uncertainty commonly rely on precise probabilistic uncertainty descriptions, which, contrary to the Bayesian view, are arguably unjustified in cases of polymorphic uncertainty. Contemporary research suggests that approaches using imprecise probabilities can lead to more reliable results, and possibility theory is an efficient framework for their description. Therefore, the goal of the proposed project is to smartly combine the theory of possibilistic uncertainty quantification with the well-established methodology of (experimental) modal analysis in order to develop advanced procedures for performing the essential predictive and inferential operations inherent to modal testing in an imprecise-probabilistic manner. In doing so, a reliable quantitative inclusion of the polymorphic uncertainty occurring in modal testing is guaranteed and a faithful prediction of the vibrational characteristics together with a quantification of the associated imprecision in form of confidence distributions for the modal parameters will be provided. In this context, a statistical procedure for the identification of these confidence distributions from data of modal testing shall be derived. Besides the critical task of uncertainty modeling, two classes of problems must be tackled: forward and inverse problems. In modal analysis, the forward problem corresponds to quantifying the uncertain vibrational characteristics of a finite-element-modeled system, induced by uncertainty about the actual model parameters or boundary conditions. Inverse problems are concerned with determining confidence distributions for the identified modal parameters under the process-inherent uncertainty of modal testing. Both types of problems shall be addressed in this project and suitable numerical implementations for their solutions will be developed, providing a new procedure of advanced modal testing with robustly reliable uncertainty quantification. Finally, the procedures shall exemplarily be applied to the experimental modal analysis of a classical guitar to ensure their practical performance and computational feasibility.

• DFG Programme: Research Grants