Beyond uncertain material properties : possibility-based uncertainty propagation in computational modal analysis

Abstract

Modal analysis relies on computational models that approximate experimental systems through the identification of material and geometry parameters. However, beyond these properties, the model creation process itself involves other critical choices, such as solver schemes, reduction order, element type, mesh density, and boundary conditions, that are typically treated as fixed choices rather than uncertain parameters. This study presents a widened perspective that treats these modeling choices as additional uncertain parameters alongside traditional material and geometry properties. Using possibility theory for forward uncertainty propagation, we quantify uncertainty without requiring probabilistic distributions over modeling choices. That is, instead of treating all choices as equally likely, possibility theory captures the range of feasible modeling options while incorporating quantitative information where available, particularly for material properties. We apply this framework to evaluate eigenfrequency predictions under imprecise input parameters, yielding uncertain output ranges rather than point estimates. A critical innovation is the accurate matching of results from varying parameters to corresponding eigenfrequencies using modal assurance criterion (MAC) clustering. The methodology is demonstrated through a case study of a guitar soundboard model, showing how possibility theory provides a robust framework for uncertainty quantification in structural dynamics without requiring probabilistic assumptions about modeling choices.