Tutorial and Application of Bayesian Statistics on Assessing Model Form Uncertainty in Vibration Isolation

Document Type

Book Chapter

Publication Date

2025

Department

Department of Mechanical and Aerospace Engineering

Abstract

This contribution gives a general background of Bayesian statistics with a real application example. It includes the background and meaning of the essential elements: the prior probability of a hypothetical event, the likelihood of a symptomatic event under the condition that the hypothetical event already happened, the total probability of the symptomatic event, and the posterior probability of the hypothetical event under the condition that the symptomatic event already happened. The Bayesian approach is the framework to estimate the uncertainty of two different analytical model forms used to predict the vibration isolation behavior for an oscillating mass. The first model form describes the oscillating mass as part of a simple one-mass oscillator; the second model form uses the oscillating mass as part of a simple two-mass oscillator. Both model forms contain assumptions about inertia, damping, and stiffness properties representing hypothetical events. The experimental vibrational data measured from a realized test setup featuring the oscillating mass serves as the symptomatic outcome or event. This approach allows the direct and consistent application of the Bayesian framework on a vibration isolation problem in early stage design. This work is part of IMAC’s ongoing round-robin challenge about model form uncertainty quantification on vibration isolation.

Publication Title

Model Validation and Uncertainty Quantification

ISBN

9783031688935

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