Quantifying Uncertainty in Material Damage from Vibrational Data

TL;DR

This paper develops and compares multiple methods to quantify uncertainty in damage detection of vibrating beams, using both simulated and experimental data, to improve damage assessment accuracy under uncertain conditions.

Contribution

It introduces a comprehensive framework combining various methods for uncertainty quantification in damage detection from vibrational data, supported by mathematical analysis and sequential application.

Findings

Methods effectively estimate damage parameters under uncertainty.

Numerical results validate the approaches with simulated data.

Experimental data demonstrate practical applicability.

Abstract

The response of a vibrating beam to a force depends on many physical parameters including those determined by material properties. Damage caused by fatigue or cracks result in local reductions in stiffness parameters and may drastically alter the response of the beam. Data obtained from the vibrating beam are often subject to uncertainties and/or errors typically modeled using probability densities. The goal of this paper is to estimate and quantify the uncertainty in damage modeled as a local reduction in stiffness using uncertain data. We present various frameworks and methods for solving this parameter determination problem. We also describe a mathematical analysis to determine and compute useful output data for each method. We apply the various methods in a specified sequence that allows us to interface the various inputs and outputs of these methods in order to enhance the inferences drawn from the numerical results obtained from each method. Numerical results are presented using both simulated and experimentally obtained data from physically damaged beams.