Prognosis under Uncertainty – An Idealised Computational Case Study

Keith Worden,Graeme Manson

doi:10.1155/2008/958343

Abstract

The object of this paper is to investigate computationally the possibility of damage prognosis in a structure under the most idealised circumstances. A simple isotropic material – Titanium alloy Ti-6Al-4V – is assumed. The structure is a simple finite plate under harmonic uniaxial loading and the damage is assumed to be a central mode 1 through crack for which various approximations to the stress intensity factor are known. The damage propagation model is the Paris-Erdogan law. Where the paper departs from complete simplicity is in the assumption that the parameters of the damage propagation law are uncertain. The paper investigates the effect of the parameter uncertainty on the estimated lifetime of the specimen. Two approaches are adopted for the uncertainty propagation, a statistical Monte Carlo scheme and one based on interval arithmetic.

Highlights

One of the most difficult problems in Structural Health Monitoring (SHM) is prognosis, i.e. given an accurate diagnosis of the damage state of a structure and a characterisation of the future loading to be experienced by the structure, what is its expected residual life? Under normal circumstances, this will depend critically on the soundness of the diagnosis and a good understanding of the underlying physics of damage progression
The most important advantage is the conservative nature of the lifetime estimate
The Monte Carlo calculation suggested that the specimen could last another 164 hours before failure, whereas the interval and vertex calculations showed that the lifetime could be as low as 134 hours, failure occurring over a day earlier

Summary

Introduction

One of the most difficult problems in Structural Health Monitoring (SHM) is prognosis, i.e. given an accurate diagnosis of the damage state of a structure and a characterisation of the future loading to be experienced by the structure, what is its expected residual (safe) life? Under normal circumstances, this will depend critically on the soundness of the diagnosis and a good understanding of the underlying physics of damage progression. The object of the current paper is to investigate damage propagation in a idealised situation in order to explore the feasibility of the approach. In order to obtain the full statistics of the lifetime, it is possible to carry out a Monte Carlo analysis; this is often computationally intensive It is made feasible here by the fact that the PE law only involves two parameters. In Section Four, a different specification of the PE parameters in terms of an interval range is considered, again using Monte Carlo analysis in order to facilitate comparison with the results of Section Five where an interval approach to the uncertainty propagation is adopted.

The computational model

Monte Carlo case study 1

Monte Carlo case study 2

Interval analysis

Discussion and conclusions