Sensitivity analysis and variance reduction in a stochastic non-destructive testing problem

Abstract

In this paper, we present a framework to deal with uncertainty quantification in case where the ranges of variability of the random parameters are ill-known. Namely the physical properties of the corrosion product (magnetite) which frequently clogs the tube support plate of steam generator, which is inaccessible in nuclear power plants. The methodology is based on polynomial chaos (PC) for the direct approach and on Bayesian inference for the inverse approach. The direct non-intrusive spectral projection (NISP) method is first employed by considering prior probability densities and therefore constructing a PC surrogate model of the large-scale non-destructive testing finite element model. To face the prohibitive computational cost underlying the high-dimensional random space, an adaptive sparse grid technique is applied on NISP resulting in drastic time reduction. The PC surrogate model, with reduced dimensionality, is used as a forward model in the Bayesian procedure. The posterior probability densities are then identified by inferring from few noisy experimental data. We demonstrate effectiveness of the approach by identifying the most influential parameter in the clogging detection as well as a variability range reduction.

Keywords:

• uncertainty quantification
• polynomial chaos
• Bayesian inference
• non-destructive testing

(2010) AMS Subject Classifications:

• 62F15
• 35R30
• 62P30
• 35Q61