Metamodel-Based Nested Sampling for Model Selection in Eddy-Current Testing

Abstract

Metamodel-based nested sampling for model selection in eddy-current testing. AbstractIn Non-Destructive Testing, model selection is a common problem, e.g, to determine the number of defects present in the inspected workpiece. Statistical model selection requires to approximate the marginal likelihood also called model evidence. Its numerical approximation is usually computationally expensive. Nested Sampling (NS) offers a good compromise between estimation accuracy and computational cost. But it requires to evaluate the forward model many times. Here, we first propose a general framework where data-fitting surrogate models are used to accelerate the computation. Then, improvements benefiting from surrogate modeling are introduced into the traditional NS algorithm to further reduce the computational cost. These improvements include the use of a sparse grid surrogate model to deal with the "curse-of-dimensionality" in large dimensional problems and of the pre-estimated posterior space to save warming-up time. Based on eddy-current simulations, we show that this improved model selection approach has high model selection ability and can jointly perform model selection and parameter inversion.

BME VIK Annual Research Report on Electrical Engineering and Computer Science 2016

“…A database generation technique using the sparse grid approach is introduced in [81], while a metamodel-based nested sampling strategy is reported in [82].…”

Cost-Efficient Bi-Layer Modeling of Antenna Input Characteristics Using Gradient Kriging Surrogates

“…Another reason is the availability of numerous and wellestablished techniques, among others, polynomial regression [35], radial-basis functions (RBF) [36], kriging [35], neural networks [36], support vector regression (SVR) [37], Gaussian process regression [38], or polynomial chaos expansion [39]. The downside of conventional data-driven methods is a rapid increase of the training data set size necessary to render a reliable surrogate (as a function of the number of the system variables and the ranges thereof), known as the curse of dimensionality [40]. Because modern antenna structures are typically described by many parameters, and design-ready models have to cover broad ranges of operating conditions, the aforementioned issues constitute a serious limitation.…”

Sensitivity analysis of inverse problems in EM non‐destructive testing

“…Decades ago, gradientbased methods were available only [2]. Nowadays, various global optimisation techniques are applied (particle swarm optimisation [3], genetic algorithms [4], methods based on kriging interpolation [5], Monte Carlo sampling coupled with Bayesian inference [6] etc. ).…”

“…Hence, surrogate models have been introduced to provide a low-cost approximation of the EM simulation. Indeed, in the majority of the above-cited works, surrogate models are applied: the EM simulation is replaced by an interpolation using radial basis functions [3], kriging [5,7,9] or piecewise linear basis functions supported by a sparse grid (SG) database [6].…”

“…Inversion by means of global optimisation, without setup uncertainty, was addressed in [5]. An SG surrogate model for the forward problem has been introduced in [17] and applied for inversion in [6]. Sensitivity analysis of EM-NdT forward problems has been discussed using a polynomial chaos expansion (PCE) in [12] and a low-rank tensor decomposition in [18].…”