Model Assisted Probability of Detection Curves: New Statistical Tools and Progressive Methodology

Abstract

The Probability Of Detection (POD) curve is a standard tool in several industries to evaluate the performance of Non Destructive Testing (NDT) procedures for the detection of harmful defects for the inspected structure. Due to new capabilities of NDT process numerical simulation, Model Assisted Probability of Detection (MAPOD) approaches have also been recently developed. In this paper, a generic and progressive MAPOD methodology is proposed. Limits and assumptions of the classical methods are enlightened, while new metamodel-based methods are proposed. They allow to access to relevant information based on sensitivity analysis of MAPOD inputs. Applications are performed on Eddy Current Non Destructive Examination numerical data.

Uncertainty and sensitivity analysis of functional risk curves based on Gaussian processes

“…As shown in [13], this model can easily be improved by considering a Box-Cox transformation [25] instead of a simple logarithmic one on Y :Ỹ = Y λ −1 λ . λ is determined by maximum likelihood as the real number that offers the best linear regression ofỸ regarding the parameter a.…”

“…To overcome this problem, it is possible to resort to numerical simulation of NDT processes. This approach is commonly called MAPOD for "Model Assisted Probability of Detection" [17,18,13].…”

“…where a is the POD parameter of interest (for example the size flaw) and X are the other input parameters. When simulated experiments are used to build the POD (see for example [13]), Y is a scalar output of a numerical model (see Eq.…”

“…In Sections 3 and 4 of this paper, we will illustrate the mathematical methods for FRC building and analysis on a case study on the eddy current examination of the wear induced on steam generator tubes by anti-vibration bars [15]. For details, the reader is referred to [16,13]. The study involves the finite element computer code C3D [19].…”

“…Several works have focused on estimating global sensitivity indices (especially the variance-based ones, known as the Sobol' indices) using Gaussian process models [11,12,8]. In this paper, we present global sensitivity indices attached to the whole FRC (firstly introduced in [13] in a particular context), while showing how to develop them with a Gaussian process model. We also focus on a recently developed method, the Perturbed-Law based sensitivity Indices (PLI) of [14], which seems promising in terms of computational efficiency and interpretation.…”