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access icon free Sensitivity analysis of inverse problems in EM non-destructive testing

© The Institution of Engineering and Technology
Received 13/08/2019, Accepted 07/01/2020, Revised 14/11/2019, Published 09/01/2020

The inverse problem of electromagnetic (EM) non-destructive testing (NdT) consists of reconstructing material defect parameters invoking EM field measurements. Uncertainties of the configuration (e.g. imprecise constitutive and geometrical parameters) are inevitably present; hence, the reconstructed defect parameters are also uncertain. In this study, the different sources of uncertainty are ranked by means of sensitivity analysis. The model-based inversion (involving EM simulation) is computationally demanding; moreover, sensitivity analysis usually requires a vast number of repeated runs of the inversion. To overcome the computational complexity, surrogate models are applied at different levels. Interpolation on a sparse grid is used as a surrogate model of the EM simulation. The sensitivity of the reconstructed defect parameters concerning configuration uncertainties is characterised by means of Sobol indices. The Sobol indices are obtained from a polynomial chaos expansion surrogate model of the entire inversion scheme. A numerical example drawn from eddy-current NdT is thoroughly analysed to illustrate the proposed methodology and to demonstrate its performance.

Inspec keywords: inverse problems; sensitivity analysis; stochastic processes; nondestructive testing; polynomials; chaos; eddy current testing

Other keywords: EM-NdT; Sobol indices; polynomial chaos expansion surrogate model; model-based inversion; inverse problem; entire inversion scheme; material defect parameters; EM simulation; reconstructed defect parameters; sensitivity analysis; EM field measurements; electromagnetic nondestructive testing; configuration uncertainties; eddy-current NdT; computational complexity

Subjects: Probability theory, stochastic processes, and statistics; Theory and models of chaotic systems; Algebra, set theory, and graph theory; Numerical approximation and analysis

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