Three-Dimensional Crack Detection in Magnetic Slabs Using an Advanced Deconvolution Framework

Abstract

Magnetic slab integrity is a critical factor in industrial and energy applications, where undetected defects such as micro-cracks can compromise structural reliability, operational efficiency, and safety. Conventional inspection methods, including visual assessment and two-dimensional magnetic flux leakage (MFL) imaging, are limited in their ability to detect subsurface defects or accurately characterize three-dimensional crack morphology. This paper proposes a novel three-dimensional crack detection methodology leveraging an advanced deconvolution framework designed to reconstruct volumetric defect profiles with high spatial fidelity. The approach integrates high-resolution magnetic flux measurement, coordinate transformation for precise spatial mapping, and regularized deconvolution to resolve flux perturbations induced by cracks. Theoretical foundations are drawn from signal processing, inverse problem formulation, and adaptive state estimation, enabling robust reconstruction under measurement noise and sensor uncertainties. The framework is validated through comprehensive simulations on magnetic slabs with variable crack geometries, including complex orientations and multi-crack interactions. Results demonstrate that the proposed method significantly outperforms conventional two-dimensional detection approaches in terms of localization accuracy, depth estimation, and morphological reconstruction, with reconstruction errors consistently below 5%. Furthermore, the methodology provides quantitative metrics, including crack length, depth, and orientation, allowing for predictive maintenance and structural health assessment. Comparative analysis with existing signal inversion techniques illustrates that the integration of coordinate transformation with iterative deconvolution improves sensitivity to subtle flux variations and mitigates the effects of measurement noise. Critical evaluation highlights practical limitations such as the requirement for high-density sensor arrays and computational overhead for large-scale slabs, but these challenges are offset by the framework’s scalability and adaptability. By bridging the gap between advanced signal processing and non-destructive evaluation (NDE), this research offers a robust, theoretically grounded solution for three-dimensional crack detection, contributing to enhanced safety, operational reliability, and informed maintenance strategies in magnetic slab applications.