Physically constrained two-stage residual network for defect sizing using capacitive imaging technique

The Capacitive Imaging (CI) technique has emerged as an effective and versatile electromagnetic Nondestructive Evaluation (NDE) method with significant potential for detecting internal defects in insulating materials and allowing image reconstruction, particularly in the assessment of insulation layers of critical pipes and/or vessels. Although conventional CI techniques are primarily used as a screening tool to identify the presence of defects, they are considered less effective for accurately quantifying critical parameters such as defect size, thickness, and depth, which are essential in engineering applications. This paper proposes a Two-Stage Residual Network (TS-ResNet) that incorporates physical constraints through two customized layers: a gradient layer and a wavelet layer. The gradient layer utilizes a dual-gradient compensation fusion algorithm to extract critical information regarding the length and width of the detected signals. The wavelet layer employs a Gaussian wavelet base to effectively filter out noise from the signals, enhancing the distinction between signals due to defects at varying thicknesses and depths, from the shallowest to those buried in the sample. By integrating these customized layers into the neural network architecture, the proposed TS-ResNet is capable of accurately quantifying the size parameters of defects situated at greater depths. Experimental results indicate that this method can reliably quantify defect length, width, thickness, and depth, demonstrating a high level of accuracy.