Multi-Frequency Time-Reversal and Topological Derivative Fusion Imaging of Steel Pipe Defects via Sparse Bayesian Learning

Steel pipes play a vital role in energy and industrial transportation systems, where undetected defects such as cracks and wall thinning may lead to severe safety hazards. Although ultrasonic guided waves enable long-range inspection, their defect imaging performance is often limited by dispersion, multimode interference, and strong noise. In this work, a multi-frequency fusion imaging method integrating time-reversal, topological derivative, and sparse Bayesian learning is proposed for guided wave-based defect detection in steel pipes. Multi-frequency guided waves are employed to enhance defect sensitivity and suppress frequency-dependent ambiguity. Time-reversal focusing is used to concentrate scattered energy at defect locations, while the topological derivative provides a global sensitivity map as physics-guided prior information. These results are further fused within a sparse Bayesian learning framework to achieve probabilistic defect imaging and uncertainty quantification. Dispersion compensation based on the semi-analytical finite element method is introduced to ensure accurate wavefield reconstruction at different frequencies. Domain randomization is also incorporated to improve robustness against uncertainties in material properties, temperature, and measurement noise. Numerical simulation results verify that the proposed method achieves high localization accuracy and significantly outperforms conventional TR-based imaging in terms of resolution, false alarm suppression, and stability. The proposed approach provides a reliable and robust solution for guided wave inspection of steel pipelines and offers strong potential for engineering applications in nondestructive evaluation and structural health monitoring.