Axial crack detection in steel pipelines remains challenging because the crack-reflected guided-wave response is usually weak, frequency-dependent, and susceptible to dispersion, modal interference, sensor-coupling variation, and environmental noise. To address this issue, a reliability-adaptive probabilistic imaging and semi-quantitative severity-assessment framework is proposed using multi-frequency ultrasonic guided-wave signals. A T(0,1)-dominated torsional guided-wave packet is selected as the target response, and dispersion analysis is used to support mode selection and reflection-window prediction. Time-domain, frequency-domain, and time-frequency-domain features are extracted from the crack-reflection window to characterize the defect response from complementary perspectives. For each excitation frequency, a single-frequency probability image is constructed by combining reflected-response strength and travel-time consistency. A reliability-adaptive fusion strategy is then developed to integrate the probability images obtained at different frequencies, where the contribution of each frequency is determined by echo quality, inter-sensor consistency, and modal purity. Equal-weight fusion and SNR-weighted fusion are introduced as baseline methods to evaluate the contribution of the proposed reliability-adaptive weighting strategy. A confidence-enhancement step is further applied to suppress uncertain secondary hotspots and improve noise-interference stability under the tested controlled condition. Experiments were conducted on a Q235 steel pipe specimen containing three axial surface crack depths. The results show that amplitude- and energy-related features increase progressively with crack depth, indicating their sensitivity to severity variation under the present configuration. Compared with equal-weight and SNR-weighted fusion, the proposed method produces more compact probability distributions, lower background interference, and improved localization concentration around the actual crack region. The posterior-distribution-based severity index provides effective semi-quantitative grading of mild, moderate, and severe crack cases. The present study should be interpreted as controlled-condition verification of the proposed framework, while broader validation with different crack geometries, crack locations, sensor-coupling states, and environmental conditions is required in future work.

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.

1. Steel pipelines are widely used in energy transportation, petrochemical processing, urban utilities, and industrial production, and their integrity is closely related to operational safety and s...