Study on multi-parameter response characteristics of weak-magnetic inspection signals in stress-damaged zones of long-distance oil and gas pipelines

Weak-magnetic internal inspection technology has been applied to stress detection in oil and gas pipelines, but quantifying the relationship between stress-damage zones (SDZs) and weak magnetic signals (WMSs) remains challenging due to multi-parameter responses and inherently weak signal intensity. To address this, this study incorporates the magneto-mechanical response of pipeline materials into a Maxwellian magnetic-spatial-distribution framework, establishing a magneto-mechanical constitutive model for WMSs under multi-parameter response. The signal-rate-variation factor (SRVF) is extracted from the model to enhance detection signal recognition and enable analysis of SDZs characteristics and probe placement principles. Results show that the constitutive model effectively achieves quantitative mapping of WMSs magnetic distribution to SDZs parameters. The extracted SRVF elevates the order of magnitude of the detection signal exponent to a confidence interval of [5.8, 6.2] and reduces the error by 4.8. SRVF is approximately linearly positively correlated with stress (radial sensitivity exceeding axial), increases nonlinearly with damage size (stronger response to crack depth), and decays exponentially with probe lift-off and circumferential offset. Axial detection parameters are larger than radial ones. These findings provide a theoretical model and experimental basis for SDZs characterization and optimized probe placement.