Research on identification method for true deflection angle of probe in ultrasonic internal inspection

Abstract Ultrasonic internal inspection accuracy is highly sensitive to probe deflection, as deviations between the ultrasonic beam axis and the pipeline surface normal induce echo-amplitude attenuation and defect-sizing errors. In practical inspection scenarios, angular deviation may occur independently in either the circumferential or axial direction; however, these components commonly coexist simultaneously. In this study, the term true deflection angle is defined as the coupled circumferential–axial deviation of the ultrasonic beam from the local surface normal of the pipeline, clearly distinguishing it from conventional single-direction deflection (i.e. circumferential-only or axial-only deviation). Current relevant studies mostly focus on the analysis of single-direction deflection angles and pay relatively limited attention to the issue of true deflection angles prevalent in engineering practice. In this study, a true deflection angle identification framework based on characteristic-parameter polynomial surface modeling is proposed. A dedicated ultrasonic internal inspection experimental system was established to systematically investigate echo signal behavior under coupled deflection conditions to solve the existing problem. Experimental results reveal that echo amplitude exhibit a nonlinear rotational-paraboloid decay pattern within the angular domain. Three characteristic parameters—the primary interface echo peak ( K 1 ), primary bottom echo peak ( K 2 ), and transit time ( t ) between the two peaks—were extracted, and a fourth-order polynomial surface fitting model was constructed. Model training was performed within a circumferential range of 0°–1.5° and axial range of 0°–0.8°, while the effective monotonic identification region was determined as 0°–0.8° (circumferential) and 0°–0.4° (axial). Using K 1 / t as the optimal feature parameter, the proposed model achieved an average identification error of 2.33%, with a maximum deviation not exceeding 5%. Cross-validation and noise-sensitivity analysis further confirm the robustness and generalization capability of the approach. The proposed method provides a practical and accurate solution for probe deflection compensation in ultrasonic pipeline inspection.