Nonlinear Ultrasonic Time-Domain Identification Based on Chaos Sensitivity and Its Application to Fatigue Detection of U71Mn Rail Steels

A nonlinear ultrasonic time-domain identification method based on chaos sensitivity was proposed in this study. The Duffing chaotic system was introduced into the weak second harmonic identification to realize early detection and quantitative evaluation of fatigue damage in U71Mn steel. First, to ensure the reliability of nonlinear ultrasonic testing, a probe-pressure monitoring device was designed. Through pressure-stability experiments, 16 N was determined as the optimal pressure, which effectively suppresses contact nonlinearity interference and ensures coupling stability. Subsequently, the Duffing chaos detection system was established. The signal-system frequency-matching problem was resolved through time-scale transformation. Simultaneously, the issue of unknown initial phases was resolved using phase traversal compensation. Based on the chaotic system’s sensitivity to specific frequency signals and immunity to noise, the amplitudes of the fundamental wave and second harmonics in the target signals were quantified to calculate the nonlinear coefficient. Experimental results demonstrate that the proposed method can extract these amplitudes directly in the time domain, thereby effectively overcoming the spectral leakage inherent in traditional frequency-domain methods. The nonlinear coefficient of U71Mn steel exhibits a “double-peak” characteristic as fatigue damage increases. Specifically, the first peak appears at approximately 50% of fatigue life, while the second occurs at approximately 80%. This phenomenon is closely correlated with the distinct stages of internal fatigue crack propagation, reflecting a complex damage-evolution mechanism. This study not only provides a novel method for the precise extraction of weak nonlinear signals but also establishes a critical theoretical and experimental foundation for accurate fatigue life prediction for U71Mn rail steel.