The crack growth process in metals can be continuously monitored and recorded in real time using highly sensitive acoustic emission technology. To predict this complex behavior, an improved largest Lyapunov exponent method, enhanced by a small data optimization approach named the small data method, is applied. Meanwhile, experimental results reveal that the acoustic emission signals collected during the fatigue crack growth process display distinct chaotic characteristics. By employing the small data method and cross-comparison analysis with the traditional Wolf method, the prediction accuracy and efficiency are significantly enhanced, even when only a limited amount of data is available. Compared to conventional techniques, this method demonstrates higher reliability and robustness, offering a powerful tool for early-stage monitoring and life prediction of metallic materials.

Acoustic emission (AE) technology was used to monitor the fatigue crack growth process of superalloy. The analysis results show that both the cumulative values and the K-entropy values of AE parameters have good correspondences with the three stages described by fracture mechanics, which makes it possible to characterize the process of fatigue crack growth. Since K-entropy is more sensitive to changes in fatigue state, the turning points between the second stage and the third stage are earlier than those defined by fracture mechanics, indicating that it has an early warning capability. The K-entropy of AE parameter was first proposed to represent the growth rate of fatigue crack. This method not only effectively decreased the large dispersion of change rate of AE parameters but also ensured the similarity with the fatigue crack growth rate, thereby optimizing the characterization of fatigue crack growth.