An Improved Hidden Markov Model with Magnetic Barkhausen Noise and Optimized Gaussian Mixture Feature for Fatigue Prediction

Abstract Evaluating fatigue states of metallic materials is essential for predicting their failures and ensuring structural safety. Magnetic Barkhausen noise (MBN) analysis, a non-destructive testing method, provides efficient and reliable methods for identifying and categorising material parameters such as hardness and residual stresses. To establish a quantitative relationship between MBN signals and fatigue states, an improved hidden Markov model (HMM) is proposed based on optimised Gaussian mixture features (GMFs) and the Kullback-Leibler (KL) divergence measure for fatigue prediction. The MBN-GMFs replicate the probability characteristics of MBN signals and track the fatigue degradation trend throughout the fatigue life; thus, they are superior to some widely used statistical features. A Gaussian component optimisation (GCO) algorithm is proposed to automatically adjust the appropriate number of components in the Gaussian mixture model (GMM) and enhance the representation of MBN-GMFs. Then, the KL divergence is introduced to quantify the similarity and accurately classify the degree of MBN-GMF migration. The HMM is constructed to obtain the probability transfer relationship between the observations and states and obtain accurate fatigue predictions. Experiments on two 20R metallic materials at three excitation frequencies are conducted to collect the MBN signals. The experimental results and comparisons indicate that the proposed HMM can accurately predict fatigue states and provide a practical and robust analysis tool for MBN-based fatigue predictions.