A Method for Detecting the Randomness of Barkhausen Noise in a Material Fatigue Test Using Sensitivity and Uncertainty Analysis

Abstract

The magnetic Barkhausen noise (MBN) signal provides interesting clues about the evolution of microstructure of the magnetic material (internal stresses, level of degradation, etc.). This makes it widely used in non-destructive evaluation of ferromagnetic materials. Although researchers have made great effort to explore the intrinsic random characteristics and stable features of MBN signals, they have failed to provide a deterministic definition of the stochastic quality of the MBN signals. Because many features are not reproducible, there is no quantitative description for the stochastic nature of MBN, and no uniform standards to evaluate performance of features. We aim to make further study on the stochastic characteristics of MBN signal and transform it into the quantification of signal uncertainty and sensitivity, to solve the above problems for fatigue state prediction. In the case of parameter uncertainty in the prediction model, a prior approximation method was proposed. Thus, there are two distinct sources of uncertainty: feature(observation) uncertainty and model uncertainty were discussed. We define feature uncertainty from the perspective of a probability distribution using a confidence interval sensitivity analysis, and uniformly quantize and re-parameterize the feature matrix from the feature probability distribution space. We also incorporate informed priors into the estimation process by optimizing the Kullback–Leibler divergence between prior and posterior distribution, approximating the prior to the posterior. Thus, in an insufficient data situation, informed priors can improve prediction accuracy. Experiments prove that our proposed confidence interval sensitivity analysis to capture feature uncertainty has the potential to determine the instability in MBN signals quantitatively and reduce the dispersion of features, so that all features can produce positive additive effects. The false prediction rate can be reduced to almost 0. The proposed priors can not only measure model parameter uncertainties but also show superior performance similar to that of maximum likelihood estimation (MLE). The results also show that improvements in parameter uncertainties cannot be directly propagated to improve prediction uncertainties.