Hou Yuting, Li Xiang, Zheng Yang, Zhou Jinjie, Tan Jidong, Chen Xiaoping
School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 611731, China.
China Special Equipment Inspection and Research Institute, Beijing 100029, China.
Sensors (Basel). 2020 Sep 20;20(18):5383. doi: 10.3390/s20185383.
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.
磁巴克豪森噪声（MBN）信号为磁性材料微观结构的演变（内应力、退化程度等）提供了有趣的线索。这使得它在铁磁材料的无损评估中得到广泛应用。尽管研究人员付出了巨大努力来探索MBN信号的内在随机特性和稳定特征，但他们未能对MBN信号的随机质量给出确定性定义。由于许多特征不可重现，对于MBN的随机性质没有定量描述，也没有统一的标准来评估特征的性能。我们旨在进一步研究MBN信号的随机特性，并将其转化为信号不确定性和灵敏度的量化，以解决上述疲劳状态预测问题。在预测模型存在参数不确定性的情况下，提出了一种先验近似方法。因此，存在两种不同的不确定性来源：特征（观测）不确定性和模型不确定性，并对其进行了讨论。我们使用置信区间灵敏度分析从概率分布的角度定义特征不确定性，并从特征概率分布空间对特征矩阵进行统一量化和重新参数化。我们还通过优化先验分布和后验分布之间的库尔贝克-莱布勒散度，将有信息先验纳入估计过程，使先验近似于后验。因此，在数据不足的情况下，有信息先验可以提高预测精度。实验证明，我们提出的用于捕获特征不确定性的置信区间灵敏度分析有潜力定量确定MBN信号中的不稳定性，并减少特征的离散性，从而使所有特征都能产生正向累加效应。误预测率可降至几乎为0。所提出的先验不仅可以测量模型参数的不确定性，而且表现出与最大似然估计（MLE）相似的卓越性能。结果还表明，参数不确定性的改善不能直接传播以提高预测不确定性。
