A Hankel Matrix-Based Multivariate Control Chart With Shrinkage Estimator for Condition Monitoring of Rolling Bearings

Rolling element bearings are crucial key components in rotating machinery, and it is essential to monitor their condition to prevent unexpected breakdown or safety incidents. However, features that indicate the operating condition are often affected by strong background noise, leading to inaccurate detection. Additionally, classical monitoring methods often rely on a multivariate normal distributed (MND) assumption, which may not be suitable in real-world applications due to noise interference, outliers, and sampling errors. To address the aforementioned issues, this paper proposes a novel Hankel matrix-based multivariate homogeneously weighted moving average control chart with shrinkage estimator (HMHS chart). The first step involves segmenting the bearing vibration signal to create Hankel matrix sequences, and the singular features are obtained via singular value decomposition (SVD). To determine the optimal singular sequence, a criterion called mode entropy (ME) is proposed. Secondly, a shrinkage estimator is applied to establish a robust statistic with low covariance bias. Thirdly, a health index is constructed using the HMHS chart to track the bearing’s degradation process. Simulation studies and two real case studies are performed with comparison to classical charts to demonstrate the effectiveness and accuracy of the proposed method. The results demonstrate the effectiveness and accuracy of the proposed method in the condition monitoring of rolling bearings.
Note to Practitioners
—A novel condition monitoring method of rolling bearings is proposed in this work. Existing methods often rely on traditional statistics (such as kurtosis, root mean square), which can be easily disturbed by noise and outliers in training samples. Moreover, the MND assumption needed is not always tolerated in real applications, leading to poor performance in condition monitoring. To solve this problem, a Hankel matrix-based multivariate control chart is proposed in this paper, which includes several steps for implementation. These steps include: 1) collecting vibration signals of rolling bearings; 2) conducting Hankel matrix-based adaptive feature extraction; 3) constructing the monitoring statistic with robust estimators, and estimating the control limit; 4) conducting online health monitoring of rolling bearings. Extensive simulation studies and two real case studies are conducted to evaluate the accuracy and effectiveness of the proposed method in bearing condition monitoring.