Historical data sets for fault stage diagnosis in industrial machines are often imbalanced and consist of multiple categories or classes. Learning discriminative models from such data sets is challenging due to the lack of representative data and the bias of traditional classifiers toward the majority class. Sampling methods like synthetic minority oversampling technique (SMOTE) have been traditionally used for such problems to artificially balance the data set before being trained by a classifier. This paper proposes a weighted kernel-based SMOTE (WK-SMOTE) that overcomes the limitation of SMOTE for nonlinear problems by oversampling in the feature space of support vector machine (SVM) classifier. The proposed oversampling algorithm along with a cost-sensitive SVM formulation is shown to improve performance when compared to other baseline methods on multiple benchmark imbalanced data sets. In addition, a hierarchical framework is developed for multiclass imbalanced problems that have a progressive class order. The proposed WK-SMOTE and hierarchical framework are validated on a real-world industrial fault detection problem to identify deterioration in insulation of high-voltage equipments.

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Decentralized uniform input-to-state stabilization of hierarchically interconnected triangular switched systems with arbitrary switchings. Automatica,