Due to the complexity of their working conditions, historical rolling bearing datasets are mostly limited and imbalanced. The fault data may be composed of multiple subclusters; that is, the historical rolling bearing data have both between-class and within-class imbalances. While support vector machines (e.g., least squares support vector machines (LS-SVMs)) offer advantages when dealing with limited data, traditional fault diagnosis using an LS-SVM has the disadvantages of easy failure of complex imbalanced data and large dependence on the classifier hyperparameters. Therefore, this paper presents a new imbalanced fault diagnosis framework based on a cluster-majority weighted minority oversampling technique (Cluster-MWMOTE) and a moth-flame optimization (MFO)-based LS-SVM classifier. As an extension of MWMOTE, our proposed Cluster-MWMOTE combines the clustering algorithm represented by agglomerative hierarchical clustering (AHC) with MWMOTE. Unlike MWMOTE, Cluster-MWMOTE can avoid the ignoring of small subclusters of faulty (minority) instances far from normal (majority) instances. That is, Cluster-MWMOTE further improves the adaptation to within-class imbalances. As a novel heuristic intelligent algorithm, MFO exhibits faster convergence and higher precision than the traditional optimization algorithms (e.g., particle swarm optimization (PSO) and genetic algorithm (GA)). Therefore, we utilize MFO to optimize the hyperparameters (Sigma & $\gamma$) of the LS-SVM classifier for the first time. The fault diagnosis results represented by CWRU and IMS bearing data suggest that the proposed framework provides higher fault diagnosis recognition rates and algorithm robustness than 16 existing algorithms.

由于其工作条件的复杂性，历史滚动轴承数据集大多是有限且不平衡的。故障数据可能由多个子簇组成；也就是说，历史滚动轴承数据同时具有类间和类内不平衡。虽然支持向量机（例如，最小二乘支持向量机（LS-SVM））在处理有限数据时具有优势，但使用LS-SVM的传统故障诊断的缺点是容易导致复杂的不平衡数据失败以及对分类器的依赖性大超参数。因此，本文提出了一种基于聚类多数加权少数过采样技术（Cluster-MWMOTE）和基于蛾-火焰优化（MFO）的LS-SVM分类器的新的不平衡故障诊断框架。作为MWMOTE的扩展，我们提出的Cluster-MWMOTE结合了以聚类层次聚类（AHC）为代表的聚类算法和MWMOTE。与MWMOTE不同，群集MWMOTE可以避免忽略故障（少数）实例与正常（多数）实例相距甚远的小型子集群。也就是说，群集MWMOTE进一步提高了对类内部失衡的适应性。作为一种新颖的启发式智能算法，MFO比传统的优化算法（例如，粒子群优化（PSO）和遗传算法（GA））具有更快的收敛性和更高的精度。因此，我们利用MFO优化超参数（Sigma和 群集MWMOTE可以避免忽略远离正常（多数）实例的故障（少数）实例的小子簇。也就是说，群集MWMOTE进一步提高了对类内部失衡的适应性。作为一种新颖的启发式智能算法，MFO比传统的优化算法（例如，粒子群优化（PSO）和遗传算法（GA））具有更快的收敛性和更高的精度。因此，我们利用MFO优化超参数（Sigma和 群集MWMOTE可以避免忽略远离正常（多数）实例的故障（少数）实例的小子簇。也就是说，群集MWMOTE进一步提高了对类内部失衡的适应性。作为一种新颖的启发式智能算法，MFO比传统的优化算法（例如，粒子群优化（PSO）和遗传算法（GA））具有更快的收敛性和更高的精度。因此，我们利用MFO优化超参数（Sigma和$\gamma$）。由CWRU和IMS承载数据表示的故障诊断结果表明，与现有的16种算法相比，该框架提供了更高的故障诊断识别率和算法鲁棒性。