Intelligent fault diagnosis gives timely information about the condition of mechanical components. Since rolling element bearings are often used as rotating equipment parts, it is crucial to identify and detect bearing faults. When there are several defects in components or machines, early fault detection becomes necessary to avoid catastrophic failure. This work suggests a novel approach to reliably identifying compound faults in bearings when the availability of experimental data is limited. Vibration signals are recorded from single ball bearings consisting of compound faults, i.e., faults in the inner race, outer race, and rolling elements with a variation in rotational speed. The measured vibration signals are pre-processed using the Hilbert–Huang transform, and, afterward, a Kurtogram is generated. The multiscale-SinGAN model is adapted to generate additional Kurtogram images to effectively train machine-learning models. To identify the relevant features, metaheuristic optimization algorithms such as teaching–learning-based optimization, and Heat Transfer Search are applied to feature vectors. Finally, selected features are fed into three machine-learning models for compound fault identifications. The results demonstrate that extreme learning machines can detect compound faults with 100% Ten-fold cross-validation accuracy. In contrast, the minimum ten-fold cross-validation accuracy of 98.96% is observed with support vector machines.