Fault Detection and Diagnosis of electrical machine and drive systems are of utmost importance in modern industrial automation. The widespread use of Machine Learning techniques has made it possible to replace traditional motor fault detection techniques with more efficient solutions that are capable of early fault recognition by using large amounts of sensory data. However, the detection of concurrent failures is still a challenge in the presence of disturbing noises or when the multiple faults cause overlapping features. Multi-label classification has recently gained popularity in various application domains as an efficient method for fault detection and monitoring of systems with promising results. The contribution of this work is to propose a novel methodology for multi-label classification for simultaneously diagnosing multiple faults and evaluating the fault severity under noisy conditions. In this research, the Electrical Signature Analysis as well as traditional vibration data have been considered for modeling. Furthermore, the performance of various multi-label classification models is compared. Current and vibration signals are acquired under normal and fault conditions. The applicability of the proposed method is experimentally validated under diverse fault conditions such as unbalance and misalignment.