With the increase in machine automation, intelligent fault diagnosis has become more important. Major faults like motor, bearing, gears, shaft misalignment, mechanical unbalance, etc., occur in industrial machines. It is found that multiple component faults or multi-faults may occur in a machine at a time, which needs to be identified incipiently for better resource utilisation. The diagnosis of multi-faults is at its beginning stage in condition monitoring. Therefore, in this work, for incipient multi-fault diagnosis of rotating machines different motor and mechanical unbalance with fault severities were experimentally simulated in a test rig. Vibration signals were acquired at two different constant speed conditions, which were statistically analysed further. A strategy was developed to classify the multi-fault conditions involving signal segmentation, multi-domain signal conversion and machine learning-based model training. An in-depth performance analysis of the models was carried out, and it was found that the proposed diagnosis strategy could help diagnose multi-faults at the incipient stage. This strategy can be helpful for industries to increase their productivity with improved asset management and lower energy consumption.