The detection of common incipient faults in rotating machinery operating under varying speeds is presently investigated via two unsupervised machine learning type methods using a limited number of vibration signals from a single sensor for their training. The first utilizes advanced Functional Pooled (FP) AutoRegression (AR) modelling for the explicit interpretation of the machinery healthy dynamics within the complete range of rotating speeds, while the second employs a cloud of typical AR models within a Multiple Model framework. The methods’ performance is systematically assessed and compared based on hundreds of experiments with the healthy and faulty machinery that consists of two electric motors coupled via a claw clutch and operate under 75 different rotating speeds. Three types of incipient faults are separately incorporated, a slight unbalance, minor wear at the base of a single claw clutch (coupler) tooth, and mechanical looseness at one of the four main mounting bolts of the machinery. The results indicate the clear superiority of the FP based method that achieves impressive detection of all considered faults even under rotating speeds for which it is not trained