The continuous and online monitoring of the condition of electrical machines is key to their safe operation. This study introduces a novel fault detection and diagnosis technique for continuous monitoring of faults in permanent magnet synchronous motors (PMSM). The proposed method relies solely on built-in sensors (stator phase currents only) to detect three types of faults: inter-turn short circuit, partial demagnetisation, and static eccentricity. Our fault detection and diagnosis strategy was developed by combining variational mode decomposition (VMD), the Hilbert-Huang transform (HHT) and a convolutional neural network (CNN). The VMD is first applied to the stator phase current signals to analyse the characteristic behaviour of the current signals by decomposing the current signals into several intrinsic mode functions. The intrinsic mode functions of the healthy and faulty signals are compared, and that with the frequency shift characteristics is selected. HHT is then applied to extract the fault feature by calculating the instantaneous frequency. Finally, the instantaneous frequency feature is fed into the CNN, which is designed to detect and classify motor faults. Experimental results clearly show that the variation of the instantaneous frequency of the PMSM, working at different operating states, can be utilised for condition monitoring and fault detection.