Permanent Magnet Synchronous Motor (PMSM) is widely used due to its advantages of high power density, high efficiency and so on. In order to ensure the reliability of a PMSM system, it is extremely vital to accurately diagnose the incipient faults. In this paper, a variety of optimization algorithms are utilized to realize the diagnosis of the faulty position and severity of the inter-turn short-circuit (ITSC) fault, which is one of the most destructive and frequent faults in PMSM. Compared with the existing research results gained by particle swarm optimization algorithms, in this paper, the methods using other optimization algorithms incorporating genetic algorithm, whale optimization algorithm and stochastic parallel gradient descent algorithm (SPGD) can acquire more stable and precise results. In particular, the method based on SPGD can obtain the most desirable performance among the methods mentioned above; that is, the relative error of short-circuit turns ratio is approximately as low as 0.03%. In addition, in the case of asymmetric input three-phase voltage and with the adverse impact of high-order harmonics at different load moments, the fault diagnosis method based on SPGD still maintains relatively satisfactory properties. Finally, the verification on the actual PMSM platform demonstrates that the SPGD can still diagnose the faulty severity.