The fractional slot permanent magnet motor winding adopts a star-delta (Y-Δ) connection multi-layer winding structure, which can restrain the low order harmonic of armature magnetic field and improve the operation efficiency. However, this structure is more complex than the conventional Y connection double-layer winding structure, and the risk of inter-turn short circuit is higher. Firstly, a circuit model of inter-turn short circuit in Y-Δ connection fractional-slot permanent magnet motor (FS-PMM) is established. The fault three-phase current is derived, and fault current will be affected by the position of the inter-turn short circuit. Secondly, the whale optimization algorithm is improved by adaptive weights and Cauchy Gaussian mutation strategy. The improved whale optimization algorithm is adopted for optimizing the parameters of variational mode decomposition, and a parameter optimized variational mode decomposition algorithm for processing current signal is proposed. Finally, by calculating the multi-scale fuzzy entropy of current and torque, a fault diagnosis method for Y-Δ connection FS-PMM inter-turn short circuit is proposed. The accuracy of this fault diagnosis method can reach over 95%, and it can effectively distinguish the inter-turn short circuit fault between the Y connection part and the Δ connection part.