Abstract: To address the challenge of weak vibration signal characteristics in generator stator inter-turn short-circuit faults, this paper proposes an enhanced detection method based on adaptive multi-scale morphological gradient product operation. The approach first designs a novel star-shaped structural element tailored to generator stator vibration characteristics and constructs a multi-scale morphological gradient product operation framework. Subsequently, the white shark optimization algorithm is employed to optimize both amplitude and scale parameters of the structural element, enabling adaptive multi-scale morphological processing for vibration signal enhancement. The method validates generator operational status by comparing theoretical fault characteristic frequencies with prominent spectral components in processed signals. Experimental results demonstrate the method's effectiveness in enhancing stator vibration signal characteristics and improving inter-turn short-circuit fault detection rates, confirming its practical engineering significance.