To address the abnormal vibration and noise in power grid transformers caused by stray currents from urban subways, a transformer instability identification method based on the mapping relationship between stray current variations and inherent noise is proposed. First, the primary paths and mechanisms of stray current interference in the power grid are analyzed, and the characteristics of the stray current variations are summarized based on measured data. Next, a multi-physics transformer coupling model considering stray current interference is proposed, dividing the electromagnetic-mechanical-acoustic coupling into an electromagnetic interference domain and a vibration-noise propagation domain. Through simulation analysis under different scenarios, the interference and propagation patterns of stray current mutation rate and timing on transformer parameters such as current and magnetic flux are studied. Finally, an experimental platform is set up to measure the multi-physics characteristics of transformers, while the correctness of the proposed model and conclusions are verified by comparing experimental and simulation results. Moreover, an instability criterion is established based on the mapping between the stray current mutation rate and noise. The results indicate that the vibration and noise of the transformer intensify significantly at points of stray current mutation, with the problem being most severe when the phase angle difference between the stray current mutation timing and the initial phase of power frequency excitation is 90°, leading to an approximately 10% increase in the inherent noise level. This method provides a basis for situational awareness and equipment protection of grid transformers near rail transit systems.