As critical equipment in the power system, the operation status of oil-immersed transformers directly affects the safety and stability of the power grid. Based on COMSOL, a finite element simulation software, a 10kV/400V oil-immersed transformer electromagnetic–structural multiphysics coupling calculation model is established to analyze the effect of added/unadded clamping devices on the core vibration displacement. On this basis, the vibration characteristics of the core, windings, and tank wall are analyzed, and their corresponding vibration acceleration signals are extracted. Subsequently, the Kendall and Spearman correlation coefficients are employed to calculate the correlation among the vibration signals of the core, windings, and tank wall, obtaining the optimal position for measuring vibration. Based on the Copula function, a vibration inversion model for the oil-immersed transformer is developed, which utilizes the external tank wall signals to reflect the operation status of the internal core and windings. The inversion results for the core and winding vibration acceleration are obtained under different load conditions. Finally, the model’s accuracy is evaluated using the coefficient of determination (R2) and mean absolute error. The results show that the inverse model achieves an accuracy rate of above 94%. The findings provide a reference for transformer vibration fault detection.