<p>The dynamic and complex nature of rotating systems makes them more susceptible to specific vibration modes, instability, and failure mechanisms. This emphasizes the need for advanced analysis techniques, like those provided by Dynamic Mode Decomposition (DMD), to accurately capture and analyse their dynamic behaviour. The present study deals with the nonlinear behaviour of vibration due to rotor–stator rub. The aim is to understand the dynamics involved in rotor rub through experimental data, and to highlight the usefulness of Dynamic Mode Decomposition (DMD) method for various applications in nonlinear vibratory systems. This study also aims to address the issues in generating experimental Poincaré maps due to noise in the system. The DMD method has been applied to the rotor–stator rub system for the first time. First, the experimental setup has been explained along the data acquisition procedure. Next, the dynamics of the system has been studied using Fast Fourier transform, Poincaré maps, time–frequency domain analysis and waterfall plots. The hindrance in understanding the dynamics has been established due to presence of experimental noise. Further, DMD has been applied to the vibration data, which linearizes the system and can help in reconstruction and noise filtering from the data. The Poincaré map generated from the reconstructed data is clear and the dynamics can be identified from it using standard 0–1 test. The use of DMD method in forecasting of experimental as well as analytical chaotic vibration, which seems to be unpredictable, has been explored.</p>