A rub-impact fault is a complex, nonstationary, and nonlinear fault that occurs in turbines. Extracting features for diagnosing rubbing faults at their early stages requires complex and computationally expensive signal processing approaches that are not always suitable for industrial applications. In this article, a hybrid approach that uses a combination of deep learning and control theory algorithms is introduced for diagnosing rubbing faults of various intensities. Specifically, the system is first modeled based on the autoregressive with eXogenous input Laguerre (ARX-Laguerre) technique. In addition, the ARX-Laguerre proportional-integral observer (PIO) is used to increase the estimation accuracy for the vibration signals containing rubbing faults. Finally, a scalable deep neural network is applied to the output signal of the PIO to perform fault diagnosis and overcome potential problems that may appear when applying a linear observation technique to nonlinear signals. The experimental results demonstrate that the proposed hybrid approach improves the fault differentiation capabilities of a relatively simple linear observation technique when it is applied to a complex nonlinear rubbing fault signal and attains high fault classification accuracy. This result means that the proposed framework is highly suitable for applications in actual industrial environments.