A rub-impact fault is recognized as a complex, non-stationary, and non-linear type of mechanical fault that frequently 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. Furthermore, most of the known techniques experience challenges when applied to multivariate signals. In this paper, an intelligent approach that utilizes multivariate signals and a multivariate one-dimensional convolutional neural network is proposed for diagnosing rubbing faults of various intensities. Specifically, the vibration signals are first collected using multiple sources and then they are resampled into windows with overlap. Next, the envelope power spectra are extracted from the resampled signals to create patterns that are used as the inputs for the multivariate one-dimensional convolutional neural network and to reduce the signal dimensionality to speed up the operation of the intelligent framework. The pairs of convolutional and subsampling layers are used to extract the discriminative local features from the signals collected using multiple sources. These features are used to make a decision about the state of the system in the output layer of the proposed convolutional neural network. The proposed methodology is tested on two different rubbing fault datasets. The experimental results demonstrate that the proposed intelligent fault diagnosis framework is capable of differentiating rubbing faults of various intensities with high classification accuracy.