As one classical anomaly detection technology, support vector data description (SVDD) has been successfully applied to nonlinear chemical process monitoring. However, the basic SVDD model cannot achieve a satisfactory fault detection performance in the complicated cases because of its intrinsic shallow learning structure. Motivated by the deep learning theory, one improved SVDD method, called ensemble deep SVDD (EDeSVDD), is proposed in order to monitor the process faults more effectively. In the proposed method, a deep support vector data description (DeSVDD) framework is firstly constructed by introducing the deep feature extraction procedure. Different to the traditional SVDD with only one feature extraction layer, DeSVDD is designed with multi-layer feature extraction structure and optimized by minimizing the data-enclosing hypersphere with the regularization of the deep network weights. Further considering the problem that DeSVDD monitoring performance is easily affected by the model structure and the initial weight parameters, an ensemble DeSVDD (EDeSVDD) is presented by applying the ensemble learning strategy based on Bayesian inference. A series of DeSVDD sub-models are generated at the parameter level and the structure level, respectively. These two levels of sub-models are integrated for a holistic monitoring model. To identify the cause variables for the detected faults, a fault isolation scheme is designed by applying the distance correlation coefficients to measure the nonlinear dependency between the original variables and the holistic monitoring index. The applications to the Tennessee Eastman process demonstrate that the proposed EDeSVDD model outperforms the traditional SVDD model and the DeSVDD model in terms of fault detection performance and can identify the fault cause variables effectively.