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Remaining useful life (RUL) prediction has been increasingly considered in many industrial fields for the reliability and safety of their systems. As a data analysis tool of deep learning, deep convolutional neural network (CNN) shows great potential for RUL prediction. This paper proposes an intelligent RUL prediction method based on a double-CNN model architecture. Given the powerful feature extraction capability of CNN, the proposed method is fed with original vibration signals with no need to resort to any feature extractor, which can also retain the useful information in maximum. The prediction includes two stages: first, incipient fault point is identified by the first CNN model and a proposed “3/5” principle; then, the second CNN model is constructed for RUL prediction. In practice, RULs of identical components are different from each other, which poses a major challenge in RUL prediction. To overcome this problem, an intermediate reliability variable is first calculated in this paper, instead of directly predicting the RUL value. Then, a mapping algorithm is proposed to map reliability to RUL. To demonstrate the effectiveness of the proposed method, data of four tests of bearing degradation are utilized for RUL prediction. Compared with state-of-the-art methods, the proposed method shows higher prediction accuracy and robustness. The prediction results and evaluation indexes demonstrated the effectiveness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]