The extraction of early fault features from time-series data is very crucial for convolutional neural networks (CNNs) in bearing fault diagnosis. To address this problem, a CNN framework based on identity mapping and Adam optimizer is presented for learning temporal dependencies and extracting fault features. The introduction of four identity mappings allows the deep layers to directly learn the data from the shallow layers, which alleviates the gradient disappearance problem caused by the

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... ase of network depth. A new Adam optimizer with power-exponential learning rate is proposed to control the iteration direction and step size of CNN method, which solves the problems of local minima, overshoot or oscillation caused by the fixed values of the learning rates during the updating of network parameters. Compared to existed methods, the identification accuracy of the proposed method outperformed that of other methods for bearing fault diagnosis.