IEEE Transactions on Industrial Electronics, March 2021, DOI:10.1109/TIE.2020.2972458

Deep Residual Networks with Adaptively Parametric Rectifier Linear Units for Fault Diagnosis

Minghang Zhao1, Shisheng Zhong1, Xuyun Fu1, Baoping Tang2, Shaojiang Dong3 and Michael G. Pecht4
1 School of Naval Architecture and Ocean Engineering, Harbin Institute of Technology at Weihai, Weihai, Shandong China
2 State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing, Chongqing China
3 School of Mechatronics and Automotive Engineering, Chongqing Jiaotong University, 47912 Chongqing, Chongqing China
4 CALCE, Center for Advanced Life Cycle Engineering, Department of Mechanical Engineering, University of Maryland, College Park, Maryland 20740, USA


Vibration signals under the same health state often have large differences due to changes in operating conditions. Likewise, the differences among vibration signals under different health states can be small under some operating conditions. Traditional deep learning methods apply fixed nonlinear transformations to all the input signals, which has a negative impact on the discriminative feature learning ability, i.e., projecting the intra-class signals into the same region and the inter-class signals into distant regions. Aiming at this issue, this paper develops a new activation function, i.e., adaptively parametric rectifier linear units, and inserts the activation function into deep residual networks to improve the feature learning ability, so that each input signal is trained to have its own set of nonlinear transformations. To be specific, a sub-network is inserted as an embedded module to learn slopes to be used in the nonlinear transformation. The slopes are dependent on the input signal, and thereby the developed method has more flexible nonlinear transformations than the traditional deep learning methods. Finally, the improved performance of the developed method in learning discriminative features has been validated through fault diagnosis applications.

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