Applied Soft Computing Journal 89 (2020) 106119 Contents lists available at ScienceDirect Applied Soft Computing Journal journal homepage: www.elsevier.com/locate/asoc Constructing a health indicator for roller bearings by using a stacked auto-encoder with an exponential function to eliminate concussion Fan Xu a , Zhelin Huang a,b,∗ , Fangfang Yang a , Dong Wang c , Kwok Leung Tsui a a School of Data Science, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong 990777, PR China b Department of Statistics, School of Economics, Shenzhen University, Shenzhen 518061, PR China c The State Key Laboratory of Mechanical Systems and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China article info Article history: Received 17 March 2019 Received in revised form 23 December 2019 Accepted 17 January 2020 Available online 23 January 2020 Keywords: Roller bearings Deep learning Stacked auto-encoder Health indicator Exponent function abstract Most deep-learning models, especially stacked auto-encoders (SAEs), have been used in recent years for the diagnosis of faults in rotating machinery. However, very few studies have reported on health indicator (HI) construction by using SAEs in deep learning. SAEs have a good feature-extraction ability when several hidden layers are used to reconstruct the original input. In this study, we first introduce a method to reduce dependence on prior knowledge that is based on SAEs and enables extraction of the preliminary degradation trend from the bearing’s frequency domain directly. Second, to construct the final HI and improve the monotonicity of the indicators, an exponential function is used to eliminate global severe vibration after an SAE has extracted the preliminary degradation trend. To prove the effect of our presented method, some other HI construction models, such as root mean square, kurtosis, approximate entropy, permutations entropy, empirical mode decomposition-singular value decomposition, K-means/K-medoids, and various time–frequency fusion indicators are used for comparison. Moreover, to prove that the exponential-function effect exceeds other severe vibration- eliminating methods, examples of the latter methods such as exponentially weighted moving-average and outlier detection are used for comparative analysis. Finally, the results shows that our proposed model is better than the above-mentioned existing models. © 2020 Elsevier B.V. All rights reserved. 1. Introduction Roller bearings ensure the reliable operation of a mechanical system and are some of the most commonly used and vulnerable mechanical parts in industry. Reducing the maintenance cost of such equipment is very important because it is known that increased bearing running-time leads to degradation of the bear- ing’s performance [1–3]. To achieve a quantitative assessment of the bearing health status, the concept of a health indicator (HI) is invoked to describe and model the entire degradation procedure from the intact state to a series of different degraded states. Such HI-derived information can assist in predicting the remaining useful life for a bearing. Many HI construction models have been developed. Shen et al. studied root-mean-square (RMS) analysis to determine the useful degradation characteristics of bearings [4]. Lei et al. also used RMS analysis and constructed an HI to evaluate the abrasion status of bearings [5]. Kosasih et al. used the RMS and kurtosis to detect bearing-status after a low-frequency filter had been applied to the ∗ Corresponding author. E-mail addresses: fanxu8@cityu.edu.hk (F. Xu), zhuang44@cityu.edu.hk (Z. Huang). original vibration signal. Tse et al. used various time–frequency indicators with principal component analysis (PCA) to build an HI construct model. Accordingly, time–frequency indicators, in- cluding RMS, kurtosis, and variance, were used to calculate the original vibrational signal. PCA was then used to reduce the dimension of the extracted feature vector, and the first principal component was selected as the extracted degradation trend and used to construct HI [6]. Yan et al. used approximate entropy (AE) and permutation entropy (PE) to build an HI and achieved good results [7,8]. Ye et al. also used PE to extract the vibrational signal fault-feature to diagnose faults [9]. Because the vibration signal has nonlinear and random complexity, these time–frequency statistical indicators cannot adaptively decompose the vibrational signal. However, empirical mode decomposition (EMD) can adaptively disinte- grate the signal into a series of intrinsic mode functions (IMFs). Rai et al. devised a combined method based on EMD, singular- value decomposition (SVD), and K-medoids to construct an HI for bearing performance-assessment and showed that this model was superior to RMS, kurtosis, and K-means approaches [10]. However, even though these traditional HI construction mod- els yielded good results, they also presented some challenges. First, prior knowledge is needed to understand the collected https://doi.org/10.1016/j.asoc.2020.106119 1568-4946/© 2020 Elsevier B.V. All rights reserved.