Mode determination in variational mode decomposition and its application in fault diagnosis of rolling element bearings

The non-stationary nature of bearing vibrations makes it difficult to extract features from the real-time signature of faulty rolling element bearings (REBs). The present work suggests to improve the diagnostic accuracy of fault detection in REBs by enhancing the mode selection property of variational mode decomposition, manipulating its initialization and input parameters (bandwidth selection parameter, α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document} and the number of modes, k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}) and then extracting energy entropy features and using cross-validation in support vector machine (SVM) classifier. The alpha values and the number of modes are varied from (100, 1000000) and (4, 10), respectively. Mean absolute error (MAE) is used as the indicator which calculates error values obtained between the respective sum of modes and the original signal. The particular α-k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha - k$$\end{document} combination with the least MAE value is chosen. The above method is tested using REB signals obtained from the bearing prognostics test rig. The results obtained from the proposed approach shows 100% diagnostic accuracy in detecting faulty REB vibration signature using five-fold cross-validation in SVM classifier.