METHODOLOGIES AND APPLICATION Fault diagnosis of rolling element bearing by using multinomial logistic regression and wavelet packet transform D. H. Pandya • S. H. Upadhyay • S. P. Harsha Ó Springer-Verlag Berlin Heidelberg 2013 Abstract This paper is focused on comparison of effec- tiveness of artificial intelligence (AI) techniques in fault diagnosis of rolling element bearings. The features for classification are extracted through wavelet packet decomposition using RBIO 5.5 wavelet. The whole clas- sification is done using two features: energy and Kurtosis. The data samples for classification are taken with reference to a healthy bearing, thus, minimizing the errors from the experimental set-up. Four bearing conditions such as bearing with outer race defect, inner race defect, ball defect and combined defect on outer race, inner race and ball have been used in this paper. Localized defects of micron level are induced through laser machining. The effectiveness of three AI techniques viz. ANN, SVM and multinomial logistic regression are compared. The results show that the Logistic Regression technique is the more effective than other two techniques as ANN and SVM. Keywords Energy  Kurtosis  Wavelet packet decomposition  ANN  SVM  Multinomial logistic regression 1 Introduction Rolling element bearings have wide applications ranging from heavy rotating machineries to small hand-held devi- ces. Fault diagnosis is a type of classification problem and artificial intelligence techniques based classifiers, which can be effectively used to classify normal and faulty machine conditions. Fault diagnosis of these bearings and subsequent replacement prevents the machinery breakdown and accidents. By comparing the signals of a machine running in normal and faulty conditions, the detection of faults is possible. There have been several attempts to use supervised or unsupervised machine learning approaches for fault diagnoses of bearing extracting features using different wavelet and different feature selection methods to identify the best suitable classifier and valuable features. Samanta and Al-Balushi (2003) have presented a pro- cedure for fault diagnosis of rolling element bearings through artificial neural network (ANN). The characteristic features of time-domain vibration signals of the rotating machinery with normal and defective bearings have been used as inputs to the ANN. Lin and Qu (2000) have mentioned that to analyze vibration signals and extract features, different techniques such as time domain, fre- quency domain and time–frequency domain are exten- sively used. In time-domain, the interpretation of the signal was done through several parameters. Some of the parameters are: RMS, crest factor, peak, probability density function, along-with the second, third and fourth order statistical moments, which can be extracted from vibration signal, which was performed by Kankar et al. (2011a, b). Whereas, in frequency domain based analysis Fourier transformations were employed to transform time domain signals into frequency domain. The key point in both the analysis techniques was that the direct use of informational Communicated by D. Liu. D. H. Pandya (&)  S. H. Upadhyay  S. P. Harsha Vibration and Noise Control Lab, Mechanical and Industrial Engineering Department, Indian Institute of Technology Roorkee, Roorkee 247 667, India e-mail: veddhrumi@gmail.com S. H. Upadhyay e-mail: shumefme@iitr.ernet.in S. P. Harsha e-mail: surajfme@iitr.ernet.in 123 Soft Comput DOI 10.1007/s00500-013-1055-1