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Least Square Fitting for Adaptive Wavelet Generation and Automatic Prediction of Defect Size in the Bearing Using Levenberg–Marquardt Backpropagation

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Abstract

In this communication, an attempt has been made to develop an algorithm for automatic prediction of the size of the bearing defect during operation of a machine. Features for the purpose are meticulously designed so as defect commencement and termination events in the signal could be easily spotted. Information on commencement of defect in the signal, in general, is very weak. It is enhanced by approximating the burst in the signal to a wavelet, making use of least squares fitting. Levenberg–Marquardt back propagation network is used for prediction of defect size from defect features. The comparison shows that the Levenberg–Marquardt back propagation network outperforms another network in terms of accuracy. The experimental validation of the proposed scheme is carried out for four different defect sizes each for the inner race, outer race, and roller defect. The maximum deviation in the width measurement result is 5.35% which occurs in the case of bearing with roller defect of width 1.12 mm. The performance evaluation of the method is also carried out using t test. The result of t test validates the accuracy of proposed method in the prediction of defect width.

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Acknowledgements

Authors are thankful to Associate Editor for facilitating reviewer’s feedback to the manuscript. The valuable suggestions of anonymous reviewers in improving the manuscript are thankfully acknowledged. The first author, Anil Kumar wants to thank Sant Longowal Institute of Engineering and Technology, Government of India for providing fellowship for this research work.

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Authors and Affiliations

  1. Precision Metrology Laboratory, Department of Mechanical Engineering, Sant Longowal Institute of Engineering and Technology, Longowal, 148 106, India

    Anil Kumar & Rajesh Kumar

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  1. Anil Kumar
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  2. Rajesh Kumar
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Correspondence to Rajesh Kumar.

Appendix 1

Appendix 1

See Table 10.

Table 10 Formula for calculation of bearing defect frequency [28]
Full size table

where n is the number of rollers, \(F_{s}\) is the shaft speed, d is the average roller diameter, D is the pitch circle diameter and \(\varphi \) is the roller contact angle.

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Kumar, A., Kumar, R. Least Square Fitting for Adaptive Wavelet Generation and Automatic Prediction of Defect Size in the Bearing Using Levenberg–Marquardt Backpropagation. J Nondestruct Eval 36, 7 (2017). https://doi.org/10.1007/s10921-016-0385-1

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