Monitoring Fault Condition During Manufacturing Using The Karhunen-Loève Transform

Monitoring the condition of parts and machine components is a crucial task in ensuring fault-free manufacturing. In this work, we propose an alternative condition monitoring technique, with great potential in extracting and isolating individual fault patterns from manufacturing signals. We propose that the Karhunen-Lo eve transform provides the ability to decompose measured signals into decorrelated fault patterns, in the form of fundamental eigenvectors. These fundamental eigenvectors can then be monitored by means of coeecient vectors, which indicate any changes in the fault patterns. The technique can provide accurate fault information, whether the manufacturing signals are deterministic, stochastic, stationary, or nonstation-ary. This paper presents the fundamentals of the proposed technique and its extension to condition monitoring. The outputs of the Karhunen-Lo eve transform are studied to interpret their physical signiicance. Then, a subset of general manufacturing signals is used to understand the mathematical foundations of the technique. Extensions to general functions are investigated by means of numerical simulations. The technique proposed in this paper has great potential in providing a robust condition monitoring tool.

[1]  S. Zahorian.  Principal‐Components Analysis for Low Redundancy Encoding of Speech Spectra , 1979 .

[2]  David J. Whitehouse,et al.  The use of dual space-frequency functions in machine tool monitoring , 1992 .

[3]  Kristin L. Wood,et al.  Characterization of surface fault patterns with application to a layered manufacturing process , 1998 .

[4]  H. Saunders,et al.  Mechanical Signature Analysis—Theory and Applications , 1988 .

[5]  W. Steckelmacher.  Handbook of surface metrology , 1995 .

[6]  M. Hundal.  Mechanical signature analysis , 1983 .

[7]  M.J. Ready,et al.  Transform representation of the spectra of acoustic speech segments with applications. I. General approach and application to speech recognition , 1993, IEEE Trans. Speech Audio Process..

[8]  L Sirovich,et al.  Low-dimensional procedure for the characterization of human faces. , 1987, Journal of the Optical Society of America. A, Optics and image science.

[9]  Liangsheng Qu,et al.  Vibrational diagnosis of machine parts using the wavelet packet technique , 1994 .

[10]  Orthogonal transforms for digital signal processing , 1978, Proceedings of the IEEE.

[11]  Irem Y. Tumer,et al.  Improving Manufacturing Precision Using the Karhunen-lo Eve Transform Improving Part Production in Manufacturing Detection of Faults for Manufacturing and Design Motivation and Current Focus , 2007 .

[12]  Dan Luss,et al.  Proper orthogonal decomposition analysis of spatiotemporal temperature patterns , 1993 .

[13]  W. Kozek,et al.  Matched generalized Gabor expansion of nonstationary processes , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[14]  J. Sottile,et al.  An overview of fault monitoring and diagnosis in mining equipment , 1994 .

[15]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[16]  Melvin J. Hinich,et al.  Monitoring Rotating Tool Wear Using Higher-Order Spectral Features , 1993 .