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Clonal optimization-based negative selection algorithm with applications in motor fault detection

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Abstract

The Negative Selection Algorithm (NSA) and clonal selection method are two typical kinds of artificial immune systems. In this paper, we first introduce their underlying inspirations and working principles. It is well known that the regular NSA detectors are not guaranteed to always occupy the maximal coverage of the nonself space. Therefore, we next employ the clonal optimization method to optimize these detectors so that the best anomaly detection performance can be achieved. A new motor fault detection scheme using the proposed NSA is also presented and discussed. We demonstrate the efficiency of our approach with an interesting example of motor bearings fault detection, in which the detection rates of three bearings faults are significantly improved.

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Acknowledgments

This research work was funded by the Academy of Finland under Grants 214144 and 124721. The authors would like to thank the anonymous reviewers for their insightful comments and constructive suggestions that have improved the paper.

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Authors and Affiliations

  1. Department of Electrical Engineering, Helsinki University of Technology, Otakaari 5 A, 02150, Espoo, Finland

    X. Z. Gao, S. J. Ovaska & X. Wang

  2. Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC, 27695, USA

    M.-Y. Chow

Authors
  1. X. Z. Gao
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  2. S. J. Ovaska
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  3. X. Wang
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  4. M.-Y. Chow
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Corresponding author

Correspondence to X. Z. Gao.

Appendix

Appendix

Detectors generated in the regular NSA:

$$ \left[ {\begin{array}{*{20}c} { - 0. 0 7 8 9} & { 0. 0 7 6 6} & { - 0. 0 9 1 9} & { 0. 0 9 8 4} & { 0. 0 7 6 2} & { 0. 0 6 9 2} & { 0. 0 7 8 4} & { - 0. 0 8 5 2} & { 0. 0 9 6 3} & { 0. 0 9 5 3} \\ { 0. 0 9 4 5} & { 0. 0 8 8 7} & { 0. 0 9 6 5} & { - 0. 0 9 8 9} & { - 0. 0 8 1 3} & { 0. 0 6 7 9} & { 0. 0 8 1 7} & { - 0. 0 2 6 4} & { - 0. 0 9 0 2} & { 0. 0 9 6 1} \\ { - 0. 0 6 5 4} & { 0. 0 9 7 6} & { - 0. 0 7 4 6} & { 0. 0 8 1 6} & { 0. 0 9 9 8} & { 0. 0 9 6 0} & { 0. 0 3 4 2} & { - 0. 0 9 0 1} & { 0. 0 9 0 6} & { 0. 0 7 3 2} \\ { 0. 0 8 7 1} & { 0. 0 8 7 8} & { - 0. 0 9 6 0} & { 0. 0 6 5 3} & { 0. 0 9 1 9} & { - 0. 0 7 7 4} & { 0. 0 8 0 4} & { 0. 0 8 9 6} & { 0. 0 9 4 0} & { 0. 0 5 8 5} \\ { 0. 0 7 9 5} & { 0. 0 9 8 7} & { 0. 0 9 1 1} & { 0 . 0 8 8 7} & { 0. 0 6 6 7} & { 0. 0 6 2 4} & { 0. 0 9 9 8} & { - 0. 0 2 8 2} & { 0. 0 7 8 0} & { 0. 0 6 4 9} \\ { 0. 0 9 9 7} & { 0. 0 4 8 3} & { 0. 0 9 1 8} & { 0. 0 7 0 7} & { 0. 0 9 8 0} & { - 0. 0 9 3 9} & { 0. 0 5 7 2} & { 0. 0 6 7 9} & { 0. 0 6 1 2} & { 0. 0 9 8 4} \\ { 0. 0 9 5 6} & { 0. 0 9 7 6} & { - 0. 0 5 8 9} & { 0. 0 5 1 6} & { 0. 0 7 1 8} & { 0. 0 9 5 9} & { 0. 0 9 2 0} & { 0. 0 6 1 9} & { - 0. 0 5 2 2} & { 0. 0 9 4 3} \\ { - 0. 0 8 7 3} & { 0. 0 7 1 5} & { - 0. 0 7 5 8} & { - 0. 0 9 4 8} & { 0. 0 9 2 5} & { - 0. 0 9 2 6} & { 0. 0 9 9 3} & { 0. 0 6 5 3} & { 0. 0 7 1 9} & { 0. 0 9 6 8} \\ { - 0. 0 2 5 0} & { 0. 0 9 2 0} & { 0. 0 8 9 8} & { 0. 0 9 9 2} & { - 0. 0 1 6 5} & { 0. 0 6 1 9} & { 0. 0 7 8 8} & { - 0. 0 9 9 1} & { 0. 0 8 4 3} & { 0. 0 9 8 5} \\ { 0. 0 5 0 6} & { 0. 0 5 8 5} & { 0. 0 2 4 9} & { 0. 0 9 9 6} & { 0 . 0 9 9 9} & { 0. 0 9 5 9} & { 0. 0 9 9 0} & { - 0. 0 0 9 7} & { 0. 0 9 0 0} & { 0. 0 9 7 3} \\ \end{array} } \right] $$

Clonal optimized detectors for single bearings fault detection:

$$ \begin{gathered} \left[ {\begin{array}{*{20}c} { - 0. 0 6 5 1} & { 0. 0 9 7 9} & { - 0. 0 7 4 7 } & { 0. 0 8 0 7} & { 0. 0 9 8 1} & { 0. 0 9 5 5} & { 0. 0 3 4 1} & { - 0. 0 9 0 9} & { 0. 0 8 9 7} & { 0 . 0 7 2 3} \\ { 0. 0 9 5 9} & { 0. 0 8 8 3} & { - 0. 1 0 0 5} & { 0. 0 9 3 6} & { 0. 0 7 3 0} & { - 0. 0 8 1 1} & { 0. 1 0 0 9} & { - 0. 0 8 0 6} & { 0. 0 3 6 8} & { - 0. 0 7 3 7} \\ { - 0. 0 7 0 2} & { 0. 0 9 5 1} & { - 0. 0 9 4 1} & { 0. 0 9 1 4} & { - 0. 0 6 5 1} & { 0. 0 8 9 5} & { 0. 0 7 7 4} & { - 0. 0 9 6 1} & { 0. 0 8 6 7} & { 0. 0 5 5 7} \\ { 0. 0 9 6 6} & { - 0. 0 9 7 7} & { 0. 0 8 0 9} & { 0. 0 9 8 0} & { - 0. 0 3 7 4} & { - 0. 0 2 8 8} & { 0. 0 9 7 1} & { 0. 0 8 0 6} & { - 0. 0 8 3 7} & { 0. 0 9 6 3} \\ { 0. 0 8 0 1} & { - 0. 0 6 3 8} & { - 0. 0 9 2 1} & { 0. 0 9 0 5} & { - 0. 0 8 6 0} & { 0 . 0 8 7 4} & { - 0. 0 7 9 3} & { 0. 0 9 7 0} & { 0. 0 5 8 3} & { 0. 0 8 6 1} \\ { 0. 0 8 1 3} & { 0. 0 9 7 4} & { 0. 0 9 7 8} & { - 0. 0 9 0 6} & { 0. 0 9 7 3} & { 0. 0 0 4 0} & { - 0. 0 9 9 6} & { - 0. 0 6 3 4} & { 0. 0 8 9 8} & { 0. 0 6 8 5} \\ { 0. 0 9 0 2} & { - 0. 0 8 9 6} & { 0. 0 6 4 9} & { 0. 0 8 5 6} & { - 0. 0 9 3 9} & { 0. 0 9 6 5} & { - 0. 0 9 9 0} & { 0. 0 1 7 3} & { - 0. 0 9 8 5} & { 0. 0 8 5 7} \\ { - 0. 0 9 1 4} & { 0. 1 0 0 2} & { - 0. 0 4 3 8} & { - 0. 0 2 1 4} & { - 0. 0 8 3 8} & { 0. 0 9 1 5} & { 0. 0 9 0 9} & { - 0. 0 8 9 5} & { 0. 0 9 5 1} & { 0. 0 9 8 9} \\ { 0. 0 9 3 3} & { 0. 0 7 5 1} & { - 0. 0 9 4 8} & { 0. 0 9 5 3} & { 0. 0 7 2 1} & { - 0. 0 8 9 5} & { 0. 0 9 3 1} & { - 0. 0 4 1 3} & { - 0. 0 9 0 0} & { 0. 0 8 3 6} \\ { 0. 0 5 4 5} & { 0. 0 9 3 6} & { - 0. 0 7 8 7} & { 0. 0 7 8 3} & { 0. 0 5 9 8} & { 0. 0 8 3 9} & { 0. 0 9 3 8} & { - 0. 0 9 3 4} & { 0. 0 7 8 5} & { - 0. 0 9 1 2} \\ \end{array} } \right] \hfill \\ \hfill \\ \end{gathered} $$

Clonal optimized detectors for dual bearings fault detection:

$$ \left[ {\begin{array}{*{20}c} { - 0. 0 6 5 4} & { 0. 0 9 7 3} & { - 0. 0 7 4 6} & { 0. 0 8 1 6} & { 0. 0 9 9 8} & { 0. 0 9 6 1} & { 0. 0 3 4 3} & { - 0. 0 9 0 2} & { 0. 0 9 0 5} & { 0. 0 7 2 9} \\ { 0. 0 9 4 5} & { 0. 0 8 8 4} & { - 0. 0 9 8 4} & { 0. 0 9 2 3} & { 0. 0 7 4 4} & { - 0. 0 8 1 5} & { 0. 0 9 9 9} & { - 0. 0 8 2 1} & { 0. 0 3 6 5} & { - 0. 0 7 2 1} \\ { - 0. 0 7 0 2} & { 0. 0 9 5 1} & { - 0. 0 9 4 2} & { 0. 0 9 2 1} & { - 0. 0 6 3 6} & { 0. 0 8 9 2} & { 0. 0 7 6 8} & { - 0. 0 9 5 6} & { 0. 0 8 7 2} & { 0. 0 5 6 7} \\ { 0. 0 9 6 7} & { - 0. 0 9 6 7} & { 0. 0 8 1 5} & { 0. 0 9 6 8} & { - 0. 0 3 5 9} & { - 0. 0 2 9 5} & { 0. 0 9 8 6} & { 0. 0 8 2 0} & { - 0 . 0 8 4 6} & { 0. 0 9 5 4} \\ { 0. 0 7 9 5} & { - 0. 0 6 5 4} & { - 0. 0 9 3 0} & { 0. 0 9 3 3} & { - 0. 0 8 5 5} & { 0. 0 8 6 4} & { - 0 . 0 8 0 3} & { 0. 0 9 9 1} & { 0. 0 5 8 4} & { 0. 0 8 8 2} \\ { 0. 0 7 9 5} & { 0. 0 9 9 4} & { 0. 0 9 9 2} & { - 0. 0 8 9 6} & { 0. 0 9 8 1} & { 0. 0 0 3 7} & { - 0 . 0 9 8 4} & { - 0. 0 6 3 2} & { 0. 0 8 9 5} & { 0. 0 6 9 0} \\ { 0. 0 9 2 2} & { - 0. 0 8 6 1} & { 0. 0 6 2 6} & { 0. 0 8 4 5} & { - 0. 0 9 7 9} & { 0. 0 9 6 9} & { - 0 . 0 9 6 9} & { 0. 0 1 5 1} & { - 0 . 0 9 8 8} & { 0. 0 8 4 5} \\ { - 0. 0 9 2 0} & { 0. 0 9 9 8} & { - 0. 0 4 2 9} & { - 0. 0 2 1 4} & { - 0. 0 8 4 4} & { 0. 0 9 0 1} & { 0. 0 9 2 4} & { - 0. 0 8 8 3} & { 0. 0 9 4 6} & { 0. 0 9 9 6} \\ { 0. 0 9 1 4} & { 0. 0 7 6 6} & { - 0. 0 9 5 4} & { 0. 0 9 6 7} & { 0. 0 7 5 6} & { - 0. 0 9 0 6} & { 0. 0 9 4 2} & { - 0. 0 4 2 2} & { - 0 . 0 9 0 2} & { 0. 0 8 4 2} \\ { 0. 0 5 9 0} & { 0. 0 9 6 8} & { - 0. 0 7 6 1} & { 0. 0 8 1 2} & { 0. 0 6 1 9} & { 0. 0 8 6 5} & { 0. 0 9 6 6} & { - 0 . 0 9 4 9} & { 0. 0 8 1 9} & { - 0. 0 9 5 2} \\ \end{array} } \right] $$

Clonal optimized detectors for triple bearings fault detection:

$$ \left[ {\begin{array}{*{20}c} { - 0. 0 6 5 2} & { 0. 0 9 7 3} & { - 0. 0 7 4 7} & { 0. 0 8 1 5} & { 0. 0 9 9 8} & { 0. 0 9 5 9} & { 0. 0 3 4 2} & { - 0. 0 9 0 1} & { 0. 0 9 0 3} & { 0. 0 7 3 1} \\ { 0. 0 9 4 5} & { 0. 0 8 8 5} & { - 0. 0 9 8 4} & { 0. 0 9 2 2} & { 0. 0 7 4 3} & { - 0. 0 8 1 5} & { 0. 0 9 9 8} & { - 0. 0 8 2 1} & { 0. 0 3 6 6} & { - 0. 0 7 2 3} \\ { - 0. 0 6 9 6} & { 0. 0 9 5 4} & { - 0. 0 9 3 7} & { 0. 0 9 2 0} & { - 0. 0 6 4 6} & { 0. 0 8 9 1} & { 0. 0 7 7 1} & { - 0. 0 9 6 1} & { 0. 0 8 6 6} & { 0. 0 5 6 7} \\ { 0. 0 9 7 5} & { - 0. 0 9 7 4} & { 0. 0 8 2 3} & { 0. 0 9 7 9} & { - 0. 0 3 6 7} & { - 0. 0 2 8 0} & { 0. 0 9 9 0} & { 0. 0 8 3 1} & { - 0. 0 8 4 9} & { 0. 0 9 6 1} \\ { 0. 0 7 9 5} & { - 0. 0 6 5 5} & { - 0. 0 9 2 9} & { 0. 0 9 3 2} & { - 0. 0 8 5 5} & { 0. 0 8 6 5} & { - 0. 0 8 0 3} & { 0. 0 9 9 1} & { 0. 0 5 8 4} & { 0. 0 8 8 2} \\ { 0. 0 9 6 6} & { - 0. 0 6 9 3} & { 0. 0 9 6 4} & { - 0. 0 9 5 5} & { 0. 0 8 0 3} & { 0. 0 3 1 1} & { 0. 0 8 1 6} & { 0. 0 5 9 9} & { 0. 0 9 1 4} & { 0. 0 9 8 1} \\ { 0. 0 9 2 8} & { - 0. 0 9 3 2} & { 0. 0 8 6 2} & { - 0. 0 6 7 6} & { - 0. 0 9 2 6} & { 0. 0 9 7 1} & { 0. 0 9 7 3} & { - 0. 0 3 4 1} & { 0. 0 9 9 9} & { 0. 0 8 1 2} \\ { - 0. 0 9 1 7} & { 0. 0 9 9 0} & { - 0. 0 4 1 8} & { - 0. 0 2 1 5} & { - 0. 0 8 4 1} & { 0. 0 8 9 2} & { 0. 0 9 1 5} & { - 0. 0 8 8 1} & { 0. 0 9 4 1} & { 0. 0 9 8 4} \\ { 0. 0 9 2 4} & { 0. 0 7 6 5} & { - 0. 0 9 6 6} & { 0. 0 9 7 2} & { 0. 0 7 5 7} & { - 0. 0 9 0 8} & { 0. 0 9 5 5} & { - 0. 0 4 2 0} & { - 0. 0 9 0 4} & { 0. 0 8 4 4} \\ { 0. 0 5 9 1} & { 0. 0 9 7 0} & { - 0. 0 7 6 2} & { 0. 0 8 1 3} & { 0. 0 6 1 8} & { 0. 0 8 6 5} & { 0. 0 9 6 5} & { - 0. 0 9 5 1} & { 0. 0 8 1 6} & { - 0. 0 9 5 3} \\ \end{array} } \right] $$

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Gao, X.Z., Ovaska, S.J., Wang, X. et al. Clonal optimization-based negative selection algorithm with applications in motor fault detection. Neural Comput & Applic 18, 719–729 (2009). https://doi.org/10.1007/s00521-009-0276-9

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