Norm theory of error separation and its application to harmonic distribution parameters of rolling bearing surfaces

Xintao Xia; Xiaoyang Chen; Zhongyu Wang; Yongzhen Zhang

doi:10.1117/12.717139

24 October 2006 Norm theory of error separation and its application to harmonic distribution parameters of rolling bearing surfaces

Xintao Xia, Xiaoyang Chen, Zhongyu Wang, Yongzhen Zhang

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Proceedings Volume 6357, Sixth International Symposium on Instrumentation and Control Technology: Signal Analysis, Measurement Theory, Photo-Electronic Technology, and Artificial Intelligence; 63572M (2006) https://doi.org/10.1117/12.717139
Event: Sixth International Symposium on Instrumentation and Control Technology, 2006, Beijing, China

Abstract

Error separation technologies are widely used in practical engineering. Many methods such as least squares techniques, Kalman filtering, three-probe method, so on and so forth are adopted in error separation technologies. However, It has been proved that these methods above can be disturbed by the outlier of measured data and is likely to induce a biased estimation. Therefore a new method of error separation in data analysis is introduced in this paper by developing the minimum norm solution to estimation of nonlinear parameter vector. Three norms, i.e. 1-norm, 2-norm and ∞-norm, are proposed to establish the equation of error separation. As an application of this method, estimation of harmonic distribution parameters of rolling bearing raceway surfaces is studied in this paper. Experimental investigation by this method shows that the bug of least-squares method can be avoided by efficiently deadening the disturbing errors of the outlier of measuring data and the nature character of measured data can then be reflected truly, that unbiased estimate of distribution characteristics can be achieved and standard deviation through this method can then be less than that through linear least squares techniques. The feasibility of the proposed method is validated by experiments on harmonic distribution parameters of rolling bearing raceway surfaces.

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Xintao Xia, Xiaoyang Chen, Zhongyu Wang, and Yongzhen Zhang "Norm theory of error separation and its application to harmonic distribution parameters of rolling bearing surfaces", Proc. SPIE 6357, Sixth International Symposium on Instrumentation and Control Technology: Signal Analysis, Measurement Theory, Photo-Electronic Technology, and Artificial Intelligence, 63572M (24 October 2006); https://doi.org/10.1117/12.717139

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KEYWORDS

Error analysis

Data analysis

Electronic filtering

Filtering (signal processing)

Control systems design

Numerical analysis

Astronomical engineering

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