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

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.