Estimation of non-statistical uncertainty in precision measurement using grey system theory

Abstract

A new uncertainty assessment method is proposed to characterize non-statistical uncertainties in precision measurement. The proposed method is based on grey system theory to address the problem involved in uncertainty assessment where the sampling size is small and the distribution of the data is unknown. The advantage of the proposed approach is that the requirements of the statistics based methods are removed. In the proposed method, an accumulated true size vector and an accumulated measurement data vector are established to reduce the effects of the errors in the measurement and in the numerical calculation. The uncertainty assessment is based on the l ¥ norm of the difference between the accumulation of the sorted measurement data vector and that of the true size vector. A number of computational and experimental tests were carried out. The results demonstrated the effectiveness and consistency of the proposed method in non-statistical uncertainty assessment, compared with the existing methods.

Outlier Detection and Correction for the Deviations of Tooth Profiles of Gears

“…These methods require that the deviations conform to the Gaussian distribution or other known distribution, but the deviations of tooth profiles do not conform to the known distribution. Recently, more and more researchers have been focusing on the method of outlier detection and correction based on the grey system theory, because this method does not require the data to conform to the known distribution [13][14][15]. Meng proposes an outlier detection method based on the GM(1,1) model to detect the abnormal data during dynamic measurement of discontinuous surfaces [16].…”