A bearing fault feature extraction method based on cepstrum pre-whitening and a quantitative law of symplectic geometry mode decomposition

In order to extract the fault feature of the bearing effectively and prevent the impact components caused by bearing damage being interfered with by discrete frequency components and background noise,a method of fault feature extraction based on cepstrum pre-whitening(CPW)and a quantitative law of symplectic geometry mode decomposition(SGMD)is proposed.First,CPW is performed on the original signal to enhance the impact feature of bearing fault and remove the periodic frequency components from complex vibration signals.The pre-whitening signal contains only background noise and non-stationary shock caused by damage.Secondly,a quantitative law that the number of effective eigenvalues of the Hamilton matrix is twice the number of frequency components in the signal during SGMD is found,and the quantitative law is verified by simulation and theoretical derivation.Finally,the trajectory matrix of the pre-whitening signal is constructed and SGMD is performed.According to the quantitative law,the corresponding feature vector is selected to reconstruct the signal.The Hilbert envelope spectrum analysis is performed to extract fault features.Simulation analysis and application examples prove that the proposed method can clearly extract the fault feature of bearings.

Trends in precipitation over the low latitude highlands of Yunnan, China

The precipitation regime of the low latitude highlands of Yunnan in Southwest China is subject to the interactions between the East Asian Summer Monsoon and the Indian Summer Monsoon, and the influence of surface orography. An understanding of changes in its spatial and temporal patterns is urgently needed for climate change projection, hydrologi- cal impact modelling, and regional and downstream water resources management. Using daily precipitation records of the low latitude highlands over the last several decades （1950s-2007）, a time series of precipitation indices, including annual precipitation, number of rainy days, mean annual precipitation intensity, the dates of the onset of the rainy season, degree and period of precipitation seasonal concentration, the highest 1-day, 3-day and 7-day precipitation, and precipitation amount and number of rainy days for precipitation above dif- ferent intensities （such as 〉~10 mm, 〉~25 mm and 〉~50 mm of daily precipitation）, was con- structed. The Trend-Free Pre-Whitening Mann-Kendall trend test was then used to detect trends of the time series data. The results show that there is no significant trend in annual precipitation and strong seasonal differentiation of precipitation trends across the low latitude highlands. Springs and winters are getting wetter and summers are getting drier. Autumns are getting drier in the east and wetter in the west. As a consequence, the seasonality of pre- cipitation is weakening slightly. The beginning of the rainy season and the period of the highest precipitation tend to be earlier. In the meantime, the low latitude highlands has also witnessed less rainy days, more intense precipitation, slightly longer moderate and heavy precipitation events, and more frequent extreme precipitation events. Additionally, regional differentiation of precipitation trends is remarkable. These variations may be associated with weakening of the East Asian summer monsoon and strengthening of the South Asian summer monsoon, as well as the ＂corridor-barrier＂ effects of special mountainous terrain. However, the physical mechanisms involved still need to be uncovered in the future.

Natural gradient-based recursive least-squares algorithm for adaptive blind source separation

This paper focuses on the problem of adaptive blind source separation (BSS). First, a recursive least-squares (RLS) whitening algorithm is proposed. By combining it with a natural gradient-based RLS algorithm for nonlinear principle component analysis (PCA), and using reasonable approximations, a novel RLS algorithm which can achieve BSS without additional pre-whitening of the observed mixtures is obtained. Analyses of the equilibrium points show that both of the RLS whitening algorithm and the natural gradient-based RLS algorithm for BSS have the desired convergence properties. It is also proved that the combined new RLS algorithm for BSS is equivariant and has the property of keeping the separating matrix from becoming singular. Finally, the effectiveness of the proposed algorithm is verified by extensive simulation results.