Decomposition in blocks at the level of wavelet coefficients and T（1 ） theorem on Hardy space

This paper deals with the establishment of \%T(1)\% theorem on Hardy space \%H 1\% under condition of weak regularity. An operator or a function is identified on the basis of their wavelet coefficients which are regrouped on some blocks. The actions of each block operator (pseudo\|annular operator) on each block function (atom) are exactly analyzed to establish \%T(1)\% theorem on Hardy space.

Quantitative Diagnosis of Fault Severity Trend of Rolling Element Bearings

The condition monitoring and fault diagnosis of rolling element bearings are particularly crucial in rotating mechanical applications in industry. A bearing fault signal contains information not only about fault condition and fault type but also the severity of the fault. This means fault severity quantitative analysis is one of most active and valid ways to realize proper maintenance decision. Aiming at the deficiency of the research in bearing single point pitting fault quantitative diagnosis, a new back-propagation neural network method based on wavelet packet decomposition coefficient entropy is proposed. The three levels of wavelet packet coefficient entropy（WPCE） is introduced as a characteristic input vector to the BPNN. Compared with the wavelet packet decomposition energy ratio input vector, WPCE shows more sensitive in distinguishing from the different fault severity degree of the measured signal. The engineering application results show that the quantitative trend fault diagnosis is realized in the different fault degree of the single point bearing pitting fault. The breakthrough attempt from quantitative to qualitative on the pattern recognition of rolling element bearings fault diagnosis is realized.

Development of Instrument Control System Using Biosignals Created by the Change of Eyes Movement Sequence

A new biosi gn al control system that offers the disables the opportunities to control electric appliances is proposed.The four types of signals created by the eyes movements in four directions(up,down,left,and right),which are taken as four basic signals , are detected at the forehead.Permutation of 2 signals out of them creates 16 d ifferent signals.Permutation of 3 signals out of them creates 64 signals.They al l amounts to 84 control signals.They are thought to be applicable for the operat ion of some instruments.Furthermore,the dynamic biosignals created by the slow e yes movement is speculated to be applicable for the more convenient control of t hem.

TESTING FOR OUTLIERS IN TIME SERIES USING WAVELETS

One remarkable feature of wavelet decomposition is that the waveletcoefficients are localized, and any singularity in the input signals can only affect the waveletcoefficients at the point near the singularity. The localized property of the wavelet coefficientsallows us to identify the singularities in the input signals by studying the wavelet coefficients atdifferent resolution levels. This paper considers wavelet-based approaches for the detection ofoutliers in time series. Outliers are high-frequency phenomena which are associated with the waveletcoefficients with large absolute values at different resolution levels. On the basis of thefirst-level wavelet coefficients, this paper presents a diagnostic to identify outliers in a timeseries. Under the null hypothesis that there is no outlier, the proposed diagnostic is distributedas a χ_1~2. Empirical examples are presented to demonstrate the application of the proposeddiagnostic.

Transient Mould Friction Based on the Wavelet Theory

The mould friction is an important parameter reflecting the initial shell and mould lubrication conditions.The research of mould friction is very important to the optimization and developing of continuous casting.The measured mould friction under hydraulic oscillation mode was researched with wavelet analysis to reveal its time-frequency characteristics.Firstly,the mould friction signals under different production conditions were monitored and the mould friction was calculated.Then,mother wavelet function was selected from three wavelet functions which were chosen preliminary according to the characteristics of mould friction and wavelet theory.Through wavelet transformation,mould friction signal was projected onto the wavelet domain,and the time-frequency characteristics of mould friction under different production conditions were obtained and discussed.Mould friction under different production conditions such as different oscillation mode,casting speed fluctuation,increasing and decreasing stage of casting speed and breakout occurrence was reported in detail in the wavelet time-frequency maps.The characteristics of mould friction were reflected well through wavelet transformation which proved that wavelet analysis had a good feasibility for mould friction study and can further reveal the nature of mould friction.

A robust object tracking framework based on a reliable point assignment algorithm

Visual tracking, which has been widely used in many vision fields, has been one of the most active research topics in computer vision in recent years. However, there are still challenges in visual tracking, such as illumination change, object occlu- sion, and appearance deformation. To overcome these difficulties, a reliable point assignment （RPA） algorithm based on wavelet transform is proposed. The reliable points are obtained by searching the location that holds local maximal wavelet coefficients. Since the local maximal wavelet coefficients indicate high variation in the image, the reliable points are robust against image noise, illumination change, and appearance deformation. Moreover, a Kalman filter is applied to the detection step to speed up the detection processing and reduce false detection. Finally, the proposed RPA is integrated into the tracking-learning-detection （TLD） framework with the Kalman filter, which not only improves the tracking precision, but also reduces the false detections. Experimental results showed that the new framework outperforms TLD and kernelized correlation filters with respect to precision, f-measure, and average overlap in percent.