作者: Qing Jiang Chen, Yu Ying Wang

摘要: Wavelet analysis has become a popular subject in scientific research during the past twenty years. In this work, we introduce the notion of vector-valued multiresolution analysis and vector-valued multivariate wavelet packets associated with an integer-valued dilation matrix. A novel method for constructing multi-dimen-
-sional vector-valued wavelet packet is presented. Their characteristics are researched by means of operator theory, time-frequency analysis method and matrix theory. Three orthogonality formulas concerning the wavelet packets are established. Orthogonality decomposition relation formulas of the space are derived by constructing a series of subspaces of wavelet packets. Finally, one new orthonormal wavelet packet bases of are constructed from these wavelet packets.

896

作者: Jian Tang Zhao, Jie Li

摘要: In this paper, the notion of orthogonal vector-valued bivariate wavelet packets, which is a generalization of uni-wavelet packets, is introduced. A procedure for constructing them is presented. Their characteristics is investigated by using time-frequency analysis method, matrix theory and finite group theory. Orthogonality formulas are established. Orthonormal wavelet packet bases are obtained.

1184

作者: Qing Jiang Chen, Jian Tang Zhao

摘要: In this work, the notion of vector-valued multiresolution analysis and biort- ogonal vector–valued wavelets is introduced. The existence of finitely supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal finitely supported vector-valued scaling functions is investigated. A new method for construc- -ting a class of biorthogonal finitely supported vector-valued wavelet functions is presented by using multiresolution analysis and matrix theory. A sufficient condition for the existence of multiple pseudoframes for subspaces is derived

323

作者: Zheng Wang, Yan Jun Li, Xiao Wei Sun

摘要: In order to detect and isolate orbiting satellite actuator faults, a decoupling parity space method was extended. The decoupling parity vector was obtained using this method by singular value decomposition. Sometimes this vector may not exist, then by singular value substitution or generalized Eigen value method was used for solving the optimal approximation. The vector can easily make satellite actuator fault detected and isolated. The simulation results showed the effectiveness of the proposed algorithm.

4406

作者: Xiao Yun Gong, Jie Han, Hong Chen, Wen Ping Lei

摘要: Wavelet envelope demodulation method can distinguish the fault information from complex bearing vibration signal. However, traditional signal analysis method, which is solely based on a single source data, is imperfect. In this paper, an approach to wavelet packet and envelope analysis based on full vector spectrum technology was proposed. Firstly, two different data from the same source were respectively decomposed and recomposed by wavelet packet transform. Then, in order to improve the accuracy of detecting fault, the recomposed signals were merged by using the full vector spectrum method. Compared to the traditional signal analysis method, the advantage of the new method is presented by showing their application to bearings. Finally, results from the bearing vibration signal analysis show that the new approach is more effective because of its inheritance and all-sided feature.

873