Although the SSA （singular spectral analysis） is a potential tool for analysing time series of different physical processes, the processing of large geophysical data set requires more time and is found to be computa...Although the SSA （singular spectral analysis） is a potential tool for analysing time series of different physical processes, the processing of large geophysical data set requires more time and is found to be computationally expansive. In particular for the SVD （singular value decomposition） of large trajectory matrix, the processing units require huge memory and high performance computing system. In the present work, we propose an alternative scheme based on WSSA （windowed singular spectral analysis）, which is robust for analysing long data sets without losing any valuable low-frequency information contained in the data. The underlying scheme reduces the floating point operations in SVD computations as the size of the trajectory matrix is small in windowed processing. In order to test the efficiency, the authors applied the proposed method on two geophysical data sets i.e., the climatic record with 30,000 data points and seismic reflection trace with 8,000 data points. The authors have shown that without distorting any physical information, the low-frequency contents of the data are well preserved after the windowed processing in both the cases.展开更多
The problem of speech enhancement using threshold de-noising in wavelet domain was considered.The appropriate decomposition level is another key factor pertinent to de-noising performance.This paper proposed a new wav...The problem of speech enhancement using threshold de-noising in wavelet domain was considered.The appropriate decomposition level is another key factor pertinent to de-noising performance.This paper proposed a new wavelet-based de-noising scheme that can improve the enhancement performance significantly in the presence of additive white Gaussian noise.The proposed algorithm can adaptively select the optimal decomposition level of wavelet transformation according to the characteristics of noisy speech.The experimental results demonstrate that this proposed algorithm outperforms the classical wavelet-based de-noising method and effectively improves the practicability of this kind of techniques.展开更多
In the diagnosis of rotor crack based on wavelet analysis, it is a painful task to find out an adaptive mother wavelet as many of them can be chosen and the analytic results of different mother wavelets are yet not th...In the diagnosis of rotor crack based on wavelet analysis, it is a painful task to find out an adaptive mother wavelet as many of them can be chosen and the analytic results of different mother wavelets are yet not the same. For this limitation of wavelet analysis, a novel diagnostic approach of rotor crack based on multi-scale singular-spectrum analysis （MS-SSA） is proposed. Firstly, a Jeffcott model of a cracked rotor is developed and the forth-order Runge-Kutta method is used to solve the motion equations of this rotor to obtain its time response （signals）. Secondly, a comparatively simple approach of MS-SSA is presented and the empirical orthogonal functions of different orders in various scales are regarded as analyzing functions. At last, the signals of the cracked rotor and an uncracked rotor are analyzed using the proposed approach of MS-SSA, and the simulative results are compared. The results show that, the data-adaptive analyzing functions can capture many features of signals and the rotor crack can be identified and diagnosed effectively by comparing the analytic results of signals of the cracked rotor with those of the uncracked rotor using the analyzing functions of different orders.展开更多
A measuring profile was set up in both sides of the Qiongzhou strait to carry out the simultaneous observation of three component geomagnetic variation. The observed synchronous geomagnetic vertical variations of shor...A measuring profile was set up in both sides of the Qiongzhou strait to carry out the simultaneous observation of three component geomagnetic variation. The observed synchronous geomagnetic vertical variations of short periods were reversed on the both sides of the strait. It means that there is a abnormal concentration of electric current in the area. Spatial wave number domain analysis was performed by Sompi spectral analysis for the spatial distribution and the internal and the external parts of the geomagnetic variation field were separated. Inversion of the internal field was carried out by generalized inverse matrix inversion based on singular value decomposition and the distribution of undergrond current density was obtained. The discussion suggests that this abnormal current concentration comes from current channelling effect in the Quaternary sediment in this region.展开更多
In this paper,a Jacobi-collocation spectral method is developed for a Volterraintegro-differential equation with delay,which contains a weakly singular kernel.We use a function transformation and a variable transforma...In this paper,a Jacobi-collocation spectral method is developed for a Volterraintegro-differential equation with delay,which contains a weakly singular kernel.We use a function transformation and a variable transformation to change the equation into a new Volterra integral equation defined on the standard interval[-1,1],so that the Jacobi orthogonal polynomial theory can be applied conveniently.In order to obtain high order accuracy for the approximation,the integral term in the resulting equation is approximated by Jacobi spectral quadrature rules.In the end,we provide a rigorous error analysis for the proposed method.The spectral rate of convergence for the proposed method is established in both the L^(∞)-norm and the weighted L^(2)-norm.展开更多
文摘Although the SSA （singular spectral analysis） is a potential tool for analysing time series of different physical processes, the processing of large geophysical data set requires more time and is found to be computationally expansive. In particular for the SVD （singular value decomposition） of large trajectory matrix, the processing units require huge memory and high performance computing system. In the present work, we propose an alternative scheme based on WSSA （windowed singular spectral analysis）, which is robust for analysing long data sets without losing any valuable low-frequency information contained in the data. The underlying scheme reduces the floating point operations in SVD computations as the size of the trajectory matrix is small in windowed processing. In order to test the efficiency, the authors applied the proposed method on two geophysical data sets i.e., the climatic record with 30,000 data points and seismic reflection trace with 8,000 data points. The authors have shown that without distorting any physical information, the low-frequency contents of the data are well preserved after the windowed processing in both the cases.
文摘The problem of speech enhancement using threshold de-noising in wavelet domain was considered.The appropriate decomposition level is another key factor pertinent to de-noising performance.This paper proposed a new wavelet-based de-noising scheme that can improve the enhancement performance significantly in the presence of additive white Gaussian noise.The proposed algorithm can adaptively select the optimal decomposition level of wavelet transformation according to the characteristics of noisy speech.The experimental results demonstrate that this proposed algorithm outperforms the classical wavelet-based de-noising method and effectively improves the practicability of this kind of techniques.
基金This project is supported by National Fundamental Research and Development Project Foundation of China(No.G1998020321).
文摘In the diagnosis of rotor crack based on wavelet analysis, it is a painful task to find out an adaptive mother wavelet as many of them can be chosen and the analytic results of different mother wavelets are yet not the same. For this limitation of wavelet analysis, a novel diagnostic approach of rotor crack based on multi-scale singular-spectrum analysis （MS-SSA） is proposed. Firstly, a Jeffcott model of a cracked rotor is developed and the forth-order Runge-Kutta method is used to solve the motion equations of this rotor to obtain its time response （signals）. Secondly, a comparatively simple approach of MS-SSA is presented and the empirical orthogonal functions of different orders in various scales are regarded as analyzing functions. At last, the signals of the cracked rotor and an uncracked rotor are analyzed using the proposed approach of MS-SSA, and the simulative results are compared. The results show that, the data-adaptive analyzing functions can capture many features of signals and the rotor crack can be identified and diagnosed effectively by comparing the analytic results of signals of the cracked rotor with those of the uncracked rotor using the analyzing functions of different orders.
文摘A measuring profile was set up in both sides of the Qiongzhou strait to carry out the simultaneous observation of three component geomagnetic variation. The observed synchronous geomagnetic vertical variations of short periods were reversed on the both sides of the strait. It means that there is a abnormal concentration of electric current in the area. Spatial wave number domain analysis was performed by Sompi spectral analysis for the spatial distribution and the internal and the external parts of the geomagnetic variation field were separated. Inversion of the internal field was carried out by generalized inverse matrix inversion based on singular value decomposition and the distribution of undergrond current density was obtained. The discussion suggests that this abnormal current concentration comes from current channelling effect in the Quaternary sediment in this region.
基金supported by the State Key Program of National Natural Science Foundation of China(11931003)the National Natural Science Foundation of China(41974133,11671157)。
文摘In this paper,a Jacobi-collocation spectral method is developed for a Volterraintegro-differential equation with delay,which contains a weakly singular kernel.We use a function transformation and a variable transformation to change the equation into a new Volterra integral equation defined on the standard interval[-1,1],so that the Jacobi orthogonal polynomial theory can be applied conveniently.In order to obtain high order accuracy for the approximation,the integral term in the resulting equation is approximated by Jacobi spectral quadrature rules.In the end,we provide a rigorous error analysis for the proposed method.The spectral rate of convergence for the proposed method is established in both the L^(∞)-norm and the weighted L^(2)-norm.
