The relations between Gaussian function and Γ function is revealed first at one dimensional situation. Then, the Fourier transformation of n dimensional Gaussian function is deduced by a lemma. Following th...The relations between Gaussian function and Γ function is revealed first at one dimensional situation. Then, the Fourier transformation of n dimensional Gaussian function is deduced by a lemma. Following the train of thought in one dimensional situation, the relation between n dimensional Gaussian function and Γ function is given. By these, the possibility of arbitrary derivative of an n dimensional Gaussian function being a mother wavelet is indicated. The result will take some enlightening role in exploring the internal relations between Gaussian function and Γ function as well as in finding high dimensional mother wavelets.展开更多
湿法炼锌浸出液中存在多金属组分,如Zn(Ⅱ)和Co(Ⅱ),针对重叠峰分离提出一种基于类Gaussian分布的线性扫描极谱重叠峰分离方法。通过分析线性扫描极谱曲线的特性构造类Gaussian分布作为待分离重叠峰子峰的模型,并利用多分辨率小波分解...湿法炼锌浸出液中存在多金属组分,如Zn(Ⅱ)和Co(Ⅱ),针对重叠峰分离提出一种基于类Gaussian分布的线性扫描极谱重叠峰分离方法。通过分析线性扫描极谱曲线的特性构造类Gaussian分布作为待分离重叠峰子峰的模型,并利用多分辨率小波分解确定各子峰波峰和波谷位置,基于该模型及确定值对重叠峰及其导数峰进行非线性加权最小二乘(nonlinear weighted least squares,NWLS)拟合,根据重构参数将重叠峰分离为独立的子峰,实现该类重叠峰的分离。该类重叠峰分离的结果表明:多分辨率小波分解的分辨误差小于1%,NWLS拟合的分离精度高于96%,本方法可以有效分离Zn(Ⅱ)和Co(Ⅱ)产生的极谱重叠峰。展开更多
During environment testing, the time histories of some dynamic environments follow non-Gaussian distribution. It is always assumed that the random vibration simulated follows Gaussian distribution, because the traditi...During environment testing, the time histories of some dynamic environments follow non-Gaussian distribution. It is always assumed that the random vibration simulated follows Gaussian distribution, because the traditional digital random vibration control system can only supply the random vibration excitation signal of Gaussian. Yo simulate the real environment of product, a method is developed in this paper that can generate non-Gaussian random signal with specified power spectrum density （PSD）, skewness and kurtosis by shot noise. In this way, non-Gaussian random vibration can be produced on traditional electrodynamic shaker. It solves the problems of spectral valley and energy shortage in low frequency on omni-axis shaker. At last, the wavelet is used to analyze the non-Gaussian signal展开更多
An approach to identification of linear continuous-time system is studied with modulating functions. Based on wavelet analysis theory, the multi-resolution modulating functions are designed, and the corresponding filt...An approach to identification of linear continuous-time system is studied with modulating functions. Based on wavelet analysis theory, the multi-resolution modulating functions are designed, and the corresponding filters have been analyzed. Using linear modulating filters, we can obtain an identification model that is parameterized directly in continuous-time model parameters. By applying the results from discrete-time model identification to the obtained identification model, a continuous-time estimation method is developed. Considering the accuracy of parameter estimates, an instrumental variable (Ⅳ) method is proposed, and the design of modulating integral filter is discussed. The relationship between the accuracy of identification and the parameter of modulating filter is investigated, and some points about designing Gaussian wavelet modulating function are outlined. Finally, a simulation study is also included to verify the theoretical results.展开更多
A novel model named Multi-scale Gaussian Processes (MGP) is proposed. Motivated by the ideas of multi-scale representations in the wavelet theory, in the new model, a Gaussian process is represented at a scale by a li...A novel model named Multi-scale Gaussian Processes (MGP) is proposed. Motivated by the ideas of multi-scale representations in the wavelet theory, in the new model, a Gaussian process is represented at a scale by a linear basis that is composed of a scale function and its different translations. Finally the distribution of the targets of the given samples can be obtained at different scales. Compared with the standard Gaussian Processes (GP) model, the MGP model can control its complexity conveniently just by adjusting the scale pa-rameter. So it can trade-off the generalization ability and the empirical risk rapidly. Experiments verify the fea-sibility of the MGP model, and exhibit that its performance is superior to the GP model if appropriate scales are chosen.展开更多
文摘The relations between Gaussian function and Γ function is revealed first at one dimensional situation. Then, the Fourier transformation of n dimensional Gaussian function is deduced by a lemma. Following the train of thought in one dimensional situation, the relation between n dimensional Gaussian function and Γ function is given. By these, the possibility of arbitrary derivative of an n dimensional Gaussian function being a mother wavelet is indicated. The result will take some enlightening role in exploring the internal relations between Gaussian function and Γ function as well as in finding high dimensional mother wavelets.
基金Project(2012BAF03B05)supported by the National Key Technology R&D Program of ChinaProject(61025015)supported by the National Natural Science Foundation for Distinguished Young Scholars of China+1 种基金Project(61273185)supported by the National Natural Science Foundation of ChinaProject(2012CK4018)supported by the Science and Technology Project of Hunan Province,China
文摘湿法炼锌浸出液中存在多金属组分,如Zn(Ⅱ)和Co(Ⅱ),针对重叠峰分离提出一种基于类Gaussian分布的线性扫描极谱重叠峰分离方法。通过分析线性扫描极谱曲线的特性构造类Gaussian分布作为待分离重叠峰子峰的模型,并利用多分辨率小波分解确定各子峰波峰和波谷位置,基于该模型及确定值对重叠峰及其导数峰进行非线性加权最小二乘(nonlinear weighted least squares,NWLS)拟合,根据重构参数将重叠峰分离为独立的子峰,实现该类重叠峰的分离。该类重叠峰分离的结果表明:多分辨率小波分解的分辨误差小于1%,NWLS拟合的分离精度高于96%,本方法可以有效分离Zn(Ⅱ)和Co(Ⅱ)产生的极谱重叠峰。
文摘During environment testing, the time histories of some dynamic environments follow non-Gaussian distribution. It is always assumed that the random vibration simulated follows Gaussian distribution, because the traditional digital random vibration control system can only supply the random vibration excitation signal of Gaussian. Yo simulate the real environment of product, a method is developed in this paper that can generate non-Gaussian random signal with specified power spectrum density （PSD）, skewness and kurtosis by shot noise. In this way, non-Gaussian random vibration can be produced on traditional electrodynamic shaker. It solves the problems of spectral valley and energy shortage in low frequency on omni-axis shaker. At last, the wavelet is used to analyze the non-Gaussian signal
基金This project was supported by China Postdoctoral Science Foundation (2003034466)Scientific Research Fund of Hunan Provincial Education Department (02B032).
文摘An approach to identification of linear continuous-time system is studied with modulating functions. Based on wavelet analysis theory, the multi-resolution modulating functions are designed, and the corresponding filters have been analyzed. Using linear modulating filters, we can obtain an identification model that is parameterized directly in continuous-time model parameters. By applying the results from discrete-time model identification to the obtained identification model, a continuous-time estimation method is developed. Considering the accuracy of parameter estimates, an instrumental variable (Ⅳ) method is proposed, and the design of modulating integral filter is discussed. The relationship between the accuracy of identification and the parameter of modulating filter is investigated, and some points about designing Gaussian wavelet modulating function are outlined. Finally, a simulation study is also included to verify the theoretical results.
文摘A novel model named Multi-scale Gaussian Processes (MGP) is proposed. Motivated by the ideas of multi-scale representations in the wavelet theory, in the new model, a Gaussian process is represented at a scale by a linear basis that is composed of a scale function and its different translations. Finally the distribution of the targets of the given samples can be obtained at different scales. Compared with the standard Gaussian Processes (GP) model, the MGP model can control its complexity conveniently just by adjusting the scale pa-rameter. So it can trade-off the generalization ability and the empirical risk rapidly. Experiments verify the fea-sibility of the MGP model, and exhibit that its performance is superior to the GP model if appropriate scales are chosen.
