In the present paper, the formulae for matrix Padé-type approximation were improved. The mixed model reduction method of matrix Padé-type-Routh for the multivariable linear systems was presented. A well-know...In the present paper, the formulae for matrix Padé-type approximation were improved. The mixed model reduction method of matrix Padé-type-Routh for the multivariable linear systems was presented. A well-known example was given to illustrate that the mixed method is efficient.展开更多
Matrix Padé approximation is a widely used method for computing matrix functions. In this paper, we apply matrix Padé-type approximation instead of typical Padé approximation to computing the matrix exp...Matrix Padé approximation is a widely used method for computing matrix functions. In this paper, we apply matrix Padé-type approximation instead of typical Padé approximation to computing the matrix exponential. In our approach the scaling and squaring method is also used to make the approximant more accurate. We present two algorithms for computing and for computing with many espectively. Numerical experiments comparing the proposed method with other existing methods which are MATLAB’s functions expm and funm show that our approach is also very effective and reliable for computing the matrix exponential . Moreover, there are two main advantages of our approach. One is that there is no inverse of a matrix required in this method. The other is that this method is more convenient when computing for a fixed matrix A with many t ≥ 0.展开更多
This paper proposes a novel Multivariate Quotient-Difference(MQD)method to obtain the approximate analytical solution for AC power flow equations.Therefore,in the online environment,the power flow solutions covering d...This paper proposes a novel Multivariate Quotient-Difference(MQD)method to obtain the approximate analytical solution for AC power flow equations.Therefore,in the online environment,the power flow solutions covering different operating conditions can be directly obtained by plugging values into multiple symbolic variables,such that the power injections and consumptions of selected buses or areas can be independently adjusted.This method first derives a power flow solution through a Multivariate Power Series(MPS).Next,the MQD method is applied to transform the obtained MPS to a Multivariate Pad´e Approximants(MPA)to expand the Radius of Convergence(ROC),so that the accuracy of the derived analytical solution can be significantly increased.In addition,the hypersurface of the voltage stability boundary can be identified by an analytical formula obtained from the coefficients of MPA.This direct method for power flow solutions and voltage stability boundaries is fast for many online applications,since such analytical solutions can be derived offline and evaluated online by only plugging values into the symbolic variables according to the actual operating conditions.The proposed method is validated in detail on New England 39-bus and IEEE 118-bus systems with independent load variations in multi-regions.展开更多
A recursive rational algorithm for matrix exponentials was obtained by making use of the generalized inverse of a matrix in this paper. On the basis of the n th convergence of Thiele type continued fraction expa...A recursive rational algorithm for matrix exponentials was obtained by making use of the generalized inverse of a matrix in this paper. On the basis of the n th convergence of Thiele type continued fraction expansion, a new type of the generalized inverse matrix valued Padé approximant (GMPA) for matrix exponentials was defined and its remainder formula was proved. The results of this paper were illustrated by some examples.展开更多
We propose a new model based on the convolutional networks and SAX(Symbolic Aggregate Approximation)discretization to learn the representation for multivariate time series.The deep neural networks has excellent expres...We propose a new model based on the convolutional networks and SAX(Symbolic Aggregate Approximation)discretization to learn the representation for multivariate time series.The deep neural networks has excellent expressiveness,which is fully exploited by the convolutional networks with means of unsupervised learning.We design a network structure to obtain the cross-channel correlation with means of convolution and deconvolution,the pooling operation is utilized to perform the dimension reduction along each position of the channels.Discretization which based on the Symbolic Aggregate Approximation is applied on the feature vectors to extract the bag of features.We collect two different representations from the convolutional networks,the compression from bottle neck and the last convolutional layers.We show how these representations and bag of features can be useful for classification.We provide a full comparison with the sequence distance based approach on the standard datasets to demonstrate the effectiveness of our method.We further build the Markov matrix according to the discretized representation abstracted from the deconvolution,time series is visualized to complex networks through Markov matrix visualization,which show more class-specific statistical properties and clear structures with respect to different labels.展开更多
This paper proposes a method for modelling volatilities(conditional covariance matrices)of high dimensional dynamic data.We combine the ideas of approximate factor models for dimension reduction and multivariate GARCH...This paper proposes a method for modelling volatilities(conditional covariance matrices)of high dimensional dynamic data.We combine the ideas of approximate factor models for dimension reduction and multivariate GARCH models to establish a model to describe the dynamics of high dimensional volatilities.Sparsity condition and thresholding technique are applied to the estimation of the error covariance matrices,and quasi maximum likelihood estimation(QMLE)method is used to estimate the parameters of the common factor conditional covariance matrix.Asymptotic theories are developed for the proposed estimation.Monte Carlo simulation studies and real data examples are presented to support the methodology.展开更多
基金Project supported by National Natural Science Foundation of China (Grant No .10271074)
文摘In the present paper, the formulae for matrix Padé-type approximation were improved. The mixed model reduction method of matrix Padé-type-Routh for the multivariable linear systems was presented. A well-known example was given to illustrate that the mixed method is efficient.
文摘Matrix Padé approximation is a widely used method for computing matrix functions. In this paper, we apply matrix Padé-type approximation instead of typical Padé approximation to computing the matrix exponential. In our approach the scaling and squaring method is also used to make the approximant more accurate. We present two algorithms for computing and for computing with many espectively. Numerical experiments comparing the proposed method with other existing methods which are MATLAB’s functions expm and funm show that our approach is also very effective and reliable for computing the matrix exponential . Moreover, there are two main advantages of our approach. One is that there is no inverse of a matrix required in this method. The other is that this method is more convenient when computing for a fixed matrix A with many t ≥ 0.
基金supported by the National Natural Science Foundation of China under Project 52007133 and U22B20100。
文摘This paper proposes a novel Multivariate Quotient-Difference(MQD)method to obtain the approximate analytical solution for AC power flow equations.Therefore,in the online environment,the power flow solutions covering different operating conditions can be directly obtained by plugging values into multiple symbolic variables,such that the power injections and consumptions of selected buses or areas can be independently adjusted.This method first derives a power flow solution through a Multivariate Power Series(MPS).Next,the MQD method is applied to transform the obtained MPS to a Multivariate Pad´e Approximants(MPA)to expand the Radius of Convergence(ROC),so that the accuracy of the derived analytical solution can be significantly increased.In addition,the hypersurface of the voltage stability boundary can be identified by an analytical formula obtained from the coefficients of MPA.This direct method for power flow solutions and voltage stability boundaries is fast for many online applications,since such analytical solutions can be derived offline and evaluated online by only plugging values into the symbolic variables according to the actual operating conditions.The proposed method is validated in detail on New England 39-bus and IEEE 118-bus systems with independent load variations in multi-regions.
文摘A recursive rational algorithm for matrix exponentials was obtained by making use of the generalized inverse of a matrix in this paper. On the basis of the n th convergence of Thiele type continued fraction expansion, a new type of the generalized inverse matrix valued Padé approximant (GMPA) for matrix exponentials was defined and its remainder formula was proved. The results of this paper were illustrated by some examples.
基金the International Cooperation Project of the Department of Science&Technology of Henan Province under Grant No.172102410065Basic Research Project of the Education Department of Henan Province under Grant No.17A520057Frontier Interdisciplinary Project of Zhengzhou University under Grant No.XKZDQY202010.
文摘We propose a new model based on the convolutional networks and SAX(Symbolic Aggregate Approximation)discretization to learn the representation for multivariate time series.The deep neural networks has excellent expressiveness,which is fully exploited by the convolutional networks with means of unsupervised learning.We design a network structure to obtain the cross-channel correlation with means of convolution and deconvolution,the pooling operation is utilized to perform the dimension reduction along each position of the channels.Discretization which based on the Symbolic Aggregate Approximation is applied on the feature vectors to extract the bag of features.We collect two different representations from the convolutional networks,the compression from bottle neck and the last convolutional layers.We show how these representations and bag of features can be useful for classification.We provide a full comparison with the sequence distance based approach on the standard datasets to demonstrate the effectiveness of our method.We further build the Markov matrix according to the discretized representation abstracted from the deconvolution,time series is visualized to complex networks through Markov matrix visualization,which show more class-specific statistical properties and clear structures with respect to different labels.
基金supported by the National Natural Science Foundation of China(Nos.11731015,11701116)Innovative Team Project of Ordinary Universities in Guangdong Province(No.2020WCXTD018)Guangzhou University Research Fund(Nos.YG2020029,YH202108)。
文摘This paper proposes a method for modelling volatilities(conditional covariance matrices)of high dimensional dynamic data.We combine the ideas of approximate factor models for dimension reduction and multivariate GARCH models to establish a model to describe the dynamics of high dimensional volatilities.Sparsity condition and thresholding technique are applied to the estimation of the error covariance matrices,and quasi maximum likelihood estimation(QMLE)method is used to estimate the parameters of the common factor conditional covariance matrix.Asymptotic theories are developed for the proposed estimation.Monte Carlo simulation studies and real data examples are presented to support the methodology.
