In this paper, we research the probability theory and matrix transformation based technique to manage the data for processing and analysis. Clustering analysis research has a long history, over the decades, the import...In this paper, we research the probability theory and matrix transformation based technique to manage the data for processing and analysis. Clustering analysis research has a long history, over the decades, the importance and the cross characteristics with other research direction to get the affirmation of the people. The probability theory and linear algebra act as the powerful tool for analyzing and mining data. The experimental result illustrates the effectiveness. In the near future, we plan to conduct more theoretical analysis on the topic.展开更多
The method of Zeng et al. (1991) employed diameter growth to estimate the transition probability of the matrix model in uneven-aged forest stands. In this paper the Weibull distribution for even-aged forest stands ins...The method of Zeng et al. (1991) employed diameter growth to estimate the transition probability of the matrix model in uneven-aged forest stands. In this paper the Weibull distribution for even-aged forest stands instead of uniform distribution chosen by Zeng is used. By comparing the results of the improved method with those of the original method of Zeng, it turns out that the improved method of Zeng given in this paper is more efficient.展开更多
This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix i...This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.展开更多
In this paper, we consider the problem of irregular shapes tracking for multiple extended targets by introducing the Gaussian surface matrix（GSM） into the framework of the random finite set（RFS） theory. The Gaussi...In this paper, we consider the problem of irregular shapes tracking for multiple extended targets by introducing the Gaussian surface matrix（GSM） into the framework of the random finite set（RFS） theory. The Gaussian surface function is constructed first by the measurements, and it is used to define the GSM via a mapping function. We then integrate the GSM with the probability hypothesis density（PHD） filter, the Bayesian recursion formulas of GSM-PHD are derived and the Gaussian mixture implementation is employed to obtain the closed-form solutions. Moreover, the estimated shapes are designed to guide the measurement set sub-partition, which can cope with the problem of the spatially close target tracking. Simulation results show that the proposed algorithm can effectively estimate irregular target shapes and exhibit good robustness in cross extended target tracking.展开更多
Accurate descriptions of matrix diffusion across the fracture/matrix interface are critical to assessing contaminant migration in fractured media. The classical transfer probability method is only applicable for relat...Accurate descriptions of matrix diffusion across the fracture/matrix interface are critical to assessing contaminant migration in fractured media. The classical transfer probability method is only applicable for relatively large diffusion coefficients and small fracture spacings, due to an intrinsic assumption of an equilibrium concentration profile in the matrix blocks. Motivated and required by practical applications, we propose a direct numerical simulation （DNS） approach without any empirical assumptions. A three-step Lagrangian algorithm was developed and validated to directly track the particle dynamics across the fracture/matrix interface, where particle＇s diffusive displacement across the discontinuity is controlled by an analytical, one-side reflection probability. Numerical experiments show that the DNS approach is especially efficient for small diffusion coefficients and large fracture spacings, alleviating limitations of the classical modeling approach.展开更多
Based on equivalence relation,the classical rough set theory is unable to deal with incomplete information systems.In this case,an extended rough set model based on valued tolerance relation and prior probability obta...Based on equivalence relation,the classical rough set theory is unable to deal with incomplete information systems.In this case,an extended rough set model based on valued tolerance relation and prior probability obtained from incomplete information systems is firstly founded.As a part of the model,the corresponding discernibility matrix and an attribute reduction of incomplete information system are then proposed.Finally,the extended rough set model and the proposed attribute reduction algorithm are verified under an incomplete information system.展开更多
Random Matrix Theory (RMT) is a valuable tool for describing the asymptotic behavior of multiple systems,especially for large matrices. In this paper,using asymptotic random matrix theory,a new cooperative Multiple-In...Random Matrix Theory (RMT) is a valuable tool for describing the asymptotic behavior of multiple systems,especially for large matrices. In this paper,using asymptotic random matrix theory,a new cooperative Multiple-Input Multiple-Output (MIMO) scheme for spectrum sensing is proposed,which shows how asymptotic free property of random matrices and the property of Wishart distribution can be used to assist spectrum sensing for Cognitive Radios (CRs). Simulations over Rayleigh fading and AWGN channels demonstrate the proposed scheme has better detection performance compared with the energy detection techniques even in the case of a small sample of observations.展开更多
A new analysis framework based on probability density evolution method(PDEM)and its Chebyshev collocation solution are introduced to predict the dynamic response and short-term extreme load of offshore wind turbine(OW...A new analysis framework based on probability density evolution method(PDEM)and its Chebyshev collocation solution are introduced to predict the dynamic response and short-term extreme load of offshore wind turbine(OWT)towers subjected to random sea state.With regard to the stochastic responses,random function method is employed to generate samples of sea elevation,the probability density evolution equation(PDEE)is solved to calculate time-variant probability density functions of structural responses.For the probabilistic load estimation,a FAST model of NREL 5MW offshore turbine is established to obtain samples of bending moment at the tower base.The equivalent extreme event theory is used to construct a virtual stochastic process(VSP)to assess the short-term extreme load.The results indicate that the proposed approach can predict time-variant probability density functions of the structural responses,and shows good agreement with Monte Carlo simulations.Additionally,the predicted short-term extreme load can capture the fluctuation at the tail of the extreme value distribution,thus is more rational than results from the typical distribution models.Overall,the proposed method shows good adaptation,precision and efficiency for the dynamic response analysis and load estimation of OWT towers.展开更多
The multi-sensor multi-target localization and data fusion problem is discussed, and a new data fusion method called joint probability density matrix （JPDM） has been proposed, which can associate with and fuse measu...The multi-sensor multi-target localization and data fusion problem is discussed, and a new data fusion method called joint probability density matrix （JPDM） has been proposed, which can associate with and fuse measurements from spatially distributed heterogeneous sensors to produce good estimates of the targets. Based on probabilistic grids representation, the uncertainty regions of all the measurements are numerically combined in a general framework. The NP-hard multi-sensor data fusion problem has been converted to a peak picking problem in the grids map. Unlike most of the existing data fusion methods, the JPDM method does not need association processing, and will not lead to combinatorial explosion. Its convergence to the CRB with a diminishing grid size has been proved. Simulation results are presented to illustrate the effectiveness of the proposed technique.展开更多
文摘In this paper, we research the probability theory and matrix transformation based technique to manage the data for processing and analysis. Clustering analysis research has a long history, over the decades, the importance and the cross characteristics with other research direction to get the affirmation of the people. The probability theory and linear algebra act as the powerful tool for analyzing and mining data. The experimental result illustrates the effectiveness. In the near future, we plan to conduct more theoretical analysis on the topic.
基金This paper was supported by the National Natural Science Foundation of China
文摘The method of Zeng et al. (1991) employed diameter growth to estimate the transition probability of the matrix model in uneven-aged forest stands. In this paper the Weibull distribution for even-aged forest stands instead of uniform distribution chosen by Zeng is used. By comparing the results of the improved method with those of the original method of Zeng, it turns out that the improved method of Zeng given in this paper is more efficient.
基金This work was supported by the National Natural Science Foundation of China(No.60474013)Specialized Research Fund for the Doctoral Program of Higher Education (No. 20050424002)the Doctoral Foundation of Shandong Province (No. 2004BS01010)
文摘This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.
基金supported by the National Natural Science Foundation of China(6130501761304264+1 种基金61402203)the Natural Science Foundation of Jiangsu Province(BK20130154)
文摘In this paper, we consider the problem of irregular shapes tracking for multiple extended targets by introducing the Gaussian surface matrix（GSM） into the framework of the random finite set（RFS） theory. The Gaussian surface function is constructed first by the measurements, and it is used to define the GSM via a mapping function. We then integrate the GSM with the probability hypothesis density（PHD） filter, the Bayesian recursion formulas of GSM-PHD are derived and the Gaussian mixture implementation is employed to obtain the closed-form solutions. Moreover, the estimated shapes are designed to guide the measurement set sub-partition, which can cope with the problem of the spatially close target tracking. Simulation results show that the proposed algorithm can effectively estimate irregular target shapes and exhibit good robustness in cross extended target tracking.
基金supported by the United States Department of Energythe Desert Research Institute IR&D Funds
文摘Accurate descriptions of matrix diffusion across the fracture/matrix interface are critical to assessing contaminant migration in fractured media. The classical transfer probability method is only applicable for relatively large diffusion coefficients and small fracture spacings, due to an intrinsic assumption of an equilibrium concentration profile in the matrix blocks. Motivated and required by practical applications, we propose a direct numerical simulation （DNS） approach without any empirical assumptions. A three-step Lagrangian algorithm was developed and validated to directly track the particle dynamics across the fracture/matrix interface, where particle＇s diffusive displacement across the discontinuity is controlled by an analytical, one-side reflection probability. Numerical experiments show that the DNS approach is especially efficient for small diffusion coefficients and large fracture spacings, alleviating limitations of the classical modeling approach.
基金supported by the Foundation and Frontier Technologies Research Plan Projects of Henan Province of China under Grant No. 102300410266
文摘Based on equivalence relation,the classical rough set theory is unable to deal with incomplete information systems.In this case,an extended rough set model based on valued tolerance relation and prior probability obtained from incomplete information systems is firstly founded.As a part of the model,the corresponding discernibility matrix and an attribute reduction of incomplete information system are then proposed.Finally,the extended rough set model and the proposed attribute reduction algorithm are verified under an incomplete information system.
基金Supported by the National Natural Science Foundation of China (No.60972039)Natural Science Foundation of Jiangsu Province (No.BK2007729)Natural Science Funding of Jiangsu Province (No.06KJA51001)
文摘Random Matrix Theory (RMT) is a valuable tool for describing the asymptotic behavior of multiple systems,especially for large matrices. In this paper,using asymptotic random matrix theory,a new cooperative Multiple-Input Multiple-Output (MIMO) scheme for spectrum sensing is proposed,which shows how asymptotic free property of random matrices and the property of Wishart distribution can be used to assist spectrum sensing for Cognitive Radios (CRs). Simulations over Rayleigh fading and AWGN channels demonstrate the proposed scheme has better detection performance compared with the energy detection techniques even in the case of a small sample of observations.
基金This research is supported by the National Natural Science Foundation of China(Grant No.51578444)Key Science Research Program of Education Department of Shaanxi Province(Grant No.20JY032).
文摘A new analysis framework based on probability density evolution method(PDEM)and its Chebyshev collocation solution are introduced to predict the dynamic response and short-term extreme load of offshore wind turbine(OWT)towers subjected to random sea state.With regard to the stochastic responses,random function method is employed to generate samples of sea elevation,the probability density evolution equation(PDEE)is solved to calculate time-variant probability density functions of structural responses.For the probabilistic load estimation,a FAST model of NREL 5MW offshore turbine is established to obtain samples of bending moment at the tower base.The equivalent extreme event theory is used to construct a virtual stochastic process(VSP)to assess the short-term extreme load.The results indicate that the proposed approach can predict time-variant probability density functions of the structural responses,and shows good agreement with Monte Carlo simulations.Additionally,the predicted short-term extreme load can capture the fluctuation at the tail of the extreme value distribution,thus is more rational than results from the typical distribution models.Overall,the proposed method shows good adaptation,precision and efficiency for the dynamic response analysis and load estimation of OWT towers.
基金Supported by the National Natural Science Foundation of China （No. 60736006 and 60875019）
文摘The multi-sensor multi-target localization and data fusion problem is discussed, and a new data fusion method called joint probability density matrix （JPDM） has been proposed, which can associate with and fuse measurements from spatially distributed heterogeneous sensors to produce good estimates of the targets. Based on probabilistic grids representation, the uncertainty regions of all the measurements are numerically combined in a general framework. The NP-hard multi-sensor data fusion problem has been converted to a peak picking problem in the grids map. Unlike most of the existing data fusion methods, the JPDM method does not need association processing, and will not lead to combinatorial explosion. Its convergence to the CRB with a diminishing grid size has been proved. Simulation results are presented to illustrate the effectiveness of the proposed technique.
