A novel concept of nonlinear singular vector and nonlinear singular value is introduced, which is a natural generalization of the classical linear singular vector and linear singular value to the nonlinear category. T...A novel concept of nonlinear singular vector and nonlinear singular value is introduced, which is a natural generalization of the classical linear singular vector and linear singular value to the nonlinear category. The optimization problem related to the determination of nonlinear singular vectors and singular values is formulated. The general idea of this approach is demonstrated by a simple two-dimensional quasigeostrophic model in the atmospheric and oceanic sciences. The advantage and its applications of the new method to the predictability, ensemble forecast and finite-time nonlinear instability are discussed. This paper makes a necessary preparation for further theoretical and numerical investigations.展开更多
Grinding chatter is a self?induced vibration which is unfavorable to precision machining processes. This paper proposes a forecasting method for grinding state identification based on bivarition empirical mode decompo...Grinding chatter is a self?induced vibration which is unfavorable to precision machining processes. This paper proposes a forecasting method for grinding state identification based on bivarition empirical mode decomposition(BEMD) and least squares support vector machine(LSSVM), which allows the monitoring of grinding chatter over time. BEMD is a promising technique in signal processing research which involves the decomposition of two?dimen?sional signals into a series of bivarition intrinsic mode functions(BIMFs). BEMD and the extraction criterion of its true BIMFs are investigated by processing a complex?value simulation chatter signal. Then the feature vectors which are employed as an amplification for the chatter premonition are discussed. Furthermore, the methodology is tested and validated by experimental data collected from a CNC guideway grinder KD4020 X16 in Hangzhou Hangji Machine Tool Co., Ltd. The results illustrate that the BEMD is a superior method in terms of processing non?stationary and nonlinear signals. Meanwhile, the peak to peak, real?time standard deviation and instantaneous energy are proven to be e ec?tive feature vectors which reflect the di erent grinding states. Finally, a LSSVM model is established for grinding status classification based on feature vectors, giving a prediction accuracy rate of 96%.展开更多
为了降低恶意评价对信任模型造成的影响,提出了一种适用于开放分布式网络环境下的基于信任领域和评价可信度量的信任模型(trust model based on the trust area and evaluation credibility,TMEC),并给出了模型流程及相关定义.TMEC模型...为了降低恶意评价对信任模型造成的影响,提出了一种适用于开放分布式网络环境下的基于信任领域和评价可信度量的信任模型(trust model based on the trust area and evaluation credibility,TMEC),并给出了模型流程及相关定义.TMEC模型中将节点的信誉值区分为节点的全局信誉值和反馈信誉值,并基于信任领域进行模型的构建;提出了基于节点评分行为相似性的共谋团体识别算法;提出了基于评价支持度和评价一致性因子确定节点反馈权重的方法,从而使所构建的信任模型更加可信和可靠.仿真实验表明,该模型能够有效地检测和抵制夸大、诋毁和共谋等恶意评价行为,具有良好的抗攻击性.展开更多
Complete and reliable field traffic data is vital for the planning, design, and operation of urban traf- fic management systems. However, traffic data is often very incomplete in many traffic information systems, whic...Complete and reliable field traffic data is vital for the planning, design, and operation of urban traf- fic management systems. However, traffic data is often very incomplete in many traffic information systems, which hinders effective use of the data. Methods are needed for imputing missing traffic data to minimize the effect of incomplete data on the utilization. This paper presents an improved Local Least Squares （LLS） ap- proach to impute the incomplete data. The LLS is an improved version of the K Nearest Neighbor （KNN） method. First, the missing traffic data is replaced by a row average of the known values. Then, the vector angle and Euclidean distance are used to select the nearest neighbors. Finally, a regression step is used to get weights of the nearest neighbors and the imputation results. Traffic flow volume collected in Beijing was analyzed to compare this approach with the Bayesian Principle Component Analysis （BPCA） imputation ap- proach. Tests show that this approach provides slightly better performance than BPCA imputation to impute missing traffic data.展开更多
A large unsymmetric linear system problem is transformed into the problem of computing the eigenvector of a large symmetric nonnegative definite matrix associated with the eigenvalue zero, i.e., the computation of the...A large unsymmetric linear system problem is transformed into the problem of computing the eigenvector of a large symmetric nonnegative definite matrix associated with the eigenvalue zero, i.e., the computation of the elgenvector of the cross-product matrix of an augmented matrix associated with the eigenvalue zero. The standard Lanczos method and an improved refined Lanczos method are proposed that compute approximate eigenvectors and return approximate solutions of the linear system. An implicitly restarted Lanczos algorithm and its refined version are developed. Theoretical analysis and numerical experiments show the refined method is better than the standard one. If the large matrix has small eigenvalues, the two new algorithms are much faster than the unpreconditioned restarted GMRES.展开更多
The Ritz vectors obtained by Arnoldi's method may not be good approxima- tions and even may not converge even if the corresponding Ritz values do. In order to improve the quality of Ritz vectors and enhance the e...The Ritz vectors obtained by Arnoldi's method may not be good approxima- tions and even may not converge even if the corresponding Ritz values do. In order to improve the quality of Ritz vectors and enhance the efficiency of Arnoldi type algorithms, we propose a strategy that uses Ritz values obtained from an m-dimensional Krylov subspace but chooses modified approximate eigenvectors in an (m + 1)-dimensional Krylov subspace. Residual norm of each new approximate eigenpair is minimal over the span of the Ritz vector and the (m+1)th basis vector, which is available when the m-step Arnoldi process is run. The resulting modi- fied m-step Arnoldi method is better than the standard m-step one in theory and cheaper than the standard (m + 1)-step one. Based on this strategy, we present a modified m-step restarted Arnoldi algorithm. Numerical examples show that the modified m-step restarted algorithm and its version with Chebyshev acceleration are often considerably more efficient than the standard (m+ 1)-step restarted ones.展开更多
The approximate eigenvectors or Ritz vectors obtained by the block Arnoldi method may converge very slowly and even fail to converge even if the approximate eigenvalues do. In order to improve the quality of the Ritz ...The approximate eigenvectors or Ritz vectors obtained by the block Arnoldi method may converge very slowly and even fail to converge even if the approximate eigenvalues do. In order to improve the quality of the Ritz vectors, a modified strategy is proposed such that new approximate eigenvectors are certain combinations of the Ritz vectors and the waSted (m+1) th block basis vector and their corresponding residual norms are minimized in a certain sense. They can be cheaply computed by solving a few small 'dimensional minimization problems. The resulting modified m-step block Arnoldi method is better than the standard m-step one in theory and cheaper than the standard (m+1)-step one. Based on this strategy, a modified m-step iterative block Arnoldi algorithm is presented. Numerical experiments are reported to show that the modified m-step algorithm is often considerably more efficient than the standard (m+1)-step iterative one.展开更多
文摘A novel concept of nonlinear singular vector and nonlinear singular value is introduced, which is a natural generalization of the classical linear singular vector and linear singular value to the nonlinear category. The optimization problem related to the determination of nonlinear singular vectors and singular values is formulated. The general idea of this approach is demonstrated by a simple two-dimensional quasigeostrophic model in the atmospheric and oceanic sciences. The advantage and its applications of the new method to the predictability, ensemble forecast and finite-time nonlinear instability are discussed. This paper makes a necessary preparation for further theoretical and numerical investigations.
基金National Natural Science Foundation of China(Grant No.51475432)Zhejiang Provincial National Natural Science Foundation of China(Grant No.LZ13E050003)State Key Program of National Natural Science of China(Grant Nos.U1234207,U1709210)
文摘Grinding chatter is a self?induced vibration which is unfavorable to precision machining processes. This paper proposes a forecasting method for grinding state identification based on bivarition empirical mode decomposition(BEMD) and least squares support vector machine(LSSVM), which allows the monitoring of grinding chatter over time. BEMD is a promising technique in signal processing research which involves the decomposition of two?dimen?sional signals into a series of bivarition intrinsic mode functions(BIMFs). BEMD and the extraction criterion of its true BIMFs are investigated by processing a complex?value simulation chatter signal. Then the feature vectors which are employed as an amplification for the chatter premonition are discussed. Furthermore, the methodology is tested and validated by experimental data collected from a CNC guideway grinder KD4020 X16 in Hangzhou Hangji Machine Tool Co., Ltd. The results illustrate that the BEMD is a superior method in terms of processing non?stationary and nonlinear signals. Meanwhile, the peak to peak, real?time standard deviation and instantaneous energy are proven to be e ec?tive feature vectors which reflect the di erent grinding states. Finally, a LSSVM model is established for grinding status classification based on feature vectors, giving a prediction accuracy rate of 96%.
文摘为了降低恶意评价对信任模型造成的影响,提出了一种适用于开放分布式网络环境下的基于信任领域和评价可信度量的信任模型(trust model based on the trust area and evaluation credibility,TMEC),并给出了模型流程及相关定义.TMEC模型中将节点的信誉值区分为节点的全局信誉值和反馈信誉值,并基于信任领域进行模型的构建;提出了基于节点评分行为相似性的共谋团体识别算法;提出了基于评价支持度和评价一致性因子确定节点反馈权重的方法,从而使所构建的信任模型更加可信和可靠.仿真实验表明,该模型能够有效地检测和抵制夸大、诋毁和共谋等恶意评价行为,具有良好的抗攻击性.
基金Partially supported by the National High-Tech Research and Development (863) Program of China (Nos. 2009AA11Z206 and 2011AA110401)the National Natural Science Foundation of China (Nos. 60721003 and 60834001)Tsinghua University Innovation Research Program (No. 2009THZ0)
文摘Complete and reliable field traffic data is vital for the planning, design, and operation of urban traf- fic management systems. However, traffic data is often very incomplete in many traffic information systems, which hinders effective use of the data. Methods are needed for imputing missing traffic data to minimize the effect of incomplete data on the utilization. This paper presents an improved Local Least Squares （LLS） ap- proach to impute the incomplete data. The LLS is an improved version of the K Nearest Neighbor （KNN） method. First, the missing traffic data is replaced by a row average of the known values. Then, the vector angle and Euclidean distance are used to select the nearest neighbors. Finally, a regression step is used to get weights of the nearest neighbors and the imputation results. Traffic flow volume collected in Beijing was analyzed to compare this approach with the Bayesian Principle Component Analysis （BPCA） imputation ap- proach. Tests show that this approach provides slightly better performance than BPCA imputation to impute missing traffic data.
文摘A large unsymmetric linear system problem is transformed into the problem of computing the eigenvector of a large symmetric nonnegative definite matrix associated with the eigenvalue zero, i.e., the computation of the elgenvector of the cross-product matrix of an augmented matrix associated with the eigenvalue zero. The standard Lanczos method and an improved refined Lanczos method are proposed that compute approximate eigenvectors and return approximate solutions of the linear system. An implicitly restarted Lanczos algorithm and its refined version are developed. Theoretical analysis and numerical experiments show the refined method is better than the standard one. If the large matrix has small eigenvalues, the two new algorithms are much faster than the unpreconditioned restarted GMRES.
基金the China State Key Project for Basic Researchesthe National Natural Science Foundation of ChinaThe Research Fund for th
文摘The Ritz vectors obtained by Arnoldi's method may not be good approxima- tions and even may not converge even if the corresponding Ritz values do. In order to improve the quality of Ritz vectors and enhance the efficiency of Arnoldi type algorithms, we propose a strategy that uses Ritz values obtained from an m-dimensional Krylov subspace but chooses modified approximate eigenvectors in an (m + 1)-dimensional Krylov subspace. Residual norm of each new approximate eigenpair is minimal over the span of the Ritz vector and the (m+1)th basis vector, which is available when the m-step Arnoldi process is run. The resulting modi- fied m-step Arnoldi method is better than the standard m-step one in theory and cheaper than the standard (m + 1)-step one. Based on this strategy, we present a modified m-step restarted Arnoldi algorithm. Numerical examples show that the modified m-step restarted algorithm and its version with Chebyshev acceleration are often considerably more efficient than the standard (m+ 1)-step restarted ones.
基金Supported by the National Natural Science Foundation of China under Grant No.60503021(国家自然科学基金)the High-Tech Research Program of Jiangsu Province of China under Grant No.BG2006027(江苏省高技术研究计划)
文摘基于点的算法是部分可观察马尔可夫决策过程(partially observable Markov decision processes,简称POMDP)的一类近似算法.它们只在一个信念点集上进行Backup操作,避免了线性规划并使用了更少的中间变量,从而将计算瓶颈由选择向量转向了生成向量.但这类算法在生成向量时含有大量重复和无意义计算,针对于此,提出了基于点的POMDP算法的预处理方法(preprocessing method for point-based algorithms,简称PPBA).该方法对每个样本信念点作预处理,并且在生成α-向量之前首先计算出该选取哪个动作和哪些α-向量,从而消除了重复计算.PPBA还提出了基向量的概念,利用问题的稀疏性避免了无意义计算.通过在Perseus上的实验,表明PPBA很大地提高了算法的执行速度.
文摘The approximate eigenvectors or Ritz vectors obtained by the block Arnoldi method may converge very slowly and even fail to converge even if the approximate eigenvalues do. In order to improve the quality of the Ritz vectors, a modified strategy is proposed such that new approximate eigenvectors are certain combinations of the Ritz vectors and the waSted (m+1) th block basis vector and their corresponding residual norms are minimized in a certain sense. They can be cheaply computed by solving a few small 'dimensional minimization problems. The resulting modified m-step block Arnoldi method is better than the standard m-step one in theory and cheaper than the standard (m+1)-step one. Based on this strategy, a modified m-step iterative block Arnoldi algorithm is presented. Numerical experiments are reported to show that the modified m-step algorithm is often considerably more efficient than the standard (m+1)-step iterative one.
