The main faults existing in current scale methods are that the scales do not represent the real importance of alternatives and their relations. This paper presents a proportion judgment scale and introduces a new meth...The main faults existing in current scale methods are that the scales do not represent the real importance of alternatives and their relations. This paper presents a proportion judgment scale and introduces a new method based on the proportion scale for construction comparison matrix in the analytic hierarchy process (AHP). The proportion judgment scales do not have the faults existing in current scale methods and the comparison matrix constructed by the new scale展开更多
In this paper we study the perturbation bound of the projection ( W A ) ( W A )+,where both the matrices A and W are given with W positive diagonal and severely stiff.When the perturbed matrix (A)= A + δA satisfy sev...In this paper we study the perturbation bound of the projection ( W A ) ( W A )+,where both the matrices A and W are given with W positive diagonal and severely stiff.When the perturbed matrix (A)= A + δA satisfy several row rank preserving conditions,we derive a new perturbation bound of the projection.展开更多
In this paper, we extend matrix scaled total least squares (MSTLS) problem with a single right-hand side to the case of multiple right-hand sides. Firstly, under some mild conditions, this paper gives an explicit expr...In this paper, we extend matrix scaled total least squares (MSTLS) problem with a single right-hand side to the case of multiple right-hand sides. Firstly, under some mild conditions, this paper gives an explicit expression of the minimum norm solution of MSTLS problem with multiple right-hand sides. Then, we present the Kronecker-product-based formulae for the normwise, mixed and componentwise condition numbers of the MSTLS problem. For easy estimation, we also exhibit Kronecker-product-free upper bounds for these condition numbers. All these results can reduce to those of the total least squares (TLS) problem which were given by Zheng et al. Finally, two numerical experiments are performed to illustrate our results.展开更多
With the increase of gray scale and flat panel display （FPD） size, subspace bitwise scanning strategy can be replaced traditional scanning method to cut down frame frequency. However, the direct searching strategy ...With the increase of gray scale and flat panel display （FPD） size, subspace bitwise scanning strategy can be replaced traditional scanning method to cut down frame frequency. However, the direct searching strategy （DSS） becomes unfeasible to obtain corresponding high gray scale scanning matrix. Thus, particle swarm optimization （PSO） is introduced to accelerate searching for high gray scale weights scanning matrix （WSM） with its parallelism and global optimization feature. Finally a WSM of 256 gray scales is found out successfully with Matlab, which both gray linearity and scanning efficiency are satisfied.展开更多
The improvement of mechanical properties must be achieved by designing and constructing more suitable microstructure,such as hierarchical microstructure.In order to significantly enhance the creep resistance of titani...The improvement of mechanical properties must be achieved by designing and constructing more suitable microstructure,such as hierarchical microstructure.In order to significantly enhance the creep resistance of titanium matrix composites(TMCs),two-scale network microstructure was constructed including the first-scale network(<150μm)with micro-TiB whisker(TiBw)reinforcement and the second-scale network(<30μm)with nano-Ti5Si3 reinforcement by powder metallurgy and in-situ synthesis.The results showed that the creep rate of the composite was remarkably reduced by an order of magnitude compared with the Ti6Al4V alloy at 550℃,600℃,650℃ under the stresses between 100 MPa and 350 MPa.Moreover,the rupture time of the composite was increased by 20 times,compared with that of the Ti6Al4 Valloy at 550℃/300 MPa.The superior creep resistance could be attributed to the hierarchical microstructure.The micro-TiBw reinforcement in the first-scale network boundary contributed to creep resistance primarily by blocking grain boundary sliding,while the nano-Ti5Si3 particle in the second-scale network boundary mainly by hindering phase boundary sliding.In addition,the nano-Ti5Si3 particle was dissolved,and precipitated with smaller size than the primary Ti5Si3.This phenomenon was attributed to Si element diffusion under high temperature and external stress,which could further continuously enhance the creep resistance.Finally,the creep rate during steady-state stage was significantly decreased,which manifested superior creep resistance of the composite.展开更多
Ceramic Matrix Composite （CMC） turbine guide vanes possess multi-scale stress and strain with inhomogeneity at the microscopic scale. Given that the macroscopic distribution cannot reflect the microscopic stress flu...Ceramic Matrix Composite （CMC） turbine guide vanes possess multi-scale stress and strain with inhomogeneity at the microscopic scale. Given that the macroscopic distribution cannot reflect the microscopic stress fluctuation, the macroscopic method fails to meet the requirements of stress and strain analysis of CMC turbine guide vanes. Furthermore, the complete thermodynamic properties of 2D woven SiC/SiC-CMC cannot be obtained through experimentation, Accordingly, a method to calculate the thermodynamic properties of CMC and analyze multi-scale stress and strain of the turbine guide vanes should be established. In this study, the multi-scale thermodynamic analysis is investigated. The thermodynamic properties of Chemical Vapor Infiltration （CVI） pro- cessed SiC/SiC-CMC are predicted by a Representative Volume Element （RVE） model with porosity, leading to the result that the relative error between the calculated in-plane tensile modulus and the experimental value is 4.2%. The macroscopic response of a guide vane under given conditions is predicted. The relative error between the predicted strain on the trailing edge and the experimental value is 9.7%. The calculation of the stress distribution of micro-scale RVE shows that the maximum value of microscopic stress, which is located in the interlayer matrix, is more than 1.5 times that of macroscopic stress in the same direction and the microscopic stress distribution of the interlayer matrix is related to the pore distribution of the composite.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
In this paper, we introduce matrix-valued multiresolution analysis and matrix- valued wavelet packets. A procedure for the construction of the orthogonal matrix-valued wavelet packets is presented. The properties of t...In this paper, we introduce matrix-valued multiresolution analysis and matrix- valued wavelet packets. A procedure for the construction of the orthogonal matrix-valued wavelet packets is presented. The properties of the matrix-valued wavelet packets are investigated. In particular, a new orthonormal basis of L2(R, Cs×s) is obtained from the matrix-valued wavelet packets.展开更多
In this study, the matrix structure, state and composition of the mill scales of four typical domestically made 510L hot-rolled strips were observed and analyzed by means of optical microscopy （OM） ,scanning electro...In this study, the matrix structure, state and composition of the mill scales of four typical domestically made 510L hot-rolled strips were observed and analyzed by means of optical microscopy （OM） ,scanning electron microscopy （SEM） and X-ray diffraction （XRD）. The corrosion behavior of the steels with and without mill scales were investigated by means of hot-humid corrosion tests under the condition of relative humidity （ RH ） of 95% at 50℃ and 70℃, respectively. The results show that the matrix structures, state, composition and thickness of mill scales vary in the strips. The rusting starting time of the specimens with scales is generally a bit longer than that of the specimens without scales, but their corrosion mass-gain is higher. For these two kinds of specimens ,their corrosion rate increases significantly with the increase of temperature. The rusting behavior of the 510L strips produced by various plants is different due to the variations of hot-rolling processes and designed chemical compositions. Various relevant aspects should be taken into account in the evaluation of the corrosion behavior of hot-rolled strips.展开更多
Decentralized robust stabilization problem of discrete-time fuzzy large-scale systems with parametric uncertainties is considered. This uncertain fuzzy large-scale system consists of N interconnected T-S fuzzy subsyst...Decentralized robust stabilization problem of discrete-time fuzzy large-scale systems with parametric uncertainties is considered. This uncertain fuzzy large-scale system consists of N interconnected T-S fuzzy subsystems, and the parametric uncertainties are unknown but norm-bounded. Based on Lyapunov stability theory and decentralized control theory of large-scale system, the design schema of decentralized parallel distributed compensation （DPDC） fuzzy controllers to ensure the asymptotic stability of the whole fuzzy large-scale system is proposed. The existence conditions for these controllers take the forms of LMIs. Finally a numerical simulation example is given to show the utility of the method proposed.展开更多
The polar codes defined by the kernel matrix are a class of codes with low coding-decoding complexity and can achieve the Shannon limit. In this paper, a novel method to construct the 2<sup>n</sup>-dimensi...The polar codes defined by the kernel matrix are a class of codes with low coding-decoding complexity and can achieve the Shannon limit. In this paper, a novel method to construct the 2<sup>n</sup>-dimensional kernel matrix is proposed, that is based on primitive BCH codes that make use of the interception, the direct sum and adding a row and a column. For ensuring polarization of the kernel matrix, a solution is also put forward when the partial distances of the constructed kernel matrix exceed their upper bound. And the lower bound of exponent of the 2<sup>n</sup>-dimensional kernel matrix is obtained. The lower bound of exponent of our constructed kernel matrix is tighter than Gilbert-Varshamov (G-V) type, and the scaling exponent is better in the case of 16-dimensional.展开更多
Time-delays,due to the information transmission between subsystems,naturally exist in large-scale systems and the existence of the delay is frequently a source of instability. This paper considers the problems of robu...Time-delays,due to the information transmission between subsystems,naturally exist in large-scale systems and the existence of the delay is frequently a source of instability. This paper considers the problems of robust non-fragile fuzzy control for a class of uncertain discrete nonlinear large-scale systems with time-delay and controller gain perturbations described by T-S fuzzy model. An equivalent T-S fuzzy model is represented for discrete-delay nonlinear large-scale systems. A sufficient condition for the existence of such non-fragile controllers is further derived via the Lyapunov function and the linear matrix inequality( LMI) approach. Simulation results demonstrate the feasibility and the effectiveness of the proposed design and the proper stabilization of the system in spite of controller gain variations and uncertainties.展开更多
基金This project was supported by Zhejiang Provincial Natural Science Foundation of China (No. 601076).
文摘The main faults existing in current scale methods are that the scales do not represent the real importance of alternatives and their relations. This paper presents a proportion judgment scale and introduces a new method based on the proportion scale for construction comparison matrix in the analytic hierarchy process (AHP). The proportion judgment scales do not have the faults existing in current scale methods and the comparison matrix constructed by the new scale
文摘In this paper we study the perturbation bound of the projection ( W A ) ( W A )+,where both the matrices A and W are given with W positive diagonal and severely stiff.When the perturbed matrix (A)= A + δA satisfy several row rank preserving conditions,we derive a new perturbation bound of the projection.
文摘In this paper, we extend matrix scaled total least squares (MSTLS) problem with a single right-hand side to the case of multiple right-hand sides. Firstly, under some mild conditions, this paper gives an explicit expression of the minimum norm solution of MSTLS problem with multiple right-hand sides. Then, we present the Kronecker-product-based formulae for the normwise, mixed and componentwise condition numbers of the MSTLS problem. For easy estimation, we also exhibit Kronecker-product-free upper bounds for these condition numbers. All these results can reduce to those of the total least squares (TLS) problem which were given by Zheng et al. Finally, two numerical experiments are performed to illustrate our results.
基金supported by the Shanghai University Innovation Fundation (Grant No.SHUCX102370)
文摘With the increase of gray scale and flat panel display （FPD） size, subspace bitwise scanning strategy can be replaced traditional scanning method to cut down frame frequency. However, the direct searching strategy （DSS） becomes unfeasible to obtain corresponding high gray scale scanning matrix. Thus, particle swarm optimization （PSO） is introduced to accelerate searching for high gray scale weights scanning matrix （WSM） with its parallelism and global optimization feature. Finally a WSM of 256 gray scales is found out successfully with Matlab, which both gray linearity and scanning efficiency are satisfied.
基金financially supported by the National Key R&D Program of China (No. 2017YFB0703100)the National Natural Science Foundation of China (NSFC) under Grant Nos. 51822103, 51671068 and 51731009the Fundamental Research Funds for the Central Universities (No. HIT.BRETIV.201902)
文摘The improvement of mechanical properties must be achieved by designing and constructing more suitable microstructure,such as hierarchical microstructure.In order to significantly enhance the creep resistance of titanium matrix composites(TMCs),two-scale network microstructure was constructed including the first-scale network(<150μm)with micro-TiB whisker(TiBw)reinforcement and the second-scale network(<30μm)with nano-Ti5Si3 reinforcement by powder metallurgy and in-situ synthesis.The results showed that the creep rate of the composite was remarkably reduced by an order of magnitude compared with the Ti6Al4V alloy at 550℃,600℃,650℃ under the stresses between 100 MPa and 350 MPa.Moreover,the rupture time of the composite was increased by 20 times,compared with that of the Ti6Al4 Valloy at 550℃/300 MPa.The superior creep resistance could be attributed to the hierarchical microstructure.The micro-TiBw reinforcement in the first-scale network boundary contributed to creep resistance primarily by blocking grain boundary sliding,while the nano-Ti5Si3 particle in the second-scale network boundary mainly by hindering phase boundary sliding.In addition,the nano-Ti5Si3 particle was dissolved,and precipitated with smaller size than the primary Ti5Si3.This phenomenon was attributed to Si element diffusion under high temperature and external stress,which could further continuously enhance the creep resistance.Finally,the creep rate during steady-state stage was significantly decreased,which manifested superior creep resistance of the composite.
文摘Ceramic Matrix Composite （CMC） turbine guide vanes possess multi-scale stress and strain with inhomogeneity at the microscopic scale. Given that the macroscopic distribution cannot reflect the microscopic stress fluctuation, the macroscopic method fails to meet the requirements of stress and strain analysis of CMC turbine guide vanes. Furthermore, the complete thermodynamic properties of 2D woven SiC/SiC-CMC cannot be obtained through experimentation, Accordingly, a method to calculate the thermodynamic properties of CMC and analyze multi-scale stress and strain of the turbine guide vanes should be established. In this study, the multi-scale thermodynamic analysis is investigated. The thermodynamic properties of Chemical Vapor Infiltration （CVI） pro- cessed SiC/SiC-CMC are predicted by a Representative Volume Element （RVE） model with porosity, leading to the result that the relative error between the calculated in-plane tensile modulus and the experimental value is 4.2%. The macroscopic response of a guide vane under given conditions is predicted. The relative error between the predicted strain on the trailing edge and the experimental value is 9.7%. The calculation of the stress distribution of micro-scale RVE shows that the maximum value of microscopic stress, which is located in the interlayer matrix, is more than 1.5 times that of macroscopic stress in the same direction and the microscopic stress distribution of the interlayer matrix is related to the pore distribution of the composite.
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This work is partially supported by the Natural Science Foundation of Henan (0211044800).
文摘In this paper, we introduce matrix-valued multiresolution analysis and matrix- valued wavelet packets. A procedure for the construction of the orthogonal matrix-valued wavelet packets is presented. The properties of the matrix-valued wavelet packets are investigated. In particular, a new orthonormal basis of L2(R, Cs×s) is obtained from the matrix-valued wavelet packets.
文摘In this study, the matrix structure, state and composition of the mill scales of four typical domestically made 510L hot-rolled strips were observed and analyzed by means of optical microscopy （OM） ,scanning electron microscopy （SEM） and X-ray diffraction （XRD）. The corrosion behavior of the steels with and without mill scales were investigated by means of hot-humid corrosion tests under the condition of relative humidity （ RH ） of 95% at 50℃ and 70℃, respectively. The results show that the matrix structures, state, composition and thickness of mill scales vary in the strips. The rusting starting time of the specimens with scales is generally a bit longer than that of the specimens without scales, but their corrosion mass-gain is higher. For these two kinds of specimens ,their corrosion rate increases significantly with the increase of temperature. The rusting behavior of the 510L strips produced by various plants is different due to the variations of hot-rolling processes and designed chemical compositions. Various relevant aspects should be taken into account in the evaluation of the corrosion behavior of hot-rolled strips.
基金This project was supported by NSFC Project (60474047), (60334010) and GuangDong Province Natural Science Foundationof China(31406)and China Postdoctoral Science Foundation (20060390725).
文摘Decentralized robust stabilization problem of discrete-time fuzzy large-scale systems with parametric uncertainties is considered. This uncertain fuzzy large-scale system consists of N interconnected T-S fuzzy subsystems, and the parametric uncertainties are unknown but norm-bounded. Based on Lyapunov stability theory and decentralized control theory of large-scale system, the design schema of decentralized parallel distributed compensation （DPDC） fuzzy controllers to ensure the asymptotic stability of the whole fuzzy large-scale system is proposed. The existence conditions for these controllers take the forms of LMIs. Finally a numerical simulation example is given to show the utility of the method proposed.
文摘The polar codes defined by the kernel matrix are a class of codes with low coding-decoding complexity and can achieve the Shannon limit. In this paper, a novel method to construct the 2<sup>n</sup>-dimensional kernel matrix is proposed, that is based on primitive BCH codes that make use of the interception, the direct sum and adding a row and a column. For ensuring polarization of the kernel matrix, a solution is also put forward when the partial distances of the constructed kernel matrix exceed their upper bound. And the lower bound of exponent of the 2<sup>n</sup>-dimensional kernel matrix is obtained. The lower bound of exponent of our constructed kernel matrix is tighter than Gilbert-Varshamov (G-V) type, and the scaling exponent is better in the case of 16-dimensional.
文摘Time-delays,due to the information transmission between subsystems,naturally exist in large-scale systems and the existence of the delay is frequently a source of instability. This paper considers the problems of robust non-fragile fuzzy control for a class of uncertain discrete nonlinear large-scale systems with time-delay and controller gain perturbations described by T-S fuzzy model. An equivalent T-S fuzzy model is represented for discrete-delay nonlinear large-scale systems. A sufficient condition for the existence of such non-fragile controllers is further derived via the Lyapunov function and the linear matrix inequality( LMI) approach. Simulation results demonstrate the feasibility and the effectiveness of the proposed design and the proper stabilization of the system in spite of controller gain variations and uncertainties.
