To solve the homogeneous transformation equation of the form AX=XB in hand-eye calibration, where X represents an unknown transformation from the camera to the robot hand, and A and B denote the known movement transfo...To solve the homogeneous transformation equation of the form AX=XB in hand-eye calibration, where X represents an unknown transformation from the camera to the robot hand, and A and B denote the known movement transformations associated with the robot hand and the camera, respectively, this paper introduces a new linear decomposition algorithm which consists of singular value decomposition followed by the estimation of the optimal rotation matrix and the least squares equation to solve the rotation matrix of X. Without the requirements of traditional methods that A and B be rigid transformations with the same rotation angle, it enables the extension to non-rigid transformations for A and B. The details of our method are given, together with a short discussion of experimental results, showing that more precision and robustness can be achieved.展开更多
Under certain load pattern, the geometrically indeterminate pin-jointed mechanisms will present certain shapes to keep static equalization. This paper proposes a matrix-based method to determine the mobility and equil...Under certain load pattern, the geometrically indeterminate pin-jointed mechanisms will present certain shapes to keep static equalization. This paper proposes a matrix-based method to determine the mobility and equilibrium stability of mechanisms according to the effects of the external loads. The first and second variations of the potential energy function of mechanisms under conservative force field are analyzed. Based on the singular value decomposition (SVD) method, a new crite- rion for the mobility and equilibrium stability of mechanisms can be concluded by analyzing the equilibrium matrix. The mobility and stability of mechanisms can be classified by unified matrix formulae. A number of examples are given to demonstrate the proposed criterion. In the end, criteria are summarized in a table.展开更多
对矩阵的奇异值分解(SVD,Singular Value Decomposition)进行了分析。推导证明了奇异值分解和M-P广义逆矩阵之间的关系,得出奇异值分解的广义逆矩阵为矩阵的M-P广义逆;分析了奇异值分解和线性方程组最小范数最小二乘解的关系,推导了应...对矩阵的奇异值分解(SVD,Singular Value Decomposition)进行了分析。推导证明了奇异值分解和M-P广义逆矩阵之间的关系,得出奇异值分解的广义逆矩阵为矩阵的M-P广义逆;分析了奇异值分解和线性方程组最小范数最小二乘解的关系,推导了应用奇异值分解进行秩亏网平差解算的平差解算公式和精度估算公式;推导了加权最小二乘最小范数解的奇异值分解解算问题,扩展了奇异值分解求解未知参数最小范数最小二乘解;最后通过秩亏网算例进行了解算,验证了方法的正确性和矩阵分解的有效性。展开更多
针对聚合经验模式分解(Ensemble empirical model decomposition,EEMD)的等效滤波特性依然存在模式分量间频带重叠较大的根本缺陷,提出一种高速列车万向轴动不平衡动态检测的新方法。该方法的核心是对万向节安装机座的振动信号进行EEMD...针对聚合经验模式分解(Ensemble empirical model decomposition,EEMD)的等效滤波特性依然存在模式分量间频带重叠较大的根本缺陷,提出一种高速列车万向轴动不平衡动态检测的新方法。该方法的核心是对万向节安装机座的振动信号进行EEMD分解得到基本模式分量,应用基本模式分量信号来构造Hankel矩阵,对该矩阵进行正交化奇异值(Singular value decomposition,SVD)分解,以奇异值关键叠层作为奇异值的选择准则对信号进行重构,应用重构信号的傅里叶谱来检测高速列车万向轴的动不平衡,消除EEMD分解模式频带重叠对故障特征的淹没和混淆效应,提高了谱的清晰度,凸显了故障特征。应用万向轴动不平衡试验数据对该方法进行试验验证,结果表明,该方法能够有效检测万向轴动不平衡引起的故障特征和万向轴的固有振动特征,与纯EEMD方法相比,该方法在谱的清晰度和故障表征力上得到了显著提高。展开更多
针对经典的奇异值分解(singular value decomposition,SVD)在图像处理中的不足,提出了一种6通道多尺度奇异值分解(multi-scale SVD,MSVD)的构造方法,并将其应用于多聚焦图像融合中。首先,在经典SVD的基础上,利用矩阵分块的方法,给出了一...针对经典的奇异值分解(singular value decomposition,SVD)在图像处理中的不足,提出了一种6通道多尺度奇异值分解(multi-scale SVD,MSVD)的构造方法,并将其应用于多聚焦图像融合中。首先,在经典SVD的基础上,利用矩阵分块的方法,给出了一种6通道MSVD的构造方法。其次,对参加融合的多聚焦图像进行6通道MSVD分解,得到高层低频和各层5个方向的高频,对分解的低频子图像采用取平均、高频子图像采用区域能量取大的融合规则进行融合,并进行MSVD逆变换得到融合结果图像。最后,对融合结果图像进行主观分析和客观评价。实验结果表明该方法有好的视觉效果,融合结果图像有较高的清晰度和较丰富的边缘细节信息,且没有方块效应。从客观指标看,该方法有较高的清晰度和空间频率,其清晰度和空间频率比基于离散小波变换、基于提升小波变换、基于曲波变换和基于轮廓波变换的融合方法都高。展开更多
基金Project (No. 60703002) supported by the National Natural Science Foundation of China
文摘To solve the homogeneous transformation equation of the form AX=XB in hand-eye calibration, where X represents an unknown transformation from the camera to the robot hand, and A and B denote the known movement transformations associated with the robot hand and the camera, respectively, this paper introduces a new linear decomposition algorithm which consists of singular value decomposition followed by the estimation of the optimal rotation matrix and the least squares equation to solve the rotation matrix of X. Without the requirements of traditional methods that A and B be rigid transformations with the same rotation angle, it enables the extension to non-rigid transformations for A and B. The details of our method are given, together with a short discussion of experimental results, showing that more precision and robustness can be achieved.
基金Project supported by the National Natural Science Foundation of China (Nos. 50378083 and 50638050)the Research Foundation for the Doctoral Program of Higher Education of China (No. 20050335097)
文摘Under certain load pattern, the geometrically indeterminate pin-jointed mechanisms will present certain shapes to keep static equalization. This paper proposes a matrix-based method to determine the mobility and equilibrium stability of mechanisms according to the effects of the external loads. The first and second variations of the potential energy function of mechanisms under conservative force field are analyzed. Based on the singular value decomposition (SVD) method, a new crite- rion for the mobility and equilibrium stability of mechanisms can be concluded by analyzing the equilibrium matrix. The mobility and stability of mechanisms can be classified by unified matrix formulae. A number of examples are given to demonstrate the proposed criterion. In the end, criteria are summarized in a table.
文摘对矩阵的奇异值分解(SVD,Singular Value Decomposition)进行了分析。推导证明了奇异值分解和M-P广义逆矩阵之间的关系,得出奇异值分解的广义逆矩阵为矩阵的M-P广义逆;分析了奇异值分解和线性方程组最小范数最小二乘解的关系,推导了应用奇异值分解进行秩亏网平差解算的平差解算公式和精度估算公式;推导了加权最小二乘最小范数解的奇异值分解解算问题,扩展了奇异值分解求解未知参数最小范数最小二乘解;最后通过秩亏网算例进行了解算,验证了方法的正确性和矩阵分解的有效性。
文摘针对聚合经验模式分解(Ensemble empirical model decomposition,EEMD)的等效滤波特性依然存在模式分量间频带重叠较大的根本缺陷,提出一种高速列车万向轴动不平衡动态检测的新方法。该方法的核心是对万向节安装机座的振动信号进行EEMD分解得到基本模式分量,应用基本模式分量信号来构造Hankel矩阵,对该矩阵进行正交化奇异值(Singular value decomposition,SVD)分解,以奇异值关键叠层作为奇异值的选择准则对信号进行重构,应用重构信号的傅里叶谱来检测高速列车万向轴的动不平衡,消除EEMD分解模式频带重叠对故障特征的淹没和混淆效应,提高了谱的清晰度,凸显了故障特征。应用万向轴动不平衡试验数据对该方法进行试验验证,结果表明,该方法能够有效检测万向轴动不平衡引起的故障特征和万向轴的固有振动特征,与纯EEMD方法相比,该方法在谱的清晰度和故障表征力上得到了显著提高。
文摘针对经典的奇异值分解(singular value decomposition,SVD)在图像处理中的不足,提出了一种6通道多尺度奇异值分解(multi-scale SVD,MSVD)的构造方法,并将其应用于多聚焦图像融合中。首先,在经典SVD的基础上,利用矩阵分块的方法,给出了一种6通道MSVD的构造方法。其次,对参加融合的多聚焦图像进行6通道MSVD分解,得到高层低频和各层5个方向的高频,对分解的低频子图像采用取平均、高频子图像采用区域能量取大的融合规则进行融合,并进行MSVD逆变换得到融合结果图像。最后,对融合结果图像进行主观分析和客观评价。实验结果表明该方法有好的视觉效果,融合结果图像有较高的清晰度和较丰富的边缘细节信息,且没有方块效应。从客观指标看,该方法有较高的清晰度和空间频率,其清晰度和空间频率比基于离散小波变换、基于提升小波变换、基于曲波变换和基于轮廓波变换的融合方法都高。
