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
An observation localization scheme is introduced into an ensemble-based three-dimensional variational （3DVar） assimilation method based on the singular value decomposition technique （SVD-En3DVar） to im- prove assi...An observation localization scheme is introduced into an ensemble-based three-dimensional variational （3DVar） assimilation method based on the singular value decomposition technique （SVD-En3DVar） to im- prove assimilation skill. A point-by-point analysis technique is adopted in which the weight of each obser- vation decreases with increasing distance between the analysis point and the observation point. A set of numerical experiments, in which simulated Doppler radar data are assimilated into the Weather Research and Forecasting （WRF） model, is designed to test the scheme. The results are compared with those ob- tained using the original global and local patch schemes in SVD-En3DVar, neither of which includes this type of observation localization. The observation localization scheme not only eliminates spurious analysis increments in areas of missing data, but also avoids the discontinuous analysis fields that arise from the local patch scheme. The new scheme provides better analysis fields and a more reasonable short-range rainfall forecast than the original schemes. Additional forecast experiments that assimilate real data from i0 radars indicate that the short-term precipitation forecast skill can be improved by assimilating radar data and the observation localization scheme provides a better forecast than the other two schemes.展开更多
针对滚动轴承复合故障难以分离的问题,课题组提出了一种自适应多尺度形态滤波分离方法。首先,利用具有提取周期性特征的多尺度形态滤波器和峭度特征能量积(kurtosis feature energy product, KF)提取出一种主要的故障特征分量;然后,利...针对滚动轴承复合故障难以分离的问题,课题组提出了一种自适应多尺度形态滤波分离方法。首先,利用具有提取周期性特征的多尺度形态滤波器和峭度特征能量积(kurtosis feature energy product, KF)提取出一种主要的故障特征分量;然后,利用奇异值分解(singular value decomposition, SVD)降噪方法对提取的故障特征进行降噪处理,增强故障特征;最后,对去噪信号进行迭代筛选分离,得到多个故障特征模式分量。通过仿真信号与异步牵引电机实际故障信号对比实验,结果表明:该方法能够分离复合故障特征,并有效提取噪声干扰下的故障特征信息。该方法滤波效果强于传统方法,具有较好的工程应用价值。展开更多
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。
基金Supported by the Open Project Fund of the State Key Laboratory of Severe Weather of Chinese Academy of Meteorological Sciences, National Natural Science Foundation of China (40875063 and 41275102)Fundamental Research Fund for Central Universities of China (lzujbky-2010-9)
文摘An observation localization scheme is introduced into an ensemble-based three-dimensional variational （3DVar） assimilation method based on the singular value decomposition technique （SVD-En3DVar） to im- prove assimilation skill. A point-by-point analysis technique is adopted in which the weight of each obser- vation decreases with increasing distance between the analysis point and the observation point. A set of numerical experiments, in which simulated Doppler radar data are assimilated into the Weather Research and Forecasting （WRF） model, is designed to test the scheme. The results are compared with those ob- tained using the original global and local patch schemes in SVD-En3DVar, neither of which includes this type of observation localization. The observation localization scheme not only eliminates spurious analysis increments in areas of missing data, but also avoids the discontinuous analysis fields that arise from the local patch scheme. The new scheme provides better analysis fields and a more reasonable short-range rainfall forecast than the original schemes. Additional forecast experiments that assimilate real data from i0 radars indicate that the short-term precipitation forecast skill can be improved by assimilating radar data and the observation localization scheme provides a better forecast than the other two schemes.
文摘针对滚动轴承复合故障难以分离的问题,课题组提出了一种自适应多尺度形态滤波分离方法。首先,利用具有提取周期性特征的多尺度形态滤波器和峭度特征能量积(kurtosis feature energy product, KF)提取出一种主要的故障特征分量;然后,利用奇异值分解(singular value decomposition, SVD)降噪方法对提取的故障特征进行降噪处理,增强故障特征;最后,对去噪信号进行迭代筛选分离,得到多个故障特征模式分量。通过仿真信号与异步牵引电机实际故障信号对比实验,结果表明:该方法能够分离复合故障特征,并有效提取噪声干扰下的故障特征信息。该方法滤波效果强于传统方法,具有较好的工程应用价值。
