A closed-loop subspace identification method is proposed for industrial systems subject to noisy input-output observations, known as the error-in-variables (EIV) problem. Using the orthogonal projection approach to el...A closed-loop subspace identification method is proposed for industrial systems subject to noisy input-output observations, known as the error-in-variables (EIV) problem. Using the orthogonal projection approach to eliminate the noise influence, consistent estimation is guaranteed for the deterministic part of such a system. A strict proof is given for analyzing the rank condition for such orthogonal projection, in order to use the principal component analysis (PCA) based singular value decomposition (SVD) to derive the extended observability matrix and lower triangular Toeliptz matrix of the plant state-space model. In the result, the plant state matrices can be retrieved in a transparent manner from the above matrices. An illustrative example is shown to demonstrate the effectiveness and merits of the proposed subspace identification method.展开更多
针对含缺失数据的变量带误差(EIV)系统,直接利用协方差匹配(CM)算法进行辨识的精度有限,为此提出一种协方差匹配迭代(covariance matching based iterative,CMI)算法。首先基于不完整数据集,利用CM算法获得模型参数的初始估计,然后采用...针对含缺失数据的变量带误差(EIV)系统,直接利用协方差匹配(CM)算法进行辨识的精度有限,为此提出一种协方差匹配迭代(covariance matching based iterative,CMI)算法。首先基于不完整数据集,利用CM算法获得模型参数的初始估计,然后采用交互估计理论,利用获得的参数计算缺失输出数据的估计,重构得到完整的数据集后再进一步利用CM算法更新参数估计。两者执行了递阶计算过程,通过迭代辨识逐步提高参数估计精度。仿真结果表明,CMI算法的参数估计误差在输出数据缺失率达到60%时仍然能够保持在2%以下,且随输入端和输出端噪信比的变化速率仅为CM算法的16.8%和10.8%,验证了所提算法具有较高的辨识精度和良好的鲁棒性。展开更多
基金Supported in part by Chinese Recruitment Program of Global Young Expert,Alexander von Humboldt Research Fellowship of Germany,the Foundamental Research Funds for the Central Universitiesthe National Natural Science Foundation of China (61074020)
文摘A closed-loop subspace identification method is proposed for industrial systems subject to noisy input-output observations, known as the error-in-variables (EIV) problem. Using the orthogonal projection approach to eliminate the noise influence, consistent estimation is guaranteed for the deterministic part of such a system. A strict proof is given for analyzing the rank condition for such orthogonal projection, in order to use the principal component analysis (PCA) based singular value decomposition (SVD) to derive the extended observability matrix and lower triangular Toeliptz matrix of the plant state-space model. In the result, the plant state matrices can be retrieved in a transparent manner from the above matrices. An illustrative example is shown to demonstrate the effectiveness and merits of the proposed subspace identification method.
文摘针对含缺失数据的变量带误差(EIV)系统,直接利用协方差匹配(CM)算法进行辨识的精度有限,为此提出一种协方差匹配迭代(covariance matching based iterative,CMI)算法。首先基于不完整数据集,利用CM算法获得模型参数的初始估计,然后采用交互估计理论,利用获得的参数计算缺失输出数据的估计,重构得到完整的数据集后再进一步利用CM算法更新参数估计。两者执行了递阶计算过程,通过迭代辨识逐步提高参数估计精度。仿真结果表明,CMI算法的参数估计误差在输出数据缺失率达到60%时仍然能够保持在2%以下,且随输入端和输出端噪信比的变化速率仅为CM算法的16.8%和10.8%,验证了所提算法具有较高的辨识精度和良好的鲁棒性。
