With the estimation of Kalman filtering states on oblique projection spaces, the subspace identification (SID) provides an effective data-driven method in handling input noises by transforming them into process noises. However, the estimation of system matrices under the least-squares framework would lead to a biased identification. Therefore, an expectation-maximization (EM) SID (EMSID) algorithm is proposed to reduce the influence of such biased results in data-driven soft sensor modeling. First, the system matrices are estimated by using SID. Second, the EM algorithm is used to calibrate these biased system matrices by tuning the estimated state from SID. Finally, limited iterations of the EM algorithm are executed by analyzing the predictive performance of validation data. In this way, the biased SID has been modified to improve predictive ability. Applications to numerical simulation and the Tennessee Eastman process are used to evaluate the performance of the proposed method.

中文翻译：

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使用有限迭代期望最大化的修改子空间识别的数据驱动软传感方法

通过在倾斜投影空间上估计卡尔曼滤波状态，子空间识别 (SID) 提供了一种有效的数据驱动方法，通过将输入噪声转换为过程噪声来处理输入噪声。然而，在最小二乘框架下对系统矩阵的估计会导致有偏差的识别。因此，提出了一种期望最大化 (EM) SID (EMSID) 算法，以减少这种偏差结果在数据驱动的软传感器建模中的影响。首先，系统矩阵是通过使用 SID 来估计的。其次，EM 算法用于通过调整来自 SID 的估计状态来校准这些有偏差的系统矩阵。最后，通过分析验证数据的预测性能来执行 EM 算法的有限迭代。这样，有偏差的 SID 已被修改以提高预测能力。数值模拟和田纳西伊士曼过程的应用被用来评估所提出方法的性能。