A Data-Driven Soft Sensing Approach Using Modified Subspace Identification With Limited Iterative Expectation-Maximization

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.