Intelligent Modeling for Batch Polymerization Reactors with Unknown Inputs

While system identification methods have developed rapidly, modeling the process of batch polymerization reactors still poses challenges. Therefore, designing an intelligent modeling approach for these reactors is important. This paper focuses on identifying actual models for batch polymerization reactors, proposing a novel recursive approach based on the expectation-maximization algorithm. The proposed method pays special attention to unknown inputs (UIs), which may represent modeling errors or process faults. To estimate the UIs of the model, the recursive expectation-maximization (EM) technique is used. The proposed algorithm consists of two steps: the E-step and the M-step. In the E-step, a Q-function is recursively computed based on the maximum likelihood framework, using the UI estimates from the previous time step. The Kalman filter is utilized to calculate the estimates of the states using the measurements from sensor data. In the M-step, analytical solutions for the UIs are found through local optimization of the recursive Q-function. To demonstrate the effectiveness of the proposed algorithm, a practical application of modeling batch polymerization reactors is presented. The performance of the proposed recursive EM algorithm is compared to that of the augmented state Kalman filter (ASKF) using root mean squared errors (RMSEs). The RMSEs obtained from the proposed method are at least <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>6.52</mn><mo>%</mo></mrow></semantics></math></inline-formula> lower than those from the ASKF method, indicating superior performance.