An EM/ECME-based algorithm for simultaneous data reconciliation and gross error detection using t-distribution noise model in chemical industry

Data reconciliation plays a crucial role in the field of process control by mitigating the influence of random errors and ensuring that data conforms to process constraints. However, besides random errors, actual measurement data may contain various degrees of gross errors, significantly affecting the accuracy of data reconciliation. Due to the robustness and flexibility of the t-distribution, this work adopts the t-distribution to characterize the noise model in order to address gross errors in data reconciliation. Based on this assumption, a maximum likelihood framework is established to simultaneously perform data reconciliation and gross error detection, with the Expectation-Maximization (EM) algorithm applied to solve the parameter estimation problem involving hidden variables. Furthermore, an Expectation/Conditional Maximization Either (ECME) algorithm framework is constructed based on the foundation of the EM algorithm to increase the convergence speed of the algorithm, making it more efficient for solving complex optimization problems. The proposed method is shown to be effective through numerical case studies and an industrial process named acid-catalyzed process.