The Autocovariance Least-Squares Method for Batch Processes: Application to Experimental Chemical Systems

Abstract

Chemical engineering processes need careful monitoring in order to ensure product specification (i.e., composition, quality, etc.). Physicochemical analytical techniques can be applied for characterization, but those techniques can be time-consuming and become impractical for chemical processes for which online monitoring is needed. Calorimetry is frequently used to monitor and control batch and semibatch reactions. State and covariance estimation for batch processes employing advanced techniques, such as moving horizon estimation (MHE) for state and autocovariance least-squares (ALS) for covariance, have not been studied together. In this paper, the ALS technique is extended for batch processes and validated using laboratory data of three experimental case studies, with focus on polymerization processes. The problem of the simultaneous online estimation of states and parameters in these systems, employing recursive, extended Kalman filter (EKF) and unscented Kalman filter (UKF), and optimization-based (MHE) estimators with covariances estimated by the ALS, is examined. The results of the implementation of the proposed approach show accuracy of the estimated variables for the polymerization processes considered. Thus, this work provides a systematic procedure for the successful determination of covariances and states for experimental batch cases, including systems under repeated perturbations.

Challenges and Opportunities on Nonlinear State Estimation of Chemical and Biochemical Processes

“…The finite sliding-estimation window in MHE is a way to overcome the computational burden associated with solving the full information problem (that considers the entire trajectory of states) online, where the information prior to the sliding window is represented by the arrival cost term [17]. As an optimization-based method, MHE is able to deal explicitly with system constraints, providing improved robustness for several process applications [3,5,6,11,13]. However, computational cost in the MHE implementation for large-scale industrial processes is still a challenge today, due to the requirement of solving nonlinear optimization problems online at every time step.…”

“…in which x ∈ R n , y ∈ R p , and u ∈ R m are the process states, measured outputs, and input variables, respectively. G k = G(x k ) is the disturbance model that maps the process noises to state variables [5].…”

“…For Bayesian estimators, the process and measurement noise covariance matrices (Q and R, respectively) are the tuning parameters. These matrices can be adjusted manually or automatically by employing advanced algorithms, such as the autocovariance least-squares (ALS) technique [4][5][6]15].…”

“…A considerable amount of literature has been published on the development and application of state estimators to improve monitoring of chemical [3][4][5][6][7][8][9][10] and biochemical [11][12][13][14] processes. Previous research and review articles have also covered state estimation aspects in terms of classification [1,15,16], design, and applications [1,17,18], as well as challenges and trends on nonlinear state estimation [1,16,19,20].…”

Estimation of Biomass Enzymatic Hydrolysis State in Stirred Tank Reactor through Moving Horizon Algorithms with Fixed and Dynamic Fuzzy Weights

“…In optimization-based estimators, a nonlinear optimization is run for a time window for each time step to find an estimation of the current state that accounts for both the instrumentation and the model predictions. Furthermore, state constraints can be incorporated into the formulation and the effect of disturbances can be significantly reduced [15].…”