Robust Data Reconciliation in a Chemical Reactor Through Simulated Annealing Optimization

Abstract

Robust data reconciliation (RDR) is an effective technique designed to minimize/annul gross errors drawbacks over estimated process variables. In the present work, a brief review on heuristic optimization methods devoted to RDR in chemical processes is performed. Twelve robust estimators were evaluated, including Smith and Bell estimators, which were never before used within this context. The performance of these estimators was evaluated in a Van de Vusse reaction system, described by a nonlinear system of equations. The problem was solved by both the simulated annealing method and the IPOPT framework. The results showed the efficiency and consistency of both schemes and, despite the relevance of gross errors, the redescending estimators exhibited better global performance.

Development of a Robust Receding-Horizon Nonlinear Kalman Filter Using M-Estimators

“…M-estimators are independent of a noise distribution and are insensitive to the outliers. Recently de Menezes et al listed multiple M-estimators and in this work, four popular M-estimators are considered which are Huber’s fair function estimator, Welsch estimator, Smith estimator, and Hampel’s redescending estimator . However, the proposed methodology can incorporate any type of M-estimators listed in de Menezes et al Further, Huber’s fair function estimator is a monotone (convex) estimator, Welsch estimator is a soft redescending (pseudoconvex) estimator, while the Smith and Hampel’s estimators are considered as hard redescending (quasi-convex) estimators .…”

“…The Welsch estimator behavior for different values of ζ k , q can be seen from Figures and . For large values of ζ k , q , the influence function approaches zero asymptotically and when ζ k , q approach to infinity, then the effect of ζ q , k is entirely neglected, thereby robust to large measurement errors. Smith estimator: The Smith estimator is defined as follows: where δ S is the tuning parameter. The influence function and its gradient of the Smith function estimator are given as follows The behavior of the Smith function for different values of ζ k , q is shown in Figures and .…”

“…Smith estimator: The Smith estimator is defined as follows: where δ S is the tuning parameter. The influence function and its gradient of the Smith function estimator are given as follows The behavior of the Smith function for different values of ζ k , q is shown in Figures and .…”

“…For large values of ζ k,q , the influence function approaches zero asymptotically and when ζ k,q approach to infinity, then the effect of ζ q,k is entirely neglected, thereby robust to large measurement errors. • Smith estimator: The Smith estimator is defined as follows: 26…”