Bidirectional branch and bound for controlled variable selection. Part II: exactlocal method for self-optimizing control

摘要

The selection of controlled variables (CVs) from available measurements throughenumeration of all possible alternatives is computationally forbidding forlarge-dimensional problems. In Part I of this work [Cao, Y., & Kariwala, V.(2008). Bidirectional branch and bound for controlled variable selection: PartI. Principles and minimum singular value criterion. Comput. Chem. Eng., 32(10),2306-2319], we proposed a bidirectional branch and bound (BAB) approach forsubset selection problems and demonstrated its efficiency using the minimumsingular value criterion. In this paper, the BAB approach is extended for CVselection using the exact local method for self-optimizing control. Byredefining the loss expression, we show that the CV selection criterion forexact local method is bidirectionally monotonic. A number of novel determinantbased criteria are proposed for fast pruning and branching purposes resulting ina computationally inexpensive BAB approach. We also establish a link between theproblems of selecting a subset and combinations of measurements as CVs andpresent a partially bidirectional BAB method for selection of measurements,whose combinations can be used as CVs. Numerical tests using randomly generatedmatrices and binary distillation column case study demonstrate the computationalefficiency of the proposed methods. (C) 2009 Elsevier Ltd. All rights reserved.