Convex optimization approach to design sensor networks using information theoretic measures

Abstract

Accurate and precise estimation of process variables is key to effective process monitoring. The estimation accuracy depends on the choice of the sensor network. Therefore, the article aims at developing convex optimization formulations for designing the optimal sensor network using information‐theoretic measures in linear steady‐state data reconciliation. To this end, the estimation errors are characterized by a multivariate Gaussian distribution, and thus the analytical form for entropy and Kullback–Leibler divergences (forward, reverse, and symmetric) of estimation errors can be obtained to formulate the optimal sensor network design. The proposed information theoretic‐based optimal sensor selection problems are shown to be integer semi‐definite programming problems where the relaxation of binary decision variables results in solving a convex optimization problem. Thus, we use a branch and bound method to obtain a globally optimal sensor network design. Demonstrative case studies are presented to illustrate the efficacy of the proposed optimal sensor selection formulations.