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, this paper 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 semidefinite
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.