Optimal sensor placement strategies for large scale systems

Sensors play an important role in process industries for measurement, monitoring, control and diagnosis. There is a limitation on the number of measurement locations due to restrictions on cost, installation, maintenance, power and safety requirements. Hence sensor placement can be posed as an optimal design problem where the objective is to optimize a utility function subject to constraints. Our focus is on minimizing the estimation error which is quantified by a scalar norm of the covariance matrix of the estimates of process variables. Given a linear steady state or dynamic model of the process, it is possible to express the covariance matrix in terms of the linear model, sensor locations and the respective instrument variances. In this work, we propose two approximate methods to arrive at near optimal solutions to large scale problems. In the first method, we decompose the problem into two sub-problems and use a heuristic approach. In the second approach, we use Extended Cutting Plane (ECP) algorithms to arrive at near optimal solutions. We demonstrate the ideas on large scale systems and compare the results.