(684a) Value Based Sensor Network Design

In many control system hardware selection problems the objective in to minimize the capital cost of hardware, while satisfying pre-specified bounds with respect to operating performance [1, 2, 3, 4]. However, in the value based hardware selection problem the performance bounds are removed and replaced with an operating cost term in the objective function [5, 6, 7]. While this combined capital and operating cost formulation is more reflective of the industrial objectives of a chemical process, this class of design problems presents significant computational challenges. For example, in the data reconciliation based formulation it has been shown, [6], that the value based objective function contains a number of local minima and thus disrupts the global optimality of the tree search algorithm of [1]. In the case of closed-loop dynamic process, such a formulation will introduce a set of reverse-convex constraints along with the nonlinearities associated with the steady-state process model, [7]. In this work, we illustrate that a simple reformulation of the value based hardware selectin problem and subsequent application the generalized Benders decomposition will result in massive reductions in computational effort and in some cases lead to previously unachievable global solutions.

[1] Bagajewicz, MJ Design and retrofit of sensor networks in process plants, AIChE J, 9, pp 2300-2306 (1997).

[2] Chmielewski D. J., T. Palmer and V. Manousiouthakis, â??On the Theory of Optimal Sensor Placement,â? AIChE J., 48(5), pp 1001-1012, (2002).

[3] Peng, J.K., and D.J. Chmielewski, â??Covariance Based Hardware Selection-Part II: Equivalence Results for the Sensor, Actuator and Simultaneous Selection Problems,â? IEEE Trans. Cont. Sys. Tech., 14(2), pp 362-368, (2006).

[4] Ahmed S.K., J.-K. Peng, and D.J. Chmielewski, "Covariance-Based Hardware Selection-Part III: Distributed Parameters Systems" AIChE J., 58(9), pp 2705-2713, (2012).

[5] Bagajewicz M, Markowski M, Budek A. Economic value of precision in the monitoring of linear system. AICHE J. 2005;51:1304â?? 615 1309. 616 27.

[6] Nguyen DQ, Bagajewicz MJ. New sensor network design and retrofit 617 method based on value of information. AICHE J. 2011;57:2136â?? 618 2148. 619 28.

[7] Peng JK, Chmielewski DJ. Optimal sensor network design using the 620 minimally backed-off operating point notion of profit. American 621 Control Conference, Portland, OR, USA, 2005.