Pergamon Computers and Chemical Engineering Supplement (1999) S593-5596 I!) 1999 Elsevier Science Ltd. All rights reserved PH: S0098·1354/99/00131·3 Sensor Network Design and Upgrade for Plant Parameter Estimation Miguel Bagajewicz and Mabel Sanchez "School of Chemical Engineering and Materials Science - University of Oklahoma 100 E Boyd, room T-335, Norman, OK, USA email: bagajewicz@ou.edu "PlantaPiloto de Ingenieria Quimica (UNS - CONICET) Camino La Carrindanga Km 7 (8000) Bahia Blanca, ARGENTINA e-mail: msanchez@plapiquLedu.ar Abstract This work concentrates on the comparison of two approaches for the design of sensor networks with parameter estimation purposes. After extending a Maximum Precision Model recently published to multiple parameter estimation and binary variables, its equivalence with the Minimum Cost Model is presented. Industrial heat exchanger units are used to illustrate the results. Keywords: Sensor network design, Parameter estimation, Data reconciliation, Observability Introduction The availability of reliable process knowledge is essential to parameter estimation. This information is obtained through monitoring and data reconciliation only when an adequate set of instruments has been located at the right places. The measurement arrangement should guarantee the observability and precision of the variables involved in the estimation scheme. Furthermore, the assessment of cost optimal measurement structures for performance estimation is a challenging issue for complex plants. Several authors have addressed the problem of selecting measurement structures to determine accurate parameter values. Furthermore, several works have appeared in the literature to design sensor networks for steady state process. The designs satisfied different purposes, such as observability, precision, cost, reliability and robustness. A survey of the state of the art can be found in Bagajewicz (1997). Among these strategies, we are concerned with Maximum Precision Models and Minimum Cost Models for parameter estimation. The incorporation of measurements to observable systems in order to simultaneously minimize additional cost and error estimates has been addressed by Kretsovalis and Mah (1987). Madron and Veverka (1992) obtained a set of sensors that minimizes a measure of all the error estimates after reconciliation, without considering sensor costs. Later on, Alheritiere et al. (1997) presented the optimization of the existing resources allocated to the sensors in an industrial site, for improving the accuracy of one parameter. In this formulation, neither binary variables nor multiple parameter estimation are included in the analysis. In Bagajewicz (1997) a MINLP problem is proposed to obtain Minimum Cost sensor structures for linear systems subject to constraints on precision and robustness. Robustness measures are Gross error detectability, Precision availability and Resilience. The analysis of the existing NLP Maximum Precision Model reveals some limitations in their application, which motivates the development of a more comprehensive model for this approach. This work proposes a MINLP problem that overcomes the detected limitations by using binary variables and inequality cost constraints. Both the design and upgrade models are proposed. Furthermore, the mathematical connection between Minimum Cost Models with precision constraints (Bagajewicz,1997) and the new Maximum Precision Model will be shown. In particular, it will be shown when these two models provide the same solution. The comparison between both approaches will be done using industrial heat exchanger units. Parameter sensitivities have a fundament role in the resolution of both types of problems, thus, the importance of redundancy in the accuracy of estimation procedures for the design stage will also be shown.