Process modeling and optimization using focused attention neural networks James D. Keeler*, Eric Hartman, Stephen Piche Pavilion Technologies, Inc., 11100 Metric Blvd., #700, Austin, TX 78758, U.S.A. Abstract Neural networks have been shown to be very useful for modeling and optimization of nonlinear and even chaotic processes. However, in using standard neural network approaches to modeling and optimization of processes in the presence of unmeasured disturbances, a dilemma arises between achieving the accurate predictions needed for modeling and computing the correct gains required for optimization. As shown in this paper, the Focused Attention Neural Network (FANN) provides a solution to this dilemma. Unmeasured disturbances are prevalent in process industry plants and frequently have signi®cant eects on process outputs. In such cases, process outputs often cannot be accu- rately predicted from the independent process input variables alone. To enhance prediction accuracy, a common neural network modeling practice is to include other dependent process output variables as model inputs. The inclusion of such variables almost invariably bene®ts prediction accuracy, and is benign if the model is used for prediction alone. However, the process gains, necessary for optimization, sensitivity analysis and other process characterizations, are almost always incorrect in such models. We describe a neural network architecture, the FANN, which obtains accuracy in both predictions and gains in the presence of unmeasured disturbances. The FANN architecture uses dependent process variables to perform feed-forward estimation of unmeasured disturbances, and uses these estimates together with the independent variables as model inputs. Process gains are then calculated correctly as a function of the esti- mated disturbances and the independent variables. Steady-state optimization solutions thus include compensation for unmeasured disturbances. The eectiveness of the FANN architecture is illustrated using a model of a process with two unmeasured disturbances and using a model of the chaotic Belousov±Zhabotinski chemical reaction. # 1998 Elsevier Science Ltd. All rights reserved. Keywords: Neural Networks; Steady state optimization; Disturbance rejection; Process modeling 1. Introduction Arti®cial neural networks represent a set of powerful mathematical techniques for modeling, control, and optimization, in which models ``learn'' processes behavior directly from process data. Examples of the extensive literature on neural networks include papers on basic algo- rithms [1,2], variations on basic algorithms [3,4], theoretical proofs of universal function approx- imation properties of neural networks [5,6], and applications to problem domains, including pre- diction, optimization, and control of industrial processes [7±12]. Given data of reasonable quality, building a neural network model that simply predicts accu- rately is relatively straightforward [1,13]. How- ever, when modeling industrial processes for ISA TRANSACTIONS 1 ISA Transactions 37 (1998) 41±52 0968-0896/98/$19.00 # 1998 Elsevier Science Ltd. All rights reserved PII: S0019-0578(98)00005-6 * Corresponding author. Tel: 1-800-880-5432; e-mail: keeler@pav.com