CS 539: Introduction to Artificial Neural Networks and Fuzzy Systems FINAL PROJECT FORMULATION NEURAL NETWORK SURROGATE MODELS IN CHEMICAL PROCESS OPTIMIZATION By Carlos Henao Department of Chemical Engineering University of Wisconsin November 2008CS 539 PROJECT: NEURAL NETWORK SURROGATE MODELS IN CHEMICAL PROCESS OPTIMIZATION -3- PROBLEM STATEMENT The systematic design and optimization of chemical process facilities involves a considerable effort in terms of the development of mathematical models that are both reliable and suitable for analysis trough the use of current multivariable – nonlinear optimization techniques. One of the most important challenges has to do with the highly non-linear nature of the physic-chemical phenomena ruling the behavior of the process equipment constituting such facilities. These characteristic is responsible for the high number of nonlinear equations required to accurately describe the relationships between the process variables. Now, in the context of a chemical optimization problem, such relationships become integral part of the mathematical formulation in the form of equality and inequality constraints, a fact that raises a new set of challenges from the perspective of the available algorithms for the solution of non-linear constrained optimization. Such challenges go around aspects such as the numerical tractability and the guarantee of global optimality; both of them affect how practical these formulations are from the engineering practice point of view. In the particular case of global optimality, state of the art solvers such as BARON, can only handle is a very reduced number of variables (i.e. 50 approximately) and even in such cases there are practical restrictions in the formulation, such as the need to supply tight bounds for every variable and every equation in your formulation, transform the whole approach into a difficult task even for small size problems. PROPOSED WORK In order to solve the mentioned difficulties in the formulation and solution of chemical process optimization problems, this project will investigate the advantages of replacing detailed process unit mathematical models with pre-trained neural networks. The immediate benefits foreseen with in this approach are the reduction inCS 539 PROJECT: NEURAL NETWORK SURROGATE MODELS IN CHEMICAL PROCESS OPTIMIZATION -4- the total number of variables involved in the problem and the simplification in the definition of bound for every variable in the new model. The first benefit comes from the fact that the neural networks will be conceived as non-linear mappings relating only important variables such as the independent variables in each process unit and the variables included in the problem objective function. The second benefit comes from the fact that neural activation functions have a simple mathematical formulation, properties and bounds. Aspects such as the suitability of different training algorithms as well as the network structure (e.g. number of hidden layers and number of neurons per layer) will be investigated trough the solution of realistic industrial reactor optimization problems. REFERENCES • L. T. Biegler, I. E. Grossmann, A. W. Westerberg, Systematic Methods of Chemical Process Design, Prentice Hall PTR, March 27, 1997. • Fernandes, FAN. Optimization of Fischer-Tropsch synthesis using neural networks CHEMICAL ENGINEERING & TECHNOLOGY, 29 (4): 449-453 APR 2006 • K. P. Papalexandri and E. N. Pistikopoulos, A multiperiod MINLP model for the synthesis of flexible heat and mass exchange networks, Computers & Chemical Engineering, Volume 18, Issues 11-12, November-December 1994, Pages 1125-1139. • Nandi, S; Badhe, Y; Lonari, J; Sridevi, U; Rao, BS; Tambe, SS; Kulkarni, BD. Hybrid process modeling and optimization strategies integrating neural networks/support vector regression and genetic algorithms: study of benzene isopropylation on Hbeta catalyst. CHEMICAL ENGINEERING JOURNAL, 97CS 539 PROJECT: NEURAL NETWORK SURROGATE MODELS IN CHEMICAL PROCESS OPTIMIZATION -5- (2-3): 115-129 FEB 15 2004 • Soterios A. Papoulias and Ignacio E. Grossmann, A structural optimization approach in process synthesis--II : Heat recovery networks, Computers & Chemical Engineering, Volume 7, Issue 6, 1983, Pages
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