Decision support has two distinct but interrelated aspects: optimization based on mathematical modelling of physical plants and processes, and the fuzzy optimization involving mental processing by human operators. The research will build on our recent research results concerning analogue neural networks, and extends other researcher's work which confirmed the feasibility of mapping both numerical and fuzzy optimization tasks onto appropriate neural networks. The novelty of the project is in defining more efficient neural network models for optimization, as well as enhancing existing models, and then combining them into a coherent environment for robust optimization of industrial processes. Neural network technology has matured enough to indicate its potential use in real-time industrial situations. However, industrial application is hindered by noisy and incomplete measurements, large scale non-linear models, existence of many local minima in optimization problems, and different process operation regimes requiring different control strategies and time constraints. The project will address each of these difficulties. All parts of the project and their interconnections can be presented in a form of this block diagram.
The proposed solution to this nonlinear optimization problem utilizes the Newton-Raphson iterative method. This method has been widely and successfully used in the context of water distribution systems. It relies on the linearised model of a water network. The solution is found by iteratively solving a system of linear equations and adjusting the state vector values. The focus of this work was to implement and test neural networks for solving systems of linear equations.
The process of constructing the neural network for solving a system of linear equations according to some appropriate criteria is presented here. Several neural networks for solving an overdetermined system of linear equations according to Least Mean Squares(LMS), Least Absolute Value (LAV) and MinMax (Chebyshev) criterias have been implemented and tested in MATLAB/SIMULINK environment as well as in C on the SUN SPARC station.
A paper (`Neural Simulation of Water Systems for Efficient State Estimation'), in which one of the neural networks has been used to obtain state estimates optimal for LMS and LAV criterias, was presented at European Simulation Multiconference, ESM'95.
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