(194h) Model Reduction-Based Global Optimisation for Large-Scale Steady State Nonlinear Systems
The aim of this work is to construct deterministic global optimisation methods for large-scale input/output simulators. Deterministic global optimisation methods are usually computationally intensive due to the repeated utilisation of branch-and-bound algorithms. Hence, in terms of computation cost, detailed models of large-scale problems are very hard or even impossible to deal with. Model reduction techniques can produce low-order systems that are computationally amenable. In this work, a combined principal component analysis (PCA) and artificial neural networks (ANNs)-based model reduction methodology is employed for the global optimisation of large-scale distributed steady state systems. The basic PCA-ANN-GOP framework performs well for small-scale problems. However, the optimisation problem is hard to solve due to the high non-convexity of activation functions in the reduced ANN structure . To enlarge capability of our optimisation framework, two kinds of improvements has been made: The first, is a novel piece-wise linear approximation (PWA) reformulation for the nonlinear activation function. The computation results show this PWA model can reduce the complexity and ensure the accuracy. The second improvement is the replacement of the nonlinear activation function with a continuous piece-wise linear function. The performance of the improved PCA-ANN-GOP framework is demonstrated through an illustrative nonlinear large-scale chemical engineering example: a complex large-scale combustion process.
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