Reduced model-based global optimisation of largescale steady state nonlinear systems

Many engineering systems can be accurately simulated using partial differential equations (PDEs), resulting in large-scale distributed parameter systems. Deterministic global optimisation algorithms (GOP) can compute global optimal solutions offering theoretical guarantees on the global optimality. However, distributed parameter systems pose computational challenges for these optimisation methods. 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. Still, the optimisation problem is hard to solve due to the high nonlinearity of activation functions in the reduced ANN structure. A novel piece-wise linear approximation reformulation is introduced to reduce the complexity of the original problem and to provide a good globally approximate solution. The performance of the proposed PCA-ANN-GOP framework is demonstrated through an illustrative example: a tubular reactor where an exothermic reaction takes place.