Adaptive Sampling for Surrogate Modelling with Artificial Neural Network and its Application in an Industrial Cracking Furnace

Abstract

In surrogate modelling, a simple functional approximation of a complex system model is always constructed to reduce the computational expense, and the selection of a suitable surrogate model and a sampling method are key to obtaining a surrogate model for a complex system. To construct an appropriate surrogate model, three methods of adaptive surrogate modelling that use artificial neural networks (ANN) are developed by incorporating a new mechanism for automatically determining the number of hidden nodes and/or a new prediction error-based mixed adaptive sampling method. In the automatic determination, the number of hidden nodes can adaptively change according to the effective rate of parameters in the ANN during the adaptive surrogate modelling process. As a result, an improper number of hidden nodes determined by the empirical method can be avoided. The prediction error-based mixed adaptive sampling method is capable of finding the strong nonlinear behaviour of the underlying system, which is easily missed by the traditional prediction variance-based sampling method. The three methods and the previous method for adaptive surrogate modelling that use ANN are tested and compared in terms of replicating the behaviours of three types of challenge functions to determine the efficacy of the developed methods. Furthermore, these methods are used in an engineering problem of surrogate modelling for a cracking reaction simulator to validate the efficacy of the developed methods.

Experimental methods in chemical engineering: Artificial neural networks–ANNs

“…Eng. [5][6][7][8][9][32][33][34] ), ANNs are unboundedwe apply them across all specialties including polymerization, oil production, battery heating, modelling, control of industrial plants, and catalysis. Most of this research applies commercial software packages like the MATLAB Deep Learning Toolbox.…”

“…As well as modelling new relationships, ANNs can be used as surrogate models to reduce computational costs. These black box models approximate complex models but are unsuitable for extrapolation outside the range of conditions for which they were intended …”

“…These black box models approximate complex models but are unsuitable for extrapolation outside the range of conditions for which they were intended. [8] It is possible to combine ANNs with first principle models to develop hybrid or grey box models. Zahedi et al [52] did this to model the reaction of ethylene to ethylene oxide in a fixed bed reactor.…”

“…In chemical engineering, ANN applications vary from the control of oil production processes to modelling biosorption . Furthermore, they address computationally intensive problems related to fluid dynamics, predicting new process output, or estimating vapour‐liquid equilibria . Schmidhuber reviews the broader application of ANNs and their ties to big data, multi‐core systems, parallel computing, and application specific integrated circuits (ASICs).…”

A Critical Review of the Modeling and Optimization of Combined Heat and Power Dispatch

“…Furthermore, over recent decades, novel modeling techniques have been developed which can substantially aid the optimization of process systems. For instance, surrogate models such as Kriging [39][40][41][42][43][44], radial basis functions [45][46][47][48][49][50], artificial neural networks [51][52][53][54][55][56], splines [57,58], among others were shown to accurately represent complex physical systems while aiding optimal search algorithms. No literature exists which explores the application of such techniques to advance the study of CHP dispatch.…”