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Nonlinear Process Modelling Using Echo State Networks Optimised by Covariance Matrix Adaption Evolutionary Strategy

Lookup NU author(s): Dr Kai Liu, Dr Jie ZhangORCiD



This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND).


Echo state networks (ESN) have been shown to be an effective alternative to conventional recurrent neural networks (RNNs) due to its fast training process and good performance in dynamic system modelling. However, the performance of ESN can be affected by the randomly generated reservoir. This paper presents nonlinear process modelling using ESN optimized by covariance matrix adaption evolutionary strategy (CMA-ES). CMA-ES is used to optimize the structural parameters of ESN: reservoir size, spectral radius, and leak rate. The proposed method is applied to three case studies: modelling a time series, modelling a conic tank, and modelling a fed-batch penicillin fermentation process. The results are compared with those from the original ESN, long short-term memory network, GA-ESN (ESN optimized by genetic algorithm), and feedforward neural networks. It is shown that the proposed method gives much better performance than the original ESN and other networks on all the three case studies.

Publication metadata

Author(s): Liu K, Zhang J

Publication type: Article

Publication status: Published

Journal: Computers & Chemical Engineering

Year: 2020

Volume: 135

Print publication date: 06/04/2020

Online publication date: 13/01/2020

Acceptance date: 11/01/2020

Date deposited: 13/01/2020

ISSN (print): 0098-1354

ISSN (electronic): 1873-4375

Publisher: Elsevier


DOI: 10.1016/j.compchemeng.2020.106730


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