Derivation of NARX models by expanding activation functions in neural networks.

A method was developed to derive an NARX model from a neural network so that the usability of open‐source libraries for network learning was combined with the NARX advantage of revealing the system structure. After the neural network model was trained on input and output data, the sigmoid activation functions were expanded into Taylor series. Candidate parameters in the NARX model were calculated from the connection weights in the neural network and coefficients in the series. The NARX model structure was determined by the extended least‐squares (ELS) method and the Bayesian information criterion (BIC). Correct NARX models were successfully detected in computer simulations and an experiment. The developed method can be used for any activation functions, including the sigmoid function, if they are expanded into Taylor series. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]