Soft Computing

, Volume 22, Issue 7, pp 2205–2215 | Cite as

A novel hybrid neural network based on phase space reconstruction technique for daily river flow prediction

  • Hadi Delafrouz
  • Abbas Ghaheri
  • Mohammad Ali Ghorbani
Methodologies and Application


The main purpose of this study is to construct a new hybrid model (PSR–ANN) by combining phase space reconstruction (PSR) and artificial neural network (ANN) techniques to raise the accuracy for the prediction of daily river flow. For this purpose, river flow data at three measurement stations of the USA were used. To reconstruct the phase space and determine the input data for the PSR–ANN method, the delay time and embedding dimension were calculated by average mutual information and false nearest neighbors analysis. The presence of chaotic dynamics in the used data was identified by the correlation dimension methods. The results of the PSR–ANN, pure ANN and gene expression programming (GEP) models were inter-compared using the Nash–Sutcliffe and root-mean-square error criteria. The inter-comparisons showed that the proposed PSR–ANN method provides the best prediction of daily river flow. Moreover, the ANN model showed higher ability than the pure GEP in estimation of the river flow.


Artificial neural network Gene expression programming Phase space reconstruction Prediction River flow 



The authors are grateful to editor and anonymous reviewers for their helpful and constructive comments which greatly improved the quality of this paper.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Human and animals participants

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Hadi Delafrouz
    • 1
  • Abbas Ghaheri
    • 1
  • Mohammad Ali Ghorbani
    • 2
  1. 1.School of Civil EngineeringIran University of Science and TechnologyNarmakIran
  2. 2.Department of Water EngineeringUniversity of TabrizTabrizIran

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