Environmental Science and Pollution Research

, Volume 25, Issue 10, pp 9360–9370 | Cite as

Application of experimental design for the optimization of artificial neural network-based water quality model: a case study of dissolved oxygen prediction

  • Aleksandra Šiljić Tomić
  • Davor Antanasijević
  • Mirjana Ristić
  • Aleksandra Perić-Grujić
  • Viktor Pocajt
Research Article


This paper presents an application of experimental design for the optimization of artificial neural network (ANN) for the prediction of dissolved oxygen (DO) content in the Danube River. The aim of this research was to obtain a more reliable ANN model that uses fewer monitoring records, by simultaneous optimization of the following model parameters: number of monitoring sites, number of historical monitoring data (expressed in years), and number of input water quality parameters used. Box–Behnken three-factor at three levels experimental design was applied for simultaneous spatial, temporal, and input variables optimization of the ANN model. The prediction of DO was performed using a feed-forward back-propagation neural network (BPNN), while the selection of most important inputs was done off-model using multi-filter approach that combines a chi-square ranking in the first step with a correlation-based elimination in the second step. The contour plots of absolute and relative error response surfaces were utilized to determine the optimal values of design factors. From the contour plots, two BPNN models that cover entire Danube flow through Serbia are proposed: an upstream model (BPNN-UP) that covers 8 monitoring sites prior to Belgrade and uses 12 inputs measured in the 7-year period and a downstream model (BPNN-DOWN) which covers 9 monitoring sites and uses 11 input parameters measured in the 6-year period. The main difference between the two models is that BPNN-UP utilizes inputs such as BOD, P, and PO43−, which is in accordance with the fact that this model covers northern part of Serbia (Vojvodina Autonomous Province) which is well-known for agricultural production and extensive use of fertilizers. Both models have shown very good agreement between measured and predicted DO (with R2 ≥ 0.86) and demonstrated that they can effectively forecast DO content in the Danube River.


Dissolved oxygen Modeling ANN Design of experiment Parameter selection 



This work was supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia [Project No. 172007].

Supplementary material

11356_2018_1246_MOESM1_ESM.pdf (4.6 mb)
ESM 1 (PDF 4733 kb)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Technology and MetallurgyUniversity of BelgradeBelgradeSerbia
  2. 2.Innovation Center of the Faculty of Technology and MetallurgyUniversity of BelgradeBelgradeSerbia

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