Application of Artificial Neural Networks for Modelling of Nicolsky-Eisenman Equation and Determination of Ion Activities in Mixtures

  • Józef Wiora
  • Dariusz Grabowski
  • Alicja Wiora
  • Andrzej Kozyra
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 322)


The paper deals with the problem of ion activity determination for a mixture by means of ion-selective electrodes. Mathematical model of the analysed phenomenon is described by the Nicolsky-Eisenman equation, which relates activities of ions and ion-selective electrode potentials. The equation is strongly nonlinear and, especially in the case of multi-compound assays, the calculation of ion activities becomes a complex task. Application of multilayer perceptron artificial neural networks, which are known as universal approximators, can help to solve this problem. A new proposition of such network has been presented in the paper. The main difference in comparison with the previously proposed networks consists in the input set, which includes not only electrode potentials but also electrode parameters. The good network performance obtained during training has been confirmed by additional tests using measurement results and finally compared with the original as well as the simplified analytical model.


Artificial neural network Potentiometry Ion-selective electrode 


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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Józef Wiora
    • 1
  • Dariusz Grabowski
    • 2
  • Alicja Wiora
    • 1
  • Andrzej Kozyra
    • 1
  1. 1.Institute of Automatic ControlSilesian University of TechnologyGliwicePoland
  2. 2.Institute of Electrical Engineering and Computer ScienceSilesian University of TechnologyGliwicePoland

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