HYBRID NEURAL MODELING OF THE ELECTRICAL CONDUCTIVITY PROPERTY OF RECOMBINED MILK

Abstract

This paper focuses on modeling the electrical conductivity of recombined milk by a hybrid neural modeling technique. It aims to establish a model that accounts for the effect of milk constituents (protein, lactose, and fat) and temperature on the electrical conductivity of recombined milk. Such a model should provide physical insight to the underlying relationship, in addition to its high precision. A hybrid neural model was established by combining a mechanistic model to explain the major interrelation and an ANN model to deal with the difference and noise. Two mechanistic models and two 4-layer ANN models were developed. The best mechanistic model in terms of the smallest sum square error (SSE) combined a linear equation describing the effect of milk component concentration and a non-linear equation describing the effect of temperature. For this model, the correlation coefficient between the actual electrical conductivity and the modelled electrical conductivity was 0.9878 and SSE was 1.3376. Combining it with the 4-layer ANN model that produced the smallest SSE, the resulted hybrid neural model provided the best performance, with a correlation coefficient of 0.9982 between the actual electrical conductivity and the modelled electrical conductivity and a SSE of 0.1410. Abbreviations: ANN, artificial neural network; EC, electrical conductivity (mS/cm); c, concentration (mol.m−3); D, diffusion coefficient (m2.s−1); F, Faraday constant (A.s.mol−1); ΔG, Gibbs free energy of activation for the reaction (kJ.mol−1); K, specific conductivity (Ω−1.m−1); k, dissociation constant (mol.m−3); R, ideal gas constant (J.K−1.mol−1); T, temperature (K); Λ0, molar conductivity at infinite dilution (Ω−1.m2.mol−1); Λc, molar conductivity at finite dilution (Ω−1.m2.mol−1); z i , charge number