HYBRID NEURAL MODELING OF THE ELECTRICAL CONDUCTIVITY PROPERTY OF RECOMBINED MILK

Figures & data

Structure of hybrid neural model.

Electrical Conductivity at Different Temperatures in the First Mechanistic Model

T	Equation	R	SSE
50°C	K 50=791.0c P −2.6c L −1.5c F +2.5	0.9849	0.1712
55°C	K 55=851.9c P −2.9c L −1.6c F +2.7	0.9864	0.1792
60°C	K 60=918.2c P −3.1c L −2.2c F +3.0	0.9849	0.2317
65°C	K 65=976.3c P −3.2c L −2.1c F +3.1	0.9814	0.3221

Concentration Coefficients in the First Mechanistic Model

Component	Equation	R	SSE
Protein	A=+9.87×10^4exp(−1.54×10^3/T)	0.9994	7329.5
Lactose	B=−2.00×10^2exp(−1.40×10^3/T)	0.9501	0.0220
Fat	C=−1.99×10^4exp(−3.09×10^3/T)	0.8987	0.0941
Constant	D=+6.02×10^2exp(−1.77×10^3/T)	0.9969	0.0019

Electrical Conductivity at Different Temperatures in the Second Mechanistic Model

T	Equation	R	SSE
50°C	(K ^2+2K)50=5978.3c P −20.0c L −11.2c F +11.2	0.9794	0.2346
55°C	(K ^2+2K)55=6852.3c P −23.7c L −12.9c F +13.0	0.9811	0.2511
60°C	(K ^2+2K)60=7868.8c P −26.7c L −18.7c F +14.8	0.9774	0.3505
65°C	(K ^2+2K)65=8879.6c P −28.9c L −19.4c F +16.4	0.9731	0.4688

Concentration Coefficients in the Second Mechanistic Model

Component	Equation	R	SSE
Protein	A=+4.86×10^7exp(−2.89×10^3/T)	0.9998	2170.6
Lactose	B=−8.08×10^4exp(−2.68×10^3/T)	0.9882	1.0748
Fat	C=−9.82×10^6exp(−4.42×10^3/T)	0.9459	5.3777
Constant	D=+5.99×10^4exp(−2.78×10^3/T)	0.9975	0.0764

Performance of the Two ANN Models for Hybrid Neural Modelling

Models	Training	Verification
ANN model to be combined with the first mechanistic model (4-4-4-1 structure with log-sigmoid transfer function)	SSE=0.4826	SSE=0.5397
	MSE=0.0042	MSE=0.0415
	R=0.9278	R=0.9069
ANN model to be combined with the second mechanistic model (4-4-4-1 structure with log-sigmoid transfer function)	SSE=0.6308	SSE=0.0479
	MSE=0.0055	MSE=0.0037
	R=0.8988	R=0.9420

Model Performance of Various EC Models

Performance	ANN Model[12]	The First Mechanistic Model	The Second Mechanistic Model	The First Hybrid Neural Model^1	The Second Hybrid Neural Model^2
SSE	0.4864	1.3376	1.5656	0.1410	0.2747
MSE	0.0038	0.0104	0.0122	0.0011	0.0021
R	0.9937	0.9878	0.9822	0.9982	0.9964

¹Combining the first mechanistic model and the first ANN model in Table 5.

²Combining the second mechanistic model and the second ANN model in Table 5.

Figure 2.Correlation between the actual EC and the modelled EC by the 1st hybrid neural model.

Figure 3. Correlation between the actual EC and the modelled EC by the 2nd hybrid neural model.

Therdthai , N. and Zhou , W. 2001 . Artificial Neural Network Modelling of the Electrical Conductivity Property of Recombined Milk . Journal of Food Engineering , 50 ( 2 ) : 107 – 111 .

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