Artificial Neural Network and Regression Models to Evaluate Rheological Properties of Selected Brazilian Honeys

Model			Training data				Test data				Total data

			Mean	STD	Min	Max	Mean	STD	Min	Max
1^(*)	Inputs	WC (%)	15.78	1.02	14.23	18.86	15.78	1.03	14.23	18.86	320
	Inputs	T (°C)	30.90	15.88	10.00	60.00	32.31	17.82	10.00	60.00
	Outputs	η (Pa.s)	24.92	36.91	0.37	225.27	27.17	38.73	0.23	177.99

2^(*)	Inputs	WC (%)	15.82	1.03	14.23	18.86	15.75	0.99	14.23	18.86	800
	Inputs	T (°C)	39.28	21.42	3.67	74.57	39.22	21.83	3.61	74.48
	Outputs	G′ (Pa)	1.27	3.56	0.00	36.67	1.18	2.76	0.00	20.82
		G″ (Pa)	299.97	744.95	0.92	6174.37	308.74	676.12	1.43	4571.52
		η* (Pa.s)	47.74	118.56	0.15	982.70	49.14	107.61	0.23	727.59

3^(*)	Inputs	WC (%)	15.80	1.03	14.23	18.86	15.73	0.99	14.23	18.86	800
		T (°C)	35.96	21.35	0.55	71.43	35.95	21.71	0.57	71.42
		G′ (Pa)	28.29	70.77	0.00	772.13	22.85	48.72	0.00	354.15
	Outputs	G″(Pa)	493.78	1169.19	0.83	8455.12	530.61	1282.02	1.02	8398.52
		η* (Pa.s)	78.93	186.42	0.13	1346.14	84.66	204.16	0.16	1336.82

4^(**)		WC (%)	15.78	1.02	14.23	18.86	15.79	1.02	14.23	18.86	4160
	Inputs	T (°C)	31.08	16.24	10.00	60.00	31.76	16.67	10.00	60.00
		F (Hz)	2.42	2.95	0.10	10.00	2.34	2.89	0.10	10.00
		G′ (Pa)	2.42	8.29	0.00	233.52	2.29	7.14	0.00	151.11
	Outputs	G″ (Pa)	407.86	1081.78	0.18	16404.51	405.20	1052.59	0.23	9751.40
		η* (Pa.s)	27.74	40.98	0.28	268.32	26.94	39.96	0.28	266.10

WC: water content; T: temperature; η: steady shear viscosity; G′: Storage moduli; G″: loss moduli; η*: complex viscosity; F: Frequency.

Reference:

(*) Silva et al (2016) and

(**) Silva et al. (2018).

RMSE of training (solid line) and test (dotted line) sets versus number of iterations for optimum MLP ANN: a) model 1; b) model 2; c) model 3; d) model 4.

Table 2

RMSE and correlation coefficient (r) of models 1, 2 and 3 variables from the development and test process of a nonlinear exponential and of models 1, 2, 3 and 4 from the best ANNs models

Model	Estimated variable	Empirical constants¹			Exponential Model (Training data)		Exponential Model (Test data)		ANN (Training)		ANN (Test)

		A	B	C	RMSE	r	RMSE	r	RMSE	r	RMSE	r
1	η (Pa.s)	0.799	2.036	6.415	0.0101	0.9981	0.0433	0.9700	0.0359	0.9760	0.0430	0.9681

	G′ (Pa)	0.805	3.302	14.696	0.0343	0.9356	0.0290	0.9293	0.0338	0.9398	0.0261	0.9390
2	G″ (Pa)	0.881	2.549	10.953	0.0282	0.9725	0.0272	0.9688	0.0296	0.9704	0.0252	0.9731
	η* (Pa.s)	0.881	2.549	10.953	0.0282	0.9725	0.0272	0.9688	0.0295	0.9705	0.0252	0.9731

	G′ (Pa)	0.489	2.628	8.542	0.0659	0.6948	0.0521	0.7055	0.0675	0.6969	0.0486	0.6629
3	G″ (Pa)	0.911	1.684	12.549	0.0313	0.9742	0.0320	0.9779	0.0308	0.9758	0.0326	0.9794
	η* (Pa.s)	0.913	1.687	12.526	0.0314	0.9742	0.0320	0.9779	0.0309	0.9759	0.0326	0.9794

	G′ (Pa)	-	-	-	-	-	-	-	0.0260	0.7244	0.0158	0.7301
4	G″ (Pa)	-	-	-	-	-	-	-	0.0195	0.9604	0.0176	0.9581
	η* (Pa.s)	-	-	-	-	-	-	-	0.0420	0.9636	0.0406	0.9647

(1) Empirical constants of the exponential model using the training data.

Table 3

RMSE and correlation coefficient (r) of model 4 variables from the development and test process of a multiple-second order polynomial regression

Variable	Model Coefficient¹											Training data		Test data

	β₀	β₁	β₂	β₃	β₁₂	β₁₃	β₂₃	β₁₂₃	β₁₁	β₂₂	β₃₃	RMSE	r	RMSE	r
G′ (Pa)	-	0.01	−0.04	0.10	−0.02	−0.17	−0.17	0.26	-	0.05	0.06	0.0295	0.6189	0.0170	0.6932
G″ (Pa)	0.03	−0.03	−0.20	0.38	-	−0.40	−0.51	0.56	0.04	0.20	-	0.0362	0.8503	0.0293	0.8539
η* (Pa.s)	0.49	−0.53	−1.29	-	0.52	-	-	-	0.16	0.81	-	0.0680	0.8964	0.0640	0.9018

(1) Coefficients of the multiple regression model using the training data of model 4.

( - ) p-value > 0.05 obtained by ANOVA.

References

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Articles in this issue

DOI: https://doi.org/10.2478/jas-2020-0017 | Journal eISSN: 2299-4831 | Journal ISSN: 1643-4439 (formerly 2299-4831)

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Language: English

Page range: 219 - 228

Submitted on: Jul 12, 2019

Accepted on: May 8, 2020

Published on: Nov 7, 2020

Published by: The National Institute of Horticultural Research and Apicultural Research Association

In partnership with: Paradigm Publishing Services

Keywords:

artificial neural network models,

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© 2020 Vanelle M. D. Silva, Wilian S. Lacerda, Jaime V. de Resende, published by The National Institute of Horticultural Research and Apicultural Research Association
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 64 (2020): Issue 2 (December 2020)

Artificial Neural Network and Regression Models to Evaluate Rheological Properties of Selected Brazilian Honeys

Figures & Tables

Table 1

Fig. 1

Table 2

Table 3

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