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

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

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