Dynamic Mechanical Spectra of Selected Turkish Honeys: Construction of Predictive Models for Complex Viscosity Using Two Different Nonlinear Modeling Techniques

Abstract

Dynamic oscillatory shear rheological characteristics of honey samples from different floral sources were evaluated using frequency sweep test and stress sweep test at three different temperatures (10, 15, and 20°C). All honey samples showed liquid-like behavior because the loss modulus was significantly greater than the elastic modulus. Pine honey showed the highest complex viscosity (86.33 Pa s at 10°C), while the lowest complex viscosity was observed in citrus honey (22.15 Pa s) at the same temperature. Temperature dependency of complex viscosity of honey samples was modeled by Arrhenius model and activation energy values of honeys ranged from 83.13 to 97.46 kJ/mol. An efficient predictive model for complex viscosity values of honeys was constructed using adaptive neuro fuzzy inference system that showed satisfactory prediction performance with high coefficient of determination (0.995) and low root mean square error (0.04) in the validation period compared to artificial neural networks.

Keywords:

• Honey
• Dynamic rheology
• Arrhenius
• ANFIS
• ANN

INTRODUCTION

Honey is a sweet and natural liquid-like food with high nutritional value produced by honeybees from plant nectar or honeydew. It contains readily digestible sugar, different organic acids, many amino acids, and different bioactive compounds.[1, 2] Honey contains different sugar types depending on the variety, most of which are in monosaccharide form, namely, glucose and fructose, and also some disaccharides are present in honey.[3] Honey is one of the most important food products produced in Turkey, which ranks fourth in honey production among the honey-producing countries. Many different honey types are present with different floral origins in the world and the common honey varieties are chestnut, citrus, pine, thyme, linden, sunflower, and cotton.[4] Since honey is a semi-solid food product, its rheological characteristics as well as physicochemical properties are important for the food industries and consumers. One of the most important rheological characteristics of honey is viscosity. Apparent viscosity as a function of shear rate is related to steady state shear rheology and it is particularly critical during storage, handling, and processing.[5, 6] The magnitudes of viscosity values and other rheological characteristics are influenced by different factors, including composition, temperature, amount and size of crystals, and moisture content. Due to the differences in variety, rheological characteristics and physicochemical properties change depending on the structure of the honey.[3, 5]

Many different studies are present in the literature related to physicochemical properties and rheological characterization of different honey types from different countries.[2, 3, 7– 11] According to the information given in the literature, honey is a Newtonian fluid. But some honey samples showed a thixotropic behavior due to the presence of colloids in their structure, such as buckwheat, heather, and white clover.[3, 12]

Adaptive neuro fuzzy inference system (ANFIS) and artificial neural networks (ANN) are effective and novel nonlinear modeling techniques used in food science to model a complex nonlinear system. Effective predictive models can be constructed using ANFIS and ANN because foods have a complex nonlinear nature. There are different studies related to application of these nonlinear modeling techniques to estimate the different parameters of food samples, and effective predictive models were constructed.[13– 16]

In our previous work, some Turkish honey samples were rheologically characterized.[4] All honey samples studied showed Newtonian behavior in steady state shear rheological measurements. Until today, no study has appeared in the literature focusing on the dynamic mechanical spectra of Turkish honeys. For that reason, the main aim of this study was to determine the dynamic mechanical properties of some Turkish honey samples and temperature dependency of some important rheological parameters. Also, it was aimed that the construction of predictive models using effective nonlinear modeling techniques, such as ANFIS and ANN, would estimate the complex viscosity values of sample depending on the variety, measurement temperature, and frequency.

MATERIALS AND METHODS

Honey Samples

Three honey varieties (citrus, flower, and pine) used in the present study were obtained from Anavarza Company (Anavarza Brand, Sezen Food Co., Adana, Turkey). Citrus and flower honeys were nectar honeys, while pine honey was from honeydew. Before the rheological measurements, commercial grade honeys were preconditioned because the viscosity may be influenced by air bubbles and crystals present in the honey. For this purpose, the honey samples were held at 55°C in a water bath for 1 h, and afterwards placed overnight in an oven (Nuve, Ankara, Turkey) at 30°C.

Physicochemical Analysis

The dry matter content of the samples was determined according to the standard procedures.[17] Ash content was found by incinerating samples at 625°C in a muffle oven (Protherm, Ankara, Turkey) after drying and pH of honey samples was determined using a pH meter (WTW-Inolab, Weilheim, Germany) in a solution of 10% (w/v) honey in distilled water at 25°C. Water activity of the samples at 20°C was determined using an Aqualab water activity (A_w) meter (Decagon, Pullman, WA, USA). A colorimeter (Lovibond RT Series Reflectance Tintometer, Amesbury, England) was used to determine the color values of the samples; the color values were recorded as L (brightness), a (±red–green), and b (±yellow–blue). Each analysis was repeated three times.

Dynamic Mechanical Analysis

Dynamic mechanical properties of honey samples were determined using a stress/strain controlled rheometer (RheoStress 1, Haake, Karlsruhe, Germany) equipped with a temperature control unit (Thermo-Haake, Karlsruhe, Germany). Cone and plate geometry was used (cone diameter 35 mm, angle 4°, and gap size 0.140 mm) for the measurements. Before applying the frequency sweep test, the stress sweep test procedure was carried out to determine the linear viscoelastic region (LVR) of samples. Using this test, variation of dynamic mechanical spectra of honey varieties versus increased stress was characterized and LVR of samples over a stress range of 0.1–10 Pa at constant frequency (1 Hz) was determined since LVR is essential for the frequency sweep test application. In an oscillatory frequency sweep test, dynamic mechanical spectra of the honey sample were evaluated in the frequency range of 0.1–10 Hz at constant stress (within the range of LVR) at three different temperatures (10, 15, and 20°C). Low temperatures were selected for the rheological measurements since honey is very sensitive to the temperature. A sinusoidal stress or strain with an increasing frequency was applied to the honey sample at selected temperatures. The elastic modulus G′ and the viscous modulus G′′ are calculated as a function of frequency:[18]

(1)

(2)

The overall response of the sample against the oscillatory shear may be characterized using the equations of complex modulus G* and complex viscosity η*:

(3)

(4)

The temperature dependency of complex viscosity and complex modulus of honey samples at a specified frequency (1 Hz) was described by the Arrhenius model:[19, 20]

(5)

(6)

where η* and G* are the complex viscosity (Pa·s) and complex modulus (Pa), respectively; η₀ ^* and G ₀ ^* are a constant for complex viscosity (Pa s) and complex modulus (Pa), respectively; E _a is the activation energy (kj/mol); R is the universal gas constant (8.314 J/mol K); and T is the absolute temperature (K).

The activation energy was obtained by linear plotting of ln (η* and G*) against (1/T). The mean absolute percentage error (MAPE) was assessed according to the following equation to determine the deviance of calculated viscosity by the Arrhenius model from the observed value:

(7)

where Y_o is the observed viscosity, Y_c is the calculated viscosity using Arrhenius model, and n is the number of pairs.[4]

Nonlinear Modeling Procedure

The fuzzy logic toolbox of MATLAB 7.0.1 was used for the construction of the ANFIS model. Before starting the modeling, experimental complex viscosity data of samples were classified into three groups. Half of the selected data (90 data points) was determined as training data matrix. For the testing and validation of a fuzzy model system, 45 data points different from the data selected for training were used, separately. In the construction of the fuzzy model, three membership functions and product-of-sigmoidals membership function type (psig mf) for input and constant membership function type for output were used and models were constructed using ANFIS and Sugeno-type fuzzy inference system. Determination of coefficient (R ²), root mean square error (RMSE), and mean absolute error (MAE) were calculated as comparison criteria for the evaluation of developed model parameters. Honey type, measurement frequency of dynamic mechanical spectra, and temperature were selected as input while the complex viscosity was output. Ten learning epochs and a radius of 0.5 were used for the development and implementation of models.

ANN modeling was carried out using MATLAB 7.0.1. (Statistics Toolbox, MatLab 7.0.1., The MathWorks, Inc., MA, USA). It has one or more hidden layers, whose computation nodes are called hidden neurons. Computed outputs are compared with experimental outputs, and obtained errors are back propagated to obtain the appropriate weight adjustments necessary to minimize errors in this modeling technique.

In the present study, the ANN was trained using the Levenberg–Marquardt technique because this technique is more powerful and faster compared to the conventional gradient descent technique.[21, 22] The number of hidden layer neurons was determined using a simple trial–error technique in all applications. The ANN networks training were stopped after 50 epochs since the variation of error was too small after this period. The number of nodes in a layer was determined as 3-3-1 for ANN.

Statistical Analysis

The statistical analysis software package MINITAB[23] for Windows Release 13 was used for the statistical analysis. The effect of independent variables on the dependent variable was determined using one-way Analysis of Variance (ANOVA) with the general linear model procedure. Duncan Multiple Range Test was used to determine the difference between mean combination values using MstatC software.[24]

RESULTS AND DISCUSSION

Physicochemical Properties

The results of physicochemical analysis of honey samples were tabulated in Table 1. As can be seen from the table, moisture content of samples showed no significant differences (p > 0.05). These results are consistent with the results obtained in our previous work. Moisture content of honey samples were found to be close to each other and very important differences were not observed among the moisture of them, which is determined by the refractometric method.[4] The ash content of the sample was determined in the range of 0.08–0.80%. The difference among the ash content of the samples was found to be significant (p < 0.05). The highest ash content was determined for pine honey, which is honeydew, compared to nectar honeys. Similar results were obtained in different studies. Ouchemoukh et al.[25] found that the highest ash content (0.54%) for honeydew botanical origin and nectar honeys showed lower ash content compared to honeydew. A similar trend was determined by Kayacier and Karaman.[4] pH value of the honey samples ranged from 4.45 to 5.63. It can be said that Turkish honeys have an acidic characteristic. The lowest pH was measured for citrus honey; the differences were statistically significant (p < 0.05). Pine honey, a honeydew honey, showed the highest pH. Similar results were reported by Terrab et al.[26] They found the average pH values of the citrus and honeydew honey to be 3.55 and 4.28, respectively. Nanda et al.[27] stated that the acidic character of honeys is attributed to the presence of organic acid and variations in those constituents may be caused by a variation in acidity among the different honeys. Water activity values were determined to be low (0.57–0.58) as expected because honey has a high amount of sugar and no significant difference among the water activity of samples was shown (p > 0.05). Kayacier and Karaman[4] reported that there was no difference among the water activity values of pine, citrus, and flower honey (p > 0.05), and the values were in the range of 0.51–0.52. In another study, water activity values of the honey samples were in the range of 0.528–0.663.[28]

Table 1  Physicochemical properties of different honey samples

	Type of honey
Parameters	Pine	Flower	Citrus
Dry matter (%)	80.99 ± 0.364^A	80.98 ± 0.241^A	80.86 ± 0.439^A
Ash (%)	0.80 ± 0.012^A	0.28 ± 0.003^B	0.08 ± 0.005^C
pH	5.63 ± 0.006^A	4.84 ± 0.005^B	4.45 ± 0.005^C
aw	0.57 ± 0.001^B	0.58 ± 0.001^A	0.57 ± 0.001^B
L	8.93 ± 0.025^C	10.81 ± 0.079^B	19.29 ± 0.225^A
a	5.82 ± 0.031^A	4.71 ± 0.006^B	4.03 ± 0.015^C
b	11.23 ± 0.091^B	11.34 ± 0.092^B	17.30 ± 0.176^A
The superscript uppercase letters show statistical significance in each column (p < 0.05).

Citrus honey was found to be the highest bright honey sample because L values were found to be the highest (19.29) compared to the pine (8.93) and flower (10.81) and differences were found to be significant (p < 0.05). On the contrary, redness was determined to be high in pine honey with a high value (5.82), while the lowest was in citrus honey (4.03). The b value of citrus honey showed a significant difference compared to pine and flower honey (p < 0.05) and ranged between 11.23–17.30.

Rheological Characteristics

Frequency sweep test results

It is well known that most of the honey samples show a Newtonian flow behavior.[3, 7– 9] As stated in our previous work, pine, citrus, and flower honeys studied in the present work showed Newtonian flow behavior. The shear stress of Turkish honey samples increased while the apparent viscosity remained constant with increasing shear rate.[4] Figure 1 illustrates the oscillatory shear rheological parameters of honey samples obtained from frequency sweep test. It is clear that complex viscosity of pine, flower, and citrus honey remained constant with increasing frequency. Independence of complex or apparent viscosity of sample from shear rate or frequency means typical liquid like macromolecular solution.[29] Hence, it could be claimed that rheology of honey samples is similar to that of a liquid-like macromolecular solution. Complex viscosity of pine honey was measured to be 44.63 Pa s at 1 Hz and 15°C, while the complex viscosity of flower and citrus were 21.73 and 12.91 Pa s, respectively (Table 2). Complex modulus as a function of loss modulus and storage modulus increased with increasing frequency and showed a similar behavior to loss modulus because it has a high impact on complex modulus because of its high value; the highest complex modulus value was observed for the pine honey (280.43 Pa) at 1 Hz and 15°C, while the lowest was observed for the citrus honey (81.14 Pa). Loss modulus that is a measure of the energy lost as viscous dissipation and indicates liquid behavior was found to be very high. The highest loss modulus value was measured for pine honey for all temperatures compared to those of others (Table 2). Storage modulus (G′) that is a measure of the energy stored in the material was found to be very low for all honey samples and it increased with increasing frequency (Fig. 1). It could be said that storage modulus is less important than loss modulus due to its very low values.[11, 30] Also, small fluctuations were observed in storage modulus for all honeys because samples do not have elastic behavior. For that reason, loss modulus was characterized mostly compared to storage modulus in the present study. Because of the liquid-like nature of the honey samples, change of loss modulus (G″) with frequency is more important compared to the storage modulus with respect to providing knowledge about viscoelasticity of honey samples. For that reason, dependency of loss modulus of honey samples on angular frequency was modeled using a power law type relationship:

(8)

where A and b were empirical constants that are intercept and magnitude of slope, respectively. The loss modulus data (ln G″) versus frequency (ln ω) were subjected to the linear regression analysis as stated by Rao and Cooley.[31] Table 3 shows the magnitude of slopes, intercepts, and coefficient of determinations of the power law model for loss modulus. As can be seen from the table, the magnitude of intercept for pine honey was in the range of 131.9–522.8, while the intercepts were changed from 41.34–138.02 for citrus honey. As expected, temperature increment caused a decrement in the intercepts and slopes. Coefficient of determinations were calculated to be greater than 0.998. The slopes of the model ranged between 1.004–1.040 depending on the honey variety and measurement temperature. Yoo[11] reported that the loss modulus intercepts of the different honey samples were in the range of 2.37–1936 with a slope range of 1.00–1.01. Similarly, Ahmed et al.[2] reported that the slope of the honey samples was in the range of 0.95 and 1, which means that all honey samples rheologically were very similar to each other whatever their source, and the results supported the true liquid-like nature of honey samples.

Table 2  Dynamic mechanical spectra values of different honeys at 1 Hz

Type of honey	Temperature (°C)	η*	G*	G′	G″
Pine	10	86.33	542.47	0.34	542.47
	15	44.63	280.43	0.24	280.27
	20	21.02	132.07	0.06	132.07
Flower	10	48.60	305.37	0.25	305.37
	15	21.73	136.53	0.05	136.53
	20	12.42	78.03	0.02	78.03
Citrus	10	22.15	139.13	0.54	139.13
	15	12.91	81.14	0.22	81.14
	20	6.63	41.69	0.10	41.69
η*: complex viscosity; G*: complex modulus; G′: storage modulus; G″: loss modulus.

Table 3  Slopes and intercepts of ln G″ versus ln ω data of different honeys at different temperatures

Type of honey	Temperature (°C)	A	b	R ^2
Pine	10	522.8	1.039	0.998
	15	282.7	1.020	0.999
	20	131.9	1.007	0.999
Flower	10	296.3	1.040	0.998
	15	136.7	1.022	0.999
	20	78.29	1.010	0.999
Citrus	10	138.02	1.021	0.999
	15	79.88	1.017	0.999
	20	41.34	1.004	0.999

Figure 1 Oscillatory shear rheological parameters obtained from frequency sweep test of different honeys at 15°C.

Figure 2 shows the effect of temperature on the complex viscosity and complex modulus of three different Turkish honey samples. Temperature increment caused a decrement in the complex viscosity and complex modulus as expected because it is a well known phenomenon that increment in temperature caused a decrease in viscosity of fluids due to the increment of kinetic energy in the structure of fluids.[32] The complex viscosity of pine honey was measured to be 86.33 Pa s at 10°C while it decreased to 21.02 at 20°C. Similarly, complex modulus of pine honey was determined to be 542.47 Pa while it decreased to 132.07 due to the increase in temperature to 20°C. Citrus honey showed the lowest complex viscosity and complex modulus values compared to others (Table 2). Apparent viscosity of citrus honey was determined to be the lowest compared to pine and flower in our previous work.[4]

Figure 2 Effect of temperature on complex viscosity and complex modulus obtained from frequency sweep test of different honeys. (a, b) Pine honey; (c, d) flower honey; and (e, f) citrus honey.

The effect of temperature on the dynamic mechanical spectra of Turkish honeys was determined and temperature dependency of parameters was adequately described using the Arrhenius equation with the determination coefficient of 0.991 or greater. The measured and computed complex viscosity and complex modulus as a function of temperature at 1 Hz are superimposed in Fig. 3. The mean absolute percentage error for the honey samples was in the range of 1.39–1.76 (Table 4). Kleijnen[33] reported that the recommended upper limit on the acceptability of MAPE is 10%. It could be concluded that the description of the complex viscosity and complex modulus as a function of temperature using Arrhenius is satisfactory. In other studies, Arrhenius equation was successfully used for describing the apparent viscosity of honey samples with high coefficient of determination.[3, 4, 7] Activation energy calculated for the complex viscosity and complex modulus change as a function of temperature, Arrhenius constants, and coefficient of determinations were tabulated in Table 4. The differences based on the honey variety in activation energy values were found to be significant (p < 0.05). The activation energy was in the range of 83.13–97.46 kJ/mol for complex viscosity, while it was in the range of 83.12–97.45 kJ/mol for complex modulus. The highest E _a was calculated for the complex viscosity and complex modulus of pine honey while the citrus honey had the lowest value. In general, activation energy values were inconsistent with those reported in the literature. The activation energy of Greek honeys calculated from apparent viscosity values varied between 69.1–93.8 kJ/mol.[28] In another study, the activation energy of Polish honeys calculated from apparent viscosity was in the range of 92.3–105.3 kJ/mol.[1] From these results, it can be said that dynamic mechanical spectra of honeys varies depending on the type of honey. All honey samples showed a liquid-like nature because their loss modulus values were higher than storage modulus. Using the rheological data obtained from the present study, the processing conditions of honeys depending on the honey type can be determined. And also, pumping power for the processes can be calculated using the viscosity values of the honey samples. Citrus honey flows easily in the pipe lines compared to pine honey due to its low viscosity.

Figure 3 The observed and predicted complex viscosity and complex modulus obtained using Arrhenius model of honey samples as a function of temperature at constant frequency (1 Hz) (•: observed data; −: predicted data).

Table 4  Arrhenius model constants obtained from different honeys

Type of honey	Parameter	μ 0 (Pa.s)	E a (kJ/mol)	R ^2	MAPE
Pine	η*	9.23 × 10^−17	97.46	0.998	1.39
	G*	5.82 × 10^−16	97.45	0.998	1.43
Flower	η*	1.91 × 10^−16	94.26	0.991	1.76
	G*	1.21 × 10^−15	94.25	0.991	1.74
Citrus	η*	1.05 × 10^−14	83.13	0.995	1.64
	G*	6.61 × 10^−14	83.12	0.995	1.65
η*: complex viscosity; G*: complex modulus; E a: activation energy; MAPE: mean absolute percentage error.

Stress sweep test results

Figure 4 illustrates the dynamic mechanical spectra of honey samples obtained from a stress sweep test at a constant temperature (15°C). It is clear that the complex viscosity values of samples did not change in the range of 0.1–10 Pa. And also, the highest complex viscosity value was observed for the pine honey as in the frequency sweep test of honey samples. Citrus honey samples showed the lowest complex viscosity. A similar trend was also observed for the complex modulus. Storage modulus decreased with increasing stress and loss modulus that is important for the honey because they show liquid-like flow behavior did not change with increasing stress, and linear viscoelastic region was observed in the range of 0.1–10 Pa. Similar results were reported by Da Costa and Pereira.[34] They determined that the complex modulus that is a function of loss modulus and storage modulus of wild flora pure honey remained constant with increasing stress from 0.1 to 10 Pa. It means that the stress in this range can be applied to the honey without adulterating or breaking the structure of the sample.

Figure 4 Oscillatory shear rheological parameters obtained from stress sweep test of different honeys at 15°C.

The effect of temperature on the complex viscosity and complex modulus for all Turkish honey samples was illustrated in Fig. 5. As can be seen from the figure, complex viscosity and complex modulus remained constant with increasing stress during a stress sweep test at all measurement temperatures and a decrement was observed with increment in temperature. The highest complex viscosity was determined for pine honey while the lowest was for citrus honey. The effect of temperature in the decrement of complex viscosity and complex modulus was found to be statistically significant (p < 0.05). Figure 6 shows the change in loss modulus, which is one of the most important dynamic mechanic parameters for all honey samples at different temperatures. As it can be seen from the figure, loss modulus decreased with increment of temperature as expected and increased with the increment of frequency and remained constant with the increment of stress. The highest loss modulus value was observed for pine honey after both frequency sweep and stress sweep test. Similar results were reported by Yoo,[11] who investigated the temperature dependency of dynamic rheology of Korean honeys and determined that the magnitudes of loss modulus (G″), which are related to liquid-like response, decreased with increasing temperature and also an increment in loss modulus was observed with the increment of angular frequency. In another study, complex modulus as a function of loss modulus and storage modulus increased with an increase in angular velocity, indicating a more pronounced viscoelastic behavior of honey samples.[34] Ahmed et al.[2] reported that the viscous modulus (loss modulus, G″) was significantly higher compared to the elastic modulus (storage modulus, G′) throughout the frequency range employed confirming the liquid-like nature of the honey. Also, they stated that the viscous modulus of honey samples systematically increased as a function of angular frequency, while inconsistent elastic modulus data were observed in the rheogram. The lower elastic modulus means that there is a weak particle-particle interaction and there is no network formation in honey structure.[2]

Figure 5 Effect of temperature on complex viscosity and complex modulus obtained from stress sweep test of different honeys. (a, b) Pine honey; (c, d) flower honey; and (e, f) citrus honey.

Figure 6 Effect of temperature on loss modulus obtained from stress sweep and frequency sweep test of different honeys. (a, b) Pine honey; (c, d) flower honey; and (e, f) citrus honey.

Nonlinear modeling results

Complex viscosity values of all honey samples were modeled using adaptive neuro fuzzy inference system (ANFIS) and artificial neural network (ANN) that are effective nonlinear modeling techniques to estimate the interval complex viscosity values at different frequency and temperature. Table 5 summarizes the testing performance of ANFIS and ANN models for complex viscosity values of honey samples. As can be seen from the table, the best fit was observed for ANFIS model because of high coefficient of determination (R ² ≥ 0.995) in both test and validation data compared to the ANN model. ANFIS model showed rather good performance for the estimation of complex viscosity depending on honey type, temperature, and frequency. RMSE values for test and validation data were calculated to be 1.003 and 3.131 in the ANFIS model, while these values were 1.037 and 4.988 in the ANN model, respectively. Figures 7 and 8 illustrate the measured and computed complex viscosity values of honey samples using ANFIS and ANN modeling techniques in training, test, and validation periods, respectively. As can be seen from those figures, a very good fit was obtained from the model. A regression equation can be used for the computation of complex viscosity values obtained from the model in both figures. It could be said that the ANFIS was well trained for the modeling of complex viscosity of honey samples since its predicted values are a close match of the measured one. As can be seen from Figs. 7b and 8b, training performance of ANFIS was higher compared to ANN because of high coefficient of determination. Due to the good training of the ANFIS model, it predicted the actual complex viscosity values very well compared to ANN (Figs. 7f and 8f). Karaman and Kayacier[15] applied the ANFIS modeling techniques for the prediction of the apparent viscosity of date and apricot molasses and they concluded that the ANFIS model can be efficiently used for the prediction of apparent viscosity of molasses with coefficients of determination greater than 0.979. Similarly, Gänzle et al.[35] stated that fuzzy inference systems can be efficiently used with the precise rules for the construction of effective predictive models to estimate the different parameters in nonlinear systems. As stated in the literature, physicochemical and rheological properties, such as viscosity or stability of foods, are regarded as complex nonlinear systems.[13] It was found that the ANFIS was an efficient technique to be used for the prediction of viscosity and stability for mayonnaise in the food industry because the average percentage errors in the modeling of viscosity and stability were found to be 5 and 8%, respectively, in the validation period. Kavdir and Guyer[36] developed an apple grading system using a fuzzy logic modeling system and the result showed that fuzzy logic was 89% in general agreement with results given by experts.

Figure 7 Measured and computed complex viscosity values of honeys using ANFIS model in training (a, b), test (c, d), and validation (e, f) period. Measured (•); ANFIS (—).

Figure 8 Measured and computed complex viscosity values of honeys using ANN model in training (a, b), test (c, d), and validation (e, f) period. Measured (•); ANN (—).

Table 5  Testing performance of ANFIS and ANN model for estimation of complex viscosity of honeys

	R ^2			RMSE			MAE
Model type	X 1	X 2	X 3	X 1	X 2	X 3	X 1	X 2	X 3
ANFIS	0.995	0.999	0.995	0.0387	1.003	3.131	0.040	1.343	3.781
ANN	0.990	0.998	0.985	2.207	1.037	4.988	1.385	2.503	3.233
RMSE: root mean square error; MAE: mean absolute error; R ^2: coefficient of determination; X 1: training data; X 2: test data; X 3: validation data.

CONCLUSION

All honey samples showed Newtonian flow behavior and their complex viscosity remained constant with increasing frequency and stress. The highest complex viscosity values were measured in pine honey, while the lowest values were in citrus honey. It was determined that the viscous modulus (loss modulus) of all honey samples was significantly higher than elastic modulus (storage modulus) during the frequency and stress range employed. Increasing frequency and stress provided an increment in loss modulus and complex modulus. Temperature dependency of complex viscosity and complex modulus was modeled by Arrhenius model with a coefficient of determination greater than 0.991. An increment in temperature caused a significant decrement in complex viscosity and complex modulus. Nonlinear modeling techniques, such as ANFIS and ANN, used for the prediction of complex viscosity performed well with coefficient of determination greater than 0.995 and 0.985, respectively. It could be concluded that ANFIS model can be used effectively for the estimation of complex viscosity values of different honey samples.