energies Article
Measurement and Artificial Neural Network Modeling of Electrical Conductivity of CuO/Glycerol Nanofluids at Various Thermal and Concentration Conditions Reza Aghayari 1 , Heydar Maddah 1 , Mohammad Hossein Ahmadi 2, *, Wei-Mon Yan 3,4, * and Nahid Ghasemi 5 1 2 3 4 5
*
Department of Chemistry, Payame Noor University (PNU), P.O. Box, Tehran 19395-3697, Iran;
[email protected] (R.A.);
[email protected] (H.M.) Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood 3619995161, Iran Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, Taipei 10608, Taiwan Research Center of Energy Conservation for New Generation of Residential, Commercial, and Industrial Sectors, National Taipei University of Technology, Taipei 10608, Taiwan Department of Chemistry, Arak Branch, Islamic Azad University, Arak 38361119131, Iran;
[email protected] Correspondence:
[email protected] (M.H.A.);
[email protected] (W.-M.Y.)
Received: 20 April 2018; Accepted: 4 May 2018; Published: 8 May 2018
Abstract: In this work, the electrical conductivity of CuO/glycerol nanofluid was measured at a temperature range of 20–60 ◦ C, volume fraction of 0.1–1.5% and nanoparticle size of 20–60 nm. The experimental data were predicted by the perceptron neural network. The results showed that the electrical conductivity increases with temperature, especially in higher volume fractions. These results are attributed to the accumulation of nanoparticles in the presence of the field and their Brownian motion at different temperatures and the reduction of electrical conductivity at higher nanoparticle sizes is attributed to the decreased mobility of nanoparticles as load carriers as well as to their decrease in volume unit per constant volume fraction. The results revealed that sonication time up to 70 min increases the nanofluid stability, while further increase in the sonication time decreases the nanofluid stability. In the modeling, input data to perceptron artificial neural network are nanofluid temperature, nanoparticle size, sonication time and volume fraction and electrical conductivity is considered as output. The results obtained from self-organizing map (SOM) showed that the winner neuron which has the most data is neuron 31. The values of the correlation coefficient (R2 ), the mean of squared errors (MSE) and maximum error(emax ) used to evaluate the perceptron artificial neural network with 2 hidden layers and 31 neurons are 1, 2.3542 × 10−17 and 0 respectively, indicating the high accuracy of the network. Keywords: electrical conductivity; perceptron artificial neural network; nanofluid
1. Introduction During past decades, a subject which was comprehensively investigated can be enumerated as heat transfer in industrial apparatus. This activity is so crucial since the generated heat can impede the operation of the device as the impacts of the heat on the equipment. Additionally, it can be caused severe damage to the device. The utilization of fluids with the characteristic of high heat transfer rate can be mentioned as a method for augmenting heat transfer in cooling systems. Thus, specialists have focused on the capacity identified in nanofluids. Nanoparticles in the scale Energies 2018, 11, 1190; doi:10.3390/en11051190
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of 1–100 nm are utilized in nanofluids [1]. Various investigations have been presented for the sake of identifying the dynamics of nanofluids heat transfer [2–10] and thermal properties like specific heat capacity [11], thermal diffusivity [12], density [13]. Adio et al. [14] studied factors affecting the electrical conductivity of magnesium oxide–ethylene glycol (MgO–EG) nanofluid. The effects of temperature and volume fraction were investigated. The experimental results showed that electrical conductivity increased with temperature. Moreover, the increase in the MgO volume fraction increased electrical conductivity values of the MgO–EG nanofluid. In a study, the electrical conductivity of thulium oxides–ethylene glycol nanofluids based on nanoparticles with different sizes has been investigated. Measurements were conducted at constant temperature of 293.15 (K) for various mass concentrations from 0 to 20% with 5% interval. Their results indicate that increase in mass concentration of nanoparticles in base fluid causes increase in electrical conductivity of Tm2 O3 –EG nanofluids. The enhancement in the electrical conductivity of nanosuspensions of thulium oxide is dependent on particle size [15]. Zakaria et al. [16] investigated electrical conductivity of Al2 O3 nanofluid in water—ethylene glycol mixture experimentally. The obtained results revealed that electrical conductivities measured in 0.1, 0.3 and 0.5% volume concentration of Al2 O3 in base fluid decreased as the EG concentration increased even though the base fluids’ electrical conductivity behave differently. Additionally, the calculation of the electrical conductivity associated with iron oxide nanofluids has been provided in another examination. This study presented the electrical conductivity contributed to iron oxide nanoparticles at various particle volume fractions and temperatures. A 4-cell conductivity electrode meter measures the electrical conductivity. By increasing temperature and the particle volume fraction, the electrical conductivity of iron oxide nanofluids linearly rises. Owing to temperature and the particle volume fraction of 22.55% and 160.49%, respectively, the highest improvement of electrical conductivity of iron oxide nanofluids is obtained [17]. In other evaluations by Abdolbaqi et al. [18], the thermal conductivity and electrical conductivity of bioglycol-water mixed nanofluids containing Al2 O3 nanoparticles were investigated. According to their result, bioglycol-water mixtures have displayed improvement in thermal performance of 7.5% in comparison with propylene glycol in similar circumstances. The thermal conductivity of nanofluid increased as a function of volume concentration and temperature. Electrical conductivity was observed to decrease as the volume concentration increased. The influence of nanoparticle concentration and temperature on viscosity and thermal conductivity of a nanofluid has been experimentally studied by Águila et al. [19]. According to the obtained results of the NanoPCM, thermal conductivity is approximately consistent in the examined temperature range, the viscosity reduces non-linearly with temperature. Regarding the influence of nanoparticle concentration, both viscosity and thermal conductivity augmented with nanoparticle concentration. Regarding the base fluid, thermal conductivity increased up to 9%. Also, viscosity enhanced up to 60% in both cases with increasing concentration. Aghayari et al. [20] used artificial neural networks, including two-layer perceptron feed forward and a back propagation Levenberg-Marquardt training algorithm to evaluate and predict the thermal conductivity of iron oxide nanofluid at different temperatures and volume fractions by using experimental data. They found that artificial neural networks model has a reasonable agreement in predicting experimental data. So it can be concluded that the ANN model is an effective method for prediction of the thermal conductivity of nanofluids and has better prediction accuracy and simplicity compared with the other existing theoretical methods. The conclusion of the thermal conductivity associated with Water-Ethylene glycol and Silica as the base nanofluid has been presented by Ahmadi Esfahani et al. [21] with the temperature range of 25–50 ◦ C for samples with volume fractions of 0.1%, 0.5%, 1%, 1.5%, 2%, 3% and 5%. As indicated in the results, by augmenting volume fraction and temperature, thermal conductivity enhanced significantly. The highest thermal conductivity (45.5%) happened at the temperature of 50 ◦ C and volume fraction of 5%. Based on the assessment, the maximum quantity contributed to the margin of deviation for the presented equation has been found to be 2.2%, which is favorable in an experimental equation.
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Akbari et al. [22] used SiO2 /EG nanofluids for measuring viscosity in different temperatures ranging from 30 to 50 ◦ C and volume fraction range of 0.1–3.0%. The measurements showed that the viscosity rises with growing the nanoparticles concentration and diminishes with rising temperature. The values of viscosity ratio indicated that with increasing the solid volume fraction from 0.1 to 3%, the viscosity increases up to 116%. Other researcher presented the effects of temperature (20 ◦ C < T < 50 ◦ C) and volume fraction (0 < ϕ < 4%) on the thermal conductivity of zinc oxide/ethylene glycol-water nanofluid. Results showed that the thermal conductivity increases uniformly with increasing solid volume fraction and temperature. The results also revealed that the thermal conductivity of nanofluids significantly increases with increasing solid volume fraction at higher temperatures. Experimental thermal conductivity enhancement of the nanofluid in comparison with the Maxwell model indicated that Maxwell model was unable to predict the thermal conductivity of the present nanofluid [23]. Hemmat Esfe et al. [24] used experimental data to predict viscosity and thermal conductivity of nanofluid aluminum oxide in a mixture of water and ethylene glycol by Artificial Neural Network. The inputs of ANN were temperature and volume fraction and outputs were viscosity and thermal conductivity. Finally, Pareto Front and the corresponding optimum points were provided and introduced. Optimal results showed that the optimum viscosity and thermal conductivity occurs at maximum temperature. In 2017, Abdollahi Moghaddam et al. [25] evaluated rheological variations of MWCNT-CuO (30–70)/SAE40 nanohybrid with temperature and solid volume fraction. The viscosity at volume fractions 0.0625–1% was measured in temperatures 25–50 ◦ C and different shear rates. The results showed that in a concentration of 1 vol %, the viscosity of hybrid nanolubricant was 29.47% more than the viscosity of the base oil. They also used, an Artificial Neural Network including multilayer perceptron method with two hidden layers, one of which had five neurons and the other one had four neurons. The modeling results were R-squared (0.9966), MSE (0.00002081) and AARD (0.0055). Hemmat Esfe et al. [26] applied artificial neural network in order to model the viscosity of the aqueous nanofluid of TiO2 using experimental data. The inputs for the applied model were temperature and nanoparticles mass fraction. A network with one hidden layer and 4 neurons was used. The regression coefficient was obtained 0.9998 in this modeling, showing very high precision of neural network with a very simple structure. In another study, the thermal conductivity of copper oxide nanofluid was predicted using feed forward back propagation artificial neural network (FFBP-ANN). In addition, in order to evaluate accuracy prediction, indices of root-mean-square error, coefficient of determination (R2 ) and mean absolute percentage error were used. FFBP-ANN with two input parameters (volume fraction and nanofluid temperature) and one output parameter (nanofluid thermal conductivity) in addition to two hidden layers and one outer layer for which purelin, logsig and tansig functions used was considered as the most optimum structure for modeling with neuron number of 4-10-1. The modeling results were fitted with experimental data well [27]. In this work, the electrical conductivity of CuO/glycerol nanofluid was measured experimentally and then, the measured data were predicted using the multilayer perceptron neural network with the certain number of neurons obtained from self-organizing map neural network. Among the goals and novelties of this paper is using a self-organizing map (SOM) artificial neural network for finding the winner neuron. In the present study, the winner neuron with most experimental data is identified and then used in the perceptron artificial neural network for prediction of the electrical conductivity of the CuO/glycerol nanofluid and contrary to the previous studies done for finding the winner neuron, there is no need for trial and error method. 2. Materials and Methods 2.1. Preparation and Characterization of CuO/Glycerol Nanofluid In this work, copper oxide nanoparticles and glycerol as base fluid were purchased from Sigma Aldrich. The scanning electron microscopy (SEM) image of the nanoparticles supplied by
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the manufacturer is clearly shown in Figure 1. As shown in Figure 1, nanoparticles have a size about 20–60 arePEER almost spherical. Energies 2018,nm 11, and x FOR REVIEW 4 of 16
Figure 1. Scanning electron imageofofa acopper copper oxide nanoparticle. Figure 1. Scanning electronmicroscope microscope (SEM) (SEM) image oxide nanoparticle.
2.2. Preparation of CuO/Glycerol Nanofluid 2.2. Preparation of CuO/Glycerol Nanofluid A two-step method was used CuO/glycerolnanofluid. nanofluid. Initially, when powder A two-step method was usedtotoprepare prepareaa stable stable CuO/glycerol Initially, when powder of CuO nanoparticles was addedtotothe the base base fluid, fluid, aa non-homogeneous and unstable statestate was was of CuO nanoparticles was added non-homogeneous and unstable formed. To this end, a certain number of nanoparticles and acetyltri methyl ammonium with the the formed. To this end, a certain number of nanoparticles and acetyltri methyl ammonium with optimal of about to were 20 were mixed using a Hanna instrumentsmagnetic magnetic stirrer stirrer at optimal ratioratio of about 1 to120 mixed using a Hanna instruments at aa rate rate of of 500 500 rpm for 5 h. Subsequently, for complete stability of the nanofluid for a few weeks, an ultrasonic rpm for 5 h. Subsequently, for complete stability of the nanofluid for a few weeks, an ultrasonic bar bar sonicator (-UP GmbH Hielscher 400S, Hielscher Co., Teltow, Berlin, Germany) was used with a sonicator (-UP GmbH Hielscher 400S, Hielscher Co., Teltow, Berlin, Germany) was used with a frequency of 24 kHz, wave amplitude of 100 and an output power of 400 Watts. Since the ultrasonic frequency of 24 kHz, wave amplitude of 100 and an output power of 400 Watts. Since the ultrasonic waves break down the particle accumulation into smaller pieces and make the distribution of the waves break down the particle accumulation into smaller pieces and make the distribution of the nanoparticles uniform, the effect of the ultrasonic sonication time on the nanofluid stability was nanoparticles the effectofofnanoparticles the ultrasonic sonication on vessel the nanofluid stability measured. uniform, The sedimentation at the bottom oftime the test was considered as was measured. The sedimentation of nanoparticles at the with bottom of the test vessel was considered a significant criterion for stability and was measured a high-precision millimeter ruler. In the as a significant criterion for stability and was measured with a high-precision millimeter ruler. In the present study, we used very low volume fraction of 0.1%, 0.4%, 0.8%, 1% and 1.5% to fully guarantee the nanofluid Sodium dodecyl fraction sulfate and polyvinylpyrrolidone used respectively as present study, westability. used very low volume of 0.1%, 0.4%, 0.8%, 1%were and 1.5% to fully guarantee anionic and nonionic surfactants because these materials, respectively by increasing the electrostatic the nanofluid stability. Sodium dodecyl sulfate and polyvinylpyrrolidone were used respectively as repulsion force andsurfactants the spatial repulsion force materials, between therespectively particles, improve the dispersion of the anionic and nonionic because these by increasing the electrostatic nanoparticles in the base fluid. repulsion force and the spatial repulsion force between the particles, improve the dispersion of the nanoparticles in Conductivity the base fluid. 2.3. Electrical Measuring Device The Conductivity electrical conductivity CuO/glycerol nanofluid was measured by a Model AZ8351 2.3. Electrical MeasuringofDevice
with accuracy of ±1% at various temperatures ranging from 20 to 60 ◦ C and different volume The electricalofconductivity of CuO/glycerol nanofluid was measured by a Model AZ8351 with concentrations 0.1%, 0.4%, 0.8%, 1% and 1.5%. Before conducting electrical conductivity experiments, ◦ cond.meter wasat calibrated 25 C using reference solutions 1413°C andand 80 µS/cm and volume the accuracy of ±1% variousat temperatures ranging from of 20 KCL to 60 different calibration results are shown in Table 1. Model AZ8351 cond.meter has a small and compact size concentrations of 0.1%, 0.4%, 0.8%, 1% and 1.5%. Before conducting electrical conductivity measuringcond.meter range of 0–1999 and withat a waterproof can be solutions easily used.ofItKCL can display both experiments, wasµS calibrated 25 °C usingbody reference 1413 and 80the μS/cm temperature and conductivity simultaneously. and the calibration results are shown in Table 1. Model AZ8351 cond.meter has a small and compact
size measuring range of 0–1999 μS and with a waterproof body can be easily used. It can display both the temperature and conductivity simultaneously.
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Table 1. Values obtained from calibration of cond.meter with reference solutions. No.
Temperature (◦ C)
Reference Conductance
Ave. of Reading
Error
Exp. UN
1 2
25 25
1413 80
1413 81
0 1
±8 ±1
2.4. Artificial Neural Network Artificial neural network (ANN) is one of the computational methods, which attempts to offer a mapping between the input space (input layer) and the desirable space (output layer) by understanding the intrinsic relationships between the data using learning process and the processors called the neurons. The hidden layer(s) processes the received information from the input layer and provides the output layer with this processed information. Each network is trained by receiving examples. Training is a process that ultimately leads to learning. Network learning is performed when the communication weights between the layers change so that the difference between predicted and calculated values is acceptable [28]. Having achieved these conditions, the learning process has been realized. These weights represent the memory and network knowledge. Trained neural network can be used to predict outputs appropriate to the new set of data [28]. Due to the structure of the artificial neural network, its main features are high processing speed, ability to learn pattern, ability to generalize knowledge after learning, flexibility to deal with unwanted errors and not causing significant disturbance in the event of problems in part of the connections due to the distribution of network weights [28]. 2.5. Artificial Neural Network Design Considering three factors of nanofluid temperature, different sizes of nanoparticles and volume concentration of nanofluid, changes in the electrical conductivity of CuO/glycerol nanofluid under different conditions are obtained. The proposed neural network topology and the input and output parameters for the network are shown with the different number of layers. An artificial neural network with 1 and 2 layers has been used, containing neurons in each layer. In this work, the data of nanofluid temperature, nanoparticle size and volume concentration of nanofluid are considered as input to the network as well as the electrical conductivity data obtained from experimental results are considered as output. The MLP neural network was used to predict the electrical conductivity of CuO/glycerol nanofluid in the sigmoid tangent function. One of the problems may arise when training a neural network is the overtraining of network so that during the network training, the error reaches an acceptable amount but when evaluated, the network error is far more than the training data error [28,29]. There are two ways to avoid overtraining: (a) stopping the training quickly and (b) selecting the lowest number of neurons in hidden layer [28]. To train the network, data were first randomly divided into three parts, so that 70% of the data for training, 15% of the data for evaluating and 15% of the data for testing the network were used. During the training, the training process is interrupted when the error between the training and evaluation data increases. The values of the correlation coefficient (R2 ) and mean square error (MSE) were used to evaluate the obtained results [29]. MSE and R2 were used to evaluate the obtained results [29]: MSE = Exp
2
R =
∑N i=1 (σi
2 1 N Exp (σi − σANN ) i N i∑ =1 2
Exp
− σ ) − ∑N i=1 (σi Exp
(σi
− σ)
2
− σANN ) i
(1) 2
(2)
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Exp
where N is the number of experimental data, σi is the experimental data dedicated to electrical conductivity and σANN is predicted by neural network. Moreover, σ is the mean value of electrical i conductivity and e is the mean value of error. The Levenberg-Marquardt (LM) training algorithm was used to update the artificial neural network weights, which is one of the most widely used algorithms because it performs network training very quickly and minimizes the level of error available [30,31]. In fact, this algorithm is designed to increase the speed of network learning based on the Hysen matrix. For mathematical explanation of the solution, it can be concluded that the output of the input layer neurons is considered as the input for the hidden layer. Similarly, the output of hidden layer neurons is considered as input of the output layer. Each neuron in the input layer based on the following equation performs the process on the input parameters of the neural network: yk = ϕ
l
m
k =1
i =1
∑ wk ϕ( ∑ (xi .wki ) + bk ) + w0
! (3)
In Equation (3), yk is the output neuron, ϕ is neuron activation function and m is the number of network input parameters. xi represents the ith input parameter. wki is the weight of each neuron and bk is the bias of the input parameters. In the present study, the hyperbolic tangent activation function is used in the middle layers and the linear function in the output layer. Table 2 shows the minimum, average and maximum values for the input data. Table 2. The minimum, average and maximum values for the input data. Parameter
Minimum
Average
Maximum
Temperature Volume fraction Nanoparticle size Sonication time
20 0 20 0
40 0.75 40 50
60 1.5 60 100
3. Results and Discussion Figure 2 shows the effect of sonication time on the height of the sediment layer of CuO/glycerol nanoparticles in different volume fraction. The results of the evaluation showed that by increasing sonication time up to 70 min, the height of the sediment layer decreases, while further increase in the sonication time leads to an increase in the height of the sediment layer. These results can be explained by the fact that when the CuO/glycerol nanofluid is exposed to ultrasound sonication, all of the fluid’s points are exposed to extreme oscillations and acceleration. In such a high acceleration, at these points, a cavitation bubble is created, growing over a period of time and reaching a critical diameter and eventually collapsing. During this process, there is a special local condition called hot spot, resulting in a high temperature and a high-pressure and rapid micro-flow of the liquid. The movement of this flow among the nanoparticles exert a very strong shear force on the electrostatic forces between particles (gravity and Van der Waals forces). In this way, the particles are separated from each other and the nanofluid stability increases. When the nanofluid is exposed to ultrasound sonication for more than 70 min, the suspension temperature increases and the smaller particles are accelerated and collided with ultrasonic wave vibrations at the same rate as micro-flow passing through particles. Therefore, a mass of particles has been formed, causing nanofluid instability. By increasing sonication time, a larger mass of particles is formed and the nanofluid stability decreases. An excessive increase in sonication time may increase the temperature of the nanofluid so that eventually it evaporates. Usually, there is a direct relationship between higher inputs and higher excitability. The higher the number of inputs, the more excitable the neurons are and the smaller the number of data, the less excitable the neurons are. According to Figure 3, neuron 31 is the most successful ones and the most data assigned to themselves are 21 data. These neurons have covered more points than other neurons.
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4.5 4.5 4 4 3.5 3.5
Sediment Layer Height(mm)
Sediment Layer Height(mm)
The neurons without data are indicative of their failure to absorb data. According to the results of the artificial neural network SOM, the winner neuron is neuron 31 that can be used in the MLP neural network. The scattered of the electrical conductivity of CuO/glycerol nanofluid predicted by Energies 2018, 11, x FOR values PEER REVIEW 7 ofthe 16 neural network versus the experimental values obtained with 2 hidden layers are shown in Figure 4. Energies 2018, 11, x FOR PEER REVIEW 7 of 16 model in the data estimation. This figure largely represents the efficacy of the selected neural network Less scattered predicted data around the regression line are indicative of the high accuracy of the model model. The purpose of thefigure comparison of predicted values (y) andselected datanetwork (x)model. is to in the data This the efficacy of the neuralneural network model inestimation. the data estimation. Thislargely figure represents largely represents the efficacy of experimental the selected determine the accuracy of the network introduced during the network testing process. The regression Themodel. purpose the comparison of predictedofvalues (y) and experimental data (x) is todata determine Theofpurpose of the comparison predicted values (y) and experimental (x) is tothe line is depicted inaccuracy order to theduring overlapping ofduring the values obtained in this figure.The As be seen, determine thenetwork ofshow the network introduced the network process. regression accuracy of the introduced the network testing process.testing The regression linecan is depicted 2) and mean square error (MSE) for the data of the electrical the values ofshow the correlation (Rvalues line is to depicted in order to coefficient show the overlapping of the values obtained figure. As can seen, of in order the overlapping of the obtained in this figure. in Asthis can be seen, the be values 2) and 2 conductivity coefficient of the CuO/glycerol nanofluid with 2 hidden layers are 1 and 2.3542 × 10−17, the values of the correlation coefficient (R mean square error (MSE) for the data of the electrical the correlation coefficient (R ) and mean square error (MSE) for the data of the electrical conductivity − 17 conductivity the nanofluid CuO/glycerol nanofluid 2 hidden layers are × 1 and × 10−17, respectively, theofhigh accuracy with of the coefficient of indicating thecoefficient CuO/glycerol 2network. hiddenwith layers are 1 and 2.3542 10 2.3542 , respectively, respectively, indicating the of high of the network. indicating the high accuracy theaccuracy network.
3
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Sonication time (min) Sonication (min) Figure Effect sonicationtime timeon onthe thestability stability of CuO/glycerol Figure 2. 2. Effect ofof sonication time on the stability of CuO/glycerol CuO/glycerolnanofluid. nanofluid. Figure 2. Effect of sonication nanofluid. 3.5 3.5 Hits
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Figure 3. Statistics chart of winning neurons of self-organizing map (SOM) neural network.
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Figure Figure 3. 3. Statistics Statisticschart chartof ofwinning winningneurons neurons of of self-organizing self-organizing map map (SOM) (SOM) neural neural network. network.
The maximum error (emax) obtained by the two-layer configuration is zero, which is very favorable and represents prediction. the accuracy of the results of thewhich prediction of The maximum error a(esuccessful max) obtained by theAlso, two-layer configuration is zero, is very the electrical conductivity of the nanofluid for the training, validation and all data isof favorable and represents a successful prediction. Also, the accuracy ofand the testing resultsdata of the prediction in Figure 5. As can seen, the values the correlation coefficient the sum the squared theshown electrical conductivity ofbe the nanofluid for of the training, validation andand testing dataofand all data is errors are very normal and represent a successful prediction and evaluation. The computational time shown in Figure 5. As can be seen, the values of the correlation coefficient and the sum of the squared for 1 and 2-layer configurations is 4 and 7 seconds, respectively, which does not differ greatly errors are very normal and represent a successful prediction and evaluation. The computationaland time shows the stability of both configurations clearly. for 1 and 2-layer configurations is 4 and 7 seconds, respectively, which does not differ greatly and
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The maximum error (emax ) obtained by the two-layer configuration is zero, which is very favorable and represents a successful prediction. Also, the accuracy of the results of the prediction of the electrical conductivity of the nanofluid for the training, validation and testing data and all data is shown in Figure 5. As can be seen, the values of the correlation coefficient and the sum of the squared errors are very normal and represent a successful prediction and evaluation. The computational time for 1 and 2-layer configurations is 4 and 7 s, respectively, which does not differ greatly and shows the stability of both Energies configurations clearly. 2018, 11, x FOR 8 of 16 8 of 16 Energies 2018, 11, PEER x FORREVIEW PEER REVIEW
Figure 4. Comparison of of thethe electrical conductivity predicted the neural network experimental Figure 4. Comparison electrical conductivity predicted byby the neural network and and experimental Figure 4. Comparison of the electrical conductivity predicted by the neural network and experimental results for all data in a network with 2 hidden layers and 31 neurons. resultsresults for all data a network with 2 with hidden layers layers and 31and neurons. for allindata in a network 2 hidden 31 neurons.
MeanMean Square Error Error (Mse)(Mse) Square 30
Mean Mean SquareSquare Error (Mse) Error (Mse)
30 30
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LinearLinear regression (R) (R) regression 1
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0.98 0.98 0.98 0.98 0 Training Validation Test AllAll AllAll Training Validation TestTest Training Validation Training Validation Test ANN Model ANN Model ANN Model ANN Model
(a)
(a)
Training Validation Test Test All All Training Validation Test All Training Validation Test All Training Validation ANN ANN ModelModel ANN Model ANN Model
(b)
(b)
FigureFigure 5. The 5. obtained valuesvalues of the of correlation coefficient and the sum the of squared errors errors in a in a The obtained the correlation coefficient and theofsum the squared
Figure 5. Thewith obtained values the correlation coefficient and the sum of the squared errors in a network hidden layers of and 31and neurons. (a) mean error; (b) linear network2 with 2 hidden layers 31 neurons. (a) square mean square error; (b) regression. linear regression. network with 2 hidden layers and 31 neurons. (a) mean square error; (b) linear regression.
To evaluate ANN ANN modelmodel and compare it withitother sources of information, data from 12 To evaluate and compare with other sources of information, data nearly from nearly 12 references were used to collect 520 data. Table 3 represents the general characteristics of the references were used to collect 520 data. Table 3 represents the general characteristics of the To evaluate ANN model and compare it with other sources of information, data from nearly 12 nanofluids their range.range. In thisIndatabase including 520 data under the the nanofluids used and measurement their measurement this including 520 and data andnanofluids under references were used usedand to collect 520 data. Table 3 represents thedatabase general characteristics of the different temperature, nanoparticle size and fraction conditions, 70, 15 70, and1515and percent of the of the different temperature, nanoparticle sizevolume and volume fraction conditions, 15 percent used and their measurement range. In this database including 520 data and under the different data were as training, validation and testing data, respectively. data evaluated were evaluated as training, validation and testing data, respectively. temperature, nanoparticle size and volume fraction conditions, 70, 15 and 15coefficient, percent ofsum theof data were As shown clearly in Figures 6–9, the values obtained for thefor correlation theof the As shown clearly in Figures 6–9, the values obtained the correlation coefficient, sum evaluated as training, validation and testing data, respectively. squared errorserrors and the maximum error for 70% the of data, contains 364 data, very squared and the maximum error forof70% the which data, which contains 364 are data, arenormal very normal for thefor network training and are 0.99999, 0.02103 and 0.5427. These values for validation and the network training and are 0.99999, 0.02103 and 0.5427. These values for validationtesting and testing data, which collectively contain 156 data, 0.9997, 0.38509, 3.36463.3646 and 0.99972, 0.29029 and 3.3646. data, which collectively contain 156 are data, are 0.9997, 0.38509, and 0.99972, 0.29029 and 3.3646. Therefore, it can it becan said network with two and 31and neurons is properly trained and no Therefore, bethat saidthe that the network withlayers two layers 31 neurons is properly trained and no phenomena such as overfitting have occurred and the network has successfully predicted the the phenomena such as overfitting have occurred and the network has successfully predicted electrical conductivity of theofnanofluids and the outputoutput is veryis normal. If the Ifcorrelation electrical conductivity the nanofluids andnetwork the network very normal. the correlation coefficient is close to 1, then valuesvalues are identical with the measured in thein the coefficient is close to 1, the thenpredicted the predicted are identical withvalues the values measured
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As shown clearly in Figures 6–9, the values obtained for the correlation coefficient, sum of the squared errors and the maximum error for 70% of the data, which contains 364 data, are very normal for the network training and are 0.99999, 0.02103 and 0.5427. These values for validation and testing data, which collectively contain 156 data, are 0.9997, 0.38509, 3.3646 and 0.99972, 0.29029 and 3.3646. Therefore, it can be said that the network with two layers and 31 neurons is properly trained and no phenomena such as overfitting have occurred and the network has successfully predicted the electrical conductivity of the and the network output is very normal. If the correlation coefficient is Energies 2018, 11, xnanofluids FOR PEER REVIEW 9 of 16 Energies 2018, 11, x FOR PEER REVIEW 9 of 16 close to 1, then the predicted values are identical with the values measured in the laboratory. One of the laboratory. One for of the problems that occurs neural with low is data their training is the problems that occurs neural networks withfor low datanetworks in their training theinoverfitting phenomenon laboratory. of the problems neural networks withOne lowofdata their training is the overfitting One phenomenon causingthat theoccurs model for to become non-general. the in methods for detecting causingoverfitting the model to becomecausing non-general. One of the methods forOne detecting the overfitting problem is phenomenon the the model to become of thedata. methods detecting the overfitting problem is to check error rate for non-general. testing and validation The for proximity of to check the error rate for testing and validation data. The proximity of correlation coefficient the overfitting problem is to check the error rate for testing andthe validation data. The proximity of values correlation coefficient values for this type of data indicates that overfitting phenomenon has not for thiscorrelation type of data that has not occurred in the model. forthe thisoverfitting type of dataphenomenon indicates that the overfitting phenomenon has not occurred incoefficient theindicates model.values occurred in the model.
40 40 30 30 20 20 R=0.99999 Mse=0.02103 e max=0.5427 R=0.99999 Mse=0.02103 e max=0.5427 10 20 30 40 50 60 70 10 Electrical 20 30conductivity 40 50 60 70 Exprimental Electrical conductivityExprimental
60 6070 70 60
Mse=0.11579 e max = R=0.9999 Mse=0.11579 e max =3
Validation Real Data Fit Data Validation Real Y=T Fit Y=T
50 60 5050 50
40 40 40 30 40 30
20 30 20 30 10 10
0.999*removal removal real + 0.104 ANN ~= ~= 0.999*removal removal real + 0.104 ANN
50 50
10 10
Real Data Real Fit Data Fit Y=T R=0.9999 Y=T
70 70 ANN + 0.027 ~= 1.001*removal removal real ANN real ANN
60 60
Real Data Real Fit Data Fit Y=T Y=T Training Training
Electrical conductivity Electrical conductivity + 0.027 ~= 1.001*removal ANN removal
Electrical conductivity Electrical conductivity ANN ANN
70 70
R=0.99972 Mse=0.2902 R=0.99972 Mse=0.29029 70 10 70 10 60
20 Fit Real Data 20 Y=T Fit
10 10
60 50
Y=T
Real Data Fit Data Real Y=T Fit
70 70
10
20
30
40
50
10 20 30 removal 40 =3.3646 50 R=0.9999 Mse=0.11579 e max real removal R=0.9999 Mse=0.11579 e =3.3646 real R=0.99972 Mse=0.29029 e max
60 max
Real Data Fit Data Real Y=T Fit
20 20 10
70
70
60 60
All All
Real Data Real Fit Data Fit Y=T Y=T Validation Validation
40 40 30 30 20 20 R=0.9997 Mse=0.38509 e max=3.3646 R=0.9997 Mse=0.38509 e max=3.3646 10 20 30 40 50 60 70 10 Electrical 20 30 conductivity 40 50 60 70 Exprimental Electrical conductivityExprimental
Test 40 50 60 70 Test 30 20 removal 40 30real 50 40 60 50 70 Figure 7. Comparison of predicted values of electrical conductivity of nanofluids by neural networks 60 70 removalreal Figure 7. Comparison of predicted values of conductivity of nanofluids by neural networks Figure 7. Comparison of predicted values of electrical electrical conductivity of nanofluids by neural networks 20 30 removal 40 real 50 60 70 and experimental results for validation data 30
removal realand
and experimental results validationdata. data. experimental results for for validation
.
40 removal 40 real removalreal
50 50
R=0.9997 Mse=0.38509 e R=0.9997 Mse=0.38509 e m 40 3010 20 30 40 50 3010 Electrical 20 30conductivity 40 50 20 Expr Electrical conductivityExpri 20 10
50 50
10 10
Y=T
10
Training Training
=3.3646 R=0.99972 Mse=0.29029 e max =3.3646
al Data
Data T
60
Electrical conductivity Electrical conductivity ANN ANN
Y=T
30 30
50 40
Figure 6. Comparison of predicted values of electrical conductivity of nanofluids by neural networks 10 Figure 6. Comparison of predicted values of electrical conductivity of nanofluids by neural networks Figure 6. Comparison of predicted values and experimental results for training dataof . electrical conductivity of nanofluids by neural networks and experimental results for for training data. and experimental results training data.
R=0.99999 Mse=0.02103 e max =0.5427 R=0.99999 Mse=0.02103 e max =0.5427
Real Data
20 20
10 10
20 20
30 30
40
removal 40 rea removal real
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Table 3. Details of data bank used for developing the artificial neural network (ANN) model. Source
Nanofluid (s)
Dnp (nm)
φ (%)
T (◦ C)
Hadadian et al. [32]
graphene oxide-water graphene oxide-ethyleneglycol
20
0.0001–0.0006 0.0001–0.0006
25–65 25–60
Glover et al. [33]
single-wall carbon nanotubes −50% DI water/50% ethylene glycol
-
0–0.5
25–27
Dong et al. [34]
Aluminum-nitride-(AlN)-transformer oil
50
0.1–0.5
25–60
White et al. [35]
ZnO-propylene glycol
20–60
0–7
25
KalpanaSarojini et al. [36]
CuO-Water Cu-Water Al2 O3 -Water CuO-Ethylene glycol Cu-Ethylene glycol Al2 O3 -Ethylene glycol
20–80
0.05–1
30–60
Azimi et al. [37]
CuO-Water
89–112
0.12–0.18
25–50
Kole et al. [38]
graphene nanosheets-ethylene glycol-water
20
0.041–0.395
10–70
Ganguly el al. [39]
Al2 O3 -Water
13
0.005–0.03
25–45
Goharshadi et al. [40]
silver nanoparticles in distilled water and ethylene glycol
200–800
0–2
20–50
Konakanchi et al. [41]
aluminum oxide-propylene glycol/water silicon dioxide propylene glycol/water zincoxide-propylene glycol/water.
20–70
1–5
0–90
Zawrah et al. [42]
Al2 O3 -Water Al2 O3 / Water + 0.01 wt% SDS Al2 O3 /Water + 0.01 wt% SDS MgO/Water MgO/Water + 0.01 wt% SDS MgO/Water + 0.01 wt% SDS ZnO/Water ZnO/Water + 0.01 wt% SDS ZnO/Water + 0.01 wt% SDS MWCNTs/Water MWCNTs/Water + 0.01 wt% SDS MWCNTsWater + 0.01 wt% SDS TiO2-Water TiO2/Water + 0.01 wt% SDS TiO2/Water + 0.01 wt% SDS CuO-Water CuO/Water + 0.01 wt% SDS CuO/Water + 0.01 wt% SDS
10–20
0.01–2
20–70
Bagheli et al. [43]
Fe3 O4 /Water
14.2
0–0.5
10–60
Energies 2018, 11, 1190 Energies2018, 2018,11, 11,xxFOR FORPEER PEERREVIEW REVIEW Energies
00
Data ata
RealData Data Real Fit Fit Y=T Y=T
70 70
00 Validation Validation RealData Data Real Y=T Y=T
00
00
00
00 R=0.9997 Mse=0.38509 Mse=0.38509 ee max=3.3646 =3.3646 R=0.9997 max
Electrical Electrical conductivity conductivityANN
ANN
00Fit Fit
20 40 60=0.5427 =0.99999 Mse=0.02103 =0.5427 20 40 60 =0.99999 Mse=0.02103 eemax max Electricalconductivity conductivityExprimental Electrical Exprimental 20 30 40 40 50 50 60 60 70 70 0 30 ctricalconductivity conductivityExprimental ctrical Exprimental R=0.9999 Mse=0.11579 Mse=0.11579 =3.3646 R=0.9999 ee max=3.3646
60 60
11 of 16 11ofof16 16 11
Test Test
50 50 40 40 30 30 20 20 10 10
R=0.99972 Mse=0.29029 Mse=0.29029 ee max=3.3646 =3.3646 R=0.99972 max
10 10
max
20 30 30 40 40 50 50 60 60 70 70 00 20 Electricalconductivity conductivityExprimental Electrical Exprimental
20 30 40 50 60 70 20 30 40 50 60 70 Electricalconductivity conductivityExprimental Electrical Exprimental
Figure Comparisonof ofpredicted predictedvalues valuesof ofelectrical electricalconductivity conductivity of nanofluids by neural networks Figure Comparison of predicted values by neural networks Figure 8.8.8. Comparison of electrical conductivityof ofnanofluids nanofluids by neural networks and experimental results for testing data . and experimental results for testing data . and experimental results for testing data.
RealData Data Real Fit Fit Y=T Y=T
Mse=0.29029 ee max=3.3646 =3.3646 Mse=0.29029 max
70 70 Electrical Electrical conductivity conductivityANN ANN
ation tion
Test Test
30 0
40 40
50 50
60 60
70 70
removalreal removal real
997 Mse=0.38509 Mse=0.38509 eemax =3.3646 997 =3.3646 max
40 60=0.5427 40 60 920Mse=0.02103 Mse=0.02103 =0.5427 920 eemax max ical conductivityExprimental cal conductivity Exprimental 40 50 60 70 40 50 60 70 onductivityExprimental onductivity Exprimental
All 60 All 60
50 50 40 40 30 30 20 20 10 10 R=0.9999 Mse=0.11579 Mse=0.11579 eemax =3.3646 R=0.9999 =3.3646 max
10 10
20 30 40 40 50 60 70 20 30 50 60 70 Electricalconductivity conductivityExprimental Electrical Exprimental
Figure Comparisonof ofpredicted predictedvalues valuesof ofelectrical electricalconductivity conductivity of nanofluids by neural networks Figure Comparison of predicted by neural networks Figure 9.9.9. Comparison of electrical conductivityof ofnanofluids nanofluids by neural networks and experimental resultsfor forall alldata. data. . and experimental results for all data and experimental results
In Figure Figure 10 10 the the data data allocated allocated to to the the program program isis shown shown in in 33 colors: colors: violet, violet, green green and and red. red. In In Figure 10 the data allocated to the program is shown in 3 colors: violet, green and red. Horizontalaxis axisshows showsthe thedifference differencebetween betweenpredicted predictedvalues valuesand andexperimental experimentalvalues. values.As Ascan canbe be Horizontal Horizontal axis shows the difference between predicted values and experimental values. As can be seen,the thehighest highestand andlowest lowesterror errorrates ratesfor forthe theelectrical electricalconductivity conductivitywere werevery verygood. good.The Thecloser closerthe the seen, seen, the highest and lowest error rates for the electrical conductivity were very good. The closer the data to to the the base base line line laying laying in in the the middle middle means means aa successful successful prediction prediction with with low low error. error. For For the the data data to the section, base linethe laying indata the middle means a successful with For the training section, the violet data are closer closer to the the base line. line.prediction So itit shows shows thatlow theerror. percentage oftraining data training violet are to base So that the percentage of data section, theto violet data are closer the successful base line. in So it shows that the percentage of data allocated to allocated this has been more allocated to thissection section has beento more successful inpredicting. predicting. this section has been more successful in predicting.
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Energies 2018, 11, x FOR PEER REVIEW
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Energies 2018, 11, x FOR PEER REVIEW Error Histogram with 20 Bins 400
350300
Test Zero Error
12 of 16
Instances Instances
Error Histogram with 20 Bins 400350
Training Validation Test Training Zero Error Validation
300250 250200 200150 150100
1.288
1.049 1.288
1.049
0.8105
0.572 0.8105
0.3334 0.572
0.0948 0.3334
-0.1438
-0.3824
Errors = Targets - Outputs
0.0948
-0.3824
-0.1438
-0.6209
-1.098
-0.8595 -0.6209
-1.098
-0.8595
-1.337
-1.575 -1.337
-1.814 -1.575
-1.814
-2.291
-2.052
-2.052
-2.53 -2.291
-2.53
-2.768
-3.007 -2.768
-3.007
0
-3.245
50 0
-3.245
100 50
Figure 10. Error distribution diagram for electrical conductivity of nanofluids (x-axis: difference of
= Targets - Outputs of nanofluids (x-axis: difference of Figure 10. Error distribution diagramErrors for electrical conductivity error value between experimental and predicted results, y-axis: number of data). error value experimental andfor predicted y-axis:ofnumber of data). Figure 10.between Error distribution diagram electricalresults, conductivity nanofluids (x-axis: difference of error between experimental and predicted results, y-axis: number of data). As value shown in Figure 11, the training routine for the electrical conductivity data of the nanofluids
is stopped evaluation error occurs in 15 repetitions. This stop has in As shown ifinthe Figure 11, thesettraining routine forconsecutive the electrical conductivity data ofoccurred the nanofluids As shown in Figure 11,for the training routine fortesting the electrical of the nanofluids repeat Training data validation section conductivity for electrical data conductivity areoccurred on the in is stopped if11.the evaluation setthe error occurs and in 15 consecutive repetitions. This stop has is normal stoppedline. if the evaluation set error occurs 15away consecutive has occurred in But for thefor training section, wein go from therepetitions. normal lineThis withstop increasing number repeat 11. Training data the validation and testing section for electrical conductivity are of on the repeat 11. Training data for the validation and testing section for electrical conductivity are on the repetitions. This descending value for training data is very good because the error rate is very low normal line. But for the training section, we go away from the normal line with increasing number of normal line.normal. But for the training section, we go away from the normal line with increasing number of and very repetitions. This descending value for training data is very good because the error rate is very low and repetitions. This descending value for training data is very good because the error rate is very low very normal. and very normal. 0
Mean Squared Error (mse) Mean Squared Error (mse)
10 0
10
-5
10
-5
10
-10
10
Train Validation Test Train Best Validation Test Best
-10
10
-15
10
-15
10
-20
10
-20
10
-25
10
Best Validation Performance is 0.38509 at epoch 11 -25
10
0
5
10
15
Best Validation Performance is 0.38509 at 11 15epoch Epochs
0 5 10 15 Epochs electrical conductivity of the nanofluids Figure 11. Network performance diagram for the15 predicted (the number of repetitions in terms of mean squared error). Figure 11. Network performance diagram for the predicted electrical conductivity of the nanofluids Figure 11. Network performance diagram for the predicted electrical conductivity of the nanofluids (the of repetitions of model, mean squared error).of the prediction of electrical conductivity of It number can be said that for in theterms ANN the results
(the number of repetitions in terms of mean squared error). nanofluids in the work of researchers are very normal and the lowest error rate and the highest It can be coefficient said that for thebeANN model, thethese results of theare prediction of with electrical conductivity of correlation can obtained and results consistent the experimental and It can be said that for the ANN model, the results of the prediction of electrical conductivity nanofluids in the work of researchers are very normal and the lowest error rate and the highest predicted results of this study, indicating a correct evaluation with the least error. of nanofluids in the work are veryresults normal the lowest error rate and the correlation coefficient canof beresearchers obtained and these are and consistent with the experimental andhighest predicted results of this study, indicating a correct evaluation with the least error. correlation coefficient can be obtained and these results are consistent with the experimental and
predicted results of this study, indicating a correct evaluation with the least error. The experimental results of the electrical conductivity of CuO/glycerol nanofluid in the two-dimensional and three-dimensional forms are shown in Figures 12 and 13. As can be seen,
at a temperature of 50 °C and size of 20 nm, the electrical conductivity is about 40 μS/cm, causing 33.33% increase in the electrical conductivity. With the volume concentration of 1.5% and a temperature of 50 °C, the electrical conductivity is approximately 60 μS/cm. The electrical conductivity increases with temperature, especially in higher volume fractions. These results are attributed the accumulation of nanoparticles in the presence of the field and their Brownian motion Energies 2018, 11,to 1190 13 of 16 at various temperatures. One of the reasons for the reduction of electrical conductivity at higher nanoparticle sizes is decreasing the mobility of nanoparticles as load carriers, as well as decreasing number per volumeincreases unit for aas constant volume fraction. the their electrical conductivity the temperature and volume fraction of the nanofluid increases. Electric relative to nanoparticles, temperature with almost constant gradient. An However, with conductivity an increase increases in the size of the theanelectrical conductivity decreases. ◦ increase in electric conductivity with temperature is associated with an increase in ionic mobility with For example, at a temperature of 30 C and size of 50 nm, the electrical conductivity is 30 µS/cm. temperature that plays a major thesize conductivity theelectrical nanofluid.conductivity Since the nanofluid viscosity ◦ C in However, at a temperature of 50role and of 20 nm,ofthe is about 45 µS/cm, decreases with increasing temperature, the ionic mobility increases with increasing temperature and causing 33.33% increase in the electrical conductivity. With the volume concentration of 1.5% and a thus causes an increase in the electrical conductivity with temperature [44]. As the temperature temperature of 50 ◦ C, the electrical conductivity is approximately 60 µS/cm. The electrical conductivity increases, the bonds of the base fluid molecules are weakened and the structure of its mass molecules increases with temperature, especially in higher volume fractions. These results are attributed to the disappears, so the number of free molecules in the base fluid around the nanoparticles increases. This accumulation of nanoparticles the presence field andmolecules their Brownian layer, created by the van derinWaals forces of of thethe base fluid and the motion surface at of various the temperatures. One of the reasons for the reduction of electrical conductivity at higher nanoparticle nanoparticles, has high electrical conductivity and therefore increases it [44]. It can also be said that sizes is decreasing the mobility of almost nanoparticles asthen loadthe carriers, well as decreasing number since the nanoparticles used are spherical, ratio ofasthe surface to volume their increases per and volume forana increase constantinvolume fraction. thus unit causes the electrical conductivity, too.
(a)
(b)
Figure 12. Effect of temperature and volume fraction variations on the electrical conductivity of
Figure 12. Effect of temperature and volume fraction variations on the electrical conductivity of CuO/glycerol. (a) 2 dimensional; (b) 3 dimensional. CuO/glycerol. (a) 2PEER dimensional; Energies 2018, 11, x FOR REVIEW (b) 3 dimensional. 14 of 16
(a)
(b)
Figure 13. Effect of temperature and nanoparticles size variations on the electrical conductivity of
Figure 13. Effect of temperature and nanoparticles size variations on the electrical conductivity of CuO/glycerol nanofluid. (a) 2 dimensional; (b) 3 dimensional. CuO/glycerol nanofluid. (a) 2 dimensional; (b) 3 dimensional.
4. Conclusions In the present study, electrical conductivity of CuO/Glycerol nanofluid was investigated experimentally. Then, the artificial neural network was used to predict the electrical conductivity. Volume fraction, temperature and particle size were considered as network inputs and electrical conductivity as output. The electrical conductivity increases with temperature, especially in higher volume fractions. These results are attributed to the accumulation of nanoparticles in the presence of
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Electric conductivity increases relative to temperature with an almost constant gradient. An increase in electric conductivity with temperature is associated with an increase in ionic mobility with temperature that plays a major role in the conductivity of the nanofluid. Since the nanofluid viscosity decreases with increasing temperature, the ionic mobility increases with increasing temperature and thus causes an increase in the electrical conductivity with temperature [44]. As the temperature increases, the bonds of the base fluid molecules are weakened and the structure of its mass molecules disappears, so the number of free molecules in the base fluid around the nanoparticles increases. This layer, created by the van der Waals forces of the base fluid molecules and the surface of the nanoparticles, has high electrical conductivity and therefore increases it [44]. It can also be said that since the nanoparticles used are almost spherical, then the ratio of the surface to volume increases and thus causes an increase in the electrical conductivity, too. 4. Conclusions In the present study, electrical conductivity of CuO/Glycerol nanofluid was investigated experimentally. Then, the artificial neural network was used to predict the electrical conductivity. Volume fraction, temperature and particle size were considered as network inputs and electrical conductivity as output. The electrical conductivity increases with temperature, especially in higher volume fractions. These results are attributed to the accumulation of nanoparticles in the presence of the field and their Brownian motion at various temperatures. The obtained results showed that there is a good agreement between the predicted and experimental results and the sum of mean square error (MES) and correlation coefficient (R2 ) are desirable. Author Contributions: The work is conducted and wrote by R.A. under supervision of H.M., M.H.A., W.-M.Y. and N.G. Acknowledgments: The authors appreciate the financial support from Ministry of Science and Technology, Taiwan, under grant number MOST 106-2221-E-027-102-MY2 and MOST 106-2622-E-027-025-CC2. Conflicts of Interest: The authors declare no conflicts of interest.
Nomenclatures SOM SEM ANN MLP BP MSE
self-organizing map scanning electron microscopy artificial neural network multi-layer perceptron back propagation mean square error
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