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Modeling and prediction of retardance in citric acid coated ferrofluid using artificial neural network
Author’s Accepted Manuscript Modeling and prediction of retardance in citric acid coated ferrofluid using artificial neural network Jing-Fung Lin, Jer-Jia Sheu
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S0304-8853(16)30077-4 http://dx.doi.org/10.1016/j.jmmm.2016.01.077 MAGMA61101
To appear in: Journal of Magnetism and Magnetic Materials Received date: 1 July 2015 Revised date: 10 November 2015 Accepted date: 23 January 2016 Cite this article as: Jing-Fung Lin and Jer-Jia Sheu, Modeling and prediction of retardance in citric acid coated ferrofluid using artificial neural network, Journal of Magnetism and Magnetic Materials, http://dx.doi.org/10.1016/j.jmmm.2016.01.077 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Modeling and Prediction of Retardance in Citric Acid Coated Ferrofluid Using Artificial Neural Network
Jing-Fung Lina, *, and Jer-Jia Sheub a
b
Department of Industrial Design, Far East University, Taiwan, R.O.C.
Department of Mechanical Engineering, Southern Taiwan University of Science and Technology, Taiwan, R.O.C. *Corresponding Author: [email protected]
Abstract Citric acid coated (citrate-stabilized) magnetite (Fe3O4) magnetic nanoparticles have been conducted and applied in the biomedical fields. Using Taguchi-based measured retardances as the training data, an artificial neural network (ANN) model was developed for the prediction of retardance in citric acid (CA) coated ferrofluid (FF). According to the ANN simulation results in the training stage, the correlation coefficient between predicted retardances and measured retardances was found to be as high as 0.9999998. Based on the well-trained ANN model, the predicted retardance at excellent program from Taguchi method showed less error of 2.17% compared with a multiple regression (MR) analysis of statistical significance. Meanwhile, the parameter analysis at excellent program by the ANN model had the guiding significance to find out a possible program for the maximum retardance. It was concluded that the proposed ANN model had high ability for the prediction of retardance in CA coated FF.
Keywords: Artificial Neural Network; Ferrofluid; Multiple Regression; Retardance; Taguchi Method. 1
1. Introduction Citric acid coated (citrate-stabilized) magnetite (Fe3O4) magnetic nanoparticles (MNPs) have been conducted and hold their potential therapeutic applications such as conjugation and release of doxorubicin [1]. Also, they have been used as contrast agent in magnetic resonance imaging for biomedical application [2] and as feasible adsorbent for the removal of cadmium in industrial wastewater application [3]. The synthesis and magnetic properties of citric acid (CA) coated Fe3O4 MNPs will be investigated essentially. To produce the CA coated Fe3O4 MNPs with good magneto-optical properties [4], two influence factors including pH value of suspension and double centrifugations were adopted. Highly dispersed water-based ferrofluids (FFs) were obtained successfully. Owing to the use of Taguchi method, the excellent program (parametric combination) for the CA coated FFs with high retardance or low dichroism was found readily [4]. Based on the Stokes polarimeter, the optical configuration for measuring optically linear birefringence (LB) and linear dichroism (LD) properties was constructed. The measurement principle was well explained in [5]. Nowadays, computer-based methods such as artificial neural network (ANN) and multiple regression (MR) analysis have attracted some attentions to be replaced with high-cost experimental studies [6]. Detailed study of regression as well as ANN models have shown that regression analysis is one of the most widely used methodologies for expressing the relation between a dependent variable (response) and several independent variables (predictor) [7-9]. ANN has been successfully employed in solving complex problems in various fields such as function approximation, pattern association and pattern recognition, associative memories and generation of new meaningful pattern [9]. We have recently developed a MR model that has statistically significant predictive ability in the retardance of CA coated FFs [10]. In this study, the measured retardances of CA coated FFs samples using Taguchi orthogonal design method-L9(34) [10] were used as the training data in the ANN model. Based on the trained ANN model, the predicted retardance at excellent program from Taguchi method showed less error 2
of 2.17% compared with a MR analysis of statistical significance. The parameter analysis at excellent program by the developed ANN model was conducted. Compared with the MR analysis, the use of ANN for modeling and prediction in the clinical application was discussed.
2. Experimental results of Taguchi method Taguchi method was straightforward and easy to apply to many engineering situations, making it a powerful yet simple tool. Subsequently, the optimal synthesis condition of CA coated Fe3O4 FFs with high retardance was determined by the Taguchi orthogonal design method-L9(34), i.e. four parameters with three levels, respectively, and nine tests of FFs with a concentration of 1000 g/L, correspondingly. Influence parameters were (A) pH value of suspension after coating (4.5, 5, 5.5), (B) molar ratio of CA to Fe3O4 MNPs (0.03, 0.06, 0.12), (C) CA volume (10 ml, 20 ml, 40 ml), and (D) coating temperature (70 ℃, 80 ℃, 90 ℃). The manufacture procedure for stabilized CA coated FFs could be found [4]. The retardance (magneto-optical property) of FF was measured by a Stokes polarimeter with a feasible algorithm [5]. From the investigation of retardance results in the nine samples, as shown in Fig. 1, the retardance of the A3 sample reached the highest value of 29.3618° under 64.5 mT (parameters’ values were of A1B3C3D3, were close to the excellent program as A1B3C3D1, as shown in Table 1 [4], only difference in coating temperature), and the A5 sample had the second highest retardance value as 23.6294° under 64.5 mT. Considering the retardance in the A3 sample varied severely in the magnetic fields, may be due to the excess CA and higher coating temperature (parameter B and parameter D), its larger secondary diameter or agglomerations might have influenced the formation of chain-order under the magnetic fields. Further, it was found that the influence sequence between these parameters in retardance was B>A>D>C. According to the range analysis, excellent program (parametric combination) was pH value of suspension after coating was 4.5, molar ratio of CA to 3
Fe3O4 MNPs was 0.12, CA volume was 40 ml, and coating temperature was 70 ℃[4], i.e. expressed by [4.5, 0.12, 40, 70] in this study.
Fig. 1. Experimental results of retardance in CA coated FF samples using Taguchi method-L9(34).
Table 1 Orthogonal test results of retardance No.
A
B
C
D
Retardance (deg)
A1
1
1
1
1
7.8228
A2
1
2
2
2
11.9872
A3
1
3
3
3
29.3618
A4
2
1
2
3
4.0525
A5
2
2
3
1
23.6294
A6
2
3
1
2
18.1662
A7
3
1
3
2
-0.4628
A8
3
2
1
3
4.5877
A9
3
3
2
1
20.2021
k1
16.3906
3.8042 10.1922 17.2181 4
k2
15.2827 13.4014 12.0806 9.8969
k3
8.1090 22.5767 17.5095 12.6673
Range
8.2816 18.7725 7.3173 7.3213
Influence Parameters
B>A>D>C
Excellent Program
B3A1D1C3
Via the results of range analysis as shown in Table 1, it was found that the effect induced by molar ratio of CA to Fe3O4 MNPs on the retardance value of CA coated FFs was significant. It was also indicated that molar ratio of CA to Fe3O4 MNPs played an important role in the retardance value due to its high sensitivity, as pointed out by the influence curves of the parameter level on the retardance in Fig. 2. In Table 1, it was noted that ki (i = 1, 2, 3) was the average value of the three experimental results of the same level under the corresponding process parameter. Range was the difference between the maximum value in k1, k2, and k3 and the minimum value in k1, k2, and k3 under the corresponding process parameter.
Fig. 2. Influence curves of the parameter level on the retardance of FFs under Taguchi analysis. 5
3. Artificial neutral network model 3.1. Artificial neutral network Artificial Neural Networks (ANNs) emulating the biological connections between neurons are known as soft computing techniques. ANNs can reproduce some functions of human behavior, which are formed by a finite number of layers with different computing elements called neurons. In order to construct a network, the neurons are interconnected. The organization of connections determines the type and objectives of the ANNs. The processing ability of the network is stored in the interunit connection strengths, or weights, which are tuned in the learning process. The training (or learning) algorithm is defined as a procedure that consists of adjusting the weights and biases of a network that minimize selected function of the error between the actual and desired outputs [11]. ANNs are widely used in many applications such as forecasting, control, data compression, pattern recognition, speech, vision, medicine, and power systems. Neural network models provide an alternative approach to analyze the data, because they can deduce patterns in the data [11]. There are many different types of ANN. Some of the more popular include Multi-Layer Perceptron (MLP), learning vector quantization, radial basis function (RBF), Hopfield and Kohonen, to name a few. Some ANN are classified as feedforward while others are recurrent (i.e., implement feedback) depending on how data is processed through the network [12]. There are several ANN models and architectures that have been used in engineering applications to model or approximate properties. The most widely used ANN models among feedforward models, are the Multi-Layer Perceptron (MLP) and the Radial Basis Function (RBF) models [13]. The MLP network uses a back-propagation learning algorithm. Different back-propagation (BP) algorithms (Scaled Conjugate Gradient (SCG), Levenberg-Marquardt (LM), Gradient Descent with variable learning rate back-propagation (GDX) and Resilient back Propagation (RP)) can be used for network training [13]. Some parameters (i.e. the number of
6
training and testing data, learning rate, number of hidden layers, and processing function used) affect the accuracy, reliability, and effectiveness of the neural network.
3.2. Modeling and prediction of the retardance in CA coated FFs by the ANN model The current work used MLP feedforward network with three layers input (4 neurons), hidden, and output (1 neuron) to predict the retardances of CA coated FFs. Two transfer functions (tan-sigmoid and log-sigmoid) were used and the network was trained with Gradient Descent with variable learning rate back-propagation (GDX), which was indicated as traingdx in neutral network toolbox in MATLAB. The structure of the ANN model with input and output parameters was shown as Fig. 3. The pH value of suspension after coating, molar ratio of CA to Fe3O4 MNPs, CA volume, and coating temperature were taken as the input parameters whereas the retardance was taken as the output parameter. The Taguchi-based measured retardances were used for training the network. It was noted that the retardance value of the A7 sample was deleted for a possible error in Table 1 as well as MR analysis did [10].
Fig. 3. ANN model. In the initial stage of training ANN, the epoch (iteration) was set as 1000 and performance goal (mean square error) was chosen as 1e-3. The GDX algorithm with variable learning rate for training 7
moderate-sized feedforward neural networks was adopted. The number of neurons in the input layer and output layer was 4 and 1, respectively. The number of neurons in hidden layer was varied from 4 to 14 in increments of 2. As evident in Fig. 4 for the comparisons between trained results and measured results, it was found that the average absolute relative error (AARE) for the trained predicted retardance results was 12.39% and the root mean square error (RMSE) was 1.832 (the lowest) in the case where the number of neurons in the hidden layer was 6. Accordingly, the correlation coefficient R between ANN predicted results and Taguchi-based measured results was 0.9974. Therefore the optimum number of neurons in the hidden layer was considered to be 6. Instead of using GDX algorithm the GD algorithm with constant learning rate was adopted under the same setting. From the comparisons, it was found that the AARE for these trained predicted retardance data was 15.64% and the RMSE was 2.217. Therefore, the commonly used GDX with variable learning rate was superior to GD with constant learning rate. Two difficulties of the BP method in practice (the steepest decent back prorogation, the training function as traingd in MATLAB) as the extremely slow convergence and false local minimum might be avoided [14].
Fig. 4. Determination of the optimum number of neurons in the hidden layer for selected GDX algorithm used in the initial training network. 8
Subsequently the feedforward network with input (4 neurons), hidden (6 neurons), and output (1 neuron) layer was adopted in the training stage of ANN. The epoch was particularly set as 1000000 and performance goal was chosen as 1e-7 to predict the retardance. The neutral network training was shown as Fig. 5. The performance plot was shown as Fig. 6 and the best training performance happened at the epoch of 244921. The regression results were plotted as Fig. 7. The solid blue line represented the best fit linear regression line between predicted outputs and actual targets. The relationship between outputs and targets was indicated by the R value of one. There was a perfect linear relationship between outputs and targets as shown in Fig. 7. It was apparent that the developed ANN model was well-trained and predictive.
Fig. 5. ANN training.
9
Fig. 6. Performance plot.
Fig. 7. Regression plot. 10
According to the ANN simulation results in the training stage, as shown in Fig. 8, it was found that the correlation coefficient R between ANN predicted retardances and Taguchi-based measured retardances was as high as 0.9999998, while it was achieved as 0.9999999 for a MR analysis [10]. However, the AARE was calculated as 9.36%, which was an acceptable error range (less 10%) for a certain application. Hence the well-trained ANN model was further used to predict the retardance value at excellent program from Taguchi method.
Fig. 8. Comparisons of ANN predicted retardances and Taguchi-based measured retardances.
3.3. Comparisons between artificial neural network and multiple regression The regression equations for MR linear/nonlinear model were obtained in an earlier study [10]. The ANOVA for MR nonlinear model indicated that F value of 1320535.0358 was much greater than the critical value of F as 232.986, and P value of 0.0007 (95% confidence interval, P < 0.05) which suggested that the model was statistically significant [10]. From the regression analysis, the correlation coefficient R between predicted retardances and measured retardances was found to be 0.9999999, which was much close to 1. Further, according to the R2 value, it was found that the MR nonlinear model was able to explain 99.99998% of the variation as compared to 88.8% variation 11
explained by the MR linear model [10]. This meant that the MR nonlinear model was able to explain more variation in the response variable which ultimately would result in higher reliability of prediction. Further, the AARE of MR-nonlinear-model predicted retardances to Taguchi-based measured retardances was determined as just 0.03%. For testing the well-trained ANN model, we performed the prediction of retardance at three programs, including excellent program of [4.5, 0.12, 40, 70] from Taguchi method and two programs of [5, 0.12, 40, 70] and [5.5, 0.12, 40, 70]. The predicted retardances and those obtained by MR analysis (nonlinear model) for these programs were shown as Fig. 9. The correlation coefficient R was -0.998 between predicted retardances by ANN model and those achieved by MR analysis. The AARE between predicted retardances by ANN model and MR analysis for these programs was 1.44%. The predicted retardance of 33.41° at excellent program showed less error of 2.17% compared with MR analysis of 32.7°. The retardance at a program of [5, 0.12, 40, 70] by ANN model was predicted as 33.15°, which was much close (0.13%) to that predicted by MR analysis. It was noted that the proposed ANN model could save time and avoid carrying some high-cost experimental studies due to its accurate predictions with acceptable errors (less 5%).
Fig. 9. Comparisons of predicted retardances at three programs by ANN model and MR analysis. 12
In this study, the MR nonlinear model (considering the interaction between X1 and X3) was found to be more significant and reliable [10] than the MR second-order model (without considering the interaction between X1 and X3, the values of R and F were 0.99968 and 624.8176, respectively). The absolute errors of the A4 sample (retardance was 4.0525°) were determined to be 0.06% and 7.72%, respectively, considering and without considering the interaction between X1 and X3. The MR nonlinear model was obtained by investing long time and endeavor. To the best of the authors’ knowledge, the MR nonlinear model could be developed systematically by a stepwise regression analysis with Matlab [15]. Although the MR models are easily applied, the reliability decreases as the problems become more complicated [7]. The fundamental problem with MR is the correlation coefficient R derived by MR can sometimes be of rather limited reliability if there are a lot of interactions among the data to be considered [16]. While MR is dealing with large number of independent variables, it is of significance importance to determine best combination of these variables to predict dependent variable [9]. In contrast, in the clinical data analysis using ANN of patient with breast cancer, it has been concluded that ANN analysis offers a promising method in the analysis of multivariable data (variable number was considered as 11) on cancer patient [16]. In the clinical application such as medical diagnosis [17], several advantages of ANN method were proposed as the ability to process large amount of data, reduced likelihood of overlooking relevant information and reduction of diagnosis time. And some advantages using ANN were explained and expressed as neural network models require less formal statistical training to develop; neural networks can implicitly detect complex nonlinear relationships between independent and dependent variables; neural networks have the ability to detect all possible interactions between predictor variables; neural networks can be developed using multiple different training algorithms [18]. In this study, the trained ANN model was comparable with the MR analysis in the R value and not accurate than the MR analysis in the AARE value. The reason why higher AARE existed in our 13
trained model might be influenced by the amount of data set, the selected GDX algorithm, and the ANN architecture. It was known that the learning problems (overlearning or insufficient learning) might affect the accuracy of the ANN models [7]. Further, it was shown that the AARE between predicted retardances by ANN model and those obtained by MR analysis for three programs ([4.5, 0.12, 40, 70], [5, 0.12, 40, 70], and [5.5, 0.12, 40, 70]) was just 1.44%. Indeed, there existed a different variation between them two. In the future study, we will consider the selection of training data, choose other training algorithm such as the Levenberg-Marquardt algorithm [6, 9], and adopt more hidden layers with different transfer function group [17]. Moreover, the ANN method could be considered applicable to the single-objective optimization of low dichroism or the multi-objective optimization of high retardance and low dichroism in the CA coated FFs.
3.3.1. The single parameter effect and mutual influence analysis in MR The ANN sensitivity analysis provided insight into the usefulness of individual variables [16], therefore the simulation of single parameter effect at excellent program by the developed ANN model was performed in this study. In contrast, the single parameter effect and mutual influence analysis in MR were also provided as below. The regression equation for MR nonlinear model [10] was expressed as Eq. (1), and shown as below. Three of the four parameters in Eq. (1) were fixed at the mean values, where the mean values of pH value of suspension after coating, molar ratio of CA to Fe3O4 MNPs, CA volume, and coating temperature were 5, 0.07, 23.33 ml, and 80 ℃, respectively. The corresponding regression equations of single-parameter were then obtained as Eqs. (2)-(5). Single-parameter curves of all four parameters were shown as in Fig. 10; there were obtained by standardizing the levels for each parameter in a range of -2 to 2 [19]. Retardance = 38.87-6.46X1+158.04X2-1.11X3+0.013X32-0.001X42+0.18X1X3 (1) 14
Retardance-1 for pH value of suspension after coating = 14.20029-0.27749X1 (2) Retardance-2 for molar ratio of CA to Fe3O4 MNPs = 3.76779+3.55592X2
(3)
Retardance-3 for CA volume = 14.35375+3.35925X3+0.72563X32
(4)
Retardance-4 for coating temperature = 13.64533-0.8X4-0.025X42
(5)
As shown in Fig. 10, with the increase in pH value of suspension after coating, the retardance of CA coated FFs decreased over a small range. However, with the increase in molar ratio of CA to Fe3O4 MNPs, the retardance of CA coated FFs increased over a large range; the effect of molar ratio of CA to Fe3O4 MNPs was shown to have a significant increase on the retardance value of CA coated FFs. It was noted that both Eq. (2) and Eq. (3) belonged to straight line equation, and the positive effect of molar ratio of CA to Fe3O4 MNPs was significant. The effect of CA volume on the retadance of CA coated FFs was shown in Fig. 10, where the retardance increased with increasing CA volume over a large range. In addition, the effect of temperature was shown in Fig. 10, where the retardance decreased with increasing temperature over a small range. The negative effect induced by temperature on the retardance value of CA coated FFs was smaller than that induced by CA volume.
15
Fig. 10. Effects of pH, molar ratio, CA volume and temperature on the retardance value of CA coated FFs in the mean values of four parameters. Subsequently, two parameters including molar ratio of CA to Fe3O4 MNPs and coating temperature were kept at the middle level as 0.07 and 80 ℃, respectively. The mathematical formula was obtained as Eq. (6). Then the mutual influence (response surface) of pH value of suspension after coating and CA volume on the retardance value of CA coated Fe3O4 FFs was shown as Fig. 11. From Fig. 11, the retardance value of CA coated Fe3O4 FFs changed significantly with the increase of CA volume at low pH value of suspension, while the retardance value increased more significantly with the increase of CA volume at high pH value of suspension. Retardance-6 for pH value of suspension after coating and CA volume = 43.52885-6.4613X1-1.1061X3+0.0129X32 +0.1818 X1X3 (6) From Table 2 [10], shown as below, it was concluded the mutual influence between pH value of suspension after coating and CA volume was very significant (p < 0.01). The influence of the linearity term (p < 0.01) of CA volume was negative and the influence of its quadratic term (p < 0.01) was positive [10].
16
Retardance (deg)
25
20
15
10
5 40 5.5
30 20 CA Volume (ml)
5 10
4.5
pH
Fig. 11. Response surface showing the effect of pH value of suspension after coating and CA volume on the retardance value of CA coated FFs. The retardance of CA coated Fe3O4 FFs was at the highest level (24.38°) at both high pH value and high CA volume, while the retardance of CA coated Fe3O4 FFs was at the lowest level at both high pH value and low CA volume. It was noted that when molar ratio of CA to Fe3O4 MNPs and coating temperature were changed as 0.12 and kept at 80 ℃, respectively, the effect of the pH value and CA volume on the retardance value of CA coated Fe3O4 FFs was similar, and the highest retardance (32.28°) of CA coated Fe3O4 FFs was larger than that for molar ratio of CA to Fe3O4 MNPs and coating temperature were 0.07 and 80 ℃, respectively, by an increment of 7.9°.
Table 2
Predictors' values for multiple nonlinear regression model
Coefficient
Standard Error
t Stat
P value
Intercept X1 X2
38.8660 -6.4613 158.0407
0.2094 0.0493 0.1401
185.6040 -131.1701 1127.8218
0.0034 0.0049 0.0006
X3 X3*X3 X4*X4
-1.1061 0.0129 -0.0010
0.0134 0.0000 0.0000
-82.3726 343.9284 -180.3813
0.0077 0.0019 0.0035
17
X1*X3
0.1818 R =0.9999998
0.0026
2
71.1905 R adj=0.9999992
0.0089
2
3.3.2. The simulation of single parameter effect at excellent program by the ANN model The developed ANN model was simulated for the variation of retardance at excellent program of [4.5, 0.12, 40, 70], on the cases of varying the value of one parameter and fixing the value of the other three parameters. The simulation results of single parameter effect at excellent program by the ANN model were shown as Figs. 12-15. As shown in Fig. 12, on the condition of varying the pH value from 4.5 to 5 in increments of 0.2, molar ratio of CA to Fe3O4 MNPs was fixed as 0.12, CA volume was 40 ml, and coating temperature was 70 ℃, the retardance value started to decrease at pH 5.3 and down to pH 5.5, the trend of the variation of retardance with pH value was similar to the curve A in Fig. 2. As shown in Fig. 13, on the condition of varying the molar ratio of CA to Fe3O4 MNPs from 0.03 to 0.12 in increments of 0.015, pH value was fixed as 4.5, CA volume was 40 ml, and coating temperature was 70 ℃, the retardance value increased apparently from molar ratio of 0.03 to molar ratio of 0.075, and increased slightly from molar ratio of 0.075 to 0.12 (the retardance was varied from 31.61° to 32.58°). Compared to the curve B in Fig. 2, the fact that the retardance increased with the increase of molar ratio of CA to Fe3O4 MNPs existed accordingly.
18
Fig. 12. Effect of the pH value of suspension after coating at excellent program on the retardance.
Fig. 13. Effect of the molar ratio of CA to Fe3O4 MNPs at excellent program on the retardance. As shown in Fig. 14, on the condition of varying the CA volume from 10 ml to 40 ml in increments of 5 ml, pH value was fixed as 4.5, molar ratio of CA to Fe3O4 MNPs was 0.12, and coating temperature was 70 ℃, the retardance value increased apparently from 10 ml CA volume to 20 ml (the increment of retardance was close to 20°), and increased slightly from 20 ml CA 19
volume to 40 ml (the retardance was varied from 30.51° to 32.60°). The trend of the variation of retardance with the increase of CA volume was similar to the curve C in Fig. 2. As shown in Fig. 15, on the condition of varying the coating temperature from 70 ℃ to 90 ℃ in increments of 2.5 ℃, pH value was fixed as 4.5, molar ratio of CA to Fe3O4 MNPs was 0.12, and CA volume was 40 ml, the retardance value increased gradually from temperature of 70 ℃ to 85 ℃ with a slight increase of just 0.37° and the retardance decreased down to 90 ℃. The variation of retardance was opposite to the curve D (to decrease then increase in retardance) in Fig. 2 and different from the curve for temperature in Fig. 10. The simulated maximum retardance appeared at the temperature of 85 ℃ in Fig. 15, which was slightly deviated from the low retardance at temperature of 80 ℃ as shown in Fig. 2.
Fig. 14. Effect of the CA volume at excellent program on the retardance.
20
Fig. 15. Effect of the coating temperature at excellent program on the retardance. It was said that the formation of a CA coating layer on the particle surface was known to be the chemical bond formation between the carboxyl groups of CA on the Fe-OH sites of the iron oxide nanoparticles [20]. Since the chemical reaction rate increased with temperature, the adsorption of CA onto the particle surface could be enhanced by the increased coating temperature. Thus, the increased coating temperature could enhance the CA coating rate [20]. It was noted that the level of each parameter was chosen to be three in Taguchi method; only three k values were obtained. However, the ANN could increase the number of level in parameter randomly and increase data set. The parameter analysis performed by the developed ANN model was better than that done by Taguchi method. Compared with the MR analysis, the developed ANN model provided a different insight into the temperature effect on the retardance of CA coated FF. In addition, through the ANN simulation results of single parameter effect at excellent program, they not only showed the trend of single parameter effect but also had the guiding significance to find a possible optimal program of [4.5, 0.12, 40, 85] for the maximum retardance. Accordingly, the ANN model could predict the retardance value at different programs; it could shorten the period of
21
research and save the manpower and material resource. Above all, the ANN model also could effectively decrease the time and effort required for the design optimization process.
4. Conclusions From the training and testing of the ANN simulation results, an ANN model was developed successfully and had high ability for the prediction of retardance in CA coated FF. The ANN simulation results in the training stage showed a high correlation coefficient between experimental data and predicted data. Further, the predicted retardance at excellent program from Taguchi method showed less error of 2.17% compared with a MR analysis of statistical significance. In addition, through the ANN simulation results of single parameter effect at excellent program, they provided a different insight into the temperature effect and had the guiding significance to find a possible optimal program for the maximum retardance of CA coated FF.
Acknowledgements The financial support provided to this study by the Ministry of Science and Technology in Taiwan under
Grant
MOST 102-2221-E-269-005
and 103-2221-E-269-004
is
gratefully
acknowledged.
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Figure captions: Figure 1.
Experimental results of retardance in CA coated FF samples using Taguchi method-L9(34).
Figure 2.
Influence curves of the parameter level on the retardance of FFs under Taguchi analysis.
Figure 3.
ANN model.
Figure 4.
Determination of the optimum number of neurons in the hidden layer for selected GDX algorithm used in the initial training network.
Figure 5.
ANN training.
Figure 6.
Performance plot.
Figure 7.
Regression plot.
Figure 8.
Comparisons of ANN predicted retardances and Taguchi-based measured retardances. 25
Figure 9.
Comparisons of predicted retardances at three programs by ANN model and MR analysis.
Figure 10. Effects of pH, molar ratio, CA volume and temperature on the retardance value of CA coated FFs in the mean values of four parameters. Figure 11. Response surface showing the effect of pH value of suspension after coating and CA volume on the retardance value of CA coated FFs. Figure 12. Effect of the pH value of suspension after coating at excellent program on the retardance. Figure 13. Effect of the molar ratio of CA to Fe3O4 MNPs at excellent program on the retardance. Figure 14. Effect of the CA volume at excellent program on the retardance. Figure 15. Effect of the coating temperature at excellent program on the retardance.
Research Highlights of MAGAM-D-15-01327 1. The feedforward ANN is applied for modeling of retardance in CA coated FFs. 2. ANN can predict the retardance at excellent program with acceptable error to MR. 3. The proposed ANN has high ability for the prediction of retardance.
26
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PII: DOI: Reference:
S0304-8853(16)30077-4 http://dx.doi.org/10.1016/j.jmmm.2016.01.077 MAGMA61101
To appear in: Journal of Magnetism and Magnetic Materials Received date: 1 July 2015 Revised date: 10 November 2015 Accepted date: 23 January 2016 Cite this article as: Jing-Fung Lin and Jer-Jia Sheu, Modeling and prediction of retardance in citric acid coated ferrofluid using artificial neural network, Journal of Magnetism and Magnetic Materials, http://dx.doi.org/10.1016/j.jmmm.2016.01.077 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Modeling and Prediction of Retardance in Citric Acid Coated Ferrofluid Using Artificial Neural Network
Jing-Fung Lina, *, and Jer-Jia Sheub a
b
Department of Industrial Design, Far East University, Taiwan, R.O.C.
Department of Mechanical Engineering, Southern Taiwan University of Science and Technology, Taiwan, R.O.C. *Corresponding Author: [email protected]
Abstract Citric acid coated (citrate-stabilized) magnetite (Fe3O4) magnetic nanoparticles have been conducted and applied in the biomedical fields. Using Taguchi-based measured retardances as the training data, an artificial neural network (ANN) model was developed for the prediction of retardance in citric acid (CA) coated ferrofluid (FF). According to the ANN simulation results in the training stage, the correlation coefficient between predicted retardances and measured retardances was found to be as high as 0.9999998. Based on the well-trained ANN model, the predicted retardance at excellent program from Taguchi method showed less error of 2.17% compared with a multiple regression (MR) analysis of statistical significance. Meanwhile, the parameter analysis at excellent program by the ANN model had the guiding significance to find out a possible program for the maximum retardance. It was concluded that the proposed ANN model had high ability for the prediction of retardance in CA coated FF.
Keywords: Artificial Neural Network; Ferrofluid; Multiple Regression; Retardance; Taguchi Method. 1
1. Introduction Citric acid coated (citrate-stabilized) magnetite (Fe3O4) magnetic nanoparticles (MNPs) have been conducted and hold their potential therapeutic applications such as conjugation and release of doxorubicin [1]. Also, they have been used as contrast agent in magnetic resonance imaging for biomedical application [2] and as feasible adsorbent for the removal of cadmium in industrial wastewater application [3]. The synthesis and magnetic properties of citric acid (CA) coated Fe3O4 MNPs will be investigated essentially. To produce the CA coated Fe3O4 MNPs with good magneto-optical properties [4], two influence factors including pH value of suspension and double centrifugations were adopted. Highly dispersed water-based ferrofluids (FFs) were obtained successfully. Owing to the use of Taguchi method, the excellent program (parametric combination) for the CA coated FFs with high retardance or low dichroism was found readily [4]. Based on the Stokes polarimeter, the optical configuration for measuring optically linear birefringence (LB) and linear dichroism (LD) properties was constructed. The measurement principle was well explained in [5]. Nowadays, computer-based methods such as artificial neural network (ANN) and multiple regression (MR) analysis have attracted some attentions to be replaced with high-cost experimental studies [6]. Detailed study of regression as well as ANN models have shown that regression analysis is one of the most widely used methodologies for expressing the relation between a dependent variable (response) and several independent variables (predictor) [7-9]. ANN has been successfully employed in solving complex problems in various fields such as function approximation, pattern association and pattern recognition, associative memories and generation of new meaningful pattern [9]. We have recently developed a MR model that has statistically significant predictive ability in the retardance of CA coated FFs [10]. In this study, the measured retardances of CA coated FFs samples using Taguchi orthogonal design method-L9(34) [10] were used as the training data in the ANN model. Based on the trained ANN model, the predicted retardance at excellent program from Taguchi method showed less error 2
of 2.17% compared with a MR analysis of statistical significance. The parameter analysis at excellent program by the developed ANN model was conducted. Compared with the MR analysis, the use of ANN for modeling and prediction in the clinical application was discussed.
2. Experimental results of Taguchi method Taguchi method was straightforward and easy to apply to many engineering situations, making it a powerful yet simple tool. Subsequently, the optimal synthesis condition of CA coated Fe3O4 FFs with high retardance was determined by the Taguchi orthogonal design method-L9(34), i.e. four parameters with three levels, respectively, and nine tests of FFs with a concentration of 1000 g/L, correspondingly. Influence parameters were (A) pH value of suspension after coating (4.5, 5, 5.5), (B) molar ratio of CA to Fe3O4 MNPs (0.03, 0.06, 0.12), (C) CA volume (10 ml, 20 ml, 40 ml), and (D) coating temperature (70 ℃, 80 ℃, 90 ℃). The manufacture procedure for stabilized CA coated FFs could be found [4]. The retardance (magneto-optical property) of FF was measured by a Stokes polarimeter with a feasible algorithm [5]. From the investigation of retardance results in the nine samples, as shown in Fig. 1, the retardance of the A3 sample reached the highest value of 29.3618° under 64.5 mT (parameters’ values were of A1B3C3D3, were close to the excellent program as A1B3C3D1, as shown in Table 1 [4], only difference in coating temperature), and the A5 sample had the second highest retardance value as 23.6294° under 64.5 mT. Considering the retardance in the A3 sample varied severely in the magnetic fields, may be due to the excess CA and higher coating temperature (parameter B and parameter D), its larger secondary diameter or agglomerations might have influenced the formation of chain-order under the magnetic fields. Further, it was found that the influence sequence between these parameters in retardance was B>A>D>C. According to the range analysis, excellent program (parametric combination) was pH value of suspension after coating was 4.5, molar ratio of CA to 3
Fe3O4 MNPs was 0.12, CA volume was 40 ml, and coating temperature was 70 ℃[4], i.e. expressed by [4.5, 0.12, 40, 70] in this study.
Fig. 1. Experimental results of retardance in CA coated FF samples using Taguchi method-L9(34).
Table 1 Orthogonal test results of retardance No.
A
B
C
D
Retardance (deg)
A1
1
1
1
1
7.8228
A2
1
2
2
2
11.9872
A3
1
3
3
3
29.3618
A4
2
1
2
3
4.0525
A5
2
2
3
1
23.6294
A6
2
3
1
2
18.1662
A7
3
1
3
2
-0.4628
A8
3
2
1
3
4.5877
A9
3
3
2
1
20.2021
k1
16.3906
3.8042 10.1922 17.2181 4
k2
15.2827 13.4014 12.0806 9.8969
k3
8.1090 22.5767 17.5095 12.6673
Range
8.2816 18.7725 7.3173 7.3213
Influence Parameters
B>A>D>C
Excellent Program
B3A1D1C3
Via the results of range analysis as shown in Table 1, it was found that the effect induced by molar ratio of CA to Fe3O4 MNPs on the retardance value of CA coated FFs was significant. It was also indicated that molar ratio of CA to Fe3O4 MNPs played an important role in the retardance value due to its high sensitivity, as pointed out by the influence curves of the parameter level on the retardance in Fig. 2. In Table 1, it was noted that ki (i = 1, 2, 3) was the average value of the three experimental results of the same level under the corresponding process parameter. Range was the difference between the maximum value in k1, k2, and k3 and the minimum value in k1, k2, and k3 under the corresponding process parameter.
Fig. 2. Influence curves of the parameter level on the retardance of FFs under Taguchi analysis. 5
3. Artificial neutral network model 3.1. Artificial neutral network Artificial Neural Networks (ANNs) emulating the biological connections between neurons are known as soft computing techniques. ANNs can reproduce some functions of human behavior, which are formed by a finite number of layers with different computing elements called neurons. In order to construct a network, the neurons are interconnected. The organization of connections determines the type and objectives of the ANNs. The processing ability of the network is stored in the interunit connection strengths, or weights, which are tuned in the learning process. The training (or learning) algorithm is defined as a procedure that consists of adjusting the weights and biases of a network that minimize selected function of the error between the actual and desired outputs [11]. ANNs are widely used in many applications such as forecasting, control, data compression, pattern recognition, speech, vision, medicine, and power systems. Neural network models provide an alternative approach to analyze the data, because they can deduce patterns in the data [11]. There are many different types of ANN. Some of the more popular include Multi-Layer Perceptron (MLP), learning vector quantization, radial basis function (RBF), Hopfield and Kohonen, to name a few. Some ANN are classified as feedforward while others are recurrent (i.e., implement feedback) depending on how data is processed through the network [12]. There are several ANN models and architectures that have been used in engineering applications to model or approximate properties. The most widely used ANN models among feedforward models, are the Multi-Layer Perceptron (MLP) and the Radial Basis Function (RBF) models [13]. The MLP network uses a back-propagation learning algorithm. Different back-propagation (BP) algorithms (Scaled Conjugate Gradient (SCG), Levenberg-Marquardt (LM), Gradient Descent with variable learning rate back-propagation (GDX) and Resilient back Propagation (RP)) can be used for network training [13]. Some parameters (i.e. the number of
6
training and testing data, learning rate, number of hidden layers, and processing function used) affect the accuracy, reliability, and effectiveness of the neural network.
3.2. Modeling and prediction of the retardance in CA coated FFs by the ANN model The current work used MLP feedforward network with three layers input (4 neurons), hidden, and output (1 neuron) to predict the retardances of CA coated FFs. Two transfer functions (tan-sigmoid and log-sigmoid) were used and the network was trained with Gradient Descent with variable learning rate back-propagation (GDX), which was indicated as traingdx in neutral network toolbox in MATLAB. The structure of the ANN model with input and output parameters was shown as Fig. 3. The pH value of suspension after coating, molar ratio of CA to Fe3O4 MNPs, CA volume, and coating temperature were taken as the input parameters whereas the retardance was taken as the output parameter. The Taguchi-based measured retardances were used for training the network. It was noted that the retardance value of the A7 sample was deleted for a possible error in Table 1 as well as MR analysis did [10].
Fig. 3. ANN model. In the initial stage of training ANN, the epoch (iteration) was set as 1000 and performance goal (mean square error) was chosen as 1e-3. The GDX algorithm with variable learning rate for training 7
moderate-sized feedforward neural networks was adopted. The number of neurons in the input layer and output layer was 4 and 1, respectively. The number of neurons in hidden layer was varied from 4 to 14 in increments of 2. As evident in Fig. 4 for the comparisons between trained results and measured results, it was found that the average absolute relative error (AARE) for the trained predicted retardance results was 12.39% and the root mean square error (RMSE) was 1.832 (the lowest) in the case where the number of neurons in the hidden layer was 6. Accordingly, the correlation coefficient R between ANN predicted results and Taguchi-based measured results was 0.9974. Therefore the optimum number of neurons in the hidden layer was considered to be 6. Instead of using GDX algorithm the GD algorithm with constant learning rate was adopted under the same setting. From the comparisons, it was found that the AARE for these trained predicted retardance data was 15.64% and the RMSE was 2.217. Therefore, the commonly used GDX with variable learning rate was superior to GD with constant learning rate. Two difficulties of the BP method in practice (the steepest decent back prorogation, the training function as traingd in MATLAB) as the extremely slow convergence and false local minimum might be avoided [14].
Fig. 4. Determination of the optimum number of neurons in the hidden layer for selected GDX algorithm used in the initial training network. 8
Subsequently the feedforward network with input (4 neurons), hidden (6 neurons), and output (1 neuron) layer was adopted in the training stage of ANN. The epoch was particularly set as 1000000 and performance goal was chosen as 1e-7 to predict the retardance. The neutral network training was shown as Fig. 5. The performance plot was shown as Fig. 6 and the best training performance happened at the epoch of 244921. The regression results were plotted as Fig. 7. The solid blue line represented the best fit linear regression line between predicted outputs and actual targets. The relationship between outputs and targets was indicated by the R value of one. There was a perfect linear relationship between outputs and targets as shown in Fig. 7. It was apparent that the developed ANN model was well-trained and predictive.
Fig. 5. ANN training.
9
Fig. 6. Performance plot.
Fig. 7. Regression plot. 10
According to the ANN simulation results in the training stage, as shown in Fig. 8, it was found that the correlation coefficient R between ANN predicted retardances and Taguchi-based measured retardances was as high as 0.9999998, while it was achieved as 0.9999999 for a MR analysis [10]. However, the AARE was calculated as 9.36%, which was an acceptable error range (less 10%) for a certain application. Hence the well-trained ANN model was further used to predict the retardance value at excellent program from Taguchi method.
Fig. 8. Comparisons of ANN predicted retardances and Taguchi-based measured retardances.
3.3. Comparisons between artificial neural network and multiple regression The regression equations for MR linear/nonlinear model were obtained in an earlier study [10]. The ANOVA for MR nonlinear model indicated that F value of 1320535.0358 was much greater than the critical value of F as 232.986, and P value of 0.0007 (95% confidence interval, P < 0.05) which suggested that the model was statistically significant [10]. From the regression analysis, the correlation coefficient R between predicted retardances and measured retardances was found to be 0.9999999, which was much close to 1. Further, according to the R2 value, it was found that the MR nonlinear model was able to explain 99.99998% of the variation as compared to 88.8% variation 11
explained by the MR linear model [10]. This meant that the MR nonlinear model was able to explain more variation in the response variable which ultimately would result in higher reliability of prediction. Further, the AARE of MR-nonlinear-model predicted retardances to Taguchi-based measured retardances was determined as just 0.03%. For testing the well-trained ANN model, we performed the prediction of retardance at three programs, including excellent program of [4.5, 0.12, 40, 70] from Taguchi method and two programs of [5, 0.12, 40, 70] and [5.5, 0.12, 40, 70]. The predicted retardances and those obtained by MR analysis (nonlinear model) for these programs were shown as Fig. 9. The correlation coefficient R was -0.998 between predicted retardances by ANN model and those achieved by MR analysis. The AARE between predicted retardances by ANN model and MR analysis for these programs was 1.44%. The predicted retardance of 33.41° at excellent program showed less error of 2.17% compared with MR analysis of 32.7°. The retardance at a program of [5, 0.12, 40, 70] by ANN model was predicted as 33.15°, which was much close (0.13%) to that predicted by MR analysis. It was noted that the proposed ANN model could save time and avoid carrying some high-cost experimental studies due to its accurate predictions with acceptable errors (less 5%).
Fig. 9. Comparisons of predicted retardances at three programs by ANN model and MR analysis. 12
In this study, the MR nonlinear model (considering the interaction between X1 and X3) was found to be more significant and reliable [10] than the MR second-order model (without considering the interaction between X1 and X3, the values of R and F were 0.99968 and 624.8176, respectively). The absolute errors of the A4 sample (retardance was 4.0525°) were determined to be 0.06% and 7.72%, respectively, considering and without considering the interaction between X1 and X3. The MR nonlinear model was obtained by investing long time and endeavor. To the best of the authors’ knowledge, the MR nonlinear model could be developed systematically by a stepwise regression analysis with Matlab [15]. Although the MR models are easily applied, the reliability decreases as the problems become more complicated [7]. The fundamental problem with MR is the correlation coefficient R derived by MR can sometimes be of rather limited reliability if there are a lot of interactions among the data to be considered [16]. While MR is dealing with large number of independent variables, it is of significance importance to determine best combination of these variables to predict dependent variable [9]. In contrast, in the clinical data analysis using ANN of patient with breast cancer, it has been concluded that ANN analysis offers a promising method in the analysis of multivariable data (variable number was considered as 11) on cancer patient [16]. In the clinical application such as medical diagnosis [17], several advantages of ANN method were proposed as the ability to process large amount of data, reduced likelihood of overlooking relevant information and reduction of diagnosis time. And some advantages using ANN were explained and expressed as neural network models require less formal statistical training to develop; neural networks can implicitly detect complex nonlinear relationships between independent and dependent variables; neural networks have the ability to detect all possible interactions between predictor variables; neural networks can be developed using multiple different training algorithms [18]. In this study, the trained ANN model was comparable with the MR analysis in the R value and not accurate than the MR analysis in the AARE value. The reason why higher AARE existed in our 13
trained model might be influenced by the amount of data set, the selected GDX algorithm, and the ANN architecture. It was known that the learning problems (overlearning or insufficient learning) might affect the accuracy of the ANN models [7]. Further, it was shown that the AARE between predicted retardances by ANN model and those obtained by MR analysis for three programs ([4.5, 0.12, 40, 70], [5, 0.12, 40, 70], and [5.5, 0.12, 40, 70]) was just 1.44%. Indeed, there existed a different variation between them two. In the future study, we will consider the selection of training data, choose other training algorithm such as the Levenberg-Marquardt algorithm [6, 9], and adopt more hidden layers with different transfer function group [17]. Moreover, the ANN method could be considered applicable to the single-objective optimization of low dichroism or the multi-objective optimization of high retardance and low dichroism in the CA coated FFs.
3.3.1. The single parameter effect and mutual influence analysis in MR The ANN sensitivity analysis provided insight into the usefulness of individual variables [16], therefore the simulation of single parameter effect at excellent program by the developed ANN model was performed in this study. In contrast, the single parameter effect and mutual influence analysis in MR were also provided as below. The regression equation for MR nonlinear model [10] was expressed as Eq. (1), and shown as below. Three of the four parameters in Eq. (1) were fixed at the mean values, where the mean values of pH value of suspension after coating, molar ratio of CA to Fe3O4 MNPs, CA volume, and coating temperature were 5, 0.07, 23.33 ml, and 80 ℃, respectively. The corresponding regression equations of single-parameter were then obtained as Eqs. (2)-(5). Single-parameter curves of all four parameters were shown as in Fig. 10; there were obtained by standardizing the levels for each parameter in a range of -2 to 2 [19]. Retardance = 38.87-6.46X1+158.04X2-1.11X3+0.013X32-0.001X42+0.18X1X3 (1) 14
Retardance-1 for pH value of suspension after coating = 14.20029-0.27749X1 (2) Retardance-2 for molar ratio of CA to Fe3O4 MNPs = 3.76779+3.55592X2
(3)
Retardance-3 for CA volume = 14.35375+3.35925X3+0.72563X32
(4)
Retardance-4 for coating temperature = 13.64533-0.8X4-0.025X42
(5)
As shown in Fig. 10, with the increase in pH value of suspension after coating, the retardance of CA coated FFs decreased over a small range. However, with the increase in molar ratio of CA to Fe3O4 MNPs, the retardance of CA coated FFs increased over a large range; the effect of molar ratio of CA to Fe3O4 MNPs was shown to have a significant increase on the retardance value of CA coated FFs. It was noted that both Eq. (2) and Eq. (3) belonged to straight line equation, and the positive effect of molar ratio of CA to Fe3O4 MNPs was significant. The effect of CA volume on the retadance of CA coated FFs was shown in Fig. 10, where the retardance increased with increasing CA volume over a large range. In addition, the effect of temperature was shown in Fig. 10, where the retardance decreased with increasing temperature over a small range. The negative effect induced by temperature on the retardance value of CA coated FFs was smaller than that induced by CA volume.
15
Fig. 10. Effects of pH, molar ratio, CA volume and temperature on the retardance value of CA coated FFs in the mean values of four parameters. Subsequently, two parameters including molar ratio of CA to Fe3O4 MNPs and coating temperature were kept at the middle level as 0.07 and 80 ℃, respectively. The mathematical formula was obtained as Eq. (6). Then the mutual influence (response surface) of pH value of suspension after coating and CA volume on the retardance value of CA coated Fe3O4 FFs was shown as Fig. 11. From Fig. 11, the retardance value of CA coated Fe3O4 FFs changed significantly with the increase of CA volume at low pH value of suspension, while the retardance value increased more significantly with the increase of CA volume at high pH value of suspension. Retardance-6 for pH value of suspension after coating and CA volume = 43.52885-6.4613X1-1.1061X3+0.0129X32 +0.1818 X1X3 (6) From Table 2 [10], shown as below, it was concluded the mutual influence between pH value of suspension after coating and CA volume was very significant (p < 0.01). The influence of the linearity term (p < 0.01) of CA volume was negative and the influence of its quadratic term (p < 0.01) was positive [10].
16
Retardance (deg)
25
20
15
10
5 40 5.5
30 20 CA Volume (ml)
5 10
4.5
pH
Fig. 11. Response surface showing the effect of pH value of suspension after coating and CA volume on the retardance value of CA coated FFs. The retardance of CA coated Fe3O4 FFs was at the highest level (24.38°) at both high pH value and high CA volume, while the retardance of CA coated Fe3O4 FFs was at the lowest level at both high pH value and low CA volume. It was noted that when molar ratio of CA to Fe3O4 MNPs and coating temperature were changed as 0.12 and kept at 80 ℃, respectively, the effect of the pH value and CA volume on the retardance value of CA coated Fe3O4 FFs was similar, and the highest retardance (32.28°) of CA coated Fe3O4 FFs was larger than that for molar ratio of CA to Fe3O4 MNPs and coating temperature were 0.07 and 80 ℃, respectively, by an increment of 7.9°.
Table 2
Predictors' values for multiple nonlinear regression model
Coefficient
Standard Error
t Stat
P value
Intercept X1 X2
38.8660 -6.4613 158.0407
0.2094 0.0493 0.1401
185.6040 -131.1701 1127.8218
0.0034 0.0049 0.0006
X3 X3*X3 X4*X4
-1.1061 0.0129 -0.0010
0.0134 0.0000 0.0000
-82.3726 343.9284 -180.3813
0.0077 0.0019 0.0035
17
X1*X3
0.1818 R =0.9999998
0.0026
2
71.1905 R adj=0.9999992
0.0089
2
3.3.2. The simulation of single parameter effect at excellent program by the ANN model The developed ANN model was simulated for the variation of retardance at excellent program of [4.5, 0.12, 40, 70], on the cases of varying the value of one parameter and fixing the value of the other three parameters. The simulation results of single parameter effect at excellent program by the ANN model were shown as Figs. 12-15. As shown in Fig. 12, on the condition of varying the pH value from 4.5 to 5 in increments of 0.2, molar ratio of CA to Fe3O4 MNPs was fixed as 0.12, CA volume was 40 ml, and coating temperature was 70 ℃, the retardance value started to decrease at pH 5.3 and down to pH 5.5, the trend of the variation of retardance with pH value was similar to the curve A in Fig. 2. As shown in Fig. 13, on the condition of varying the molar ratio of CA to Fe3O4 MNPs from 0.03 to 0.12 in increments of 0.015, pH value was fixed as 4.5, CA volume was 40 ml, and coating temperature was 70 ℃, the retardance value increased apparently from molar ratio of 0.03 to molar ratio of 0.075, and increased slightly from molar ratio of 0.075 to 0.12 (the retardance was varied from 31.61° to 32.58°). Compared to the curve B in Fig. 2, the fact that the retardance increased with the increase of molar ratio of CA to Fe3O4 MNPs existed accordingly.
18
Fig. 12. Effect of the pH value of suspension after coating at excellent program on the retardance.
Fig. 13. Effect of the molar ratio of CA to Fe3O4 MNPs at excellent program on the retardance. As shown in Fig. 14, on the condition of varying the CA volume from 10 ml to 40 ml in increments of 5 ml, pH value was fixed as 4.5, molar ratio of CA to Fe3O4 MNPs was 0.12, and coating temperature was 70 ℃, the retardance value increased apparently from 10 ml CA volume to 20 ml (the increment of retardance was close to 20°), and increased slightly from 20 ml CA 19
volume to 40 ml (the retardance was varied from 30.51° to 32.60°). The trend of the variation of retardance with the increase of CA volume was similar to the curve C in Fig. 2. As shown in Fig. 15, on the condition of varying the coating temperature from 70 ℃ to 90 ℃ in increments of 2.5 ℃, pH value was fixed as 4.5, molar ratio of CA to Fe3O4 MNPs was 0.12, and CA volume was 40 ml, the retardance value increased gradually from temperature of 70 ℃ to 85 ℃ with a slight increase of just 0.37° and the retardance decreased down to 90 ℃. The variation of retardance was opposite to the curve D (to decrease then increase in retardance) in Fig. 2 and different from the curve for temperature in Fig. 10. The simulated maximum retardance appeared at the temperature of 85 ℃ in Fig. 15, which was slightly deviated from the low retardance at temperature of 80 ℃ as shown in Fig. 2.
Fig. 14. Effect of the CA volume at excellent program on the retardance.
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Fig. 15. Effect of the coating temperature at excellent program on the retardance. It was said that the formation of a CA coating layer on the particle surface was known to be the chemical bond formation between the carboxyl groups of CA on the Fe-OH sites of the iron oxide nanoparticles [20]. Since the chemical reaction rate increased with temperature, the adsorption of CA onto the particle surface could be enhanced by the increased coating temperature. Thus, the increased coating temperature could enhance the CA coating rate [20]. It was noted that the level of each parameter was chosen to be three in Taguchi method; only three k values were obtained. However, the ANN could increase the number of level in parameter randomly and increase data set. The parameter analysis performed by the developed ANN model was better than that done by Taguchi method. Compared with the MR analysis, the developed ANN model provided a different insight into the temperature effect on the retardance of CA coated FF. In addition, through the ANN simulation results of single parameter effect at excellent program, they not only showed the trend of single parameter effect but also had the guiding significance to find a possible optimal program of [4.5, 0.12, 40, 85] for the maximum retardance. Accordingly, the ANN model could predict the retardance value at different programs; it could shorten the period of
21
research and save the manpower and material resource. Above all, the ANN model also could effectively decrease the time and effort required for the design optimization process.
4. Conclusions From the training and testing of the ANN simulation results, an ANN model was developed successfully and had high ability for the prediction of retardance in CA coated FF. The ANN simulation results in the training stage showed a high correlation coefficient between experimental data and predicted data. Further, the predicted retardance at excellent program from Taguchi method showed less error of 2.17% compared with a MR analysis of statistical significance. In addition, through the ANN simulation results of single parameter effect at excellent program, they provided a different insight into the temperature effect and had the guiding significance to find a possible optimal program for the maximum retardance of CA coated FF.
Acknowledgements The financial support provided to this study by the Ministry of Science and Technology in Taiwan under
Grant
MOST 102-2221-E-269-005
and 103-2221-E-269-004
is
gratefully
acknowledged.
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Figure captions: Figure 1.
Experimental results of retardance in CA coated FF samples using Taguchi method-L9(34).
Figure 2.
Influence curves of the parameter level on the retardance of FFs under Taguchi analysis.
Figure 3.
ANN model.
Figure 4.
Determination of the optimum number of neurons in the hidden layer for selected GDX algorithm used in the initial training network.
Figure 5.
ANN training.
Figure 6.
Performance plot.
Figure 7.
Regression plot.
Figure 8.
Comparisons of ANN predicted retardances and Taguchi-based measured retardances. 25
Figure 9.
Comparisons of predicted retardances at three programs by ANN model and MR analysis.
Figure 10. Effects of pH, molar ratio, CA volume and temperature on the retardance value of CA coated FFs in the mean values of four parameters. Figure 11. Response surface showing the effect of pH value of suspension after coating and CA volume on the retardance value of CA coated FFs. Figure 12. Effect of the pH value of suspension after coating at excellent program on the retardance. Figure 13. Effect of the molar ratio of CA to Fe3O4 MNPs at excellent program on the retardance. Figure 14. Effect of the CA volume at excellent program on the retardance. Figure 15. Effect of the coating temperature at excellent program on the retardance.
Research Highlights of MAGAM-D-15-01327 1. The feedforward ANN is applied for modeling of retardance in CA coated FFs. 2. ANN can predict the retardance at excellent program with acceptable error to MR. 3. The proposed ANN has high ability for the prediction of retardance.
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