DOI : 10.17577/IJERTV3IS080981
- Open Access
- Total Downloads : 291
- Authors : Olajide , John Oluranti, Afolabi, Tinuade Jolaade, Adeniran, Jamiu Adetayo
- Paper ID : IJERTV3IS080981
- Volume & Issue : Volume 03, Issue 08 (August 2014)
- Published (First Online): 08-09-2014
- ISSN (Online) : 2278-0181
- Publisher Name : IJERT
- License:
This work is licensed under a Creative Commons Attribution 4.0 International License
Optimization of Oil Yield from Shea Kernels using Response Surface Methodology and Adaptive Neuro Fuzzy Inference System (ANFIS)
Olajide, John Oluranti1, Afolabi, Tinuade Jolaade2* and Adeniran, Jamiu Adetayo2
1Department of Food Science and Engineering, Ladoke Akintola University of Technology, Ogbomoso, Nigeria.
2Department of Chemical Engineering, Ladoke Akintola University of Technology,Ogbomoso, Nigeria.
*Corresponding Authour
Abstract – The present study applied response surface methodology (RSM) and the adaptive neuro fuzzy inference system (ANFIS) to optimize oil yield from shea kernels in an hydraulic press. A central composite design (CCD) was adopted to study the effects of five factors namely: moisture content, heating temperature, heating time, applied pressure and pressing time on oil yield. For ANFIS, subtractive clustering method was used in generating the FIS. The experimental data were divided into training and checking data. Cluster centers were evaluated for the training data by competitive learning. RSM suggested that the combination of moisture content and temperature has the most significant effect on the oil yield while ANFISplaced temperature and heating time as the most influential variables. RSM gave a better prediction performance having R2 of 0.9998 while ANFIS has R2 of 0.9865. Themodels developed are useful for the prediction of performance measure, optimization and training for operators.
Keywords: ANFIS, Optimization, Response Surface Methodology, Variables
-
INTRODUCTION
Shea butter is extracted from the dried kernels of the shea tree (Vitellariaparadoxa). The shea tree grows naturally in the wild in the dry Savannah belt of West Africa with Nigeria inclusive. The shea fruit consists of a thin, tart, nutritious pulp that surrounds a relatively large, oil-rich seed from which shea butter is extracted. The kernel contains about 60% edible fat and the shea cake which is considered as a very good supplement for animal feed [1,2]. Shea products are considered to be of great economic significance as they have been found to have a very wide area of application ranging from food preparation to industrial applications [3,4]. It is therefore important to maximize the recovery of valuable components such as oil from this economic material.
Optimization of oil yield from oil seed using response surface methodology has been a subject of research in recent years [5,6,7,8]. Adaptive neuro- fuzzy inference system (ANFIS) has also be found to be an important optimization tool in the process industries [9,10].
Comparison of both methods could give insight into the selection of influential input variables and their levels that will give an appreciable product yield. The objective of this study is to optimize the recovery of oil from shea kernel using both response surface methodology (RSM) and adaptive neuro-fuzzy inference system (ANFIS). The information obtained on the optimum process conditions would give insight into the input variables combination that would favour the extraction of oil from shea kernel.
-
METHODOLOGY
-
Sample Collection and Preparation
Shea kernels were purchased from the local markets of Ogbomoso, Southwestern Nigeria. The moisture content was determined according to ASAE standard S410.1. The sample (100 g) were weighted into sample containers and oven dried at 130oC for 6hrs. The samples were cooled in a desiccator and weighed to determine moisture loss.
The moisture content of kernels in percent wet basis (D) is calculated as:
= 100 ( ) 1
In determining the oil content, the direct gravimetric method of solvent extraction was used.The method involved using normal Hexane of boiling point 80oC. Grounded samples (50 g) were weighed into the thimble of the Soxhlet extractor. Reflux condenser was attached and the extraction was carried out for nine(9) hours after which the solvent was distilled off. The traces of solvent were removed by heating the flask containing the oil by using an air-oven method. The oil extracted was weighed while the defatted cake was kept.
The percentage of oil was calculated as follow
% = 100 2
Where, A= Weight of flask +oil; B= Weight of flask only; W= Weight of sample taken.
-
EXPERIMENTAL DESIGN
-
Response Surface Methodology (RSM)
Response surface methodology (RSM) is a collection of mathematical and statistical technique useful for analyzing problems in which several independent variables influence a dependent variable or response and the goal is to optimize the response. In many experimental conditions, it is possible to represent independent factors in quantitative form as given inEquation 3.
= 1, 2, , + 3
Where is the real response function, and its format is unknown, Y is the response, x1, x2,,xn are the input
Table 1: Factors and levels for Central Composite Design
variables which can affect the response, n is the number of independent variables and is the residual error that represents other sources of variability not accounted for by .
Previous studiesiindicated that the most important process parameters during oil expression are the moisture content of the feed materials, temperature, pressing time, applied pressure and the heating time [8,11,12,13].In this study, a central composite design (CCD) was adopted to study the interaction effects of five factors namely: moisture content, heating temperature, heating time, applied pressure and pressing time which are denoted as Xi(i=1, 2, 3, 4, 5), respectively. Response surface methodology (RSM) was used to determine the effect of these independent variables on product qualities as shown in Table 1.
A second degree polynomial equation was fitted in each response to study the effect of variables and to describe the process mathematically. The quality of the fit of the model was evaluated using analysis of variance (ANOVA). The fitted quadratic response model is as described in Equation 4
.
Variable
Symbol
Coded levels
-2
-1
0
1
2
Moisture content(%wb)
A
7
9
11
13
15
Heating Temperature(oC)
B
90
100
110
120
130
Heating Time(Mins)
C
20
30
40
50
60
Applied Pressure(Mpa)
D
5
10
15
20
25
Pressing time(min)
E
3
4
5
6
7
system results were obtained by thinking and reasoning capability of the fuzzy logic [14].
Figure 1 represents a typical ANFIS architecture consisting of five layers including the input layer (Layer 0). Layer 1 is the fuzzification layer in which each node represents a membership function, layer 2 provides the strength of the rule by means of multiplication
= 0 +
+ 2 +
+
operator in each node, layer 3 is the normalization layer
=1
=1
1<
4
which normalizes the firing strength of the rules, layer 4
where Y is response factor (% Oil yield), and i and j denote linear and quadratic coefficients,
respectively. bo is the intercept, bi is the first order model coefficient, k is the number of
factors, and e is a random number.
-
Adaptive Neuro Fuzzy Inference System (ANFIS)
ANFIS is an adaptive network that permits the application of neural network topology and fuzzy logic to predict the behaviour of variables and reduce optimization search space. It not only includes the characteristics of both methods but also eliminates some disadvantages of separate application. ANFIS uses the learningability of ANN to define the inputoutput relationship and construct the fuzzy rules by determining the inputs structure. The
has adaptive nodes and layer 5 has a single node which is fixed the summation of the inputs of the nodes in layer 4[14,15,16].
Figure 1: Basic ANFIS structure
Subtractive clustering is a very fast and efficient clustering method designed for a moderate number of input
( )( )
= 5
( )2 ( )2
patterns, because its computation grows linearly with the
data dimension and as the square of the number of data
points. The subtractive clustering method is available in the fuzzy logic toolbox for MATLAB. In the subtractive clustering method, the training data are divided according to their respective class labels and then the subtractive clustering algorithm is applied on each group of data individually to extract the rules for identifying each class of data. A group of data points was specified for a particular class in the feature space. Subtractiveclustering was done to normalize the data in the feature space in the range [0, 1]. Each data point in the class was considered a potential cluster center while the data points outside this radius had little influence on the potential of the data points within this radius. Thus, the measure of the potential of a data point became a function of its distances to all other data points. A data point with many neighboring data points had a high potential value. After the potential of every data point had been computed, the data point with the highest potential as the first cluster center was selected as suggested by [15].
In this work, subtractive clustering method was used in generating the fuzzy inference system (FIS). The experimental data were divided into training and checking data. Cluster centers were evaluated for the training data by competitive learning. Antecedents and consequents were calculated using the initial fuzzy model and input parameter features were gotten with the neural fuzzy model. The training features were selected by applying subtractive clustering to obtain cluster centers, these cluster centers were then used to develop the fuzzy rule base and the membership function of the fuzzy rule was optimized using the back propagation algorithm. The model was developed, trained and evaluated.
-
-
Model Estimation
The performance of ANFIS model in training and testing sets is validated in terms of the common statistical measures; R (coefficient of determination which presents the degree of association between predicted and true values) and RMSE (which is preferred in many iterative prediction and optimization schemes).
1 2
= 6
Where = observed data, = predicted data, = average value of observed data and =average value of predicted data.In the RSM model developed, the analysis of the variance including the sequential F-test and lack of fit test were used in the assessment of the performance of the model. Also residual analysis and diagnostics case statistics were checked to ensure adequacy of the model.
The quality of fit
of the quadratic model was expressed by the coefficient of determination (R-squared).
2 = 1 7
+
Where SS = sum of square.
-
-
RESULTS AND DISCUSSION
3.1 RSM Modeling Analysis
The experimental results, the predicted values and the residuals were shown in Table 2. The residual measured the experimental errors. From table 2, the residuals having less value indicated that the actual and predicted values were relatively close. The quadratic model equation in terms of the coded factors was presented in Equation 8.
The adequacy of the developed model was tested using the analysis of variance(ANOVA) technique and the results of second order response surface model fitting in the form of analysis of variance (ANOVA) are given in Table
-
The determination coefficient (R2) indicates the goodness of fit for the model. In this case, the value of the determination coefficient (R2=0.9998) indicates that only less than 1% of the total variations are not explained by the model. The value of adjusted determination coefficient (adjusted R2=0.9995) is also high, which indicates a high significance of the model. Predicted R2 is also in a good agreement with the adjusted R2. Adequate precision compares the range of predicted values at the design points to the average prediction error.
Table 2: Experimental Design for Variables and the Response
Run
Variables
Oil Yield(%)
A(%wb)
B(deg C)
C(mins)
D(Mpa)
E(min)
Actual
Predicted
Residual
1
9
100
30
10
6
22.27
22.273
-0.0034
2
13
100
30
10
4
30.81
30.811
-0.0009
3
9
120
30
10
4
25.22
25.223
-0.0034
4
13
120
30
10
6
36.89
36.890
-0.0001
5
9
100
50
10
4
25.61
25.615
-0.0051
6
13
100
50
10
6
29.18
29.182
-0.0018
7
9
120
50
10
6
29.11
29.114
-0.0043
8
13
120
50
10
4
39.42
39.422
-0.0018
9
9
100
30
20
4
28.44
28.443
-0.0026
10
13
100
30
20
6
37.14
37.139
0.0007
11
9
120
30
20
6
28.15
28.152
-0.0018
12
13
120
30
20
4
41.88
41.879
0.0007
9
100
50
20
6
30.64
30.643
-0.0034
14
13
100
50
20
4
38.27
38.271
-0.0009
15
9
120
50
20
4
33.87
33.873
-0.0034
16
13
120
50
20
6
44.31
44.310
-0.0001
17
7
110
40
15
5
17.71
17.700
0.0098
18
15
110
40
15
5
36.34
36.342
-0.0019
19
11
90
40
15
5
32.2
32.195
0.0048
20
11
130
40
15
5
41.32
41.317
0.0031
21
11
110
20
15
5
29.84
29.839
0.0015
22
11
110
60
15
5
34.75
34.744
0.0065
23
11
110
40
5
5
26.09
26.084
0.0065
24
11
110
40
25
5
37.13
37.129
0.0015
25
11
110
40
15
3
41.01
41.005
0.0048
26
11
110
40
15
7
39.55
39.547
0.0031
27
11
110
40
15
5
37.68
37.640
0.0403
28
11
110
40
15
5
37.63
37.640
-0.0097
29
11
110
40
15
5
38.01
37.640
0.3703
30
11
110
40
15
5
37.45
37.640
-0.1897
31
11
110
40
15
5
37.41
37.640
-0.2297
32
11
110
40
15
5
37.65
37.640
0.0103
= 37.63 + 9.32 + 4.56 + 2.45 + 5.52 0.73 + 4.44 2.67 + 1.60 + 0.028 + 2.38 2.26 + 0.49 + 0.84 0.51 + 0.35 10.622 0.882 5.352 6.032 +
2.632 8
Table 3: ANOVA for Response Surface Methodology
Sum of
Mean
F
p-value
Source
Squares
df
Square
Value
Prob> F
Model
1229.52
20
61.48
2965.19
<0.0001
significant
A
521.27
1
521.27
25142.36
<0.0001
B
124.81
1
124.81
6019.84
<0.0001
C
36.09
1
36.09
1740.66
<0.0001
D
182.99
1
182.99
8826.08
<0.0001
E
3.19
1
3.19
153.87
<0.0001
AB
19.60
1
19.60
945.50
<0.0001
AC
7.14
1
7.14
344.49
<0.0001
AD
2.57
1
2.57
123.86
<0.0001
AE
0.00
1
0.00
0.04
0.8520
BC
5.68
1
5.68
273.79
<0.0001
BD
5.12
1
5.12
246.90
<0.0001
BE
0.24
1
0.24
11.70
0.0057
CD
0.70
1
0.70
33.83
0.0001
CE
0.26
1
0.26
12.42
0.0048
DE
0.12
1
0.12
5.82
0.0344
A^2
206.72
1
206.72
9970.67
<0.0001
B^2
1.43
1
1.43
69.05
<0.0001
C^2
52.45
1
52.45
2529.72
<0.0001
D^2
66.74
1
66.74
3219.18
<0.0001
E^2
12.74
1
12.74
614.61
<0.0001
Residual
0.23
11
0.02
Lack of Fit
0.00
6
0.00
0.00
1.0000
not significant
Pure Error
0.23
5
0.05
Cor Total
1229.75
31
Std. Dev.
0.144
R2
0.9998
Mean
33.843
AdjR2
0.9995
C.V. %
0.425
PredR2
0.9997
PRESS
0.331
Adeq Precision
228.1296
The model value of 2965.19 indicates that the model is significant. Values of prob>F less than 0.05 indicate the model terms are significant. From this table 3, A, B, C, D, E, AB, AC, AD, BC, BD, BE, CD, CE, DE, A2,
B2, C2, D2, E2 are significant model terms. The parameter with highest F-value of 25142.36 is moisture content (A), therefore it is the most significant for the oil yield
d value
percentage. In terms of two factors interaction, the combination of moisture content and heating temperature (AB) has the highest effect on the oil yield while the factors that had least effect on oil yield are the moisture content and pressing time.
50.00
40.00
Oil Yield
30.00
20.00
10.00
0.00
50.00
40.00
Oil Yield
30.00
20.00
10.00
0.00
130.00
122.00
114.00
106.00
11.00
13.00
15.00
60.00
52.00
44.00
13.00
15.00
B: Heating Temperature 98.00
90.00
7.00
9.00
A: Moisture Content
C: Heating Time
36.00
28.00
20.00
7.00
9.00
11.00
A: Moisture Content
2a. Heating Temperature and Moisture Content 2b.Heating Time and Moisture Content
50.00
50.00 40.00
40.00 30.00
30.00
Oil Yield
20.00
Oil Yield
20.00
10.00
10.00
0.00
0.00
25.00
13.00
15.00
7.00
6.00
11.00
13.00
15.00
20.00
15.00
10.00
9.00
11.00
A: Moisture Content
5.00
E: Pressing Time
4.00
3.00 7.00
9.00
A: Moisture Content
D: Applied Pressure
5.00 7.00
2c.Applied Pressure and Moisture Content 2d.Pressing time and Moisture content
50.00
40.00
30.00
20.00
10.00
50.00
40.00
Oil Yield
30.00
20.00
10.00
0.00
0.00
60.00
52.00
44.00
36.00
106.00
114.00
122.00
130.00
25.00
20.00
15.00
114.00
122.00
130.00
C: Heating Time
28.00
20.00
90.00
98.00
B: Heating Temperature
D: Applied Pressure
10.00
5.00
90.00
106.00
98.00 B: Heating Temperature
2e.Heating Time and Heating temperature 2f.Applied Pressure and Heating temperature
ue ue
50.00
40.00
Oil Yield
30.00
20.00
10.00
0.00
50.00
40.00
Oil Yield
30.00
20.00
10.00
0.00
3.00
4.00
5.00
106.00
98.00
90.00
5.00
10.00
15.00
36.00
28.00
20.00
E: Pressing Time
6.00
7.00 130.00
122.00
114.00
B: Heating Temperature
D: Applied Pressure
20.00
25.00
60.00
52.00
44.00
C: Heating Time
2g.Pressing Time and Heating Temperature 2h.Applied Pressure and Heating Time
alue alue
alue alue
50.00
40.00
Oil Yield
30.00
20.00
10.00
0.00
50.00
40.00
Oil Yield
30.00
20.00
10.00
0.00
3.00
4.00
5.00
44.00
36.00
28.00
20.00
3.00
4.00
5.00
15.00
10.00
5.00
E: Pressing Time
6.00
7.00
60.00
52.00
C: Heating Time
E: Pressing Time
6.00
7.00 25.00
20.00
D: Applied Pressure
2i.Pressing Time and Heating time 2j.Pressing Time and Applied Pressure.
Figure 2: Response surface plots for the effect of input variables on the Oil Yield.
The interactive effect of the process parameters on the response was reported in Figure 2a-j. Figure 2a shows the effect of moisture content and heating temperature on the oil yield keeping all other variables constant. At low heating temperature 90oC, oil yield was minimal and as temperature increases to 130oC, the oil yield was increased to 44.45%. This therefore indicates that oil extraction depends on heating temperature. Also, at temperature of 110oC, oil yield increased with increase in moisture content.
Figure 2b shows the effect of moisture content and heating time on the percentage oil yield, keeping all other
variables constant. At low heating time of 20minutes and moisture content of 7%wb, the oil yield was 7.23%, as moisture content increases to 15%wb and time 20minutes, oil yield gave 31.2%. Generally, oil yield increases with increase in moisture content. Also, at high moisture content 15% wb and time 60minutes, oil yield decreases to 30.7%. This indicates that higher oil yield will be obtained at high heating time and low moisture content 11%wb. The interaction of moisture content and applied pressure on the oil yield was seen in Figure 2c. At pressure of 5MPa and moisture content of 11%wb, oil yield was found to be 26.1% and at high pressure of 25MPa and 15%wb, high oil
yield was obtained. This indicates that oil yield increases with increase in moisture content and applied pressure.
The effect of moisture content and pressing time was observed on the response as shown in Figure 2d, keeping all other variables constant. High oil yield was obtained at low pressing time 3minutes and high moisture content. But as pressing time increases to 7minutes and high moisture content 15%wb, the oil yield was reduced. This therefore indicates that high oil yield will be achieved at high moisture content and short pressing time. Figure 2e shows the effect of heating temperature and heating time on percentage oil yield. When the heating time was 20minutes and the heating temperature increased within the range (90-130oC), the oil extracted was 31.1%. High oil yield was favoured at high heating time 60minutes and high heating temperature. From Figure 2f, it was observed that oil extracted from sheabutter is favoured with increase in applied pressure 25MPa and heating temperature of 130oC giving oil yield of 38.54%. At low pressure 5MPa and high temperature, oil yield was 32%.
Interaction effect of heating temperature and pressing time on the oil yield was shown in Figure 2g. Low pressing time favoured the yield of oil at temperature of 90oC than high pressing time of 7minutes at the same temperature. At 3minutes and 110oC, oil yield was 41% while it is 39% at 110oC and 7minutes. This indicated that high oil yield was obtained at low pressing time and high temperature. Figure 2h shows the interaction effect of heating time and applied pressure on the oil yield. At low pressure of 5MPa, low amount of oil was extracted with increase in heating time. At 60minutes heating time and high applied pressure of 25MPa, high oil yield of 35% was obtained. The interaction of heating time and pressing time on percentage oil yield was shown in Figure 2i. High oil yield was obtained at low pressing time of 3minutes in the range of heating time 20-60minutes while the oil yield was minimal at increase in pressing time to 7minutes. At heating time of 40minutes and pressing time 3minutes, oil yield was found to be 41%. From Figure 2j, the effect of applied pressure and pressing time was seen on the oil yield percentage. At low pressing time 3minutes, oil yield increases from 29.8% to 40.1% with increase in the range of applied pressure (5-25MPa) while at 7minutes and 15MPa, oil yield was 39.5%. This indicated that oil yield increases with increase in applied pressure and decrease in pressing time.
3.2 ANFIS MODELLING ANALYSIS
From the clusters formed from the data, exhaustive search was performed to determine the single parameter which is most influential in predicting the oil yield.
Training (Circles) and Checking (Asterisks) Errors
RMS Errors
1
0.5
HEATING TIME
TEMPERATURE
APPLIED PRESSURE
PRESSING TIME
MOISTURE
0
Figure 3: Plot of RMS errors of the input parameters
The effect of each input parameter in predicting the oil yield extraction was shown in Figure 3 with their corresponding RMS errors. Heating time, which is the left- most parameter, has the least training error value of 0.8871 and checking value of 1.1570. Therefore, it is the most influential parameter followed by temperature with training error of 0.8892 and 1.1175 as the checking error value. The variable with least influence on oil yield was moisture content with training and checking error of 0.9274 and 1.2362, respectively.
The effect of two input combination on the oil yield was reported in Table 4. The combination of temperature and heating time has the least training error of 0.7062 and checking error of 1.0379, thereby, the most significant in predicting the oil yield percentage. The least significant effect was observed when combining applied pressure with pressing time having the highest training error of 0.8708 and 1.2270 as the checking error.
Table 4: Input parameter combination with RMS errors.
S/N
Input Combination
Training Error
Checking Error
1
Moisture content and Temperature
0.8137
1.4262
2
Moisture content and Heating time
0.7693
1.1896
3
Moisture content and Applied pressure
0.8069
1.1281
4
Moisture content and Pressing time
0.8666
1.2855
5
Temperature and Heating time
0.7062
1.0379
6
Temperature and Applied pressure
0.7498
0.966
7
Temperature and Pressing time
0.8055
1.1806
8
Heating time and Applied pressure
0.7661
1.1341
9
Heating time and Pressing time
0.7366
1.1393
10
Applied pressure and Pressing time
0.8708
1.227
Subtractive clustering algorithm was simulated for various values of radius in the range 0.2 to 1.4. The results so obtained in terms of efficiency of the algorithm on the data are plotted in Figure 4. The radius determines the number of clusters formed which is the corresponding membership function. As the radius increases, the number of clusters formed decreases, thereby increasing the degree of accuracy
(R) value and decreasing the RMSE. An Epoch number 500 was used as benchmark. Radius 1.4 has MF of 2, 1.2 radius has MF of 3, 7 MF for radius. The
120
lower the MF number, the better the performance of the model. The plot of accuracy showing the correlation coefficient (R-value) of 0.9865 was shown in Figure 5. The predicted data values cluster round the straight line indicating nearness of predicted value with experimental value of the oil yield extraction with less disparity.
100
80
% Accuracy
60
40
20
0
0.2 0.4 0.6 0.8 1 1.2 1.4
Radius
Figure 4: Percentage accuracy of the developed model for different radii values.
Figure 5: Experimental data value against the predicted value for the oil yield.
3.3 Comparison of RSM and ANFIS
RSM and ANFIS are both data driven model used in predicting the outcome of an experimental work. In this study, both models were used to predict the extraction of oil yield from shearbutter. The ability of RSM is powerful in identifying the insignificant main factors and interaction factors or insignificant quadratic terms in the model and thereby can reduce the complexity of the problem. On the other hand, ANFIS is a black box model approach which requires large and sufficient data for better performance. In this study, RSM gave a better prediction performance having R2 of 0.9998 while ANFIS has R-value of 0.9865. RSM is more statistical in analyzing and optimizing process variables.
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CONCLUSION
This study looked into the optimization of process parameters involved in oil yield extraction from shea kernel using RSM and ANFIS (sub-clustering) as predictive tools. From the input parameters, RSM suggested the combination of Moisture content and Temperature has the most significant effect on the oil yield percentage with the highest F-value of 945.50 and R2 value of 0.9998. On the other hand, the best combination of two input parameter suggested by ANFIS is Temperature and Heating time having less RMSE of 0.1876 and R-value of 0.9865. Optimum oil yield of 47.13% was obtained when the moisture content, heating temperature, heating time, applied pressure and pressing time were 14.09%wb, 128.70oC, 35.93minutes, 19.21MPa and 6.69minutes,
respectively. The two models proved effective at predicting the percentage oil yield on 99% accuracy. RSM gave a better prediction than ANFIS with reference to the obtained R2 values for both models. The model developed can be used for process behaviour prediction, performance measure, optimization and as training tools for operators.
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