- Email: [email protected]
Prediction of the cetane number of biodiesel using artificial neural networks and multiple linear regression
Energy Conversion and Management 65 (2013) 255–261
Contents lists available at SciVerse ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Prediction of the cetane number of biodiesel using artificial neural networks and multiple linear regression Ramón Piloto-Rodríguez a,⇑, Yisel Sánchez-Borroto a, Magin Lapuerta b, Leonardo Goyos-Pérez a, Sebastian Verhelst c a b c
Faculty of Mechanical Engineering, Technical University of Havana, Calle 114, No. 11901 e/119 y 127, Cujae, Marianao 15, 19390 Ciudad de la Habana, Cuba Escuela Técnica Superior de Ingenieros Industriales, University of Castilla-La Mancha, Avda. Camilo José Cela s/n, 13071 Ciudad Real, Spain Department of Flow, Heat and Combustion Mechanics, Faculty of Engineering, Ghent University, Sint-Pietersnieuwstraat 41, 9000 Gent, Belgium
a r t i c l e
i n f o
Article history: Received 23 May 2012 Received in revised form 18 July 2012 Accepted 26 July 2012 Available online 17 October 2012 Keywords: Cetane number Biodiesel Neural network Fatty acid Ester composition
a b s t r a c t Models for estimation of cetane number of biodiesel from their fatty acid methyl ester composition using multiple linear regression and artificial neural networks were obtained in this work. For the obtaining of models to predict the cetane number, an experimental data from literature reports that covers 48 and 15 biodiesels in the modeling-training step and validation step respectively were taken. Twenty-four neural networks using two topologies and different algorithms for the second training step were evaluated. The model obtained using multiple regression was compared with two other models from literature and it was able to predict cetane number with 89% of accuracy, observing one outlier. A model to predict cetane number using artificial neural network was obtained with better accuracy than 92% except one outlier. The best neural network to predict the cetane number was a backpropagation network (11:5:1) using the Levenberg–Marquardt algorithm for the second step of the networks training and showing R = 0.9544 for the validation data. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Several physical properties of biodiesel fuels depend on their fatty acid ester composition [1–3]. Also related to the ester composition is the cetane number which is one of the most cited indicators of diesel fuel quality [3–6]. The cetane number measures the readiness of the fuel to autoignite when it is injected into the combustion chamber. It is generally dependent on the composition of the fuel and can influence the engine stability, noise level, and exhaust emissions. The cetane number (CN), determined by a standard (diesel engine) test ASTM D613, is a measure of the ignition quality of a diesel fuel in a compression ignition engine. A fuel with higher cetane number has a shorter ignition delay period and starts the combustion shortly after it is injected into the chamber [4]. While the ignition delay can be influenced by engine type and operation conditions, the cetane number mainly depends on the chemical composition of the fuel. The cetane number of biodiesel is generally higher than the standard diesel fuel. Experimental data shows values varying between 45 and 67 for biodiesel and ranged between 40 and 49 for diesel fuel [7,8]. A single fatty acid alkyl ester molecule can have
⇑ Corresponding author. Tel.: +53 7 2663624. E-mail address: [email protected] (R. Piloto-Rodríguez). 0196-8904/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.enconman.2012.07.023
a cetane number between 42 and 89, depending on its molecular structure [7]. Van Gerpen [7] studied the effect of adding pure esters to diesel fuel. A linear regression fit on the CN data for each ester as a function of the percent of ester in the blend was used. The obtained values of the coefficient of correlation were ranged between 0.4889 and 0.9965 depending on the fatty acid added to the blend. Equations for predicting the cetane number of diesel or biodiesel fuels have been published [4,9–15], correlating this parameter with different input experimental factors or using different mathematical methods. Yang et al. [9] developed multiple linear correlation equations for predicting the CN for 12 hydrocarbons in order to compare with a model developed using artificial neural networks (ANNs). A model for the estimation of the cetane number of biodiesel fuels based on a literature review was proposed by Lapuerta et al. [13,14]. The model was built up from experimental data obtained using different methods, initially divided in those from a diesel engine called Cooperative Fuel Research engine (CFR) and those from an Ignition Quality Tester (IQT) device, and finally brought together. A quadratic correlation with the number of carbon atoms in the original fatty acid and the number of double bonds was statistically selected as the most suitable. The R2 obtained were ranged between 0.918 and 0.947. Bamgboye et al. [15] applied multiple linear regression for obtaining a model for predicting cetane number were the R2
256
R. Piloto-Rodríguez et al. / Energy Conversion and Management 65 (2013) 255–261
Nomenclature CN ASTM ANNs CFR IQT R2 FAMEs MLR BP CGD QP BD La
cetane number American standard artificial neural networks Cooperative Fuel Research engine Ignition Quality Tester coefficient of determination fatty acid methyl esters multiple linear regression backpropagation conjugate gradient descend quick propagation biodiesel percent of lauric
obtained was 0.883 and he validated the model using data from literature. Ramos et al. [16] reports the use of a previously published equation to predict cetane number from the cetane number of the individual fatty acid methyl esters (FAMEs). Its use cannot avoid the engine tests or collecting cetane numbers of pure FAMEs from literature reports. Most of the models published for cetane number prediction were developed with Multiple Linear Regression (MLR) techniques. That procedure requires the user to specify a priori a mathematical model to fit the data in order to obtain the empirical correlation. An alternative to avoid that problem is the use of artificial neural networks. Unlike the correlation techniques, the neural network can identify and learn the correlative patterns between the input and output data once a training set is provided. The use of ANNs for predicting and modeling of energetic and mechanical systems is reported [17–24]. Their use in the modeling of engines combustion processes is also reported [25–28]. Very few reported the use of ANNs for obtaining models to predict the cetane number of diesel fuels [9,29,30], and only one for its prediction in biodiesel fuels [12]. Yang et al. [9] used a backpropagation neural network model with a training step and a validation step. The results shown a higher coefficient of determination (R2 = 0.97) than using MLR. Basu et al. [29] obtained relationships between the CN of diesel fuels using nuclear magnetic resonance. The cetane number was determined using an IQT. Ramadhas et al. [12] used an ANN to predict cetane number selecting four types of networks. Santana et al. [30] estimated the CN of individual components of diesel fuel using ANNs. The neural networks have also been applied to the prediction of other fuel properties [31]. Determination of the CN by an experimental procedure at present is an expensive and time consuming process. Therefore, the obtaining of accurate models to predict the CN of a biodiesel from its FAME composition in a wide range of feedstocks characteristics would be useful for the scientific community. The purpose of this work is to obtain models for the estimation of the cetane number of biodiesel from their FAME composition using MLR and ANNs searching for the best suitable model to predict cetane number in the range of biofuels studied, covering biodiesels from 63 feedstocks.
M P Pt S O Li Ln Ei Er Ot wt R
percent of myristic percent of palmitic percent of palmitoleic percent of stearic percent of oleic percent of linoleic percent of linolenic percent of eicosanoic percent of erucic sum of residual FAMEs to reach 100% weight percent coefficient of correlation
for predicting the cetane number. The FAME main composition presented in biodiesel obtained from different feedstocks is covered by ten FAMEs selected [10,12,15,16,32–36]. The input data covers FAME composition and the output covers the cetane number. The validation of the models obtained was done using a separate data set selected from literature reports, which was not used for developing the models. The data selected for validation covers 15 samples. The degree of relationship between measured and fitted cetane number data was expressed as the R and R2. The best fit was expressed as the higher R and the lower mean absolute error. The obtained model using MLR was compared with two models available in literature [10,15]. Due to the type of data inputs collected for this work, the comparison with correlations as those proposed by Lapuerta et al. [14] and Tong [33] was discarded. With the aim of comparing the models obtained using MLR and ANNs, different networks were developed using two basic topologies (11:5:1) and (11:7:1). As an example, one of the topologies used in this work is shown in Fig. 1. The ANNs used were the multilayer Perceptrons, with one hidden layer and five or seven units. The inputs of the network were ten, representing the chemical composition of 10 FAME and one input representing the total amount of the other FAMEs found in the biodiesel sample. The CN was the unique variable output of the network. The chemical formula and the structure of the FAMEs on which this research is focused are shown in Table 1. The ten FAMEs listed represent the inputs for the CN modeling. The basic structural
2. Experimental set-up and procedures In the present work 48 different biodiesel fuels (including 10 pure fatty acids) were taken from references as input and output data for the obtaining of a MLR and for the implementation of ANNs
Fig. 1. Network (11:5:1) for the prediction of the cetane number.
257
R. Piloto-Rodríguez et al. / Energy Conversion and Management 65 (2013) 255–261 Table 1 Chemical structure and name of the FAMEs. Fatty acid
Structure
Formula
Lauric Myristic Palmitic Palmitoleic Stearic Oleic Linoleic Linolenic Eicosanoic Erucic
12:0 14:0 16:0 16:1 18:0 18:1 18:2 18:3 20:1 22:1
C12H24O2 C14H28O2 C16H32O2 C16H30O2 C18H36O2 C18H34O2 C18H32O2 C18H30O2 C20H38O2 C22H42O2
The training was developed for 10,000 epochs with a learning rate of 0.01. Linear and logistic functions in the range of 0.9 were used as the output functions in different networks variants. Twenty-four different ANNs were tested for the prediction of the CN using two phases. The phase one was a backpropagation (BP) and the second phase was varied among different possibilities: backpropagation, conjugate gradient descend (CGD), Levenberg–Marquardt, quick propagation (QP), quasi-Newton and Delta-bar-Delta. The experimental data used for obtaining the regression model and the training step for the ANNs is shown in Table 2.
3. Results and discussion description for the input FAMEs used in this work (XX:X) covers the information about the number of carbon atoms (XX) and the number on the right (X) represents the number of unsaturations in the molecule. In the training step two phases were implemented, keeping constant the phase 1 (backpropagation) for all the ANNs evaluated.
3.1. Multiple linear regression To predict the CN of biodiesel fuels from their FAME composition a MLR model was obtained by processing the full data shown in Table 2. As can be observed in Table 2, the input data used has an
Table 2 (a) Inputs given for MLR and ANN models [4,32–34]. (b) Inputs given for MLR and ANN models [16,32,34,35]. BD Panel (a) Lauric Myristic Palmitic Stearic Oleic Palmitoleic Linoleic Erucic Eicosanoic Linolenic Soybean Inedible tallow Thevetia peruviana M. Moringa oleifera Lam Pongamia pinnata P. Holoptelia integrifolia Vallaris solanacea K. Aleurites moluccana Euphorbia helioscopia L Garnicia morella D. Saturega hortensis Linn Actinodaphne angust. Litsea glutinosa Robins Neolitsea cassia Linn Swietenia mahagoni J. Panel (b) Argemone mexicana Salvadora persica Linn Madhuca butyracea M. Rhus succedanea Linn Basella rubra Linn Corylus avellana Jatropa curcas Linn Croton tiglium Linn Princeptia utilis Royle Vernonia cinerea Less Joannesia princeps V. Garcinia combogia D. Garcinia indica Choisy Illicium verum Hook Melia azadirach Linn Myristica malabarica L Urtica dioica Linn Tectona grandis Linn Canola Lard Yellow grease Rape Linseed
12:0
14:0
16:0
16:1
18:0
18:1
18:2
18:3
20:1
22:1
CN
100 0 0 0 0 0 0 0 0 0 0 0.1 0 0 0 0 0 0 2.8 0 0 87.9 96.3 85.9 0
0 100 0 0 0 0 0 0 0 0 0.1 2.1 0 0 0 3.5 0 0 5.5 0 0 1.9 0 3.8 0
0 0 100 0 0 0 0 0 0 0 10.5 23.9 15.6 9.1 10.6 35.1 7.2 5.5 9.9 0.7 0.4 0.5 0 0 9.5
0 0 0 0 0 100 0 0 0 0 0.1 2.8 0 2.1 0 1.9 0 0 0 0 0 0 0 0 0
0 0 0 100 0 0 0 0 0 0 3.7 19.5 10.5 2.7 6.8 4.5 14.4 6.7 1.1 46.4 0.4 5.4 0 0 18.4
0 0 0 0 100 0 0 0 0 0 23.2 38.5 60.9 79.4 49.4 53.3 35.3 10.5 15.8 49.5 12.0 0 2.3 4.0 56.0
0 0 0 0 0 0 100 0 0 0 48.9 6.4 5.2 0.7 19.0 0 40.4 48.5 22.1 0.9 18.0 0 0 3.3 0
0 0 0 0 0 0 0 0 0 100 1.2 0.3 7.4 0.2 0 0 0 28.5 42.7 0 62.0 0 0 0 16.1
0 0 0 0 0 0 0 0 100 0 0.3 0.5 0 0 2.4 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 100 0 0 0.1 0.1 0 0 0 0 0 0 0 0 0 0 0 0 0
61.4 66.2 74.5 86.9 55.0 51.0 42.2 76.0 64.8 20.4 47.2 61.7 57.5 56.7 55.8 61.2 50.3 34.2 34.2 63.5 25.5 63.2 64.8 64.0 52.3
0 19.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.1 0 0 0
0.8 54.5 0 0 0.4 3.2 1.4 11.0 1.8 8.0 2.4 0 0 4.4 0.1 39.2 0 0.2 0.1 1.9 1.1 0 0
14.5 19.6 66.0 25.4 19.7 3.1 15.6 1.2 15.2 23.0 5.4 2.3 2.5 0 8.1 13.3 9.0 11.0 5.2 24.5 17.3 4.8 5.0
0 0 0 0 0.4 0 0 0 0 0 0 0 0 0 1.5 0 0 0 0.2 2.8 2.2 0 0
3.8 0 3.5 0 6.5 2.6 9.7 0.5 4.5 8.0 0 38.3 56.4 7.9 1.2 2.4 0 10.2 2.5 14.4 9.5 1.6 2.0
18.5 5.4 27.5 46.8 50.3 88.0 40.8 56.0 32.6 32.0 45.8 57.9 39.4 63.2 20.8 44.1 14.6 29.5 58.1 38.3 45.3 33.0 20.0
61.4 0 3.0 27.8 21.6 2.9 32.1 29.0 43.6 22.0 46.4 0.8 1.7 24.4 67.7 1.0 73.7 46.4 28.1 13.4 14.5 20.4 18.0
0 0 0 0 1.1 0 0 0 0 0 0 0.4 0 0 0 0 2.7 0.4 0.4 0.3 1.3 7.9 55.0
0 0 0 0 0 0 0 0 0 0 0 0.3 0 0 0 0 0 0 1.6 0.7 1.3 9.3 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.4 0.1 0 23.0 0
44.5 67.5 65.3 52.2 54.0 54.5 52.3 49.9 48.9 57.5 45.2 61.5 65.2 50.7 41.4 61.8 38.7 48.3 55.0 63.6 52.9 55.0 52.0
258
R. Piloto-Rodríguez et al. / Energy Conversion and Management 65 (2013) 255–261
important amount of biodiesel with high percent of unsaturation. The unsaturation range covered was between 0% and 93.6% (without considering the pure FAMEs). All the values in Table 2 are in weight percent. The model is shown in the following equation.
CN ¼ 56:16 þ 0:07 La þ 0:1 M þ 0:15 P 0:05 Pt þ 0:23 S 0:03 O 0:19 Li 0:31 Ln þ 0:08 Ei þ 0:18 Er 0:1 Ot
Table 3 Correlations comparison according to the linear fit of CN predicted and reported values. Item
Gopinath [10]
Bamboye [15]
New model
R R2 (%) Standard error Residual interval
0.9270 85.94 2.8 ±13.8
0.9211 84.85 4.3 ±14.9
0.9563 91.46 3.2 ±7.1
ð1Þ
where the independent variables represent the FAME composition found in biodiesel: La is the % of lauric, M is myristic, P is palmitic, Pt is palmitoleic, S is stearic, O is oleic, Li is linoleic, Ln is linolenic, Ei is eicosanoic, Er is erucic and Ot is the sum of the other FAMEs found. All the FAME compositions in Eq. (1) are in weight percent: wt (%). The main statistics results for the MLR are: R = 0.9191 and a standard error of estimate of 4.6. The obtained values of these statistics are not adequate enough. This can be due to the complexity of the selected data that is covering a wide range of biodiesel composition concerning percentages of saturated and unsaturated compounds. This result also had shown the difficulty to obtain adequate correlation for this purpose when a parametric analysis is implemented. As is observed in Eq. (1), there is a positive influence of the FAME content of lauric, myristic, palmitic, stearic, eicosanoic and euric in the CN, but a negative influence for palmitoleic, oleic, linoleic and linolenic. Concerning the saturated FAMEs, the stearic acid shows the higher influence on the CN. For the unsaturated FAMEs that shown negative influence, the higher negative influence on the CN corresponds to linolenic acid. These results were also observed by Gopinath et al. [10] but not exactly with the same values of coefficients in the regression model. Two of the unsaturated FAMEs (eicosanoic and euric) shown positive influence in the CN due to even when a negative influence in CN when unsaturation is presented, in this cases the length of the carbon chain has a predominant influence. For the evaluation of the relative capability of the MLR model obtained for predicting the CN, a comparison with two other MLR models was made. The comparative plot of the results obtained is shown in Fig. 2. The basic evaluation of the linear regression fit obtained is shown in Table 3 beside the obtained values using the two other models from references [10,15]. As is observed in Fig. 2, there are some outliers in the prediction of cetane number that involves in some cases all the models and others for specific models. These
outliers directly affect the model correlation coefficients, standard errors and mainly the residual values. From Table 3 it can be observed that the best model is the one proposed in this work, with the highest correlations coefficients and one of the lowest residual intervals. The worst case is the Bamboye model because it is showing the lowest correlation coefficient jointly with the highest residual interval.
3.2. Artificial neural networks The results from the ANNs in order to correlate the cetane number with the FAMEs present in 48 biodiesel samples are shown in Table 4. Twelve ANNs (11:5:1) were evaluated keeping constant the function for phase 1 (backpropagation) and changing phase 2 and the regression output function. The use of ANNs based on adding two more units in the hidden layer (11:7:1) are shown in Table 5. In a comparison between results obtained using MLR and ANNs for predicting the cetane number, best fit is generally observed when ANNs are used. The results of better correlation coefficients when ANNs are used are in good agreement with other reports [9,12,29]. The critical point is that in many cases it is not possible to obtain absolute error values below 2. Only two ANNs are below this value. All the ANNs were tested in the validation step in order to select the best ANN. Basu et al. [29] also used backpropagation, Levenberg, quick propagation and delta-bar-delta as training algorithms in three layer (8:3:1) neural networks. For diesel fuels, he found correlation values for the network in the training step (R = 0.9539). Yang et al. [9] obtained R = 0.8602 for the training step in a three layer backpropagation network with 2.1 for the mean absolute error but his network is only applied to diesel fuels. Ramadhas et al. [12] used four types of ANNs, not reporting the absolute error of the networks. The author used 5 inputs corresponding to 5 FAMEs while in this work it is extended to 11 inputs. Ramadhas used a data
Table 4 Results of the (11:5:1) ANNs evaluated for the prediction of the cetane number. Network number 1 2 3 4 5 6 7 8 9 10 11 12 Fig. 2. Relationship between actual and predicted values of cetane number.
Phase 2
R
Absolute error
Regression output function
BP CGD Levenberg QP QuasiNewton Delta-bardelta BP CGD Levenberg QP QuasiNewton Delta-bardelta
0.9386 0.9486 0.9520 0.9497 0.9587
2.3 2.6 2.3 2.1 2.1
Linear
0.9528
2.0
0.9330 0.9484 0.9385 0.9615 0.9566
2.2 2.5 2.4 2.1 2.2
0.9292
2.0
Logistic
259
R. Piloto-Rodríguez et al. / Energy Conversion and Management 65 (2013) 255–261 Table 5 Results of the (11:7:1) ANNs evaluated for the prediction of the cetane number. Network number
Phase 2
R
Absolute error
Regression output function
13 14 15 16 17
BP CGD Levenberg QP QuasiNewton Delta-bardelta BP CGD Levenberg QP QuasiNewton Delta-bardelta
0.9403 0.9491 0.9577 0.9429 0.9537
2.7 2.3 2.0 2.1 1.8
Linear
0.9256
2.6
0.9478 0.9349 0.9103 0.9101 0.9313
1.9 2.3 2.5 2.3 2.5
0.9116
2.2
18 19 20 21 22 23 24
the ideal linear regression fit is observed for more than the 95% of the data processed. 3.3. Model validation For the validation of models obtained by ANN and using MLR, a data set not related to the modeling data was used. The validation data covers 15 samples from other references. The collected data includes the experimental evaluation of FAME composition and CN, covering a wide range of possible values of cetane number (between 41 and 69) and they were taken from experiments using engine tests or an ignition quality tester. All the information about the validation data is presented in Table 6. All the values in Table 6 are in weight percent. The results of the models validation for the ANN # 10 and the MLR models are presented in Fig. 4. The comparison is based on the differences between the actual value of CN and the predicted value using each model. In the plot presented in Fig. 4 a line that represents the ideal fit between predicted and actual value for any model is also superposed. In the comparison between both models shown in Fig. 4, even when there are some points with the same predicted values for both models, a general analysis of outlier points shows that the best model for CN prediction is the ANN. The linear regression fit applied to the plotted data in Fig. 4 shows correlation coefficients (including outliers) of 0.9544 for ANN # 10 and 0.8888 for the MLR model. The zone in Fig. 4 that covers the range 50–60 of cetane number corresponds to the common CN value of biodiesel from many feedstocks. As is observed, this is the zone that shows the lowest outlier points in both cases. In this zone the capability of prediction
Logistic
Fig. 3. Relationship between measured (actual) and predicted values of cetane number using the selected ANN and MLR.
set that covers biofuels with cetane number between 22.7 and 75.6, similar to the range applied in the present work. In the validation step the best results were obtained for the ANN # 10 corresponding to a (11:5:1) with a logistic output function and the Levenberg algorithm. The plot of cetane number actual values against those predicted by the ANN # 10 and the MLR is shown in Fig. 3 where a good distribution of the points near
Fig. 4. Comparison between ANNs in the validation step.
Table 6 Experimental data selected for models validation [16,32,35,37–39]. Sample
12:0
14:0
16:0
16:1
18:0
18:1
18:2
18:3
20:1
22:1
CN
Wild mustard Waste palm oil Balanites roxburhii Garnicia echinocarpa Neolitsea umbrosa G. Anamirta cocculus Broussonetia p. Vent. Salvadora oleoiles D. Nephelium L. Ziziphus maurit. L. Jojoba Rape Peanut Grape Sunflower
0 0 0 0 59.1 0 0 35.6 0 0 0 0 0 0 0
0.1 1.0 0 0 11.5 0 0 50.7 0 0 0 0 0.1 0.1 0
2.6 39.0 17.0 3.7 0 6.1 4.0 4.5 0.2 10.4 1.2 4.9 8.0 6.9 6.0
0.2 0.2 4.3 0 0 0 0 0 0 0 0 0 0 0.1 0.1
0.9 4.3 7.8 43.7 0 47.5 6.1 0 13.8 5.5 0 1.6 1.8 4.0 2.9
7.8 43.7 32.4 52.6 21.0 46.4 14.8 8.3 45.3 64.4 10.7 33.0 53.3 19.0 17.0
14.2 10.5 31.3 0 6.7 0 71.0 0.1 0 12.4 0.1 20.4 28.4 69.1 74.0
13.0 0.2 7.2 0 0 0 1.0 0 0 0 0.4 7.8 0.3 0.3 0
5.4 0.2 0 0 0 0 0 0 4.2 2.6 59.5 9.3 2.4 0 0
45.7 0 0 0 0 0 0 0 0 1.7 12.3 23.0 0 0 0
61.1 60.4 50.5 63.1 60.8 64.3 41.2 66.1 64.9 55.4 69.0 55.0 53.0 48.0 49.0
260
R. Piloto-Rodríguez et al. / Energy Conversion and Management 65 (2013) 255–261
for the ANN is the best. Assuming outlier points corresponding to a lack of accuracy higher than 10%, the MLR model has 3 outliers while the ANN # 10 has only one outlier point. For 90% of the data evaluated the ANN # 10 shows accuracy better than 6% Ramadhas et al. [12] reported accuracy between 3.4% and 5% for predicting the CN, depending of the type of neural network used for the CN prediction, but he used only 5 FAMEs as inputs, therefore the prediction capability of his ANNs can only be restricted to the composition of 5 FAMEs that is quite limited due to the amount of feedstocks, different in chemical composition that can be found in these biofuels. Therefore, the best network is the ANN # 10 that correspond to an artificial neural network implemented using a topology (11:5:1) of 11 inputs, 1 output variable and five nodes. This ANN was implemented using two phases in the training step (backpropagation and Levenberg–Marquardt). The developed model using ANN is more suitable to predict cetane number for biodiesel in a wide range of cetane number values based on the FAME composition of ten fatty acids while the rest of fatty acids found in the composition are taken in an additional factor. The model is not recommended for predicting cetane number of pure FAMEs different that the ten selected for this work. Even when the obtained R values for the prediction capability of cetane number using ANNs or MLR are of the same order of magnitude, the modeling based on ANNs brings more advantages because opens the possibility of the use of networks ensembles for prediction of more complex parameters. One example is the prediction of the ignition delay, that depends on several related factors and one of them is the cetane number. Therefore, the prediction of the cetane number using ANNs is a first step for a further modeling of the ignition delay period where ANNs can play an important role. 4. Conclusions Using multiple linear regression, a model to predict the cetane number based on the composition of ten FAMEs presented in biodiesel was developed and it was able to predict cetane number with 89% accuracy, except one outlier. A model to predict the cetane number based on the composition of ten FAMEs presented in biodiesel using an artificial neural network was obtained with better accuracy than 92% except for one outlier. The best neural network for predicting the cetane number was a backpropagation network (11:5:1) using a Levenberg–Marquardt algorithm for the second training step and showing R = 0.9544 for the validation data. The models based on multiple linear regressions cannot predict cetane number with similar accuracy as the obtained for the selected neural network. Acknowledgments The authors wish to express their thanks to the Flemish Interuniversity Council’s (VLIR) University Development Cooperation, funding an Own Initiatives Program, with whose support much of this work was performed under a project entitled ‘‘Knowledge cell on biofuels (from non-edible crops and waste products) for use in internal combustion engines’’. References [1] Yuan W, Hansen AC, Zhang Q. Vapor pressure and normal boiling point predictions for pure methyl esters and biodiesel fuels. Fuel 2005;84:943–50. [2] Wadumesthrige K, Smith JC, Wilson JR, Salley SO, Simon KY. Investigation of the parameters affecting the cetane number of biodiesel. J Am Oil Chem Soc 2008;85:1073–81. [3] Ramirez-Verduzco LF, Rodriguez-Rodriguez JE, Jaramillo-Jacob A. Predicting cetane number, kinematic viscosity, density and higher heating value of biodiesel from its fatty acid methyl ester composition. Fuel 2012;91:102–11.
[4] Knothe G. Dependence of biodiesel fuel properties on the structure of fatty acid alkyl esters. Fuel Process Technol 2005;86:1059–70. [5] Knothe G. Cetane numbers of branched and straight-chain fatty esters determined in an ignition quality tester. Fuel 2003;82:971–5. [6] Icingur Y, Altiparmak D. Effect of fuel cetane number and injection pressure on a DI diesel engine performance and emissions. Energy Convers Manage 2003;44:389–97. [7] Van Gerpen JH. Cetane number testing of biodiesel. In: Proceedings of the third liquid fuel conference liquid fuels and industrial products from renewable resources, Nashville; 1996. p. 197–206. [8] Murphy MJ, Taylor JD, McCormick RL. Compendium of experimental cetane number data. In: N.R.E. Laboratory, National Renewable Energy Laboratory, Colorado; 2004. [9] Yang H, Ring Z, Briker Y, McLean N, Friesen W, Fairbridge C. Neural network prediction of cetane number and density of diesel fuel from its chemical composition determined by LC and GC–MS. Fuel 2002;81:65–74. [10] Gopinath A, Puhan S, Nagarajan G. Relating the cetane number of biodiesel fuels to their fatty acid composition: a critical study. J Automob Eng 2009;223:565–83. [11] Krisnangkura K. A simple method for estimation of cetane index of vegetable oil methyl esters. J Am Oil Chem Soc 1980;63:552–3. [12] Ramadhas AS, Jayaraj S, Muraleedharan C, Padmakurami K. Artificial neural networks used for the prediction of the cetane number of biodiesel fuel. Renew Energy 2006;31:2524–33. [13] Lapuerta M, Rodriguez-Fernandez J, Armas O. Correlation for the estimation of the density of fatty acid esters fuels and its implications. A proposed biodiesel cetane index. Chem Phys Lipids 2010;163:720–7. [14] Lapuerta M, Rodriguez-Fernandez J, Font de Mora E. Correlation for the estimation of the cetane number of biodiesel fuels and implications on the iodine number. Energy Policy 2009;37:4337–44. [15] Bamgboye AI, Hansen AC. Prediction of cetane number of biodiesel fuel from the fatty acid methyl ester (FAME) composition. Int Agrophys 2008;22:21–9. [16] Ramos MJ, Fernandez CM, Casas A, Rodriguez L, Perez A. Influence of fatty acid composition of raw materials on biodiesel properties. Bioresour Technol 2009;100:261–8. [17] Esen H, Inalli M, Sengur A, Esen M. Performance prediction of a groundcoupled heat pump system using artificial neural networks. Exp Syst Appl 2008;35:1940–8. [18] Esen H, Inalli M, Sengur A, Esen M. Forecasting of a ground-coupled heat pump performance using neural networks with statistical data weighting preprocessing. Int J Therm Sci 2008;47:431–41. [19] Esen H, Inalli M, Sengur A, Esen M. Modeling a ground-coupled heat pump system by a support vector machine. Renew Energy 2008;33:1814–23. [20] Esen H, Ozgen F, Esen M, Sengur A. Modeling of a new solar air heater through least-squares support vector machines. Exp Syst Appl 2009;36:10673–82. [21] Karatepe E, Boztepe M, Colak M. Neural network based solar cell model. Energy Convers Manage 2006;47:1159–78. [22] Kalogirou SA. Application of artificial neural networks in energy systems – a review. Energy Convers Manage 1999;40:1073–87. [23] In-Ho Y, Myoung-Souk Y, Kwang-Woo K. Application of artificial neural network to predict the optimal start time for heating system in building. Energy Convers Manage 2003;44:2791–809. [24] Reddy KS, Ranjan M. Solar resource estimation using artificial neural networks and comparison with other correlation models. Energy Convers Manage 2003;44:2519–30. [25] Kalogirou SA. Artificial intelligence for the modeling and control of combustion processes: a review. Prog Energy Combust Sci 2003;29:515–66. [26] Blasco JA, Fueyo N, Dopazo C, Chen JY. A self organizing – map approach to chemistry representation in combustion applications. Combust Theory Model 2000;4:61–76. [27] Heister F, Froehlich M. Non-linear time series analysis of combustion pressure data for neural network training with the concept of mutual information. Proc Inst Mech Eng, Part D: J Automob Eng 2001;215:299–304. [28] Thompson GJ, Atkinson CM, Clark NN, Long TW, Hanzeback E. Neural network modeling of the emissions and performance of a heavy-duty diesel engine. Proc Inst Mech Eng, Part D: J Automob Eng 2001;214:111–26. [29] Basu B, Kapur GS, Sarpal AS, Meusinger R. A neural network approach to the prediction of cetane number of diesel fuels using Nuclear Magnetic Resonance (NMR) spectroscopy. Energy Fuels 2003;17:1570–5. [30] Santana RC, Do PT, Santikunaporn M, Alvarez WE, Taylor JD, Sughrue EL, et al. Evaluation of different reaction strategies for the improvement of cetane number in diesel fuels. Fuel 2006;85:643–56. [31] Korres DM, Anastopoulos G, Lois E, Alexandridis A, Sarimveis H, Bafas G. A neural network approach to the prediction of diesel fuel lubricity. Fuel 2002;81:1243–50. [32] Mohibbe AM, Waris A, Nahar NM. Prospects and potential of fatty acid methyl esters of some non-traditional seed oils for use as biodiesel in India. Biomass Bioenergy 2005;29:293–302. [33] Tong D, Hu C, Jiang K, Li Y. Cetane number prediction of biodiesel from the composition of the fatty acid methyl esters. J Am Oil Chem Soc 2011;88:415–23. [34] Kinast JA. Production of biodiesels from multiple feedstocks and properties of biodiesels and biodiesel/diesel blends. In: NREL/SR-510-31460. NREL, Illinois; 2003. [35] Agarwal AK. Biofuels (alcohols and biodiesel) applications as fuels for internal combustion engines. Prog Energy Combust Sci 2007;33:233–71.
R. Piloto-Rodríguez et al. / Energy Conversion and Management 65 (2013) 255–261 [36] Moser BR. Biodiesel production, properties, and feedstocks. In Vitro Cell Dev Biol Plant 2009;45:229–66. [37] Ozsezen AN, Canakci M. Determination of performance and combustion characteristics of a diesel engine fueled with canola and waste palm oil methyl esters. Energy Convers Manage 2011;52:108–16. [38] Jham GN, Moser BR, Shah SN, Holser RA, Dhingra OD, Vaughn SF, et al. Wild Brazilian Mustard (Brassica juncea L.) seed oil methyl esters as biodiesel fuel. J Am Oil Chem Soc 2009;86:917–26.
261
[39] Shah SN, Sharma BK, Moser BR, Erhan SZ. Preparation and evaluation of Jojoba oil methyl esters as biodiesel and as a blend component in ultra-low sulfur diesel fuel. Bioenergy Resour 2010;3:214–23.
Contents lists available at SciVerse ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Prediction of the cetane number of biodiesel using artificial neural networks and multiple linear regression Ramón Piloto-Rodríguez a,⇑, Yisel Sánchez-Borroto a, Magin Lapuerta b, Leonardo Goyos-Pérez a, Sebastian Verhelst c a b c
Faculty of Mechanical Engineering, Technical University of Havana, Calle 114, No. 11901 e/119 y 127, Cujae, Marianao 15, 19390 Ciudad de la Habana, Cuba Escuela Técnica Superior de Ingenieros Industriales, University of Castilla-La Mancha, Avda. Camilo José Cela s/n, 13071 Ciudad Real, Spain Department of Flow, Heat and Combustion Mechanics, Faculty of Engineering, Ghent University, Sint-Pietersnieuwstraat 41, 9000 Gent, Belgium
a r t i c l e
i n f o
Article history: Received 23 May 2012 Received in revised form 18 July 2012 Accepted 26 July 2012 Available online 17 October 2012 Keywords: Cetane number Biodiesel Neural network Fatty acid Ester composition
a b s t r a c t Models for estimation of cetane number of biodiesel from their fatty acid methyl ester composition using multiple linear regression and artificial neural networks were obtained in this work. For the obtaining of models to predict the cetane number, an experimental data from literature reports that covers 48 and 15 biodiesels in the modeling-training step and validation step respectively were taken. Twenty-four neural networks using two topologies and different algorithms for the second training step were evaluated. The model obtained using multiple regression was compared with two other models from literature and it was able to predict cetane number with 89% of accuracy, observing one outlier. A model to predict cetane number using artificial neural network was obtained with better accuracy than 92% except one outlier. The best neural network to predict the cetane number was a backpropagation network (11:5:1) using the Levenberg–Marquardt algorithm for the second step of the networks training and showing R = 0.9544 for the validation data. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Several physical properties of biodiesel fuels depend on their fatty acid ester composition [1–3]. Also related to the ester composition is the cetane number which is one of the most cited indicators of diesel fuel quality [3–6]. The cetane number measures the readiness of the fuel to autoignite when it is injected into the combustion chamber. It is generally dependent on the composition of the fuel and can influence the engine stability, noise level, and exhaust emissions. The cetane number (CN), determined by a standard (diesel engine) test ASTM D613, is a measure of the ignition quality of a diesel fuel in a compression ignition engine. A fuel with higher cetane number has a shorter ignition delay period and starts the combustion shortly after it is injected into the chamber [4]. While the ignition delay can be influenced by engine type and operation conditions, the cetane number mainly depends on the chemical composition of the fuel. The cetane number of biodiesel is generally higher than the standard diesel fuel. Experimental data shows values varying between 45 and 67 for biodiesel and ranged between 40 and 49 for diesel fuel [7,8]. A single fatty acid alkyl ester molecule can have
⇑ Corresponding author. Tel.: +53 7 2663624. E-mail address: [email protected] (R. Piloto-Rodríguez). 0196-8904/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.enconman.2012.07.023
a cetane number between 42 and 89, depending on its molecular structure [7]. Van Gerpen [7] studied the effect of adding pure esters to diesel fuel. A linear regression fit on the CN data for each ester as a function of the percent of ester in the blend was used. The obtained values of the coefficient of correlation were ranged between 0.4889 and 0.9965 depending on the fatty acid added to the blend. Equations for predicting the cetane number of diesel or biodiesel fuels have been published [4,9–15], correlating this parameter with different input experimental factors or using different mathematical methods. Yang et al. [9] developed multiple linear correlation equations for predicting the CN for 12 hydrocarbons in order to compare with a model developed using artificial neural networks (ANNs). A model for the estimation of the cetane number of biodiesel fuels based on a literature review was proposed by Lapuerta et al. [13,14]. The model was built up from experimental data obtained using different methods, initially divided in those from a diesel engine called Cooperative Fuel Research engine (CFR) and those from an Ignition Quality Tester (IQT) device, and finally brought together. A quadratic correlation with the number of carbon atoms in the original fatty acid and the number of double bonds was statistically selected as the most suitable. The R2 obtained were ranged between 0.918 and 0.947. Bamgboye et al. [15] applied multiple linear regression for obtaining a model for predicting cetane number were the R2
256
R. Piloto-Rodríguez et al. / Energy Conversion and Management 65 (2013) 255–261
Nomenclature CN ASTM ANNs CFR IQT R2 FAMEs MLR BP CGD QP BD La
cetane number American standard artificial neural networks Cooperative Fuel Research engine Ignition Quality Tester coefficient of determination fatty acid methyl esters multiple linear regression backpropagation conjugate gradient descend quick propagation biodiesel percent of lauric
obtained was 0.883 and he validated the model using data from literature. Ramos et al. [16] reports the use of a previously published equation to predict cetane number from the cetane number of the individual fatty acid methyl esters (FAMEs). Its use cannot avoid the engine tests or collecting cetane numbers of pure FAMEs from literature reports. Most of the models published for cetane number prediction were developed with Multiple Linear Regression (MLR) techniques. That procedure requires the user to specify a priori a mathematical model to fit the data in order to obtain the empirical correlation. An alternative to avoid that problem is the use of artificial neural networks. Unlike the correlation techniques, the neural network can identify and learn the correlative patterns between the input and output data once a training set is provided. The use of ANNs for predicting and modeling of energetic and mechanical systems is reported [17–24]. Their use in the modeling of engines combustion processes is also reported [25–28]. Very few reported the use of ANNs for obtaining models to predict the cetane number of diesel fuels [9,29,30], and only one for its prediction in biodiesel fuels [12]. Yang et al. [9] used a backpropagation neural network model with a training step and a validation step. The results shown a higher coefficient of determination (R2 = 0.97) than using MLR. Basu et al. [29] obtained relationships between the CN of diesel fuels using nuclear magnetic resonance. The cetane number was determined using an IQT. Ramadhas et al. [12] used an ANN to predict cetane number selecting four types of networks. Santana et al. [30] estimated the CN of individual components of diesel fuel using ANNs. The neural networks have also been applied to the prediction of other fuel properties [31]. Determination of the CN by an experimental procedure at present is an expensive and time consuming process. Therefore, the obtaining of accurate models to predict the CN of a biodiesel from its FAME composition in a wide range of feedstocks characteristics would be useful for the scientific community. The purpose of this work is to obtain models for the estimation of the cetane number of biodiesel from their FAME composition using MLR and ANNs searching for the best suitable model to predict cetane number in the range of biofuels studied, covering biodiesels from 63 feedstocks.
M P Pt S O Li Ln Ei Er Ot wt R
percent of myristic percent of palmitic percent of palmitoleic percent of stearic percent of oleic percent of linoleic percent of linolenic percent of eicosanoic percent of erucic sum of residual FAMEs to reach 100% weight percent coefficient of correlation
for predicting the cetane number. The FAME main composition presented in biodiesel obtained from different feedstocks is covered by ten FAMEs selected [10,12,15,16,32–36]. The input data covers FAME composition and the output covers the cetane number. The validation of the models obtained was done using a separate data set selected from literature reports, which was not used for developing the models. The data selected for validation covers 15 samples. The degree of relationship between measured and fitted cetane number data was expressed as the R and R2. The best fit was expressed as the higher R and the lower mean absolute error. The obtained model using MLR was compared with two models available in literature [10,15]. Due to the type of data inputs collected for this work, the comparison with correlations as those proposed by Lapuerta et al. [14] and Tong [33] was discarded. With the aim of comparing the models obtained using MLR and ANNs, different networks were developed using two basic topologies (11:5:1) and (11:7:1). As an example, one of the topologies used in this work is shown in Fig. 1. The ANNs used were the multilayer Perceptrons, with one hidden layer and five or seven units. The inputs of the network were ten, representing the chemical composition of 10 FAME and one input representing the total amount of the other FAMEs found in the biodiesel sample. The CN was the unique variable output of the network. The chemical formula and the structure of the FAMEs on which this research is focused are shown in Table 1. The ten FAMEs listed represent the inputs for the CN modeling. The basic structural
2. Experimental set-up and procedures In the present work 48 different biodiesel fuels (including 10 pure fatty acids) were taken from references as input and output data for the obtaining of a MLR and for the implementation of ANNs
Fig. 1. Network (11:5:1) for the prediction of the cetane number.
257
R. Piloto-Rodríguez et al. / Energy Conversion and Management 65 (2013) 255–261 Table 1 Chemical structure and name of the FAMEs. Fatty acid
Structure
Formula
Lauric Myristic Palmitic Palmitoleic Stearic Oleic Linoleic Linolenic Eicosanoic Erucic
12:0 14:0 16:0 16:1 18:0 18:1 18:2 18:3 20:1 22:1
C12H24O2 C14H28O2 C16H32O2 C16H30O2 C18H36O2 C18H34O2 C18H32O2 C18H30O2 C20H38O2 C22H42O2
The training was developed for 10,000 epochs with a learning rate of 0.01. Linear and logistic functions in the range of 0.9 were used as the output functions in different networks variants. Twenty-four different ANNs were tested for the prediction of the CN using two phases. The phase one was a backpropagation (BP) and the second phase was varied among different possibilities: backpropagation, conjugate gradient descend (CGD), Levenberg–Marquardt, quick propagation (QP), quasi-Newton and Delta-bar-Delta. The experimental data used for obtaining the regression model and the training step for the ANNs is shown in Table 2.
3. Results and discussion description for the input FAMEs used in this work (XX:X) covers the information about the number of carbon atoms (XX) and the number on the right (X) represents the number of unsaturations in the molecule. In the training step two phases were implemented, keeping constant the phase 1 (backpropagation) for all the ANNs evaluated.
3.1. Multiple linear regression To predict the CN of biodiesel fuels from their FAME composition a MLR model was obtained by processing the full data shown in Table 2. As can be observed in Table 2, the input data used has an
Table 2 (a) Inputs given for MLR and ANN models [4,32–34]. (b) Inputs given for MLR and ANN models [16,32,34,35]. BD Panel (a) Lauric Myristic Palmitic Stearic Oleic Palmitoleic Linoleic Erucic Eicosanoic Linolenic Soybean Inedible tallow Thevetia peruviana M. Moringa oleifera Lam Pongamia pinnata P. Holoptelia integrifolia Vallaris solanacea K. Aleurites moluccana Euphorbia helioscopia L Garnicia morella D. Saturega hortensis Linn Actinodaphne angust. Litsea glutinosa Robins Neolitsea cassia Linn Swietenia mahagoni J. Panel (b) Argemone mexicana Salvadora persica Linn Madhuca butyracea M. Rhus succedanea Linn Basella rubra Linn Corylus avellana Jatropa curcas Linn Croton tiglium Linn Princeptia utilis Royle Vernonia cinerea Less Joannesia princeps V. Garcinia combogia D. Garcinia indica Choisy Illicium verum Hook Melia azadirach Linn Myristica malabarica L Urtica dioica Linn Tectona grandis Linn Canola Lard Yellow grease Rape Linseed
12:0
14:0
16:0
16:1
18:0
18:1
18:2
18:3
20:1
22:1
CN
100 0 0 0 0 0 0 0 0 0 0 0.1 0 0 0 0 0 0 2.8 0 0 87.9 96.3 85.9 0
0 100 0 0 0 0 0 0 0 0 0.1 2.1 0 0 0 3.5 0 0 5.5 0 0 1.9 0 3.8 0
0 0 100 0 0 0 0 0 0 0 10.5 23.9 15.6 9.1 10.6 35.1 7.2 5.5 9.9 0.7 0.4 0.5 0 0 9.5
0 0 0 0 0 100 0 0 0 0 0.1 2.8 0 2.1 0 1.9 0 0 0 0 0 0 0 0 0
0 0 0 100 0 0 0 0 0 0 3.7 19.5 10.5 2.7 6.8 4.5 14.4 6.7 1.1 46.4 0.4 5.4 0 0 18.4
0 0 0 0 100 0 0 0 0 0 23.2 38.5 60.9 79.4 49.4 53.3 35.3 10.5 15.8 49.5 12.0 0 2.3 4.0 56.0
0 0 0 0 0 0 100 0 0 0 48.9 6.4 5.2 0.7 19.0 0 40.4 48.5 22.1 0.9 18.0 0 0 3.3 0
0 0 0 0 0 0 0 0 0 100 1.2 0.3 7.4 0.2 0 0 0 28.5 42.7 0 62.0 0 0 0 16.1
0 0 0 0 0 0 0 0 100 0 0.3 0.5 0 0 2.4 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 100 0 0 0.1 0.1 0 0 0 0 0 0 0 0 0 0 0 0 0
61.4 66.2 74.5 86.9 55.0 51.0 42.2 76.0 64.8 20.4 47.2 61.7 57.5 56.7 55.8 61.2 50.3 34.2 34.2 63.5 25.5 63.2 64.8 64.0 52.3
0 19.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.1 0 0 0
0.8 54.5 0 0 0.4 3.2 1.4 11.0 1.8 8.0 2.4 0 0 4.4 0.1 39.2 0 0.2 0.1 1.9 1.1 0 0
14.5 19.6 66.0 25.4 19.7 3.1 15.6 1.2 15.2 23.0 5.4 2.3 2.5 0 8.1 13.3 9.0 11.0 5.2 24.5 17.3 4.8 5.0
0 0 0 0 0.4 0 0 0 0 0 0 0 0 0 1.5 0 0 0 0.2 2.8 2.2 0 0
3.8 0 3.5 0 6.5 2.6 9.7 0.5 4.5 8.0 0 38.3 56.4 7.9 1.2 2.4 0 10.2 2.5 14.4 9.5 1.6 2.0
18.5 5.4 27.5 46.8 50.3 88.0 40.8 56.0 32.6 32.0 45.8 57.9 39.4 63.2 20.8 44.1 14.6 29.5 58.1 38.3 45.3 33.0 20.0
61.4 0 3.0 27.8 21.6 2.9 32.1 29.0 43.6 22.0 46.4 0.8 1.7 24.4 67.7 1.0 73.7 46.4 28.1 13.4 14.5 20.4 18.0
0 0 0 0 1.1 0 0 0 0 0 0 0.4 0 0 0 0 2.7 0.4 0.4 0.3 1.3 7.9 55.0
0 0 0 0 0 0 0 0 0 0 0 0.3 0 0 0 0 0 0 1.6 0.7 1.3 9.3 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.4 0.1 0 23.0 0
44.5 67.5 65.3 52.2 54.0 54.5 52.3 49.9 48.9 57.5 45.2 61.5 65.2 50.7 41.4 61.8 38.7 48.3 55.0 63.6 52.9 55.0 52.0
258
R. Piloto-Rodríguez et al. / Energy Conversion and Management 65 (2013) 255–261
important amount of biodiesel with high percent of unsaturation. The unsaturation range covered was between 0% and 93.6% (without considering the pure FAMEs). All the values in Table 2 are in weight percent. The model is shown in the following equation.
CN ¼ 56:16 þ 0:07 La þ 0:1 M þ 0:15 P 0:05 Pt þ 0:23 S 0:03 O 0:19 Li 0:31 Ln þ 0:08 Ei þ 0:18 Er 0:1 Ot
Table 3 Correlations comparison according to the linear fit of CN predicted and reported values. Item
Gopinath [10]
Bamboye [15]
New model
R R2 (%) Standard error Residual interval
0.9270 85.94 2.8 ±13.8
0.9211 84.85 4.3 ±14.9
0.9563 91.46 3.2 ±7.1
ð1Þ
where the independent variables represent the FAME composition found in biodiesel: La is the % of lauric, M is myristic, P is palmitic, Pt is palmitoleic, S is stearic, O is oleic, Li is linoleic, Ln is linolenic, Ei is eicosanoic, Er is erucic and Ot is the sum of the other FAMEs found. All the FAME compositions in Eq. (1) are in weight percent: wt (%). The main statistics results for the MLR are: R = 0.9191 and a standard error of estimate of 4.6. The obtained values of these statistics are not adequate enough. This can be due to the complexity of the selected data that is covering a wide range of biodiesel composition concerning percentages of saturated and unsaturated compounds. This result also had shown the difficulty to obtain adequate correlation for this purpose when a parametric analysis is implemented. As is observed in Eq. (1), there is a positive influence of the FAME content of lauric, myristic, palmitic, stearic, eicosanoic and euric in the CN, but a negative influence for palmitoleic, oleic, linoleic and linolenic. Concerning the saturated FAMEs, the stearic acid shows the higher influence on the CN. For the unsaturated FAMEs that shown negative influence, the higher negative influence on the CN corresponds to linolenic acid. These results were also observed by Gopinath et al. [10] but not exactly with the same values of coefficients in the regression model. Two of the unsaturated FAMEs (eicosanoic and euric) shown positive influence in the CN due to even when a negative influence in CN when unsaturation is presented, in this cases the length of the carbon chain has a predominant influence. For the evaluation of the relative capability of the MLR model obtained for predicting the CN, a comparison with two other MLR models was made. The comparative plot of the results obtained is shown in Fig. 2. The basic evaluation of the linear regression fit obtained is shown in Table 3 beside the obtained values using the two other models from references [10,15]. As is observed in Fig. 2, there are some outliers in the prediction of cetane number that involves in some cases all the models and others for specific models. These
outliers directly affect the model correlation coefficients, standard errors and mainly the residual values. From Table 3 it can be observed that the best model is the one proposed in this work, with the highest correlations coefficients and one of the lowest residual intervals. The worst case is the Bamboye model because it is showing the lowest correlation coefficient jointly with the highest residual interval.
3.2. Artificial neural networks The results from the ANNs in order to correlate the cetane number with the FAMEs present in 48 biodiesel samples are shown in Table 4. Twelve ANNs (11:5:1) were evaluated keeping constant the function for phase 1 (backpropagation) and changing phase 2 and the regression output function. The use of ANNs based on adding two more units in the hidden layer (11:7:1) are shown in Table 5. In a comparison between results obtained using MLR and ANNs for predicting the cetane number, best fit is generally observed when ANNs are used. The results of better correlation coefficients when ANNs are used are in good agreement with other reports [9,12,29]. The critical point is that in many cases it is not possible to obtain absolute error values below 2. Only two ANNs are below this value. All the ANNs were tested in the validation step in order to select the best ANN. Basu et al. [29] also used backpropagation, Levenberg, quick propagation and delta-bar-delta as training algorithms in three layer (8:3:1) neural networks. For diesel fuels, he found correlation values for the network in the training step (R = 0.9539). Yang et al. [9] obtained R = 0.8602 for the training step in a three layer backpropagation network with 2.1 for the mean absolute error but his network is only applied to diesel fuels. Ramadhas et al. [12] used four types of ANNs, not reporting the absolute error of the networks. The author used 5 inputs corresponding to 5 FAMEs while in this work it is extended to 11 inputs. Ramadhas used a data
Table 4 Results of the (11:5:1) ANNs evaluated for the prediction of the cetane number. Network number 1 2 3 4 5 6 7 8 9 10 11 12 Fig. 2. Relationship between actual and predicted values of cetane number.
Phase 2
R
Absolute error
Regression output function
BP CGD Levenberg QP QuasiNewton Delta-bardelta BP CGD Levenberg QP QuasiNewton Delta-bardelta
0.9386 0.9486 0.9520 0.9497 0.9587
2.3 2.6 2.3 2.1 2.1
Linear
0.9528
2.0
0.9330 0.9484 0.9385 0.9615 0.9566
2.2 2.5 2.4 2.1 2.2
0.9292
2.0
Logistic
259
R. Piloto-Rodríguez et al. / Energy Conversion and Management 65 (2013) 255–261 Table 5 Results of the (11:7:1) ANNs evaluated for the prediction of the cetane number. Network number
Phase 2
R
Absolute error
Regression output function
13 14 15 16 17
BP CGD Levenberg QP QuasiNewton Delta-bardelta BP CGD Levenberg QP QuasiNewton Delta-bardelta
0.9403 0.9491 0.9577 0.9429 0.9537
2.7 2.3 2.0 2.1 1.8
Linear
0.9256
2.6
0.9478 0.9349 0.9103 0.9101 0.9313
1.9 2.3 2.5 2.3 2.5
0.9116
2.2
18 19 20 21 22 23 24
the ideal linear regression fit is observed for more than the 95% of the data processed. 3.3. Model validation For the validation of models obtained by ANN and using MLR, a data set not related to the modeling data was used. The validation data covers 15 samples from other references. The collected data includes the experimental evaluation of FAME composition and CN, covering a wide range of possible values of cetane number (between 41 and 69) and they were taken from experiments using engine tests or an ignition quality tester. All the information about the validation data is presented in Table 6. All the values in Table 6 are in weight percent. The results of the models validation for the ANN # 10 and the MLR models are presented in Fig. 4. The comparison is based on the differences between the actual value of CN and the predicted value using each model. In the plot presented in Fig. 4 a line that represents the ideal fit between predicted and actual value for any model is also superposed. In the comparison between both models shown in Fig. 4, even when there are some points with the same predicted values for both models, a general analysis of outlier points shows that the best model for CN prediction is the ANN. The linear regression fit applied to the plotted data in Fig. 4 shows correlation coefficients (including outliers) of 0.9544 for ANN # 10 and 0.8888 for the MLR model. The zone in Fig. 4 that covers the range 50–60 of cetane number corresponds to the common CN value of biodiesel from many feedstocks. As is observed, this is the zone that shows the lowest outlier points in both cases. In this zone the capability of prediction
Logistic
Fig. 3. Relationship between measured (actual) and predicted values of cetane number using the selected ANN and MLR.
set that covers biofuels with cetane number between 22.7 and 75.6, similar to the range applied in the present work. In the validation step the best results were obtained for the ANN # 10 corresponding to a (11:5:1) with a logistic output function and the Levenberg algorithm. The plot of cetane number actual values against those predicted by the ANN # 10 and the MLR is shown in Fig. 3 where a good distribution of the points near
Fig. 4. Comparison between ANNs in the validation step.
Table 6 Experimental data selected for models validation [16,32,35,37–39]. Sample
12:0
14:0
16:0
16:1
18:0
18:1
18:2
18:3
20:1
22:1
CN
Wild mustard Waste palm oil Balanites roxburhii Garnicia echinocarpa Neolitsea umbrosa G. Anamirta cocculus Broussonetia p. Vent. Salvadora oleoiles D. Nephelium L. Ziziphus maurit. L. Jojoba Rape Peanut Grape Sunflower
0 0 0 0 59.1 0 0 35.6 0 0 0 0 0 0 0
0.1 1.0 0 0 11.5 0 0 50.7 0 0 0 0 0.1 0.1 0
2.6 39.0 17.0 3.7 0 6.1 4.0 4.5 0.2 10.4 1.2 4.9 8.0 6.9 6.0
0.2 0.2 4.3 0 0 0 0 0 0 0 0 0 0 0.1 0.1
0.9 4.3 7.8 43.7 0 47.5 6.1 0 13.8 5.5 0 1.6 1.8 4.0 2.9
7.8 43.7 32.4 52.6 21.0 46.4 14.8 8.3 45.3 64.4 10.7 33.0 53.3 19.0 17.0
14.2 10.5 31.3 0 6.7 0 71.0 0.1 0 12.4 0.1 20.4 28.4 69.1 74.0
13.0 0.2 7.2 0 0 0 1.0 0 0 0 0.4 7.8 0.3 0.3 0
5.4 0.2 0 0 0 0 0 0 4.2 2.6 59.5 9.3 2.4 0 0
45.7 0 0 0 0 0 0 0 0 1.7 12.3 23.0 0 0 0
61.1 60.4 50.5 63.1 60.8 64.3 41.2 66.1 64.9 55.4 69.0 55.0 53.0 48.0 49.0
260
R. Piloto-Rodríguez et al. / Energy Conversion and Management 65 (2013) 255–261
for the ANN is the best. Assuming outlier points corresponding to a lack of accuracy higher than 10%, the MLR model has 3 outliers while the ANN # 10 has only one outlier point. For 90% of the data evaluated the ANN # 10 shows accuracy better than 6% Ramadhas et al. [12] reported accuracy between 3.4% and 5% for predicting the CN, depending of the type of neural network used for the CN prediction, but he used only 5 FAMEs as inputs, therefore the prediction capability of his ANNs can only be restricted to the composition of 5 FAMEs that is quite limited due to the amount of feedstocks, different in chemical composition that can be found in these biofuels. Therefore, the best network is the ANN # 10 that correspond to an artificial neural network implemented using a topology (11:5:1) of 11 inputs, 1 output variable and five nodes. This ANN was implemented using two phases in the training step (backpropagation and Levenberg–Marquardt). The developed model using ANN is more suitable to predict cetane number for biodiesel in a wide range of cetane number values based on the FAME composition of ten fatty acids while the rest of fatty acids found in the composition are taken in an additional factor. The model is not recommended for predicting cetane number of pure FAMEs different that the ten selected for this work. Even when the obtained R values for the prediction capability of cetane number using ANNs or MLR are of the same order of magnitude, the modeling based on ANNs brings more advantages because opens the possibility of the use of networks ensembles for prediction of more complex parameters. One example is the prediction of the ignition delay, that depends on several related factors and one of them is the cetane number. Therefore, the prediction of the cetane number using ANNs is a first step for a further modeling of the ignition delay period where ANNs can play an important role. 4. Conclusions Using multiple linear regression, a model to predict the cetane number based on the composition of ten FAMEs presented in biodiesel was developed and it was able to predict cetane number with 89% accuracy, except one outlier. A model to predict the cetane number based on the composition of ten FAMEs presented in biodiesel using an artificial neural network was obtained with better accuracy than 92% except for one outlier. The best neural network for predicting the cetane number was a backpropagation network (11:5:1) using a Levenberg–Marquardt algorithm for the second training step and showing R = 0.9544 for the validation data. The models based on multiple linear regressions cannot predict cetane number with similar accuracy as the obtained for the selected neural network. Acknowledgments The authors wish to express their thanks to the Flemish Interuniversity Council’s (VLIR) University Development Cooperation, funding an Own Initiatives Program, with whose support much of this work was performed under a project entitled ‘‘Knowledge cell on biofuels (from non-edible crops and waste products) for use in internal combustion engines’’. References [1] Yuan W, Hansen AC, Zhang Q. Vapor pressure and normal boiling point predictions for pure methyl esters and biodiesel fuels. Fuel 2005;84:943–50. [2] Wadumesthrige K, Smith JC, Wilson JR, Salley SO, Simon KY. Investigation of the parameters affecting the cetane number of biodiesel. J Am Oil Chem Soc 2008;85:1073–81. [3] Ramirez-Verduzco LF, Rodriguez-Rodriguez JE, Jaramillo-Jacob A. Predicting cetane number, kinematic viscosity, density and higher heating value of biodiesel from its fatty acid methyl ester composition. Fuel 2012;91:102–11.
[4] Knothe G. Dependence of biodiesel fuel properties on the structure of fatty acid alkyl esters. Fuel Process Technol 2005;86:1059–70. [5] Knothe G. Cetane numbers of branched and straight-chain fatty esters determined in an ignition quality tester. Fuel 2003;82:971–5. [6] Icingur Y, Altiparmak D. Effect of fuel cetane number and injection pressure on a DI diesel engine performance and emissions. Energy Convers Manage 2003;44:389–97. [7] Van Gerpen JH. Cetane number testing of biodiesel. In: Proceedings of the third liquid fuel conference liquid fuels and industrial products from renewable resources, Nashville; 1996. p. 197–206. [8] Murphy MJ, Taylor JD, McCormick RL. Compendium of experimental cetane number data. In: N.R.E. Laboratory, National Renewable Energy Laboratory, Colorado; 2004. [9] Yang H, Ring Z, Briker Y, McLean N, Friesen W, Fairbridge C. Neural network prediction of cetane number and density of diesel fuel from its chemical composition determined by LC and GC–MS. Fuel 2002;81:65–74. [10] Gopinath A, Puhan S, Nagarajan G. Relating the cetane number of biodiesel fuels to their fatty acid composition: a critical study. J Automob Eng 2009;223:565–83. [11] Krisnangkura K. A simple method for estimation of cetane index of vegetable oil methyl esters. J Am Oil Chem Soc 1980;63:552–3. [12] Ramadhas AS, Jayaraj S, Muraleedharan C, Padmakurami K. Artificial neural networks used for the prediction of the cetane number of biodiesel fuel. Renew Energy 2006;31:2524–33. [13] Lapuerta M, Rodriguez-Fernandez J, Armas O. Correlation for the estimation of the density of fatty acid esters fuels and its implications. A proposed biodiesel cetane index. Chem Phys Lipids 2010;163:720–7. [14] Lapuerta M, Rodriguez-Fernandez J, Font de Mora E. Correlation for the estimation of the cetane number of biodiesel fuels and implications on the iodine number. Energy Policy 2009;37:4337–44. [15] Bamgboye AI, Hansen AC. Prediction of cetane number of biodiesel fuel from the fatty acid methyl ester (FAME) composition. Int Agrophys 2008;22:21–9. [16] Ramos MJ, Fernandez CM, Casas A, Rodriguez L, Perez A. Influence of fatty acid composition of raw materials on biodiesel properties. Bioresour Technol 2009;100:261–8. [17] Esen H, Inalli M, Sengur A, Esen M. Performance prediction of a groundcoupled heat pump system using artificial neural networks. Exp Syst Appl 2008;35:1940–8. [18] Esen H, Inalli M, Sengur A, Esen M. Forecasting of a ground-coupled heat pump performance using neural networks with statistical data weighting preprocessing. Int J Therm Sci 2008;47:431–41. [19] Esen H, Inalli M, Sengur A, Esen M. Modeling a ground-coupled heat pump system by a support vector machine. Renew Energy 2008;33:1814–23. [20] Esen H, Ozgen F, Esen M, Sengur A. Modeling of a new solar air heater through least-squares support vector machines. Exp Syst Appl 2009;36:10673–82. [21] Karatepe E, Boztepe M, Colak M. Neural network based solar cell model. Energy Convers Manage 2006;47:1159–78. [22] Kalogirou SA. Application of artificial neural networks in energy systems – a review. Energy Convers Manage 1999;40:1073–87. [23] In-Ho Y, Myoung-Souk Y, Kwang-Woo K. Application of artificial neural network to predict the optimal start time for heating system in building. Energy Convers Manage 2003;44:2791–809. [24] Reddy KS, Ranjan M. Solar resource estimation using artificial neural networks and comparison with other correlation models. Energy Convers Manage 2003;44:2519–30. [25] Kalogirou SA. Artificial intelligence for the modeling and control of combustion processes: a review. Prog Energy Combust Sci 2003;29:515–66. [26] Blasco JA, Fueyo N, Dopazo C, Chen JY. A self organizing – map approach to chemistry representation in combustion applications. Combust Theory Model 2000;4:61–76. [27] Heister F, Froehlich M. Non-linear time series analysis of combustion pressure data for neural network training with the concept of mutual information. Proc Inst Mech Eng, Part D: J Automob Eng 2001;215:299–304. [28] Thompson GJ, Atkinson CM, Clark NN, Long TW, Hanzeback E. Neural network modeling of the emissions and performance of a heavy-duty diesel engine. Proc Inst Mech Eng, Part D: J Automob Eng 2001;214:111–26. [29] Basu B, Kapur GS, Sarpal AS, Meusinger R. A neural network approach to the prediction of cetane number of diesel fuels using Nuclear Magnetic Resonance (NMR) spectroscopy. Energy Fuels 2003;17:1570–5. [30] Santana RC, Do PT, Santikunaporn M, Alvarez WE, Taylor JD, Sughrue EL, et al. Evaluation of different reaction strategies for the improvement of cetane number in diesel fuels. Fuel 2006;85:643–56. [31] Korres DM, Anastopoulos G, Lois E, Alexandridis A, Sarimveis H, Bafas G. A neural network approach to the prediction of diesel fuel lubricity. Fuel 2002;81:1243–50. [32] Mohibbe AM, Waris A, Nahar NM. Prospects and potential of fatty acid methyl esters of some non-traditional seed oils for use as biodiesel in India. Biomass Bioenergy 2005;29:293–302. [33] Tong D, Hu C, Jiang K, Li Y. Cetane number prediction of biodiesel from the composition of the fatty acid methyl esters. J Am Oil Chem Soc 2011;88:415–23. [34] Kinast JA. Production of biodiesels from multiple feedstocks and properties of biodiesels and biodiesel/diesel blends. In: NREL/SR-510-31460. NREL, Illinois; 2003. [35] Agarwal AK. Biofuels (alcohols and biodiesel) applications as fuels for internal combustion engines. Prog Energy Combust Sci 2007;33:233–71.
R. Piloto-Rodríguez et al. / Energy Conversion and Management 65 (2013) 255–261 [36] Moser BR. Biodiesel production, properties, and feedstocks. In Vitro Cell Dev Biol Plant 2009;45:229–66. [37] Ozsezen AN, Canakci M. Determination of performance and combustion characteristics of a diesel engine fueled with canola and waste palm oil methyl esters. Energy Convers Manage 2011;52:108–16. [38] Jham GN, Moser BR, Shah SN, Holser RA, Dhingra OD, Vaughn SF, et al. Wild Brazilian Mustard (Brassica juncea L.) seed oil methyl esters as biodiesel fuel. J Am Oil Chem Soc 2009;86:917–26.
261
[39] Shah SN, Sharma BK, Moser BR, Erhan SZ. Preparation and evaluation of Jojoba oil methyl esters as biodiesel and as a blend component in ultra-low sulfur diesel fuel. Bioenergy Resour 2010;3:214–23.