Prediction of selected biodiesel fuel properties using artificial neural network

Abstract

Biodiesel is an alternative fuel to replace fossil-based diesel fuel. It has fuel properties similar to diesel which are generally determined experimentally. The experimental determination of various properties of biodiesel is costly, time consuming and a tedious process. To solve these problems, artificial neural network (ANN) has been considered as a vital tool for estimating the fuel properties of biodiesel, especially from its fatty acid (FA) composition. In this study, four ANNs have been designed and trained to predict the cetane number (CN), flash point (FP), kinematic viscosity (KV) and density of biodiesel using ANN with logsig and purelin transfer functions in the hidden layer of all the networks. The five most prevalent FAs from 55 feedstocks found in the literature utilized as the input parameters for the model are palmitic, stearic, oleic, linoleic and linolenic acids except for density network with a sixth parameter (temperature). Other FAs that are present in the biodiesels have been considered based on the number of carbon atom chains and the level of saturation. From this study, the prediction accuracy and the average absolute deviation of the networks are CN (96.69%; 1.637%), KV (95.80%; 1.638%), FP (99.07%; 0.997%) and density (99.40%; 0.101%). These values are reasonably better compared to previous studies on empirical correlations and ANN predictions of these fuel properties found in literature. Hence, the present study demonstrates the ability of ANN model to predict fuel properties of biodiesel with high accuracy.

Keywords

biodiesel / fuel properties / artificial neural network / fatty acid / prediction

Introduction

Biodiesel has been considered as one of the alternative fuels to be used as a good replacement for diesel fuel in compression ignition engines for several reasons, among which is its production from a renewable source such as vegetable oils (VOs) and animal fats [ 1, 2] Biodiesel is produced from the various feedstocks which are readily available in our environment. Biodiesel is produced from different sources; majorly from VOs, animal oils and fats, waste cooking oils, algae, grease [ 3, 4], insect oils [ 5, 6] and other oil-based wastes [ 7− 9].

The physical and chemical fuel properties of biodiesel fundamentally depend on the fatty acids (FAs) distribution of the triglyceride obtained from the raw material used for biodiesel production [ 10, 11]. The amounts and types of FA compositions contained in VOs determine the overall fuel properties of biodiesels such as viscosity, flash point (FP), high heating values, etc. [ 5, 12]. The properties of the various fatty esters are determined by the structural features of the FA and the alcohol moieties that comprise a fatty ester. Structural features that influence the physical and fuel properties of a fatty ester molecule are chain length, degree of unsaturation, and branching of the chain [ 10, 11].

Experimental methods are often used in the determination of fuel properties which provide good and high degree of accuracy results. This experimental determination of biodiesel fuel properties has to be conducted in accordance with standard test methods which have been provided for in different standards world over. The cost of running these tests is high, and is technically challenging, energy and time consuming. In a case in which these three issues are considered to be a minor issue, the availability of a well-equipped laboratory to perform these tests is scarce. Subject to the above, mathematical models, statistical models and artificial neural network (ANN) have been used in predicting the properties of biodiesel either from the FA composition or the level of saturation of VOs [ 11].

Mathematical models have been developed which can be used, to a great extent, with a high level of accuracy in predicting the properties of biodiesels from their FA compositions [ 13− 17]. Some studies have reported the development of statistical models for predicting the fuel properties of biodiesels by the correlation of their different FA compositions [ 12, 18, 19]. Of note is the fact that transesterification does not alter the FA composition of the feedstock employed in biodiesel production [ 11].

Artificial intelligence systems are widely used as a technology offering an alternative way to tackle complex and ill-defined problems. ANNs are types of artificial intelligence systems that endeavor to mimic the way the human brain works. They are nonlinear information processing devices, which are built from interconnected elementary processing devices called neurons. They can learn from examples or garnered data and are fault tolerant in that they are able to handle noisy and incomplete data. They are also able to deal with nonlinear problems or data, and once trained can perform prediction and generalization at high speeds [ 20].

The ANN method involves the use of certain properties of biodiesel which have been previously known or obtained via experimental results to predict future biodiesel properties. Few studies have employed ANN to predict the properties of biodiesels from their FA compositions. Cheenkachorn [ 12] combined statistical models (using best subset method) and ANNs to predict viscosity, higher heating and cetane number (CN) of biodiesels. The data primarily collected from literature has been used to predict the properties of biodiesels using the FA compositions of various VOs. It has been concluded that the statistical model can fairly predict viscosity and CN of biodiesel while the ANN model can accurately predict these properties, and that the predicted values are close to the experimental results. Ramadhas et al. [ 21] have developed and trained a multi-layer feed forward ANN to reliably predict the CN of biodiesel using the FA compositions of biodiesels and the experimental values of CN. ANN predicted CNs has been found to be in good agreement with the experimental CNs. Furthermore, ANN has been designed to predict the density of various VO-based methyl esters. The experimental densities obtained have been used to train the networks by applying a three-layer back propagation neural network. The results from the networks are in good agreement with the measured data [ 22].

The facts that previous studies employing ANN for the prediction of biodiesel properties from their FA compositions are scarce and that few numbers of feedstocks have been used for such work have necessitated the present study. To effectively train and predict biodiesel fuel properties from the FA compositions of feedstocks using ANN, FA compositions of 55 different feedstocks obtained from literature have been used during the course of this study. The primary objective of this study is to train and predict some key fuel properties of biodiesel from the FA composition using ANN model.

Materials and method

Artificial neural network　(ANN)

ANN is trained to learn the complex relationship between two or more variables or data sets. Usually, ANN are trained and adjusted so that a particular input leads to a specific target output. To achieve a good network, many data sets, that is, input/target pairs are needed to train the network. How the ANN transforms its input vector into output vector depends on the neuron model and architecture. The computation of the output includes the product of the output and weight of the neuron summed with the bias of the neuron, which is passed through a transfer function in order to get the output of the neuron. Neurons may be simulated with or without bias [ 22].

ANN modeling

ANN modeling consists of the input layer, the hidden layer and the output layer which are connected to each other. The input layer receives the input data outside the network and sends it to the hidden layer. The hidden layer contains interconnected neurons for adjusting the weights on the connections. They contain several functions and variables including weights, transfer functions, and methods to add up all inputs and bias values. The sum of all products of all the inputs multiplying the weights and the bias values pass through a nonlinear transfer function as the output of each neuron [ 12]. Neurons that receive the same input and use the same transfer function may be grouped in layers. In back propagation (BP), networks often have one or more layers of sigmoid neurons followed by an output layer of linear neurons. The results from the hidden layer are sent to the output layer as the outputs. A 5:2:4 ANN architecture with neurons in each layer has been used in this study as shown in Fig. 1.

It has been proven that the two-layer networks with sigmoid transfer functions in the hidden layer and linear transfer functions in the output layer can approximate virtually any function of interest to any degree of accuracy provided that a sufficient amount of hidden units are available [ 23]. Therefore, the behavior of any designed network is dependent on the neuron model and the transfer function used for the design.

Data collection and selection

The data used in this study are sourced from literature authored by various researchers on the production of biodiesel from different feedstocks. The FA composition of oils or FA methyl ester (FAME) of biodiesels and their fuel properties are obtained from previous works (experimental results) which satisfied biodiesel standards, and are used as inputs for the ANN modeling. The five most prevalent constituents (FA/FAME) of the biodiesels from the data garnered are selected for use. These are palmitic (C16:0), stearic (C18:0), oleic (C18:1), linoleic (C18:2) and the linolenic (C18:3) acids. These FAs have been reported as the most prevalent of all FAs contained in biodiesel fuels [ 22]. Both the palmitic and stearic acids are the saturated acids while the other three are unsaturated acids. This study involving the ANN modeling dwells on the fundamental fact that the FA composition of oil employed in biodiesel preparation significantly dictates biodiesel fuel properties.

Consideration of FAs with less than 16 and greater than 18 carbon chains

Some feedstocks in the data garnered have FAs with less than 16 and more than 18 carbon chains. To consider these FAs, the percent values of all saturated acids with the carbon chain less than 16 are added to the amount of palmitic acid (C16:0) present while the saturated acids with carbon chain more than 18 are added to the stearic acid (C18:0) [ 13]. Besides, the amount (%) of acids with a single bond (carbon chain more than 18) are added to the amount of oleic acid (C18:1), those with double bonds added to linoleic acid (C18:2) while those with triple bonds added to linolenic acid (C18:3) [ 13]. Consideration is also given to feedstocks with more than three bonds which are always in trace amounts. The amount (%) of acid with four bonds are added to oleic acid (C18:1) and those with five bonds added to linoleic acid (C18:2) while those with six bonds to linolenic acid (C18:3).

ANN model analysis

Parameters of key importance employed in the training of ANNs that cannot be overlooked are the type of network, training function, adaptation learning (transfer) function, performance function, number of layers and properties of layers. The same network type (feed forward propagation network) is used for all the trainings. The train Levenberg-Marquardt (LM) back propagation, learn GDM (gradient descent with momentum weight and bias learning functions), and mean-squared error MSE are used as the training, adaptation learning and performance functions, respectively.

The following steps were taken in training the network using Matlab® (7.01) software:

1) The FA compositions and fuel properties of all selected feedstocks are used as input and target parameters, respectively, and are written in suitable format in the Matlab® workspace.

2) Feed forward ANNs with hidden layers (1 to 4) are used in this study because it can approximate virtually any linear or nonlinear function to an acceptable accuracy if sufficient hidden layer neurons are provided with the sigmoid function as the hidden layer transfer function.

3) The LM algorithm is chosen to train the network because it is one of the most widely used and validated back-propagation algorithms [ 22− 24] and it converges fast and has been proved to be accurate enough in most cases [ 16, 22− 24].

4) Trainlim, sigmoid (tangent and logistic) and purelin functions are selected as the training and transfer functions, respectively, because they have been widely validated and proved to be accurate to a great extent in most works using ANN [ 21, 23]. Purelin is used as the transfer function in the output layer.

5) Since there is no general rule for determining the optimum number of neurons in the hidden layer and usually, it is determined through trial and error, hence, four to eight neurons are selected during the process of training and learning to determine the optimum number of neurons for each fuel property trained in the network. In addition, the input and target parameters are introduced to the created network and the weight initialized.

6) The training parameters such as epoch, maximum failure, hidden layer, error goal etc. are adjusted and the network gradually trained until the defined error is reached.

The logsig and purelin transfer functions are expressed in mathematical terms as provided in Eqs. (1) and (2).

(1) \mathrm{Logsig}(n)={\displaystyle \frac{\mathrm{1}}{\mathrm{1}+e^{-n}}},

(2) \mathrm{P}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{l}\mathrm{i}\mathrm{n}(n)=n.

Modeling of properties

Input parameters

For all the networks to be modeled, the input layer consists of five inputs which are the palmitic, stearic, oleic, linoleic and linolenic acids. However, an exception goes for the density (fuel property) network which has an additional input parameter (temperature (°C)), making the input parameters of this fuel property six in all. The reason for this is that the densities of biodiesels captured in the data are observed to be at different temperatures.

Output parameters

The output parameters are the fuel properties (kinematic viscosity, CN, FP and density) being predicted by the ANNs. These properties are predicted with high accuracy using the procedures earlier mentioned in Section 2.5. Several ANNs with different hidden layers, number of neurons, transfer functions and training parameters are trained in order to determine the optimum hidden layer, number of neurons, transfer functions (pair) and training parameters value, which would give the best prediction accuracy for each property. Prediction errors resulting from this work are estimated using mean absolute error (MAE) and average absolute deviation (AAD) as expressed in Eqs. (3) and (4).

(3) \mathrm{MAE=}{\displaystyle \frac{\mathrm{1}}{n}}\left|f_{\exp }-f_{\mathrm{calc}}\right|,

(4) \mathrm{AAD=}{\displaystyle \frac{1}{n}}{\displaystyle \sum _{j=1}^n\left|{\displaystyle \frac{\left(f_{\exp }-f_{\mathrm{calc}}\right)}{f_{\exp }}}\times 100\%\right|}.

Results and discussion

Neural network trainings

In this present study, it has been found that the hidden layer containing logsig and purelin as the transfer functions yield the best result for all the networks trained. It has also been observed that the same neurons do not give the best outputs for all the fuel properties considered in this study. In all, six neurons have been found to give an acceptable result for both FP and CN networks with the density and kinematic viscosity (KV) networks needing five and seven neurons, respectively, to give an acceptable output. The sets of data (FA compositions and experimental values) used in the training; validation and testing of the performance of all the networks are provided in the supplementary material. [ 5− 6, 11, 21, 25− 59])

Network prediction of CN

CN is a very important diesel fuel property analogous to the octane number of petrol fuel. CN is the measure of the ignition quality of diesel engines. The minimum limits of CN as recommended by ASTM D 613 and EN ISO 5165 specifications are 47 and 51, respectively. Thirty five different biodiesel feedstocks with five pure FAs have been used to train the ANN of CN. All the necessary data to train, validate and test the network performance are input into the network. 60% of the total data (24 samples) have been used in training the network, 20% of the total data (8 samples) have been used in the validation while the remaining 20% (8 samples) have been used in testing the performance of the network. It is worth noting that the selection of data used at different operations (training, validation and testing) is done randomly by the software during the training. At the start of the training of the network using six neurons, the initiation values of the network parameters provided by Matlab® have been adjusted before being used. The training has been repeated many times until the predicted output and actual values have the acceptable accuracy. Figure 2 provides the plot of regression of the data used in the training, validation, testing and performance of the entire network.

Figure 2 shows straight lines for the training, validation, testing and performance of the network with correlation coeffiecients (R) of 0.981, 0.978, 0.993 and 0.967, respectively. For the trained network, the determination coefficient (R²) is equal to 0.935. The straight lines in Fig. 2 are the linear relationships obtained between the output (predicted) and the target (actual) data of CN used in this present study. The high coefficients of correlation obtained during the training, validation and testing of the CN network display very good relationship between the output and the actual CN values. This is apparent in the high coefficient of correlation (R = 0.967) of the whole network. The values of the actual and the output including the error (difference between the target and the output) and the percent error are listed in Table 1.

As can be observed from Table 1, the outputs of the CN network are in close agreement with the actual values of CN and hence a high level of prediction accuracy. However, a maximum absolute error of 4.692 (7.354%) has been obtained for rice bran which has CNs of 63.8 and 59.11 for the actual and the predicted values, respectively (Table 1 and supplementary material [ 5− 6, 11, 21, 25− 59]). Besides the pure FAs used to support the network data and the soybean oil biodiesel, all other predicted values of the various biodiesels satisfy the minimum specification of 47 stipulated by the ASTM D6751 standard. Though the soybean oil biodiesel has been reported to have a CN of 45, this is considered to check the outcome of using ANN to predict the CN of a feedstock whose CN will not satisfy the minimum requirement even when determined experimentally. Sunflower, grape and tallow biodiesels have been reported to have CNs of 55.6, 48.0 and 58.8 and the network predicted values of 53.4, 49.4 and 61.5 which correspond to 3.952%, −2.907% and −4.596%, respectively (Table 1 and supplementary material [ 5− 6, 11, 21, 25− 59]).

From the difference between the actual and the output (Table 1), it is found out that the error in prediction ranges from −2.702 (−4.596%) to 4.692 (7.35%). These errors could be attributed to FA composition determination and CN measurement via respective instruments, as slightly different values of FA composition and CN are often reported by authors for the same feedstock used for biodiesel production.

Network prediction of KV

Transesterification is aimed at reducing the high viscosity of VOs which limits its use as a substitute fuel for diesel. The fuel with a high viscosity has a greater tendency of forming deposit in the engine combustion chamber. The KV range of 1.9 to 6.0 mm²/s is accepted by ASTM D6751 while a boundary of 3.5 to 5.0 mm²/s is required by EN 14214, both measured at 40 °C.

For this study, 47 sets of data from various feedstocks used in biodiesel production have been chosen in training the KV network including five pure FAs. Of the 47 feedstocks, 28 feedstocks (59.6%) have been used for the network training, nine (19.1%) for the validation and the remaining ten (21.3%) for testing the performance of the network. Figure 3 illustrates the plots of the data used for the training, validation, testing and the performance of the entire KV network. The straight lines (Fig. 3) are the linear relationships between the output and the target data of KV used in this study. The correlation coefficients (R) between the actual and the predicted values are found to be 0.977 (training), 0.965 (validation), 0.969 (testing) and 0.958 (performance). The determination coefficient (R²) for the KV network is 0.918. The high coefficients of correlation (training, validation and testing) obtained demonstrate the high prediction accuracy of this network as also reflected in the high coefficient of correlation (R = 0.958) of the entire KV network. Table 1 lists the actual KV and predicted output, including the error and the percentage error.

From Table 1 and supplementary material [ 5− 6, 11, 21, 25− 59], a maximum absolute error of 0.207 mm²/s corresponding to −4.709% is observed for rapeseed oil biodiesel in the KV network. Apart from the aforementioned, every other predicted output has an absolute percentage error of less than 3.9. For the KV network, the range of error is between −0.207 and 0.157 mm²/s while that of percentage error is between −4.709 and 3.482 (Table 1). Over 80% of the predicted values of KV have a percentage error of less than 3.000 while more than 54% of the same have a percentage error of less than 2.000, which indicates very good correlation between the actual and the output values.

Network prediction of FP

The FP is the temperature at which the fuel will ignite or start to burn when it comes in contact with fire. In general, the FP of biodiesel is high compare to its diesel counterpart which makes it safer for transportation and storage. For this study, the FPs of biodiesels experimentally determined using the standard test methods as recommended by biodiesel standards are selected from literature.

Thirty one feedstocks were selected in the training of the FP network using six neurons. The correlation plots for the training, validation, testing and the performance of the network are demonstrated in Fig. 4. As can be seen from Fig. 4, the straight lines show the linear relationship between the target and the output. The close agreement between the target and the output of the FP network is obviously reflected in the high correlation coefficients (R) of 0.997 (training), 0.989 (validation), 0.984 (testing) and 0.991 (performance of the network). In addition, the determination coefficient (R²) of the FP network is 0.981 which signifies a high level of accuracy for the prediction of FP. The outputs of the network, the actual FPs, error and percentage error of the prediction are presented in Table 2.

As can be seen from Table 2, the maximum absolute error and percentage error of the FP network are 5.906°C and 3.394, respectively. The least absolute error observed in the output of the network is 0.041°C corresponding to −0.057%. The network recorded error is between −3.394°C and 3.173°C and percentage error is between −5.906 and 5.649. Over 93% of the predicted FPs fall within±3.0% while over 80% of them are within±2.0%. Consequently, the use of the network for future prediction of FP of biodiesel would possibly give a result within the limit of±3.4°C.

Network prediction of density

The density of biodiesel is determined experimentally using the standard test methods recommended by biodiesel standards. The EN ISO 3675 test method specifies the range of 860 to 900 kg/m³ for biodiesel density at 15°C while no specification is given for the ASTM D5002 test method. For this study, the data selected are those whose densities are reported at 15°C and also satisfy the specification as stated above. Thirteen samples (61.92%) of the data were used for the training, four samples (19.04%) for the validation and the last four samples (19.04%) for testing the performance of the developed ANN for density. Few sets of data (21 feedstocks) have been used in training this network due to the fact that most authors in the literature have not measured the density of the prepared biodiesel or reported the density at 15°C.

Figure 5 depicts the linear relationships between the target and the output observed for the training, validation, testing and the performance of the density network. The correlation coefficients of 1.000 (training), 0.996 (validation), 0.993 (testing) and 0.994 (performance) have been obtained for the density network. These results demonstrate very good agreement between the target and output for this network. Also, the goodness of fit of this network as indicated by the high determination coefficient (R² = 0.988) implies that 98.8% of the data go into the prediction. The error and the percentage error recorded between the target and output for each set of data are provided in Table 2. For this study, a maximum absolute error of 4.32 kg/m³ has been observed in the prediction of the density of jatropha oil biodiesel with actual value of 880 kg/m³ and predicted value of 884.31 kg/m³ which corresponds to −0.491% (Table 2 and supplementary material [ 5− 6, 11, 21, 25− 59]). Moreso and Kusum oil biodiesel give the least absolute error and percentage error of 0.0071 kg/m³ and 0.00082, respectively (Table 2 and supplementary material [ 5− 6, 11, 21, 25− 59]). In addition, the range of prediction of density in this network is between −4.322 and 3.539 kg/m³ for the error while that of the percentage error is between −0.491 and 0.401.

With 5 (21 feedstocks; density), 6 (31 feedstocks; FP), 6 (40 feedstocks; CN) and 7 (47 feedstocks; KV) neurons obtained as the optimum numbers of neurons to train the networks to acceptable accuracies, it can be reasonably deduced that the more the feedstocks available for the network training, the more the optimum numbers of neutrons needed to train the network to an acceptable accuracy.

Comparison with previous studies

The resulting errors between the actual and the output values for all the networks modeled have been estimated as MAE and AAD. For comparison purpose, the AAD obtained in this study and those of previous studies for the properties predicted are provided in Table 3. The previous works utilized for this comparison are those that predicted using empirical and ANN methods.

It can be seen from Table 3 that the MAE and the AAD of the CN network are 0.955 and 1.637%, respectively. The AAD value obtained in this study is significantly lower than those reported by both Ref. [ 15] and Ref. [ 60] (5.66%−12.34%). It is worth mentioning that their predictions have been conducted using empirical correlations but not ANN models. Besides, this study is able to predict CN better with slightly higher values of R (0.967) and R² (93.49%) compared to those of Ref. [ 18] (R = 0.921; R² = 84.85%) and Ref. [ 17] (R = 0.956; R² = 91.46%).

It can be seen from Table 3 that the AAD and the MAE values for the KV network are 1.689% and 0.0717 mm²/s, respectively. The AAD recorded for this study is slightly lower than the value of 2.57% and the range of values between 2.57% and 8.04% previously reported. It can also be seen that the AAD of the FP network resulting from this study are 1.705°C and 0.997% while that of the density network are 1.312 kg/m³ and 0.101%, respectively. The AAD of the FP network is slightly less than the value of 1.81% earlier reported while that of the density network is close to 0.11% previously recorded as provided in Table 3.

It is seen obviously from this study (comparison) that few studies are available in the literature which have investigated the use of ANN to predict biodiesel fuel properties from their FA components. Conclusively, the ANN model developed in this study is able to predict the fuel properties (CN, KV, FP and density) of biodiesel from its FA composition to a high degree of accuracy. The fact that ANN gives a better prediction of biodiesel fuel properties than other methods of estimation as evident in this study has been stressed by several authors [ 12, 21, 22, 24, 61].

Conclusions

The purpose of this study is to predict the properties (CN, KV, FP and density) of biodiesel from the FA composition in order to reduce the cost and time spent on experimental analysis of these properties. Five FAs prominent in the FA compositions of the biodiesels collected from literature and the corresponding experimental values of the properties (CN, KV, FP and density) have been employed in developing an ANN model for the prediction of the aforementioned properties. The ANN model consists of five input layers (five inputs for CN, KV and FP networks, and six inputs for density network), hidden layer (logsig and purelin transfer functions) and four output layers (CN, KV, FP and density). All networks are able to predict values very close to the experimental values with regression coefficients of 0.967, 0.958, 0.991 and 0.994 for CN, KV, FP and density networks, respectively. In addition, the AAD for all the networks are 1.637% (CN), 1.689% (KV), 0.997% (FP) and 0.149% (density) which are all less compared with what have been previously reported in the literature on the prediction of these properties. It can be reasonably deduced that the more the feedstocks available for the network training, the more the optimum numbers of neutrons needed to train the network to an acceptable accuracy.

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