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Prediction of heat capacities of ionic liquids using chemical structure based networks
Prediction of heat capacities of ionic liquids using chemical structure based networks Ali Barati-Harooni, Adel Najafi-Marghmaleki, Amir H Mohammadi PII: DOI: Reference:
S0167-7322(16)32695-2 doi: 10.1016/j.molliq.2016.11.119 MOLLIQ 6666
To appear in:
Journal of Molecular Liquids
Received date: Revised date: Accepted date:
11 September 2016 20 October 2016 27 November 2016
Please cite this article as: Ali Barati-Harooni, Adel Najafi-Marghmaleki, Amir H Mohammadi, Prediction of heat capacities of ionic liquids using chemical structure based networks, Journal of Molecular Liquids (2016), doi: 10.1016/j.molliq.2016.11.119
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ACCEPTED MANUSCRIPT Prediction of Heat Capacities of Ionic Liquids Using Chemical Structure based Networks
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Ali Barati-Harooni,a1 Adel Najafi-Marghmaleki,a Amir H Mohammadib,c,d 2
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Young Researchers and Elite Club, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran Discipline of Chemical Engineering, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban 4041, South Africa c Institut de Recherche en Génie Chimique et Pétrolier (IRGCP), Paris Cedex, France d Département de Génie des Mines, de la Métallurgie et des Matériaux, Faculté des Sciences et de Génie, Université Laval, Québec, QC G1V 0A6, Canada
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b
Abstract - Ionic liquids (ILs) have various desired properties which bring them as useful and
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applicable compounds in different industrial processes. Heat capacity of ILs is one of the main
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properties of them which is required in various engineering and design applications. Hence, developing accurate and general models for prediction of this property is important. In this
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communication, two accurate and general models based on radial basis function neural network (RBF-NN) and multilayer perceptron neural network (MLP-NN) were developed for estimation of heat capacities of ILs. The input parameters of the models are temperature, molecular weight of IL and several structural related parameters for each IL. The models were developed based on 2940 experimental data for 56 ILs. The reliability and accuracy of predictions of the developed models were examined by using statistical and graphical methods as well as comparing the results of the models with outcomes of recently developed literature correlations. Results show that the developed models are accurate and reliable and are superior to literature correlations for
Corresponding author: 1 1. Email Address: [email protected] (A. Barati-Harooni) 2
2. Email Address: [email protected] and [email protected] (A. H. Mohammadi)
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ACCEPTED MANUSCRIPT predictions of heat capacity of ILs. The average absolute relative deviation of RBF-NN and
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MLP-NN models for predicted heat capacity data was 0.828% and 1.042% respectively.
Keywords - Ionic liquid (IL); Heat capacity; Chemical structure; Model; Radial basis function
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neural network (RBF-NN); Multilayer perceptron neural network (MLP-NN).
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Introduction
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Ionic liquids (ILs) are compounds composed of large cation and anion parts which are
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liquid salts at temperatures below 100 oC because at these temperatures their ions fail to pack
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appropriately. ILs have different characteristics from common salts which normally have melting
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points higher than 100 oC [1-10].
ILs are interesting compounds which are applied in various applications including
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batteries, solar cells, solvents, thermal fluids, etc. This diverse application of ILs is because their structure is tunable. In another word, it is possible to alter the type, branching and lengths of
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anion and cation parts in an IL to achieve a desired property [11]. ILs possess various unique
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viscosity, etc [12].
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characteristics such as nearly low volatility, relative high thermal and chemical stability, tunable
Because of the increase in the applications of ILs in industrial processes, a significant number of publications that theoretically and experimentally have focused on evaluation and prediction of physicochemical properties of ILs and the possibility of their use in various applications can be found in literature [6, 13-25]. One of the most important properties of ILs is their heat capacity which is required to determine the heat transfer in industrial design units including reactors and heat exchangers [26]. Literature review shows that there are few reports concerning prediction of heat capacity for ILs [26-33]. Preiss et al. [28] proposed a two parameter model for estimation of heat capacity of ILs based on relation between molar volume and heat capacity. However, the dependency of heat capacity to temperature was not considered in their model.
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ACCEPTED MANUSCRIPT Gardas and Coutinho [27] predicted heat capacity of ILs by focusing on the concept of second order group additivity. They used a number of 2400 data from 19 ILs. However, their
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databank was gathered from few citations which bring limitations in generalization ability of
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their model.
Soriano et al. [29] predicted the heat capacity of 32 ILs using 3149 data points. They
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utilized a similar approach to the work done by Gardas and Coutinho [27]. However, their model
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presents inefficient results for estimation of heat capacity of ILs which their cation or anion groups were not considered in their data set for example ammonium-based ILs.
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Farahani et al. [26] also developed a temperature dependent five parameter model for prediction of heat capacity of ILs. In addition to temperature, they used four structural related
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parameters for development of their model. The average absolute relative deviation of their predictions was 2.5%. Sattari et al. [34, 35] published two different works for prediction of heat
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capacity of ILs using 3726 data from 82 ILs. In their first work, they used the combination of group contribution method and genetic function approximation and they obtained an average relative deviation of 1.68%. In the second work they used the concept of quantitative structure– property relationship (QSPR) for prediction of heat capacity of ILs. Recently, Ahmadi et al. [32] also proposed a 12 parameter correlation for prediction of heat capacity of ILs. The input parameters of their correlation were temperature, molecular weight of IL and several structural related parameters. Their correlation predicted the experimental data with an average absolute relative deviation of 5.8%. Nancarrow et al. [36] used two group contribution methods called Meccano and Lego approaches for prediction of heat capacity of ILs. They utilized 2396 experimental data from 19 ILs for development of the models. They concluded that although the Meccano approach provided better predictions, the
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ACCEPTED MANUSCRIPT applicability domain of Lego approach is higher than Meccano method. The experimental data utilized in this work covers a limited number of 19 ILs. Moreover, the use of their methods
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requires determination of various structural related parameters for each IL which restricts the
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applicability of these models and makes the computational process a difficult task. In addition, the use of Lego method for prediction of heat capacity requires prediction of critical temperature
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of IL by another group contribution method. This also brings uncertainty for this approach
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because it is reported that different methods such as group contribution methods for prediction of critical temperature of ILs are not able to provide reliable predictions [37].
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Zhao et al. [33] developed two models for prediction of heat capacity of ILs named multiple linear regression (MLR) and extreme learning machine (ELM) methods. The input
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parameters of these models were temperature, molecular weight of ionic liquid and several molecular descriptors based on quantum-chemical based charge distribution area ( S profile ) of
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ILs. They used 2416 experimental data from 46 ILs. They concluded that although both models provided acceptable predictions; the ELM method was superior to MLR method and presented more accurate predictions.
Albert and Müller [38] utilized first order group contributions to describe the structure of ions. They utilized 2419 experimental data from 106 ILs for development of their models. They separated their data points into two subsets for data fitting and testing to evaluate the performance of their method. Their model provided a mean absolute error of 5.4% for test data. The fact that their model is an ion contribution model brings applicability limitations for this model. In another word, this model is limited to those particular ILs that the groups have been predetermined.
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ACCEPTED MANUSCRIPT This work focuses on prediction of heat capacity of ILs using two soft computing approaches named radial basis function neural network (RBF-NN) and multilayer perceptron
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neural network (MLP-NN). The predictions of developed models in present work were also
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compared with predictions of Farahani et al. [26] and Ahmadi et al. [32] correlations and it was
Artificial Neural Networks (ANNs)
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observed that developed models present more accurate results.
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ANNs are simple and accurate modeling tools which their concept was inspired from human brain functionality. Their structure composes of specific processing units called neurons
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which are arranged in layers and work in parallel. ANNs exhibit unique characteristics such as capability for processing large data sets, fast modeling process, capability to recognize the
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existing patterns between input and output data and good generalization ability [39-41]. There are basically two types of ANNs named Radial Basis Function Neural Networks (RBF-NNs) and Multilayer Perceptron Neural Networks (MLP-NNs) which are described here briefly.
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Radial Basis Function Neural Networks (RBF-NNs) One of the most useful types of ANNs is radial basis function neural networks (RBF-NNs).
These networks have three layers including a fixed hidden layer and one input and one output layer [40, 42-44]. Every neuron in the hidden layer holds a radial activation function [42]. During training process of a RBF-NN model first, it is required to evaluate the weight terms. Next, the training data is used to train the model by optimizing the structural related parameters of network. Usually a cost function such as average absolute relative deviation (AARD%) or 6
ACCEPTED MANUSCRIPT mean square error (MSE) between model outputs and actual data is utilized as an indication for training the model [45]. After training the structure of model the next step is to evaluate the
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performance of model in prediction of unseen data or test data [46]. The main characteristics of
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RBF-NNs are as follows [43, 45, 47, 48]:
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1. The network training composes of two steps: initially the weights from input to hidden layer, and then weights from hidden to output layer.
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2. The Gaussian type activation functions are usually decided for neurons in hidden layer.
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3. They have significant interpolation ability toward nonlinear functions. 4. They exhibit faster learning and training process compared to other ANN algorithms.
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In modeling with RBF-NNs, the purpose is to determine a function f(x) such
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that f (Xp ) t p 1,..., D in which t is the target vector, D is the number of input parameters
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and Xp is the
p-th input vector. For this respect, it is needed to map each one of D-dimensional input
X p [X ip :1,2,..., N ] onto the output t . The RBF-NN uses N basic functions (radial activation functions). The input of these functions is the Euclidian distance between each input parameter and its center denoted by ( x x p ) where is the activation function. The x x p term is the Euclidian
distance.
In
addition,
the
output
function
has
the
general
form
of:
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f (x) w p( x x p ) . Hence the final formulation for output of a RBF-NN can be expressed p 1
as: f (xq )
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w ( x p 1
p
q
x p ) tq . This equation can be represented in matrix form by
defining: t {t p}, w {wp} , and {pq ( x q x p )} as the output, weight and activation
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ACCEPTED MANUSCRIPT function matrixes. Hence, the matrix form of aforementioned equation is expressed as w t and matrix inversion techniques can be performed to give w 1 t .
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Thus far, various empirical and theoretical methods have been utilized to show the
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independency of some qualities of interpolating function to the accurate form of main
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function (r) . The Gaussian function is one of the widely used radial basis kernel functions represented as below:
r2 ) 2 2
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(r) exp(
(1)
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In this equation r>0 denotes the distance from a center c to a data point x and the parameter
Multilayer Perceptron Neural Networks (MLP-NNs)
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2.2
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determines the smoothness of interpolating function.
Similar to RBF-NNs, these networks also compose of three layers. However, the hidden layer of MLP-NNs is not single and it is possible to define several numbers of hidden layers for these networks. The neurons which are located in hidden layers are linked to each other with different weight terms. These weight terms indicate the relative impact of output of neuron on the total output of MLP-NN. Each neuron accepts its corresponding input vector and multiplies it with a weight vector and sums the result with a bias term. Then, it applies a transfer function on the resultant. The output of a hidden neuron in MLP-NN can be formulated as follows [49]:
N Y i f w ij x i bi j 1
(2)
In which Yi is the output of i-th neuron, f is the transfer function, wij is the j-th weight term of i-th neuron, N is the number of data points, xi is the input of i-th neuron and bi is the bias term 8
ACCEPTED MANUSCRIPT of i-th neuron. The output of a neuron will be the input signal for next neuron in the following layer. There are various types of transfer functions which can be utilized in hidden neurons of
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MLP-NN; however, the purelin, hyperbolic tangent sigmoid (tansig) and logarithm sigmoid
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(logsig) are three popular types which are widely used by researchers. The purelin type transfer function is usually used for output layer, while tansig and logsig transfer functions are frequently
1 1e Si
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Logsig: f (S i )
e Si e Si e Si e Si
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Tansig: f (S i )
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utilized in neurons of hidden layer. The formulation of these functions is as follows [50]:
(4) (5)
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Purelin: f (S i ) S i
(3)
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formulated as below:
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Where Si is the sum of weighted inputs and the bias term of i-th neuron which is
S i w ij x i bi j 1
(6)
The weight terms are internal adjustable parameters of MLP-NNs. These weight terms should be optimized by a proper algorithm to provide a more accurate performance for developed model. The process of determining the optimum weight terms for these networks is called the training of network. A cost function such as AARD% or MSE is utilized to determine the performance of network during training process. The optimum weight terms are those in which minimize this cost function. The back propagation (BP) algorithms are utilized to determine the optimum weight values in these networks. There are different types of BP algorithms such as Levenberg-Marquardt (LM), Scaled Conjugate Gradient (SCG), Resilient Back Propagation (RBP), etc [49]. However, the LM method is most popular among other
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ACCEPTED MANUSCRIPT methods because it provides stable training process and fast convergence of network to optimum
Data acquisition
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3.1
Results and discussion
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solution [51]. In present work the LM technique was utilized to train the developed network.
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It is of great importance to use reliable and extensive data in the process of development of a model for prediction of physical properties of various compounds. As a result, in this work a
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number of 2940 experimental heat capacity data from 56 ILs at various temperatures were gathered from published works in literature [52-74]. The name of ILs, the experimental data and
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the references at which each experimental data was used is provided as Supplementary Material
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in an Excel file. The input parameters of both models were temperature, molecular weight of IL,
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number of carbon atoms in cation part of IL (CC), number of carbon atoms in anion part of IL (CA), number of IL nitrogen atoms (N ), number of IL sulfur atoms (S), number of IL oxygen atoms (O), number of IL phosphorous atoms (P), number of IL fluorine atoms (F ), number of IL bromine atoms (Br ), number of IL chlorine atoms (Cl ), number of IL boron atoms (B) and the number of hydrogen atoms in anion part (nHA). The heat capacity of IL was also the output parameter of both models. Table 1 shows the detail analysis of input and output parameters of developed models.
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ACCEPTED MANUSCRIPT 3.2
Model development
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3.2.1 RBF-NN model In this work the Matlab® 2014a environment was used to model the heat capacity values
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with RBF-NN model. First, two subsets of train and test data were used. The initial structure of
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RBF model was constructed by using the train data. The test data was implemented to evaluate
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the performance and reliability of model in estimation of unseen data. About 80% of data were used for training phase and the remaining 20% was utilized for testing phase. The performance
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and accuracy of RBF model is significantly affected by two tuning parameters which are in its structure. These parameters are named maximum number of neurons (MNN) and spread
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respectively. As a result, evaluating the optimum values of these parameters will provide a more
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accurate and reliable performance for implemented model. The trial and error approach was used
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in this work to evaluate the optimum parameters of spread and MNN. Consequently, the values of MNN and spread were changed and the performance of model for prediction of target heat capacity data was examined. The performance of model was evaluated by recording the overall average absolute relative deviation (AARD%) value between model estimations and target data as a cost function. The AARD% value is defined by following formula:
AARD%
100 N (Cp, P red (i) Cp, Exp(i)) N Cp, Exp(i) i1
(7)
Where Cp,Pred is predicted heat capacity and Cp,Exp is actual heat capacity. The optimum values are those which provide the minimum AARD% value for implemented model. Table 2 presents some of the trial and error iterations conducted for evaluating the best values of spread and MNN. According to this table the optimum values which provide most accurate performance for RBF model are 45 and 200 for spread and MNN, respectively. 11
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3.2.2 MLP-NN model For development of MLP-NN model 80% of data were also utilized for train set and 20%
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of data was used for test set. As mentioned earlier, it is possible to define several numbers of
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hidden layers for a MLP-NN model; however, according to literature works [50, 51] using one
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hidden layer is sufficient to accurately model a nonlinear data modeling process. In present work, in addition to networks with one hidden layer, the performance of different networks with two
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and three hidden layers was also examined. However, it was observed that accuracy of estimations of these networks was not significantly different from networks with one hidden
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layer. Moreover, in most situations the accuracy of networks with one hidden layer was better
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than two and three hidden layer networks. Hence, in order to develop a simple model, the
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performance of different networks with one hidden layer was examined by using the overall AARD% of their predictions. In all networks the transfer function of output layer was purelin and the transfer function of hidden layer was tansig. As mentioned before, the LM algorithm was used to train the structure of networks. Figure shows the change in total AARD% of different networks with different numbers of neurons in hidden layer. According to this figure the network with 12 neurons in hidden layer exhibits the lowest AARD% value and is the best network structure for prediction of experimental heat capacity values.
3.3
Accuracy of the proposed model and validation In order to examine the accuracy of outcomes of developed models for estimation of actual
heat capacity data it is important to evaluate the statistical parameters of proposed models. For 12
ACCEPTED MANUSCRIPT this respect, the statistical parameters of models such as correlation factor (R2), Average Absolute Relative Deviation (AARD%), Standard Deviation (STD), and Root Mean Square
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Error (RMSE) (Equations (8)-(11)) are measured for different subsets of train, test and total data
(C i1
(i) Cp, Exp(i))2
p, P red
(i) Cp, Exp)
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i1 N
p, P red
2
(C
RMSE ( i1
p, P red
(i) Cp, Exp(i))2 N
N
(Cp, P red (i) Cp, Exp(i))2
i1
N
(9)
(10)
)0.5
(11)
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STD (
)0.5
(8)
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N
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100 N (Cp, P red (i) Cp, Exp(i)) N Cp, Exp(i) i1
AARD%
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R2 1
(C
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and are presented in Table 3. The formulation of these parameters is as below:
Table 3 indicates that the RBF-NN model has a low AARD% value of 0.828 for total data which reveals that the model is able to estimate the target data with lowest possible error. Furthermore, the overall R2 value of 0.9931 indicates the accuracy and effectiveness of model in reproduction of target data. In addition, the R2 and AARD% values of MLP-NN model are 0.9919 and 1.042 respectively. This indicates that the RBF-NN model provides better predictions compared to MLP-NN model. Figure
depicts the cross plot of data points which is the
comparison between estimated data by proposed models and actual data. It is clear from this figure that in the case of both models, the distributions of data points construct a unit slope line which indicates that the outcomes of proposed models and target values are in acceptable agreement. The relative error distribution plot of estimations of proposed models versus
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ACCEPTED MANUSCRIPT experimental data is shown in Figure . According to this figure, a significant concentration of data points near the line with zero relative error for both models indicates that these models
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could estimate the total set of target data with an acceptable error. The maximum deviation of estimations of RBF-NN model is no more than 23% and most of data points fall in the area
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between relative deviations of 5%. The relative errors of MLP-NN model also are mostly
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concentrated in region with relative deviations between 10%. In the case of eliminating a data
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point with an absolute relative error of 59%, the maximum relative error of MLP-NN model is no more than 20%. This also indicates that the MLP-NN model exhibits predictions with
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reasonable relative errors; however, the accuracy and reliability of RFB-NN model is higher than MLP-NN model. Figure shows the trend plot of experimental and estimated values plotted
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versus the index of data points. According to this figure the predictions of both models are appropriately follow the trend of experimental data which indicates acceptable accuracy of
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implemented models.
At this point the predictions of RBF-NN and MLP-NN models will be compared with two recently developed literature correlations for prediction of heat capacity of ILs. These correlations were proposed by Farahani et al. [26] and Ahmadi et al. [32]. The details of these correlations including their input parameters and constant coefficients are represented in Appendix A. The statistical parameters of these correlations are listed in Table 4. Figure also shows the graphical comparison between statistical parameters of proposed models and literature correlations. It is evident that the RBF-NN and MLP-NN models are superior to two other correlations and provide better estimations thank to higher R2 and lower values of AARD%, RMSE and STD. Figure
also shows the cumulative frequency of developed models and
literature correlations against their absolute relative errors. This figure indicates that the RBF-
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ACCEPTED MANUSCRIPT NN and MLP-NN models are able to predict about 95% and 92% of data points with errors less than 5%. However, the Farahani et al. [26] and Ahmadi et al. [32] correlations are able to predict
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about 80% and 74% of data with an error less than 5%. This also indicates the accuracy and
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reliability of proposed models in present work over literature correlations.
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4. Conclusion
In this work, two models namely RBF-NN and MLP-NN were developed for prediction of
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heat capacity of ILs. An extensive database including 2940 data points from 56 ILs was used to develop a general model. The tuning parameters of developed models were determined by trial
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and error approach. The predictions of developed models were evaluated by utilizing various
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statistical and graphical methods. Results showed that the RBF-NN model presents accurate
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predictions compared to MLP-NN model with an overall AARD% and R2 of 0.828 and 0.9931. The predictions of developed models were also compared with two literature correlations and it was concluded that the developed models present more accurate and reliable results. As the developed models exhibit acceptable generality, results of these models can be used in situations in which rapid and accurate prediction of heat capacity of ILs is required.
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Correlation
Formula
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Appendix A. literature correlations for prediction of heat capacities of ILs
C p 122.16826 0.45794T 12.8395N C 56.85424CH 3RC 19.25836N a 11.36109nH a N C number of atoms of cation, Na number of atoms of anion, CH3RC number of methyl groups in cation counter parts nHa number of hydrogen atoms in anion, T=temperature
Ahmadi et al. [32]
C p 0.2808T 1.0854 17.5066ln(T ) 0.6593MW 1.0793 15.9932C A 16.1292CC 2.8956N 11.7667S 1.3729O 4.1977(F Br Cl ) 6.7438B 12.399 T temperature, MW=molecular weight of IL, CA number of carbon atoms of anion, CC number of carbon atoms of cation N , S ,O , F , Br , Cl and B =number of nitrogen, sulfur, oxygen, fluorine, bromine, chlorine and boron atoms of IL
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Farahani et al. [26]
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Appendix B. Instructions for running the program
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First download the Supplementary file then change the directory of Matlab® (Version 2014) to the download folder. Use below stages to get a response from model:
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1. Open the “Sample.xlsx” file. Two sheets are located in this file named “Input” and “Output”.
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In the “Input” sheet fill the specified cells. It is possible to fill more than one data sample. Save and close the Excel file.
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2. Open and run the “Sample.m” file by Matlab®.
3. After running the “Sample.m” file go to “Output” sheet of the “Sample.xlsx”. The results of
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RBF-NN and MLP-NN models are provided in the corresponding cell (Cell A3 for RBF-NN
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model and Cell B3 for MLP-NN model).
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To better use the instruction of RBF-NN and MLP-NN models, below example has been provided.
Example: Calculate the heat capacity of IL by RBF-NN and MLP-NN models with the following data:
Mw
T (K)
nHA
CA
CC
N
S
O
F
Br
Cl
B
2
0
0
6
0
0
0
(g/mol) 300.81
0
0
8
284.2
Solution: Open the “Sample.m” and run it then turn to “Output” sheet of “sample.xlsx” file to see the predicted value of the heat capacity of IL.
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(the absolute relative deviation is 0.31%)
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imide [C4mim] NTf2 ionic liquid, The Journal of Physical Chemistry B, 112 (2008) 4357-4364.
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Thermodynamics, 41 (2009) 161-166.
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calculations, The Journal of Chemical Thermodynamics, 41 (2009) 334-341. [64] Y. Paulechka, A. Blokhin, G. Kabo, A. Strechan, Thermodynamic properties and
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polymorphism of 1-alkyl-3-methylimidazolium bis (triflamides), The Journal of Chemical Thermodynamics, 39 (2007) 866-877.
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[65] Y. Paulechka, G. Kabo, A. Blokhin, A. Shaplov, E. Lozinskaya, Y.S. Vygodskii, Thermodynamic properties of 1-alkyl-3-methylimidazolium bromide ionic liquids, The Journal of Chemical Thermodynamics, 39 (2007) 158-166. [66] J. Troncoso, C.A. Cerdeiriña, Y.A. Sanmamed, L. Romaní, L.P.N. Rebelo, Thermodynamic properties of imidazolium-based ionic liquids: densities, heat capacities, and enthalpies of fusion of [bmim][PF6] and [bmim][NTf2], Journal of Chemical & Engineering Data, 51 (2006) 18561859. [67] G.J. Kabo, A.V. Blokhin, Y.U. Paulechka, A.G. Kabo, M.P. Shymanovich, J.W. Magee, Thermodynamic properties of 1-butyl-3-methylimidazolium hexafluorophosphate in the condensed state, Journal of Chemical & Engineering Data, 49 (2004) 453-461.
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pp. 121-133.
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mim][BF 4]+ water as a case study to model ionic liquid aqueous solutions, Green Chemistry, 6
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(2004) 369-381.
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ethanol: Experimental results and theoretical description using the ERAS model, Fluid Phase Equilibria, 274 (2008) 59-67.
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[71] K.-S. Kim, B.-K. Shin, H. Lee, F. Ziegler, Refractive index and heat capacity of 1-butyl-3methylimidazolium bromide and 1-butyl-3-methylimidazolium tetrafluoroborate, and vapor
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pressure of binary systems for 1-butyl-3-methylimidazolium bromide+ trifluoroethanol and 1butyl-3-methylimidazolium tetrafluoroborate+ trifluoroethanol, Fluid Phase Equilibria, 218 (2004) 215-220.
[72] Y. Shimizu, Y. Ohte, Y. Yamamura, K. Saito, Effects of thermal history on thermal anomaly in solid of ionic liquid compound,[C4mim][Tf2N], Chemistry letters, 36 (2007) 14841485. [73] A.V. Blokhin, Y.U. Paulechka, G.J. Kabo, Thermodynamic properties of [C6mim][NTf2] in the condensed state, Journal of Chemical & Engineering Data, 51 (2006) 1377-1388. [74] C. Nieto de Castro, M. Lourenço, A. Ribeiro, E. Langa, S. Vieira, P. Goodrich, C. Hardacre, Thermal properties of ionic liquids and ionanofluids of imidazolium and pyrrolidinium liquids†, Journal of Chemical & Engineering Data, 55 (2009) 653-661.
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neurons.
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Figure 1. Variation of total AARD% of different MLP networks with the number of hidden
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(a)
(b)
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MLP-NN model.
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Figure 2. Cross plot predicted heat capacity data against target data: (a) RBF-NN model, (b)
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(a)
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Figure 3. Relative deviation plot of predictions of the developed models: (a) RBF-NN, (b) MLP-
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NN.
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Figure 4. Trend plot of experimental and estimated heat capacity data versus index of data: (a) RBF-NN, (b) MLP-NN.
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(b)
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Figure 5. Graphical comparison between statistical parameters of the developed models and the literature correlations: (a) R2, (b) AARD%, (c) RMSE, and (d) STD.
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literature correlations.
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Figure 6. Cumulative frequency versus absolute relative error for the developed models and the
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Table 1. Details of input and output data of RBF-NN model. Min.
Temperature (K)
Input
188.06
Molecular weight (g/mol)
Input
174.7
CC
Input
CA
Input
nHA
Input
N
Input
S
Max.
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Status
Average 372.15
763.21
315.39
6
32
8.43
0
20
0.85
0
37
0.73
1
5
2.18
Input
0
2
0.62
O
Input
0
9
1.55
F
0
15
4.92
Input
0
1
0.01
Input
0
1
0.005
Input
0
1
0.04
Output
226
1413
499.76
B Cp (J/mol.K)
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Cl
Input
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Br
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Parameter
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Table 2. The results of several trial and error approaches for evaluating the optimum values of
MNN
50
200
50
170
50
120
50
Total AARD% 0.9075 0.9019
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1.0769 1.5299
170
0.9264
130
1.1613
80
1.5946
60
1.8806
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Spread
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Spread and MNN.
200
0.8693
40
160
1.3126
40
110
1.2232
40
70
1.8699
30
200
0.9255
30
180
0.9598
30
140
1.1545
30
70
2.0308
20
200
1.1245
20
170
1.2523
20
120
1.8407
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0.8283
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2.5101
10
200
2.0994
10
170
2.2601
10
140
10
90
10
50
5
200
5
170
5
130
4.0033 6.1316 1.94
70
4.7583
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2.4167
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2.9394
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3.1305
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Table 3. Statistical parameters of the developed models for prediction of experimental heat
AARD%
Train data
0.9944
0.767
Test data
0.9861
Total data
0.9931
Train data
0.9941
Test data
0.9910
Total data
0.9919
RMSE
0.0207
9.30
1.071
0.0406
12.93
0.828
0.0259
10.13
1.038
0.0241
10.59
1.056
0.0265
11.17
1.042
0.0260
11.05
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STD
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MLP-NN
R2
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RBF-NN
Data set
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Model
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capacity data.
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Table 4. Statistical parameters of the literature correlations for prediction of experimental data.
Farahani et al. [26]
0.9753
2.48
Ahmadi et al. [32]
0.9612
2.73
STD
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AARD%
0.0451
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0.0531
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R2
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Correlation
RMSE 19.18 24.14
ACCEPTED MANUSCRIPT Research Highlights Two models namely RBF-NN and MLP-NN were developed for prediction of heat
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capacities of ILs.
The input parameters of the models are temperature, molecular weight of IL and chemical
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structure information.
The models were developed based on 2940 experimental data for 56 ILs.
Results show that the developed models are accurate and reliable and are superior to
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literature correlations.
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S0167-7322(16)32695-2 doi: 10.1016/j.molliq.2016.11.119 MOLLIQ 6666
To appear in:
Journal of Molecular Liquids
Received date: Revised date: Accepted date:
11 September 2016 20 October 2016 27 November 2016
Please cite this article as: Ali Barati-Harooni, Adel Najafi-Marghmaleki, Amir H Mohammadi, Prediction of heat capacities of ionic liquids using chemical structure based networks, Journal of Molecular Liquids (2016), doi: 10.1016/j.molliq.2016.11.119
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Prediction of Heat Capacities of Ionic Liquids Using Chemical Structure based Networks
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Ali Barati-Harooni,a1 Adel Najafi-Marghmaleki,a Amir H Mohammadib,c,d 2
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Young Researchers and Elite Club, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran Discipline of Chemical Engineering, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban 4041, South Africa c Institut de Recherche en Génie Chimique et Pétrolier (IRGCP), Paris Cedex, France d Département de Génie des Mines, de la Métallurgie et des Matériaux, Faculté des Sciences et de Génie, Université Laval, Québec, QC G1V 0A6, Canada
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Abstract - Ionic liquids (ILs) have various desired properties which bring them as useful and
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applicable compounds in different industrial processes. Heat capacity of ILs is one of the main
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properties of them which is required in various engineering and design applications. Hence, developing accurate and general models for prediction of this property is important. In this
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communication, two accurate and general models based on radial basis function neural network (RBF-NN) and multilayer perceptron neural network (MLP-NN) were developed for estimation of heat capacities of ILs. The input parameters of the models are temperature, molecular weight of IL and several structural related parameters for each IL. The models were developed based on 2940 experimental data for 56 ILs. The reliability and accuracy of predictions of the developed models were examined by using statistical and graphical methods as well as comparing the results of the models with outcomes of recently developed literature correlations. Results show that the developed models are accurate and reliable and are superior to literature correlations for
Corresponding author: 1 1. Email Address: [email protected] (A. Barati-Harooni) 2
2. Email Address: [email protected] and [email protected] (A. H. Mohammadi)
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ACCEPTED MANUSCRIPT predictions of heat capacity of ILs. The average absolute relative deviation of RBF-NN and
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MLP-NN models for predicted heat capacity data was 0.828% and 1.042% respectively.
Keywords - Ionic liquid (IL); Heat capacity; Chemical structure; Model; Radial basis function
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neural network (RBF-NN); Multilayer perceptron neural network (MLP-NN).
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Introduction
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Ionic liquids (ILs) are compounds composed of large cation and anion parts which are
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liquid salts at temperatures below 100 oC because at these temperatures their ions fail to pack
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appropriately. ILs have different characteristics from common salts which normally have melting
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points higher than 100 oC [1-10].
ILs are interesting compounds which are applied in various applications including
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batteries, solar cells, solvents, thermal fluids, etc. This diverse application of ILs is because their structure is tunable. In another word, it is possible to alter the type, branching and lengths of
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anion and cation parts in an IL to achieve a desired property [11]. ILs possess various unique
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viscosity, etc [12].
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characteristics such as nearly low volatility, relative high thermal and chemical stability, tunable
Because of the increase in the applications of ILs in industrial processes, a significant number of publications that theoretically and experimentally have focused on evaluation and prediction of physicochemical properties of ILs and the possibility of their use in various applications can be found in literature [6, 13-25]. One of the most important properties of ILs is their heat capacity which is required to determine the heat transfer in industrial design units including reactors and heat exchangers [26]. Literature review shows that there are few reports concerning prediction of heat capacity for ILs [26-33]. Preiss et al. [28] proposed a two parameter model for estimation of heat capacity of ILs based on relation between molar volume and heat capacity. However, the dependency of heat capacity to temperature was not considered in their model.
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ACCEPTED MANUSCRIPT Gardas and Coutinho [27] predicted heat capacity of ILs by focusing on the concept of second order group additivity. They used a number of 2400 data from 19 ILs. However, their
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databank was gathered from few citations which bring limitations in generalization ability of
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their model.
Soriano et al. [29] predicted the heat capacity of 32 ILs using 3149 data points. They
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utilized a similar approach to the work done by Gardas and Coutinho [27]. However, their model
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presents inefficient results for estimation of heat capacity of ILs which their cation or anion groups were not considered in their data set for example ammonium-based ILs.
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Farahani et al. [26] also developed a temperature dependent five parameter model for prediction of heat capacity of ILs. In addition to temperature, they used four structural related
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parameters for development of their model. The average absolute relative deviation of their predictions was 2.5%. Sattari et al. [34, 35] published two different works for prediction of heat
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capacity of ILs using 3726 data from 82 ILs. In their first work, they used the combination of group contribution method and genetic function approximation and they obtained an average relative deviation of 1.68%. In the second work they used the concept of quantitative structure– property relationship (QSPR) for prediction of heat capacity of ILs. Recently, Ahmadi et al. [32] also proposed a 12 parameter correlation for prediction of heat capacity of ILs. The input parameters of their correlation were temperature, molecular weight of IL and several structural related parameters. Their correlation predicted the experimental data with an average absolute relative deviation of 5.8%. Nancarrow et al. [36] used two group contribution methods called Meccano and Lego approaches for prediction of heat capacity of ILs. They utilized 2396 experimental data from 19 ILs for development of the models. They concluded that although the Meccano approach provided better predictions, the
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ACCEPTED MANUSCRIPT applicability domain of Lego approach is higher than Meccano method. The experimental data utilized in this work covers a limited number of 19 ILs. Moreover, the use of their methods
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requires determination of various structural related parameters for each IL which restricts the
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applicability of these models and makes the computational process a difficult task. In addition, the use of Lego method for prediction of heat capacity requires prediction of critical temperature
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of IL by another group contribution method. This also brings uncertainty for this approach
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because it is reported that different methods such as group contribution methods for prediction of critical temperature of ILs are not able to provide reliable predictions [37].
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Zhao et al. [33] developed two models for prediction of heat capacity of ILs named multiple linear regression (MLR) and extreme learning machine (ELM) methods. The input
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parameters of these models were temperature, molecular weight of ionic liquid and several molecular descriptors based on quantum-chemical based charge distribution area ( S profile ) of
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ILs. They used 2416 experimental data from 46 ILs. They concluded that although both models provided acceptable predictions; the ELM method was superior to MLR method and presented more accurate predictions.
Albert and Müller [38] utilized first order group contributions to describe the structure of ions. They utilized 2419 experimental data from 106 ILs for development of their models. They separated their data points into two subsets for data fitting and testing to evaluate the performance of their method. Their model provided a mean absolute error of 5.4% for test data. The fact that their model is an ion contribution model brings applicability limitations for this model. In another word, this model is limited to those particular ILs that the groups have been predetermined.
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ACCEPTED MANUSCRIPT This work focuses on prediction of heat capacity of ILs using two soft computing approaches named radial basis function neural network (RBF-NN) and multilayer perceptron
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neural network (MLP-NN). The predictions of developed models in present work were also
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compared with predictions of Farahani et al. [26] and Ahmadi et al. [32] correlations and it was
Artificial Neural Networks (ANNs)
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observed that developed models present more accurate results.
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ANNs are simple and accurate modeling tools which their concept was inspired from human brain functionality. Their structure composes of specific processing units called neurons
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which are arranged in layers and work in parallel. ANNs exhibit unique characteristics such as capability for processing large data sets, fast modeling process, capability to recognize the
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existing patterns between input and output data and good generalization ability [39-41]. There are basically two types of ANNs named Radial Basis Function Neural Networks (RBF-NNs) and Multilayer Perceptron Neural Networks (MLP-NNs) which are described here briefly.
2.1
Radial Basis Function Neural Networks (RBF-NNs) One of the most useful types of ANNs is radial basis function neural networks (RBF-NNs).
These networks have three layers including a fixed hidden layer and one input and one output layer [40, 42-44]. Every neuron in the hidden layer holds a radial activation function [42]. During training process of a RBF-NN model first, it is required to evaluate the weight terms. Next, the training data is used to train the model by optimizing the structural related parameters of network. Usually a cost function such as average absolute relative deviation (AARD%) or 6
ACCEPTED MANUSCRIPT mean square error (MSE) between model outputs and actual data is utilized as an indication for training the model [45]. After training the structure of model the next step is to evaluate the
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performance of model in prediction of unseen data or test data [46]. The main characteristics of
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RBF-NNs are as follows [43, 45, 47, 48]:
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1. The network training composes of two steps: initially the weights from input to hidden layer, and then weights from hidden to output layer.
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2. The Gaussian type activation functions are usually decided for neurons in hidden layer.
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3. They have significant interpolation ability toward nonlinear functions. 4. They exhibit faster learning and training process compared to other ANN algorithms.
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In modeling with RBF-NNs, the purpose is to determine a function f(x) such
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that f (Xp ) t p 1,..., D in which t is the target vector, D is the number of input parameters
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and Xp is the
p-th input vector. For this respect, it is needed to map each one of D-dimensional input
X p [X ip :1,2,..., N ] onto the output t . The RBF-NN uses N basic functions (radial activation functions). The input of these functions is the Euclidian distance between each input parameter and its center denoted by ( x x p ) where is the activation function. The x x p term is the Euclidian
distance.
In
addition,
the
output
function
has
the
general
form
of:
N
f (x) w p( x x p ) . Hence the final formulation for output of a RBF-NN can be expressed p 1
as: f (xq )
N
w ( x p 1
p
q
x p ) tq . This equation can be represented in matrix form by
defining: t {t p}, w {wp} , and {pq ( x q x p )} as the output, weight and activation
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ACCEPTED MANUSCRIPT function matrixes. Hence, the matrix form of aforementioned equation is expressed as w t and matrix inversion techniques can be performed to give w 1 t .
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Thus far, various empirical and theoretical methods have been utilized to show the
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independency of some qualities of interpolating function to the accurate form of main
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function (r) . The Gaussian function is one of the widely used radial basis kernel functions represented as below:
r2 ) 2 2
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(r) exp(
(1)
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In this equation r>0 denotes the distance from a center c to a data point x and the parameter
Multilayer Perceptron Neural Networks (MLP-NNs)
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2.2
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determines the smoothness of interpolating function.
Similar to RBF-NNs, these networks also compose of three layers. However, the hidden layer of MLP-NNs is not single and it is possible to define several numbers of hidden layers for these networks. The neurons which are located in hidden layers are linked to each other with different weight terms. These weight terms indicate the relative impact of output of neuron on the total output of MLP-NN. Each neuron accepts its corresponding input vector and multiplies it with a weight vector and sums the result with a bias term. Then, it applies a transfer function on the resultant. The output of a hidden neuron in MLP-NN can be formulated as follows [49]:
N Y i f w ij x i bi j 1
(2)
In which Yi is the output of i-th neuron, f is the transfer function, wij is the j-th weight term of i-th neuron, N is the number of data points, xi is the input of i-th neuron and bi is the bias term 8
ACCEPTED MANUSCRIPT of i-th neuron. The output of a neuron will be the input signal for next neuron in the following layer. There are various types of transfer functions which can be utilized in hidden neurons of
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MLP-NN; however, the purelin, hyperbolic tangent sigmoid (tansig) and logarithm sigmoid
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(logsig) are three popular types which are widely used by researchers. The purelin type transfer function is usually used for output layer, while tansig and logsig transfer functions are frequently
1 1e Si
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Logsig: f (S i )
e Si e Si e Si e Si
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Tansig: f (S i )
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utilized in neurons of hidden layer. The formulation of these functions is as follows [50]:
(4) (5)
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Purelin: f (S i ) S i
(3)
N
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formulated as below:
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Where Si is the sum of weighted inputs and the bias term of i-th neuron which is
S i w ij x i bi j 1
(6)
The weight terms are internal adjustable parameters of MLP-NNs. These weight terms should be optimized by a proper algorithm to provide a more accurate performance for developed model. The process of determining the optimum weight terms for these networks is called the training of network. A cost function such as AARD% or MSE is utilized to determine the performance of network during training process. The optimum weight terms are those in which minimize this cost function. The back propagation (BP) algorithms are utilized to determine the optimum weight values in these networks. There are different types of BP algorithms such as Levenberg-Marquardt (LM), Scaled Conjugate Gradient (SCG), Resilient Back Propagation (RBP), etc [49]. However, the LM method is most popular among other
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Data acquisition
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3.1
Results and discussion
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solution [51]. In present work the LM technique was utilized to train the developed network.
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It is of great importance to use reliable and extensive data in the process of development of a model for prediction of physical properties of various compounds. As a result, in this work a
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number of 2940 experimental heat capacity data from 56 ILs at various temperatures were gathered from published works in literature [52-74]. The name of ILs, the experimental data and
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the references at which each experimental data was used is provided as Supplementary Material
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in an Excel file. The input parameters of both models were temperature, molecular weight of IL,
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number of carbon atoms in cation part of IL (CC), number of carbon atoms in anion part of IL (CA), number of IL nitrogen atoms (N ), number of IL sulfur atoms (S), number of IL oxygen atoms (O), number of IL phosphorous atoms (P), number of IL fluorine atoms (F ), number of IL bromine atoms (Br ), number of IL chlorine atoms (Cl ), number of IL boron atoms (B) and the number of hydrogen atoms in anion part (nHA). The heat capacity of IL was also the output parameter of both models. Table 1 shows the detail analysis of input and output parameters of developed models.
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Model development
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3.2.1 RBF-NN model In this work the Matlab® 2014a environment was used to model the heat capacity values
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with RBF-NN model. First, two subsets of train and test data were used. The initial structure of
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RBF model was constructed by using the train data. The test data was implemented to evaluate
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the performance and reliability of model in estimation of unseen data. About 80% of data were used for training phase and the remaining 20% was utilized for testing phase. The performance
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and accuracy of RBF model is significantly affected by two tuning parameters which are in its structure. These parameters are named maximum number of neurons (MNN) and spread
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respectively. As a result, evaluating the optimum values of these parameters will provide a more
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accurate and reliable performance for implemented model. The trial and error approach was used
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in this work to evaluate the optimum parameters of spread and MNN. Consequently, the values of MNN and spread were changed and the performance of model for prediction of target heat capacity data was examined. The performance of model was evaluated by recording the overall average absolute relative deviation (AARD%) value between model estimations and target data as a cost function. The AARD% value is defined by following formula:
AARD%
100 N (Cp, P red (i) Cp, Exp(i)) N Cp, Exp(i) i1
(7)
Where Cp,Pred is predicted heat capacity and Cp,Exp is actual heat capacity. The optimum values are those which provide the minimum AARD% value for implemented model. Table 2 presents some of the trial and error iterations conducted for evaluating the best values of spread and MNN. According to this table the optimum values which provide most accurate performance for RBF model are 45 and 200 for spread and MNN, respectively. 11
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3.2.2 MLP-NN model For development of MLP-NN model 80% of data were also utilized for train set and 20%
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of data was used for test set. As mentioned earlier, it is possible to define several numbers of
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hidden layers for a MLP-NN model; however, according to literature works [50, 51] using one
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hidden layer is sufficient to accurately model a nonlinear data modeling process. In present work, in addition to networks with one hidden layer, the performance of different networks with two
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and three hidden layers was also examined. However, it was observed that accuracy of estimations of these networks was not significantly different from networks with one hidden
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layer. Moreover, in most situations the accuracy of networks with one hidden layer was better
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than two and three hidden layer networks. Hence, in order to develop a simple model, the
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performance of different networks with one hidden layer was examined by using the overall AARD% of their predictions. In all networks the transfer function of output layer was purelin and the transfer function of hidden layer was tansig. As mentioned before, the LM algorithm was used to train the structure of networks. Figure shows the change in total AARD% of different networks with different numbers of neurons in hidden layer. According to this figure the network with 12 neurons in hidden layer exhibits the lowest AARD% value and is the best network structure for prediction of experimental heat capacity values.
3.3
Accuracy of the proposed model and validation In order to examine the accuracy of outcomes of developed models for estimation of actual
heat capacity data it is important to evaluate the statistical parameters of proposed models. For 12
ACCEPTED MANUSCRIPT this respect, the statistical parameters of models such as correlation factor (R2), Average Absolute Relative Deviation (AARD%), Standard Deviation (STD), and Root Mean Square
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Error (RMSE) (Equations (8)-(11)) are measured for different subsets of train, test and total data
(C i1
(i) Cp, Exp(i))2
p, P red
(i) Cp, Exp)
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i1 N
p, P red
2
(C
RMSE ( i1
p, P red
(i) Cp, Exp(i))2 N
N
(Cp, P red (i) Cp, Exp(i))2
i1
N
(9)
(10)
)0.5
(11)
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STD (
)0.5
(8)
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N
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100 N (Cp, P red (i) Cp, Exp(i)) N Cp, Exp(i) i1
AARD%
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R2 1
(C
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N
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and are presented in Table 3. The formulation of these parameters is as below:
Table 3 indicates that the RBF-NN model has a low AARD% value of 0.828 for total data which reveals that the model is able to estimate the target data with lowest possible error. Furthermore, the overall R2 value of 0.9931 indicates the accuracy and effectiveness of model in reproduction of target data. In addition, the R2 and AARD% values of MLP-NN model are 0.9919 and 1.042 respectively. This indicates that the RBF-NN model provides better predictions compared to MLP-NN model. Figure
depicts the cross plot of data points which is the
comparison between estimated data by proposed models and actual data. It is clear from this figure that in the case of both models, the distributions of data points construct a unit slope line which indicates that the outcomes of proposed models and target values are in acceptable agreement. The relative error distribution plot of estimations of proposed models versus
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ACCEPTED MANUSCRIPT experimental data is shown in Figure . According to this figure, a significant concentration of data points near the line with zero relative error for both models indicates that these models
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could estimate the total set of target data with an acceptable error. The maximum deviation of estimations of RBF-NN model is no more than 23% and most of data points fall in the area
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between relative deviations of 5%. The relative errors of MLP-NN model also are mostly
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concentrated in region with relative deviations between 10%. In the case of eliminating a data
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point with an absolute relative error of 59%, the maximum relative error of MLP-NN model is no more than 20%. This also indicates that the MLP-NN model exhibits predictions with
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reasonable relative errors; however, the accuracy and reliability of RFB-NN model is higher than MLP-NN model. Figure shows the trend plot of experimental and estimated values plotted
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versus the index of data points. According to this figure the predictions of both models are appropriately follow the trend of experimental data which indicates acceptable accuracy of
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implemented models.
At this point the predictions of RBF-NN and MLP-NN models will be compared with two recently developed literature correlations for prediction of heat capacity of ILs. These correlations were proposed by Farahani et al. [26] and Ahmadi et al. [32]. The details of these correlations including their input parameters and constant coefficients are represented in Appendix A. The statistical parameters of these correlations are listed in Table 4. Figure also shows the graphical comparison between statistical parameters of proposed models and literature correlations. It is evident that the RBF-NN and MLP-NN models are superior to two other correlations and provide better estimations thank to higher R2 and lower values of AARD%, RMSE and STD. Figure
also shows the cumulative frequency of developed models and
literature correlations against their absolute relative errors. This figure indicates that the RBF-
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ACCEPTED MANUSCRIPT NN and MLP-NN models are able to predict about 95% and 92% of data points with errors less than 5%. However, the Farahani et al. [26] and Ahmadi et al. [32] correlations are able to predict
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about 80% and 74% of data with an error less than 5%. This also indicates the accuracy and
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reliability of proposed models in present work over literature correlations.
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4. Conclusion
In this work, two models namely RBF-NN and MLP-NN were developed for prediction of
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heat capacity of ILs. An extensive database including 2940 data points from 56 ILs was used to develop a general model. The tuning parameters of developed models were determined by trial
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and error approach. The predictions of developed models were evaluated by utilizing various
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statistical and graphical methods. Results showed that the RBF-NN model presents accurate
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predictions compared to MLP-NN model with an overall AARD% and R2 of 0.828 and 0.9931. The predictions of developed models were also compared with two literature correlations and it was concluded that the developed models present more accurate and reliable results. As the developed models exhibit acceptable generality, results of these models can be used in situations in which rapid and accurate prediction of heat capacity of ILs is required.
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Correlation
Formula
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Appendix A. literature correlations for prediction of heat capacities of ILs
C p 122.16826 0.45794T 12.8395N C 56.85424CH 3RC 19.25836N a 11.36109nH a N C number of atoms of cation, Na number of atoms of anion, CH3RC number of methyl groups in cation counter parts nHa number of hydrogen atoms in anion, T=temperature
Ahmadi et al. [32]
C p 0.2808T 1.0854 17.5066ln(T ) 0.6593MW 1.0793 15.9932C A 16.1292CC 2.8956N 11.7667S 1.3729O 4.1977(F Br Cl ) 6.7438B 12.399 T temperature, MW=molecular weight of IL, CA number of carbon atoms of anion, CC number of carbon atoms of cation N , S ,O , F , Br , Cl and B =number of nitrogen, sulfur, oxygen, fluorine, bromine, chlorine and boron atoms of IL
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Farahani et al. [26]
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Appendix B. Instructions for running the program
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First download the Supplementary file then change the directory of Matlab® (Version 2014) to the download folder. Use below stages to get a response from model:
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1. Open the “Sample.xlsx” file. Two sheets are located in this file named “Input” and “Output”.
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In the “Input” sheet fill the specified cells. It is possible to fill more than one data sample. Save and close the Excel file.
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2. Open and run the “Sample.m” file by Matlab®.
3. After running the “Sample.m” file go to “Output” sheet of the “Sample.xlsx”. The results of
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RBF-NN and MLP-NN models are provided in the corresponding cell (Cell A3 for RBF-NN
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model and Cell B3 for MLP-NN model).
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To better use the instruction of RBF-NN and MLP-NN models, below example has been provided.
Example: Calculate the heat capacity of IL by RBF-NN and MLP-NN models with the following data:
Mw
T (K)
nHA
CA
CC
N
S
O
F
Br
Cl
B
2
0
0
6
0
0
0
(g/mol) 300.81
0
0
8
284.2
Solution: Open the “Sample.m” and run it then turn to “Output” sheet of “sample.xlsx” file to see the predicted value of the heat capacity of IL.
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ACCEPTED MANUSCRIPT The outcome of RBF-NN model will be 410.31, where its experimental value is equal to 410.4 (the absolute relative deviation is 0.022%). The output of MLP-NN will also be 409.13
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(the absolute relative deviation is 0.31%)
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ACCEPTED MANUSCRIPT [52] Y.-H. Yu, A.N. Soriano, M.-H. Li, Heat capacities and electrical conductivities of 1-n-butyl3-methylimidazolium-based ionic liquids, Thermochimica Acta, 482 (2009) 42-48.
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Thermochemical properties of 1-butyl-3-methylimidazolium nitrate, Thermochimica Acta, 474 (2008) 25-31.
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liquid heat-transfer fluids, Thermochimica Acta, 425 (2005) 181-188. [56] R. Ge, C. Hardacre, J. Jacquemin, P. Nancarrow, D.W. Rooney, Heat capacities of ionic
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liquids as a function of temperature at 0.1 MPa. Measurement and prediction, Journal of Chemical & Engineering Data, 53 (2008) 2148-2153.
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ACCEPTED MANUSCRIPT [61] A.V. Blokhin, Y.U. Paulechka, A.A. Strechan, G.J. Kabo, Physicochemical properties, structure, and conformations of 1-butyl-3-methylimidazolium bis (trifluoromethanesulfonyl)
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[71] K.-S. Kim, B.-K. Shin, H. Lee, F. Ziegler, Refractive index and heat capacity of 1-butyl-3methylimidazolium bromide and 1-butyl-3-methylimidazolium tetrafluoroborate, and vapor
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pressure of binary systems for 1-butyl-3-methylimidazolium bromide+ trifluoroethanol and 1butyl-3-methylimidazolium tetrafluoroborate+ trifluoroethanol, Fluid Phase Equilibria, 218 (2004) 215-220.
[72] Y. Shimizu, Y. Ohte, Y. Yamamura, K. Saito, Effects of thermal history on thermal anomaly in solid of ionic liquid compound,[C4mim][Tf2N], Chemistry letters, 36 (2007) 14841485. [73] A.V. Blokhin, Y.U. Paulechka, G.J. Kabo, Thermodynamic properties of [C6mim][NTf2] in the condensed state, Journal of Chemical & Engineering Data, 51 (2006) 1377-1388. [74] C. Nieto de Castro, M. Lourenço, A. Ribeiro, E. Langa, S. Vieira, P. Goodrich, C. Hardacre, Thermal properties of ionic liquids and ionanofluids of imidazolium and pyrrolidinium liquids†, Journal of Chemical & Engineering Data, 55 (2009) 653-661.
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neurons.
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Figure 1. Variation of total AARD% of different MLP networks with the number of hidden
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(a)
(b)
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Figure 2. Cross plot predicted heat capacity data against target data: (a) RBF-NN model, (b)
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(a)
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Figure 3. Relative deviation plot of predictions of the developed models: (a) RBF-NN, (b) MLP-
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Figure 4. Trend plot of experimental and estimated heat capacity data versus index of data: (a) RBF-NN, (b) MLP-NN.
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(b)
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Figure 5. Graphical comparison between statistical parameters of the developed models and the literature correlations: (a) R2, (b) AARD%, (c) RMSE, and (d) STD.
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literature correlations.
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Figure 6. Cumulative frequency versus absolute relative error for the developed models and the
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Table 1. Details of input and output data of RBF-NN model. Min.
Temperature (K)
Input
188.06
Molecular weight (g/mol)
Input
174.7
CC
Input
CA
Input
nHA
Input
N
Input
S
Max.
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Average 372.15
763.21
315.39
6
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8.43
0
20
0.85
0
37
0.73
1
5
2.18
Input
0
2
0.62
O
Input
0
9
1.55
F
0
15
4.92
Input
0
1
0.01
Input
0
1
0.005
Input
0
1
0.04
Output
226
1413
499.76
B Cp (J/mol.K)
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Input
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Br
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Parameter
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Table 2. The results of several trial and error approaches for evaluating the optimum values of
MNN
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200
50
170
50
120
50
Total AARD% 0.9075 0.9019
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1.0769 1.5299
170
0.9264
130
1.1613
80
1.5946
60
1.8806
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Spread
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200
0.8693
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160
1.3126
40
110
1.2232
40
70
1.8699
30
200
0.9255
30
180
0.9598
30
140
1.1545
30
70
2.0308
20
200
1.1245
20
170
1.2523
20
120
1.8407
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0.8283
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2.5101
10
200
2.0994
10
170
2.2601
10
140
10
90
10
50
5
200
5
170
5
130
4.0033 6.1316 1.94
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4.7583
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2.9394
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Table 3. Statistical parameters of the developed models for prediction of experimental heat
AARD%
Train data
0.9944
0.767
Test data
0.9861
Total data
0.9931
Train data
0.9941
Test data
0.9910
Total data
0.9919
RMSE
0.0207
9.30
1.071
0.0406
12.93
0.828
0.0259
10.13
1.038
0.0241
10.59
1.056
0.0265
11.17
1.042
0.0260
11.05
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STD
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R2
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Data set
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Model
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Table 4. Statistical parameters of the literature correlations for prediction of experimental data.
Farahani et al. [26]
0.9753
2.48
Ahmadi et al. [32]
0.9612
2.73
STD
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0.0531
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Correlation
RMSE 19.18 24.14
ACCEPTED MANUSCRIPT Research Highlights Two models namely RBF-NN and MLP-NN were developed for prediction of heat
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capacities of ILs.
The input parameters of the models are temperature, molecular weight of IL and chemical
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structure information.
The models were developed based on 2940 experimental data for 56 ILs.
Results show that the developed models are accurate and reliable and are superior to
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literature correlations.
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