A neural network for predicting normal boiling point of pure refrigerants using molecular groups and a topological index

international journal of refrigeration 63 (2016) 63–71

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A neural network for predicting normal boiling point of pure refrigerants using molecular groups and a topological index Shuai Deng, Wen Su, Li Zhao * Key Laboratory of Efficient Utilization of Low and Medium Grade Energy (Tianjin University), MOE, Tianjin 300072, China

A R T I C L E

I N F O

A B S T R A C T

Article history:

An artificial neuron network based on genetic algorithm is presented to predict the normal

Received 27 April 2015

boiling point (Tb) of refrigerants from 16 molecular groups and a topological index. The 16

Received in revised form 10 August

molecular groups used in this paper can cover most refrigerants or working fluids in re-

2015

frigeration, heat pump and organic Rankine cycle; the chosen topological index is able to

Accepted 24 October 2015

distinguish all the refrigerant isomers. A total of 334 data points from previous experi-

Available online 2 November 2015

ments are used to create this network. The calculated results, which are based on a developed numerical method, show a good agreement with experimental data; the average absolute

Keywords:

deviations for training, validation and test sets are 1.83%, 1.77%, 2.13%, respectively. A per-

Normal boiling point

formance comparison between the developed numerical model and the other two existing

Refrigerant

models, namely QSPR approach and UNIFAC group contribution method, shows that the

Property prediction

proposed model can predict Tb of refrigerants in a better accord with experimental data.

Artificial neuron network

© 2015 Elsevier Ltd and International Institute of Refrigeration. All rights reserved.

Molecular groups Topological index

Un réseau neuronal pour prédire le point d’ébullition normal de purs frigorigènes en utilisant les groupes moléculaires et un indice topologique Mots clés : Point d’ébullition normal ; Frigorigène ; Prévision de propriété ; Réseau neuronal artificiel ; Groupes moléculaires ; Indice topologique

* Corresponding author. Key Laboratory of Efficient Utilization of Low and Medium Grade Energy (Tianjin University), MOE, Tianjin 300072, China. Tel.: +86 022 27404188; Fax: +86 022 27404188. E-mail address: [email protected] (L. Zhao). http://dx.doi.org/10.1016/j.ijrefrig.2015.10.025 0140-7007/© 2015 Elsevier Ltd and International Institute of Refrigeration. All rights reserved.

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international journal of refrigeration 63 (2016) 63–71

Nomenclature

Standard A a AAD ANN ANN-GCM ARD Bias CAMD CFCs EA ea EATII f GA GWP HCFCs HFEs m MSE

1.

adjacency matrix of compound element of adjacency matrix absolute average deviation, % artificial neural network artificial neural network-group contribution method absolute relative deviation, % average percent deviation, % computer-aided molecular design chlorofluorocarbons extended matrix of compound element of extended matrix topological index fitness function genetic algorithm global warming potential hydrochlorofluorocarbons hydrofluoroethers number of hidden nodes mean squared error

Introduction

Investigation of refrigerants is the basis of refrigeration, heat pump and organic Rankine cycle (ORC) system research. The accuracy of thermal physical properties is an important consideration in engineering design and fundamental research. Although a large number of physical properties for refrigerants have been measured and published in the literature (Calm and Hourahan, 2011), it is urgent to design alternative refrigerants with desired properties (Samudra and Sahinidis, 2013a) due to the growing concerns regarding the depletion of the ozone layer and the greenhouse effect. Approximate property models to predict a set of desired properties are necessary in the process of computer-aided molecular design (CAMD) of refrigerants (Khetib et al., 2009; Samudra and Sahinidis, 2009). Therefore, prediction models in high accuracy are required for scientists and engineers working in this field. Normal boiling point (Tb) is one of the most important thermal properties of refrigerants. Most other thermal properties are predictable from Tb (Poling et al., 2001). Tb is defined as the temperature at which a liquid’s vapor pressure equals to an atmospheric pressure. There are a number of methods proposed for prediction of Tb (Poling et al., 2001). Joback and Reid (1987) proposed a group contribution method that presents an approximate value of Tb for aliphatic and aromatic hydrocarbons. Tb is estimated with the sum of contributions of all structural groups that occurred in the molecule. This method is not particularly accurate but can be acceptable for preliminary calculations. Later, Devotta and Pendyala (1992) modified the Joback method to calculate Tb of halogenated compounds much more accurately. Then Constantinou and Gani (1994) developed an advanced group contribution method

N n NC ODP ORC QSPR T Radii

total number of data points number of groups found in the molecule network’s complexity function ozone depletion potential organic Rankine cycle quantitative structure property relationship temperature, K  covalence radii of groups, A

RMS

root mean square error

Greek symbols weight of an edge connecting two groups ω δ connected degree of molecular group Subscripts i j b cal exp

index of a matrix or data for ith sample index of a matrix normal boiling point network’s calculation of normal boiling point experimental value of normal boiling point

Superscripts * sum of power series of extended matrix

based on the UNIFAC group. The accuracy was enhanced by providing contributions at a “second order” level for Tb. A different group contribution model was presented by Marrero-Morejón and Pardillo-Fontdevila (1999). They called the model a group interaction contribution technique. Wang et al. (2009) predicted the Tb of organic compounds based on the position group contribution method, which could distinguish most isomers. There are already some group-contribution models improved by the introduction of molecular descriptors (Abooali and Sobati, 2014); the main molecular descriptors are the symmetry number and the flexibility number (Wang et al., 2009). A quantitative structure property relationship (QSPR) approach for pure refrigerants was proposed by Abooali and Sobati (2014) based on solely five molecular descriptors. It should be noted that the proposed models above have some important disadvantages. For example, these models have limited applicability for distinction of isomers because the isomers have the same number and kind of groups. Besides, the existing property estimation models are for all the organics, and their accuracy in refrigerant is deficiency; they are very complicated in dividing molecular groups for a quick prediction of refrigerant properties. Artificial neural network (ANN) is a suitable alternative to model the different properties of organic compounds. The primary advantage is that ANN can simulate the nonlinear relationship between structural information and properties of compounds during the training process and then generalize the knowledge among homologous series without the need for theoretical formulas (Liu et al., 1997). A few attempts have been made for predicting properties of refrigerants using ANN. Liu et al. (1997) set up five topological indexes, such as the connection index and the polarity number, as input parameters of a neural network to predict Tb and other properties

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international journal of refrigeration 63 (2016) 63–71

A 1

elements of refrigerants

H

2

A

Hydrogen 3

A

Li

Lithium 11 N a Sodium 19 K Potassium 37 R b Rubidium

4

Be

Berylium

A

A 5

B

6

Boron

12 M g

13 Al

Magnesium

Aluminium

20 Ca

31 Ga

Calcium 38 Sr Strontium

C Carbon

14 Si

Gallium 49 In

Silicon 32 Ge Germanium 50 Sn

Indium

Tin

A

A 7

N

8

Nitrogen

O Oxygen

15 P

16 S

Phosphorus 33 As

Sulphur 34 Se

Arsenic

Selenium

51 Sb

52 Te

Antimony

A 9

F

Flourine 17 Cl Chlorine 35 Br Bromine 53 I

Tellurium

Iodine

He Helium

10 N e Neon 18 Ar Argon 36 Kr Krypton 54 Xe Xenon

Fig. 1 – Elements of refrigerants.

of alkenes. Mohebbi et al. (2008) developed a neural network for predicting saturated liquid density using genetic algorithm for pure and mixed refrigerants. In their work, the neural model was devoted to the computation of the saturated liquid density, as a function of Pitzer’s acentric factor and reduced temperature of the refrigerant. Moosavi et al. (2014) used the artificial neural network-group contribution method (ANNGCM) to predict liquid density of five different classes of refrigerant systems (HCFCs, HFEs, etc.). The results indicate that the ANN-GCM model represents an excellent alternative to estimate refrigerant properties with a good accuracy. However, in these works, the authors do not combine the topological index with molecular groups to predict properties using ANN. On the other hand, traditional neural network design uses a time consuming iterative trial and error approach. Consequently, the time and effort needed to design a network are entirely dependent on the nature of the task and the designer’s experience. This will cause a lot of time and effort being expended to find a network with optimal structure for the desired task. The above literature review shows that existing studies have three limitations in properties estimation, including the difficulties in the prediction of isomers, the complexity of group division and the problem of network structure. The purpose of this paper is to solve these problems and establish a network to predict Tb for refrigerants. The 16 refrigerant groups and one topological index are obtained as the member of the network input. The structure and initial values of the network are optimized by genetic algorithm (GA). Afterwards, the network is trained by the experimental data.The performance of the trained network is discussed and compared with other two models and an analysis of the topological index is also conducted.

frigerant, Midgely and co-workers selected 8 elements shown in Fig. 1 from the periodic table of the elements (Calm, 2008; Sahinidis et al., 2003). Since then, chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs) dominated the market of refrigerants due to its high efficiency in system cycle. Recently, refrigerants are being developed toward low global warming potential (GWP) and low ozone depletion potential (ODP) because of the increasing concerns on environmental problems. A great deal of effort has been taken to seek for the alternative refrigerants. Through molecular design of replacement refrigerants with desired properties, some ideal refrigerants have been developed successfully. The results of refrigerant design (Khetib et al., 2013; Louaer et al., 2007; Samudra and Sahinidis, 2013b) and existing refrigerants show that the refrigerants are composed of six kinds of organic compounds – alkanes, alkenes, halogenated hydrocarbons, alcohols, ethers and amines. For simplicity of molecular group division, refrigerant groups are divided in accordance with the functional groups, as shown in Fig. 2.

2.2.

Three hundred thirty-four components, which are composed of refrigerant groups, have been chosen as data set for Tb in this paper. The maximum number of carbon element for the components in the data set is 8. The data are mainly from three databases including Chemical Abstracts Service (CAS) (NIST, 2011), SciFinder (American Chemical Society, 2014) and Molbase (MOLBASE, 2013). All the data are normalized between −1 and 1 before use in calculation.

2.3.

2.

Methodology

2.1.

Group division

The first systematic research for refrigerants dates back to 1930s. Considering the toxicity, volatility, or instability of re-

Data set

Topological index

A large number of structural isomers exist in pure refrigerants. However, to the best of the authors’ knowledge, all the proposed methods in existing studies cannot completely distinguish isomers. So, in this work, a topological index EATII is introduced to distinguish structural isomers. The EATII index is a mathematical invariant derived from the structures of the

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international journal of refrigeration 63 (2016) 63–71

Table 1 – Covalence radii and connected degree of groups (Xu and Hu, 2000).

Fig. 2 – Refrigerant groups.

compounds (Guo et al., 1997). It shows a fairly good quality in structure–property correlation and a highly discriminative descriptor, which can differentiate all the isomers of 22 carbon atoms (Xu and Hu, 2000). The flow of calculating EATII index is presented in Fig. 3. The covalence radii and the connected degree of all considered groups used in the calculation process are shown in Table 1.

2.4.

ANN model optimized by GA

ANN consists of a number of neurons working in unity to solve various scientific and engineering problems such as

Group

Radii

δ

−CH3 −CH2>CH>C< =CH2 =CH=C< −F −Cl −Br −I −OH −O−NH2 >NH >N-

0.74 0.74 0.74 0.74 0.74 0.74 0.74 0.72 0.994 1.142 1.334 0.74 0.74 0.74 0.74 0.74

1 2 3 4 2 3 4 7 7 7 7 5 6 3 4 5

estimation of physical and chemical properties (Taskinen and Yliruusi, 2003). A feed forward back propagation (BP) neural network, which includes an input layer, an output layer and a hidden layer, is used in this work. There are 17 neurons in the input layer, which consists of 16 refrigerant groups and one topological index EATII. The value associated with each group was defined as: 0 when the group does not appear in the refrigerant and x when the group appears x times in the substance. The output layer has one neuron representing Tb. However, there is not a specific approach to determine the number of neurons of the hidden layer. In addition, the training algorithm of BP network based on the gradient descent method has a strong local optimizing ability; the randomly generated initial values may lead to network divergence or fall into a local extreme point. Thus, GA is applied in this study to solve the above-mentioned two problems. GA, as another kind of artificial intelligent method, is based on principles from genetics and evolution. It is one of the stochastic optimization methods which simulate the process of neural evolution. It is good at overall search and can overcome the local optimal defects of BP algorithm. GA is used as the first step to find the optimum number of the hidden nodes, and obtain the network’s initial weights and thresholds. The computer program of this model is developed on the MATLAB 2014a software platform.

2.4.1.

Fig. 3 – Flow of calculating topological index.

Genetic algorithm

In 1975, GA that mimics the process of natural evolution was introduced by Holland (1975). The algorithm starts with a randomly generated population, and the population comprises a group of encoded chromosomes that are the candidates for the solution of an optimization problem. The fitness values of all chromosomes are evaluated using an objective function in a decoded form and the applied genetic operators include the selection, crossover and mutation operators (Mohebbi et al., 2008). The current chromosomes are replaced by their offspring, which are reproduced through genetic operations, and the fitness of all offspring is evaluated using the same criterion. Such a GA cycle is repeated until a desired

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international journal of refrigeration 63 (2016) 63–71

termination criterion is reached. The best chromosome obtained in the final population can become a highly evolved and more superior solution to the problem (Saxena and Saad, 2007). In this work, to optimize the number of the hidden nodes and initial values of the neural network simultaneously, hierarchical encoding rule is adopted. A chromosomal structure consists of control genes and parameter genes; the control genes determine the number of neurons activated in the hidden layer using binary encoding, whereas the parameter genes are used to represent neuron weights and thresholds with real code (Yen and Lu, 2000). All genetic operations are based on the fitness of chromosomes,owing to the fact that natural evolution always toward a direction in a bigger fitness. So, it is important to design a suitable fitness function. The optimization process is to obtain optimum network’s weights and thresholds using minimal neurons. So, the objective function includes mean squared error (MSE) function and network’s complexity (NC) function. MSE is defined as follows:

MSE =

1 N 2 ∑ ( Texp,i − Tcal,i ) N i =1

(1)

Network’s complexity is determined by the number of hidden layer nodes. It is calculated using the following equation (Zhao, 2010):

m NC = exp ⎛⎜ ⎞⎟ ⎝2⎠

1 0.2MSE + 0.8NC

(3)

The algorithm of the selection operator is based on the normalized geometric distribution; crossover performs an interpolation along the line formed by two parents; and one of the parent’s parameters is changed in mutation stage based on a non-uniform probability distribution (Houck et al., 1995). Simultaneously, considering that the total number of experimental data points is 334, the maximum number of hidden nodes is set to be 15; the size of the population and the max generation are set to be 100 and 500, respectively. Fig. 4 shows the flow diagram of genetic algorithm in the present work.

2.4.2.

tansig ( x ) = 2 ( 1 + exp ( −2x ) ) − 1

(4)

purelin ( x ) = x

(5)

where x is a function parameter. The data set is divided into three sub data sets including the training, validation, and test sets, in order to prevent network data over fitting and improve network generalization ability of prediction. The proportion of the training, validation, and test sets is generally 70%, 15%, 15% respectively (Moosavi et al., 2014). LM algorithm uses training set to train the network. In the every-time step of training process, LM validates the performance of the network by using validation set as the input data of the network. The max number of validation check is set to be 15, which means that if the network performance does not improve after 15 consecutive validations, the algorithm will stop training and get the calculated results of the test set. In this work, every sub data set must contain all the groups to guarantee the accuracy of the network. So, the experimental data are classified into three sub data sets artificially. The classification results are presented in the appendix.The flow diagram of BP algorithm is shown in Fig. 5.

(2)

So, the fitness of chromosomes is evaluated by the following equation:

f =

are chosen to be the function of the hidden layer and the output layer respectively in the present network, and they are defined in Eqs. (4)–(5).

Hierarchical encoding

Create initial random population

Evaluate GA fitness function using Eqs. (3)

Selection operator

Crossover operator

New population

Artificial neuron network

BP neural network is based on the error back propagation. BP algorithm consists of forward and back propagations. A three layer BP network can approximate any rational function with arbitrary precision (Hecht-Nielsen, 1989). In this work, initial weights and thresholds are obtained from GA. The adjustment is performed by Levenberg–Marquardt (LM) algorithm because of its rapidity and accuracy in the process of training neural networks (Moosavi et al., 2014). The learning rate of the algorithm is set to be 0.3. There are mainly three different types of transfer functions proposed for ANN: linear (purelin) function, logarithmic sigmoid (logsig), and hyperbolic tangent sigmoid (tansig). Wang et al. (2009) used tansig function to predict Tb in their method. So, the tansig and purelin

Mutation operator

Max generation is reached?

N

Y Number of hidden nodes, weights, thresholds Fig. 4 – Flow diagram of genetic algorithm.

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international journal of refrigeration 63 (2016) 63–71

weights and thresholds of the network for predicting Tb are given in Table 2. According to the trained network, a correlation for predicting Tb of refrigerants is developed as follows:

Number of hidden nodes, weights, thresholds determined by GA

⎡ ⎤ ⎢ ⎥ 2 ⎥ Tb = 199.425∑ Wi ⎢ 16 N EATII ⎛ ⎞ k ⎢ i =1 1 + exp ⎜ −4∑ Wik − Wie + bi ⎟ ⎥ ⎢⎣ Ck 98.584 ⎝ k =1 ⎠ ⎥⎦ + 479.835

Database input

8

Train BP network and validate it by LM

where Wi is the weight of neuron i in the hidden layer; Wik is the input weight between group k and neuron i; Wie is the EATII input weight of neuron i; bi is the constant of the neuron i in the hidden layer; Ck is a constant for group k; Nk is the number of group k in the refrigerant. The value of bi and Ck are also presented in Table 2. The accuracy of the trained network to predict Tb can be evaluated using the statistical parameters namely, the absolute average deviation (AAD), the average percent deviation (bias) and the root mean square error (RMS) which are defined as follows (Moosavi et al., 2014):

N

Termination criteria

Y Test the network; Get the optimum weights and thresholds Fig. 5 – Flow diagram of BP algorithm.

AAD =

3.

Results and discussion

3.1.

ANN for prediction of Tb

(6)

The optimum number of the hidden layer nodes obtained from GA is 8. The BP network topology is constructed as 17-8-1 which indicates the number of inputs (17), the number of hidden nodes (8) and the number of outputs (1).Then, LM algorithm starts training the network from the initial values gained by GA. Optimum

T −T 1 N ∑ 100 × exp,Tiexp,i cal,i N i =1

(7)

bias =

T −T 1 N ∑ 100 × exp,Tiexp,i cal,i N i =1

(8)

RMS =

1 N 2 ∑ ( Texp,i − Tcal,i ) N i =1

(9)

The AAD characterizes the fact that the calculated values deviate from the experimental data. The bias characterizes the

Table 2 – Optimum values of the network and parameters of the correlation. Input weights Neuron #1 Neuron #2 Neuron #3 Neuron #4 Neuron #5 Neuron #6 Meuron #7 Neuron #8 C

Input weights Neuron #1 Neuron #2 Neuron #3 Neuron #4 Neuron #5 Neuron #6 Neuron #7 Neuron #8 C

Neuron Layer weights B

−CH3

>CH2

>CH-

>C<

=CH2

=CH-

=C<

−F

−Cl

1.313165 0.882196 −0.30721 0.421235 −0.11973 0.673056 −0.87203 −0.16659 6

1.105612 1.183552 −0.1823 1.638341 0.204814 0.233421 −1.72809 0.12003 9

0.077465 0.355309 0.054883 −0.15313 0.101498 0.07574 −0.41614 0.207326 3

−1.84765 −0.43498 −0.0486 0.652791 0.120177 −0.3255 −0.36581 0.34916 7

−0.48523 −0.45308 1.073259 0.27422 0.000387 0.875699 0.484721 −0.11782 2

1.113577 −0.26232 −1.00097 1.014686 0.285444 −0.66643 −0.29099 −0.06181 2

−1.33013 −0.39164 −0.18022 0.046052 0.641196 −0.18891 1.012673 0.680111 2

−1.18656 −0.06757 0.095247 0.40631 −0.72872 1.618995 0.265256 −0.46417 16

−0.7690508 0.02386378 −0.5844337 −0.4156549 −0.0999581 0.21304996 −0.2134749 −0.6309602 7

−Br

−I

−OH

−O-

−NH2

>NH

>N-

EATII

Thresholds

0.025328 0.478583 1.177965 0.399882 0.071816 0.076489 0.87549 −0.63791 2

−0.11794 −0.26319 0.001554 −0.2678 0.420533 −0.47908 −0.01972 1.232873 1

−1.41562 −1.24968 −0.35855 −0.34669 0.339073 −0.4287 −1.04737 0.233008 2

0.08835 −0.11314 1.382861 −0.03765 −0.17837 −1.63907 −0.18919 −0.67541 2

0.907394 −0.25374 0.006429 −0.36282 0.33182 −0.53313 2.366202 −0.62497 1

0.064013 −0.00872 −0.17655 0.080339 −0.16069 1.046122 −0.01475 −0.01348 1

1.318353 0.471982 0.739882 0.970657 0.053843 0.762879 −0.22375 0.957658 1

−0.2631 0.522457 −0.26976 0.189357 0.311559 0.55722 −0.54468 0.095074

−2.368998 −0.844616 −1.149955 −0.413717 1.116473 0.922517 −1.056839 1.138925

1

2

3

4

5

6

7

8

Threshold

−0.50368 1.926976

0.494604 2.54282

−0.4488 5.139729

−0.8948 9.852669

1.799541 0.964682

0.528011 1.913417

−0.7816 0.255975

−1.32001 −1.31111

−0.449485

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international journal of refrigeration 63 (2016) 63–71

550

(a)

500 450 400

Tcal(K)

quality of the distribution of the calculated data on either side of the experimental data. The RMS characterizes the absolute mean difference between the calculated values and the experimental values. Fig. 6 shows a comparison between the experimental and calculated values of the normal boiling points of refrigerants in training, validation and test sets. The coefficient of correlation, R, which is used to represent the relationship between the experimental and calculated values, has been presented for each plot. The values of R are 0.9893, 0.9958, and 0.9928 respectively for training, validation and test sets. As these plots show, there is a good agreement between the experimental data and the calculated results from the BP network in three sub data sets. Table 3 shows the three kinds of statistical parameters for training, validation, and test sets. AAD, bias and RMS for the total set are 1.87%, 0.18%, and 9.3263, respectively. The absolute relative deviation (ARD) for one compound is expressed in the following equation.

R=0.9893

350 300 250 200 150 150

200

250

300

350

400

450

500

550

400

450

500

550

400

450

500

550

Texp(K) 550

ARD = 100 ×

Texp − Tcal Texp

(b) (10)

500 450

3.2.

400

Tcal(K)

ARD represents the degree to which the calculated value of one compound deviates from the experimental value. Fig. 7 shows the distribution of ARD for 334 data points. It can be seen that the values of ARD are less than 2% for 75% of data points.

R=0.9958

350 300 250

Comparisons with existing methods

200

3.3.

150 150

200

250

300

350

Texp(K) 550

(c)

500 450 400

Tcal(K)

In order to evaluate the performance of the new method on predicting Tb of refrigerants, a comparison between the present model and the other two models, namely QSPR approach proposed by Abooali and Sobati (2014) and UNIFAC group contribution method developed by Constantinou and Gani (1994), has been conducted. The prediction of the normal boiling point by QSPR model and UNIFAC group contribution method in comparison with the present model for 30 components is shown in Fig. 8. AADs of normal boiling point prediction by ANN model, QSPR approach and UNIFAC group contribution method are 2.53%, 3.06% and 6.17%, respectively. It can be noticed that the accuracy of this work is higher than the other two methods.

R=0.9928

350 300

Analysis of topological index 250

The topological index EATII can differentiate all the isomers of 22 carbon atoms, the examples of Tb predictions for the refrigerant isomers are given in Table 4. Table 4 shows that all the isomers can be estimated precisely. However, the isomers with different groups can simultaneously be distinguished by groups and topological index. In order to analyze the function of the topological index under the same groups’ conditions, some isomers with the same groups have been listed in Table 5. It states that for low carbon isomers with same groups, the difference of EATII can be neglected. Their experimental data for Tb have no big difference, and so do predictions. But when the differences of EATII between the isomers with the same groups increase with the number of carbon atoms,

200 150 150

200

250

300

350

Texp(K) Fig. 6 – Comparison between experimental and calculated values of refrigerants for normal boiling point: (a) training, (b) validation, and (c) test data.

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Table 3 – Statistical parameters of the model for date sets. ANN model

Training set

Number of data points AAD% Bias% RMS

234 1.83 −0.10 9.6098

Validation set

Testing set

50

50

1.77 −0.33 7.4254

2.13 −0.41 9.6798

Table 4 – Predictions of this work for isomers.

Total set 334 1.87 0.18 9.3263

there would be significant differences in predicting Tb between these isomers. So the proposed model is an effective method to predict Tb for refrigerants that have a large number of isomers.

Chemical formula

ASRHAE

CHF2CHCl2 CF2ClCH2Cl CFCl2CH2F CH2ClCF2CHF2 CH3CF2CF2Cl CHF2CHClCHF2 CH2FCHClCF3

R-132a R-132b R-132c R-244ca R-244 cc R-244da R-244db

EATII

Texp/K

Tcal/K

17.3066 17.9581 17.9491 29.9679 32.7047 27.7242 28.8308

334.15 319.50 321.15 323.65 293.08 338.15 323.15

329.8653 319.1824 319.1742 325.8847 295.6397 346.1448 324.8334

Table 5 – Predictions of this work for isomers with the same groups. Chemical formula

ASRHAE

CF3CHCl2 CF2ClCHFCl CHF2CFCl2 CF3CFClCHFCl CHF2CFClCF2Cl CHCl2CF2CF3 CHFClCF2CF2Cl CF2ClCHClCF3

R-123 R-123a R-123b R-225ba R-225bb R-225ca R-225cb R-225da

4.

EATII

Texp/K

Tcal/K

23.3096 23.3154 23.3224 46.5893 46.6378 46.5213 46.5672 45.1204

300.75 301.00 303.35 325.10 329.15 324.25 325.20 324.00

299.9362 299.9417 299.9483 325.6253 325.6669 325.5669 325.6063 324.3649

Conclusions

In this paper, refrigerants are divided into 16 groups, and topology index EATII is introduced to distinguish structural isomers existing in refrigerants. In order to predict Tb of refrigerants by groups and EATII, a network is found by combining ANN with GA based on the experimental data. From the analysis of the predicted results, the following conclusions can be drawn: Fig. 7 – The distribution of ARD.

450

400

(1) The ANN model is highly accurate in predicting Tb of refrigerants; the average absolute deviation (AAD) of experimental data is 1.87%. (2) The proposed model can distinguish all the isomers of refrigerants. Tb is determined by molecular groups and topological structure. (3) The model can be applied to predict Tb for new refrigerants only based on their molecular structure.

Present method UNIFAC group contribution method QSPR method

Tcal(K)

350

300

Acknowledgment 250

This work is sponsored by the National Natural Science Foundation of China (51276123, 51476110).

200

150 150

200

250

300

350

400

450

Appendix: Supplementary material

Texp(K) Supplementary data Fig. 8 – Prediction of normal boiling point by present model in comparison with QSPR model and UNIFAC group contribution method.

Supplementary data to this article can be found online at doi:10.1016/j.ijrefrig.2015.10.025.

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