a computational intelligence scheme for prediction equilibrium water dew point of natural gas in teg...

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Fuel xxx (2014) xxx–xxx

JFUE 8331 No. of Pages 10, Model 5G

5 August 2014

Contents lists available at ScienceDirect

Fuel

journal homepage: www.elsevier .com/locate / fuel

A computational intelligence scheme for prediction of equilibrium waterdew point of natural gas in TEG dehydration systems

http://dx.doi.org/10.1016/j.fuel.2014.07.0720016-2361/� 2014 Published by Elsevier Ltd.

⇑ Corresponding author. Tel.: +61 2 6626 9412.E-mail addresses: [email protected] (M.A. Ahmadi), Alireza.bahadori@s-

cu.edu.au (A. Bahadori).1 Tel.: +98 9126364936.

Please cite this article in press as: Ahmadi MA et al. A computational intelligence scheme for prediction of equilibrium water dew point of naturaTEG dehydration systems. Fuel (2014), http://dx.doi.org/10.1016/j.fuel.2014.07.072

Mohammad Ali Ahmadi a,1, Reza Soleimani b, Alireza Bahadori c,⇑a Department of Petroleum Engineering, Ahwaz Faculty of Petroleum Engineering, Petroleum University of Technology (PUT), Iranb Department of Gas Engineering, Ahwaz Faculty of Petroleum Engineering, Petroleum University of Technology (PUT), Ahwaz, Iranc Southern Cross University, School of Environment, Science and Engineering, Lismore, NSW, Australia

h i g h l i g h t s

� Particle swarm optimization (PSO) is used to estimate the water dew point of natural gas in equilibrium with TEG.� The model has been developed and tested using 70 series of the data.� Back-propagation (BP) algorithm is used to estimate the water dew point of natural gas in equilibrium with TEG.� PSO-ANN accomplishes more reliable outputs compared with BP-ANN in terms of statistical criteria.

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a r t i c l e i n f o

Article history:Received 4 November 2013Received in revised form 24 July 2014Accepted 24 July 2014Available online xxxx

Keywords:Gas dehydrationTriethylene glycolEquilibrium water dew pointPredictionParticle swarm optimizationArtificial neural network

505152

a b s t r a c t

Raw natural gases are frequently saturated with water during production operations. It is crucial toremove water from natural gas using dehydration process in order to eliminate safety concerns as wellas for economic reasons. Triethylene glycol (TEG) dehydration units are the most common type of naturalgas dehydration. Making an assessment of a TEG system takes in first ascertaining the minimum TEG con-centration needed to fulfill the water content and dew point specifications of the pipeline system. A flex-ible and reliable method in modeling such a process is of the essence from gas engineering view point andthe current contribution is an attempt in this respect. Artificial neural networks (ANNs) trained with par-ticle swarm optimization (PSO) and back-propagation algorithm (BP) were employed to estimate theequilibrium water dew point of a natural gas stream with a TEG solution at different TEG concentrationsand temperatures. PSO and BP were used to optimize the weights and biases of networks. The modelswere made based upon literature database covering VLE data for TEG–water system for contactor tem-peratures between 10 �C and 80 �C and TEG concentrations ranging from 90.00 to 99.999 wt%. Resultsshowed PSO-ANN accomplishes more reliable outputs compared with BP-ANN in terms of statisticalcriteria.

� 2014 Published by Elsevier Ltd.

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1. Introduction

All natural gas streams contain significant amounts of watervapor as they exit from oil and gas reservoirs. Water vapor innatural gas can make several operational problems during theprocessing and transmission of natural gas such as line pluggingdue to formation of gas hydrates, reduction of line capacity dueto formation of free water (liquid), corrosion, and the decrease ofnatural gas heating value.

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Various techniques can be executed to dehydrate natural gas.Among these gas dehydration methods, glycol absorption pro-cesses, in which glycol is considered as liquid desiccant (absorptionliquid), is the most common dehydration process used in the gasindustry since it approximate the features that fulfill the commer-cial application criteria.

In a typical TEG system, shown in Fig. 1, water-free TEG (lean ordry TEG) enters at the top of the TEG contactor where it is flowcountercurrent with wet natural gas stream flowing up the tower.Elimination of water from natural gas via TEG is based on physicalabsorption.

In TEG system, specification of the minimum concentration ofTEG to fulfill the water dew point of exit gas has always beenoperationally important. Indeed, the one single change that can

l gas in

http://dx.doi.org/10.1016/j.fuel.2014.07.072

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Nomenclature

AcronymsANN artificial neural networkTEG triethylene glycolVLE Vapor–Liquid EquilibriumBP back-propagationMEG monoethylene glycolFFNN feed-forward neural networkGA genetic algorithmICA imperialist competitive algorithmMSE mean square errorPA pruning algorithmDEG diethylene glycolTREG tetraethylene glycolPSO particle swarm optimizationHGAPSO hybrid genetic algorithm and particle swarm optimiza-

tionR2 correlation coefficientMLP multilayer perceptronTST Twu–Sim–TassoneSPSO stochastic particle swarm optimizationUPSO unified particle swarm optimization

Symbols usedbH bias associated with hidden neuronsbO bias associated with output neuronc1, c2 trust parameterswt.% weight percent�C centigrade degreekPa kilopascalspsia pounds per square inch absoluteK number of input training dataA input signal (vector)W vector of weights and biases

grad the gradient of the performance functionr1, r2 random numberSH hidden neuron’s net input signalTd equilibrium water dew point temperatureT contactor temperaturesvi velocity of ith particlewH Weight between input and hidden layerxi position of ith particlexg gbest valuexi,p pbest value of particle iYpre predicted outputYexp actual outputOH output of the hidden neuron

Greek symbolsu activation functionx inertia weighta learning rate

Subscriptsi particle ij input jk in Eq. (7) kth iterationm number of neuron in the input layerz zth experimental data

Superscriptsn iteration numbermax maximummin minimumpre predictedexp experimental

2 M.A. Ahmadi et al. / Fuel xxx (2014) xxx–xxx


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be made in a TEG system, which will produce the largest effect ondew point depression, is the degree of TEG concentration (purity).To that end, it is needed to have a liquid–vapor equilibrium rela-tion/model for water–TEG system.

Several equilibrium correlations [1–7] for estimation theequilibrium water dew point of natural gas with a TEG dehydrationsystem can be found in the literature. Generally, the correlationspresented by Worley [4], Rosman [5] and Parrish et al. [1] worksatisfactorily and are suitable for most TEG system designs. How-ever, according to the literature [8], previously published correla-tions are unable to estimate precisely the equilibrium waterconcentration above TEG solutions throughout the vapor phase.

Parrish et al. [1] and Won [7] generated correlations in whichequilibrium concentrations of water throughout the vapor phasehave been ascertained at 100% TEG (unlimited dilution). Moreover,the other approaches employ data extrapolations at lower concen-trations to predict equilibrium throughout the unlimited dilutionarea [8]. The effect of pressure on TEG–water equilibrium is smallup to about 13,800 kPa (2000 psia) [1].

Recently, Bahadori and Vuthaluru [9] proposed a simple corre-lation for the prompt prediction of equilibrium water dew pointof a natural gas stream with a TEG solution in terms of TEG con-centrations and contactor temperatures. In addition, Twu et al.[10] employed the Twu–Sim–Tassone (TST) equation of state(EOS) [11] to specify the water–TEG system phase behavior.Furthermore, they presented an approach for employing the TSTEOS to determine water content and water dew point throughout

Please cite this article in press as: Ahmadi MA et al. A computational intelligenTEG dehydration systems. Fuel (2014), http://dx.doi.org/10.1016/j.fuel.2014.07

natural gas systems. Although, these methods (i.e. TST equation ofstate and simple correlation) have good predictive capability,applications of presented methods are typically limited to thesystem which they have been adapted for. As a matter of fact,aforementioned schemes need tunable parameters which shouldbe adjusted based upon experimental data points. Without exper-imental data points and adjusted parameters, aforementionedmodels are totally not reliable. In such circumstances, it ispreferable to develop and employed general models competentto predict phase behaviors of such systems. Among the variouspredictive methods, artificial neural network (ANN) is one ofthe competent methods enjoy great flexibility and capable toexplain multiple mechanisms of action [12]. ANNs are computa-tional schemes, either hardware or software which imitates thecomputational abilities of the human brain by using numbers ofinterconnected artificial neurons. The inimitability of ANN liesin its ability to acquire and create interrelationships betweendependent and independent variables without any prior knowl-edge or any assumptions of the form of the relationship madein advance [13].

In the last two decades, ANNs have become one of the most suc-cessful and widely applied techniques in many fields, includingchemistry, biology, materials science, engineering, etc. Especially,in the field of modeling of Vapor–Liquid Equilibrium (VLE) ANNshave successful track records [14–24].

Implications of artificial intelligent based approaches in variouscomplicated engineering aspects have got a noticeable attentions

ce scheme for prediction of equilibrium water dew point of natural gas in.072


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Fig. 1. Basic TEG dehydration unit.

M.A. Ahmadi et al. / Fuel xxx (2014) xxx–xxx 3


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through recent years such as application back propagation (BP)-feed forward neural network [25], couple of genetic algorithm(GA) and fuzzy logic [26], particle swarm optimization (PSO)[27–29], hybridized of PSO and GA (HGAPSO) [30,31], unified par-ticle swarm optimization (UPSO) [32], fuzzy decision tree (FDT)[33,34], imperialist competitive algorithm (ICA) [35–37], leastsquare support vector machine (LS-SVM) [38–40], and pruningalgorithm (PA) [41] have been applied to determine network struc-ture and involved parameters.

In this study, PSO is employed to specify the optimum values ofthe interconnection weights throughout feed-forward neural net-work in order to predict equilibrium water dew point temperatureof a natural gas stream with a TEG solution at different TEG con-centrations and contactor temperatures. Modeling results confirmthe integrity and show the ability of the suggested hybrid modelfor the estimation of water dew point with adequate precision incomparison with the real recorded data which are published inthe previous literatures (see Appendix A) [1,6].

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2. Artificial neural network

Artificial neural network (ANN), usually denoted to as neuralnetwork (NN), are an attempt at mimicking the information pro-cessing competences of biological nervous systems. The leading-edge picture of neural networks first came into being in the1940s by McCulloch and Pitts [42], who illustrated that networksof artificial neurons could, in principle, handle any arithmetic orlogical function. The fundamental element of processing through-out NN is a neuron (node) in which simple computations are car-ried out from a vector of input values. A neuron executes anonlinear transformation of the weighted sum of the incomingneuron inputs to yield the output of the neuron (see Fig. 2).

One of most conventional type of ANN approaches is multilayerperceptron (MLP) which belongs to a common category of config-urations named ‘‘feed-forward NN’’, a simple class of NN able ofapproaching general types of functions, counting integrable andcontinuous functions [43]. In the feed-forward NN, the track of signmovement is from the input layer, via hidden layers, to the outputlayer. Throughout the MLP configuration, the neurons areassembled into layers. The last and first layers are named outputand input layers correspondingly, because they illustrate outputs


and inputs of the general network. The residual layers are namedhidden layers. In a NN, each neuron—except neurons located inthe input layer—obtains and treats inputs from other neurons.The treated info is obtainable at the output termination of the neu-ron. Fig. 2 demonstrates the technique which the hidden layer’sneuron throughout a MLP handles the info.

Herein, each input to the 3th hidden neuron in a 3-layer feed-forward neural network is denoted by a1, a2, a3, . . . ,am, collectivelythey are referred to as the input vector. Every input is mint by a rel-evant weight wH

3,2, wH3,3, . . . ,wH

3,m which demonstrate the synap-tic neural links throughout natural nets and proceed in such amethod as to decrease or increase the input signs to the neuron.As a matter of fact, the factors of weight are adjustable constantsinside the network which specify the strength of the input signs.Weighted inputs are applied to the summation block, labeled R.The neuron has also a bias, bH

3, that is collected with the weightedinputs to create the net input. A bias demonstrates a weight whichdoes not join an input and an output of two neurons, but that isproduct by a unique sign and led to the neuron. A bias puts aspecific degree of the output sign of a neuron which is autonomousfrom input signs. The algebraic formulation for net can beexpressed as following as:

SH3 ¼ NET ¼

Xm

j¼1

wH3;j � aj þ bH

3 ð1Þ

The neuron performs as a mapping or activation function (NET)to generate an outcome OH

3 that can be shown as:

OH3 ¼ uðNETÞ ¼ u

Xm

j¼1

wH3;j � aj þ bH

3

!ð2Þ

where u stands for the neuron transfer function or the neuron acti-vation function. Three of the most commonly used activation func-tions are shown below.� Log-Sigmoid function (logsig)

uðsÞ ¼ 11þ e�s

ð3Þ

� Hyperbolic tangent function (tansig)

uðsÞ ¼ es � e�s

es þ e�sð4Þ

� Linear function (purelin)



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Fig. 2. Schematic of an artificial neuron within the hidden layer in a 3 layer feed-forward neural network.

Fig. 3. The flowchart of ANN trained with back-propagation algorithm [57].



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uðsÞ ¼ s ð5Þ

It is worth to mention that w and b are both adaptable variablesof the neuron. The principal concept of NN is that such variablescan be modified with the purpose of the network shows someinteresting or desired performance. The thresholds and factors ofweight are updated throughout process of training. Therefore, todo a specific work we can train the network by regulating the biasor weight factors. There are numerous categories of approaches fortraining NN. Back propagation (BP) approach is one of the mostconventional types of training methods for MLP-FFNNs. ANN train-ing via dint of BP, which is one of the gradient descent algorithms,is an iterative optimization approach where the introduced objec-tive function is minimized by updating the interconnectionweights properly. The mean-squared-error (MSE) is a frequentlyengaged objective function that is formulated as below:

MSE ¼ 1K

XK

l¼1

ðYexpl � Ypre

l Þ2 ð6Þ

where K denotes the number of training samples, Yexpl and Ypre

l arethe recorded values and estimated data, respectively.

The straightforward application of BP learning iterativelyadjusts the network biases and interconnection weights through-out the track wherein the objective function declines most quickly(as shown in following equation, the gradient has negative sign).Iteration throughout this strategy can be demonstrated as:

Wkþ1 ¼Wk � akgradk ð7Þ

In which Wk stands for the vector of present biases and weights,gradk represents the present gradient of the performance function,and the parameter ak denotes called the learning rate. It is worthyto be mentioned that this training algorithm needs the differentia-bility of activation functions u since the weight adjust way is onthe basis of the gradient of the performance function which isdescribed in terms of the activation functions and weights.Interested readers are referred to the literature [44–48] to knowmore descriptions of technical point of views of BP training


approach. Fig. 3 presents the flowchart of training MLP feed-for-ward neural network by application of the BP algorithm. In thisstudy, the ANN paradigm trained with BP applied the Levenberg–Marquardt algorithm.



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3. Particle swarm optimization (PSO)

PSO is a stochastic population-based search approach inventedby Kennedy and Eberhart in 1995 [49], modeled on the social behav-ior of some kinds of animals (such as bird flocks, fish schooling, andswarm of insects) with the intention of gain more complicatedactivities that can be utilized to unravel difficult issues, mostly opti-mization problems [50]. This optimization algorithm can be readilyexecuted and it is inexpensive from a computational point of viewdue to its CPU speed and memory necessities are low [51].

PSO conducts the search for finding of the optima using a pop-ulation (swarm) of particles. Every particle throughout the swarmcharacterizes a candidate answer to the optimization issue. In aPSO scheme, every particle is ‘‘flown’’ over hyper-dimensionalspace of search, iteratively modifying its position in space of searchconsistent with its own flight knowledge as well as the flyingknowledge of further particles in the entire of space of search, sinceparticles of a swarm communicate good positions to each other. Aparticle thus employs the finest position experienced by itself andthe finest position of other particles to guide itself into an optimalanswer. The effectiveness of every particle (i.e. the ‘‘nearness’’ of aparticle to the overall optima) is evaluated through objective func-tion which is associated with the issue being unraveled [50].

After finding the two best aforementioned positions, during aniteration-based process every particle throughout the swarm isadjusted executing the below formulas:

vnþ1i ¼ xvn

i þ c1rn1 xn

i;p � xni

h iþ c2rn

2 xng � xn

i

h ið8Þ

xnþ1i ¼ xn

i þ vnþ1i ð9Þ

where n stands for the number of iteration and the index of the par-ticle is denoted by i. vn

i represents the particle i velocity at nth iter-ation, vnþ1

i is the velocity of particle i at n + 1th iteration. Theindividual finest position, xn

i;p, connected with particle i is the finestposition the particle has stayed meanwhile the first time stage(pbest), xn

g is the best value, obtained up to now (i.e. at nth iteration)by any particle in the swarm (gbest). c1 and c2 are the accelerationfactors related to pbest and gbest respectively and typically c1 andc2 values are set to 2. rn

1 and rn2 are random values with constant

distribution in the range [0,1] [52]. xnþ1i and xn

i are the position ofparticle i at n + 1th and nth iteration respectively. x is the weightof inertia, presented by Shi and Eberhart [53], that controls theexploration and exploitation of the search space [54]. Generally,the inertia weight is calculated by means of linear declining meth-odology where a primarily large weight of inertia is linearly reducedto a minor value [50]:

xn ¼ xmax � xmax �xmin

nmax

� �n ð10Þ

where xmax, xmin, n and nmax are the initial weight of inertia, thefinal weight of inertia, current iteration number and total iterationnumber (maximum number of iteration used in PSO) respectively.Usually xmax and xmin values are equal to 0.9 and 0.4 respectively[27,50,55].

PSO assigns various common points with evolutionary basedapproaches such as genetic algorithms (GAs). However, PSO enjoysnoticeable advantages. The two main advantages of PSO over GAsare [31]:

� Memory of PSO, that is, the information of worthy answers isremembered by all particles, while in GA, preceding informa-tion of the issue is demolished as soon as the new populationis generated.� GA use filtering operation such as selection operation, however;

PSO does not utilize one, and all the particles of the swarm are


retained throughout the process of searching to impart theirknowledge successfully.

Optimization of functions with continuous-valued variables isdone mainly via PSO. Optimizing weights and bias of NN is oneof the first implementations of PSO. The first studies in trainingMLP feed-forward neural networks using PSO [55,56] have illus-trated that the PSO is a competent substitute for training neuralnetwork. Frequent investigations have additional surveyed theability of PSO as a training approach for a number of various neuralnetwork configurations. Investigations have also demonstrated forparticular implementations that neural networks trained execut-ing PSO afford more precise outputs.

4. Implementation of ANN training using PSO algorithm

With the intention of employ PSO for training a neural network,an appropriate representation and fitness function are necessary.Meanwhile the main objective is to minimize the error, the objec-tive function is abridge the provided error (e.g. the MSE). Everyparticle demonstrates a nominee answer to the optimization issue,and subsequently the interconnection weights of a neural networkat training step are a answer, a sole particle illustrates singlecomprehensive network. Every component of a position vector ofparticles illustrates single neural network bias or weight. Employ-ing this illustration, PSO approach can be employed to specify thefinest weights for a neural network to minimize the fitness func-tion [50].

As a matter of fact, the fitness function for each particle isgained by adjusting the interconnection weights of ANN as deter-mined by the parameters of the particle and evaluating the fitnessfunction, gained in training of ANN. In the same way, the fitnessfunctions of the whole particles in the swarm are established.gbest particle is defined as the particle having lowest fitness func-tion and the fitness function of the gbest particle is contrasted withthe pre-defined precision. If the pre-defined precision is fulfilledsubsequently the process of training is discontinued. Else, thenew position and velocity of the particles are adjusted againaccording to Eqs. (8) and (9). The similar procedure is replicated

Fig. 4. The flowchart of ANN optimized with PSO algorithm [57].



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0.7

0.75

0.8

0.85

0.9

0.95

1

0 2 4 6 8 10 12

Cor

rela

tion

Coe

ffic

ient

(R

2 )

Number Neurons

(a)

500

550

600

650

700

750

800

0 2 4 6 8 10 12

Mea

n Sq

uare

Err

or (

MSE

)

Number Neurons

(b)

Fig. 5. Variation of (a) R2 and (b) MSE with the number of hidden neurons.

Table 1Details of trained ANN with PSO for the estimation of the water dew point of a naturalgas stream in equilibrium with a TEG solution.

Type Value/comment

Input layer 2Hidden layer 7Output layer 1Hidden layer activation function LogsigOutput layer activation function PurelinNumber of data used for training 130Number of data used for testing 44Number of max iterations 200c1 and c2 in Eq. (8) 2Number of particles 22

-40-30-20-10

010203040506070

Wat

er D

ew P

oint

Tem

pera

ture

Data Index

(a)

Experimental Data

ANN Output

-50-40-30-20-10

0102030405060

0 50 100 150

0 10 20 30 40 50

Wat

er D

ew P

oint

Tem

pera

ture

Data Index

(b)

Experimental Data

ANN Output

Fig. 6. Actual versus predicted equilibrium water dew point using the BP-ANNmodel: (a) training and (b) testing.

-60

-40

-20

0

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60

80

Wat

er D

ew P

oint

Tem

pera

ture

Data Index

(a)

Experimental Data

PSO-ANN Output

-60

-40

-20

0

20

40

60

80

0 50 100 150

0 10 20 30 40 50

Wat

er D

ew P

oint

Tem

pera

ture

Data Index

(b)

Experimental Data

PSO-ANN Output

Fig. 7. Actual versus predicted equilibrium water dew point using the PSO-ANNmodel: (a) training and (b) testing.



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until the pre-defined precision is achieved [57]. The flowchart ofPSO-ANN is shown in Fig. 4. It should be mentioned that eachweight throughout the constructed NN is originally established inthe span of [�1,1] and each initial particle is an assortment ofweights produced arbitrarily in the span of [�1,1].

5. Results and discussion

As mentioned, ANNs were applied to construct reliable para-digms to predict the equilibrium water dew point temperature(Td). They were supplied by the contactor temperatures (T) andTEG concentrations (wt%) data as input variables.

The whole database was split into two divisions by a randomnumber generator: The first, which is used in the training process,includes 75% of the entire database and is equivalent to 130 datalines. The remaining points were save for validating and testingthe trained networks. This data set consists of 44 samples. It shouldbe mentioned that the first assortment is the training data bank,which is employed for optimizing the network biases and weightswhereas the testing assortment affords a wholly autonomousassessment of network integrity.


The hidden neurons’ number has a critical impact on theestimation integrity and precision. Many sources (for exampleRef. [58]) claimed that a feed-forward network with one hiddenlayer and enough neurons in the hidden layer, can fit any finiteinput–output mapping problem. In this respect, herein, networkswith one hidden layer with various hidden neurons were examined.The neurons number throughout the hidden layer illustrates the



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y = 0.5066x + 7.7335

R² = 0.9679

-40

-30

-20

-10

0

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30

40

-40 -20 0 20 40

AN

N O

utpu

t

Water Dew Point Temperature

(a)

Data

Linear (Data)

y = 0.4954x + 8.8406

R² = 0.9751

-40

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AN

N O

utpu

t


(b)

Data

Linear (Data)

Fig. 8. Regression plots of the BP-ANN model for: (a) training data set and (b)testing data set.

y = 0.9944x + 0.1149R² = 0.998

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0

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60

-40 -20 0 20 40 60

PSO

-AN

N O

utpu

t

Actual Water Dew Point Temperature

(a)

Data

Linear (Data)

y = 0.9987x + 0.1402R² = 0.9996

-40

-30

-20

-10

0

10

20

30

40

50

60

-40 -20 0 20 40 60

PSO

-AN

N O

utpu

t


(b)

Data

Linear (Data)

Fig. 9. Regression plots of the PSO-ANN model for: (a) training data set and (b)testing data set.



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complication of the network, though the more complex networksare effective in estimate within the restrictions of the data bankemployed for their training, they travail from absence of adequateextension. Specification of the number of neurons in the hiddenlayer is performed on the basis of a trial and error approach.Fig. 5a shows the change of R2 versus the hidden neurons’ numberthroughout the hidden layer. As demonstrated in Fig. 5a, it is obser-vable that rising the hidden neurons’ number from 1 to 7 improvedthe coefficient of determination; conversely, no improvement fol-lowed in an additional rise from 7 to 10. Fig. 5b shows the influenceof the neurons’ number on MSE. According to Fig. 5a and b, the high-est R2 is observed and the MSE get the minimum when 7 neuronsemployed in the hidden layer. Therefore, a three-layer networkwith a 2 (input units):7 (neurons in hidden layer):1 (output neuron)architecture is the most appropriate. The details of the PSO-opti-mized network used in this study to predict equilibrium waterdew point temperature were given in Table 1.

With the purpose of gauging the effectiveness of the PSO-ANNapproach, a BP-ANN scheme was performed with the same databanks utilized in the PSO-ANN approach. The PSO-optimizednetwork trained via 50 generations conformed by a BP trainingalgorithm. For the BP training algorithm the values of momentumcorrection factor and learning coefficient are assigned to 0.001 and0.7, correspondingly.


As can be seen in Figs. 6 and 7, a comparison between predictedand actual equilibrium water dew point during the testing andtraining steps for both hybrid PSO-ANN and common BP-ANNapproaches is executed. As shown in Fig. 7, there are not major dif-ferences between the outputs of the PSO-optimized network andthe references values of equilibrium water dew point. It is clearthat the PSO-ANN approach depicts a higher integrity in estimationof equilibrium water dew point temperature compared with BP-ANN, with lower MSE for the training and test sets 43.935 and13.472 in contrast to 551.13 and 527.098 for BP-ANN, respectively.

The performance of trained networks with PSO andconventional BP can be also evaluated by conducting an analysisof regression between the models outcomes and the relevantobject. The cross plots of actual equilibrium water dew pointversus predicted values of training and testing data set usingPSO-ANN and BP-ANN approaches are depicted in Figs. 8 and 9.It can be seen that the fitting obtained by PSO-ANN is excellentsince the regression line (the best linear fit) overlaps with the diag-onal (perfect fit), as a result of a slope value close to 1 and minorvalue of the y-intercept (see Fig. 9) [59]. The training and testingcorrelation coefficients (R2) of PSO-ANN were found to be greaterthan 0.99 while those of BP-ANN model are not as favorably asPSO-ANN model. This means that the proposed hybrid PSO-ANN



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model has been well trained and tested and is superior to BP-ANNmodel. The formula for correlation coefficient is as follows:

R2 ¼ 1�PK

l¼1ðYexpl � Ypre

l Þ2

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expl � Yexp

l Þ2 ð11Þ


where K denotes the number of training or testing samples,Yexp

l ; Yprel ; and Yexp

l are the experimental response, predictedresponse, and the mean of experimental response respectively.

Fig. 10 shows the performance plots for training, validation, testdata subset, and best models introduced for predicting equilibriumwater dew point. The performance plot shows the value of the per-formance function (MSE) against number of epochs. As can be seen,the validation and test data sets had similar trends; therefore, PSO-ANN can predict an unseen data set as well as the data set used forits validation [60].

Fig. 11 shows the scheme of actual data and % error between theactual and estimated equilibrium water dew point temperaturesduring the testing and training steps for both PSO-ANN and BP-ANN approaches. As shown in Fig. 11a, poor results are observedthrough BP-ANN model. However, the agreement between theactual equilibrium water dew point values and the PSO-ANNpredicted ones is acceptable. Considering the performance ofPSO-ANN globally, the effectiveness of the model is obvious sincethe vast majority of the training and testing data subsets falls inthe region bordered by a relative deviation less than 20%. As amatter of fact, only for six data points the deviation betweenexperimental and estimated equilibrium water dew point temper-ature was obtained to be P10% through the testing and trainingdevelopment. According to Fig. 11b, relative deviations located inthe span �18.96% to 16.33%, the magnitude of minimum relativedeviation is 0.0334%, and the average magnitude of deviation is2.909%, while for the testing data banks the relative deviationslocated in the span �14.92% to 7.545%, the magnitude of minimumrelative deviation is 0.0099%, and the average absolute deviationsis 1.676%.

6. Conclusions

1. According to the literature database, the feasibility of usingANN scheme trained with a new evolutionary algorithm,viz PSO, to predict equilibrium water dew point versus cont-actor temperature at different concentrations of TEG wasconsidered. The proposed PSO-ANN approach produced highreliability, with MSE and R2 of 13.472 and 0.998,respectively.

2. The use of PSO led to the rise of comprehensive searchingcapability for choosing appropriate initial weights of ANN.

3. To specify the optimal structure of the PSO-ANN approach,various three-layer feed-forward networks with differentneurons in hidden layer were tested. Tuning parameters(including acceleration constants (c1 and c2), number of max-imum iterations, number of particles, and time interval) ofproposed hybrid model were carefully carried out.

4. According to the graphical representations together with thestatistical error analysis, the optimum PSO-ANN scheme per-forms much better in accuracy than the common back prop-agation NN approach for the purpose of equilibrium waterdew point prediction due to unlike PSO algorithm there isa probability of trapping or undulating nearby a local min-ima in back propagation algorithms.

7. Uncited references

[61,62].

Appendix A

This section provides some of the data that used in this study.Table A1 reports the contactor temperature, concentration of TEGand corresponding equilibrium water dew point temperature.



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Table A1Data used in this study [1,6].

ContactorT (�C)

TEGpurity (%)

Equilibrium waterdew point T (�C)

ContactorT (�C)

TEGpurity (%)


ContactorT (�C)

TEGpurity (%)


10 90 �6 70 99.8 4.5 30 99.98 �5515 90 �1 10 99.8 �46.5 35 99.98 �52.520 90 3 15 99.8 �43.5 40 99.98 �5025 90 8.5 20 99.8 �40 45 99.98 �47.530 90 13 25 99.8 �36.5 50 99.98 �4535 90 18 30 99.8 �33.5 55 99.98 �42.537 90 20 35 99.8 �30 60 99.98 �4010 95 �12 40 99.8 �26.5 65 99.98 �37.515 95 �8 45 99.8 �24 70 99.98 �3520 95 �4 50 99.8 �20.5 75 99.98 �32.525 95 1 55 99.8 �17 10 99.99 �7230 95 5 60 99.8 �14 15 99.99 �6935 95 9.5 65 99.8 �11 20 99.99 �66.540 95 14 70 99.8 �8.5 25 99.99 �63.545 95 19 75 99.8 �5.5 30 99.99 �61.510 97 �18 10 99.9 �52.5 35 99.99 �5915 97 �13.5 15 99.9 �49.8 40 99.99 �56.520 97 �10 20 99.9 �47 45 99.99 �5425 97 �6 25 99.9 �43.5 50 99.99 �5230 97 �2 30 99.9 �40.5 55 99.99 �4935 97 2 35 99.9 �37.5 60 99.99 �4740 97 6 40 99.9 �34 65 99.99 �4445 97 11.5 45 99.9 �31.5 70 99.99 �4250 97 15 50 99.9 �28 75 99.99 �39.555 97 19.5 55 99.9 �25 10 99.995 �7710 98 �22 60 99.9 �22.5 15 99.995 �7415 98 �18 65 99.9 �19.5 20 99.995 �7220 98 �14.5 70 99.9 �17 25 99.995 �6925 98 �11 75 99.9 �14 30 99.995 �6730 98 �7 10 99.95 �59 35 99.995 �64.935 98 �2.5 15 99.95 �56 40 99.995 �62.540 98 1.5 20 99.95 �54 45 99.995 �6045 98 6 25 99.95 �50 50 99.995 �57.550 98 9.5 30 99.95 �47.5 55 99.995 �5555 98 13.5 35 99.95 �44 60 99.995 �5360 98 17.5 40 99.95 �42 65 99.995 �5110 99 �30 45 99.95 �38.5 70 99.995 �4815 99 �26.5 50 99.95 �36 75 99.995 �4720 99 �22.5 55 99.95 �33.5 15 99.997 �7825 99 �19 60 99.95 �30 20 99.997 �7630 99 �15 65 99.95 �27.5 25 99.997 �7335 99 �11 70 99.95 �25 30 99.997 �71.540 99 �8 75 99.95 �22.5 35 99.997 �6845 99 �4 10 99.97 �63 40 99.997 �6750 99 �0.25 15 99.97 �60 45 99.997 �6455 99 3.5 20 99.97 �57.5 50 99.997 �6260 99 7.5 25 99.97 �54.5 55 99.997 �6065 99 11.5 30 99.97 �52 60 99.997 �57.570 99 14.5 35 99.97 �49 65 99.997 �5510 99.5 �37.5 40 99.97 �47 70 99.997 �5315 99.5 �34 45 99.97 �44.5 75 99.997 �51.520 99.5 �30 50 99.97 �4125 99.5 �27 55 99.97 �38.530 99.5 �23 60 99.97 �3635 99.5 �19.5 65 99.97 �3340 99.5 �16.5 70 99.97 �3145 99.5 �12.5 75 99.97 �2850 99.5 �9 10 99.98 �66.555 99.5 �6 15 99.98 �63.560 99.5 �2.5 20 99.98 �6165 99.5 1 25 99.98 �58



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