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Research Papers: Energy Systems Analysis

Optimization and Estimation of the Thermal Energy of an Absorber With Graphite Disks by Using Direct and Inverse Neural Network OPEN ACCESS

[+] Author and Article Information
A. Márquez-Nolasco, O. R. Pérez

Centro de Investigación en Ingeniería y Ciencias
Aplicadas (CIICAp),
Universidad Autónoma del Estado de Morelos,
Avenida Universidad No. 1001,
Col Chamilpa, CP,
Cuernavaca 62209, Morelos, Mexico

R. A. Conde-Gutiérrez

Centro de Investigación en Ingeniería y Ciencias
Aplicadas (CIICAp),
Universidad Autónoma del Estado de Morelos,
Avenida Universidad No. 1001,
Col Chamilpa, CP,
Cuernavaca 62209, Morelos, Mexico
e-mail: roberto.conde@uaem.mx

J. A. Hernández

Centro de Investigación en Ingeniería y Ciencias
Aplicadas (CIICAp),
Universidad Autónoma del Estado
de Morelos (UAEM),
Avenida Universidad No. 1001,
Col Chamilpa, CP,
Cuernavaca 62209, Morelos, Mexico
e-mail: alfredo@uaem.mx

A. Huicochea

Centro de Investigación en Ingeniería y Ciencias
Aplicadas (CIICAp),
Universidad Autónoma del Estado de Morelos (UAEM),
Avenida Universidad No. 1001,
Col Chamilpa, CP,
Cuernavaca 62209, Morelos, Mexico

J. Siqueiros

Secretaría de Innovación,
Ciencia y Tecnología de Morelos,
Avenida Atlacomulco No. 13,
Colonia Acapatzingo, C.P.,
Cuernavaca 62440, Morelos, Mexico

1Corresponding authors.

Contributed by the Advanced Energy Systems Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received April 1, 2017; final manuscript received April 11, 2017; published online September 28, 2017. Editor: Hameed Metghalchi.

J. Energy Resour. Technol 140(2), 020906 (Sep 28, 2017) (13 pages) Paper No: JERT-17-1146; doi: 10.1115/1.4036544 History: Received April 01, 2017; Revised April 11, 2017

The most critical component of an absorption heat transformer (AHT) is the absorber, by which the exothermic reaction is carried out, resulting in a useful thermal energy. This article proposed a model based on improving the performance of energy for an absorber with disks of graphite during the exothermic reaction, through an optimal strategy. Two models of artificial neural networks (ANN) were developed to predict the thermal energy, through two important factors: internal heat in the absorber (QAB) and the temperature of the working solution of the absorber outlet (TAB). Confronting the simulated and real data, a satisfactory agreement was appreciated, obtaining a mean absolute percentage error (MAPE) value of 0.24% to calculate QAB and of 0.17% to calculate TAB. Furthermore, from these ANN models, the inverse neural network (ANNi) allowed improves the thermal efficiency of the absorber (QAB and TAB). To find the optimal values, it was necessary to propose an objective function, where the genetic algorithms (GAs) were indicated. Finally, by applying the ANNi–GAs model, the optimized network configuration was to find an optimal value of concentrated solution of LiBr–H2O and the vapor inlet temperature to the absorber. The results obtained from the optimization allowed to reach a value of QAB from 1.77 kW to 2.44 kW, when a concentrated solution of LiBr–H2O at 59% was used and increased the value of TAB from 104.66 °C to 109.2 °C when a vapor inlet temperature of 73 °C was used.

The environment is being seriously damaged due to pollution problems, especially as factories do not use primary energy efficiently; as a result, residual heat is released causing severe problems such as global warming [1]. For environmental regulations through recycling and reuse of this waste heat, the absorption heat pumps have presented wide attention [2].

Absorption heat transformer (AHT) has the faculty to raise the temperature of a residual heat with a medium thermal level (between 40 °C and 80 °C) to a higher thermal level (between 90 °C and 120 °C), through an exothermic reaction, where the thermal energy produced can increase the waste heat so that it can be used in an industrial application. The Energy International Agency (EIA) has considered the AHT as an important future technology for the use of energy even though the industrial applications are still very limited [3].

Several theoretical and experimental researches have been conducted to improve the performance of different AHT. Some authors made a bibliographic revision with a common focus. Rivera et al. [4] performed a comparison of the theoretical efficiency of different AHTs, reported in previous studies. Meanwhile Donnellan et al. [3] presented some general works that improve the thermodynamic cycle through new configurations. They have also been used for different work solutions and an example is the one reported by Ertas et al. [5] in which they presented a study considering a single stage AHT with binary mixture of NH3–H2O as the working fluid.

Ishida and Ji [6] with Venegas et al. [7] concluded that the absorber is the key component of the absorption heat pumps, because their performance has a notable effect in the coefficient of performance (COP) of every system. Therefore, some theoretical and experimental studies have been developed to improve the absorber. One of the reported improvements in the solution of the work was by Ryan [8], who used spraying method; the solution was sprayed in an adiabatic chamber in order to maximize the area of vapor contact and therefore withdraw the resulting heat in another exchanger. The results showed that the transfer heat coefficients increase considerably and that were capable of reducing to half the transferred heat area of a conventional absorber. On the other hand, Sözen and Yücesu [9] improved 14% for the COP and 30% for the exergy coefficient of performance (ECOP) of an AHT by theoretically analyzing an ejector placed at the inlet of the absorber to increase the pressure which, consequently, improves the temperature of the exothermic reaction. As the absorber is considered as the main component for the performance of AHT, it is also the component that contributes the most to the total percentage of the irreversibility or destruction of exergy in a thermodynamic cycle [1013].

Absorbers also play an important role in refrigeration cycles, where the performance of this device raises the operating coefficient of a process. Zhang et al. [14] improved the absorption cycle by adding components to raise the pressure between the evaporator and the absorber.

Subsequently, with the development of artificial neural networks (ANN), they are able to model processes from an experimental data base for learning and used them in various applications as the analysis of the heat exchangers with an acceptable precision of any variable. Mohanraj et al. [15] reported an ANN application revision for the thermal analysis of different heat exchangers. The ANN has been applied in refrigeration, air conditioning, and heat pumps as well [16]. Recently, this methodology has been used to optimize predictions, developing the combination of ANN with other algorithms such as particle swarm. Manshad et al. [17] developed new artificial neural network optimized by particle swarm optimization (ANN–PSO) for dew point pressure prediction. Wang and Salehi [18] optimized drilling hydraulics, applying the ANNs to have a reliable simulation of pump pressure.

Once analyzed, the importance of having the absorber is felt; because of the useful thermal energy obtained and the relationship of the ANN for the model and control in the heat exchangers, it was necessary to know the optimal parameters of the experimental equipment. Finding optimal operating conditions is a challenge, but the performance of systems or processes depends to a large extent on several important parameters, which influence not only the operation of the equipment but also other aspects, such as in technical and economic feasibility [19]. When optimizing a process, it is possible to save the energy and improve energy efficiency. The inverse artificial neural network methodology (ANNi), allowed through the ANN model, uses the same weights and biases during the training to calculate optimal operation conditions. This model has been used in experimental equipment to increase performance: Laidi and Hanini [20] developed the model to find an optimal input parameter taking into account a required solar COP, which is applied for a cooling system. For AHT with application to distill water, Hernández et al. [21] with Colorado et al. [22] applied the simplex method to calculate optimal conditions and to solve the ANNi model. Morales et al. [23] developed a model of inverse artificial neural network to increase the value of COP, applied to an AHT, finding optimal conditions in the heat supply.

When an absorber is designed, it is important to know the amount of heat that can be obtained when the exothermic reaction takes place, because an output temperature will be released from this heat, which will be useful to transfer heat internally to a fluid that goes through externally, and this can use the recollected thermal level in a useful application. In this work, the internal heat in the absorber (QAB) and the temperature of the working solution to the absorber outlet (TAB) were simulated by two ANN models, which consider the following experimental operation equipment conditions: the inlet (Tin.Sol) and outlet (Tout.Sol) temperatures of the working solution, the inlet temperature of vapor (Tin.Vap), pressure (P), concentrations in the inlet (Xin.AB) and outlet (Xout.AB) of the solution LiBr–H2O, the mass flow in the inlet (x˙in.Sol) and outlet (x˙out.Sol) of the solution, and the mass flow of vapor (x˙in.Vap), which can be optimized to reach high values of QAB and TAB.

The aim of this paper is focused on increasing the useful thermal energy by the exothermic reaction, which is carried out in an absorber with graphite disks, through developing an optimal strategy to calculate input variables, given a value of output required; by increasing the thermal energy of the device, it is possible to improve the efficiency of the thermodynamic cycle for an AHT; and, the high thermal level reached could be used for purifying water, distillation of oils, heating, and preheating among others.

Figure 1(a) shows the inner part of the absorber with 18 disks of graphite in the form of vertical column, while Fig. 1(b) shows the outer part, which has a 316 L stainless steel shell. Figure 1(c) shows how a tar-impregnated graphite disk with 0.1 m in outside diameter was designed as described by Olarte-Cortés et al. [24]

The thermodynamic cycle of AHT is shown in Fig. 2, where the overall performance of this is known and given by several authors [3,11]. For this work, only the absorber is described in order to study and analyze the useful thermal energy attained. The experimental absorber works as follows: the working mixture LiBr–H2O coming from the generator enters through the top of the absorber in high concentration; this is distributed by gravity onto the upper and lower surfaces of the graphite disks to a known flow, at the same time by the bottom of the absorber a vapor flow coming from the evaporator enters, which will be absorbed by the LiBr–H2O that descends on each side of the disk. When vapor absorption is carried out in an exothermic reaction, the solution leaving the absorber at a lower concentration and higher temperature is compared with the input solution. In the annular part of the absorber (external circuit), the heat of exothermic reaction that can be exploited in a secondary process is removed.

In order to know the performance of the absorber according to QAB and TAB, input variables were varied during experimental tests, such as Tin.Vap (°C), Tin.Sol (°C), x˙in.Sol (kg/s), and Xin.Sol (% in weight). Fourteen experimental tests were obtained in stable conditions for AHT with the absorber of graphite disks. 90 data were obtained for each experimental test of the parameters in steady state, considering a time of 15 min. The measured parameters such as mass flow, temperature, and pressure showed insignificant variation in their readings. Table 1 shows the interval of experimental conditions used.

For the experimental tests of the AHT, a thermodynamic analysis was performed to determine the COP equipment. For thermodynamic analysis, thermophysical properties of the working mixture LiBr–H2O, taken from correlations in the literature proposed with wide interval validity [25], were used. The concentrations of the working solution from the inlet and outlet of the absorber were measured by using the refractive index and a correlation reported in the literature [26].

Based on the first law of thermodynamics, the absorber was analyzed (Eqs. (1)(4)):

Mass balance Display Formula

(1)m˙inm˙out=0

Species balance Display Formula

(2)m˙inxinm˙outxout=0

Energy balance Display Formula

(3)(m˙inhinm˙outhout)+(Q˙inQ˙out)+W˙=0

Therefore, the internal heat load obtained in the absorber based on the input and output mass flows is calculated from the below equation Display Formula

(4)QAB=(m˙in.Vap*hin.Vap+m˙in.Sol*hin.Sol)m˙out.Sol*hout.Sol

Uncertainty Analysis.

In order to estimate the error in the experimental measurements, an uncertainty analysis was performed. The correlation of water properties, compared to the National Institute of Standards and Technology (NIST) database, is less than 1% [27]. To obtain the combined uncertainty the Taylor series [28] was used, which is given as Display Formula

(5)Uc2(y)=i=1N(fxi)2u2(xi)

Table 2 shows the results of the measurement uncertainty. The maximum uncertainty due to propagation of this measurement error is less than 12.8%, which was obtained in QAB.

For forming the two ANN models, the following steps were used:

  1. (1)Organize and create a database with experimental data collected from the conditions of experimental equipment.From the experimental tests, 1250 data were obtained, enough to carry out the learning of the ANN models. These data were treated [23] and were were normalized with the below equation Display Formula
    (6)xi,Norm=0.8×(Xi,RealXminXmaxXmin)+0.1
  2. (2)Develop an algorithm for the learning process for the ANN models, where the simulated outlet and the desired experimental outlet were evaluated, aiming that these two values were as close as possible.The weights (Wi) and biases (b1) were coefficients obtained from training, where these were adjusted for a better prediction of the output value and were associated with the hidden layer grouped into matrices.The learning process was performed for the two ANN models as shown in Figs. 3 and 4. According to the flow diagrams, the ANN model was first trained from the experimental data; later, within the ANN model, an architecture was chosen (neurons in the hidden layer), as it complies with the simulated output. Finally, the simulated data obtained from the training and tests are compared to be validated with the experimental ones through the learning process (back-propagation). If the simulated output meets with established error criteria, there will be an acceptable output value. If the criteria are not met, it is necessary to return to the ANN model to choose another architecture arrangement.For minimization of errors between the data obtained from the experimental base and those simulated by the neural network, the Levenberg–Marquardt algorithm was used as the back-propagation optimization algorithm, and it is considered by Bhowmik et al. [29] as the most efficient optimal network than other training algorithms and has fastest network convergence rate [30]. The statistical error criterion used during training of the neural network was the root-mean-square error (RMSE).The neurons in the hidden layer can be used to transfer functions that are appropriate and compatible with the type of desired output. The TANSIG and LOGSIG functions were compared to observe whether which one has the best prediction results. For the output layer, a PURELIN function was applied. The programming was carried out in matlab using the ANN toolbox.The transfer functions used were as follows: Display Formula
    (7)TANSIG=21+exp(2ns)1
    Display Formula
    (8)LOGSIG=11+exp(ns)
    The output layer performed the weighted sum of the signals provided by the hidden layer, and the associated coefficients were grouped into matrices Wo and b2 (obtained also during training).
  3. (3)Perform a statistical analysis between actual and simulated data

The three main criteria used are: RMSE, mean absolute percentage error (MAPE), and the coefficient of determination (R2), since they allow identifying the relationship between the actual (Exp) and simulated (Sim) data [31] Display Formula

(9)RMSE=i=1n(PSim(i)PExp(i))2n
Display Formula
(10)MAPE=i=1n(|PExp(i)PSim(i)|PExp(i))n×100(%)
Display Formula
(11)R2=1i=1n(PExp(i)PSim(i))2i=1n(PExp(i)P¯Exp)2

Finally, in order to determine compatibility between the simulated data by ANN and the experimental database, the tests of the relationship Fisher F and Student t were applied.

Fisher F test arises with the following assumptions:

  • The null hypothesis Ho: “the two databases have the same or similar variances”

  • The alternative hypothesis Hi: “the two databases have different variances”

For the null hypothesis accepted, the value obtained by Eq. (12) must be less than the critical value obtained from tables [32].

Student t test arises with the following assumptions:

  • The null hypothesis Ho: “the two databases belong to the same population or similar populations through its mean”

  • The alternative hypothesis Hi: “the two databases have different mean”

For the null hypothesis accepted, the value obtained by Eq. (13) must be less than the critical value obtained from tables [32] Display Formula

(12)F=sx2sy2
Display Formula
(13)t=|x¯y¯|s((1nx+1ny))

where S is the value of the variance, x is the experimental value of the variable, y is the value estimated by ANN, x¯ and y¯ are the mean values, and n is the total number of data.

By analyzing and comparing different configurations of transfer functions, simulating the value of QAB was necessary to use two hidden neurons (9-2-1); in the same way, it was found with seven hidden neurons (7-7-1) for the best prediction TAB values, for an absorber with disks of graphite.

To determine the best architecture of the ANN models, different numbers of neurons in the hidden layer and different transfer functions were tested. A confrontation between the different architectures and hidden transfer functions, with their respective error to predict the desired output, is shown in Tables 3 and 4. As it can be seen, in the case of prediction QAB, the transfer function TANSIG turned out to be better, but for the prediction of TAB, the transfer function LOGSIG managed to overcome the function TANSIG.

According to data obtained by the ANN training, the best values for RMSE, MAPE, and R2 were 0.0035, 0.24%, and 0.9998 to calculate the value of QAB and from 0.2245, 0.17%, and 0.9956 to calculate the value of TAB, respectively.

Figures 5 and 6 present a comparison between the predicted and experimental data, and in both models, there was a satisfactory agreement.

Table 5 shows for both models, when applying the significance tests, the approved hypothesis null H0. The results showed that samples (experimental and predicted) can be considered to have the same variance and mean, and therefore, come from the same population.

Tables 6 and 7 show the input and output of the weights and bias, used to predict the values of QAB and TAB.

Based on the best structure of an ANN (two neurons in the hidden layer), the proposed model to simulate the value QAB can be analytically represented by the following equation: Display Formula

(14)QAB=j=1S[Wo(j)(21+exp(2(k=1K(Wi(j,k)In(k))+b1(j)))1)]+b2

For the case of TAB (with seven neurons in the hidden layer), the proposed model was represented by the following equation: Display Formula

(15)TAB=j=1S[Wo(j)(11+exp((k=1K(Wi(j,k)In(k))+b1(j))))]+b2

where k is the number of neurons in the input layer, s is the number of neurons in the hidden layer, and W and b are weights and biases, respectively (see Tables 6 and 7).

After being statistically compared and analyzed, these models can be successfully used on-line for simulation and control of the experimental equipment. Applying Eq. (14), in Fig. 7, shows a simulated behavior of heat internal QAB obtained according to the temperature inlet of vapor and concentrated solution, Tin.Vap and Tin.Sol, respectively. It can be appreciated that in the Tin.Vap equal to 61 °C value decreases at QAB. For these temperatures, a set of tests were carried out and were analyzed in flow adequate of LiBr–H2O for greater distribution on disks and this increases the heat transfer area. So, QAB decreased because the amount of vapor mass that entered the absorber decreased from 0.00098 to 0.00051 kg/s; as a result, it also changes the mass flow of the concentrated solution LiBr–H2O; therefore, the amount of internal energy in the absorber decreases proportionally. Once the best mass flow of solution LiBr–H2O (0.0135 kg/s) and the best mass flow of vapor (0.0008 kg/s) are obtained, an operating interval was obtained for Tin.Vap of 66–71 °C, where it is observed that QAB favors, because the exothermic reaction increases. This same effect happens when Tin.Sol increased [33].

Moreover, it is applied in Eq. (15), in Fig. 8, and is appreciated to increase the value of TAB in the function of Tin.Vap and Tin.Sol; in both cases, it was due to the increase in the vapor inlet temperature and the concentrated solution, in carrying out the interaction between the two flows, causing an increase in the exothermic reaction, since the new saturation condition of the solution was higher; therefore, the TAB reaches more high values.

The development of this methodology leads to optimize input variables of an experimental equipment or process, with the ability to increase or improve system performance. Beginning with Eqs. (14) and (15), if the desired output was known, an optimal input variable can be found (k), as shown in the following steps [34]:

As an example, Eq. (14) is first developed. The value of QAB is now known as a value predicted by the ANN model Display Formula

(16)QAB=2[W0(1,1)1+exp(x1)+W0(1,2)1+exp(x2)](W0(1,1)+W0(1,2))+b2

In each hidden neuron (x), it is possible to choose one of the nine input variables (k) to know its optimum value and observe the results obtained with respect to QABDisplay Formula

(17)x1=2(Wi(1,1)k1+Wi(1,2)k2+Wi(1,3)k3+Wi(1,4)k4+Wi(1,5)k5+Wi(1,6)k6+Wi(1,7)k7+Wi(1,8)k8+Wi(1,9)k9+b1(1))
Display Formula
(18)x2=2(Wi(7,1)k1+Wi(7,2)k2+Wi(7,3)k3+Wi(7,4)k4+Wi(7,5)k5+Wi(7,6)k6+Wi(7,7)k7...+Wi(7,8)k8+Wi(7,9)k9+b1(7))

In this work, for the ANN model where the value QAB was simulated, the percentage of the concentrated solution of LiBr–H2O (Xin.AB) was elected as an input variable to optimize. For the model ANN where the value TAB was simulated, the vapor inlet temperature to the absorber (Tin.Vap) was elected as an input variable to optimize, because by increasing the value of these two variables the performance of QAB and TAB could be improved.

Applying the methodology of ANNi, as the values of QAB and TAB were known, it is possible to propose a function that must be minimized with respect to the known value (objective function), in order to be able to find optimal input conditions, as Eqs. (19) and (20). In this paper, the genetic algorithms were used as a search method.

  • In case QABDisplay Formula

    (19)Fun(Xin.AB)=b2j=1SWo(j)QAB+j=1S[2Wo(j)1+exp(2(Wi(j,k)In(Xin.AB)+k=1K(Wi(j,k)In(k)+b1(j)))]

  • In case TABDisplay Formula

    (20)Fun(Tin.Vap)=b2TAB+j=1S[Wo(j)1+exp((Wi(j,k)In(Tin.Vap)+k=1K(Wi(j,k)In(k)+b1(j)))]

Sensitivity Analysis of the Input Variables.

In order to evaluate the contribution of each input parameter on the ANNi models (for QAB and TAB), a sensitivity analysis was applied. The neuronal matrix of weights (Tables 6 and 7) and Eq. (21), of Garson [35], in which Ij is the relative importance, based on the partition of the weight connection (W) with their inputs and hidden neurons, were used (Ni and Nh) Display Formula

(21)Ij=m=1m=Nh((|Wjmih|/k=1Ni|Wkmih|)×|Wmnho|)k=1k=Ni{m=1m=Nh(|Wjmih|/k=1Ni|Wkmih|)×|Wmnho|}

where the superscripts “i,” “h,” and “o” attribute to input, hidden, and output layers and subscripts “k,” “m,” and “n” attribute to input, hidden, and output neurons, corresponding.

Figure 9(a) shows how the concentration of the working solution of LiBr–H2O has a significant contribution on the value of QAB; this is due to the fact that increasing the concentration in the absorber increases the internal enthalpy, generating greater internal heat. However, for Fig. 9(b), it is shown that the inlet temperature in the evaporator has a significant contribution on the value of TAB; this is due to the interaction between the concentrated solution and the vapor at higher temperature; the exothermic reaction becomes more intense since the solution absorbs the refrigerant with a higher thermal level, resulting in a higher temperature at the exit of the working solution.

In order to solve Eqs. (19) and (20), by the complexity that exists to find an optimal value input when the ANN model was inverted and whether this has several neurons in the hidden layer, the model becomes more robust and difficult to solve by algebraic methods; then it was necessary to use a computational tool to find a next or exact value according to the desired value. Genetic algorithms (GAs) apply the principles of genetics to search among a population a set of individuals that represents a possible solution to solve an optimization problem [36]. This computational tool has been used in different processes to search optimal levels [37].

According to Sec. 6, once ANNi model was developed, taking into account the value of QAB and TAB desired (must be greater than the achieved experimentally), the objective function resulting must be minimized as close to zero, in order to have correct input optimum value; for this, a genetic algorithm was programmed to search the optimum input value (Xin.AB and Tin.Vap) and to minimize the objective function as close to zero as possible. Figure 10 shows how the GAs was developed and Fig. 11 shows how the objective function was minimized as close to zero. The precision of the GAs depends largely on their genetic operators; the combination of these is shown in Table 8. The programming was carried out in matlab using the optimization toolbox.

In this article, two experimental runs were chosen in order to apply the ANNi model. In the first run, three experimental points were obtained, where the concentration of the solution of the absorber inlet was increased; at the same time, the value of QAB increased, as shown in Fig. 12(a). The ANNi model was applied for a known value of QAB and the optimal inlet conditions were determined (optimal strategy) as shown in Fig. 12(b). When comparing the ANNi model with the experimental data, a good prediction will be appreciated. Therefore, taking into account the latest experimental data, where operating conditions were Tin.Sol = 81.61 °C, x˙in.Sol = 0.018 kg/s, Tout.Sol = 99.76 °C, x˙out.Sol = 0.01898 kg/s, Tin.Vap = 60.50 °C, x˙in.Vap = 0.00098 kg/s, Xin.AB = 56.96% (in weight), Xout.AB = 54.02% (in weight), PAB = 20 kPa, and QAB = 1.7722 kW, an ANNi model was applied to analyze the QAB behavior in the function of Xin.AB, in order to raise the value of QAB, reaching a value of 2.44 kW (improved a 37.7%) when the 59% of concentrated solution was supplied; it must be pointed out that the three values last reached by the model ANNi were out from the experimental data. Furthermore, the relative error of the theoretical QAB with respect to the QAB obtained by the ANNi model has been calculated (see Table 9). The result indicated that when the value of Xin.AB increased from 56.96 to 58, 58.5, and 59% (the weight of LiBr was increased with respect to H2O), the error was increased from the theoretical value from 17.5 to 27.5%, respectively; these model errors showed a value of 320 and 520 W above the theoretical QAB; it is highly probable that the values found by the ANNi model can be reached, since the results were congruent with the experimental tendency. A certain analysis limit above the experimental interval has been considered, as the mixture LiBr–H2O has crystallization problems that prevent the equipment to function when it was concentrated above 70%.

In the second run, four experimental points were obtained, where the inlet evaporator temperature value was increased; when this variable was increased, the value of TAB also increases, as it is shown in Fig. 13(a). By applying the same process that was shown in Fig. 12(b), the ANNi model was developed for a known value of TAB, in order to optimize the vapor inlet temperature to the absorber, as shown in Fig. 13(b). Taking into account the latest experimental data, where operating conditions were Tin.Sol = 81.14 °C,x˙in.Sol = 0.0134 kg/s, Tin.Vap = 70.52 °C, x˙in.Vap = 0.0008 kg/s, Xin.AB = 55.55% (in weight), Xout.AB = 52.4% (in weight), PAB = 34 kPa, and TAB = 104.66 °C, an optimal inlet value was searched to increase the value of TAB, reaching a maximum of 109 °C when the Tin.Vap was incremented to 73 °C. An analysis of the values of Tin.Vap by ANNi model was performed outside the experimental interval. These values were compared with the theoretic TAB calculated with the thermodynamic properties of the LiBr–H2O reported by McNelly [25]. The obtained values are shown in Table 9. The table shows that for the values of Tin.Vap from 71 to 73 °C, the highest error made by the ANNi model was from 4.4%, which represents a value of TAB close to the theoretic temperature. For these new temperatures, values of Tin.Vap closest to the experimental interval of the ANNi model were reliable. On the other hand, when the value of Tin.Vap was 79 °C, the error increased up to 14.2%; being significant, it was far from the theoretic expected value and turns out not to be congruent with the experimental tendency. Therefore, this tool is recommended for data close to the experimental interval in which it was trained, and it turns out to be reliable based on the experimental criteria.

Once validated, the ANNi model with experimental and theoretical data can be widely applied for the analysis of experimental tests in various operating conditions, as shown in Fig. 14; using different mass flows of solution at different concentrations, the trend of QAB increased as there was a raise in the concentration of the solution or when the mass flow of concentrated solution increased, getting better results with a mass flow in the input of solution from 0.018 kg/s; however, it was recommended to use a flow of 0.014 kg/s due to the geometry of the graphite disks, since this flow allows greater permeability; therefore, greater heat transfer was exploited during the exothermic reaction. Figure 15 shows that by increasing the inlet temperature of the vapor also the value of TAB rises, getting better results when using a mass flow of 0.0008 kg/s. In the three trends, it was observed that the optimal value of Tin.Vap was between 70 °C and 73 °C; after this temperature, the value of TAB decreases; this may be because Tin.Vap is at a high thermal level, and the interaction between Tin.Vap and Tin.Sol no longer produced an efficient exothermic reaction.

In Table 10, the results obtained from this work are compared against other investigations; by applying the optimization, it is possible to achieve better values of TAB and QAB than those reported experimentally.

A graphite disk absorber was presented as a key component to produce useful thermal energy from waste heat sources, within an absorption heat transformer, and designed as a heat exchanger different from the conventional ones because of its high resistance to corrosion by using the working solution of LiBr–H2O.

The absorber was modeled through two ANNs, in order to simulate QAB and TAB, finding the best architecture with 9-2-1 and 7-7-1, respectively. These models were trained using an experimental base of equipment. The results of the ANN models exceeded the statistical tests successfully between the experimental data and the simulated data, as the significant tests (F-Fisher and t student), and obtaining lower errors during the training of RMSE = 0.0035 to calculate QAB and RMSE = 0.2245 to calculate TAB.

The variables that enter the absorber were optimized as: the percentage of the concentrated solution of LiBr–H2O to increase QAB, and the temperature of inlet of vapor to increase the value of TAB by ANNi model. The optimization of the concentration of the solution indicates that by increasing this from 56.9% to 59%, it is possible to improve a 37.7% of the value of QAB, the values being congruent with the experimental tendency and close to the theoretical calculated value; this optimization was limited by LiBr–H2O crystallization. On the other hand, optimizing the value of Tin.Vap from 70 °C to 73 °C, it was observed that it is possible to reach a maximum value of TAB of 109.2 °C. Under these new optimal conditions, it is possible to achieve a higher value of COP for the AHT.

Directly applying the ANNi–GAs model, it was possible to analyze the behavior of the experimental tests in various operating conditions, showing better results with high mass flows, except for x˙in.Sol, where experimentally it was observed that the disks were permeated best of the solution LiBr–H2O when a mass flow 0.014 kg/s was used, thus allowing a better exothermic reaction.

Finally, the application of ANNi–GAs can be considered as a strategy of optimization of variables and at the same time as a strategy to increase the performance of a process, system, or experimental equipment. However, it must be cleared that the extrapolation was performed from the experimental data with which the net was trained; that is why, when being compared with the theoretical equations, they could have discrepancies.

The authors of the research thank the support provided by Contact for Project No. 223013 and the doctoral fellowship awarded to A. Marquez and R. Conde.

Abumandour, E.-S. , Mutelet, F. , and Alonso, D. , 2016, “ Performance of an Absorption Heat Transformer Using New Working Binary Systems Composed of {Ionic Liquid and Water},” Appl. Therm. Eng., 94, pp. 579–589. [CrossRef]
Jung, C. W., An, S. S., and Kang, Y. T., 2014, “ Thermal Performance Estimation of Ammonia-Water Plate Bubble Absorbers for Compression/Absorption Hybrid Heat Pump Application,” Energy, 75, pp. 371–378. [CrossRef]
Donnellan, P. , Cronin, K. , and Byrne, E. , 2015, “ Recycling Waste Heat Energy Using Vapour Absorption Heat Transformers: A Review,” Renewable Sustainable Energy Rev., 42, pp. 1290–1304. [CrossRef]
Rivera, W. , Best, R. , Cardoso, M. J. , and Romero, R. J. , 2015, “ A Review of Absorption Heat Transformers,” Appl. Therm. Eng., 91, pp. 654–670. [CrossRef]
Ertas, A. , Gandhidasan, P. , and Luthan, J. J. , 1987, “ Feasibility Study of Ammonia-Water Vapor Absorption Heat Transformer,” ASME J. Energy Resour. Technol., 109(2), pp. 96–100. [CrossRef]
Ishida, M. , and Ji, J. , 1999, “ Graphical Exergy Study on Single Stage Absorption Heat Transformer,” Appl. Therm. Eng., 19(11), pp. 1191–1206. [CrossRef]
Venegas, M. , Rodríguez, P. , Leucona, A. , and Izquierdo, M. , 2005, “ Spray Absorbers in Absorption Systems Using Lithium Nitrate–Ammonia Solution,” Int. J. Refrig., 28(4), pp. 554–564. [CrossRef]
Ryan, W. A. , 1994, “ Water Absorption in an Adiabatic Spray of Aqueous Lithium Bromide Solution,” International Absorption Heat Pump Conference, New Orleans, LA, Jan. 19–21, ASME AES-Vol. 31, pp. 155–162.
Sözen, A. , and Yücesu, H. S., 2007, “ Performance Improvement of Absorption Heat Transformer,” Renewable Energy, 32(2), pp. 267–284. [CrossRef]
Rivera, W. , Siqueiros, J. , Martínez, H. , and Huicochea, A. , 2010, “ Exergy Analysis of a Heat Transformer for Water Purification Increasing Heat Source Temperature,” Appl. Therm. Eng., 30(14–15), pp. 2088–2095. [CrossRef]
Sekar, S. , and Saravanan, R. , 2011, “ Exergetic Performance of Eco Friendly Absorption Heat Transformer for Seawater Desalination,” Int. J. Exergy, 8(1), pp. 51–67.
Gomri, R. , 2009, “ Energy and Exergy Analyses of Seawater Desalination System Integrated in a Solar Heat Transformer,” Desalination, 249(1), pp. 188–196. [CrossRef]
Colorado, D. , Demesa, N. , Huicochea, A. , and Hernández, J. A. , 2015, “ Irreversibility Analysis of the Absorption Heat Transformer Coupled to a Single Effect Evaporation Process,” Appl. Therm. Eng., 92, pp. 71–80. [CrossRef]
Zhang, N. , Lior, N. , and Han, W. , 2016, “ Performance Study and Energy Saving Process Analysis of Hybrid Absorption-Compression Refrigeration Cycles,” ASME J. Energy Resour. Technol., 138(6), p. 061603. [CrossRef]
Mohanraj, M. , Jayaraj, S. , and Muraleedharan, C. , 2015, “ Applications of Artificial Neural Networks for Thermal Analysis of Heat Exchangers—A Review,” Int. J. Therm. Sci., 90, pp. 150–172. [CrossRef]
Mohanraj, M. , Jayaraj, S. , and Muraleedharan, C. , 2012, “ Applications of Artificial Neural Networks for Refrigeration, Air-Conditioning and Heat Pump Systems—A Review,” Renewable Sustainable Energy Rev., 16(2), pp. 1340–1358. [CrossRef]
Manshad, A. K. , Rostami, H. , Moein-Hosseini, S. , and Rezaei, H. , 2016, “ Application of Artificial Neural Network–Particle Swarm Optimization Algorithm for Prediction of Gas Condensate Dew Point Pressure and Comparison With Gaussian Processes Regression–Particle Swarm Optimization Algorithm,” ASME J. Energy Resour. Technol., 138(3), p. 032903. [CrossRef]
Wang, Y. , and Salehi, S. , 2015, “ Application of Real-Time Field Data to Optimize Drilling Hydraulics Using Neural Network Approach,” ASME J. Energy Resour. Technol., 137(6), p. 062903. [CrossRef]
García, J. M. , Padilla, R. V., and Sanjuan, M. E. , 2016, “ Response Surface Optimization of an Ammonia–Water Combined Power/Cooling Cycle Based on Exergetic Analysis,” ASME J. Energy Resour. Technol., 139(2), p. 022001. [CrossRef]
Laidi, M. , and Hanini, S. , 2013, “ Optimal Solar COP Prediction of a Solar-Assisted Adsorption Refrigeration System Working With Activated Carbon/Methanol as Working Pairs Using Direct and Inverse Artificial Neural Network,” Int. J. Refrig., 36(1), pp. 247–257. [CrossRef]
Hernández, J. A. , Bassam, A. , Siqueiros, J. , and Juárez-Romero, D. , 2009, “ Optimum Operating Conditions for a Water Purification Process Integrated to a Heat Transformer With Energy Recycling Using Neural Network Inverse,” Renewable Energy, 34(4), pp. 1084–1091. [CrossRef]
Colorado, D. , Hernández, J. A. , Rivera, W. , Martínez, H. , and Juárez, D. , 2011, “ Optimal Operation Conditions for a Single-Stage Heat Transformer by Means of an Artificial Neural Network Inverse,” Appl. Energy, 88(4), pp. 1281–1290. [CrossRef]
Morales, L. I. , Conde-Gutiérrez, R. A. , Hernández, J. A. , Huicochea, A. , Juárez-Romero, D. , and Siqueiros, J. , 2015, “ Optimization of an Absorption Heat Transformer With Two-Duplex Components Using Inverse Neural Network and Solved by Genetic Algorithm,” Appl. Therm. Eng., 85, pp. 322–333. [CrossRef]
Olarte-Cortés, J. , Torres-Merino, J. , and Siqueiros, J. , 2013, “ Experimental Study of a Graphite Disks Absorber Couple to a Heat Transformer,” Exp. Therm. Fluid Sci., 46, pp. 29–36. [CrossRef]
McNelly, A. , 1979, “ Thermodynamic Properties of Aqueous Solutions of Lithium Bromide,” ASHRAE Trans., 85(1), pp. 413–434.
Holland, F. A. , Siqueiros, J. , Santoyo, S. , Heard, C. L. , and Santoyo, E. R. , 1999, Water Purification Using Heat Pumps, E & FN Spon, New York.
NIST/ASME, 1998, “ Steam Properties Database. Version 2.1,” U.S. Department of Commerce, Gaithersburg, MA.
Coleman, H. W. , and Steele, W. G. , 2009, Experimentation Validation and Uncertainty Analysis for Engineers, Wiley, Hoboken, NJ. [CrossRef]
Bhowmik, S. , Panua, R. , Debroy, D. , and Paul, A. , 2017, “ Artificial Neural Network Prediction of Diesel Engine Performance and Emission Fueled With Diesel–Kerosene–Ethanol Blends: A Fuzzy-Based Optimization,” ASME J. Energy Resour. Technol., 139(4), p. 042201. [CrossRef]
Mukherjee, I. , and Routroy, S. , 2012, “ Comparing the Performance of Neural Networks Developed by Using Levenberg–Marquardt and Quasi-Newton With the Gradient Descent Algorithm for Modelling a Multiple Response Grinding Process,” Expert Syst. Appl., 39(3), pp. 2397–2407. [CrossRef]
Verma, S. P. , 2005, “ Estadística Básica Para el Manejo de Datos Experimentales: Aplicación en la Geoquímica (Geoquimiometria),” Universidad Nacional Autónoma de México, Mexico.
Verma, S. P. , 2009, “ Evaluation of Polynomial Regression Models for the Student t and Fisher F Critical Values, the Best Interpolation Equations From Double and Triple Natural Logarithm Transformation of Degrees of Freedom up to 1000, and Their Applications to Quality Control in Science and Engineering,” Rev. Mex. Cienc. Geol., 26, pp. 79–92.
Meza, M. , Márquez-Nolasco, A. , Huicochea, A. , Juárez-Romero, D. , and Siqueiros, J. , 2014, “ Experimental Study of an Absorption Heat Transformer With Heat Recycling to the Generator,” Exp. Therm. Fluid Sci., 53, pp. 171–178. [CrossRef]
Hamzaoui, Y. E. L. , Rodríguez, J. A. , Hernandez, J. A. , and Salazar, V. , 2015, “ Optimization of Operating Conditions for Steam Turbine Using an Artificial Neural Network Inverse,” Appl. Therm. Eng., 75, pp. 648–657. [CrossRef]
Garson, G. D. , 1991, “ Interpreting Neural-Network Connection Weights,” Artif. Intell. Expert Syst., 6(4), pp. 47–51.
Liu, F.-B. , 2008, “ A Modified Genetic Algorithm for Solving the Inverse Heat Transfer Problem of Estimating Plan Heat Source,” Int. J. Heat Mass Transfer, 51(15–16), pp. 3745–3752. [CrossRef]
Ilamathi, P. P. , Selladurai, V. V. , and Balamurugan, K. K. , 2013, “ Modeling and Optimization of Unburned Carbon in Coal-Fired Boiler Using Artificial Neural Network and Genetic Algorithm,” ASME J. Energy Resour. Technol., 135(3), p. 032201. [CrossRef]
Ibarra-Bahena, J. , Romero, R. J. , Velazquez-Avelar, L. , Valdez-Morales, C. V. , and Galindo-Luna, Y. R. , 2015, “ Experimental Thermodynamic Evaluation for a Single Stage Heat Transformer Prototype Build With Commercial PHEs,” Appl. Therm. Eng., 75, pp. 1262–1270. [CrossRef]
Sekar, S. , and Saravanan, R. , 2011, “ Experimental Studies on Absorption Heat Transformer Coupled Distillation System,” Desalination, 274(1–3), pp. 292–301. [CrossRef]
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References

Abumandour, E.-S. , Mutelet, F. , and Alonso, D. , 2016, “ Performance of an Absorption Heat Transformer Using New Working Binary Systems Composed of {Ionic Liquid and Water},” Appl. Therm. Eng., 94, pp. 579–589. [CrossRef]
Jung, C. W., An, S. S., and Kang, Y. T., 2014, “ Thermal Performance Estimation of Ammonia-Water Plate Bubble Absorbers for Compression/Absorption Hybrid Heat Pump Application,” Energy, 75, pp. 371–378. [CrossRef]
Donnellan, P. , Cronin, K. , and Byrne, E. , 2015, “ Recycling Waste Heat Energy Using Vapour Absorption Heat Transformers: A Review,” Renewable Sustainable Energy Rev., 42, pp. 1290–1304. [CrossRef]
Rivera, W. , Best, R. , Cardoso, M. J. , and Romero, R. J. , 2015, “ A Review of Absorption Heat Transformers,” Appl. Therm. Eng., 91, pp. 654–670. [CrossRef]
Ertas, A. , Gandhidasan, P. , and Luthan, J. J. , 1987, “ Feasibility Study of Ammonia-Water Vapor Absorption Heat Transformer,” ASME J. Energy Resour. Technol., 109(2), pp. 96–100. [CrossRef]
Ishida, M. , and Ji, J. , 1999, “ Graphical Exergy Study on Single Stage Absorption Heat Transformer,” Appl. Therm. Eng., 19(11), pp. 1191–1206. [CrossRef]
Venegas, M. , Rodríguez, P. , Leucona, A. , and Izquierdo, M. , 2005, “ Spray Absorbers in Absorption Systems Using Lithium Nitrate–Ammonia Solution,” Int. J. Refrig., 28(4), pp. 554–564. [CrossRef]
Ryan, W. A. , 1994, “ Water Absorption in an Adiabatic Spray of Aqueous Lithium Bromide Solution,” International Absorption Heat Pump Conference, New Orleans, LA, Jan. 19–21, ASME AES-Vol. 31, pp. 155–162.
Sözen, A. , and Yücesu, H. S., 2007, “ Performance Improvement of Absorption Heat Transformer,” Renewable Energy, 32(2), pp. 267–284. [CrossRef]
Rivera, W. , Siqueiros, J. , Martínez, H. , and Huicochea, A. , 2010, “ Exergy Analysis of a Heat Transformer for Water Purification Increasing Heat Source Temperature,” Appl. Therm. Eng., 30(14–15), pp. 2088–2095. [CrossRef]
Sekar, S. , and Saravanan, R. , 2011, “ Exergetic Performance of Eco Friendly Absorption Heat Transformer for Seawater Desalination,” Int. J. Exergy, 8(1), pp. 51–67.
Gomri, R. , 2009, “ Energy and Exergy Analyses of Seawater Desalination System Integrated in a Solar Heat Transformer,” Desalination, 249(1), pp. 188–196. [CrossRef]
Colorado, D. , Demesa, N. , Huicochea, A. , and Hernández, J. A. , 2015, “ Irreversibility Analysis of the Absorption Heat Transformer Coupled to a Single Effect Evaporation Process,” Appl. Therm. Eng., 92, pp. 71–80. [CrossRef]
Zhang, N. , Lior, N. , and Han, W. , 2016, “ Performance Study and Energy Saving Process Analysis of Hybrid Absorption-Compression Refrigeration Cycles,” ASME J. Energy Resour. Technol., 138(6), p. 061603. [CrossRef]
Mohanraj, M. , Jayaraj, S. , and Muraleedharan, C. , 2015, “ Applications of Artificial Neural Networks for Thermal Analysis of Heat Exchangers—A Review,” Int. J. Therm. Sci., 90, pp. 150–172. [CrossRef]
Mohanraj, M. , Jayaraj, S. , and Muraleedharan, C. , 2012, “ Applications of Artificial Neural Networks for Refrigeration, Air-Conditioning and Heat Pump Systems—A Review,” Renewable Sustainable Energy Rev., 16(2), pp. 1340–1358. [CrossRef]
Manshad, A. K. , Rostami, H. , Moein-Hosseini, S. , and Rezaei, H. , 2016, “ Application of Artificial Neural Network–Particle Swarm Optimization Algorithm for Prediction of Gas Condensate Dew Point Pressure and Comparison With Gaussian Processes Regression–Particle Swarm Optimization Algorithm,” ASME J. Energy Resour. Technol., 138(3), p. 032903. [CrossRef]
Wang, Y. , and Salehi, S. , 2015, “ Application of Real-Time Field Data to Optimize Drilling Hydraulics Using Neural Network Approach,” ASME J. Energy Resour. Technol., 137(6), p. 062903. [CrossRef]
García, J. M. , Padilla, R. V., and Sanjuan, M. E. , 2016, “ Response Surface Optimization of an Ammonia–Water Combined Power/Cooling Cycle Based on Exergetic Analysis,” ASME J. Energy Resour. Technol., 139(2), p. 022001. [CrossRef]
Laidi, M. , and Hanini, S. , 2013, “ Optimal Solar COP Prediction of a Solar-Assisted Adsorption Refrigeration System Working With Activated Carbon/Methanol as Working Pairs Using Direct and Inverse Artificial Neural Network,” Int. J. Refrig., 36(1), pp. 247–257. [CrossRef]
Hernández, J. A. , Bassam, A. , Siqueiros, J. , and Juárez-Romero, D. , 2009, “ Optimum Operating Conditions for a Water Purification Process Integrated to a Heat Transformer With Energy Recycling Using Neural Network Inverse,” Renewable Energy, 34(4), pp. 1084–1091. [CrossRef]
Colorado, D. , Hernández, J. A. , Rivera, W. , Martínez, H. , and Juárez, D. , 2011, “ Optimal Operation Conditions for a Single-Stage Heat Transformer by Means of an Artificial Neural Network Inverse,” Appl. Energy, 88(4), pp. 1281–1290. [CrossRef]
Morales, L. I. , Conde-Gutiérrez, R. A. , Hernández, J. A. , Huicochea, A. , Juárez-Romero, D. , and Siqueiros, J. , 2015, “ Optimization of an Absorption Heat Transformer With Two-Duplex Components Using Inverse Neural Network and Solved by Genetic Algorithm,” Appl. Therm. Eng., 85, pp. 322–333. [CrossRef]
Olarte-Cortés, J. , Torres-Merino, J. , and Siqueiros, J. , 2013, “ Experimental Study of a Graphite Disks Absorber Couple to a Heat Transformer,” Exp. Therm. Fluid Sci., 46, pp. 29–36. [CrossRef]
McNelly, A. , 1979, “ Thermodynamic Properties of Aqueous Solutions of Lithium Bromide,” ASHRAE Trans., 85(1), pp. 413–434.
Holland, F. A. , Siqueiros, J. , Santoyo, S. , Heard, C. L. , and Santoyo, E. R. , 1999, Water Purification Using Heat Pumps, E & FN Spon, New York.
NIST/ASME, 1998, “ Steam Properties Database. Version 2.1,” U.S. Department of Commerce, Gaithersburg, MA.
Coleman, H. W. , and Steele, W. G. , 2009, Experimentation Validation and Uncertainty Analysis for Engineers, Wiley, Hoboken, NJ. [CrossRef]
Bhowmik, S. , Panua, R. , Debroy, D. , and Paul, A. , 2017, “ Artificial Neural Network Prediction of Diesel Engine Performance and Emission Fueled With Diesel–Kerosene–Ethanol Blends: A Fuzzy-Based Optimization,” ASME J. Energy Resour. Technol., 139(4), p. 042201. [CrossRef]
Mukherjee, I. , and Routroy, S. , 2012, “ Comparing the Performance of Neural Networks Developed by Using Levenberg–Marquardt and Quasi-Newton With the Gradient Descent Algorithm for Modelling a Multiple Response Grinding Process,” Expert Syst. Appl., 39(3), pp. 2397–2407. [CrossRef]
Verma, S. P. , 2005, “ Estadística Básica Para el Manejo de Datos Experimentales: Aplicación en la Geoquímica (Geoquimiometria),” Universidad Nacional Autónoma de México, Mexico.
Verma, S. P. , 2009, “ Evaluation of Polynomial Regression Models for the Student t and Fisher F Critical Values, the Best Interpolation Equations From Double and Triple Natural Logarithm Transformation of Degrees of Freedom up to 1000, and Their Applications to Quality Control in Science and Engineering,” Rev. Mex. Cienc. Geol., 26, pp. 79–92.
Meza, M. , Márquez-Nolasco, A. , Huicochea, A. , Juárez-Romero, D. , and Siqueiros, J. , 2014, “ Experimental Study of an Absorption Heat Transformer With Heat Recycling to the Generator,” Exp. Therm. Fluid Sci., 53, pp. 171–178. [CrossRef]
Hamzaoui, Y. E. L. , Rodríguez, J. A. , Hernandez, J. A. , and Salazar, V. , 2015, “ Optimization of Operating Conditions for Steam Turbine Using an Artificial Neural Network Inverse,” Appl. Therm. Eng., 75, pp. 648–657. [CrossRef]
Garson, G. D. , 1991, “ Interpreting Neural-Network Connection Weights,” Artif. Intell. Expert Syst., 6(4), pp. 47–51.
Liu, F.-B. , 2008, “ A Modified Genetic Algorithm for Solving the Inverse Heat Transfer Problem of Estimating Plan Heat Source,” Int. J. Heat Mass Transfer, 51(15–16), pp. 3745–3752. [CrossRef]
Ilamathi, P. P. , Selladurai, V. V. , and Balamurugan, K. K. , 2013, “ Modeling and Optimization of Unburned Carbon in Coal-Fired Boiler Using Artificial Neural Network and Genetic Algorithm,” ASME J. Energy Resour. Technol., 135(3), p. 032201. [CrossRef]
Ibarra-Bahena, J. , Romero, R. J. , Velazquez-Avelar, L. , Valdez-Morales, C. V. , and Galindo-Luna, Y. R. , 2015, “ Experimental Thermodynamic Evaluation for a Single Stage Heat Transformer Prototype Build With Commercial PHEs,” Appl. Therm. Eng., 75, pp. 1262–1270. [CrossRef]
Sekar, S. , and Saravanan, R. , 2011, “ Experimental Studies on Absorption Heat Transformer Coupled Distillation System,” Desalination, 274(1–3), pp. 292–301. [CrossRef]

Figures

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Fig. 1

Experimental absorber: (a) internal graphite disks, (b) outer breastplate, (c) graphite disk

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Fig. 2

Cycle of a heat transformer by absorption

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Fig. 4

Recurrent network architecture for TAB values with the procedure used for neural network learning

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Fig. 3

Recurrent network architecture for QAB values with the procedure used for neural network learning

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Fig. 10

Development of genetic algorithms to find optimal input values at absorber

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Fig. 5

Dispersion of data between the actual values with respect to the simulated data to determine the QAB

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Fig. 6

Dispersion of data between the actual values with respect to the simulated data to determine the TAB

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Fig. 14

Direct application of model ANNi in different operating conditions to increase the value of QAB

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Fig. 15

Direct application of model ANNi in different operating conditions to increase the value of TAB

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Fig. 7

Behavior of the internal heat in the absorber, in carrying out the contact between the inlet temperature of the concentrated solution and the inlet temperature of the vapor

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Fig. 8

Behavior of the outlet temperature of the absorber, in carrying out the contact between the inlet temperature of the concentrated solution and the inlet temperature of the vapor

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Fig. 9

Important analysis of the input variables on the determined values of (a) QAB and (b) TAB

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Fig. 11

Minimization of the objective function as close to zero

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Fig. 12

(a) Experimental run and (b) application of model ANNi to improve the value of QAB with respect to the concentrated solution

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Fig. 13

(a) Experimental run and (b) application of model ANNi to improve the value of TAB with respect to the vapor inlet temperature

Tables

Table Grahic Jump Location
Table 2 Uncertainties of the measured and calculated quantity
Table Grahic Jump Location
Table 1 Interval of experimental operating conditions used to obtain the QAB and TAB values
Table Grahic Jump Location
Table 3 Determination for better architecture and transfer function to predict the value of QAB
Table Footer NoteNote: The architecture and highlighted values were the best found by the ANN model.
Table Grahic Jump Location
Table 4 Determination for better architecture and transfer function to predict the value of TAB
Table Footer NoteNote: The architecture and highlighted values were the best found by the ANN model.
Table Grahic Jump Location
Table 5 Tests fisher F and student to determine the relationship between the simulated and experimental data
Table Grahic Jump Location
Table 6 Obtained parameters of weights and biases for the ANN model to predict the value of QAB
Table Footer Note*s is the number of neurons in the hidden layer, k is the number of neurons in the input layer, l is the number of neurons in output layer (l=1).
Table Grahic Jump Location
Table 7 Obtained parameters of weights and biases for the ANN model to predict the value of TAB
Table Footer Note*s is the number of neurons in the hidden layer, k is the number of neurons in the input layer, l is the number of neurons in output layer (l=1).
Table Grahic Jump Location
Table 8 Genetic operators used to run the GAs
Table Grahic Jump Location
Table 9 Comparison between the ANNi model and theoretical model using the optimal variables found to increase the value of QAB and TAB
Table Grahic Jump Location
Table 10 QAB and TAB maximum experimental in different absorbers

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