Response Surface Methodology and Artificial Neural Network Methods Comparative Assessment for Fuel Rich and Fuel Lean Catalytic Combustion

Modeling, predictive and generalization capabilities of response surface methodology (RSM) and artificial neural network (ANN) have been performed to assess the thermal structure of the experimentally studied catalytic combustion of stabilized confined turbulent gaseous diffusion flames. The Pt/γAl2O3 and Pd/γAl2O3 disc burners were located in the combustion domain and the experiments were accomplished under both fuel-rich and fuel-lean conditions at a modified equivalence (fuel/air) ratio (Ø) of 0.75 and 0.25, respectively. The thermal structure of these catalytic flames developed over the Pt and Pd disc burners was scrutinized via measuring the mean temperature profiles in the radial direction at different discrete axial locations along with the flames. The RSM and ANN methods investigated the effect of the two operating parameters namely (r), the radial distance from the center line of the flame, and (x), axial distance along with the flame over the disc, on the measured temperature of the flames and predicted the corresponding temperatures beside predicting the maximum temperature and the corresponding input process variables. A three-layered Feed Forward Neural Network was developed in conjugation with the hyperbolic tangent sigmoid (tansig) transfer function and an optimized topology of 2:10:1 (input neurons:hidden neurons:output neurons). Also the ANN method has been exploited to illustrate the effects of coded R and X input variables on the response in the three and two dimensions and to locate the predicted maximum temperature. The results indicated the superiority of ANN in the prediction capability as the ranges of 2 adj R & F_Ratio are 0.9181 0.9809 & 634.5 3528.8 for RSM method compared to 0.9857 0.9951 & 7636.4 24,028.4 for ANN method beside lower values for error analysis terms. How to cite this paper: Gendy, T.S., Zakhary, A.S. and Ghoneim, S.A. (2021) Response Surface Methodology and Artificial Neural Network Methods Comparative Assessment for Fuel Rich and Fuel Lean Catalytic Combustion. World Journal of Engineering and Technology, 9, 816-847. https://doi.org/10.4236/wjet.2021.94057 Received: September 10, 2021 Accepted: November 7, 2021 Published: November 10, 2021 Copyright © 2021 by author(s) and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution-NonCommercial International License (CC BY-NC 4.0). http://creativecommons.org/licenses/by-nc/4.0/ Open Access


Abstract
Modeling, predictive and generalization capabilities of response surface methodology (RSM) and artificial neural network (ANN) have been performed to assess the thermal structure of the experimentally studied catalytic combustion of stabilized confined turbulent gaseous diffusion flames. The Pt/γAl 2 O 3 and Pd/γAl 2 O 3 disc burners were located in the combustion domain and the experiments were accomplished under both fuel-rich and fuel-lean conditions at a modified equivalence (fuel/air) ratio (Ø) of 0.75 and 0.25, respectively. The thermal structure of these catalytic flames developed over the Pt and Pd disc burners was scrutinized via measuring the mean temperature profiles in the radial direction at different discrete axial locations along with the flames. The RSM and ANN methods investigated the effect of the two operating parameters namely (r), the radial distance from the center line of the flame, and (x), axial distance along with the flame over the disc, on the measured temperature of the flames and predicted the corresponding temperatures beside predicting the maximum temperature and the corresponding input process variables. A three-layered Feed Forward Neural Network was developed in conjugation with the hyperbolic tangent sigmoid (tansig) transfer function and an optimized topology of 2:10:1 (input neurons:hidden neurons:output neurons). Also the ANN method has been exploited to illustrate the effects of coded R and X input variables on the response in the three and two dimensions and to locate the predicted maximum temperature. The results indicated the superiority of ANN in the prediction capability as the ranges of

Introduction
Catalytic combustion or heterogeneous combustion had been extensively investigated in recent years. The catalytic oxidation of hydrocarbons became the focus of much basic and applied catalysis research because of its increasing importance for burner's design of industrial furnaces and the techniques of power-generating gas turbines [1] [2]. For these applications, high temperature catalytic combustion was regarded as a highly efficient and clean energy system. It had been recognized that noble metals possessed the highest catalytic activities that initiated the catalytic oxidation of fuels at relatively lower reaction temperatures [3] [4].
Catalytic combustion methodologies are greatly enhancing flames stability limits at very fuel-Lean equivalence ratios [5] and resulting in ultra-low NOx emissions [6]. Fuel-rich catalytic combustion does not only have a prime catalytic partial oxidation function but also acts as a preheater and stabilizer for subsequent homogeneous combustion zone, [7] [8]. The thermal structure of stabilized confined turbulent gaseous diffusion flames using Pt/Al 2 O 3 and Pd/Al 2 O 3 catalytic disc burners situated in the combustion domain was experimentally investigated under both fuel-rich and fuel-lean conditions at the modified equivalence ratio Φ = 0.75 and 0.25, respectively [9]. The thermal structure of the catalytic flames developing over Pt disc indicates higher activity at the early upstream region of the main reaction zone compared to the flame developing over Pd disc burner under the fuel-rich condition. Also under the fuel-lean condition, flame operating over Pd catalytic disc burner indicates higher temperature values very near within the flame core compared to the flame developing over Pt catalytic disc burner.
Wierzbicki, et al. [10] presented a review of progress in catalytic conversion of JP-8 fuel and its surrogates made over the last decade. The effect of different types of catalyst, support materials and preparation methods on reforming was discussed. Sulfur tolerant catalysts and mechanisms of catalyst poisoning were understood while the role of hydrocarbon present in jet fuel during fuel reforming remains a challenge. High fidelity numerical simulations limited to gas phase non-catalytic reforming were examined. The combustion characteristics and stability of methane-air mixtures over platinum in catalytic micro-combustors were studied by Chen, et al. [11] using a two-dimensional computational fluid dynamics model with detailed chemistry and transport. It was shown that the combustor dimensions are vital in determining the combustion stability of the system. The investigation revealed that the optimal combustor length depends on the wall thermal conductivity. Shorter combustors increase the stability against T. S. Gendy et al. World Journal of Engineering and Technology blowout for high conductivity, whereas longer combustors increase the stability against blowout for low conductivity walls.
Progress in catalytic combustion depends on advances in catalyst technology and in multi-dimensional modeling for reactor design [12] investigated the premixed combustion of methane/air mixture in heat recuperation micro-combustors made of different materials. The effects of wall parameters on the combustion characters of a CH 4 /air mixture under Rhodium catalyst were explored using numerical analysis methodology. The results show that with a decrease of thermal conductivity of wall materials, the temperature of the reaction region increases and hot spots becomes more obvious. Arani et al. [13] carried out three dimensional direct numerical simulations (DNS) with detailed heterogeneous and homogenous chemistry and transport to investigate the turbulent combustion of fuel-lean hydrogen/air mixtures over a platinum coated channel where catalytic reactions occurred. The homogeneous ignition, gas-phase combustion, was concentrated close to the walls. Hydrogen was incompletely converted within the gaseous combustion zones and the leaking fuel reacted on the catalytic walls leading to combined hetro-/homogenous combustion over the entire post-ignition domain. Furthermore, Arani et al. [14] performed another investigation of threedimensional direct numerical simulation of turbulent catalytic and gas-phase H 2 /air combustion at a fuel-lean equivalence ratio Φ = 0.18 in platinum-coated planar channels at two Rynolds number, Re = 182 and 385 using detailed hetro-/homogeneous chemical reaction mechanism. It was observed that the higher turbulence intensity at Re = 385 resulted in larger near-wall hydrogen excess yielding shorter homogeneous ignition distances compared to the lower Re. The coupling of catalytic and gas-phase chemistry inhibited homogenous ignition, was characterized by intense catalytic reaction rates which could be applied in practical catalytic reactors.
Recently, Pan et al. [15] investigated experimentally and numerically the hetero/homogeneous reaction for H 2 /Air mixture in a micro catalytic combustor.
The distribution of OH radicals in the combustor was observed by plane laser induced fluorescence. Measurement of temperature variation in the combustor was determined for revealing the transition process of reaction types. The critical equivalence ratio from coupled hetero-/homogeneous reaction transforming into pure heterogeneous reaction is Ф A , while that from pure heterogeneous reaction to coupled hetero-/homogeneous reaction is Ф B . At different combustor heights and mixed gas flow rate, Φ A is always less than Φ B . The critical equivalence ratios Φ A decreases while the critical equivalence ratio Φ B increases, when the height of combustor increases. Φ A and Φ B both decrease with the increase of mixed gas flow rate. Heat loss of the combustor outer wall has an important effect on the transformation of reaction type. The research introduced by Zang, et al. [16] clarified the hazards of volatile organic compounds (VOCs) which now become a kind of harmful environmental pollutants that cannot be overlooked with the rapid development of industry. In the common catalytic combustion T. S. Gendy et al. World Journal of Engineering and Technology catalysts, noble metal catalysts and non-noble metal catalysts researches achieved progress for the elimination of VOCs. Perovaskite catalysts as one of the nonnoble catalysts play an important role in the field of catalytic combustion in recent years. This work analyzed and elaborated the reaction kinetics and the QSAR/QSPR (Quantitative structure-activity relationship/Quantitative structureproperty relationship) models for the introduction of structural properties and reaction mechanisms.
More recently, He et al. [17] presented a literature review on the catalytic methane combustion. This study revealed that the presence of catalysts enables complete oxidation of methane at much lower temperatures, typically 500˚C, so that the formation of pollutant can be largely avoided. Various aspects were discussed including the catalyst types, the reaction mechanism, kinetic characteristics, effects of various influencing operation factors and different reactor types proposed and tested. The study may serve as an essential reference to realize the performance, for future applications and propagation in different industrial sectors. Moreover a catalyst preparation method, consisting of slurry wash coating with γAl 2 O 3 followed by impregnating platinum on the micro-reactor wall, had been investigated by He, et al. [18]. The effect of various factors in the preparation procedures on the adhesion of the wash coat γAl 2 O 3 was studied. Well-adhered Pt/Al 2 O 3 catalysts were applied in a micro-reactor and investigated in terms of their performance in catalytic methane combustion. It was shown that the reaction temperature had a greater influence on the methane conversion than the flow rate, and favorable coverage of methane and oxygen on the catalyst surface is essential to obtain a good catalytic performance besides achieving the favorable methane conversion, as well as, the sufficient heat release for the potential uses of such micro-reactors for energy related applications.
Artificial neural networks (ANNs) and response surface methodology (RSM) are significant attitudes in the field of processes modeling and optimization.
These methods of modeling assess the relations between the output (response or target variable) and input variables (experimental operating factors) of the process by means of experimentally derived data. Subsequently, derived models are used to approximate the optimum situations to minimize or maximize the target variable (dependent variable) along with the involved corresponding independent variables [19]. Both RSM and ANN do not need the accurate expressions or the physical meaning of the system under exploration so they have been enormously employed in diverse fields [20] [21].
Several researchers have implemented the collective analysis on RSM and ANN to investigate the various aspects of these processes [22].
Ahmadpour et al. [19] evidenced the higher accuracy of ANN than the response surface model in their investigation of spent caustic wastewater treatment in a photocatalytic reactor. Comparing ANN and some classical modeling techniques such as RSM [23] showed the supremacy of ANN as a modeling technique in analyzing non-linear relationships of data sets, which consequently T. S. Gendy et al. World Journal of Engineering and Technology provides good fitting for data as well as better predictive ability. They stated that ANN is suitable in engineering research since most problems are non-linear in nature.
The multi-layer perceptron (MLP_ANN) models were superior to the regression model achieving a relatively lower prediction error for modeling Al6082-T6 alloy drilling [24] and better modeling accuracy than RSM for prednisone release from a multipartite System [25], in addition to the superiority for predicting and optimizing the process of ultrasound-assisted extraction [26].
RSM and ANN were studied and compared for modeling highly nonlinear responses found in impact-related problems. Despite the computation cost of ANN, these studies concluded the supremacy of ANN over RSM in such optimization problems [27]. Also, Qadir et al. [28] mentioned that ANN is a more valuable tool to interpret the relationship between the input and output data of augmented experimentations and ANN is an efficient algorithm to identify any function with limited number of discontinuities. Moreover, Habeeb et al. [29] found the application of ANN for predictive modeling of the adsorption process will help the understanding of the non-linear relationship between the input and output variables besides enhancing monitoring the process variables for optimum performance.
Recently, Cisternas et al. [30] in their study of Trends in Modeling stated that ANN and RSM models substantially reduce the computational cost involved in simulation and sensitivity analyses. Ayodele et al. [31] demonstrated the robustness of back propagation artificial neural network for predictive modeling of photodegradation of organic pollutants beside the determination of the level of importance of the process parameters. Also, Srinidhi et al. [32] stated that ANN is showing promise for tackling multivariate and complex modeling problems.
The ANNs algorithms are employed for their high sensitivity to change in variables, accommodation for a large number of variables, flexibility, ease in network construction, and the diverse availability of adjustable functions for precision modeling and prediction. Moreover, Agu et al. [33] in the modeling and optimization of Terminalia Catappa L. Kernel Oil (TCKO) extraction designated that ANN was a better and more effective tool than RSM indicated in its higher R 2 and F_Ratio beside lower error analyses parameters. Mohd Zin et al. [21] in the microbial decolorization process optimization declared that over a comparative scale, ANN model has higher prediction and accuracy in the fitness compared to the RSM model proven by approximated R 2 and AAD values. Beigzadeh and Rastegar [34] indicated the high accuracy of the ANN modeling in estimating the target variable in their assessment of Biosorption process. This will reduce the need for more laboratory data, allowing the determination of the optimal parameters for designing equipment. The present study deals with the evaluation of the predictive competencies of the RSM and ANN two methodologies for the formerly reported experimental data of thermal structure of catalytic stabilized confined turbulent gaseous diffusion flames over Pt/γAl 2 O 3 and Pd/γAl 2 O 3 catalytic disc burners under fuel-rich and fuel-lean conditions [9]. This has been achieved by comparing the values of coefficient of determination (R 2 ), F_Ratio besides the various error analyses parameters. Furthermore, the ANN method has been employed to illustrate the effect of input flame parameters on the response in three and two dimensions and to show the location of the optimum.

Response Surface Methodology
The RSM is a resourceful tool which is conjured of mathematical and statistical techniques for designing experiments, building models, evaluating the effects of variables, and searching optimum conditions of variables to predict targeted responses as well as the evaluation of the most influential factors on chosen responses [33] [34] [36].
RSM, since its introduction in the 1980s, has been extensively utilized for modeling and optimization of several engineering processes and studies whereby the numbers of process variables influencing the response(s) are many [33] [37].
The structured nature of the RSM is useful to exhibit the factors of contributions from the coefficients in the regression models. This ability is powerful in identifying the insignificant main factors and interaction factors or insignificant quadratic terms in the model and thereby can reduce the complexity of the problem [38].
One of the very important advantages of RSM is the reduction in the number of experimental runs which means it is time effective, inexpensive, and still, has the capability of attaining maximum efficiency and providing acceptable results as well as the evaluation of the most influential factors. RSM also has the advantage of generating second-order polynomial equation, which relates the dependent(s) or response(s) to the independent or process parameters. RSM is beneficial to determine the effects of each variable alone or in combination as it contemplates all the input variables at the same time, and therefore, interactions between variables are considered [39] [40] [41] [42]. Generating a mathematical model; its graphical perspective has led to the term Response Surface Methodology [43]. These graphic drawings of the shape of the A second order equation of the following form has been established for the functional relationships between the coded independent variables and dependent variables using multiple regression technique [52] [53]: Details of this method have been dealt with in our previous papers [54] [55] [56].

Artificial Neural Networks
Artificial neural networks (ANNs) are generic mathematical models lie at the intersection of computer science, artificial intelligence, and neuroscience. They classify data, learn models, and make predictions.ANN is an efficient algorithm to identify any function with limited number of discontinuities and valuable tool to interpret the relationship between the input and output data of augmented experimentations [57]. The capability of ANN to investigate and rationalize the performance of any complicated and non-linear process makes ANN an important modeling tool [22].

Ever since its introduction as universal function approximators by McCulloch
and Pitts in 1943 [58] ANNs have been extensively used in many areas as a powerful and reliable tool serving data mining and numerical applications because of their powerful control over regulatory parameters for pattern recognition and classification. ANNs have been around since the mid-20th century but blossomed first in the 1980s with the introduction of back propagation and then again in the 2000s with the development of deep learning. The latter has dominated the machine learning and artificial intelligence scene in recent years [57].

T. S. Gendy et al. World Journal of Engineering and Technology
Over the years, ANNs have been applied in Modeling and Prediction, Control, Optimization and Classification, Fault Detection besides solving several engineering, science, medicine, mathematics, neurology, metrology, psychology and biology problems [33].
NN is a computational mechanism that is able to acquire, represent, and compute mapping from multivariate space of information to another, given a set of data representing that mapping. ANNs are designed to simulate the human brain when analyzing data by learning from experience. Similar to the human brain, ANNs are capable of processing multi dimensional, non-linear, clustered and imprecise information and could be used to extract a pattern in nonlinear, complex and noisy or fuzzy data sets to detect the trends with high accuracy.
ANN algorithms are employed for their high sensitivity to change in variables, accommodation for a large number of variables, flexibility, ease in network construction, and the diverse availability of adjustable functions for precision modeling and prediction. ANN substantially reduces the computational cost involved in simulation and sensitivity analyses. Thus, ANN can be used to decode complicated real world problems that are sometimes challenging to evaluate using statistical approaches without the need for complicated equations, and is capable of exploring regions that are otherwise omitted when using statistical approaches. ANN using its many parameters (weights and bias) is able to predict the output of the model with high accuracy and this will reduce the need for more laboratory data, allowing us to determine the optimal parameters for designing equipment. ANNs, in particular, are best suited for descriptive problems for

Neuron Model
The most commonly used transfer functions for multilayer networks are presented below in Figure 1 inputs where each input is weighted with an appropriate w while the sum of the weighted inputs and the bias forms the input to the transfer function f [65].

Feed Forward Neural Network
The most widely used network type for approximation problems is the mul-   The output values obtained from the ANN are also in the range of −1 to 1, and utilizing the reverse method of normalization process they are transformed to values corresponding to their original data [46].
In the training of the back propagation method, the error is determined by comparing the network output and the desired response and this error is returned to the previous hidden and input layers for performing the necessary corrections in the next training processes. The network training operation ends when the error comes down below some value specified by the user [70].
To avoid overfitting the neural network model, the input-output experimental data is divided into three groups: the training set, verification set and test set.
They played different roles in the model formation.
where T. S. Gendy et al.
J is the Jacobian matrix, which contains first derivatives of the network errors with respect to the weights and biases parameters of the ANN. I is the identity matrix, E is a vector of network errors, W contains both the weights and biases of the ANN, μ is a scalar, a parameter of the algorithm, and tk represents the current training epoch [62]. Y j is the output value of the j th output neuron and T j is the desired value of the j th output neuron. The tanh sigmoid transfer function

Application of RSM and ANN to the Present Work
Experimental Details of the experimental setup and the data employed in this study have been reported previously in the work of [9].
The following formulas have been employed to calculate the coded factors of nates the effect of the output differences [70]. Also, this concept has been applied in all the evaluations of performance and errors of ANN method.    (d)

Function name Equation Reference
Chi square statistic Accuracy (A f ) 1 10 log Bias (B f ) 1 10 log % Relative Variance, RV% 0.5 2 Absolute fraction of variance ( ) ( )   For the RSM several mathematical models have been suggested to establish the relationship between the dependent and independent variables. A suitable power transformation to the response data has been recognized using the Box-Cox method for normalizing the data or equalizing its variance. This method indicated that sqrt(T) of the mean experimental temperature T dependent variable is the best transformation, so it has been employed to represent the response Y in Equation (2) [56].
In the present study the following cases have been considered Case a-The response temperature has been employed as it is for Y in Equation (2) and for training in case of ANN and the predicted temperatures were compared with the corresponding experimental temperature ones.
Case b-The sqrt(T) has been employed in Equation (2)

Results and Discussions
These  second-order polynomial regression [71]. Also, in all the studied cases, the predicted temperatures were compared with corresponding experimental ones and the error was referred to the maximum experimental temperature and this comparison is demonstrated in Table 2(a) as max error %. In all cases studied the max error % for the ANN method was less than that for the RSM method. The max error % lies between 4.7 & 12.5 for the ANN compared to the range 7.2 -21.1 for the RSM beside the range of RMSE cited in Table 2(b) varies between 0.4262 -30.13 for ANN while that for RSM is 0.9015 -86.7. These results designate that the ANN method shows a significantly excellent generalization capacity than that of the RSM. Table 2(c) presents the relevancy factor RF which reflects the effect of the independent variables on the response. The positive relevancy factor of RF(X) (0.3811 -0.7474) indicates the prominent effect of increase of X towards the increase of temperature. While the radius has a negligible value (−9.93E−04 -7.52E−02), indicating the trivial effect of radius on the measured temperature [69]. Table 2(a) discloses that the ANN method is more expensive than RSM. This is shown in the larger elapsed time for NN (3.09 -5.14) compared to that of RSM (1.19E−02 -1.04E−01), because ANN method uses a series of computationally expensive functions for a single model.
The three-dimensional concave curved response surfaces in Figures 4(a)-(d) designate the probability of obtaining a maximum value of the measured temperature within the chosen factors levels and analyses the interactive relationships among the factors and the response [36] [64].
The contour plots of Figures 5(a)-(d) consider the individual and cumulative influence of the variables and the mutual interaction between the variables and the dependent variable [72] [73]. The oval shape of the contour plots points to a significant interaction between the independent variables. The smallest ellipses in the contour plots denote the maximum predicted values [71]. World Journal of Engineering and Technology  The RSM the results of cases b & c have been reported previously in our study [56] and depicted in Table 2(a). As for case a; the values of the mean experimental temperature T dependent variable cited along with the corresponding x and r [9] have been employed utilizing Ordinary Least Squares (OLS) method to represent the response Y in Equation (2) An optimization process, exploiting Matlab 2016a (9.0.0), has been performed for the above presented Equations (8)- (11) to estimate the maximum predicted temperature and the corresponding R and X values. The Matlab implements a multidimensional unconstrained nonlinear optimization employing the Nelder-Mead simplex (direct search) method.

Comparative Evaluation of RSM and ANN
RSM is recommended for modeling of a new process as it is easier compared to T. S. Gendy et al.
ANN and its sensitivity analysis is more precise. ANN has excellent prediction and optimization abilities; it is best suited for nonlinear systems that include interactions higher than quadratic. Moreover, ANN does not require any prior specification for suitable fitting function [35] [71].
The The greater predictive accuracy of the ANN is accredited to its ability to process multi-dimensional, non-linear and clustered information whereas RSM is restricted to use of a second order polynomial. The generation of an optimum ANN is a multi-step calculation process, that is reiterated until an appropriate error is attained whereas a response surface model is based on a single step calculation [25] [76].
ANN is an alternative better than the methods based on RSM in the case of performance. Furthermore, ANN can increase the level of certainty associated with the results and simultaneously can be used to validate new technological strategies [35]. Therefore, using RSM-ANN modeling, the shortcomings of RSM can be resolved and the actual relationship between independent and response parameters can be studied through experimental data [40].

Conclusions
An artificial neural model was successfully established and compared to RSM to predict the temperature profile of the various Flame Conditions and Disc Types for three cases. A generalized, properly fit, robust feed-forward artificial neural network model was developed, using a back propagation based Levenberg-Marquardt algorithm, and utilized to train the data from the experimental laboratory testing. The study consequence proves that both the statistical and computational intelligence modeling of ANN can make a potential alternative to the time-consuming experimental studies in addition to minimizing the costly machining test trials. The main conclusions obtained in this study are as follows: 1) The neural network model, with 10 neurons in the hidden layer, produced prediction results in very good agreement with the experimental data.
2) The systematic comparative study has revealed that the properly trained ANN model has consistently performed more accurate predictions in all aspects compared to those of RSM. This accurateness of predictions is expressed in the very high values of R 2 and F_ratios and the very low value of error indicators for the ANN results compared to RSM ones.
3) The ANN model displays greater generalization capacity than the rest of the RSM models. The reason can be accredited to the universal ability of ANN to