A study on the energy and exergy of Ohmic heating (OH) process of sour orange juice using an artificial neural network (ANN) and response surface methodology (RSM)

Abstract The nonmodern statistical methods are often unusable for modeling complex and nonlinear calculations. Therefore, the present research modeled and investigated the energy and exergy of the ohmic heating process using an artificial neural network and response surface method (RSM). The radial basis function (RBF) and the multi‐layer perceptron (MLP) networks were used for modeling using sigmoid, linear, and hyperbolic tangent activation functions. The input consisted of voltage gradient; weight loss percentage, duration ohmic, Input flow, Power consumption, electrical conductivity and system performance coefficient and the output included the energy efficiency, exergy efficiency, exergy loss, and improvement potential. The response surface method was also used to predict the data. According to the result, the best prediction amount for energy and exergy efficiencies, exergy loss and improvement potential were in RBF network by sigmoid activation function and after this network, RSM had the best amount for energy efficiency, Also for exergy efficiencies, exergy loss and improvement potential obtained acceptable results in MLP network by a linear activation function. The worst amount was at MLP network by tangent hyperbolic. In general, the neural network can have more ability than the response surface method.


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VAHEDI TORSHIZI ET Al. other hand, artificial neural network is widely used in many fields.
Furthermore, its use is significantly important for researchers in solving complex and nonlinear equations in dryers and energy-consuming systems in recent years due to the fact that it uses the empirical data Özdemir, Aktaş, Şevik, & Khanlari, 2017). According to studied predictive and diagnostic techniques, most artificial neural networks (ANNs) have three layers including the input, hidden, and output layers. The output result depends on the applied weight in data of connection of output and hidden layers. During the training and learning of a network, weights indicate the worth of an ANN to produce a very close result to real output (Balogun, Salami, Aibinu, Mustafah, & Sadiku Isiaka, 2014). Artificial neural networks (ANNs) are powerful modeling techniques that, in short, work with arrays of neurons in memory and biological learning. ANNs offer many advantages over conventional modeling techniques because they can provide models based on no hypothesis about the nature of phenomenological mechanisms and understanding the mathematical fields for the main problem of process, and the ability to learn linear and nonlinear relationships between variables directly from a set of samples (Fathi, Mohebbi, & Razavi, 2011). In recent decades, most researchers in agricultural engineering have used conventional learning algorithms such as artificial neural networks (Pan et al., 2016). Unlike mathematical models, neural network models are able to identify relationships between parameters without the need to extract their relationships, and thus they are considered as very powerful tools in modeling. In this method, relationships of parameters are introduced at the stage of network training, and it then acts similar to the human brain. In the case of a proper training, the neural network will be able to predict the process and solve problems of extracting relationships of parameters. Therefore, neural network models are often used in cases in which relationships of parameters are unknown or very complex (Ghasemi, Aghayari, & Maddah, 2017). Various researchers have predicted and modeled processes using the artificial neural network: Nikbakht, Motevali, and Minaei (2014) used the neural networks to predict the exergy and energy of pomegranate drying in a thin layer dryer by microwave (Nikbakht et al., 2014). Aghbashlo, Mobli, Rafiee, and Madadlou (2012) carried out experiments by an artificial neural network to predict the performance of Spry dryer in oil and fish (Aghbashlo et al., 2012). Najafi, Faizollahzadeh Ardabili, Mosavi, Shamshirband, and Rabczuk (2018) investigated an intelligent artificial neural network-response surface methodology method for exergy and energy analysis that reported based on the mentioned results it can be concluded that employing ANN model in predicting or controlling circuit, will provide more possibility of useful work compared with that obtained by mathematical modeling (Najafi et al., 2018). Ardabili, Najafi, Ghaebi, Shamshirband, and Mostafaeipour (2017) had done a novel enhanced exergy method in analyzing HVAC system using soft computing approaches: A case study on mushroom growing hall that obtained MLP method had a poor performance in this study by linearity of 0.9511 and RMSE of 0.5584 with deviation of 12.5254 kJ/s (Ardabili et al., 2017).
The present paper aimed to investigate and predict the experimental data of the Ohmic heating method using neural networks, so that we could select a suitable network with high accuracy and speed and compare whether predicted values in the response surface method were better or predicted values by an artificial neural network.

| Sample preparation
The sour oranges were purchased from a garden located in the city of Gorgan, Golestan Province. The prepared oranges were washed and divided into two halves in the middle and immediately after purchase, all the samples juice was taken manually in the same conditions, and the samples were prepared to conduct the test during the Ohmic process with voltage gradients and the percentages of different weight loss to investigate the amount of energy efficiency, exergy efficiency, exergy loss, and improvement potential during the process. This experiment was done in 2019 at Gorgan University of Agricultural Sciences and Natural Resources; environmental conditions for testing were conducted at a temperature of 19°C and a relative humidity of 65%. F I G U R E 1 Schematic of the equipment used for the heating process of ohmic

| The experiment method
A reservoir made of plastics thermoset was considered for this process, and the samples were poured into the reservoir between two electrodes and the initial temperature was recorded after stabilization and after recording the temperature, the voltage was applied to the set, and the samples were heated. Three heating gradients of 8.33, 10.83, and 13.33 V/cm were selected for the heating process.
Approximately 10% (from 90 to 81 g), 20% (from 90 to 72 g), and 30% (from 90 to 63 g) of the total weight of the sour orange juice samples are poured into the steam cell and evaporated in the heating process. All the samples were 90 g. Figure 1 presents a schematic diagram of the heating process and the system components.
The experiments were conducted in a static Ohmic heating system. The system used consisted of a compact and transparent plastic cell (length 6 cm, width 6 cm, height 6 cm wall thickness of 0.3 cm), an electrode made of stainless steel (thickness of 0.1 cm) that the distance between the two electrodes is 6 cm, a variable transformer that is responsible for generating different voltages (3 kW, 0-300 V, 50 Hz, MST -3, Toyo, Japan), a power analyzer (Lutron DW-6090) responsible for monitoring the pattern of energy behavior of the system, a thermocouple, and a computer to store data with their profile. A scale (±0.01 g) was used to measure the cell weight and its contents during the process that was placed under the cell. All the experiments were conducted in the Biosystem Mechanics Department of Agricultural Sciences and Natural Resources of Gorgan University.

| Energy analysis
Energy used in the drying and heating process is important for production processes in the industrial and household sectors. However, the price of energy is extremely expensive; therefore, there is a strong incentive to invent processes that will use energy efficiently.
Currently, widely used drying and heating processes are complicated and inefficient; moreover, it is generally damaging to the environment. What is needed is a simplified, lower-cost approach to this process one that will be replicable in a range of situations (Azadbakht, Vahedi Torshizi, Noshad, & Rokhbin, 2018). The general equilibrium energy can be expressed by using Equation (2) that the input energy is equal to the output energy (Darvishi, Hosainpour, Nargesi, & Fadavi, 2015).
The heat capacity was calculated using the Siebel's model (Heldman & Moraru, 2014): The energy given to the system was recorded using the input current and the voltage given to the samples and calculated according to Equation (6) (Darvishi, Khostaghaza, & Najafi, 2013).
The system energy efficiency of Ohmic heating was calculated using Equation (8) (Darvishi et al., 2015).

| Exergy analysis
With the onset of the energy crisis, energy and exergy (the maximum useful work that comes from a certain amount of available energy or from the flow of materials) analyses are among the leading thermodynamic research works. In the exergy analysis, the main purpose is to determine the location and amount of irreversible production during the various processes of the thermodynamic cycle and the factors affecting the production of this irreversibility. In this way, in addition to evaluating the performance of various components of the thermodynamic cycle, methods to increase cycle efficiency are also identified (Azadbakht, Vahedi Torshizi, et al., 2018).
In the analytical range, the entrance (input) exergy, the output exergy and exergy loss of the ohmic heating system were investigated.

TA B L E 1 Neural network equations
Generally, the total exergy equation of the heating system is described using Equation (8).
Exergy components were calculated at the input and output of the Ohmic heating system using Equation (10)  The exergy efficiency of the Ohmic system can be calculated using Equation (11) (Darvishi et al., 2015).
Van Gool (1997) suggests that the maximum improvement in the exergy efficiency of a process or system becomes apparent once the exergy loss or exergy irreversible becomes its lowest level. It was suggested that the concept of "improvement potential" would be widely used in analyzing the processes or different section of the economy, and Hammond and Stapleton presented this improvement potential in the evaluation form (Hammond & Stapleton, 2001).

| ANN modeling
The training process is the important way to achieve a high accuracy from a developed model. The first step was to identify the dependent and independent variables. In this study, voltage gradient, weight loss percentage, during ohmic, input flow, power consumption, electrical conductivity and system performance coefficient (input variables) variables and energy efficiency, exergy efficiency, exergy loss and improve potential were considered as dependent variables (output variables). Therefore, by identifying the input and output variables, a MLP type of ANN was employed to develop the target model. As seen in Figure 3a, the architecture of these networks generally has three layers which include input, hidden, and output layers. Layers are connected by nodes; therefore each layer has its own node. The signal processing begins from first layer, also in Figure 3b showed RBF architecture. Receiving information from external nodes activates the related nodes on input layer and emits a signal to the next layer. Each connection between two nodes in two adjacent layers is related to each other by weighting coefficients, that this weights adjust the signal strength based on the input data. In training of the back propagation method, the error is determined by comparing the output and the desired output and this error is returned to the hidden and input layers of the next training processes. The network training operation ends when the error comes down below some value specified by the user (Najafi et al., 2018). In this research, the artificial multilayer perceptron were used for training, 15% of them were used for network evaluation (Validating Data), and 15% of the data were used for testing the network (Testing data). Before training the model, the input-output parameters in data sets were arranged, and the inputs in the data set were normalized between 0 and 1 range by using the Equation (20).
Because of the output layer activation function is linear (purelin) in all architectures; only the input parameters were normalized by Equation (20). The voltage gradient, weight loss percentage, duration ohmic, Input flow, Power consumption, electrical conductivity and system performance coefficient as network inputs energy efficiency, exergy efficiency, exergy loss, and improve potential were the considered network outputs (Figure 3). A total of 5 Run were considered to achieve the minimum error rate and maximum network stability as a mean of 5,000 Epoch for the network. The error was estimated using an algorithm with back propagation error.
Statistical parameters, including Root Mean Square Error (RMSE), R 2 , and Mean Absolute Error (MAE) were calculated for inputs, and the relationships were calculated using the formulas shown in Table 1. In Equation (20), I norm is the normalized data, I is the measured data, I min is the least measured, and I max is the most measured data.

| Analyze the response surface method
The response surface method (RSM) is a series of statistical and mathematical approaches used to analyze experimental results (Han, Li, Wu, & Shao, 2015). This method is also very useful in designing, improving, and formulating new products. The grade 2 model is suitable for industrial processes and has much strength. Also, using the ANOVA analysis, the models presented for the responses were evaluated and regression coefficients were estimated for linear, interactions and grade 2 sentences and the fitting quality of the models equation was expressed using the convergence coefficient (Myers, Montgomery, & Anderson-Cook, 2009;Khuri, 2006). In order to investigate the properties and optimization of system performance factor, heating process duration, input current, power consumption and the electrical conductivity of sour orange juice during the heating process, the surface response method, a central composite design (CCD) with 5 central points and with Design Expert 11 software was used (Table 2).
In order to investigate the properties and optimization of energy and exergy of sour orange juice during the heating process, the surface response method, a central composite design (CCD) with 5 central points and with Design Expert 11 software was used. In this study, the independent variables were voltage gradients and percentage of weight loss (Table 1), dependent variables were energy efficiency, exergy efficiency, exergy loss, and improvement potential as responses to investigate the process of    and MSE were obtained for the linear activation function for energy efficiency, improvement potential, and exergy loss; and the best values were shown for the energy efficiency of the hyperbolic tangent activation function.

| RE SULTS AND D ISCUSS I ON
According to obtained results from the data sensitivity coefficient (Figure 4), the higher sensitivity to weight loss belonged to the energy efficiency of RBF network, and also the higher sensitivity to F I G U R E 4 Sensitivity coefficient energy efficiency, exergy efficiency, improve potential, and exergy loss for sour orange juice during the ohmic heationg process results were similar to the response surface method. In this method, the weight loss had a greater effect (Table 5).
The results of the Sequential Model Sum of Squares show that how complex phrase participates in the final model. Table 6 shows the results of the models for the energy efficiency, the exergy efficiency, the improvement potential, and the exergy loss. The linear and factors interaction model was selected as the best model for the energy efficiency, and the second-order model versus the two factors was chosen as the best model for the exergy efficiency. The best models for the improvement potential and for the exergy loss were proposed the average and linear model and the second-order model versus the two factors, respectively. Table 7 shows the results of runs and Epoch for the network creation. This table generally considers the energy efficiency, exergy efficiency, exergy, and exergy loss, and improvement potential because network output layers are composed of these factors.
According to obtained results, the MLP network with a linear activation function had the best value and the fastest time for network training until the creation because it had the lowest amount of running and repetition; and the network was created after 541 Epoch per run that was better than other created networks. According to the above table, which presents the best values of topology, the best values of R 2 and MSE are seen in the same network that is certainly the best network. In addition, also in Figure 5 is showed the dispersion value of errors for RSM. Given that the values obtained are very close to the line drawn, it can be stated that the dispersion values of the error obtained are appropriate for the energy efficiency, the exergy efficiency, the improvement potential, and the exergy loss. This indicates that the difference between actual values and predicted values by the model is appropriate, so that it has been able to obtain values close to the line creating an appropriate normal distribution.
The results show the compatibility of the model and actual data with the predicted data.

| CON CLUS ION
According to results of the generated neural network for energy efficiency, exergy efficiency, exergy loss and improvement potential, rate of predicted R 2 was very acceptable; and the network-predicted data were close to real data. The MLP network was better than RBF