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3117 the International Conference on Learning Representations. New Orleans, Louisiana, United States. 6-9 May 2019; pp.1-14. [39] Ismail, S.; Shabri, A.; Samsudin, R. A Hybrid Model of Self Organizing Maps and Least Square Support Vector Machine for River Flow Forecasting. Hydrol. Earth Syst. Sci. 2012, 16, 4417- 4433.

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311 Article The Application of a Hybrid Model Using Mathematical Optimization and Intelligent Algorithms for Improving the Talc Pellet Manufacturing Process Dussadee Buntam 1, Wachirapond Permpoonsinsup 2,* and Prayoon Surin 1 1 Faculty of Engineering, Pathumwan Institute of Technology, Bangkok 10330, Thailand; [email protected] (D.B.); [email protected] (P.S.) 2 Faculty of Science and Technology, Pathumwan Institute of Technology, Bangkok 10330, Thailand * Correspondence: [email protected]; Tel.: +66-805-694-199 Received: 31 August 2020; Accepted: 22 September 2020; Published: 26 September 2020 Abstract: Moisture is one of the most important factors impacting the talc pellet process. In this study, a hybrid model (HM) based on the combination of intelligent algorithms, self-organizing map (SOM), the adaptive neuron fuzzy inference system (ANFIS) and metaheuristic optimizations, genetic algorithm (GA) and particle swarm optimization (PSO) is introduced, namely, HM-GA and HM-PSO. The main purpose is to predict the moisture in the talc pellet process related to symmetry in the aspect of real-world application problem. In the combination process, SOM classifies the suitable input data. The GA and PSO, as the training algorithms of ANFIS, are investigated to compare the prediction skill. Five factors, including talc powder, water, temperature, feed speed, and air flow of 52 experiment cases designed by central composite design (CCD), are the training set data. Three different measures evaluate the capacity of moisture prediction. The comparison results show that the HM-PSO can provide the smallest difference between train and test datasets under the condition of the moisture being less than 5%. As a result, the HM-PSO model achieves the best result in predicting the moisture for the talc pellet process with R = 0.9539, RMSE = 1.0693, and AAD = 0.393, compared to others. Keywords: SOM; ANFIS; talc; genetic algorithm; particle swarm optimization 1. Introduction Talc is a mineral occurring naturally in the form of crystalline hydrated magnesium silicate, with a chemical formula of Mg3SiO10(OH)2. Talc has low abrasion, high thermal conductivity and stability, low electrical conductivity, and high oil and grease adsorption [1]. Due to its unique surface chemistry, lamellar crystal habit, and properties, talc minerals are widely applied commercially and industrial, such as in cosmetics, pharmaceuticals, paints, polymers, and ceramics. Furthermore, the method evaluated the suitable properties of talc, which can contribute to the industry in terms of the efficiency of production planning. In the talc forming process, many factors, especially moisture, plays an important role. The more accurate the moisture forecasting, the better the quality of the talc pellet. Over the last decade, artificial neural networks (ANNs) have become a popular technique for data prediction due to their high accuracy. Loveday et al. [2] apply an ANN to decrease the time for palm oil production. The developed model provides a reliable result and high efficiency. Adaptive neuro-fuzzy inference systems (ANFIS) is a kind of ANN usually applied in various fields to study, for example, economic order quality, water level prediction, medicine, and markets [3]. The ANFIS is an algorithm that Symmetry 2020, 12, 1602; doi:10.3390/sym12101602 www.mdpi.com/journal/symmetry

312 Symmetry 2020, 12, 1602 2 of 18 combines the advantages of both ANN and fuzzy inference systems (FIS). It has the ability to capture the nonlinear structure of a process and has a rapid learning capacity [4]. In manufacturing applications, Caydas et al. [5] developed ANFIS for the prediction of a wire electrical discharge machine. Zhange and Lei [6] established ANFIS to predict the roughness of laser cutting and improve the quality level of laser cutting. Sen et al. [7] utilized ANFIS for predicting machining performance parameters of Inconel 690. The result of all research shows that the ANFIS performs with high accuracy with respect to prediction. In recent years, a hybridization of ANFIS with many optimization algorithms has been introduced to improve the forecasting accuracy of the traditional ANFIS. Abdollahi [8] introduced a novel hybrid model for forecasting the Australian option price market. In a hybrid process, it consists of an entropy method and ANFIS trained by PSO. Bui et al. [9] presented three new hybrid ANFIS with cultural, bee, and invasive weed optimization, namely, ANFIS-CA, ANFIS-BA, and ANFIS-IWO for flood susceptibility mapping (FSM). Yaseen et al. [10] proposed a new hybrid ANFIS with the firefly algorithm for monthly streamflow forecasting. Gocken and Boru [11] integrate the ANFIS with GA and harmony search (HS) in weather forecasting. However, GA and PSO are commonly combined with ANFIS. Oliverira and Schirru [12] apply PSO for tuning ANFIS in sensor monitoring compared to ANFIS using one gradient descendent (GD) and GA. It found that the PSO applied in ANFIS gives the best result. Alarifi et al. [13] combine PSO and GA with ANFIS to improve the prediction performance of the thermophysical properties of Al2O3-MWCNT/oil. Based on the result, they found that both of the ANFIS-PSO and ANFIS-GA models are able to predict the thermophysical properties appropriately. Kumar and Hynes [14] predicted and optimized the surface roughness in thermal drilling by integrating ANFIS and GA. Rezakazemi et al. [15] employed ANFIS with GA and PSO for the evaluation of H2-selective mixed matrix membranes (MMMs). The results showed that the ANFIS with PSO is more reliable than the ANFIS with GA and the traditional ANFIS. Sabeti and Deevband [16] introduced a novel training method of ANFIS by combining PSO and GA to solve the nonlinear dynamical system. The proposed PSOGA method provides the satisfactory results. On the other hand, the appropriate collection of input data has a fundamental impact on the performance of the ANFIS model. It may lead to a better explanation of the results. There are only a few studies that apply the method in selecting the proper input data to ANFIS. Dariane and Azimi [17] investigated appropriate input data selection in streamflow using GA and wavelet methods to deal with ANFIS applications. The results show that the performance of the model is improved when GA and wavelets are applied. Jeong et al. [18] used a wrapper method to select the suitable input variables applied to a neuro-fuzzy model in monthly precipitation forecasting. The uncertainty in forecasting can be reduced effectively. The self-organizing map (SOM), first introduced in 1990 by Kohonen [19], is an unsupervised learning method in ANN successfully established in data classification, pattern recognition, data compression, and data mining. It can reduce high- dimensional data to low-dimensional data. In manufacturing applications, SOM has been widely used for data clustering [20,21]. Some studies apply SOM to cluster the input data for ANFIS. Nourani et al. [22] identified the input data for ANFIS by SOM and the wavelet transform groundwater level (GWL) and to fill the missing GWL data. The obtained results show that the proposed model can predict reliable accuracy. Amiryousefi et al. [23] categorized the dataset into two clusters by SOM before feeding into an ANFIS model to predict the mass transfer kinetics in deep-fat frying (DFF). Nasir and Cool [24] classified the input dataset by the SOM approach and combined it with an ANN or ANFIS. The results show that the proposed model makes a powerful intelligent model for wood machining monitoring. The moisture in Uttaradit, Thailand is estimated by local traditional drying. It cannot determine the moisture of the talc mineral before the production process. The moisture is measured step-by- step depending on the user experience and it takes a long time to obtain the information. As mentioned previously, the novel techniques based on the combination of ANFIS with GA and PSO, using the SOM-clustering method introduced to improve the forecasting accuracy in the talc pellet forming process. The related theories are briefly described in Section 2. The schematic and the

313 Symmetry 2020, 12, 1602 3 of 18 procedures of the proposed model are indicated in Section 3. The result description is therefore investigated and discussed in Section 4. Finally, the overview of this study is concluded in Section 5. 2. Materials and Methods A talc pellet is represented as material for this study. The talc pellet forming process is explained. The traditional methods, including SOM, ANFIS, GA, and PSO, are described. 2.1. Talc Pellet Forming Process The material used in this study is a naturally occurring mineral. It can be found in Tha Pla district, Uttaradit province, Thailand. The talc pellet forming process applies the powder metallurgy production. It includes the important process of powder production, grinding, blending, compaction, and sintering, as shown in Figure 1. Figure 1. Talc pellet forming process. From Figure 1, the talc pellet forming process consists of five steps. Firstly, talc is ground by a Raymond mill. Secondly, the ground talc is conveyed into a mixing tank. Thirdly, the mixed talc is compacted with mechanical force by a double roller and the mixture pressed through a 5 mm sieve to form material for sintering. Fourthly, talc is sintered with LPG by using a spiral drying conveyer. Finally, the talc pellet is produced and sent to the hopper and drying tube for further use. In talc pellet moisture measurement, talc obtained according to the testing condition from 52 experimental designs can be measured, as in the ASTM D2216-98 standard [25]. The moisture of the processed can be calculated as: Mc = W2 − W3 × 100 , (1) W3 − W1 where M C is the talc pellet moisture (%), W1 is the weight of an empty talc container (g), W2 is the weight of talc before drying (g), and W3 is the weight after drying (g). 2.2. Method 2.2.1. Self-Organizing Map The basic concept of SOM is in the concept of a transformation a complex, high-dimensional input data into a simple low-dimensional discrete output [26]. The SOM, an unsupervised learning algorithm, comprises three essential phases: competition, cooperation, and adaptation. Before training, the initial values of the learning rate, radius of the neighborhood, the number of iterations and the number of patterns, and the SOM array size are required [27]. At the start of learning the weight vector, wi , is generated by a random number and input vector, x, is a random distribution which corresponds to the column index. The set of weight vectors is formed as wi = [wij ],i = 1, 2,..., kx , j = 1, 2,..., ky where kx is the number of row and ky is the number of columns. The three phases for calculating the SOM algorithm are shown below. In competition, the Euclidian distance between the input vector and the neuron with the weight vector of the given neuron, wc , is computed as:

314 Symmetry 2020, 12, 1602 4 of 18 d ( x,w) = x(t) - wc (t) (2) The neuron with the most similar weight vector to the input will search for the winner neuron, the best matching unit (BMU). BMU is calculated as: BMU = argmin x(t) - wc (t) (3) In cooperation, the collected neighborhood function is used in this study is the Gaussian function, computed as: (t) × e ( ) 2 2   ( )αhicj =  - Rc - Rij 2 η c t  (4) ij The parameter ηc represents the radius of the neighborhood between nodes wc and wij . Two- ij dimensional vectors, Rc and Rij , include wc and wij [28]. In adaptation, the weight vector is adjusted after obtaining the winning neuron to increase the similarity with the input vector. The rule for updating the weight vector is given by: wi (t + 1) = wi (t)+ α(t)hicj (t)(x(t) - wi (t)) (5) Here, hicj (t) is a neighborhood function and t is the order number of a current iteration. The learning rate functions, α(t) is defined as follows: t (6) α (t,T ) = α (0)× eT Here, T is the number of total iterations and t is the order number of a current iteration [28]. However, it is under the condition ηc ≤ αmax(kxky ), 1 for all cases of analysis. ij The percent of occurrence or frequency of each pattern is the number of occurrences divided by the total number of samples. The probability that specific humidity would map to any pattern is 1/n, where n is the number of patterns. The significance of the frequency can be determined by calculating the 95% confidence interval around the expected probability of 1/n. Assuming that the process is a binomial, the 95% confidence limits are calculated by: p ± 1.96 ( ) p 1 - p 1/ 2 (7)   N  where p is the probability that any sample maps to any pattern and N is the number of input vector used to train the map [27]. 2.2.2. Adaptive Neuro-Fuzzy Inference System The adaptive neuro-fuzzy inference system (ANFIS) was first introduced in 1993 by Jang [29]. It is the method that powerfully integrates ANNs and fuzzy inference systems (FIS). For constructing a set of fuzzy, if-then rules with appropriate membership are applied to determine the relationship between the input and output variables. There are two inference systems in fuzzy logic while the inference system of Takagi–Sugeno–Kang is usually applied [13]. Figure 2 shows the structure of ANFIS.

315 Symmetry 2020, 12, 1602 5 of 18 Figure 2. An architecture of ANFIS [12]. From Figure 2, there are five layers in ANFIS. The fuzzy if-then rules are considered to explain the rule of each layer as follows: If xi is Ai1 AND…AND xm is Aim then yi is f1 = x1 ,..., xm (8) • Layer 1: Adjust every node by using Equation (9): Oi1 = μij (x) (9) ( )From Equation (8), μij (x) is a Gaussian function computed by μAij (x) = exp −(xj − ci )2 / 2si2j where cij is the midpoint value and sij is the standard deviation value of the input variable at xj . • Layer 2: Calculate each node by multiplying the fuzzy value. The output is calculated as: m (10) ∏Oi2 = wi = Ai j (xi ) j=1 • Layer 3: Sum the fuzzy value of every node to one value by: 3O= wi = wi (11) i wn (12) i=1 i • Layer 4: Normalize the fuzzy value of every node by: O 4 = wi fi i where fi are the consequent parameters from Takag–-Sugeno–Kang's pattern. • Layer 5: Sum all output from layer four to obtain the final output by: n (13) Oi5 = wi fi i =1 2.2.3. The ANFIS Training Algorithm Genetic Algorithm The genetic algorithm (GA) is one of the most effective algorithms in metaheuristic optimization, first presented by [30] and completed in 1989 by [31]. GA is an imitated process of natural selection and genetics to find the optimal formula for predicting. The basic procedures of GA are as follows.

316 Symmetry 2020, 12, 1602 6 of 18 • Chromosome encodes: Design the chromosomes as the system-represented solution by using any encoding method on the solving condition. • Population initialization: Initialize the prototype population at the beginning of GA. The first population group is randomly created by matching with the defined population size. • The fitness function: Define the score of each possible solution. Every chromosome implies the fitness of the inheritance consideration for themselves in order to create the next-generation chromosome. • Selection: Select the genetic operator that supports the worthy member to transfer into the next generation. The process of selecting the best chromosome among the whole population is normally selected by good origin for good species according to the natural selection concept. • Crossover: The copying of the new chromosome is pasted at a random position of the father and behind the random position of the mother to become the first offspring chromosome. The second offspring chromosome occurs by the same process as the first offspring while switching the position of the father and mother. • Mutation: Mutate the value of the chromosome. The mutation process randomly mutates the position under the mutation possibility by changing some genes on the chromosome. • Replacement: Replace the previous generation chromosomes with mutated chromosomes. • Termination condition: Terminate the procedure when the condition is satisfied. Particle Swarm Optimization Particle swarm optimization (PSO), invented for solving the non-linear optimization introduced by Kennedy and Eberhart [32], is based on the concept of the foraging of bird flock behavior to find the optimized solution area. Each of the birds in the flock is represented with the particle. In each particle, the fitness value implies the distance between the particle and food source as having the best fitness value in each interval the fitness value of the particle which be found by the Equation (14): f (x1 , x2 , x3 ,...xn ) = f (x) (14) In defining the particle, xi is the defined fitness function. Accordingly, PSO begins with randomizing a set of particle positions, then optimizing by adjusting the parameters in each decision cycle. Each particle keeps their best position value, Pbest,i during that interval, including the whole particle best position data, in every process interval t, and the movement speed would be adjusted by using Pbest,i and Gbest , which can be demonstrated by Equation (15) at the next time step, t + 1, where t ∈[0,..., N] and can be calculated by Equation (16) at time step t, respectively [33]: Pt+1 = xPbitte++s1t1,i if f (xtt+1 ) > Pt (15) best ,i best ,i if f (xtt+1 ) ≤ Pt best ,i { }Gbest = min Pt+1 , where i ∈[1,...,n] and n>1 (16) best ,i where Pbest,i is the best position that the individual particle, i has visited since the first time step, Gbest is the best position discovered by any of the particles in the entire swarm, where Pbest,i is the best particle. In this method, each individual particle, i ∈[1,...,n] , where n > 1, has been calculated in the search space xi . The new velocity is calculated as in Equation (17): vt+1 =ω * vitj + c1r1tj [ Pt ,i − xitj ] + c2r2tj [Gbest − xitj ] (17) ij best

317 Symmetry 2020, 12, 1602 7 of 18 where v t is the velocity of the particle i in the dimension j of time t, ω is an inertia weight, x t is a ij ij position, Pt is the best position of a particle, Gbest is the best position of the whole particle system, best ,i c1 and c2 are the constant accelerations in searching, and r1tj and r2tj are the random numbers between 0 and 1 at time t. 2.2.4. Performance Evaluation In order to evaluate the superiority of the model generated by ANFIS, three techniques, absolute average deviation (AAD), root mean square error (RMSE), and correlation coefficient (R), are applied. R (Equation (18)) is used to measure how close the predicted value is to the experimental value. The closer each of these values is to 1 indicates a better prediction. RMSE (Equation (19)) and AAD (Equation (20)) are employed to investigate the accuracy of the model predictions [34]: N  (Qi − Q)(Ei − E) i =1 R= (18) NN  (Qi − Q)2 (Ei − E)2 i=1 i=1 RMSE = 1 N (19) N (Q i −E)2 i=1 AAD = 1 N Ei − Qi (20) N i=1 Qi where Q is the target value, E is the prediction value, and N is the total number of input data. 3. The Proposed Model In this section, the proposed model is introduced. It is a novel technique based on a combination of SOM and ANFIS. The experimental design is described in Section 3.1. The hybrid model is introduced in Section 3.2, and the experiment setting is determined in Section 3.3. 3.1. The Experimental Design In order to design the experiment, the central composite design (CCD) of the response surface methodology (RSM) is applied [35]. There are five factors influencing the talc pellet forming process in predicting the proper moisture. The input data consists of talc powder, water, temperature, feed speed, and air flow. According to the CCD, the maximum and minimum values of each variable are adjusted, as shown in Table 1. It consists of 52 experiments cases as shown in Table 2. Table 1. The value of α in the talc pellet forming process. Factor Symbol 1.682 The Value of α −1.682 Unit Talc Ta 18.6892 1.0 0 −1.0 16.3107 kg Water W 4.3446 3.1553 kg Temperature Temp 191.35 18 17.5 17 48.65 °c Feed Speed FS 0.56 4 3.75 3.5 m/min Air Flow AF 0.11 m/sec 8.40 150 120 90 4.29 0.43 0.34 0.24 7.21 6.35 5.48 According to Table 1, by using CCD, the maximum value of five input data, the scale value for α rotatability relative to ±1.0 in this study is tested at 2.378 when implemented in the real experiment, but the forming process failed when the scaling value for finding optimal α rotatability is changed at

318 Symmetry 2020, 12, 1602 8 of 18 2.00, 1.682, and 1.414, and also with rotatability values of −2.00, −1.682, and −1.414, respectively [36]. The experimental results found that α = 1.682 can be applied to the real forming process. Table 2. The data of experimental design. No. Ta W Temp FS AF MC No. Ta W Temp FS AF MC 1 17 3.5 90 0.24 7.21 6.31 27 17.5 3.75 120 0.34 6.35 1.38 2 18 3.5 90 0.24 5.48 2.89 28 17.5 3.75 120 0.34 6.35 2.33 3 17 4 90 0.24 5.48 3.94 29 17.5 3.75 120 0.34 6.35 3.85 4 18 4 90 0.24 7.21 7.02 30 17.5 3.75 120 0.34 6.35 3.75 5 17 3.5 150 0.24 5.48 0.56 31 17.5 3.75 120 0.34 6.35 3.07 6 18 3.5 150 0.24 7.21 0.51 32 17.5 3.75 120 0.34 6.35 2.56 7 17 4 150 0.24 7.21 0.39 33 17 3.5 90 0.24 5.48 4.19 8 18 4 150 0.24 5.48 0.42 34 18 4 90 0.24 5.48 5.37 9 17 3.5 90 0.43 5.48 11.17 35 17 3.5 150 0.24 7.21 0.45 10 18 3.5 90 0.43 7.21 8.96 36 17 4 150 0.24 5.48 0.41 11 17 4 90 0.43 7.21 7.86 37 18 3.5 90 0.43 5.48 7.47 12 18 4 90 0.43 5.48 8.76 38 17 4 90 0.43 5.48 6.16 13 17 3.5 150 0.43 7.21 1.41 39 17 3.5 150 0.43 5.48 4.34 14 18 3.5 150 0.43 5.48 2.61 40 18 3.5 150 0.43 7.21 1.08 15 17 4 150 0.43 5.48 2.22 41 17.5 3.75 120 0.34 6.35 3 16 18 4 150 0.43 7.21 0.85 42 17.5 3.75 120 0.34 6.35 3.33 17 16.31 3.75 120 0.34 6.35 2.11 43 18 4 150 0.43 5.48 2.39 18 18.69 3.75 120 0.34 6.35 1.64 44 18 3.5 90 0.24 7.21 5.61 19 17.5 3.16 120 0.34 6.35 1.56 45 17 4 90 0.24 7.21 4.66 20 17.5 4.34 120 0.34 6.35 3.19 46 18 3.5 150 0.24 5.48 0.62 21 17.5 3.75 49 0.34 6.35 15.36 47 18 4 150 0.24 7.21 0.4 22 17.5 3.75 191 0.34 6.35 0.36 48 17 3.5 90 0.43 7.21 4.74 23 17.5 3.75 120 0.11 6.35 0.66 49 18 4 90 0.43 7.21 8.38 24 17.5 3.75 120 0.56 6.35 7.7 50 17 4 150 0.43 7.21 1.28 25 17.5 3.75 120 0.34 4.29 5.54 51 17.5 3.75 120 0.34 6.35 3.04 26 17.5 3.75 120 0.34 8.4 2.21 52 17.5 3.75 120 0.34 6.35 3.25 3.2. A Hybrid Model A hybrid model (HM) is introduced based on the combination between SOM and ANFIS trained by GA and PSO. There are two main processes, including SOM and ANFIS, with two training algorithms: GA and PSO. Firstly, the SOM algorithm is applied to classify the appropriate input data before feeding into the ANFIS. Secondly, the selected input data are computed by ANFIS. In ANFIS, GA and PSO are employed as training algorithms. The HM trained by GA and PSO are called HM- GA and HM-PSO, respectively. The schematic of the proposed model is shown in Figure 3.

319 Symmetry 2020, 12, 1602 9 of 18 Figure 3. The schematic HM for moisture prediction in the talc forming process. 3.3. The Experimental Setting In order to set the appropriate parameters of SOM, ANFIS, GA, and PSO, there are no theoretical existing criteria [37]. Table 3 shows the parameter setting of SOM and ANFIS. According to previous studies [13–15,38], all parameters of GA and PSO are determined, as shown in Table 4. Two parameters of GA, including the crossover percentage and the mutation percentage, are varied to find the optimal value. The crossover percentage is investigated from 0.6 to 0.9 with a step of 0.1. The mutation percentage is varied in the range (0, 1), with a step of 0.2. The proportion between the training and test dataset is 70% and 30%, respectively. In neural networks, the amount of training and testing data are dependent on many different aspects of the experiment. Hence, there is no minimum or maximum for sample size data. Generally, the 70% and 30% split for training and testing samples, respectively, can ensure better performance for generalization and accuracy models [39]. Table 3. Parameter setting of ANFIS and SOM. SOM Value ANFIS Value 0.85 Initial learning rate Random Fuzzy type Sugeno Initial weight vector Size 10 Input/outputs 5/1 Max. radius of neighbourhood 5000 Input MF type Max. number of iterations 2 × 2, 3 × 3, 4 × 4 Output MF type Gaussian Training algorithm Linear SOM array size No. of MFs for each input Fuzzy rules GA, PSO 10 10 Table 4. Parameter setting of GA and PSO. GA Value PSO Value Population Size 350 Population size 450 Iteration 10000 Iteration 5000 Crossover percentage [0.6,0.9] Inertia weight 1.0 Mutation percentage Damping ratio 0.99 (0,1) Personal learning coefficient 1.0 Mutation ratio 0.1 Global learning coefficient 2.0 Selection pressure 8 Gamma 0.2

320 Symmetry 2020, 12, 1602 10 of 18 4. Result and Discussion In this section, the optimal map size of SOM is found in Section 4.1. Meanwhile, the optimal parameters of HM-GA and HM-PSO are searched in Sections 4.2 and 4.3, respectively. The comparison of the results and a discussion between HM-GA and HM-PSO is interpreted in Section 4.4. 4.1. The Results of the SOM Algorithm In order to predict talc pellet moisture using HM, there are two main algorithms, including SOM and ANFIS. Firstly, the SOM algorithm is applied to classify the significant input data. The map size is a major parameter that impacts on the computational time. It can support classifying the number of clusters. The suitable case can be obtained by the user requirements [40]. In this study three different map sizes of 2 × 2, 3 × 3, and 4 × 4 are investigated. According to the experiment, it is found that only four clusters are of the optimal dimension map size. If the map size is greater than 2 × 2, some clusters have no members. Table 5 shows the frequency of the input data mapped to each cluster. From Table 5 it can be seen that there are two main patterns. The probability of occurrence for each pattern of a 2 × 2 map size is 1/4 or 25%. According to Equation (7), the confidence interval is in the range of 13.23 to 36.77%. From Table 6, the patterns of nodes (1,1) and (2,2) show the only two nodes with frequency values outside the confidence interval. After classifying the input data by SOM, 47 experimental cases, 25 from node (1,1) and 22 from node (2,2), are collected to use as input data for the HM model. Table 5. Frequency of occurrence of talc forming process factors in each cluster (%). Cluster 1 2 1 48.07 7.69 2 1.92 42.31 Table 6. Comparison of performance of HM-GA, HM-PSO, ANFIS-GA, and ANFIS-PSO. Model R Train Data AAD R Test Data AAD 0.401 0.493 HM-GA 0.9682 RMSE 0.393 0.7113 RMSE 0.376 HM-PSO 0.9539 0.8984 0.314 0.9192 2.3959 0.416 ANFIS-GA 0.9784 1.0693 0.333 0.7598 0.9785 0.485 ANFIS-PSO 0.9641 0.7203 0.8431 2.5396 0.9137 2.0327 4.2. The Optimal Parameter of HM-GA To obtain the optimized structure of HM-GA model, the influencing parameters, such as population size, crossover percentage, and mutation percentage, are changed to find the suitable structure, as shown in Figure 4a,c. The root mean square error is applied to measure the applicability of the optimum parameters. From Figure 4a, the population sizes are changed in a range between 50 and 500, presented in 10 different colors. The red line gives the smallest RMSE value and reaches stability after 5000 iterations. Thus, the proper population size is examined at 350. A crossover percentage with a population size of 350 is varied in a range between 0.6 and 0.9, as shown in Figure 4b and indicated with four different colors. It can be clearly seen that the red line shows the smallest RMSE value. Hence, the crossover percentage of 0.7 is the appropriate case for this study. Simultaneously, a mutation percentage with population size of 350 and crossover percentage of 0.7 is considered in the range between 0 and 1, as shown in Figure 4c and displayed with nine different colors. At a mutation percentage of 0.3, the red line shows the experimental results providing the smallest RMSE value. As mentioned in these figures, it can be summarized that, for the HM-GA model, a population size equal

321 Symmetry 2020, 12, 1602 11 of 18 to 350, crossover percentage equal to 0.7, and mutation percentage equal to 0.3 leads to the best predictive network in moisture predicting for the talc pellet forming process. (a) (b) (c)

322 Symmetry 2020, 12, 1602 12 of 18 Figure 4. The optimal parameter of GA algorithm: (a) population size; (b) crossover percentage; (c) mutation percentage. 4.3. The Optimal Parameter of HM-PSO The optimal parameter can increase the reliability of the model. For HM-PSO, the important parameters of PSO were assessed using a trial and error process. The different values of population sizes and inertia weight are investigated. As in Figure 5a, 10 different cases of population size varied from 50 to 500 for iterations are presented. In Figure 5b, the inertia weight changed from 0.2 to 1 by a step of 0.2 for 5000 iterations are examined. From these figures, it can be concluded that, for the HM-PSO model, a population size equal to 450 and an inertia weight equal to 1.0 can lead to the best predictive network. (a) (b) Figure 5. The optimal parameters of the PSO algorithm: (a) population size; (b) inertia weight. 4.4. The Comparison Results Approach from HM-GA and HM-PSO In order to predict the moisture in the talc pellet process, SOM is applied to select the appropriate input data and then the data are fed into ANFIS. The GA and PSO are chosen as training methods. As mentioned in Section 4.2, the optimal population size, crossover percentage, and mutation percentage of HM-GA and ANFIS-GA are 350, 0.8, and 0.6, respectively. As in Section 4.3, the optimal

323 Symmetry 2020, 12, 1602 13 of 18 population size and inertia weight of HM-PSO and ANFIS-PSO are 450 and 1.0, respectively. To compare the performance of the proposed HM-GA and HM-PSO model, the ANFIS model without clustering trained by GA and PSO is examined, namely, ANFIS-GA and ANFIS-PSO. Table 6 shows the comparison of the performance between four models of HM-GA, HM-PSO, ANFIS-GA and ANFIS-PSO. From Table 6, in the process of creating a model generated by the training dataset, ANFIS-GA has the highest R of 0.9784, and the lowest RMSE and AAD of 0.7203 and 0.314, respectively. In the test process, the HM-PSO has the highest R of 0.9192, the lowest RMSE of 0.9785, and the lowest AAD of 0.376. The relationship between the target and predicted moisture is a strong positive association. The value of AAD is used to measure the average distance between each data point and the mean. As can be seen in Table 6, the HM-PSO model demonstrates the smallest different value of AAD between the training and test data. Meanwhile, other models have larger different values of AAD between the training and test data. It can be obviously seen that three indicators of the HM-PSO indicates a smaller difference in value to both the training and test data than others. Additionally, the convergence speed of HM-PSO is faster and the predictive values conform with the measured values than others. It can be concluded that the HM-PSO has the most reliable results in predicting moisture in the talc forming process. Figure 6 shows the difference between the target and output values of the training and testing datasets. According to Figure 6, the variation between the predicted moisture and target moisture is displayed. The red line represents the target moisture and the blue line is the predicted moisture. In the training process of each experiment, two models with SOM perform more similarity than two other models without SOM, although all models provide a high correlation coefficient. Simultaneously, for testing process, it is clearly seen that there are many experiment cases of ANFIS- GA and ANFIS-PSO that are too different between the target and predicted moisture values. By using SOM, the differentiation can be reduced, as in Figure 6a,b. The correlation between the target and predicted moisture values is shown in Figure 7. (a)

324 Symmetry 2020, 12, 1602 14 of 18 (b) (c) (d) Figure 6. The difference between the target and predicted moisture: (a) HM-GA; (b) HM-PSO; (c) ANFIS-GA; (d) ANFIS-PSO.

325 Symmetry 2020, 12, 1602 15 of 18 (a) (b) (c) (d) Figure 7. The correlation between the target and predicted moisture: (a) HM-GA; (b) HM-PSO; (c) ANFIS-GA; (d) ANFIS-PSO.

326 Symmetry 2020, 12, 1602 16 of 18 In Figure 7, the relationship between the target and predicted moisture of four models is performed. It can be seen that the predicted moisture of HM-PSO, Figure 7b, lies in a relatively straight line for both the training and test data. The R value obtained from the HM-PSO is close to 1, R = 0.9539 for training data and R = 0.9192 for test data. Regarding the model, HM-PSO is a representative model for moisture prediction in the talc forming process. 5. Conclusions The hybrid model, based on a combination of SOM and ANFIS, is introduced as the proposed model for moisture prediction in the talc forming process in Uttaradit, Thailand. The GA and PSO algorithms are selected as the training algorithms of ANFIS. Five important factors—talc powder, water, temperature, feed speed, and airflow—affecting moisture in the talc pellet forming process were recognized and appropriate data were collected. In order to verify the proposed model, HM- GA, HM-PSO, ANFIS-GA, and ANFIS-PSO are compared. As a result, the HM-PSO model gives a high correlation coefficient for both training and test data with R = 0.9539 and R = 0.9192, respectively. Furthermore, HM-PSO still has a similar RMSE value for training and test data, of about 0.09. For other models, it has a rather large, different RMSE value between training and test data. Therefore, HM-PSO performs more reliably compared to the other algorithms. Since it is a real-world problem occurring in Uttaradit, Thailand, no one applies this method to the talc pellet process. The results, therefore, cannot compare with earlier research. The HM has some limitations according to the optimal parameters: It is only suitable for this study. For other real-world problems, it is necessary to identify the optimal parameters of HM. In this study, it can be said that the idea of raw data management by using SOM to identify a similar group of data is very helpful to obtain the most significantly information to feed into ANFIS. This can reduce the computation time during the training process. The method with clustering can improve the prediction skill compared to the method without clustering, efficiently. For further study, more clustering methods, such as k-means, and more ANFIS training algorithms, such as bee colony or ant colony optimization, should be applied and compared with this study. Author Contributions: P.S. and D.B. conceived and planned the experiments. D.B. carried out the experiment. W.P. developed the theoretical formalism, performed the analytic calculations and performed the numerical simulations. D.B. wrote the manuscript with support from W.P. All authors contributed to the final version of the manuscript. P.S. supervised the project. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: The authors would like to acknowledge the department of advanced manufacturing technology, Pathumwan Institute of Technology and the department of logistic engineering, Uttaradit Rajabhat University for the facilities support. The authors would also like to show our gratitude to Satean Tunyasrirut and Natita Wangsoh for their kindly advice throughout this research. Conflicts of Interest: The authors declare no conflict of interest. References 1. Driscoll, M. The structure of the Talc supply market. In Proceedings of the 3rd China Liaoning International Magnesia Materials Exposition, Shenyang, China, 22–24 September 2008; pp. 1–7. 2. Loveday, A.U.; Nwanya, S.C.; Amaechi, O.P. Artificial neural network application to a process time planning problem for palm oil production. Eng. Appl. Sci. Res. 2020, 47, 161–169. 3. Talpur, N.; Salleh, M.N.; Hussain, K.; Ali, H. Modified ANFIS with Less model complexity for classification problems. In Proceedings of the Computational Intelligence in Information Systems Conference (CIIS 2018), Phuket, Thailand, 17–19 November 2018; pp. 36–47. 4. Buragohain, M. Adaptive Network Based Fuzzy Inference System (ANFIS) as a Tool for System Identification with Special Emphasis on Training Data Minimization. Ph.D. Thesis, Indian Institute of Technology Guwahati, Guwahati, India, July 2008.

327 Symmetry 2020, 12, 1602 17 of 18 5. Caydas, U.; Hascalik, A.; Ekici, S. An Adaptive Neuro-Fuzzy Inference System (ANFIS) model for wire- EDM. Expert Syst. Appl. 2009, 36, 6135–6139. 6. Zhange, Y.; Lei, J. Prediction of laser cutting roughness in intelligent manufacturing mode based on ANFIS. Procedia Eng. 2017, 174, 82–89. 7. Sen, B.; Mandal, U.K.; PrasadMondal, S. Advancement of an intelligent system based on ANFIS for predicting machining performance parameters of inconel 690—A perspective of metaheuristic approach. Measurement 2017, 109, 9–17. 8. Abdollahi, H. An Adaptive Neuro-Based Fuzzy Inference System (ANFIS) for the prediction of option price: The case of the Australian option market. Int. J. Appl. Math. Comput. 2020, 11, 99–117. 9. Bui, D.T.; Khosravi, K.; Li, S.; Shahabi, H.; Panahi, M.; Singh, V.; Chapi, K.; Shirzadi, A.; Panahi, S.; Chen, W.; et al. New hybrids of ANFIS with several optimization algorithms for flood susceptibility modeling. Water 2018, 10, 1210. 10. Yaseen, Z.M.; Ebtehaj, I.; Bonakdari, H.; Deo, R.; Mehr, A.D.; Mohtar, W.M.; Diop, L.; Ei-shafie, A.; Singh, V. Novel approach for streamflow forecasting using a hybrid ANFIS-FFA model. J. Hydrol. 2017, 554, 263– 276. 11. Gocken, M.; Boru, A. Integrating metaheuristics and ANFIS for daily mean temperature forecasting. Int. J. Glob. Warm. 2016, 9, 110–128. 12. Oliverira, M.V.; Schirru, R. Applying particle swarm optimization algorithm for tuning a neuro-fuzzy inference system for sensor monitoring. Prog. Nucl. Energy 2009, 51, 177–183. 13. Alarifi, I.M.; Nguyen, H.M.; Bakhtiyari, A.N.; Asadi, A. Feasibility of ANFIS-PSO and ANFIS-GA models in predicting thermophysical properties of Al2O3-MWCNT/Oil hybrid nanofluid. Materials 2019, 12, 3628. 14. Kumar, R.; Hynes, N.R. Prediction and optimization of surface roughness in thermal drilling using integrated ANFIS and GA approach. Eng. Sci. Technol. Int. J. 2020, 23, 30–41. 15. Rezakazemi, M.; Dashti, A.; Asghari, M.; Shirazian, S. H2-selective mixed matrix membranes modeling using ANFIS, PSO-ANFIS, GA-ANFIS. Int. J. Hydrogen Energy 2017, 42, 15211–15225. 16. Sabeti, M.; Deevband, M.R. Hybrid evolutionary algorithms based on PSO-GA for training ANFIS structure. Int. J. Comput. Sci. 2015, 12, 78–86. 17. Dariane, A.B.; Azimi, S. Forecasting streamflow by combination of genetic input selection algorithm and wavelet transform using ANFIS model. Hydrol. Sci. J. 2016, 61, 585–600. 18. Jeong, C.; Shin, J.-Y.; Kim, T.; Heo, J.-H. Monthly precipitation forecasting with a neuro-fuzzy model. Water Resour. Manag. 2012, 26, 4467–4483. 19. Kohonen, T.; Simula, O.; Visa, A.; Kangas, J. Engineering applications of the self-organizing map. Proc. IEEE 1996, 84, 1358–1384. 20. Khanzadeh, M.; Rao, P.; Jafari-Marandi, R.; Smith, B.K.; Tschopp, M.A.; Bian, L. Quantifying geometric accuracy with unsupervised machine learning: Using self-organizing map on fused filament fabrication additive manufacturing parts. J. Manuf. Sci. Eng. 2018, 140, 1–12. 21. Jha, R.; Dulikravich, G.S.; Chakraborti, N.; Fan, M.; Schwartz, J.; Koch, C.C.; Marcelo, J.; Colaco, M.J.; Poloni, C.; Egorov, I.N. Self-organizing maps for pattern recognition in design of alloys. Mater. Manuf. Processes 2017, 32, 1067–1074. 22. Nourani, V.; Alami, M.T.; Vousoughi, F.D. Hybrid of SOM-clustering method and wavelet-ANFIS approach to model and infill missing groundwater level data. J. Hydrol. Eng. 2016, 21, 1–19. 23. Amiryousefi, M.R.; Mohebbi, M.; Khodaiyan, F.; Asadic, S. An empowered adaptive neuro-fuzzy inference system using self-organizing map clustering to predict mass transfer kinetics in deep-fat frying of ostrich meat plates. Comput. Electron. Agric. 2011, 76, 89–95. 24. Nasir, V.; Cool, J. Intelligent wood machining monitoring using vibration signals combined with self- organizing maps for automatic feature selection. Int. J. Adv. Manuf. Technol. 2020, 108, 1811–1825. 25. Standard Test Method for Laboratory Determination of Water (Moisture) Content of Soil and Rock by Mass; ASTM D 2216–98; ASTM International: Washington, DC, USA, 28 March 2004. 26. Asan, U.; Ercan, S. An Introduction to Self-Organizing Maps; Atlantis Press: Istanbul, Turkey, 2012; pp. 299– 319. 27. Wangsoh, N.; Watthayu, W.; Sukawat, D. Appropriate learning rate and neighborhood function of Self- Organizing Map (SOM) for specific humidity pattern classification over Southern Thailand. Int. J. Model. Optim. 2016, 6, 61–65. 28. Stefanovic, P.; Kurasova, O. Visual analysis of Self-Organizing Maps. Nonlinear Anal. 2011, 16, 488–504.

328 Symmetry 2020, 12, 1602 18 of 18 29. Jang, J.-S.R. ANFIS: Adaptive-Network-Based Fuzzy. IEEE Trans. Syst. Man Cybern. Syst. Hum. 1993, 23, 665–685. 30. Holland, J. Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence; MIT Press: Cambridge, MA, USA, 1979. 31. Goldberg, D.E. Genetic Algorithm in Search Optimization and Machine Learning; Addison Wesley: Boston, MA, USA, 1989. 32. Kennedy, J.; Eberhart, R.C. A new optimizer using particle swarm theory. In Proceedings of the Sixth International Symposium on Micromachine and Human Science, Nagoya, Japan, 4–6 October 1995; pp. 39– 43. 33. Talukder, S. Mathematical Modelling and Applications of Particle Swarm Optimization. Master’s Thesis, Blekinge Institute of Technology, Karlskrona, Sweden, February 2011. 34. Ohale, P.E.; Uzoh, C.F.; Onukwuli, O.D. Optimal factor evaluation for the dissolution of alumina from azaraegbelu clay in acid solution using RSM and ANN comparative analysis. S. Afr. J. Chem. Eng. 2017, 24, 43–54. 35. Montogomery, D.C. Design and Analysis of Experiments; John Wiley & Sons Inc.: New York, NY, USA, 2001. 36. Pham, H. Springer Handbook of Engineering Statistics; Springer: London, UK, 2006. 37. Moayedi, H.; Raftari, M.; Sharifi, A.; Jus, W.W.; Safuan, A.; Rashid, A. Optimization of ANFIS with GA and PSO estimating α ratio in driven. Eng. Comput. 2019, 36, 227–238. 38. Wu, D.; Chen, H.; Huang, Y.; He, Y. Monitoring of weld joint penetration during variable polarity plasma arc welding based on the keyhole characteristics and PSO-ANFIS. J. Mater. Process. Technol. 2017, 239, 113– 124. 39. Lei, S.; Zhan, H.; Wang, K.; Su, Z. How training data affect the accuracy and robustness of neural networks for image classification. In Proceedings of the International Conference on Learning Representations, New Orleans, LA, USA, 6–9 May 2019; pp. 1–14. 40. Ismail, S.; Shabri, A.; Samsudin, R. A hybrid model of Self Organizing Maps and least square support vector machine for river flow forecasting. Hydrol. Earth Syst. Sci. 2012, 16, 4417–4433. © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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332Symmetry 2020, 12(10), 1605; https://doi.org/10.3390/sym12101605 (registering DOI) - 26 Sep 2020 (/) Abstract In work is introduced one new hierarchical decomposition for cubical tensor of size 2n, based on the well-known orthogonal transforms this Principal Component Analysis and Karhunen–Loeve Transform. The decomposition is called 3D Frequency-Ordered Hierarchical KLT (3D-FOHKLT). It is  separable, and its [...] Read more. (This article belongs to the Special Issue Advances in Symmetric Tensor Decomposition Methods ( /journal/symmetry/special_issues/Advances_Symmetric_Tensor_Decomposition_Methods )) ► Show Figures (/symmetry/symmetry-12-01605/article_deploy/html/images/symmetry-12-01605-ag-550.jpg)   (/2073-8994/12/10/1604/pdf) Open Access Article A New Macro-Model of Gas Flow and Parameter Extraction for a CMOS-MEMS Vacuum Sensor (/2073-8994/12/10/1604) by Shu-Jung Chen (https://sciprofiles.com/profile/672447) and Yung-Chuan Wu (https://sciprofiles.com/profile/1248176) Symmetry 2020, 12(10), 1604; https://doi.org/10.3390/sym12101604 (registering DOI) - 26 Sep 2020 Abstract When using a MEMS sensor to measure the vacuum of a medium, the transition flow between the viscous flow and molar flow is usually used to describe the gas convection due to the physical principle, which is difficult to study through analysis and [...] Read more. (This article belongs to the Special Issue Optical and Electronic Characteristics of Semiconductor Materials and Devices ( /journal/symmetry/special_issues/Optical_Electronic_Characteristics_Semiconductor_Materials_Devices )) ► Show Figures (/symmetry/symmetry-12-01604/article_deploy/html/images/symmetry-12-01604-g001-550.jpg) (/symmetry/symmetry-12- 01604/article_deploy/html/images/symmetry-12-01604-g002-550.jpg) (/symmetry/symmetry-12-01604/article_deploy/html/images/symmetry-12- 01604-g003-550.jpg) (/symmetry/symmetry-12-01604/article_deploy/html/images/symmetry-12-01604-g004-550.jpg) (/symmetry/symmetry-12- 01604/article_deploy/html/images/symmetry-12-01604-g005-550.jpg) (/symmetry/symmetry-12-01604/article_deploy/html/images/symmetry-12- 01604-g006-550.jpg) (/symmetry/symmetry-12-01604/article_deploy/html/images/symmetry-12-01604-g007-550.jpg) (/symmetry/symmetry-12- 01604/article_deploy/html/images/symmetry-12-01604-g008-550.jpg) (/symmetry/symmetry-12-01604/article_deploy/html/images/symmetry-12- 01604-g009-550.jpg) (/symmetry/symmetry-12-01604/article_deploy/html/images/symmetry-12-01604-g010-550.jpg) (/symmetry/symmetry-12- 01604/article_deploy/html/images/symmetry-12-01604-g011-550.jpg) (/symmetry/symmetry-12-01604/article_deploy/html/images/symmetry-12- 01604-g012-550.jpg) (/symmetry/symmetry-12-01604/article_deploy/html/images/symmetry-12-01604-g013-550.jpg) (/symmetry/symmetry-12- 01604/article_deploy/html/images/symmetry-12-01604-g014-550.jpg)   (/2073-8994/12/10/1603/pdf) Open Access Article The Nakano–Nishijima–Gell-Mann Formula from Discrete Galois Fields (/2073-8994/12/10/1603) by Keiji Nakatsugawa (https://sciprofiles.com/profile/1206337) , Motoo Ohaga (https://sciprofiles.com/profile/author/N3ozKzhCZFg0ditQdklORlVKQUI1dVQ2ck5Dc3BIRXF5cjZ1YWJPdkFnWT0=) , Toshiyuki Fujii (https://sciprofiles.com/profile/author/T01mTTYycER1ZGtsRjg0Wm85NmRpOUF3ell0Z3VJRkE4blBDck1BcmNRUT0=) , Toyoki Matsuyama (https://sciprofiles.com/profile/author/bTN6V2Noci9lOC9MaCt5c05OZU5QYlpWQUpqYzhJcXE2N3NWNFdKY25hYz0=) and Satoshi Tanda (https://sciprofiles.com/profile/1206338) Symmetry 2020, 12(10), 1603; https://doi.org/10.3390/sym12101603 (registering DOI) - 26 Sep 2020 Abstract The well known Nakano–Nishijima–Gell-Mann (NNG) formula relates certain quantum numbers of elementary particles to their charge number. This equation, which phenomenologically introduces the quantum numbers (isospin), S (strangeness), etc., is constructed using group theory with real numbers . But, using [...] Read more. (This article belongs to the Section Physics and Symmetry (/journal/symmetry/sections/physics_symmetry)) ► Show Figures (/symmetry/symmetry-12-01603/article_deploy/html/images/symmetry-12-01603-g001-550.jpg) (/symmetry/symmetry-12- 01603/article_deploy/html/images/symmetry-12-01603-g002-550.jpg) (/symmetry/symmetry-12-01603/article_deploy/html/images/symmetry-12- 01603-g003-550.jpg) (/symmetry/symmetry-12-01603/article_deploy/html/images/symmetry-12-01603-g004-550.jpg) Open Access Article   (/2073-8994/12/10/1602/pdf) The Application of a Hybrid Model Using Mathematical Optimization and Intelligent Algorithms for Improving the Talc Pellet Manufacturing Process (/2073-8994/12/10/1602) by Dussadee Buntam (https://sciprofiles.com/profile/1269524) , Wachirapond Permpoonsinsup (https://sciprofiles.com/profile/author/bjk1STh1RE5HWVBTZVVxT2JYeGluWDI5OXo5aER4eW9RWjdEUHVnSW and Prayoon Surin (https://sciprofiles.com/profile/author/Qm1yYmFTeHcvbklpQ3luUUNGbklBNVJCZlBIVlZQUjQ3OTFjMEhuRUNpQT0=) Symmetry 2020, 12(10), 1602; https://doi.org/10.3390/sym12101602 (registering DOI) - 26 Sep 2020 AWbsetruascet Mcoooisktiuerse oisnoonuerowf tehbesmiteostot imenpsourtraenyt ofauctgoerst timhepabcetsintgetxhpeetraielcnpceel.let process. In this study, a hybrid model (HM) based on the combination of inRteellaigdemntoarlegoarbithomutso, suerlfc-oorogkaineiszihnegrme a(/pab(SoOutM/p)r,itvhaecayd).aptive neuron fuzzy inference system (ANFIS) and metaheuristic optimizations, genetic algorithm (GA) [...] Read more. (This article belongs to the Special Issue Symmetry in Optimization and Control with Real World Applications ( Accept (/accept_cookies) /journal/symmetry/special_issues/Symmetry_Optimization_Control_Real_World_Applications )) Back to TopTop /

Open Access Article 333   (/2073-8994/12/10/1601/pdf) (/) An Ensemble Machine Learning Technique for Functional Requirement Classification (/2073-8994/12/10/1601) by Nouf Rahimi (https://sciprofiles.com/profile/1216118) , Fathy Eassa (https://sciprofiles.com/profile/1206332) and  Lamiaa Elrefaei (https://sciprofiles.com/profile/819468) Symmetry 2020, 12(10), 1601; https://doi.org/10.3390/sym12101601 (https://doi.org/10.3390/sym12101601) - 25 Sep 2020 Abstract In Requirement Engineering, software requirements are classified into two main categories: Functional Requirement (FR) and Non-Functional Requirement (NFR). FR describes user and system goals. NFR includes all constraints on services and functions. Deeper classification of those two categories facilitates the software development process. [...] Read more. (This article belongs to the Section Computer and Engineer Science and Symmetry (/journal/symmetry/sections/computer_engineer_science_symmetry)) Open Access Article   (/2073-8994/12/10/1600/pdf) Padé and Post-Padé Approximations for Critical Phenomena (/2073-8994/12/10/1600) by Simon Gluzman (https://sciprofiles.com/profile/1240087) Symmetry 2020, 12(10), 1600; https://doi.org/10.3390/sym12101600 (https://doi.org/10.3390/sym12101600) - 25 Sep 2020 Abstract We discuss and apply various direct extrapolation methods for calculation of the critical points and indices from the perturbative expansions my means of Padé-techniques and their various post-Padé extensions by means of root and factor approximants. Factor approximants are applied to finding critical [...] Read more. (This article belongs to the Special Issue Asymptotic Methods in the Mechanics and Nonlinear Dynamics ( /journal/symmetry/special_issues/Asymptotic_Methods_Mechanics_Nonlinear_Dynamics ))   (/2073-8994/12/10/1599/pdf) Open Access Article Clar Covers of Overlapping Benzenoids: Case of Two Identically-Oriented Parallelograms (/2073-8994/12/10/1599) by Henryk A. Witek (https://sciprofiles.com/profile/1191249) and Johanna Langner (https://sciprofiles.com/profile/author/c0F6VldWdHZhOVlucVh6ZGpvTlVNNDZhTnRGUlJ4MUM4NFREOUFqR3NRTT0=) Symmetry 2020, 12(10), 1599; https://doi.org/10.3390/sym12101599 (https://doi.org/10.3390/sym12101599) - 25 Sep 2020 Abstract We present a complete set of closed-form formulas for the ZZ polynomials of five classes of composite Kekuléan benzenoids that can be obtained by overlapping two parallelograms: generalized ribbons , parallelograms M, vertically overlapping parallelograms , horizontally [...] Read more. (This article belongs to the Special Issue Symmetry on the Genealogy of Conjugated Acyclic Polyenes — Dedicated to the Two Active Mathematical Chemists, Diudea and Aihara ( /journal/symmetry/special_issues/Symmetry_Genealogy_Conjugated_Acyclic_Polyenes )) More Articles... (/search?q=&journal=symmetry&sort=pubdate&page_count=50) (/journal/symmetry) Submit to Symmetry (https://susy.mdpi.com/user/manuscripts/upload?form[journal_id]=44) Review for Symmetry (https://susy.mdpi.com/volunteer/journals/review) (https(:h//ttwpistt:e//rw.cwowm./fSacyembmooektr.yc_oMmD/MPDI)PIOpenAccessPublishing) Share Journal Menu Accept (/accept_cookies) Back to TopTop ► Journal Menu /  Symmetry Home (/journal/symmetry)  Aims & Scope (/journal/symmetry/about)  Editorial Board (/journal/symmetry/editors)  Topics Board (/journal/symmetry/topic_editors)  Instructions for Authors (/journal/symmetry/instructions)  Special Issues (/journal/symmetry/special_issues)  Sections (/journal/symmetry/sections)  Article Processing Charge (/journal/symmetry/apc)  Indexing & Archiving (/journal/symmetry/indexing)  Most Cited & Viewed (/journal/symmetry/most_cited)  Journal Statistics (/journal/symmetry/stats) RWeJJeaoouduusrrmnneaaocllroAHeowisakatbioreodrsyuso(t(//njojoouuourrurnncraaowll/o/ssekyybimmessmimteheetettrroryye//eha(ni/wsastaoburrordyeus) t)y/poruivgaectyt)h. e best experience.  Conferences (/journal/symmetry/events)  Editorial Office (/journal/symmetry/editorial_office)

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Plagiarism Checking Report 335 Created on Dec 17, 2020 at 11:40 AM Submission Information ORGANIZATION FILENAME STATUS SIMILARITY ID SUBMISSION DATE SUBMITTED BY INDEX 1882616 Dec 17, 2020 at [email protected] มหาวทิ ยาลยั ราชภฏั symmetryDussade.pdf Completed 0.00 % 11:40 AM อตุ รดติ ถ์ Match Overview AUTHOR(S) SOURCE SIMILARITY INDEX NO. TITLE No data available in table /

17/12/2563 336อกั ขราวสิ ทุ ธิ Match Details TEXT FROM SUBMITTED DOCUMENT TEXT FROM SOURCE DOCUMENT(S) plag.grad.chula.ac.th/jobs/1882616/3510900475 2/2

26/9/2563 337Symmetry also developed by scimago: SCIMAGO INSTITUTIONS RANKINGS Scimago Journal & Country Rank Enter Journal Title, ISSN or Publisher Name Home Journal Rankings Country Rankings Viz Tools Help About Us Create Interactive Content No coding required. Customizable templates. 500+ Integrations. Publish anywhere. Outgrow.co OPEN Symmetry Country Switzerland  -  SIR Ranking of Switzerland 36 Subject Area and Chemistry H Index Category Chemistry (miscellaneous) Computer Science Computer Science (miscellaneous) Mathematics Mathematics (miscellaneous) Physics and Astronomy Physics and Astronomy (miscellaneous) Publisher MDPI Multidisciplinary Digital Publishing Institute Publication type Journals ISSN 20738994 Coverage 2009-2020 Scope Symmetry (ISSN 2073-8994), an international and interdisciplinary scienti c journal, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish their experimental and theoretical research in as much detail as possible. There is no restriction on the length of the papers. Full experimental and/or methodical details must be provided, so that results can be reproduced. There are in addition three unique features: - Manuscripts regarding research proposals and research ideas will be particularly welcomed. -Comments on any related papers published in this journal and other journals can be published as short letters. -Electronic les regarding the full details of the calculation and experimental procedure, if unable to be published in a normal way, will be deposited as supplementary material. Homepage How to publish in this journal Contact Join the conversation about this journal Quartiles The set of journals have been ranked according to their SJR and divided into four equal groups, four quartiles. Q1 (green) comprises the quarter of the journals with the highest values, Q2 (yellow) the second highest values, Q3 (orange) the third highest values and Q4 (red) the lowest values. Category Year Quartile https://www.scimagojr.com/journalsearch.php?q=21100201542&tip=sid&clean=0 1/4

26/9/2563 Year Quartile 338Symmetry Category 2010 Q3 ChemistryC(hmemisicsterlyla(mneisocueslla) neous) 2011 Q2 Chemistry (miscellaneous) Citations per document Computer Science (miscellaneous) SJR 0T.6he SJR is a size-independent prestige indicator that 3T.2his indicator counts the number of citations received by ranks journals by their 'average prestige per article'. It is documents from a journal and divides them by the total number of documents published in that journal. The 0be.4qauseadl'. on the idea that 'all citations are not created 2c.4hart shows the evolution of the average number of SJR is a measure of scienti c in uence of times documents published in a journal in the past two, three and four years have been cited in the current year. journals that accounts for both the number of citations The two years line is equivalent to journal impact factor 1™.6(Thomson Reuters) metric. 0r.e2ceived by a journal and the importance or prestige of the jo2u0r1n0als wh2e0re12such ci2ta0t1i4ons com20e16from It2018 measures the scienti c in uence of the average article in a journal it expresses how central to the global Total Cites Self-Cites 0.CC8iitteess per document Year Value / Doc. (4 years) 2009 0.000 4Ekvolution of the total number of citations and journal's Cites / Doc. (4 years) 2010 0.538 self-citations received by a journal's published Cites / Doc. (4 years) 2011 1.165 2Jdkooucurnmael Snteslfd-cuitraintgiotnhiestdhereenepdreavsiotuhse years. C0ites / Doc. (4 years) 2012 1.443 number of citation CCiittee2ss0//09DDoocc.. ((2440yy1ee1aarrss)) 201223001143 201115..456563 2017 2019 from a journal citing article to articles published by the CitCeiste/s D/ oDcoc. .(4(4yyeeaarrss)) 2015 1.144 s0ame journal. CitCeiste/s D/ oDcoc. .(4(3yyeeaars)) 2016 1.468 2009 2011 2013 2015 2017 2019 CitCeiste/s D/ oDcoc. .(4(2yyeeaarrss)) 2017 1.528 Cites Year Value Cites / Doc. (4 years) 2018 2.445 S lf Cit 2009 0 External Cites per Doc Cites per Doc % International Collaboration 4Evolution of the number of total citation per document 4I0nternational Collaboration accounts for the articles that and external citation per document (i.e. journal self- have been produced by researchers from several 2dciotactuiomnesnrtesmduorviendg)trheecethivreeed by a journal's published 2cd0ooucnutmrieens.tsTshiegnchedarbt yshreoswesartchheerrastiforoomf amjoourerntahla'sn one previous years. External country; that is including more than one country address. citations are calculated by subtracting the number of 0 0self-citations from the total number of citations received by t2h0e09journa2l’s01d1ocume2n0t1s3. 2015 2017 2019 Yea2r009 Inter2n0a1t1ional2C0o1l3labora2t0i1o5n 2017 2019 2009 26.67 Cit Y Vl Citable documents Non-citable documents 2010 11 54 Cited documents Uncited documents 1N.4okt every article in a journal is considered primary 1R.4aktio of a journal's items, grouped in three years windows, that have been cited at least once vs. those research and therefore \"citable\", this chart shows the 7n0o0t cited during the following year. 7(rar0et0isoeaorfcahjaorutrinclaels's, articles including substantial research conference papers and reviews) in three year windows vs. those documents other than Documents Year Value 2009 0 res0earch articles, reviews and conference papers. Un0cited documents 22010310 29015 Unci2t0e0d9docu2m01e1nts 2011 51 2009 2011 2013 2015 2017 2019 Uncited documents 2012 59 2017 2019 Uncited documents Documents Year Value N it bl d t 2009 0 ← Show this widget in your own website Just copy the code below and paste within your html code: <a href=\"https://www.scimag D Dr. Ahmadi 2 years ago 2/4 https://www.scimagojr.com/journalsearch.php?q=21100201542&tip=sid&clean=0

26/9/2563 339Symmetry Dear Dr. Ahamdi Salam This is the journal that the paper of Mrs Ameneh Asadi has been accepted for publication in this journal. The paper has been taken doi and pages number as wll as has been prepared in the format of the journal. As you see this is a high ranked journal with H-index 20 and impact factor 1.38 and in Q2. Regards Reza Ameri reply Leave a comment Name Email (will not be published) ฉันไมใ่ ชโ่ ปรแกรมอตั โนมตั ิ reCAPTCHA ขอ้ มลู สว่ นบคุ คล - ขอ้ กําหนด Submit The users of Scimago Journal & Country Rank have the possibility to dialogue through comments linked to a speci c journal. The purpose is to have a forum in which general doubts about the processes of publication in the journal, experiences and other issues derived from the publication of papers are resolved. For topics on particular articles, maintain the dialogue through the usual channels with your editor. วดั ระดบั ภาษาองั กฤษฟรี เปิ ด ตอบ 10 คําถาม เพอื วดั ระดบั พนื ฐานภาษาองั กฤษของคณุ ฟรี Wall Street English https://www.scimagojr.com/journalsearch.php?q=21100201542&tip=sid&clean=0 3/4

26/9/2563 340Symmetry วดั ระดบั ภาษาองั กฤษฟรี เปิ ด ตอบ 10 คําถาม เพอื วดั ระดบั พนื ฐานภาษาองั กฤษของคณุ ฟรี Wall Street English Developed by: Powered by: Follow us on @ScimagoJR Scimago Lab, Copyright 2007-2020. Data Source: Scopus® https://www.scimagojr.com/journalsearch.php?q=21100201542&tip=sid&clean=0 4/4

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345 Message from President of Rajamangala University of Technology Thanyaburi Rajamangala University of Technology Thanyaburi in collaboration Kyoto University, Kyoto Institute of Technology and National Institute of Technology, Kagawa College, is pleased to host the 13th Eco-Energy and Materials Science and Engineering Symposium 2016 (13th EMSES2016). This international conference is not only giving an opportunity for Thai and foreign researchers to present and discuss their research works and update their expertise but also to initially stimulate the development of research works on eco-energy, materials science and engineering. The program consists of seven research tasks; Smart Grids, Smart Materials, Smart Society, Smart Innovation, Smart Mobility, Smart Communications and Smart Building and Home. I would like to take this opportunity to express my sincere gratitude to the plenary speakers for accepting our kind invitation. I deeply appreciate the very strong support given by Kyoto University and Kyoto institute of Technology. Thanks to the spirited works of the organizing committee, the technical program committee, the invited speakers, and paper contributors and excellent program have been assembled to cover a broad spectrum of interesting topics. I warmly welcome you to the EMSES 2016 on December 1 - 4, 2016, Udon Thani, Thailand. Associate Professor Prasert PINPATHOMRAT, Ph.D. President of Rajamangala University of Technology Thanyaburi and Honorary Advisory Chair of EMSES2016

346 Message from President of Kyoto Institute of Technology It is a great honor to co-host the 13th EMSES with Rajamangala University of Technology Thanyaburi (RMUTT), Kyoto University, Kyoto Institute of Technology and National Institute of Technology, Kagawa College. While evolving over its 110 year history, Kyoto Institute of Technology, KIT, has remained firmly rooted in ancient Kyoto traditions and culture. As explo KIT has a long history of collaboration with RMUTT, especially in the field of composite materials. In January of this year, we launched our first overseas office at RMUTT, which stimulated us to seek to expand the range of fields of collaboration. As a Japanese national university receiving special globalization funding from the Ministry of Education, we hope to use this work with RMUTT and this symposium as catalysts to further our globalization process. EMSES is an ambitious symposium covering an unusually broad range of science related to eco-energy and materials which promise lifestyle improvements. We are assured you will find this time fruitful and gain new perspectives and inspiration for your research. Professor Masao FURUYAMA President of Kyoto Institute of Technology and Honorary Advisory Co-Chair of EMSES2016

347 Message from Institute of Advanced Energy, Kyoto University I want to express my warm welcome to all participants of the 13th Eco-Energy and Materials Science and Engineering Symposium (13th EMSES2016). The 13th EMSES2016 has a long history since RMUTT and Kyoto University organized the 1st EMSES in 2001 in Thailand. So far the symposium has been expanded in its scientific contents as well as the academic network. Now this symposium is aiming at realization of SMART energy and materials sciences. We sincerely hope that the symposium gives a good opportunity for participants to share their knowledge and widen their collaboration research. I would like to extend my sincere thanks to all participants who made the meeting possible, as well as the 13th EMSES2016 organizers. I am looking forward to seeing you in Udon Thani, Thailand. Professor Hideaki OHGAKI, Ph.D. Institute of Advanced Energy, Kyoto University and Honorary Advisory Co-Chair of EMSES2016

348 Message from National Institute of Technology, Kagawa College It is my great pleasure that National Institute of Technology, Kagawa College (NITKC) now join the co- organizing member of the Eco-Energy and Materials Science and Engineering Symposium (EMSES) which has been organized by Rajamangala University of Technology Thanyaburi, Kyoto University and Kyoto Institute of Technology. I have a lot of and happy memories for every EMSES since I was a professor of Kyoto University. For earnest and continuous effort to manage and develop the EMSES greater and greater, I would like to express Rajamangala University of Technology Thanyaburi the respect and I also would like to express Kyoto University and Kyoto Institute of Technology the regard. NITKC is the largest college of National Institute of Technology, Japan. We have over 1500 students. We have seven departments including mechanical engineering, material engineering, communication engineering, information engineering, electric and electronic engineering, computer engineering, control engineering, civil engineering, environment engineering, agriculture engineering and so on. We are cultivating engineers at the General Education Course for five years after graduation of junior high school. We also have further two year Advance Course. By graduation of the Advanced Course, students obtain the same degree of bachelor as those who graduate a university. I very hope NITKC to start making good contributions to EMSES. Development of energy and material science and engineering is the basic and the most important issues for the welfare and sustainable development of human beings. From this point of view, I think EMSES is taking an important role. We should solve various problems. We should promote range of researches wider. We should have worldwide considerations. At EMSES2016, I expect the attendants will make hot discussions each other and will construct networks for the information exchange and the cooperation. I expect a great success of EMSES2016. Dr. Takeshi YAO President of National Institute of Technology, Kagawa College, Emeritus Professor of Kyoto University and Honorary Advisory Co-Chair of EMSES2016

349 Message from General Chair of EMSES2016 Rajamangala University of Technology Thanyaburi (RMUTT), is pleased to host the 13th Eco-energy and Materials Science and Engineering Symposium (EMSES2016). RMUTT has a major mission on encouraging and supporting all areas of research. One of the key reasons is to assist in developing capability in science and technology in order to cope with recent rapid change in this field. We have jointly set up an academic symposium on the 13th EMSES with the perception on the significance of exchanging knowledge and research experiences between researcher in the field of energy, materials technology and environmental science. This symposium is not only giving an opportunity for Thai and foreign researcher to present and discus their research works and update their expertise but also to initially stimulate the development of research works on eco- energy and materials science and engineering. Once the cooperation among researchers has been created, the closer future cooperation incorporate with joint-research works will be developed. Thus, to support the aforesaid role, the symposium working committee would like to invite you to participate in this academic symposium. I would like to express our sincere thanks to the organizing committee, participants and contributors for your kind corporation to this symposium. I wish this symposium proceeding will be a useful reference for future scientific research development. Assistant Professor Sommai PIVSA-ART, Ph.D. The Vice President of Rajamangala University of Technology Thanyaburi and General Chair of EMSES2016

350 Message from the General Co-Chair of EMSES2016 Rajamangala University of Technology Thanyaburi (RMUTT), in conjunction with Kyoto University, Kyoto Institute of Technology and National Institute of Technology, Kagawa College, is pleased to host the 13th Eco-Energy and Materials Science and Engineering Symposium (EMSES2016). RMUTT has a major mission on encouraging and supporting all areas of research. One of the key reasons is to assist in developing capability in science and technology in order to cope with recent rapid change in this field. We have jointly set up an academic symposium on the 13th EMSES with the perception on the significance of exchanging knowledge and research experiences between researcher in the field of energy, materials technology and environmental science. This symposium is not only giving an opportunity for Thai and foreign researcher to present and discussion their research works and update their expertise but also to initially stimulate the development of research works on eco-energy and materials science and engineering. Once the cooperation among researchers has been created, the closer future cooperation incorporate with joint-research works will be developed. Thus, to support the aforesaid role, the symposium working committee would like to express our sincere thanks to the organizing committee, participants and contributors for your kind corporation to this symposium. I wish this symposium proceeding will be a useful reference for future scientific research development. Assistant Professor Sivakorn ANGTHONG, Ph.D. Dean of Faculty of Engineering, RMUTT Thanyaburi and General Co-Chair of EMSES2016

351 Message from Technical Program Committee Chair of EMSES2016 It is our great pleasure to welcome all of the participants to the 13th Eco-Energy and Materials Science and Engineering Symposium 2016 (EMSES2016) in Udon Thani, Thailand, December 1-4, 2016. The technical program of EMSES2016 covers topics of all areas of interest to c under the smart future theme that including smart Grids, smart materials, smart society, smart innovation, smart mobility, smart communications and smart building and home. Over 134 submission papers were made mainly from Asian countries, and the technical program committee selected 101 papers for oral presentation and 14 papers for poster presentation. This number of papers is quite large enough to bring together researchers, engineers, students, and others to present and discuss their works on energy and materials science. Presentations for accepted papers are organized into 16 sessions in the two days conference both oral and poster presentation. The technical program committee consists of 20 members from Japan, Korea, Laos, Indonesia, Singapore and Thailand. All submitted papers were reviewed by these members about 120 members. Based on the scores of the review reports, acceptance and rejection of the submitted papers, and the assignment of the accepted papers to oral or poster sessions were determined. We are grateful to all of the authors, reviewers, and members of the technical program committee for their enthusiastic efforts and contributions. Handling of submission and review of papers could not have been completed along a tight schedule without their helps and cooperation. We also appreciate the great effort by session chairs who accept our request to manage sessions of the conference. Finally, we would like to express our sincere gratitude to all participants of EMSES2016. Their contributions are indispensable for the success of the conference. Enjoy your stay in Udon Thani! Associate Professor Krischonme BHUMKITTIPICH, Ph.D., IEEE Member Technical Program Committee Chair of EMSES2016

352 EMSES2016 EMSES Conference Committee Honorary Advisory Chair: Prasert PINPATHOMRAT (Pr RMUTT, Thailand) Honorary Advisory Co-Chair: Masao FURUYAMA (KIT, Japan) Hideaki OHGAKI (Kyoto University, Japan) International Advisory Committees Hiroyuki HAMADA (KIT, Japan) Akinori SEITO (Kyoto University, Japan) Hitomi OHARA (KIT, Japan) Nadarajah MITHULANANTHAN (UQ, Australia) Takeshi YAO (Kayawa College., Japan) Yuichi ANADA (Hokkaido Info. Uni., Japan. Young S. CHAI (Youngnam Uni., Korea) Seonghyuk KO (Yonsei Uni., Korea) Nipon TANGTHAM (KU, Thailand) Kumron SIRATHANAKUL (NPU, Thailand) General Chair Sommai PIVSA-ART (RMUTT, Thailand) General Co-Chair Sivakorn ANGTHONG (RMUTT, Thailand) Technical Program Committee Chair Krischonme BHUMKITTIPICH (RMUTT, Thailand) Technical Program Committee Co-Chair Supakit SUTIRUENGWONG (SU, Thailand) Sumonman NIAMLANG (RMUTT, Thailand) Technical Conference Committees T. INOUE (Yamagata Uni, Japan) Sakorn RIMJEAM (CMU, Thailand) K. YAMADA (KIT, Japan) T. ITO (Kagawa College, Japan) M. OKOSHI (KIT, Japan) Nagahiro SAITO (Nagoya Uni., Japan) Bawornkit NEKHAMANURAK (RMUTR, Thailand) Pimolpan NIAMLANG (RMUTR, Thailand) Wanchai SUBSINGHA (RSU, Thailand) Monthon NAWONG (RMUTT, Thailand) Y. ANADA (HIU, Japan) Yuqiu YANG (Dong Hua University, China) Pimnapat IEMSOMBOON, RMUTT, Thailand Boonyang PLANGKLANG (RMUTT, Thailand) Sorapong PAVASUPREE (RMUTT, Thailand)

EMSES2016 353 Yuttana KUMSUWAN (CMU, Thailand) Kaan KERDCHERN (RMUTI, Thailand) Uthen KAMNAN (RMUTL, Thailand) Tanapong SUWANNASRI (TGGS, Thailand) Wirachai ROYNARIN (RMUTT, Thailand) Napaporn PHUANGPORNPITAK (KU, Thailand) Jakkree SRINONCHAT (RMUTT, Thailand) Pramook UNHALEKHAKA (RMUTSB, Thailand) Nattapong PHANTHUNA (RMUTP, Thailand) Sakorn PO-NGAM (KMUTT, Thailand) Nattawoot SUWANTHA (MSU, Thailand) Boonrit PRASARTKAEW (RMUTT, Thailand) Kittiwan NIMKERDPOL (RMUTT, Thailand) Publicity and Website Chair Somchai BIANSOONGNERN (RMUTT, Thailand) Nathabhat PHANKONG (RMUTT, Thailand) Registration Chair Anin MEMON (RMUTT, Thailand) Financial Chair Weeraporn PIVSA-ART (RMUTT, Thailand) Local Arrangement Chair Amnoiy REUNGWAREE (RMUTT, Thailand) Local Arrangement Committee Wasan PHETPHIMOON (RMUTT, Thailand) General Secretariat Porakoch SIRISUWAN (RMUTT, Thailand) Yuttana KONGJEEN (RMUTT, Thailand)

354 EMSES2016 List of Reviewers Kyoto Institute of Technology Hiroyuki Hamada Kyoto University Kyoto Institute of Technology Akinori Seito University of Queensland Hitomi Ohara Kayawa College Nadarajah Mithulananthan Hokkaido Information University Takeshi Yao Youngnam University Yuichi Anada Yonsei University Young S Chai Kasetsart University Seonghyuk Ko Nakhon Panom Universiy Nipon Tangtham Rajamangala University of Technology Thanyaburi Kumron Sirathanakul Rajamangala University of Technology Thanyaburi Pimnapat Iemsomboon Rajamangala University of Technology Thanyaburi Boonyang Plangklang Rajamangala University of Technology Rattanakosin Sorapong Pavasupree Chiang Mai University Pimolpan Niamlang Rajamangala University of Technology Isan Yuttana Kumsuwan Rajamangala University of Technology Lanna Kaan Kerdchern The Siridhorn International Thai-German Graduate School Uthen Kamnan Of Engineering, KMUTNB Tanapong Suwannasri Rajamangala University of Technology Thanyaburi Kasetsart University Wirachai Roynarin Rajamangala University of Technology Thanyaburi Napaporn Phuangpornpitak Rajamangala University of Technology Suvarnabhumi Jakkree Srinonchat Rajamangala University of Technology Pha Nakon Pramook Unhalekhaka King Mongkut s University of Technology Thonburi Nattapong Phanthuna Mahasarakham University Sakorn Po-Ngam Chulalongkorn University National Institute of Technology, Okinawa College Nattawoot Suwantha Rajamangala University of Technology Thanyaburi Tawatchai Charinpanitkul Rajamangala University of Technology Thanyaburi Mbaitiga Zacharie Kyoto Institute of Technology Natha Kuptasthien Rajamangala University of Technology Thanyaburi Pongsri Siwarasak Prince of Songkla University Yuji Aso Kasetsart University Krischonme Bhunkittipich Chulalongkorn University Sutham Niyomwas Rajamangala University of Technology Isan Napaporn Phuangpornpitak King Mongkut's Institute of Technology Ladkrabang Pramoch Rangsunvigit Silpakorn University Kaan Kerdchuen Rajamangala University of Technology Thanyaburi Winadda Wongwiriyapan Rajamangala University of Technology Thanyaburi Chanchai Thongpin Rajamangala University of Technology Thanyaburi Boonrit Prasartkaew Rajamangala University of Technology Thanyaburi Wirachai Roynarin Silpakorn University Thammasak Rojviroon Rajamangala University of Technology Lanna Nathabhat Phankong Rajamangala University of Technology Thanyaburi Supakij Suttiruengwong Rajamangala University of Technology Thanyaburi uthen kamnarn Pimnapat Bhumkittipich Boonyang Plangklang

EMSES2016 355 Pramuk Unahalekhaka Rajamangala University of Technology Suvarnabhumi Rajamangala University of Technology Phra Nakhon Nattachote Rugthaicharoencheep Silpakorn University Nattakarn Hongsriphan King Mongkut's University of Technology Thonburi Surawut Chuangchote Rajamangala University of Technology Thanyaburi Chuntip Sakulkhaemaruethai Rajamangala University of Technology Thanyaburi Sirichai Torsakul Rajamangala University of Technology Thanyaburi Sommai Pivsa-Art Kyoto Institute of Technology Supaphorn Thumsorn King Mongkut s University of Technology North Bangkok Putinun Uawongsuwan Institute of Materials Research and Engineering Leong Yew Wei Rajamangala University of Technology Thanyaburi Chatchai Suppitaksakul PTT Global Chemical Public Company Limited Apisit Kositchaitong Rajamangala University of Technology Thanyaburi Weraporn Pivsa-Art Rajamangala University of Technology Thanyaburi Sumonman Niamlang Rajamangala University of Technology Thanyaburi Natee Srisawat King Mongkut s University of Technology North Bangkok Atitaya Tohsan Watthanaphon Rajamangala University of Technology Srivijaya heewawuttipong Rangsit University Supattana Nirukkanaporn Rajamangala University of Technology Thanyaburi Winai Chanpeng Rajamangala University of Technology Thanyaburi Supawat kamtip Rajamangala University of Technology Thanyaburi Nithiwatthn Choosakul Rajamangala University of Technology Rattanakosin Pimolpun Niamlang Rajamangala University of Technology Rattanakosin Teerin Kongpun Rajamangala University of Technology Thanyaburi Thirawat Mueansichai Kyoto University Taro Sonobe Naresuan University Noppawan Motong Kyoto University Hideaki Ohgaki Kyoto University Tetsuo Tezuka National University of Laos Khampone Nanthong Kyoto Institute of Technology Hitomi Ohara

356 13th Eco-Energy and Materials Science and Engineering Symposium, Udonthani,Thailand, 1-4 December 2016 Dussadee Buntam Prayoon Surin Wachirapond Permpoonsinsub Faculty of Engineering Faculty of Engineering Faculty of Engineering Pathumwan Institute of Technology (PIT) Pathumwan Institute of Technology (PIT) Pathumwan Institute of Technology (PIT) Bangkok Thailand Bangkok Thailand Bangkok Thailand Email: [email protected] Email: [email protected] Email: [email protected] Abstract Forming process is essential and necessary for environmental management standard, ISO 14000. Thus, the manufacturing system. Mixture experiments are useful in mineral talcum factories should develop a new process to industrial situation to find the parameters in design and change original mineral talcum in Fig.1 (a) to mineral talcum development process. Artificial Neural Network (ANN) is the pellet in Fig.1 (b). According to Fig.1, mineral talcum is mixed mathematical model to approximate and predict a nonlinear with a few water, it is broken and isolated. In case of more function. In this study, the objective is to simulate optimal water, it is flat shape. In following problems on shape of parameters mixture experiments by the ANN. The ANN mineral talcum, the optimal mixture experiment design using architecture is widely used that is feed-forward back propagation. ANN is applied to solve forming process of mineral talcum. There are two design methods namely, integration with mixture ANN models are designed to predict yield forming process for design and factorial design. In the integration with mixture design, reducing the defect. In this paper, the aim is to optimize the the input data, pellet talcum, are trained for ANN. The target data components of water and mineral talcum in forming process by are from factorial design. Training algorithms in the experiments, artificial neural network model. Gradient descent, Gradient descent with momentum and Levenberg Maquardt algorithms are applied to optimize II. BACKGROUND AND LITERATURE REVIEWS components. The performance of ANN model can be indicated by mean square error (MSE) and linear regression (R). As a result, A. Literature reviews ANN can predict yield of forming process of pellet talcum. Macleod et al. have applied ANNs and Taguchi method were Keywords artificial neural network; mixture design mineral used to predict hardest of cement. Taguchi methods offer talcum potential benefits in evaluating network behavior such as the ability to examine interaction of weights within neurals a I. INTRODUCTION network [1]. Adroer et al. presented neural network model for predicting the honing process variables (grain size of abrasive, Mineral talcum production is the one of important process density of abrasive, linear speed, tangential speed and pressure) in industry. Mineral talcum is a components in cosmetic, as a function of roughness parameters [2]. Yadollahi et al. have powder paper and lime. Uttaradit province is the original investigated the optimal mixture of RSC containing lead-slag resource to produce mineral Talcum in Thailand. There are aggregate used Taguchi method and ANN. They have also many mining industry and processing factory mineral talcum in predicted component of UV-protection concrete by important Uttardit province. For 30 year ago, the most industry is only factor which had three variables as slum, compressive strength primary processing factory which is blending and packaging to and gramma linear attenuation. The coefficient were considered other suppliers. as the quality responses [3]. Sukru Ozsahin have studied an ANN model which was developed for predicting the effects of (a) Original mieral talcum (b) Mieral talcum pellet some production factors such as adhesive ratio, press pressure, Fig. 1. Mineral Talcum Process time, wood density and moisture content on some physical properties of oriented strand board (OSB). The results showed The characteristic of mineral talcum is very small pieces of that the prediction model was a useful, reliable and quite powder so it spreads during package and transportation. Not effective tool for predicting some physical properties of the OSB only it affects health but also it is the cause of environmental produced under different manufacturing conditions [4]. problems including carcinogens of cancer. To reduce spreading mineral talcum, the production process should be based on the B. Atifitual Neural Network A biological neural network is a series of interconnected neural and a biological process in the human brain. The sample processing elements are connected by weighted. The forming are combined from a number of the simple processing elements. The simple processing elements compute the output by a non- 89

357 13th Eco-Energy and Materials Science and Engineering Symposium, Udonthani,Thailand, 1-4 December 2016 linear function of weight inputs [5]. According to Fig.2, the w n1 f y biological neuron are demonstrated. The signals transmitted 11 1 through the cell body (soma) which are from the dendrite to the axon as an electrical impulse. w y2 x 1 b1 21 y3 w yM N1 1 w n2 f w 12 22 x 2 wN2 1 b2 ww23 13 n3 f wN 3 xN 1 b3 w w 2M 1M Fig. 2. A biological neuron [6] fw nM NM 1) Activation Function 1 bM In artificial neural network models, each neuron amount to Fig. 3. Feedforward neural networks without hidden layer its inputs, and then feeds the sum into a function. The activation Fig. 3 has the input vector, x and a weight vector, w in input function determines the neuron output. Commonly, the layer. The net input vector, n, a bias vector b is contained. activation functions are also called as transfer functions. The The net input vector can be deduced as net output of any node are computed by the activation function Substituting equation (4) to an activation function, the before feeding to the next layer. There are 3 typical types of activation functions; purelin, logsig and tansig [6] as shown in output is calculated as equation (1), (2) and (3), respectively. y = f(wx + b) Purelin function can be defined as f (n) n (1) (4) Logsig function is shown as b) Training algolithim f (n) 1 (2) In a learning network, a procedure for modifying the 1 e( n) weights and biases of network can be referred to as training algorithm. There are three to adjust weight namely, gradient Tansig function is derived as descent algorithm (GDA), gradient descent with momentum algorithm (GDMA) and Levenberg-Marquardt algorithm f (n) 1 e( n) (3) (RLMA). 1 e( n) Gradient descent algorithm is based on the first-order where n is the net input. derivative of objective error function. Let E(w) be objective f is the activation function. error function. To find the minima in error space, gradient vector, g of E(w) can be defined as [7] 2) Architectures of Neural Networks a) Feedforward Neural Networks Feedforward neural networks compose of a series of layers. g E(w) (5) They are the most widely used architecture of neural networks. w In feedforward neural networks, the first layer has a connection from the network input to output unit which are strictly Applying the gradient descent to the weight vector, the feedforward. Consequently, each subsequent layer has a direction is opposite the gradient vector. GDA updates the new connection from the previous layer and then the final layer weight vector at iteration, k as equation (6) produces the network's output. A feedforward multilayered neural network can approximate a continuous function arbitrary wk 1 wk gk (6) well. Fig. 3 shows a single layer of neuron. It consists of one where k is the iterative number input and an output layer. is the learning rate gk is the gradient with respect to the weights. In the iteration, weight may oscillate. If the oscillation is large then weight must be updated. Since the new weight, wk 1 90

358 13th Eco-Energy and Materials Science and Engineering Symposium, Udonthani,Thailand, 1-4 December 2016 depends on the past weight, wk and the change ( wk ). To TABLE I. EXPERIMENT CASES OF MIXTURE DESIGN fulfill this requirement, wk is added into equation (6), it is called GDMA. wk 1 is defined as Trial Component (%) 1 Water Mineral talcum 2 3 25 75 4 wk 1 wk gk wk (7) 5 10 90 6 17.5 82.5 where wk is a weight change of the previous step 21.25 78.75 13.75 86.25 is the momentum parameter. 17.5 82.5 Levenberg Marquardt algorithm outperforms the gradient Table II shows trials, percentage of components which descent and conjugate gradient methods for medium size of compose of talcum and water and percentage of each replication (Rep.) in yield. The collection data of talcum pellet process are non-linear least squares problems [8]. LMA finds the minimum shown as 1-5 trials. In trial 6, it replicates in a center. of a function that is expressed as the sum of squares of non- linear real-valued function. LMA to update new weight vector can be obtained as follows wk 1 wk (J T J k I) 1 JTk ek (8) TABLE II. RESULT OF YIELD FROM MIXTURE DESIGN k where is the scalar factor Trial Component (%) Yield (%) Rep. 2 k is the number of iteration 1 talcum water Rep. 1 Rep. 3 2 60.31 J is the Jacobian matrix 3 75 25 63.19 71.85 64.80 e is the vector of network errors. 4 63.39 80.33 68.62 5 90 10 81.59 74.99 78.70 6 72.99 85.81 71.70 82.5 17.5 82.40 80.55 86.45 83.21 80.41 C. Mixtures Design 78.75 21.25 Mixtures design is a one of factorial experimental design. It 86.25 13.75 is different from other types of experiment design because the percentage of a component increase to 100%. The increasing 82.5 17.5 level of constituent can balance the proportion of the mixtures. Following experiment design, ANOVA models are widely used C. Design neural network model based on factorial design. The regression analysis is mainly used, linear, quadratic and cubic response surfaces that are In this paper, feedforward neural networks with assumed in dependence on the mixture components. In a backpropagation were designed to find the optimal components mixture experiment, the factors are different components of a of mineral talcum and water. Supervised learning algorithm was blend to optimize components for example the tensile strength applied that is GDA, GDAM and LM. TABLE III shows the of stainless steel and the interesting factors which might be iron, experiment cases of ANN model for 18 models which have copper, nickel and chromium in the alloy. Moreover, gasoline, involved topology, transfer function and training algorithm. soaps or detergents, beverages, cake mixes, soups and so on are optimized either [9]. TABLE III. EXPERIMENT CASES OF NEURAL NETWORK MODEL III. PROPOSED METHOD Model Topology Transfer Training Function Algorithm A. Mixture process 1 2-5-1 2 2-5-1 purelin traingd Mixture process is considered the factors that affect to 3 2-5-1 purelin traingdm talcum pellet. The components between water and mineral 4 2-5-1 purelin trainlm talcum are optimized for forming process to reduce the broken 5 2-5-1 logsig traingd 6 2-5-1 logsig traingdm and isolated. Let input be mixtures of water and mineral talcum 7 2-5-1 logsig trainlm and output be weight of talcum pellet. The yield under two 8 2-5-1 tansig traingd variables is defined as equation (9). 9 2-5-1 tansig traingdm 10 2-10-1 tansig trainlm Yield (%) Output(kg) 100 (9) 11 2-10-1 purelin traingd Input(kg) 12 2-10-1 purelin traingdm 13 2-10-1 purelin trainlm B. Experimental component 14 2-10-1 logsig traingd 15 2-10-1 logsig traingdm In this paper, Table I shows the cases of the components of 16 2-10-1 logsig trainlm mineral talcum. The components are from the talcum process in 17 2-10-1 tansig traingd the real factory in Uttardit province. 18 2-10-1 tansig traingdm tansig trainlm 91