ABC-ANFIS-CTF: A Method For Diagnosis And Prediction Of Coking Degree .

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processes Article ABC-ANFIS-CTF: A Method for Diagnosis and Prediction of Coking Degree of Ethylene Cracking Furnace Tube Zhiping Peng 1 , Junfeng Zhao 1,2, * , Zhaolin Yin 3 , Yu Gu 4 , Jinbo Qiu 5 and Delong Cui 5 1 2 3 4 5 * College of Computer, Guangdong University of Petrochemical Technology, Maoming 525000, China; pengzp@foxmail.com College of Computer, Guangdong University of Technology, Guangzhou 510006, China Sinopec Maoming Branch, Maoming 525000, China; yinzhaolin888@126.com College of Automation, Guangdong University of Petrochemical Technology, Maoming 525000, China; guyu@ustb.edu.cn College of Electronic Information Engineering, Guangdong University of Petrochemical Technology, Maoming 525000, China; jinboqiu1982@163.com (J.Q.); delongcui@163.com (D.C.) Correspondence: zhaojunfenglv@outlook.com; Tel.: 86-134-3756-4131 Received: 25 September 2019; Accepted: 26 November 2019; Published: 3 December 2019 Abstract: The carburizing and coking of ethylene cracking furnace tubes are the important factors that affect the energy efficiency of ethylene production. To realize the diagnosis and prediction of the different coking degrees of cracking furnace tubes, and then take corresponding treatment measures, is of great significance for improving ethylene production and prolonging the service life of the furnace tube. Therefore, a fusion diagnosis and prediction method based on artificial bee colony (ABC) and adaptive neural fuzzy inference system (ANFIS) is proposed, which also introduces a coking-time factor (CTF). The actual data verification shows that the method not only improves the training efficiency and diagnosis accuracy of the coking diagnosis and inference system of the cracking furnace tube, but also realizes the prediction of the development trend of the coking degree of the furnace tube. Keywords: ethylene cracking furnace tube; ABC; ANFIS; coking-time factor; coking diagnosis and prediction 1. Introduction The petrochemical industry is one of the important energy-based industries for the development of the national economy [1]. While ethylene is the foundation of the chemical industry, its production level usually represents the level of development of a country’s petrochemical industry [2]. It can be seen that the ethylene industry has an extremely important position in the petrochemical industry. In ethylene industry, the ethylene cracking furnace is the key equipment to produce ethylene. As the core component of the ethylene cracking furnace, the safe and stable operation of the cracking furnace tubes is the key factor to ensure the ethylene yield [3]. However, in the ethylene production process, carburizing and coking always inevitably occur in the cracking furnace tubes [4,5]. The presence of carburization and coking will greatly shorten the service life of the ethylene cracking furnace tubes, reduce the yield of ethylene, and affect the production efficiency and economic benefits of ethylene. For the cause of coking formation, a lot of research was carried out as early as the 1950s. In 1988, the three coking principles of catalytic coking, condensation coking, and free radical coking were proposed by Albright [6], which are currently widely recognized as the principle of coking [7,8]. At present, the purpose of reducing the coking rate and inhibiting coking is to improve the material Processes 2019, 7, 909; doi:10.3390/pr7120909 www.mdpi.com/journal/processes

Processes 2019, 7, 909 2 of 17 and structure of furnace tubes, the cracking material, and cracking process conditions [9]. In the ethylene production process, if the coke deposition on the inner wall of the cracking furnace tube reaches a certain level, it is necessary to use a mixture of steam and air for decoking to ensure the normal operation of the ethylene production [8]. However, the premise of decoking treatment is to accurately diagnose the coking degree of each cracking furnace tube in the current period. Therefore, the research on the diagnosis method of the coking degree of cracking furnace tubes has important practical significance. Considering the performed literature review, there are essentially four ways of diagnosing the coking degree of the ethylene cracking furnace tube: performing a coking mechanism model [10,11], using an artificial intelligent algorithm [12,13], diagnosing the failure of the cracking furnace using infrared thermal imaging technology [14,15], and using the empirical knowledge to diagnose the problem [16]. However, coking is an extremely complex physico–chemical reaction that occurs during pyrolysis, and some parameters of the mechanism model are difficult to obtain accurately in actual production, therefore, the accuracy of the mechanism model can not be assured. In the application of artificial intelligence algorithms, models generated by artificial neural networks (ANN) and support vector machines (SVM) have a “black box” syndrome [17–19], and the difficulty in dealing with qualitative information, which limited its applications in practice. In addition, the “black box” model has higher requirements on the sample. If the change of influencing factors exceeds a certain range in practical application, the reliability of the “black box” model will obviously decline. In the application of infrared thermal imaging technology, due to the high equipment cost of infrared thermal imaging technology, installation, operation, and maintenance are difficult, and it has not been widely used in actual production. Moreover, the actual production experience shows that the application of empirical knowledge to diagnose the coking of the furnace tube has great defects in real-time and reliability. In order to overcome the shortcomings of the above existing coking diagnosis methods in many aspects, it is necessary to build a coking diagnosis system with a clear physical meaning for each network layer, and the ability to generate interpretable diagnostic IF–THEN rules, which is very important for improving the accuracy and interpretability of the coking diagnosis of cracking furnace tubes. In view of the previous research and cognition, an adaptive neural fuzzy inference system (ANFIS) is a good solution to achieve the above goals. Moreover, by searching a large number of literatures related to coking of cracking furnace tubes, ANFIS has not been effectively applied in the diagnosis of coking of cracking furnace tubes in the ethylene industry, which will become a good experimental and application practice. ANFIS is a fuzzy inference system structure that combines fuzzy logic and neural network organically [20]. ANFIS can not only use the learning mechanism of neural networks to automatically extract the optimal membership relationship and fuzzy rules between input and output variables from the training data, but also the combination of fuzzy logic and neural network makes the structure and parameters of each layer of the neural network have a clear physical meaning [21]. Therefore, compared with traditional machine learning and neural network algorithms, ANFIS is widely employed for solving engineering problems because of its advantages of being easy to understand, with strong interpretability and low requirements on training samples [22]. A key issue in the application of the ANFIS system is the setting of system structure parameters. The quality of the multivariable system parameters will directly affect the overall performance of the system. For multivariable optimization, Karaboga [23] proposed a novel intelligent clustering optimization algorithm, artificial bee colony (ABC), in 2005. The ABC algorithm can quickly find the global optimal solution in honey sourcing (set of parameter solutions) through the cooperation among three different bee species, and can avoid the problem of the local optimal solution in the search process, to a large extent. Furthermore, compared with the traditional multi-parameter optimization methods, the ABC algorithm has faster convergence speed and better optimization performance [24]. Based on the above research, a fusion-diagnosis and prediction method for the coking degree of cracking furnace tubes based on the artificial bee colony algorithm and adaptive fuzzy neural network

Processes 2019, 7, x FOR PEER REVIEW 3 of 17 Processes 2019, 7, 909 3 of 17 Based on the above research, a fusion-diagnosis and prediction method for the coking degree of cracking furnace tubes based on the artificial bee colony algorithm and adaptive fuzzy neural is proposed in this paper, which alsowhich introduces a coking-time factor (CTF), named ABC-ANFIS-CTF. network is proposed in this paper, also introduces a coking-time factor (CTF), named ABCThis method This mainly has the following three contributions: ANFIS-CTF. method mainly has the following three contributions: based on ANFIS is proposed, and an adjacent (1) A coking diagnosis and inference system based function layer layer is added added after after the the output output layer layer of the system, system, which which can can make make the the system system processing function output of the quantified coking degree of the cracking furnace tube more accurately. accurately. (2) The ABC algorithm is used to optimize the structural parameters of the ANFIS-based coking diagnosis and inference system, which which effectively effectively improves the training efficiency of the system and and the accuracy of coking diagnosis. (3) A coking-time factor factor is introduced, to predict the development development trend trend of the coking degree which provides a reliable basis for early warning and during the operation operationperiod periodofofthe thefurnace furnacetube, tube, which provides a reliable basis for early warning and efficiency protection offurnace the furnace efficiency protection of the tube.tube. The remainder remainderofofthis thispaper paper is organized as follows: Section 2 provides the framework of the is organized as follows: Section 2 provides the framework of the coking coking diagnosis and inference system of the cracking furnace tube.3 Section 3 introduces the specific diagnosis and inference system of the cracking furnace tube. Section introduces the specific principles principles and implementation steps of ABC-ANFIS-CTF method in4detail. Section 4 presents a and implementation steps of ABC-ANFIS-CTF method in detail. Section presents a verification of the verification of the proposed based on real data and comparisons with other models. Finally, proposed model based on realmodel data and comparisons with other models. Finally, the conclusions of the the conclusions study5.are drawn in Section 5. study are drawnofinthe Section 2. Framework Framework 2. The framework framework of tube is The of the the coking cokingdiagnosis diagnosisand andinference inferencesystem systemfor forethylene ethylenecracking crackingfurnace furnace tube shown inin Figure 1.1.ItItcan the ethylene ethylene is shown Figure canbe beseen seenfrom fromthe thefigure figurethat thatthe thesystem systemis is mainly mainly composed composed of: of: the cracking furnace (furnace tube temperature data acquisition source), infrared thermometer (furnace cracking furnace (furnace tube temperature data acquisition source), infrared thermometer (furnace tube temperature collection equipment), database (pressure data acquisition source), model training tube temperature collection equipment), database (pressure data acquisition source), model training machine (using specific application of machine (using for for training training diagnosis diagnosisand andinference inferencesystem) system)five fiveparts, parts,and andthe the specific application this system is divided into training process and diagnosis and prediction process. of this system is divided into training process and diagnosis and prediction process. Training flow LoRa Ethylene cracking furnace Diagnosis and prediction flow Infrared thermometer Model training machine Trained system Coking trend Coking time factor Database The framework framework of of the the coking coking diagnosis diagnosis and inference system. Figure 1. The 2.1. Training Process 2.1. Training Process 2.1.1. Data Collection 2.1.1. Data Collection The data used for the coking diagnosis and inference system are actually collected in the The data used for the coking diagnosis and inference system are actually collected in the petrochemical ethylene plant of a large state-owned petrochemical enterprise in China. The collected petrochemical ethylene plant of a large state-owned petrochemical enterprise in China. The collected data includes the tube metal temperature (TMT), cross-section pressure, venturi pressure, coil outlet data includes the tube metal temperature (TMT), cross-section pressure, venturi pressure, coil outlet temperature (COT), and coking degree of each cracking furnace tube. The temperature of the cracking temperature (COT), and coking degree of each cracking furnace tube. The temperature of the cracking furnace tube is collected by the infrared thermometer running on the side of the ethylene cracking furnace tube is collected by the infrared thermometer running on the side of the ethylene cracking furnace, and the collected data is transmitted to the model training machine through the long range radio furnace, and the collected data is transmitted to the model training machine through the long range (LoRa) wireless communication mode. The real application scene is shown in Figure 2. The infrared radio (LoRa) wireless communication mode. The real application scene is shown in Figure 2. The thermometer is integrated with industrial infrared temperature measuring sensor MI31002M (Raytek, infrared thermometer is integrated with industrial infrared temperature measuring sensor MI31002M USA) and laser ranging probe LR-TB5000 (KEYENCE, Japan), with a temperature measuring range

Processes 2019, 7, xx FOR Processes 2019, 2019, 7, 7, 909 FOR PEER PEER REVIEW REVIEW Processes 444of of 17 17 of 17 (Raytek, (Raytek, USA) USA) and and laser laser ranging ranging probe probe LR-TB5000 LR-TB5000 (KEYENCE, (KEYENCE, Japan), Japan), with with aa temperature temperature measuring measuring C, and C, range of 250–1400 and a temperature measuring accuracy 0.5%. The cross-section of 250–1400 a temperature measuring accuracy 0.5%. The cross-section pressure, venturi range of 250–1400 C, and a temperature measuring accuracy 0.5%. The cross-section pressure, pressure, venturi pressure, and coil outlet temperature are collected by the model training machine in real pressure, and coil outlet temperature are collected by the model training machine in real time by venturi pressure, and coil outlet temperature are collected by the model training machine in real time time by the of the ethylene and the of reading the database of the ethylene plant,plant, and the coking degree degree of the cracking furnace by reading reading the database database ofpetrochemical the petrochemical petrochemical ethylene plant, and the coking coking degree of the the cracking cracking furnace tube is obtained by manual marking by cracking technicians. tube is obtained by manual marking by cracking technicians. furnace tube is obtained by manual marking by cracking technicians. Figure 2. Figure 2. 2. The Figure The real real application application scene. scene. 2.1.2. 2.1.2. Data Data Processing Processing Extraction Extraction of the tube metal temperature. Extraction of of the the tube tube metal metal temperature. temperature. The The original original temperature temperature data data collected collected by by the the infrared infrared thermometer thermometer includes includes the the tube tube metal metal the furnace tube and the wall temperature of the cracking furnace. temperature of wall temperature of the cracking furnace. The temperature of the furnace tube and the wall temperature of the cracking furnace. The difference difference between between these these two two temperatures temperatures is is usually usually small small and and the the boundary boundary is is not not obvious. obvious. Thus, Thus, it it is is difficult difficult extract the tube metal temperature by setting the threshold value. an to However, there is to extract the tube metal temperature by setting the threshold value. However, there is an obvious obvious difference difference between between the the tube tube distance distance data data and and the the wall wall distance distance data data collected collected by by the the laser laser ranging ranging probe, as shown in Figure 3, where the abscissa indicates the number of collected data, and the ordinate probe, as shown in Figure 3, where the abscissa indicates the number of collected data, and probe, as shown in Figure 3, where the abscissa indicates the number of collected data, and the the indicates the distance temperature value, and value, the infrared thermometer measures themeasures temperature ordinate the or and infrared the ordinate indicates indicates theordistance distance or temperature temperature value, and the the infrared thermometer thermometer measures the and distance and datadistance synchronously. temperature data temperature and distance data synchronously. synchronously. Distance(mm) Temperature( Wall ) Tube NO. Figure 3. 3. The original original temperature and and distance data data collected by by the infrared infrared thermometer. Figure Figure 3. The The original temperature temperature and distance distance data collected collected by the the infrared thermometer. thermometer. Therefore, the specific extraction method of the tube metal temperature is described as follows: Therefore, Therefore, the the specific specific extraction extraction method method of of the the tube tube metal metal temperature temperature is is described described as as follows: follows: Assuming that T , a , · · · , a is the temperature data set of the original collection, {a } o n is the temperature data set of the original collection, where 2 1 Assuming that Assuming that TToo { aa11,,aa22,, ,, aann} is the temperature data set of the original collection, where where an is the nth temperature value, Do {b1 , b2 , · · · , bn } is the distance data set of the original collection, the nth temperature value, is the distance data set of the original collection, aan is D bb1 ,,bb2 ,, ,,bbn } is the distance data set of the original collection, Doo b{ div n is the where bn isnth thetemperature nth distancevalue, value, and threshold of the furnace tube distance and 1 is2the boundary n where the nth distance value, and is the boundary threshold bbn is bbd ivstarting where is the nth distance value, and is the boundary threshold of the furnace tube distance the furnace wall distance data. Therefore, the and ending positionof ofthe thefurnace distancetube datadistance of each n div and the furnace wall distance data. Therefore, the starting and ending position of the distance furnace in the original distance data can bethe obtained byand Equation and the tube furnace wall distance data. Therefore, starting ending(1). position of the distance data data of each furnace tube in the original distance data can be obtained by Equation (1). of each furnace tube in the original distance data can be obtained by Equation (1). ( Pstart {i1 , i2 , · · · , ik , · · · , im } , bik 1 bdiv bik 1 {i ,i , ,i , ,i } , k 1, 2, · · · , m (1) P bbik b 1 11 Pstart bbdiv Pend , j 2i11, ,i · 2·2 ·, , jk,i,kk·,· · ,,imjmm , ,b b,bjiikkk 1 bdivdiv startj1 ik 1jk 1 ,k (1) ,k 11,,22,, ,m ,m (1) P j , j , , j , , j ,b b b { Pend , jkk , , jmm} ,bjjkk 11 bdiv end j11 , j22 , div bjjkk 11

Processes 2019, 7, 909 5 of 17 where m represents the number of furnace tubes in the collected data, and ik , jk are in [1,n]. According to Equation (1), the starting and ending position (ik , jk ) of the data of the kth furnace tube in the original distance data can be obtained, and then mapping them to the original temperature data, so that the data set of tube metal temperature of the kth furnace tube can be extracted. If the data n o set of tube metal temperature of the kth cracking furnace tube extracted is Tk 0 0 0 a1 , a2 , · · · , an , where a0n is the nth tube metal temperature value, the final value of the tube metal temperature of the kth cracking furnace tube can be calculated according to Equation (2). TMT sum a01 , a02 , · · · , a0n length(Tk ) (2) Calculation of absolute pressure ratio. In the process of ethylene cracking production, cracking technicians usually take the absolute pressure ratio as an indicator to judge whether the cracking furnace tube is running normally or not, which is defined as follow: Pw Pa KAPR (3) Ph Pa where KAPR , Ph , Pw and Pa represent the absolute pressure ratio, cross-section pressure, venturi pressure, and standard atmospheric pressure, respectively. 2.1.3. Training of the Coking Diagnosis and Inference System Firstly, the network structure of the coking diagnosis and inference system based on ANFIS is constructed according to the composition characteristics of the training data, and then the obtained sample data of TMT, absolute pressure ratio, COT, and the marked coking degree are input into the coking diagnosis and inference system for training. In the training process, the ABC algorithm is used to search the optimal solution of the structural parameters of the system. If the yield of the search solution is no longer increased or the search cycle is larger than the preset range, the search process is terminated and the optimal parameter solution is obtained [25]. 2.2. Diagnosis and Prediction Processes 2.2.1. Coking Diagnosis After the training of the coking diagnosis and inference system is completed, the coking degree of the cracking furnace tube can be diagnosed in real time by inputting the tube metal temperature, absolute pressure ratio, and coil outlet temperature into the system. 2.2.2. Prediction of the Development Trend of Coking Degree Similarly, by using the trained coking diagnosis and inference system and combining with the coking-time factor proposed in this paper, the development trend of the coking degree of the cracking furnace tube in the future period can be predicted, which plays the function of early warning and efficiency protection of the furnace tube. 3. ABC-ANFIS-CTF The realization of the coking diagnosis and prediction method named ABC-ANFIS-CTF is mainly divided into three stages: the first is the construction of the coking diagnosis and inference system based on ANFIS, the second is the optimization of the system structure parameters based on ABC algorithm, and the third is the prediction of the development trend of the coking degree based on the coking-time factor.

Processes 2019, 7, x FOR PEER REVIEW Processes 2019, 7, 909 6 of 17 6 of 17 ABC algorithm, and the third is the prediction of the development trend of the coking degree based on the coking-time factor. 3.1. Construction of the ANFIS-Based System 3.1. Construction of the ANFIS-Based System ANFIS mainly mainly consists consists of of Mamdani Mamdani type type and and T-S T-S (Takagi-Sugeno) (Takagi-Sugeno) type type [26]. The difference difference ANFIS [26]. The between the two types is that the output of Mamdani type is fuzzy value, and the output of T-S between the two types is that the output of Mamdani type is fuzzy value, and the output of T-Stype typeis a linear combination of of input variables. In this paper, by analyzing the correlation between the TMT, is a linear combination input variables. In this paper, by analyzing the correlation between the absolute pressure ratio, COT, and coking degree of the furnace tube, a T-S type ANFIS coking diagnosis TMT, absolute pressure ratio, COT, and coking degree of the furnace tube, a T-S type ANFIS coking and inference system with multiple andinput singleand output is output adopted. Its systemItsstructure is shown diagnosis and inference system with input multiple single is adopted. system structure inshown Figurein 4. Figure 4. is 11 x1 x1 pn1 v1 α1 α1 m1 1 Input layer xn p11 Z1 y v2 y vh 1 n1 xn αm αm Zm p1m nm vh pnm n x1 xn Input layer Input layer Membership Rule layer Normalized Calculate layer Adjacent layer function layer layer Output layer Coking degree Figure 4. The structure of the ANFIS-based coking diagnosis and inference system. Figure 4. The structure of the ANFIS-based coking diagnosis and inference system. It can be seen from Figure 4 that the ANFIS-based coking diagnosis and inference system structure It can be seen from Figure 4 that the ANFIS-based coking diagnosis and inference system is divided into six layers, and the specific meaning of each layer is described as follows: structure is divided into six layers, and the specific meaning of each layer is described as follows: Input layer. The total number of nodes in this layer is N1 n, and each node is directly connected Input layer. The total number of nodes in this layer is N n , and each node is directly connected to the input variable X {x1 , x2 , · · · , xn }. The input variables1of this system are TMT, absolute pressure to theand input variable X x1, x2 , , xn . The input variables of this system are TMT, absolute ratio COT. pressure ratio andEach COT.node in this layer represents a fuzzy set, and the number of fuzzy values in the Fuzzy layer. Fuzzy layer. Each in this layer segmentation represents a fuzzy set,variables. and the number of fuzzy values fuzzy set represents thenode number of fuzzy of input The function of this layerinis the fuzzy setthe represents the number fuzzy segmentation of input variables. The function of this to calculate membership degree ofofeach input variable relative to each fuzzy value in the fuzzy set j layer is to calculate themembership membershipfunction degree ofµ each input variable gbellmf, relative to eachand fuzzy value in etc., the according to different , such as gaussmf, trimf, trapezium, i whichset is obtained byto Equation (4).membership function j , such as gaussmf, gbellmf, trimf, and fuzzy according different i trapezium, etc., which is obtained j by Equation (4). µi µ j (xi ), i 1, 2, · · · , n, j 1, 2, · · · , mi (4) (4) where n is the dimension of the input variable, and mi is the fuzzy segmentation number of the where n is the dimension of the input variable, and mi is the fuzzy segmentation number of the input variable. ij j xi , i 1, 2, , n, j 1, 2, , mi inputThe variable. total number of nodes in this layer is: The total number of nodes in this layer is: n X n NN2 mi 2 mi (5) (5) 1 1 ii Rule node in inthis thislayer layerrepresents representsa afuzzy fuzzy rule, and applicability of each fuzzy Rule layer. layer. Each node rule, and thethe applicability of each fuzzy rule rule is product the product of membership degree input by each node. The total number nodes this layeris is the of membership degree input by each node. The total number of of nodes inin this layer mThe is . The output this layer shown below: N3N 3 m. output of of this layer is is shown as as below: n n nn Y Y (j x x)i, k, k 1, 1, 2, , m, m mi αk k µ 2, · · · , m, m mi j i i 0 i 1 i 0 (6)(6) i 1 Normalized layer. The function of this layer is to normalize the output fuzzy rules of the last layer. The output of this layer is:

Processes 2019, 7, 909 7 of 17 Normalized layer. The function of this layer is to normalize the output fuzzy rules of the last layer. The output of this layer is: m X αk αk / αt (7) t 1 Computing layer. This layer is used to realize the joint calculation of neural network and fuzzy rules. pik is the weight corresponding to input variables in neural network. The total number of nodes in this layer is the same as that in the previous layer, and the output is: Zk n X pik αk (8) i 1 Output layer. This layer is the system output layer of ANFIS, which is used to output the coking diagnosis results corresponding to the input variables. The output formula is as follows: y(X ) m X Zk (9) k 1 In the actual production, the coking degree of the furnace tube is usually quantified into several grades, so this coking diagnosis system is added an adjacent processing function layer ϕ y after the output layer, in order to make the output result more accurately represent the coking degree of the furnace tube, and its expression is: vl , ϕy vl 1 , y vl 0.5 y vl 0.5 (10) where vl represents different quantization grades of the coking degree of the furnace tube. 3.2. Optimization of System Structure Parameters The ABC algorithm is an optimization method to simulate honey collecting behavior of bees in nature. In the ABC algorithm, bee species are divided into three types: employed bees, onlookers, and scouts [27]. The space for bees to collect nectar is called honey source or food source, which means the set of possible solutions to the parameters that need to be adjusted. The amount of nectar at each honey source represents the fitness or yield of different solutions. In the initial state, the number of employed bees and onlookers accounts for half of the total number of bees, and honey source Xs {x1 , x2 , · · · , xr } generates SN initial solutions randomly from Equation (11). xr xr,d Ld rand(0, 1)(Ud Ld ), r 1, 2, · · · , SN (11) where xr is the rth honey source, xr,d is the position of the honey source, d Dim, Dim is the dimension of the honey source, Ud and Ld are the upper and lower bounds of the space searched by the bee colony for honey, respectively. The fitness or yield of each honey source is calculated by the following formula: 1 f (xr ) 1 , f it(xr ) 1 abs( f (xr )), f (xr ) 0 f (xr ) 0 (12) where f (xr ) represents t

of the furnace tube. Keywords: ethylene cracking furnace tube; ABC; ANFIS; coking-time factor; coking diagnosis and prediction 1. Introduction The petrochemical industry is one of the important energy-based industries for the development of the national economy [1]. While ethylene is the foundation of the chemical industry, its production

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