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Nonlinear comminution process modeling based on GA–FNN in the computational comminution system
Journal of Materials Processing Technology 120 (2002) 84±89
Nonlinear comminution process modeling based on GA±FNN in the computational comminution system Li Shuipinga,*, Bin Hongzana, Huang Zhichub, Wang Jianzhongb a
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China b Wuhan University of Technology, Wuhan 430070, PR China Received 12 June 2000
Abstract A new concept named computational comminution is ®rstly proposed in this paper. Based on information technology, the structure of a computational comminution system (CCS) is built. The study on CCS is very different from the traditional ones for comminution, such as the study based on theoretic models, or the study based on experimental models. As one of the key technologies in CCS, a modeling framework for comminution processes is implemented particularly by employing GA±FNN that can model complex nonlinear processes such as the comminution process of cement by integrating arti®cial neural networks, fuzzy sets and genetic algorithms. Application results of this modeling method to the Horomill cement comminution process show that the modeling framework discussed in this paper is ef®cient. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Computational comminution; Comminution process modeling; Fuzzy neural network; Genetic algorithm
1. Introduction In many industrial ®elds, e.g. metallurgy, mining, material, medicine, and so on, comminution is an important and necessary process in which raw materials are ground into ®ne products. A general comminution system is shown in Fig. 1, where the comminution equipment and the corresponding comminution process play a key role. Comminution equipments that include a ball mill, a roller presser, a vertical mill or a Horomill are widely used in the world. In the 21st century, energy saving, environment protection and sustainable development will be paid more attention to, as the above-mentioned equipment and comminution technologies do not meet these requirements of development of the present times. Thus, deeply studying comminution equipment and the comminution process is very signi®cant. In CCS, a virtual environment is provided to simulate the comminution processes and the running process of comminution equipment by employing virtual reality technology, virtual manufacturing technology, and other information *
Corresponding author. Present address: Mechanical and Manufacturing Engineering Group, University of Technology Sydney, P.O. Box 123, Broadway, NSW 2007, Australia. E-mail addresses: [email protected], [email protected] (L. Shuiping).
technologies. Therefore, a kind of new method for the investigation of some complex processes such as comminution can be presented. Comminution process modeling is one of the key technologies of CCS, so that a modeling method is developed especially in this paper. 2. Computational comminution system 2.1. The concept of computational comminution Computational comminution is proposed as a new concept that is more dependent upon modern information technology than traditional comminution theories and technologies. Some characteristics of computational comminution are as follows: 1. Computational comminution is an integrated multiple hierarchies numerical theory system; 2. Computational comminution is a new kind of technology set for the study of the comminution process and comminution equipment; 3. Computational comminution can create a new space in which comminution process and the running of comminution equipment can be simulated; 4. The inherent characteristics of computational comminution also make it meet the requirements of sustainable
0924-0136/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 1 ) 0 1 1 7 0 - 0
L. Shuiping et al. / Journal of Materials Processing Technology 120 (2002) 84±89
85
Fig. 1. A general comminution system.
development and deal with the three problems of the world, i.e. population, resources and the environment. On the basis of the above characteristics, computational comminution may be de®ned as follow: computational comminution is an open architecture theoretical frame and technology system that meets the requirements of sustainable development and is an integrated system of the traditional comminution theories and technologies with modern information technologies. At present, computational dynamics, computational geometry and so on are becoming increasingly more development. Recently, Japanese researchers advanced the computational cutting theory [1]. American researchers are studying the computational manufacturing [2]. All of those are very helpful for the study of computational comminution. 2.2. The hierarchy of computational comminution The hierarchy of computational comminution system (CCS) includes four levels, the core level, the physical level, the abstract level and the application level, as shown in Fig. 2: 1. The core level includes some key theories and technologies, such as the mechanism of the comminution process, basic principles, theories, technologies and methods about the design and manufacturing of comminution equipment, and so on; 2. The physical level mainly includes some kinds of physical equipment and tools such as comminution
experimental instruments, all kinds of comminution equipment, and so on; 3. The abstract level is mainly made up of the so-called information infrastructures that are formed by virtue of computer technologies such as virtual reality and virtual manufacturing, e.g. a numerical model of comminution processes, and numerical comminution equipment; 4. The application level implements more efficient study of developments and applications for comminution. The above four levels are expanded stage by stage, the exterior higher levels being based on the interior lower levels. 2.3. The structure of a computational comminution system It is important to construct the system structure of computational comminution. The aim is to organize all kinds of subdivisions in the research and development of comminution to achieve the integration of information, functions and activities for the whole process of comminution. The general system structure of computational comminution is shown in Fig. 3. The structure possesses an open architecture feature, as new modules can be added easily. Each module can be improved, or self-corrected. 3. Nonlinear comminution process modeling based on GA±FNN The comminution process is too complicated to be described by an accurate mathematical model [3±6].
Fig. 2. The hierarchy of computational comminution.
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L. Shuiping et al. / Journal of Materials Processing Technology 120 (2002) 84±89
Fig. 3. The structure of a CCS.
Therefore, when designing comminution equipment, the selection of some parameters, such as rotating speed, pressure and so on, it is hard to ®nd suitable theoretical rules. In fact, these parameters have to be determined within a certain range. By all appearance, this kind of selection depends on the designer's experience. Large amounts of data generated by all kinds of comminution equipment with different design parameters in production re¯ect the inner relationship between the equipment's design parameters and the comminution results. If those data generated by the same kind of equipment when grinding the same kind of materials are collected, the inner relationship can be obtained by modeling methods based on AI. The inner relationship will be the design fundamentals and the direction of this kind of equipment in reverse. Arti®cial neural networks have powerful nonlinear modeling capability, which correlates the inputs and the outputs by learning, and can re¯ect and forecast the relationship between the inputs and outputs of the comminution system to be investigated. To implement comminution process modeling, a new modeling method named GA±FNN that combined fuzzy sets, ANN and genetic algorithms is proposed [7±10]. 3.1. Structure of GA±FNN The structure of GA±FNN is shown in Fig. 4, and includes four main parts: fuzzi®cation of inputs, fuzzy neural net-
works (FNN), defuzzi®cation of outputs, and learning algorithms of FNN (GA). After the training of FNN is ®nished, it can be used to forecast the unknown results. 3.2. Fuzzification of inputs Because errors of experimental data from the comminution process are sometimes dif®cult to eliminate by all possible measures, ®rst fuzzifying these data is very helpful. Dividing every system input into seven different fuzzy linguistics as seven sub-inputs, the error's in¯uence can be decreased; therefore, the system has the functions of error-tolerating and ®ltering to some extent. In order to fuzzify inputs, de®ning the membership function of every input is important. There are many different membership functions: in GA±FNN, triangle and Gauss membership functions are used. 3.3. Defuzzification of outputs In GA±FNN, output variables are also fuzzi®ed, each output of FNN being a value of the membership function of each fuzzy linguistic variable of outputs. The real outputs of the system can be obtained by using defuzzifying algorithms such as the max-procedure or the center-of-gravity procedure. Here, the center-of-gravity method is used provided that the seven fuzzy linguistic variables of output yi are very
L. Shuiping et al. / Journal of Materials Processing Technology 120 (2002) 84±89
87
Fig. 4. Structure of GA±FNN diagram.
small (VS), small (S), medium small (MS), medium (M), medium big (MB), big (B), very big (VB), the values of the membership function of the corresponding fuzzy linguistic variable, m yik , is shown in Fig. 5, the center-of-gravity yim being de®ned as P6 P6 yik m yik k0 yik m yik Pk0 (1) yim P6 6 k0 m yik k0 1 m yik The artificial neural net may easily denote this expression. 3.4. Structure of FNN The structure of FNN, shown in Fig. 6, includes three parts. The input part includes layers L1 and L2. After every input variable is fuzzi®ed, corresponding seven membership degrees become real net inputs. Layer L3 is as the middle part. The number of nodes and their connection method of the middle part re¯ect the fuzzy
Fig. 5. values of the membership function of linguistic variables of output.
relationship of the real process in fact. If the fuzzy relationship of the process is known, the number of nodes and their connection method of the middle part can be determined according to the fuzzy relationship. If the fuzzy relationship is not known, a complex structure of FNN that takes into account all possible fuzzy relationships can ®rstly be
Fig. 6. FNN structure for modeling.
88
L. Shuiping et al. / Journal of Materials Processing Technology 120 (2002) 84±89
Fig. 7. GA flowchart for FNN training.
constructed, and then can be simpli®ed in FNN training in the future. Output function of L3 is a sigmoid function, namely if the input of a certain node i is Ii: X wji zj yi (2) Ii j
then the output of this node is Oi: Oi
1 1e
bIi
;
b>0
(3)
where j is a certain node of L2, wji the weights between L2 and L3, zj the output of node j, and yi the threshold of node i of L3. This threshold function can also provide a judgement standard for simplifying the network. The output part consists of layers L4 and L5, and the defuzzi®cation operation can be ®nished simultaneously. Every weight and threshold can be de®ned according to the above discussion. 3.5. Training of FNN±genetic algorithms Because the genetic algorithm is an ef®cient parallel one without local convergence, it is very suitable for the training of FNN used for modeling the comminution processes with complex calculations. GA ¯owchart for FNN training is shown in Fig. 7. The key to applying genetic algorithms is how to choose coding, decoding and genetic operators. Here, since the range of FNN weights is not ambiguous and there are more coding variables, a binary system coding is unsuitable. The improved coding is described as follows.
If variable ai 2 ai min ; ai max , when coding ai, to ®nd a real number di the length of which is certain, and di 2 0; 1, then the relationship between ai and di becomes ai ai min ai max
ai min di
(4)
The above equation will also be the same as the corresponding decoding function. This method is real number coding, which can shorten string length. Because the code does not belong to the binary system, the mutation operator is not inversing, but generating random numbers of which the grade lies in the 0; 1 interval. 4. Case study: modeling the comminution process of the Horomill Horomill is a kind of new piece of comminution equipment with high ef®ciency and low energy consumption [11], the sketch diagram being shown in Fig. 8. In Horomill design, four key parameters, the diameter of cylinder D, the ratio of the diameter of the cylinder to the diameter of roller D/d, the ratio of the pressure to the ef®cient length of the roller and the rotating speed of cylinder n (or circumferential velocity v). Here, the relationship of the values of these four parameters and energy consumption per unit product is considered. In reality, it is dif®cult to de®ne the four parameters. By virtue of the above modeling method, using the experimental data obtained, the relationship of these parameters and E can be found when a certain kind of material is ground. Here, inputs of FNN are D, D/d, P/l, v, and the output is E; they are all divided into seven fuzzy linguistic variables, and fuzzi®ed according to the triangle membership function.
L. Shuiping et al. / Journal of Materials Processing Technology 120 (2002) 84±89
89
Fig. 8. Sketch map of Horomill. Fig. 9. The training of GA±FNN.
Fig. 10. Real outputs and GA±FNN forecast outputs.
After the structure of FNN has been built, GA is used to train the networks. The training process is shown in Fig. 9. When the training is ®nished, the network is checked. The output errors of training samples and checking samples are shown in Fig. 10. The maximum output error does not exceed 5% of the desired output. The above network structure includes all possible links of the nodes. On the basis of the analysis of ®nal weights and thresholds when training is ®nished, the FNN structure can be simpli®ed. In layers L2, L3 and L4, if some path is in an inactive state in most cases, the corresponding node of the middle layer and all links with it can be deleted. 5. Conclusions Computational comminution based on information models is a new concept that has been proposed for the more ef®cient treatment of comminution problems. According to the requirements of CCS, the emphasis of this paper was to investigate modeling the comminution process. The goal is accomplished by developing a modeling approach of GA±FNN that can ef®ciently treat the problems of modeling the complex nonlinear comminution processes by integrating ANN, fuzzy sets and GA. The results obtained by employing this modeling method are very helpful to de®ne the reasonable values of many important design parameters of comminution equipment that are dif®cult to be chosen because of the lack of suf®cient evidence. On the other hand, this modeling approach also enables CCS, which is dependent on information technology, to be founded on the available basis, to provide a powerful tool. This tool can
obtain the necessary information for modeling the comminution processes by analyzing, comparing and classifying the data of comminution, collected from numerous comminution workshops all over the world by internet. The application of this GA±FNN modeling frame to the cement comminution process of Horomill has testi®ed in that it is very ef®cient. References [1] R. Dazi, Computational mechanics of cuttingÐthe theory of virtual machining, Res. Mech. 49 (6) (1997) 59±63 (in Japanese). [2] Y.-S. Lee, Manufacturing-driven geometric analysis and prototyping: an investigation of computational manufacturing, Project Supported by NSF CAREER Award Grant DMI-9702374, 1999, p. 3. [3] G. Unland, G. Wang, Model of high-pressure roller mills, ZKG Int. 51 (7) (1998) 347±353. [4] H. Rosemann, H.-G. Ellerbrock, Grinding technology for cement production, ZKG Int. 51 (2) (1998) 51±62. [5] F. Feige, Theoretical considerations and experimental results relating to the comminution of particulate materials in the gap between grinding rolls, ZKG Int. 40 (10) (1987) 515±521. [6] I.B. Klymowsky, J. Liu, Progress in the modeling of comminution in a roller press, ZKG Int. 50 (9) (1997) 500±510. [7] R. Masuoka, Neurofuzzy system using a structured neural networks, in: Proceedings of the International Conference on fuzzy Logic and Neural Networks, Iizuka, Japan, 1990, pp. 173±177. [8] Coley, A. David, An Introduction to Genetic Algorithms for Scientists and Engineers, World Scientific, Singapore, 1999. [9] M. Gen, R. Cheng, Genetic Algorithms and Engineering Design, Wiley, New York, 1997. [10] A.M.S. Zalzala, Genetic Algorithms in Engineering Systems, Institute of Electrical Engineers, London, 1997. [11] S. Buzzi, The HoromillÐa new mill for fine comminution, ZKG Int. 50 (3) (1997) 127±138.
Nonlinear comminution process modeling based on GA±FNN in the computational comminution system Li Shuipinga,*, Bin Hongzana, Huang Zhichub, Wang Jianzhongb a
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China b Wuhan University of Technology, Wuhan 430070, PR China Received 12 June 2000
Abstract A new concept named computational comminution is ®rstly proposed in this paper. Based on information technology, the structure of a computational comminution system (CCS) is built. The study on CCS is very different from the traditional ones for comminution, such as the study based on theoretic models, or the study based on experimental models. As one of the key technologies in CCS, a modeling framework for comminution processes is implemented particularly by employing GA±FNN that can model complex nonlinear processes such as the comminution process of cement by integrating arti®cial neural networks, fuzzy sets and genetic algorithms. Application results of this modeling method to the Horomill cement comminution process show that the modeling framework discussed in this paper is ef®cient. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Computational comminution; Comminution process modeling; Fuzzy neural network; Genetic algorithm
1. Introduction In many industrial ®elds, e.g. metallurgy, mining, material, medicine, and so on, comminution is an important and necessary process in which raw materials are ground into ®ne products. A general comminution system is shown in Fig. 1, where the comminution equipment and the corresponding comminution process play a key role. Comminution equipments that include a ball mill, a roller presser, a vertical mill or a Horomill are widely used in the world. In the 21st century, energy saving, environment protection and sustainable development will be paid more attention to, as the above-mentioned equipment and comminution technologies do not meet these requirements of development of the present times. Thus, deeply studying comminution equipment and the comminution process is very signi®cant. In CCS, a virtual environment is provided to simulate the comminution processes and the running process of comminution equipment by employing virtual reality technology, virtual manufacturing technology, and other information *
Corresponding author. Present address: Mechanical and Manufacturing Engineering Group, University of Technology Sydney, P.O. Box 123, Broadway, NSW 2007, Australia. E-mail addresses: [email protected], [email protected] (L. Shuiping).
technologies. Therefore, a kind of new method for the investigation of some complex processes such as comminution can be presented. Comminution process modeling is one of the key technologies of CCS, so that a modeling method is developed especially in this paper. 2. Computational comminution system 2.1. The concept of computational comminution Computational comminution is proposed as a new concept that is more dependent upon modern information technology than traditional comminution theories and technologies. Some characteristics of computational comminution are as follows: 1. Computational comminution is an integrated multiple hierarchies numerical theory system; 2. Computational comminution is a new kind of technology set for the study of the comminution process and comminution equipment; 3. Computational comminution can create a new space in which comminution process and the running of comminution equipment can be simulated; 4. The inherent characteristics of computational comminution also make it meet the requirements of sustainable
0924-0136/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 1 ) 0 1 1 7 0 - 0
L. Shuiping et al. / Journal of Materials Processing Technology 120 (2002) 84±89
85
Fig. 1. A general comminution system.
development and deal with the three problems of the world, i.e. population, resources and the environment. On the basis of the above characteristics, computational comminution may be de®ned as follow: computational comminution is an open architecture theoretical frame and technology system that meets the requirements of sustainable development and is an integrated system of the traditional comminution theories and technologies with modern information technologies. At present, computational dynamics, computational geometry and so on are becoming increasingly more development. Recently, Japanese researchers advanced the computational cutting theory [1]. American researchers are studying the computational manufacturing [2]. All of those are very helpful for the study of computational comminution. 2.2. The hierarchy of computational comminution The hierarchy of computational comminution system (CCS) includes four levels, the core level, the physical level, the abstract level and the application level, as shown in Fig. 2: 1. The core level includes some key theories and technologies, such as the mechanism of the comminution process, basic principles, theories, technologies and methods about the design and manufacturing of comminution equipment, and so on; 2. The physical level mainly includes some kinds of physical equipment and tools such as comminution
experimental instruments, all kinds of comminution equipment, and so on; 3. The abstract level is mainly made up of the so-called information infrastructures that are formed by virtue of computer technologies such as virtual reality and virtual manufacturing, e.g. a numerical model of comminution processes, and numerical comminution equipment; 4. The application level implements more efficient study of developments and applications for comminution. The above four levels are expanded stage by stage, the exterior higher levels being based on the interior lower levels. 2.3. The structure of a computational comminution system It is important to construct the system structure of computational comminution. The aim is to organize all kinds of subdivisions in the research and development of comminution to achieve the integration of information, functions and activities for the whole process of comminution. The general system structure of computational comminution is shown in Fig. 3. The structure possesses an open architecture feature, as new modules can be added easily. Each module can be improved, or self-corrected. 3. Nonlinear comminution process modeling based on GA±FNN The comminution process is too complicated to be described by an accurate mathematical model [3±6].
Fig. 2. The hierarchy of computational comminution.
86
L. Shuiping et al. / Journal of Materials Processing Technology 120 (2002) 84±89
Fig. 3. The structure of a CCS.
Therefore, when designing comminution equipment, the selection of some parameters, such as rotating speed, pressure and so on, it is hard to ®nd suitable theoretical rules. In fact, these parameters have to be determined within a certain range. By all appearance, this kind of selection depends on the designer's experience. Large amounts of data generated by all kinds of comminution equipment with different design parameters in production re¯ect the inner relationship between the equipment's design parameters and the comminution results. If those data generated by the same kind of equipment when grinding the same kind of materials are collected, the inner relationship can be obtained by modeling methods based on AI. The inner relationship will be the design fundamentals and the direction of this kind of equipment in reverse. Arti®cial neural networks have powerful nonlinear modeling capability, which correlates the inputs and the outputs by learning, and can re¯ect and forecast the relationship between the inputs and outputs of the comminution system to be investigated. To implement comminution process modeling, a new modeling method named GA±FNN that combined fuzzy sets, ANN and genetic algorithms is proposed [7±10]. 3.1. Structure of GA±FNN The structure of GA±FNN is shown in Fig. 4, and includes four main parts: fuzzi®cation of inputs, fuzzy neural net-
works (FNN), defuzzi®cation of outputs, and learning algorithms of FNN (GA). After the training of FNN is ®nished, it can be used to forecast the unknown results. 3.2. Fuzzification of inputs Because errors of experimental data from the comminution process are sometimes dif®cult to eliminate by all possible measures, ®rst fuzzifying these data is very helpful. Dividing every system input into seven different fuzzy linguistics as seven sub-inputs, the error's in¯uence can be decreased; therefore, the system has the functions of error-tolerating and ®ltering to some extent. In order to fuzzify inputs, de®ning the membership function of every input is important. There are many different membership functions: in GA±FNN, triangle and Gauss membership functions are used. 3.3. Defuzzification of outputs In GA±FNN, output variables are also fuzzi®ed, each output of FNN being a value of the membership function of each fuzzy linguistic variable of outputs. The real outputs of the system can be obtained by using defuzzifying algorithms such as the max-procedure or the center-of-gravity procedure. Here, the center-of-gravity method is used provided that the seven fuzzy linguistic variables of output yi are very
L. Shuiping et al. / Journal of Materials Processing Technology 120 (2002) 84±89
87
Fig. 4. Structure of GA±FNN diagram.
small (VS), small (S), medium small (MS), medium (M), medium big (MB), big (B), very big (VB), the values of the membership function of the corresponding fuzzy linguistic variable, m yik , is shown in Fig. 5, the center-of-gravity yim being de®ned as P6 P6 yik m yik k0 yik m yik Pk0 (1) yim P6 6 k0 m yik k0 1 m yik The artificial neural net may easily denote this expression. 3.4. Structure of FNN The structure of FNN, shown in Fig. 6, includes three parts. The input part includes layers L1 and L2. After every input variable is fuzzi®ed, corresponding seven membership degrees become real net inputs. Layer L3 is as the middle part. The number of nodes and their connection method of the middle part re¯ect the fuzzy
Fig. 5. values of the membership function of linguistic variables of output.
relationship of the real process in fact. If the fuzzy relationship of the process is known, the number of nodes and their connection method of the middle part can be determined according to the fuzzy relationship. If the fuzzy relationship is not known, a complex structure of FNN that takes into account all possible fuzzy relationships can ®rstly be
Fig. 6. FNN structure for modeling.
88
L. Shuiping et al. / Journal of Materials Processing Technology 120 (2002) 84±89
Fig. 7. GA flowchart for FNN training.
constructed, and then can be simpli®ed in FNN training in the future. Output function of L3 is a sigmoid function, namely if the input of a certain node i is Ii: X wji zj yi (2) Ii j
then the output of this node is Oi: Oi
1 1e
bIi
;
b>0
(3)
where j is a certain node of L2, wji the weights between L2 and L3, zj the output of node j, and yi the threshold of node i of L3. This threshold function can also provide a judgement standard for simplifying the network. The output part consists of layers L4 and L5, and the defuzzi®cation operation can be ®nished simultaneously. Every weight and threshold can be de®ned according to the above discussion. 3.5. Training of FNN±genetic algorithms Because the genetic algorithm is an ef®cient parallel one without local convergence, it is very suitable for the training of FNN used for modeling the comminution processes with complex calculations. GA ¯owchart for FNN training is shown in Fig. 7. The key to applying genetic algorithms is how to choose coding, decoding and genetic operators. Here, since the range of FNN weights is not ambiguous and there are more coding variables, a binary system coding is unsuitable. The improved coding is described as follows.
If variable ai 2 ai min ; ai max , when coding ai, to ®nd a real number di the length of which is certain, and di 2 0; 1, then the relationship between ai and di becomes ai ai min ai max
ai min di
(4)
The above equation will also be the same as the corresponding decoding function. This method is real number coding, which can shorten string length. Because the code does not belong to the binary system, the mutation operator is not inversing, but generating random numbers of which the grade lies in the 0; 1 interval. 4. Case study: modeling the comminution process of the Horomill Horomill is a kind of new piece of comminution equipment with high ef®ciency and low energy consumption [11], the sketch diagram being shown in Fig. 8. In Horomill design, four key parameters, the diameter of cylinder D, the ratio of the diameter of the cylinder to the diameter of roller D/d, the ratio of the pressure to the ef®cient length of the roller and the rotating speed of cylinder n (or circumferential velocity v). Here, the relationship of the values of these four parameters and energy consumption per unit product is considered. In reality, it is dif®cult to de®ne the four parameters. By virtue of the above modeling method, using the experimental data obtained, the relationship of these parameters and E can be found when a certain kind of material is ground. Here, inputs of FNN are D, D/d, P/l, v, and the output is E; they are all divided into seven fuzzy linguistic variables, and fuzzi®ed according to the triangle membership function.
L. Shuiping et al. / Journal of Materials Processing Technology 120 (2002) 84±89
89
Fig. 8. Sketch map of Horomill. Fig. 9. The training of GA±FNN.
Fig. 10. Real outputs and GA±FNN forecast outputs.
After the structure of FNN has been built, GA is used to train the networks. The training process is shown in Fig. 9. When the training is ®nished, the network is checked. The output errors of training samples and checking samples are shown in Fig. 10. The maximum output error does not exceed 5% of the desired output. The above network structure includes all possible links of the nodes. On the basis of the analysis of ®nal weights and thresholds when training is ®nished, the FNN structure can be simpli®ed. In layers L2, L3 and L4, if some path is in an inactive state in most cases, the corresponding node of the middle layer and all links with it can be deleted. 5. Conclusions Computational comminution based on information models is a new concept that has been proposed for the more ef®cient treatment of comminution problems. According to the requirements of CCS, the emphasis of this paper was to investigate modeling the comminution process. The goal is accomplished by developing a modeling approach of GA±FNN that can ef®ciently treat the problems of modeling the complex nonlinear comminution processes by integrating ANN, fuzzy sets and GA. The results obtained by employing this modeling method are very helpful to de®ne the reasonable values of many important design parameters of comminution equipment that are dif®cult to be chosen because of the lack of suf®cient evidence. On the other hand, this modeling approach also enables CCS, which is dependent on information technology, to be founded on the available basis, to provide a powerful tool. This tool can
obtain the necessary information for modeling the comminution processes by analyzing, comparing and classifying the data of comminution, collected from numerous comminution workshops all over the world by internet. The application of this GA±FNN modeling frame to the cement comminution process of Horomill has testi®ed in that it is very ef®cient. References [1] R. Dazi, Computational mechanics of cuttingÐthe theory of virtual machining, Res. Mech. 49 (6) (1997) 59±63 (in Japanese). [2] Y.-S. Lee, Manufacturing-driven geometric analysis and prototyping: an investigation of computational manufacturing, Project Supported by NSF CAREER Award Grant DMI-9702374, 1999, p. 3. [3] G. Unland, G. Wang, Model of high-pressure roller mills, ZKG Int. 51 (7) (1998) 347±353. [4] H. Rosemann, H.-G. Ellerbrock, Grinding technology for cement production, ZKG Int. 51 (2) (1998) 51±62. [5] F. Feige, Theoretical considerations and experimental results relating to the comminution of particulate materials in the gap between grinding rolls, ZKG Int. 40 (10) (1987) 515±521. [6] I.B. Klymowsky, J. Liu, Progress in the modeling of comminution in a roller press, ZKG Int. 50 (9) (1997) 500±510. [7] R. Masuoka, Neurofuzzy system using a structured neural networks, in: Proceedings of the International Conference on fuzzy Logic and Neural Networks, Iizuka, Japan, 1990, pp. 173±177. [8] Coley, A. David, An Introduction to Genetic Algorithms for Scientists and Engineers, World Scientific, Singapore, 1999. [9] M. Gen, R. Cheng, Genetic Algorithms and Engineering Design, Wiley, New York, 1997. [10] A.M.S. Zalzala, Genetic Algorithms in Engineering Systems, Institute of Electrical Engineers, London, 1997. [11] S. Buzzi, The HoromillÐa new mill for fine comminution, ZKG Int. 50 (3) (1997) 127±138.