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New concept of ESP modelling based on fuzzy logic
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Journal of Electrostatics 51}52 (2001) 206}211
New concept of ESP modelling based on fuzzy logic IstvaH n Kiss*, IstvaH n Berta Department of High Voltage Engineering and Equipment, Budapest University of Technology and Economics, H-1521 Budapest 1111, Hungary
Abstract As Professor Senichi Masuda in Handbook of Electrostatics wrote, `The electrostatic precipitator is a typical fuzzy system, where a large number of factors a!ect its performance in a complicated fashion'', (Masuda and Hosokawa, in: Chang, Crowley, Kelly (Eds.), Handbook of Electrostatic Processes, Marcel Dekker, New York, 1995, pp. 441}479 (Chapter 21)). Knowing the complexity of ESP modelling from our previous experience (Kiss et al., VII, ICESP, Kyongju, Korea, 1998, pp. 196}205), it was decided to approach the problem in a new way, which is based on fuzzy logic. In order to do that, a new concept was worked out to analyse the applicability of combined models for ESPs and to analyse such cases, which have no appropriate model. This paper presents the fuzzy logic based ESP modelling and raises the possibility of the wide range of its applicability. 2001 Elsevier Science B.V. All rights reserved. Keywords: Fuzzy logic; ESP modelling
1. Introduction Nowadays, a lot of ESP models are used to determine the e$ciency of the collection and to answer the questions of operation and design. The capabilities of these models are limited, they are valid only under certain conditions. The limits of modelling originate from the complexity of the process of precipitation [1]. The interactions between the #ow and electric "eld, the in#uence of these on the charging process of particles, the e!ect of space charge requires a wide range of knowledge on the part of the modeller. The most di$cult part of modelling is the determination of the interactions and the e!ect of nonideal parameters. * Corresponding author. Tel.: #36-1-463-3239; fax: #36-1-463-3231. E-mail address: [email protected] (IstvaH n Kiss). 0304-3886/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 8 8 6 ( 0 1 ) 0 0 1 1 1 - 5
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Increasing the complexity of the models, better results can be obtained, but it requires higher computational capacity. Therefore, the task is to "nd a model, which is detailed enough to produce correct results and small enough to handle it. The purpose of our work was to create such a computational method, which works from the existing ESP models [2] as primary ones but use fuzzy logic to handle the uncertainty of the parameters and to take the nonideal factors into consideration.
2. Limits of the modelling In general, the process of precipitation could be divided into three main stages: particle charging, transport and collection. To characterise these processes #ow "eld and electric "eld calculation is necessary including the determination of ion charge density, the corona and back corona models, the particle charging, dust reentrainment, etc. Particle charging models are well known; they describe the two main charging processes: the "eld charging (dominant at particle diameter d'2 m) and the di!usion charging. Many e!orts were made to extend the calculations for arbitrary shape particles [3,4]. But some questions still remain: how to determine the particle space charge distribution in a polydisperse dust phase, containing particles having a wide range of size and arbitrary shape. Especially, non-conductive particles are interesting because the low surface conductivity does not ensure charge transport on the surface. [5]. Finding signi"cant factors plays an important role in the simpli"cation of the calculations. A number of problems originate from interactions of the processes. For example, the electric "eld depends on the charge distribution, which depends on the "eld strength. Several models exist which characterise the electric "eld. Some are valid for 2D, while others use numerical technics to calculate the electric "eld in#uenced by the space charges in 3D [6]. The boundary conditions of the models may contain such parameters, whose value cannot be de"ned exactly. Back corona, dust reentrainment and corona quenching also present the modeller with a complicated problem: to determine, that in a given arrangement with given gas, particle and electrical parameters, how these phenomena could be described; is it possible to use the existing models [7] if some of the parameters are ill-de"ned?
3. Fuzzy logic in ESP modelling Fuzzy logic is widely used in the handling of uncertainty for control purposes, in expert systems and in several other "elds like inference engines. The possibility of using it in industrial electrostatics was presented in [8]. Usually in these applications (mainly fuzzy controllers) fuzzy logic is used to create such a function generator which assigns output values to classi"ed input parameters based on a rule base. Fuzzy control also is applied in electrostatic precipitation, de"ning optimisation criteria for the output quantities. The determination of the rule base can be based on
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I. Kiss, I. Berta / Journal of Electrostatics 51}52 (2001) 206}211
the information of the expert or on the machine and learning to use known test results. For example in [9] a self-exploring mechanism is described for ESP rapping. Recognising, that the fuzzy logic is available to handle the problems of uncertainty in ESP modelling, a new concept was created. The idea is to evaluate and extend the capabilities of the ESP models, which usually requires exact boundary conditions and input parameters. The aim of this is two-fold. First, it is to evaluate the reliability of a given model in such a case, when there are uncertain parameters among the input values. Thus it is possible to determine the `sensitivitya of the model to the changes of certain input parameters and to estimate the reliability of the results. The second aim is more interesting: to change the output quantities in such a way, that they get closer to the real values at uncertain input parameters. Fig. 1 shows the schematic diagram of the methods. The starting parameters of the calculation (boundary conditions, geometric and material data, etc.) are denoted by a , 2, a , while the computed quantities are designated by b , 2, b . A part of these L K data are the input parameters of the fuzzy analyser, which fuzzy"es (classi"es) them. The fuzzy"cation means an assignment between the actual value of the input parameters and a number between 0 and 1 based on the membership functions. In the "rst case the membership functions give the degree of the truth, that at a given a value the ESP model is valid. In the second case they give the degree of G truth, that the real value of input parameter a is near to the supposed value. A typical G membership function can be seen in Fig. 2. Besides the values a there can be such G parameters ( f , 2, f ), which are not taken into consideration in the ESP model, but I they are useful inputs for the fuzzy analyser. The outputs of the fuzzy analyser are denoted by o , 2, o . In the "rst case these values are numbers between 0 and F 1 describing the reliability of the outputs of the ESP model, while in the second case they are the modi"ed values of outputs b , 2, b . K The knowledge base in the analyser gives the connection between the inputs and the outputs of the model. Knowing the fuzzy"ed value of the input parameter and using the rule base, a fuzzy value between 0 and 1 can be assigned to the output. In the second case the structure of the rule base is similar, but the content is di!erent. A certain rule gives how the uncertainty of the input parameter will modify the output value. The rule base can be created directly from measurement or the computational data of a known situation after analysis or using the data as test vectors for a learning
Fig. 1. Schematic diagram of the fuzzy modelling.
I. Kiss, I. Berta / Journal of Electrostatics 51}52 (2001) 206}211
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Fig. 2. Membership function . ?
algorithm. The main idea of the learning method described in [10] is that the possible rules are examined, whether the test data justify the given rule or not.
4. Example of using fuzzy model The practical use of the method presented is for the case of dust reentrainment. The existing models handles this problem mainly based on experimental data. According to them the mass of the reentering particles is proportional to the mass of the collected material [7]. The amount of the reentrained material y as a function of the collected dust x is y"AxX,
(1)
y"RRx . (2) Q Parameters A and z (Gooch and Marchant) depend on the operating conditions of the ESP, such as RR reentrainment fraction (Lawless and Sparks) in the examined section. The reentrainment depends on several factors, like resistivity and size of the particles d (in#uencing dust cohesivity c), the normal component of the vibrating acceleration during rapping (a ), the temperature (t ) and speed (v ) of the gas. The categories of these quantities are small (S), medium (M) and large (L). The membership functions of the categories can be seen in Fig. 3, where X means the actual quantity while represents the categories which can be seen in Fig. 3, where X means the actual quantity while represents the membership value, that a given X is small, medium or large. The output of the model is factor f, computing the reentrainment similar to (2) y"fx.
(3)
For better e$ciency, f is classi"ed by 5 membership functions (Fig. 4), which evaluates the reentrianment, heavy (HR), large (LR), signi"cant (SR), usual (UR), tri#ing (TR). The structure of the knowledge base has two levels. The "rst level contains rules describing the e!ect of t , and d on the cohesion (c). A single rule can be written in the following form: If (t is T1) C ( is R1) C (d is D1), then c is C1, where C represents a logical operation, (mainly &and'), T1, R1, D1, C1 can be S, M or L. For example, If t is small and is large and d is medium, then c is large.
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Fig. 3. Membership functions of the classi"cation.
Fig. 4. Classi"cation of f.
The second level of the rule base gives the correlation between factor f and c, a , v . A rule is very similar to the previous one: If (c is C1) C (a is A1) C (v is V1), then f is F1, the only di!erence is, that F1 can be HR, LR, SR, UR or TR. It is useful to construct the rule base according to the known principles and re"ne it using measurement results based on a learning algorithm [10]. Thus, is calculated, f can be D determined by method COG. (Centre of gravity: membership value , cuts the D appropriate membership function*like SR*at a given height. The area of the membership function under this line can be computed and the horizontal coordinate of its centre of gravity determines the relating f ).
5. Conclusions The new concept on ESP modelling based on fuzzy logic has been presented. With this, the capacity of an existing ESP model can be extended for uncertain information. The method was presented for the model of dust reentrainment. The development of a complex analyser for the total precipitation process is in progress. In the near future it will be possible to demonstrate its e$ciency in such conditions, what existing models cannot handle.
I. Kiss, I. Berta / Journal of Electrostatics 51}52 (2001) 206}211
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Acknowledgements The authors thank Professor LaH szloH T. KoH czy for his valuable discussions.
References [1] S. Masuda, S. Hosokawa, Electrostatic precipitation, in: J.S. Chang, J.M. Crowley, A.J. Kelly (Eds.), Handbook of Electrostatic Processes, Marcel Dekker, New York, 1995, pp. 441}479 (Chapter 21). [2] I. Kiss, J. Suda, G. KristoH f, I. Berta, The turbulent transport process of charged dust particles in electrostatic precipitators, in: Proceedings of the VII. ICESP, Kyongju, Korea, 1998, pp. 196}205. [3] J.S. Chang, Electrostatic charging of particles, in: J.S. Chang, J.M. Crowley, A.J. Kelly (Eds.), Handbook of Electrostatic Processes, Marcel Dekker, New York, 1995, pp. 39}49 (Chapter 3). [4] N. Szedenik, I. Kiss, Particle charging in industrial electrostatics, in: Proceedings of the Eighth International Conference on Electrostatics, 4}6 June 1997, pp. 88}92. [5] C.A.P. Zevenhoven, Uni-polar "eld charging of particles: e!ects of particle conductivity and rotation, J. Electrostat. 46 (1999) 1}11. [6] A.M. Meroth, T. Gerber, C.D. Munz, P.L. Levin, A.J. Schwab, Numerical solution of nonstationary charge coupled problems, J. Electrostat. 45 (1999) 177}198. [7] P.A. Lawless, T. Yamamoto, Modelling of electrostatic precipitators and "lters, in: J.S. Chang, J.M. Crowley, A.J. Kelly (Eds.), Handbook of Electrostatic Processes, Marcel Dekker, New York, 1995, pp. 481}507 (Chapter 22). [8] I. Kiss, L. Pula, E. Balog, T.L. KoH czy, I. Berta, Fuzzy logic in industrial electrostatics, J. Electrostat. 40}41 (1997) 561}566. [9] M. Sarna, Self exploring ESP rapping optimisation system, in: Proceedings of the VI. ICESP, Budapest, 1996. [10] L.M. Campos, S. Moral, Learning rules for a fuzzy inference model, Fuzzy Sets and Systems 59 (1993) 247}257.
Journal of Electrostatics 51}52 (2001) 206}211
New concept of ESP modelling based on fuzzy logic IstvaH n Kiss*, IstvaH n Berta Department of High Voltage Engineering and Equipment, Budapest University of Technology and Economics, H-1521 Budapest 1111, Hungary
Abstract As Professor Senichi Masuda in Handbook of Electrostatics wrote, `The electrostatic precipitator is a typical fuzzy system, where a large number of factors a!ect its performance in a complicated fashion'', (Masuda and Hosokawa, in: Chang, Crowley, Kelly (Eds.), Handbook of Electrostatic Processes, Marcel Dekker, New York, 1995, pp. 441}479 (Chapter 21)). Knowing the complexity of ESP modelling from our previous experience (Kiss et al., VII, ICESP, Kyongju, Korea, 1998, pp. 196}205), it was decided to approach the problem in a new way, which is based on fuzzy logic. In order to do that, a new concept was worked out to analyse the applicability of combined models for ESPs and to analyse such cases, which have no appropriate model. This paper presents the fuzzy logic based ESP modelling and raises the possibility of the wide range of its applicability. 2001 Elsevier Science B.V. All rights reserved. Keywords: Fuzzy logic; ESP modelling
1. Introduction Nowadays, a lot of ESP models are used to determine the e$ciency of the collection and to answer the questions of operation and design. The capabilities of these models are limited, they are valid only under certain conditions. The limits of modelling originate from the complexity of the process of precipitation [1]. The interactions between the #ow and electric "eld, the in#uence of these on the charging process of particles, the e!ect of space charge requires a wide range of knowledge on the part of the modeller. The most di$cult part of modelling is the determination of the interactions and the e!ect of nonideal parameters. * Corresponding author. Tel.: #36-1-463-3239; fax: #36-1-463-3231. E-mail address: [email protected] (IstvaH n Kiss). 0304-3886/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 8 8 6 ( 0 1 ) 0 0 1 1 1 - 5
I. Kiss, I. Berta / Journal of Electrostatics 51}52 (2001) 206}211
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Increasing the complexity of the models, better results can be obtained, but it requires higher computational capacity. Therefore, the task is to "nd a model, which is detailed enough to produce correct results and small enough to handle it. The purpose of our work was to create such a computational method, which works from the existing ESP models [2] as primary ones but use fuzzy logic to handle the uncertainty of the parameters and to take the nonideal factors into consideration.
2. Limits of the modelling In general, the process of precipitation could be divided into three main stages: particle charging, transport and collection. To characterise these processes #ow "eld and electric "eld calculation is necessary including the determination of ion charge density, the corona and back corona models, the particle charging, dust reentrainment, etc. Particle charging models are well known; they describe the two main charging processes: the "eld charging (dominant at particle diameter d'2 m) and the di!usion charging. Many e!orts were made to extend the calculations for arbitrary shape particles [3,4]. But some questions still remain: how to determine the particle space charge distribution in a polydisperse dust phase, containing particles having a wide range of size and arbitrary shape. Especially, non-conductive particles are interesting because the low surface conductivity does not ensure charge transport on the surface. [5]. Finding signi"cant factors plays an important role in the simpli"cation of the calculations. A number of problems originate from interactions of the processes. For example, the electric "eld depends on the charge distribution, which depends on the "eld strength. Several models exist which characterise the electric "eld. Some are valid for 2D, while others use numerical technics to calculate the electric "eld in#uenced by the space charges in 3D [6]. The boundary conditions of the models may contain such parameters, whose value cannot be de"ned exactly. Back corona, dust reentrainment and corona quenching also present the modeller with a complicated problem: to determine, that in a given arrangement with given gas, particle and electrical parameters, how these phenomena could be described; is it possible to use the existing models [7] if some of the parameters are ill-de"ned?
3. Fuzzy logic in ESP modelling Fuzzy logic is widely used in the handling of uncertainty for control purposes, in expert systems and in several other "elds like inference engines. The possibility of using it in industrial electrostatics was presented in [8]. Usually in these applications (mainly fuzzy controllers) fuzzy logic is used to create such a function generator which assigns output values to classi"ed input parameters based on a rule base. Fuzzy control also is applied in electrostatic precipitation, de"ning optimisation criteria for the output quantities. The determination of the rule base can be based on
208
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I. Kiss, I. Berta / Journal of Electrostatics 51}52 (2001) 206}211
the information of the expert or on the machine and learning to use known test results. For example in [9] a self-exploring mechanism is described for ESP rapping. Recognising, that the fuzzy logic is available to handle the problems of uncertainty in ESP modelling, a new concept was created. The idea is to evaluate and extend the capabilities of the ESP models, which usually requires exact boundary conditions and input parameters. The aim of this is two-fold. First, it is to evaluate the reliability of a given model in such a case, when there are uncertain parameters among the input values. Thus it is possible to determine the `sensitivitya of the model to the changes of certain input parameters and to estimate the reliability of the results. The second aim is more interesting: to change the output quantities in such a way, that they get closer to the real values at uncertain input parameters. Fig. 1 shows the schematic diagram of the methods. The starting parameters of the calculation (boundary conditions, geometric and material data, etc.) are denoted by a , 2, a , while the computed quantities are designated by b , 2, b . A part of these L K data are the input parameters of the fuzzy analyser, which fuzzy"es (classi"es) them. The fuzzy"cation means an assignment between the actual value of the input parameters and a number between 0 and 1 based on the membership functions. In the "rst case the membership functions give the degree of the truth, that at a given a value the ESP model is valid. In the second case they give the degree of G truth, that the real value of input parameter a is near to the supposed value. A typical G membership function can be seen in Fig. 2. Besides the values a there can be such G parameters ( f , 2, f ), which are not taken into consideration in the ESP model, but I they are useful inputs for the fuzzy analyser. The outputs of the fuzzy analyser are denoted by o , 2, o . In the "rst case these values are numbers between 0 and F 1 describing the reliability of the outputs of the ESP model, while in the second case they are the modi"ed values of outputs b , 2, b . K The knowledge base in the analyser gives the connection between the inputs and the outputs of the model. Knowing the fuzzy"ed value of the input parameter and using the rule base, a fuzzy value between 0 and 1 can be assigned to the output. In the second case the structure of the rule base is similar, but the content is di!erent. A certain rule gives how the uncertainty of the input parameter will modify the output value. The rule base can be created directly from measurement or the computational data of a known situation after analysis or using the data as test vectors for a learning
Fig. 1. Schematic diagram of the fuzzy modelling.
I. Kiss, I. Berta / Journal of Electrostatics 51}52 (2001) 206}211
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
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Fig. 2. Membership function . ?
algorithm. The main idea of the learning method described in [10] is that the possible rules are examined, whether the test data justify the given rule or not.
4. Example of using fuzzy model The practical use of the method presented is for the case of dust reentrainment. The existing models handles this problem mainly based on experimental data. According to them the mass of the reentering particles is proportional to the mass of the collected material [7]. The amount of the reentrained material y as a function of the collected dust x is y"AxX,
(1)
y"RRx . (2) Q Parameters A and z (Gooch and Marchant) depend on the operating conditions of the ESP, such as RR reentrainment fraction (Lawless and Sparks) in the examined section. The reentrainment depends on several factors, like resistivity and size of the particles d (in#uencing dust cohesivity c), the normal component of the vibrating acceleration during rapping (a ), the temperature (t ) and speed (v ) of the gas. The categories of these quantities are small (S), medium (M) and large (L). The membership functions of the categories can be seen in Fig. 3, where X means the actual quantity while represents the categories which can be seen in Fig. 3, where X means the actual quantity while represents the membership value, that a given X is small, medium or large. The output of the model is factor f, computing the reentrainment similar to (2) y"fx.
(3)
For better e$ciency, f is classi"ed by 5 membership functions (Fig. 4), which evaluates the reentrianment, heavy (HR), large (LR), signi"cant (SR), usual (UR), tri#ing (TR). The structure of the knowledge base has two levels. The "rst level contains rules describing the e!ect of t , and d on the cohesion (c). A single rule can be written in the following form: If (t is T1) C ( is R1) C (d is D1), then c is C1, where C represents a logical operation, (mainly &and'), T1, R1, D1, C1 can be S, M or L. For example, If t is small and is large and d is medium, then c is large.
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Fig. 3. Membership functions of the classi"cation.
Fig. 4. Classi"cation of f.
The second level of the rule base gives the correlation between factor f and c, a , v . A rule is very similar to the previous one: If (c is C1) C (a is A1) C (v is V1), then f is F1, the only di!erence is, that F1 can be HR, LR, SR, UR or TR. It is useful to construct the rule base according to the known principles and re"ne it using measurement results based on a learning algorithm [10]. Thus, is calculated, f can be D determined by method COG. (Centre of gravity: membership value , cuts the D appropriate membership function*like SR*at a given height. The area of the membership function under this line can be computed and the horizontal coordinate of its centre of gravity determines the relating f ).
5. Conclusions The new concept on ESP modelling based on fuzzy logic has been presented. With this, the capacity of an existing ESP model can be extended for uncertain information. The method was presented for the model of dust reentrainment. The development of a complex analyser for the total precipitation process is in progress. In the near future it will be possible to demonstrate its e$ciency in such conditions, what existing models cannot handle.
I. Kiss, I. Berta / Journal of Electrostatics 51}52 (2001) 206}211
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
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Acknowledgements The authors thank Professor LaH szloH T. KoH czy for his valuable discussions.
References [1] S. Masuda, S. Hosokawa, Electrostatic precipitation, in: J.S. Chang, J.M. Crowley, A.J. Kelly (Eds.), Handbook of Electrostatic Processes, Marcel Dekker, New York, 1995, pp. 441}479 (Chapter 21). [2] I. Kiss, J. Suda, G. KristoH f, I. Berta, The turbulent transport process of charged dust particles in electrostatic precipitators, in: Proceedings of the VII. ICESP, Kyongju, Korea, 1998, pp. 196}205. [3] J.S. Chang, Electrostatic charging of particles, in: J.S. Chang, J.M. Crowley, A.J. Kelly (Eds.), Handbook of Electrostatic Processes, Marcel Dekker, New York, 1995, pp. 39}49 (Chapter 3). [4] N. Szedenik, I. Kiss, Particle charging in industrial electrostatics, in: Proceedings of the Eighth International Conference on Electrostatics, 4}6 June 1997, pp. 88}92. [5] C.A.P. Zevenhoven, Uni-polar "eld charging of particles: e!ects of particle conductivity and rotation, J. Electrostat. 46 (1999) 1}11. [6] A.M. Meroth, T. Gerber, C.D. Munz, P.L. Levin, A.J. Schwab, Numerical solution of nonstationary charge coupled problems, J. Electrostat. 45 (1999) 177}198. [7] P.A. Lawless, T. Yamamoto, Modelling of electrostatic precipitators and "lters, in: J.S. Chang, J.M. Crowley, A.J. Kelly (Eds.), Handbook of Electrostatic Processes, Marcel Dekker, New York, 1995, pp. 481}507 (Chapter 22). [8] I. Kiss, L. Pula, E. Balog, T.L. KoH czy, I. Berta, Fuzzy logic in industrial electrostatics, J. Electrostat. 40}41 (1997) 561}566. [9] M. Sarna, Self exploring ESP rapping optimisation system, in: Proceedings of the VI. ICESP, Budapest, 1996. [10] L.M. Campos, S. Moral, Learning rules for a fuzzy inference model, Fuzzy Sets and Systems 59 (1993) 247}257.