- Email: [email protected]
A hybrid expert system for finite element modeling of fuselage frames
Expert Systems with Applications 24 (2003) 87–93 www.elsevier.com/locate/eswa
A hybrid expert system for finite element modeling of fuselage frames Shuixiang Lia,*, Minggao Qiaob a
Department of Mechanics and Engineering Science, Peking University, Beijing 100871, People’s Republic of China b Shanghai Aircraft Research Institute, Shanghai 200232, People’s Republic of China
Abstract A hybrid expert system which integrates expert system with neural networks is developed for finite element modeling of fuselage frame of aircraft structure. Importance order parameters are introduced to quantify the modeling control. Expert knowledge of importance order parameters, node setting and element selection in fuselage frame modeling is presented. A neural network is employed to structure type classification. The modeling procedures of fuselage frame can be carried out automatically and efficiently by this system. Example shows the frame 1022 of MD-82 passenger aircraft which is modeled by this system automatically and successfully. q 2002 Elsevier Science Ltd. All rights reserved. Keywords: Finite element modeling; Structural analysis; Expert system; Neural networks
1. Introduction To these days, various finite element analysis programs provide powerful structural analysis abilities. However, modeling is still a bottleneck of engineering structural analysis, since it depends mostly on engineering knowledge and background rather than on computing power. Inappropriate model may cause waste of computing power, loss of precision or total failure of the analysis. Engineers work more on modeling phase than on analysis phase. Additionally, different person will make different models and then get different results. Therefore, developing a reasonable analysis model becomes the most important factor to get a satisfied result. Today, automatic modeling is urgently needed to take the place of computer-aided ways. We need our computers to do not just computing, showing drawings or interface action, but also judgment, reasoning, recognition and more. Expert system is a reasoning system based on expert knowledge (rules). In recent years, it has been applied extensively in many engineering areas. A number of finite element modeling expert systems, FEASA (Taig, 1986), SACON (Mackerle & Orsborn, 1988), FEMOD (Chen & Hajela, 1988), CONSMOD (Cheng & Zeng, 1989), userfriendly structural design system (Sato, Nomoto, Kado, Yagawa, & Yoshimura 1996), have been developed in the last two decades. Most of these systems work as a consulting * Corresponding author. E-mail address: [email protected] (S.X. Li).
program and give qualitative suggestions to finite element modeling. They generate few quantitative results and lack of automation. Artificial neural networks have also been applied to finite element modeling (Benbouzid, 1998). These two approaches can be integrated to exploit the advantages and minimize the disadvantages of each method used alone (Yoon, Guimaraes, & Swales, 1994). Some integrated systems have been developed and applied to engineering. In this paper, a hybrid expert system for automatic finite element modeling of fuselage frames of aircraft structure (FEMHES) is presented. This hybrid expert system model which integrates expert system and neural networks is developed from Nabil, Ian, and Tanit (1995) model.
2. FEMHES The FEMHES consists of three major functional modules. Each module has been designed for use as a stand-alone tool, as well as to be integrated into the hybrid expert system to perform required tasks. These components are: † fuselage frame modeling system; † finite element mesh generator; † structure type classifier. The FEMHES has two reasoning engines and their databases:
0957-4174/03/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 5 7 - 4 1 7 4 ( 0 2 ) 0 0 0 8 6 - 6
88
S.X. Li, M.G. Qiao / Expert Systems with Applications 24 (2003) 87–93
Fig. 1. Hybrid expert system for fuselage frame modeling.
† expert system and knowledge base; † neural networks and weights, biases base. The FEMHES also have two auxiliary modules to manage and maintain the system: † knowledge and data management system; † knowledge acquirement system. Fig. 1 shows the relationship among these modules and overall structure of the hybrid expert system. Knowledge has different forms in expert system and neural networks. In expert system, knowledge is represented as rules, while in neural networks it is represented as weights and biases. Therefore, translation between these two knowledge forms is very important to the hybrid expert system. To translate knowledge from expert system to neural networks, several approaches have been used: EBANN (Lu & Wu, 1994), RBTNN (Kwasny & Faisal, 1991). To translate knowledge from neural networks to expert system, SIR (Ishwar & Jae, 1992) and Fu’s (1991) approach have been applied. The steps for fuselage frame modeling are
8. show both graphic and data modeling results, go to 3 if not satisfied; 9. generate input data files for NASTRAN. NASTRAN is a finite element analysis system developed by MSC software corporation. The FEMHES is programmed by Microsoft Visual Cþ þ and Visual Basic; it runs on Microsoft Windows systems. The mesh generator is developed with ObjectARX of AutoDesk, and it runs on AutoCAD platform.
3. Modeling expert knowledge Towards automatic finite element modeling of fuselage frame, expert knowledge on this area must be summarized for generating rules of the expert system. The three topics following are some of the expert knowledge used in this system. These distinctive and effective methods are developed based on researches worldwide and many years’ experiences of experts. This knowledge is represented as IF– THEN rules in the knowledge base. 3.1. Importance grade parameters
1. input geometric model from CAD software with DXF format; 2. recognize the geometric model and classify the structure type; 3. determine the importance order parameters; 4. simplify model, merge or delete nodes; 5. generate mesh; 6. select element type; 7. distribute loads onto nodes;
Fuselage frames of aircraft structure have different structure types and load types. These differences cause different modeling requirements which is critical to structure simplification, load simplification and mesh density. Importance grade parameters (IGP) are introduced in this paper to quantify these differences by expert knowledge, and then decisions can be made by expert system in an automatic way. The importance grade
S.X. Li, M.G. Qiao / Expert Systems with Applications 24 (2003) 87–93
89
Fig. 2. Expert knowledge of hs.
parameter h is defined as
h ¼ hs þ hlmax hlmax ¼ maxðhil Þ;
ð1Þ i ¼ 1; 2; …; n
ð2Þ
where hs is the IGP based on structure type of the frame, hil is the IGP based on each load type of the frame, and hlmax is the largest hil of all the load types. Fig. 2 shows the expert knowledge of hs, while Fig. 3 shows the expert knowledge of hl. The IGP h, which ranges between 1 and 10, means
different modeling requirements 8 1 may be ignored in modeling > > > > > < 2 – 4 should be considered in modeling h¼ > > 5 – 7 should pay more attention in modeling > > > : 8 – 10 should pay most attention in modeling
3.2. Node setting Node setting is another modeling procedure which
Fig. 3. Expert knowledge of hl.
90
S.X. Li, M.G. Qiao / Expert Systems with Applications 24 (2003) 87–93
Fig. 4. Expert knowledge for node setting.
needs expert knowledge. Engineers have a number of rules to set nodes in practice. Fig. 4 shows the expert knowledge for both regular and irregular node setting in fuselage frame modeling, where PD is preliminary design phase and DD is detail design phase. 3.3. Element type selection Today, commercial finite element analysis systems
usually have a large element library. To select a suitable element type is one of the key procedures to get successful results. Some general rules (Cheng & Zeng, 1992) have been used in this system, while some special knowledge for element selection on fuselage frame modeling is also adopted. Fig. 5 shows the expert knowledge for element type selection of plane frame, where Ah is the area of hatch and Aat is the area of air-tight plane frame. Fig. 6 shows the knowledge for element type selection of ring frame.
Fig. 5. Expert knowledge for element selection of plane frame.
S.X. Li, M.G. Qiao / Expert Systems with Applications 24 (2003) 87–93
91
Fig. 6. Expert knowledge for element selection of ring frame.
4. Neural networks for structure type classification In finite element modeling, structure type is closely associated with mesh generation, modeling parameters determination and element type selection. Automatic classification of structure type is another key procedure of automatic modeling. Unfortunately, expert rules are very difficult to give and are hardly applicable in practice. Neural networks work with training examples instead of rules. In this paper, a neural network is developed for structure type classification and is integrated into the hybrid expert system.
where 2 1 # x ij # 1, 2 1 # y ij # 1, 0 # DLi, DVi # 1, 2 1 # ELi, EVi # 1.
4.1. Classification distances Bitmap or vector drawing is usually not a good choice for inputs of neural networks because it will cause a very large scale of neural networks. Pre-processing should be taken to draw some classification distances for the specific problem. A vector with 20 elements {DL1, DL2,…,DL5, DV1, DV2,…,DV5, EL1,EL2,…,EL5, EV1,EV2,…,EV5} is created as input of the neural networks for structure type classification. Elements of the vector are defined as follows sffiffiffiffiffiffiffi sffiffiffiffiffiffiffi X 2 X 2 x ij y ij DLi ¼
ELi ¼
j
;
nli X x ij j
nli
EVi ¼
4.2. Neural networks The neural networks have an input layer, two hidden layers and an output layer. The input layer has 20 nodes corresponding to 20 classification distances. The output layer has four nodes corresponding to the frames of standard, reinforced, airtight and part-airtight, respectively. Each hidden layer has 30 nodes. An enhanced BP algorithm has been employed as learning algorithm.
j
DVi ¼
nvi
X ;
and vi, j is the sequence number of intersections. Datum plane of fuselage is defined as x-axis and symmetry plane of fuselage is defined as y-axis. Fig. 7 shows the x-, y-axis and intersection lines. x ij and y ij are the relative coordinates of the jth intersection on ith line and are defined as follows ( xij =xmax ; xij $ 0 x ij ¼ ; xij =lxmin l; xij , 0 ð4Þ ( yij =ymax ; yij $ 0 y ij ¼ yij =lymin l; yij , 0
; ð3Þ
5. Example
y ij
j
nvi
;
i ¼ 1; 2; …; 5
where nli and nvi are the number of intersections on line li
Fig. 7. x-, y-axis and intersection lines.
The FEMHES has been applied to finite element modeling for frame 1022 of MD-82 passenger aircraft. This example is provided by Shanghai Aircraft Institute of China. Frame 1022 is a typical reinforced frame. It connects with main landing gear and is the end frame of air-tight cargo cabin. The upper part of the frame is ring frame which is the passage of passenger cabin. The lower part of the frame is plane frame. Fig. 8 shows the original structure of frame 1022. The steps and results of finite element modeling of frame 1022 are (1) Input geometric model and calculate geometric data of frame 1022: area of frame 1022: 7329.105075;
92
S.X. Li, M.G. Qiao / Expert Systems with Applications 24 (2003) 87–93 Table 2
Fig. 8. Original structure.
Fig. 9. After simplification.
Element number
Start
End
Element type
1 2 3 4 5. .. 91 92 93 94 95 96 97
L1 L2 L3 L5 L6
L2 L3 L5 L6 L9
BAR element BAR element BAR element BAR element BAR element
H4L k7 k8 KK1 KK2 KK4 KK3
H4R k9 k10 KK2 KK4 KK3 KK1
BAR element ROD element ROD element Hatch, ignored Hatch, ignored Hatch, ignored Hatch, ignored
edges seem rough due to nodes mergence, and the hatch is ignored. Number of nodes: 93 (Table 1). (5) Generate mesh and select the type of each element by the expert system, Fig.10 shows the results (Table 2). (6) Distribute loads onto nodes. (7) Generate input data files for NASTRAN. The modeling results are very close to those modeled by experts.
Fig. 10. Element type.
area of airtight plane frame: 2260.4330465; hatch area of the airtight plane frame: 24; 22 A .. h/Aat: 1.06174345827942 £ 10 ; . (2) Frame type classification by the neural networks:
6. Conclusions
result: part-airtight fuselage frame. (3) Determine the IGPs of the frame by the expert system: IGP based on structure type hs ¼ 6; IGP based on load types hlmax ¼ 3. So IGP h ¼ 9 means the most attentions should be paid in modeling. (4) Simplify the model, set, merge, delete and number nodes by the expert system. After model simplification, 93 nodes are finally generated. The simplified model is shown in Fig. 9. The frame Table 1 Nodal number
X
Y
Mark
1 2 3 4 5 6 7 8 9 10 .. .
0 7.556 18.641 29.233 41.72733 52.382 56.61 60.09 65.811 65.241
92 91.565 89.1915 85.151 76.70467 66.03 59.752 53.031 25.811 17.535
L1 L2 L3 L5 L6 L9 L10 L11 L15 L16
Automatic finite element modeling is becoming a most important determinant of efficiency of finite element analysis and is urgently needed to engineering. Although some general studies have been reported (Tworzydlo & Oden, 1993), but due to the great differences of various engineering domains of analysis objects, special knowledge of specific area should be taken. Expert system is a suitable tool to represent and apply knowledge in modeling process. However, some knowledge is difficult to represent in rules, like structure type classification. Neural networks which are trained by examples do not need rules to solve problems. Additionally, neural networks can be used as knowledge acquirement system for expert system. The hybrid expert system provides a prefect architecture for integrating both expert system and neural networks. In this paper, a hybrid expert system is developed for finite element modeling of fuselage frames. The design purpose of this system is to maximize the automation and minimize the manual interaction. Expert knowledge for importance grade parameters, node setting and element selection has been summarized for modeling. A neural network is applied to structure type classification of fuselage frames. Example shows the finite element modeling of fuselage frame can be taken automatically and successfully by this system.
S.X. Li, M.G. Qiao / Expert Systems with Applications 24 (2003) 87–93
Acknowledgements Research work of this paper is a part of project 10102001, which is supported by National Natural Science Foundation of China.
References Benbouzid, M. E. H. (1998). Artificial neural networks for finite element modeling of giant magnetostrictive devices. IEEE Transactions on Magnetics, 34(6), 3853–3856. Chen, J. L., & Hajela, P. (1988). FEMOD—a consultative expert system for finite element modeling. Computers and Structures, 29(1), 99– 109. Cheng, G. D., & Zeng, Y. (1989). Finite element modeling expert system CONSMOD. Journal of Computational structural mechanics and applications, 6(2). Cheng, G. D., & Zeng, Y. (1992). Strategies for automatic finite element modeling. Computers and Structures, 44(4), 905–909. Fu, L. (1991). Translating neural networks into rule-based expert systems. Proceedings of International Joint Conference on Neural Network (Vol. 2, pp. 947–954), Seattle WA. Ishwar, K. S., & Jae, H. Y. (1992). SIR: simultaneous induction of rules
93
using neural network. Proceedings of International Joint Conference on Neural Network, 1. Kwasny, S. C., & Faisal, K. A. (1991). Rule-based training of neural networks. Expert Systems with Applications, 2(1), 47–58. Lu, Y. C., & Wu, R. (1994). Explanation-based artificial neural network. Proceedings of the Third Chinese Joint Conference on Artificial Intelligence (pp. 372 –375), Beijing. Mackerle, J., & Orsborn, K. (1988). Expert system for finite element analysis and design optimization—a review. Engineering Computation, 5, 90 –101. Nabil, K., Ian, F., & Tanit, T. T. (1995). Integrating knowledge-based system and artificial neural networks for engineering. Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 9, 13– 22. Sato, T., Nomoto, T., Kado, K., Yagawa, G., & Yoshimura, S. (1996). Development of user-friendly structural design system for pressure vessels. JSME International Journal Series A—Mechanics and Material Engineering, 39(3), 354–361. Tworzydlo, W. W., & Oden, J. T. (1993). Towards an automatic environment in computational mechanics. Computer Methods in Applied Mechanics and Engineering, 104, 87–143. Yoon, Y., Guimaraes, T., & Swales, G. (1994). Integrating artificial neural networks with rule-based expert systems. Decision Support Systems, 11(5), 497– 507.
A hybrid expert system for finite element modeling of fuselage frames Shuixiang Lia,*, Minggao Qiaob a
Department of Mechanics and Engineering Science, Peking University, Beijing 100871, People’s Republic of China b Shanghai Aircraft Research Institute, Shanghai 200232, People’s Republic of China
Abstract A hybrid expert system which integrates expert system with neural networks is developed for finite element modeling of fuselage frame of aircraft structure. Importance order parameters are introduced to quantify the modeling control. Expert knowledge of importance order parameters, node setting and element selection in fuselage frame modeling is presented. A neural network is employed to structure type classification. The modeling procedures of fuselage frame can be carried out automatically and efficiently by this system. Example shows the frame 1022 of MD-82 passenger aircraft which is modeled by this system automatically and successfully. q 2002 Elsevier Science Ltd. All rights reserved. Keywords: Finite element modeling; Structural analysis; Expert system; Neural networks
1. Introduction To these days, various finite element analysis programs provide powerful structural analysis abilities. However, modeling is still a bottleneck of engineering structural analysis, since it depends mostly on engineering knowledge and background rather than on computing power. Inappropriate model may cause waste of computing power, loss of precision or total failure of the analysis. Engineers work more on modeling phase than on analysis phase. Additionally, different person will make different models and then get different results. Therefore, developing a reasonable analysis model becomes the most important factor to get a satisfied result. Today, automatic modeling is urgently needed to take the place of computer-aided ways. We need our computers to do not just computing, showing drawings or interface action, but also judgment, reasoning, recognition and more. Expert system is a reasoning system based on expert knowledge (rules). In recent years, it has been applied extensively in many engineering areas. A number of finite element modeling expert systems, FEASA (Taig, 1986), SACON (Mackerle & Orsborn, 1988), FEMOD (Chen & Hajela, 1988), CONSMOD (Cheng & Zeng, 1989), userfriendly structural design system (Sato, Nomoto, Kado, Yagawa, & Yoshimura 1996), have been developed in the last two decades. Most of these systems work as a consulting * Corresponding author. E-mail address: [email protected] (S.X. Li).
program and give qualitative suggestions to finite element modeling. They generate few quantitative results and lack of automation. Artificial neural networks have also been applied to finite element modeling (Benbouzid, 1998). These two approaches can be integrated to exploit the advantages and minimize the disadvantages of each method used alone (Yoon, Guimaraes, & Swales, 1994). Some integrated systems have been developed and applied to engineering. In this paper, a hybrid expert system for automatic finite element modeling of fuselage frames of aircraft structure (FEMHES) is presented. This hybrid expert system model which integrates expert system and neural networks is developed from Nabil, Ian, and Tanit (1995) model.
2. FEMHES The FEMHES consists of three major functional modules. Each module has been designed for use as a stand-alone tool, as well as to be integrated into the hybrid expert system to perform required tasks. These components are: † fuselage frame modeling system; † finite element mesh generator; † structure type classifier. The FEMHES has two reasoning engines and their databases:
0957-4174/03/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 5 7 - 4 1 7 4 ( 0 2 ) 0 0 0 8 6 - 6
88
S.X. Li, M.G. Qiao / Expert Systems with Applications 24 (2003) 87–93
Fig. 1. Hybrid expert system for fuselage frame modeling.
† expert system and knowledge base; † neural networks and weights, biases base. The FEMHES also have two auxiliary modules to manage and maintain the system: † knowledge and data management system; † knowledge acquirement system. Fig. 1 shows the relationship among these modules and overall structure of the hybrid expert system. Knowledge has different forms in expert system and neural networks. In expert system, knowledge is represented as rules, while in neural networks it is represented as weights and biases. Therefore, translation between these two knowledge forms is very important to the hybrid expert system. To translate knowledge from expert system to neural networks, several approaches have been used: EBANN (Lu & Wu, 1994), RBTNN (Kwasny & Faisal, 1991). To translate knowledge from neural networks to expert system, SIR (Ishwar & Jae, 1992) and Fu’s (1991) approach have been applied. The steps for fuselage frame modeling are
8. show both graphic and data modeling results, go to 3 if not satisfied; 9. generate input data files for NASTRAN. NASTRAN is a finite element analysis system developed by MSC software corporation. The FEMHES is programmed by Microsoft Visual Cþ þ and Visual Basic; it runs on Microsoft Windows systems. The mesh generator is developed with ObjectARX of AutoDesk, and it runs on AutoCAD platform.
3. Modeling expert knowledge Towards automatic finite element modeling of fuselage frame, expert knowledge on this area must be summarized for generating rules of the expert system. The three topics following are some of the expert knowledge used in this system. These distinctive and effective methods are developed based on researches worldwide and many years’ experiences of experts. This knowledge is represented as IF– THEN rules in the knowledge base. 3.1. Importance grade parameters
1. input geometric model from CAD software with DXF format; 2. recognize the geometric model and classify the structure type; 3. determine the importance order parameters; 4. simplify model, merge or delete nodes; 5. generate mesh; 6. select element type; 7. distribute loads onto nodes;
Fuselage frames of aircraft structure have different structure types and load types. These differences cause different modeling requirements which is critical to structure simplification, load simplification and mesh density. Importance grade parameters (IGP) are introduced in this paper to quantify these differences by expert knowledge, and then decisions can be made by expert system in an automatic way. The importance grade
S.X. Li, M.G. Qiao / Expert Systems with Applications 24 (2003) 87–93
89
Fig. 2. Expert knowledge of hs.
parameter h is defined as
h ¼ hs þ hlmax hlmax ¼ maxðhil Þ;
ð1Þ i ¼ 1; 2; …; n
ð2Þ
where hs is the IGP based on structure type of the frame, hil is the IGP based on each load type of the frame, and hlmax is the largest hil of all the load types. Fig. 2 shows the expert knowledge of hs, while Fig. 3 shows the expert knowledge of hl. The IGP h, which ranges between 1 and 10, means
different modeling requirements 8 1 may be ignored in modeling > > > > > < 2 – 4 should be considered in modeling h¼ > > 5 – 7 should pay more attention in modeling > > > : 8 – 10 should pay most attention in modeling
3.2. Node setting Node setting is another modeling procedure which
Fig. 3. Expert knowledge of hl.
90
S.X. Li, M.G. Qiao / Expert Systems with Applications 24 (2003) 87–93
Fig. 4. Expert knowledge for node setting.
needs expert knowledge. Engineers have a number of rules to set nodes in practice. Fig. 4 shows the expert knowledge for both regular and irregular node setting in fuselage frame modeling, where PD is preliminary design phase and DD is detail design phase. 3.3. Element type selection Today, commercial finite element analysis systems
usually have a large element library. To select a suitable element type is one of the key procedures to get successful results. Some general rules (Cheng & Zeng, 1992) have been used in this system, while some special knowledge for element selection on fuselage frame modeling is also adopted. Fig. 5 shows the expert knowledge for element type selection of plane frame, where Ah is the area of hatch and Aat is the area of air-tight plane frame. Fig. 6 shows the knowledge for element type selection of ring frame.
Fig. 5. Expert knowledge for element selection of plane frame.
S.X. Li, M.G. Qiao / Expert Systems with Applications 24 (2003) 87–93
91
Fig. 6. Expert knowledge for element selection of ring frame.
4. Neural networks for structure type classification In finite element modeling, structure type is closely associated with mesh generation, modeling parameters determination and element type selection. Automatic classification of structure type is another key procedure of automatic modeling. Unfortunately, expert rules are very difficult to give and are hardly applicable in practice. Neural networks work with training examples instead of rules. In this paper, a neural network is developed for structure type classification and is integrated into the hybrid expert system.
where 2 1 # x ij # 1, 2 1 # y ij # 1, 0 # DLi, DVi # 1, 2 1 # ELi, EVi # 1.
4.1. Classification distances Bitmap or vector drawing is usually not a good choice for inputs of neural networks because it will cause a very large scale of neural networks. Pre-processing should be taken to draw some classification distances for the specific problem. A vector with 20 elements {DL1, DL2,…,DL5, DV1, DV2,…,DV5, EL1,EL2,…,EL5, EV1,EV2,…,EV5} is created as input of the neural networks for structure type classification. Elements of the vector are defined as follows sffiffiffiffiffiffiffi sffiffiffiffiffiffiffi X 2 X 2 x ij y ij DLi ¼
ELi ¼
j
;
nli X x ij j
nli
EVi ¼
4.2. Neural networks The neural networks have an input layer, two hidden layers and an output layer. The input layer has 20 nodes corresponding to 20 classification distances. The output layer has four nodes corresponding to the frames of standard, reinforced, airtight and part-airtight, respectively. Each hidden layer has 30 nodes. An enhanced BP algorithm has been employed as learning algorithm.
j
DVi ¼
nvi
X ;
and vi, j is the sequence number of intersections. Datum plane of fuselage is defined as x-axis and symmetry plane of fuselage is defined as y-axis. Fig. 7 shows the x-, y-axis and intersection lines. x ij and y ij are the relative coordinates of the jth intersection on ith line and are defined as follows ( xij =xmax ; xij $ 0 x ij ¼ ; xij =lxmin l; xij , 0 ð4Þ ( yij =ymax ; yij $ 0 y ij ¼ yij =lymin l; yij , 0
; ð3Þ
5. Example
y ij
j
nvi
;
i ¼ 1; 2; …; 5
where nli and nvi are the number of intersections on line li
Fig. 7. x-, y-axis and intersection lines.
The FEMHES has been applied to finite element modeling for frame 1022 of MD-82 passenger aircraft. This example is provided by Shanghai Aircraft Institute of China. Frame 1022 is a typical reinforced frame. It connects with main landing gear and is the end frame of air-tight cargo cabin. The upper part of the frame is ring frame which is the passage of passenger cabin. The lower part of the frame is plane frame. Fig. 8 shows the original structure of frame 1022. The steps and results of finite element modeling of frame 1022 are (1) Input geometric model and calculate geometric data of frame 1022: area of frame 1022: 7329.105075;
92
S.X. Li, M.G. Qiao / Expert Systems with Applications 24 (2003) 87–93 Table 2
Fig. 8. Original structure.
Fig. 9. After simplification.
Element number
Start
End
Element type
1 2 3 4 5. .. 91 92 93 94 95 96 97
L1 L2 L3 L5 L6
L2 L3 L5 L6 L9
BAR element BAR element BAR element BAR element BAR element
H4L k7 k8 KK1 KK2 KK4 KK3
H4R k9 k10 KK2 KK4 KK3 KK1
BAR element ROD element ROD element Hatch, ignored Hatch, ignored Hatch, ignored Hatch, ignored
edges seem rough due to nodes mergence, and the hatch is ignored. Number of nodes: 93 (Table 1). (5) Generate mesh and select the type of each element by the expert system, Fig.10 shows the results (Table 2). (6) Distribute loads onto nodes. (7) Generate input data files for NASTRAN. The modeling results are very close to those modeled by experts.
Fig. 10. Element type.
area of airtight plane frame: 2260.4330465; hatch area of the airtight plane frame: 24; 22 A .. h/Aat: 1.06174345827942 £ 10 ; . (2) Frame type classification by the neural networks:
6. Conclusions
result: part-airtight fuselage frame. (3) Determine the IGPs of the frame by the expert system: IGP based on structure type hs ¼ 6; IGP based on load types hlmax ¼ 3. So IGP h ¼ 9 means the most attentions should be paid in modeling. (4) Simplify the model, set, merge, delete and number nodes by the expert system. After model simplification, 93 nodes are finally generated. The simplified model is shown in Fig. 9. The frame Table 1 Nodal number
X
Y
Mark
1 2 3 4 5 6 7 8 9 10 .. .
0 7.556 18.641 29.233 41.72733 52.382 56.61 60.09 65.811 65.241
92 91.565 89.1915 85.151 76.70467 66.03 59.752 53.031 25.811 17.535
L1 L2 L3 L5 L6 L9 L10 L11 L15 L16
Automatic finite element modeling is becoming a most important determinant of efficiency of finite element analysis and is urgently needed to engineering. Although some general studies have been reported (Tworzydlo & Oden, 1993), but due to the great differences of various engineering domains of analysis objects, special knowledge of specific area should be taken. Expert system is a suitable tool to represent and apply knowledge in modeling process. However, some knowledge is difficult to represent in rules, like structure type classification. Neural networks which are trained by examples do not need rules to solve problems. Additionally, neural networks can be used as knowledge acquirement system for expert system. The hybrid expert system provides a prefect architecture for integrating both expert system and neural networks. In this paper, a hybrid expert system is developed for finite element modeling of fuselage frames. The design purpose of this system is to maximize the automation and minimize the manual interaction. Expert knowledge for importance grade parameters, node setting and element selection has been summarized for modeling. A neural network is applied to structure type classification of fuselage frames. Example shows the finite element modeling of fuselage frame can be taken automatically and successfully by this system.
S.X. Li, M.G. Qiao / Expert Systems with Applications 24 (2003) 87–93
Acknowledgements Research work of this paper is a part of project 10102001, which is supported by National Natural Science Foundation of China.
References Benbouzid, M. E. H. (1998). Artificial neural networks for finite element modeling of giant magnetostrictive devices. IEEE Transactions on Magnetics, 34(6), 3853–3856. Chen, J. L., & Hajela, P. (1988). FEMOD—a consultative expert system for finite element modeling. Computers and Structures, 29(1), 99– 109. Cheng, G. D., & Zeng, Y. (1989). Finite element modeling expert system CONSMOD. Journal of Computational structural mechanics and applications, 6(2). Cheng, G. D., & Zeng, Y. (1992). Strategies for automatic finite element modeling. Computers and Structures, 44(4), 905–909. Fu, L. (1991). Translating neural networks into rule-based expert systems. Proceedings of International Joint Conference on Neural Network (Vol. 2, pp. 947–954), Seattle WA. Ishwar, K. S., & Jae, H. Y. (1992). SIR: simultaneous induction of rules
93
using neural network. Proceedings of International Joint Conference on Neural Network, 1. Kwasny, S. C., & Faisal, K. A. (1991). Rule-based training of neural networks. Expert Systems with Applications, 2(1), 47–58. Lu, Y. C., & Wu, R. (1994). Explanation-based artificial neural network. Proceedings of the Third Chinese Joint Conference on Artificial Intelligence (pp. 372 –375), Beijing. Mackerle, J., & Orsborn, K. (1988). Expert system for finite element analysis and design optimization—a review. Engineering Computation, 5, 90 –101. Nabil, K., Ian, F., & Tanit, T. T. (1995). Integrating knowledge-based system and artificial neural networks for engineering. Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 9, 13– 22. Sato, T., Nomoto, T., Kado, K., Yagawa, G., & Yoshimura, S. (1996). Development of user-friendly structural design system for pressure vessels. JSME International Journal Series A—Mechanics and Material Engineering, 39(3), 354–361. Tworzydlo, W. W., & Oden, J. T. (1993). Towards an automatic environment in computational mechanics. Computer Methods in Applied Mechanics and Engineering, 104, 87–143. Yoon, Y., Guimaraes, T., & Swales, G. (1994). Integrating artificial neural networks with rule-based expert systems. Decision Support Systems, 11(5), 497– 507.