A meshless method using the Takagi-Sugeno fuzzy model

Journal of Engineering Mathematics

Volumn 72, Issue 1, 2012, Pages 159-175

  Liao, Ying Po ^a   Lin, Shiu Shin ^b  

^a Texas AandM University   (United States)

^b CHUNG YUAN CHRISTIAN UNIVERSITY   (Taiwan)

Author keywords

Adaptive neuro fuzzy inference system; Computational mechanics; Meshless method; Takagi Sugeno fuzzy system

Indexed keywords

ADAPTIVE NEURO-FUZZY INFERENCE SYSTEM; APPROXIMATION SCHEME; COLLOCATION POINTS; CONTINUOUS FUNCTIONS; DIFFERENTIAL FUNCTIONS; EUCLIDEAN DISTANCE; FUZZY INFERENCE SYSTEMS; FUZZY MODELS; HIGHER ORDER; INDEPENDENT SET; MESH-LESS METHODS; MULTI-DIMENSIONAL SPACE; NUMERICAL SOLUTION; SIMPLE RULES; TAKAGI SUGENO FUZZY MODELS; TAKAGI SUGENO FUZZY SYSTEMS;

BOUNDARY CONDITIONS; COMPUTATIONAL MECHANICS; FUZZY SYSTEMS; MEMBERSHIP FUNCTIONS;

FUZZY INFERENCE;

EID: 84856229718     PISSN: 00220833     EISSN: 15732703     Source Type: Journal    
DOI: 10.1007/s10665-011-9472-6     Document Type: Article

References (33)

1. Aluru NR, Li G (2001) Finite cloud method: a true meshless technique based on a fixed reproducing kernel approximation. Int J Numer Methods Eng 50: 2373-2410.
2. Atluri SN, Kim HG, Cho JY (1999) A critical assessment of the truly meshless local Petrov-Galerkin (MLPG), and local boundary integral equation (LBIE) methods. Comput Mech 24: 348-372.
3. Atluri SN, Cho JY, Kim HG (1999) Analysis of thin beams, using the meshless local Petrov-Galerkin method, with generalized moving least squares interpolations. Comput Mech 24: 334-347.
4. Atluri SN, Zhu TL (1998) A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput Mech 22: 117-127.
5. Atluri SN, Zhu TL (1998) A new meshless local Petrov-Galerkin (MLPG) approach to nonlinear problems in computer modeling and simulation. Comput Model Simul Eng 3(3): 187-196.
6. Babuska I, Melenk JM (1997) The partition of unity method. Int J Numer Methods Eng 40: 727-758.
7. Belytschko T, Lu YY, Gu L (1994) Element-free Galerkin methods. Int J Numer Methods Eng 37: 229-256.
8. De S, Bathe KJ (2000) The method of finite spheres. Comput Mech 25: 329-345.
9. Dissanayake MWMG, Phan-Thien N (1994) Neural-network-based approximations for solving partial differential equations. Commun Numer Methods Eng 10: 195-201.
10. Duarte CA, Oden JT (1995) Hp clouds-a meshless method to solve boundary-value problems. TICAM Report 95-05, TICAM, The University of Texas at Austin.
11. Duarte CA, Oden JT (1996a) H-p clouds-an h-p meshless method. Numer Methods Partial Differ. Equ. 12: 673-705.
12. Duarte CA, Oden JT (1996b) An h-p adaptive method using clouds. Comput Methods Appl Mech Eng 139: 237-262.
13. Fairweather G, Karageorghis A (1998) The method of fundamental solutions for elliptic boundary value problems. Adv Comput Math 9(1/2): 69-95.
14. Gingold RA, Moraghan JJ (1977) Smooth particle hydrodynamics: theory and applications to non spherical stars. Man Not R Astron Soc 181: 375-389.
15. Kansa EJ (1990a) Multiquadrics-a scattered data approximation scheme with applications to computational fluid-dynamics-I. Surface approximations and partial derivative estimates. Comput Math Appl 19(8/9): 127-145.
16. Kansa EJ (1990b) Multiquadrics-a scattered data approximation scheme with applications to computational fluid-dynamics-II: solutions to parabolic, hyperbolic and elliptic partial differential equations. Comput Math Appl 19(8/9): 147-161.
17. Li H, Ng TY, Cheng JQ, Lam KY (2003) Hermite-Cloud: a novel true meshless method. Comput Mech 33(1): 30-41.
18. Liu GR, Gu YT (2001) A point interpolation method for two-dimensional solids. Int J Numer Methods Eng 50: 937-951.
19. Liu GR, Gu YT (2001) A local point interpolation method for stress analysis of two-dimensional solids. Struct Eng Mech 11(2): 221-236.
20. Liu GR, Gu YT (2003) A meshfree method: meshfree weak-strong (MWS) form method for 2-D solids. Comput Mech 33(1): 2-14.
21. Liu WK, Jun S, Zhang Y (1995) Reproducing kernel particle methods. Int J Numer Methods Eng 20: 1081-1106.
22. Lucy LB (1977) A numerical approach to the testing of the fission hypothesis. Astron J 8(12): 1013-1024.
23. Mai-Duy N, Tran-Cong T (2001a) Numerical solution of differential equations using multiquadric radial basis function networks. Neural Netw 14: 185-199.
24. Mai-Duy N, Tran-Cong T (2001b) Numerical solution of Navier-Stokes equations using multiquadric radial basis function networks. Int J Numer Methods Fluids 37: 65-86.
25. Mathon T, Johnston RL (1977) The approximate solution of elliptic boundary-value problems by fundamental solutions. SIAM J Numer Anal 14(4): 638-650.
26. Melenk JM, Babuska I (1996) The partition of unity finite element method: basic theory and applications. Comput Methods Appl Mech Eng 139: 289-314.
27. Melenk JM, Babuska I (1997) Approximation with harmonic and generalized harmonic polynomials in the partition of unity method. Comput Assist Mech Eng Sci 4: 607-632.
28. Nayroles B, Touzot G, Villon P (1992) Generalizing the finite element method: diffuse approximation and diffuse elements. Comput Mech 10: 307-318.
29. Sugeno M, Kang GT (1988) Structure identification of fuzzy model. Fuzzy Sets Syst 28: 15-33.
30. Takagi T, Sugeno M (1985) Fuzzy identification of systems and its application to modeling and control. IEEE Trans Syst Man Cybernet 15(1): 116-132.
31. Wang QX, Li H, Lam KY (2005) Development of a new meshless-point weighted least-squares (PWLS) method for computational mechanics. Comput Mech 35: 170-181.
32. Zhang X, Song KZ, Lu MW, Liu X (2000) Meshless methods based on collocation with radial basis functions. Comput Mech 26: 333-343.
33. Zhu T, Zhang JD, Atluri SN (1998) A local boundary integral equation (LBIE) method in computational mechanics and a meshless discretization approach. Comput Mech 21: 223-235.