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Published in: International Journal of Machine Learning and Cybernetics 3/2015

01-06-2015 | Original Article

Identification of boundary shape using a hybrid approach

Authors: Na Tian, Longchao Zhu, Choi-Hong Lai

Published in: International Journal of Machine Learning and Cybernetics | Issue 3/2015

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Abstract

In this paper, a hybrid approach combining quantum-behaved particle swarm optimization (QPSO) and conjugate gradient method is proposed to identify boundary shape of the geometry under steady state conditions. No prior information about the shape is available, so the inverse problem is classified as function estimation. Least square method is used to model the inverse problem, which intends to minimize the difference between measured and calculated data. Considering ill-posedness of the inverse problem, Tikhonov regularization method is used to stabilize the solution. The numerical results show that the proposed hybrid method is able to recover the boundary shape, and can sharply reduce the required computation time. While considering the oscillations at the both boundaries of the estimated results, the parallel QPSO is used in order to both obtain better estimation and reduce computation time.

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Literature
1.
go back to reference Banks HT, Kojima F (1989) Boundary shape identification problems in two-dimensional domains related to thermal testing of materials. Quart J Appl Math 47:273–293MATHMathSciNet Banks HT, Kojima F (1989) Boundary shape identification problems in two-dimensional domains related to thermal testing of materials. Quart J Appl Math 47:273–293MATHMathSciNet
2.
go back to reference Pironneau O (1984) Optimal shape design for elliptic systems, New York Pironneau O (1984) Optimal shape design for elliptic systems, New York
3.
go back to reference Sunahara Y, Kojima F (1986) Boundary identification for a two dimensional diffusion system under noisy observations. In: Proc. 4th IFAC symp. control of distributed parameter systems, UCLA, California, Pergamon Press, New York Sunahara Y, Kojima F (1986) Boundary identification for a two dimensional diffusion system under noisy observations. In: Proc. 4th IFAC symp. control of distributed parameter systems, UCLA, California, Pergamon Press, New York
4.
go back to reference Rondi L (1999) Optimal stability estimates for determination of defects by electrostatic measurements. Inverse Prob 15(5):1193–1212CrossRefMATHMathSciNet Rondi L (1999) Optimal stability estimates for determination of defects by electrostatic measurements. Inverse Prob 15(5):1193–1212CrossRefMATHMathSciNet
5.
go back to reference Aparicio ND, Pidcock MK (1996) The boundary inverse problem for the Laplace equation in two dimensions. Inverse Prob 12(5):565–577CrossRefMATHMathSciNet Aparicio ND, Pidcock MK (1996) The boundary inverse problem for the Laplace equation in two dimensions. Inverse Prob 12(5):565–577CrossRefMATHMathSciNet
6.
7.
go back to reference Hon YC, Wu Z (2000) A numerical computation for inverse boundary determination problem. Eng Anal Bound Elem 24(7):599–606CrossRefMATH Hon YC, Wu Z (2000) A numerical computation for inverse boundary determination problem. Eng Anal Bound Elem 24(7):599–606CrossRefMATH
8.
go back to reference Nachaoui A (2003) An improved implementation of an iterative method in boundary identification problems. Numer Algorithms 33(1–4):381–398CrossRefMATHMathSciNet Nachaoui A (2003) An improved implementation of an iterative method in boundary identification problems. Numer Algorithms 33(1–4):381–398CrossRefMATHMathSciNet
9.
go back to reference Mera NS, Elliott L, Ingham DB (2004) Numerical solution of a boundary detection problem using genetic algorithm. Eng Anal Bound Elem 28(4):405–411CrossRefMATHMathSciNet Mera NS, Elliott L, Ingham DB (2004) Numerical solution of a boundary detection problem using genetic algorithm. Eng Anal Bound Elem 28(4):405–411CrossRefMATHMathSciNet
10.
go back to reference Dashti-Ardakani M, Khodadad M (2009) Identification of thermal conductivity and the shape of an inclusion using the boundary elements method and the particle swarm optimization algorithm. Inv Prob Sci Eng 17(7):855–870CrossRefMathSciNet Dashti-Ardakani M, Khodadad M (2009) Identification of thermal conductivity and the shape of an inclusion using the boundary elements method and the particle swarm optimization algorithm. Inv Prob Sci Eng 17(7):855–870CrossRefMathSciNet
11.
go back to reference Khodadad M, Dashi-Ardakani M (2008) Inclusion identification by inverse application of boundary element method, genetic algorithm and conjugate gradient method. Am J Appl Sci 5(9):1158–1166CrossRef Khodadad M, Dashi-Ardakani M (2008) Inclusion identification by inverse application of boundary element method, genetic algorithm and conjugate gradient method. Am J Appl Sci 5(9):1158–1166CrossRef
12.
go back to reference Morozov VA (1966) On the solution of functional equations by the method of regularization [J]. Soviet Math Dokl 7:414–417MATHMathSciNet Morozov VA (1966) On the solution of functional equations by the method of regularization [J]. Soviet Math Dokl 7:414–417MATHMathSciNet
13.
go back to reference Hansen PC (2001) The L-curve and its use in the numerical treatment of inverse problems, computational inverse problem in electrocardiology. WIT Press, Holland, pp 119–142 Hansen PC (2001) The L-curve and its use in the numerical treatment of inverse problems, computational inverse problem in electrocardiology. WIT Press, Holland, pp 119–142
14.
go back to reference Sun J, Feng B, Xu WB (2004) Particle swarm optimization with particles having quantum behaviour. Congress Evolutionary Computing, Portland Sun J, Feng B, Xu WB (2004) Particle swarm optimization with particles having quantum behaviour. Congress Evolutionary Computing, Portland
15.
go back to reference Sun J, Xu WB, Feng B (2004) A global search strategy of quantum-behaved particle swarm optimization, IEEE Conference on cybernetics and intelligent systems, Singapore Sun J, Xu WB, Feng B (2004) A global search strategy of quantum-behaved particle swarm optimization, IEEE Conference on cybernetics and intelligent systems, Singapore
16.
go back to reference Sun J, Xu WB, Feng B (2005) Adaptive parameter control for quantum-behaved particle swarm optimization on individual level, IEEE international conference on systems, man and cybernetics, Hawaii Sun J, Xu WB, Feng B (2005) Adaptive parameter control for quantum-behaved particle swarm optimization on individual level, IEEE international conference on systems, man and cybernetics, Hawaii
17.
go back to reference Kennedy J, Eberhart RC (1995) Particle swarm optimization, IEEE international conference neural networks, Perth, Australia Kennedy J, Eberhart RC (1995) Particle swarm optimization, IEEE international conference neural networks, Perth, Australia
18.
19.
go back to reference Hunter P, Pullan A (2001) FEM/BEM notes. The University of Auckland, New Zealand Hunter P, Pullan A (2001) FEM/BEM notes. The University of Auckland, New Zealand
20.
go back to reference Kythe PK (1995) An introduction to boundary element methods. CRC Press, Boca RatonMATH Kythe PK (1995) An introduction to boundary element methods. CRC Press, Boca RatonMATH
21.
go back to reference Eberhart RC, Shi Y (1998) Comparison between genetic algorithm and particle swarm optimization. Evolutionary programming VII. Lecture notes in computer science, vol 1447. Springer Berlin, Heidelberg, pp 611–616 Eberhart RC, Shi Y (1998) Comparison between genetic algorithm and particle swarm optimization. Evolutionary programming VII. Lecture notes in computer science, vol 1447. Springer Berlin, Heidelberg, pp 611–616
22.
go back to reference Clerc M, Kennedy J (2002) The particle swarm: explosion, stability, and convergence in a multi-dimensional complex space. IEEE Trans Evol Comput 6(1):58–73CrossRef Clerc M, Kennedy J (2002) The particle swarm: explosion, stability, and convergence in a multi-dimensional complex space. IEEE Trans Evol Comput 6(1):58–73CrossRef
23.
go back to reference Clerc M (1999) The swarm and the queen: towards a deterministic and adaptive particle swarm optimization. Congress on Evolutionary Computation, Washington D.C Clerc M (1999) The swarm and the queen: towards a deterministic and adaptive particle swarm optimization. Congress on Evolutionary Computation, Washington D.C
24.
go back to reference Bratton D, Kennedy J (2007) Defining a standard for particle swarm optimization, IEEE swarm intelligence symposium, Honolulu, Hawaii Bratton D, Kennedy J (2007) Defining a standard for particle swarm optimization, IEEE swarm intelligence symposium, Honolulu, Hawaii
25.
go back to reference Van den Bergh F (2001) An analysis of particle swarm optimizers. Ph.D. diss., University of Pretoria, South Africa Van den Bergh F (2001) An analysis of particle swarm optimizers. Ph.D. diss., University of Pretoria, South Africa
26.
go back to reference Bourgeois L, Chaulet N, Haddar H (2012) On simultaneous identification of the shape and generalized impedance boundary condition in obstacle scattering. SIAM J Sci Comput 34(3):1824–1848CrossRefMathSciNet Bourgeois L, Chaulet N, Haddar H (2012) On simultaneous identification of the shape and generalized impedance boundary condition in obstacle scattering. SIAM J Sci Comput 34(3):1824–1848CrossRefMathSciNet
27.
go back to reference Bin-Mohsin B, Lesnic D (2012) Determination of inner boundaries in modified Helmholtz inverse geometric problems using the method of fundamental solutions. Math Comput Simul 82:1445–1458CrossRefMATHMathSciNet Bin-Mohsin B, Lesnic D (2012) Determination of inner boundaries in modified Helmholtz inverse geometric problems using the method of fundamental solutions. Math Comput Simul 82:1445–1458CrossRefMATHMathSciNet
30.
go back to reference Ma W, Wang M, Zhu X (2013) Improved particle swarm optimization based approach for bilevel programming problem-an application on supply chain model. Int J Mach Learn Cybern. doi:10.1007/s13042-013-0167-3 Ma W, Wang M, Zhu X (2013) Improved particle swarm optimization based approach for bilevel programming problem-an application on supply chain model. Int J Mach Learn Cybern. doi:10.​1007/​s13042-013-0167-3
31.
go back to reference Wang X, He Y, Dong L, Zhao H (2011) Particle swarm optimization for determining fuzzy measures from data. Inf Sci 181(19):4230–4252CrossRefMATH Wang X, He Y, Dong L, Zhao H (2011) Particle swarm optimization for determining fuzzy measures from data. Inf Sci 181(19):4230–4252CrossRefMATH
Metadata
Title
Identification of boundary shape using a hybrid approach
Authors
Na Tian
Longchao Zhu
Choi-Hong Lai
Publication date
01-06-2015
Publisher
Springer Berlin Heidelberg
Published in
International Journal of Machine Learning and Cybernetics / Issue 3/2015
Print ISSN: 1868-8071
Electronic ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-014-0266-9

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