Identification of boundary shape using a hybrid approach
- PDF / 699,952 Bytes
- 13 Pages / 595.276 x 790.866 pts Page_size
- 69 Downloads / 209 Views
ORIGINAL ARTICLE
Identification of boundary shape using a hybrid approach Na Tian • Longchao Zhu • Choi-Hong Lai
Received: 12 April 2013 / Accepted: 4 May 2014 Ó Springer-Verlag Berlin Heidelberg 2014
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. Keywords Boundary element method Shape identification Quantum-behaved particle swarm optimization Tikhonov regularization Hybrid approach
N. Tian (&) Department of Educational Technology, Jiangnan University, Wuxi 214122, China e-mail: [email protected] L. Zhu Department of Information Technology, China Ship Science Research Center, Wuxi 214082, China C.-H. Lai School of Computing and Mathematical Sciences, The University of Greenwich, London SE10 9LS, UK
1 Introduction Shape identification problems are inverse problems of estimating the unknown part boundary of the domain, which arise in many branches of science and engineering [1]. The applications in structure mechanics and fluid mechanics are important in the industrial design, such as non-destructive evaluation and design optimization of airplanes, ships and engines [2]. Shape identification for elliptic and parabolic systems has been studied from the aspects of theory and numeric [2, 3]. In [26], the simultaneous identification of the boundary shape and boundary condition in obstacle scattering problems is addressed. The inner boundary identification by the method of fundamental solution is introduced in [27]. In this paper, an inverse steady heat conduction problem of estimating the shape of a part of the boundary from the measured boundary temperature is investigated. Developed methods of such identification problems can be used of material loss defect determination [4], electromagnetic crack detection [5] and corrosion detection [6, 7]. Such problems are nonlinear and ill-posed, which require special techniques in order to be accurately and stably solved numerically. In [8], Nachaoui estimated the boundary shape using the conjugate gradient method (CGM). Mera used genetic algorithm (GA) to solve the boundary detection problem in [9], which requires the information of the functional form of the boundary shape. In [10, 11], the inclusion detecti
Data Loading...
