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A new look at the response surface method for reliability analysis using chaos theory

Ding Youliang, Li Aiqun and Deng Yang

College of Civil Engineering, Southeast University, Nanjing 210096, China

Abstract: To overcome excessive computation errors and convergence failures encountered in an iterative calculation of the reliability index using the response surface method (RSM) for some nonlinear limit state functions, this study investigates an essential factor based on chaotic dynamics theory. The bifurcation diagrams of the reliability index are presented for some typical nonlinear limit state functions, and the computation results from the mapping functions due to the RSM iterations show the complicated dynamic phenomena such as the periodic oscillation, as well as bifurcation and chaos. From the numerical examples, it is concluded that the parameter of selection range f plays an important role in the convergence of the RSM iteration, and an improved RSM iterative algorithm is proposed with regard to the incorporation of the iterative sequential function of selection range f. The proposed method is shown to be efficient and to yield accurate results.

Keywords: structural reliability; response surface method; chaotic dynamics; convergence failure; selection range; nonlinearity

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Copyright© 2009 IEM. Journal of Earthquake Engineering and Engineering Vibration. All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as described below, without written permission from the Publisher. Copying of articles is not permitted except for personal and internal use, to the extent permitted by national copyright law, or under the terms of a license issued by the National Reproduction Rights Organization of China.