Adaptive alternating Lipschitz search method for structural analysis with unknown-but-bounded uncertainties |
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| Institution: | 1. Institute of Solid Mechanics, School of Aeronautic Science and Engineering, Beihang University, Beijing 100083, China;2. Shenyuan Honors College, Beihang University, Beijing 100083, China;1. School of Naval Architecture, Ocean and Civil Engineering (State Key Laboratory of Ocean Engineering), Shanghai Jiaotong University, Shanghai 200240, China;2. Departments of Civil and Environmental Engineering, Mechanical Engineering, and Materials Science and Engineering, Northwestern University, Evanston, IL 60208, USA;3. AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China;1. Key Laboratory of Electronic Equipment Structure Design, Ministry of Education, Xidian University, P.O. Box 187, Xi''an 710071, PR China;2. Xi''an Microelectronics Technology Institute, The Ninth Academy of China Aerospace Science and Technology Corporation, P.O. Box 187, Xi''an 710119, PR China;3. Institute of Continuum Mechanics, Leibniz Universität Hannover, 30167 Hannover, Germany;4. Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW 2052, Australia;1. Laboratory of Nano- and Microfluidics and Microsystems - LabMEMS, Mechanical Engineering Department and Nanoengineering Department, POLI & COPPE and Interdisciplinary Nucleus for Social Development - NIDES/CT, Universidade Federal do Rio de Janeiro, Cidade Universitária, Cx. Postal 68503, Rio de Janeiro, RJ CEP 21945-970, Brazil;2. General Directorate of Nuclear and Technological Development - DGDNTM, Brazilian Navy, Rio de Janeiro, RJ, Brazil |
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| Abstract: | Multisource uncertainties, including property dispersibility of materials and fluctuating service environments, complicate structural design and reliability assessment. In this paper, a novel method named the adaptive alternating Lipschitz search method for structural analysis with unknown-but-bounded uncertainties (or interval uncertainties) is proposed. In contrast to traditional optimization methods that search twice to obtain response bounds, an adaptive alternate iteration strategy is proposed. By sampling step by step, two acquisition functions—named the Lipschitz upper bound and the Lipschitz lower bound—are defined. Structural response bounds can be simultaneously obtained by alternately optimizing the two acquisition functions. The parameter settings do not require adjustments for different types of problems. Additionally, the Bayesian Adaptive Direct Search method is adopted to improve the performance of the strategy. Numerical and experimental cases are presented to demonstrate the validity, accuracy, and efficiency of the proposed methodology. Detailed comparisons indicate that the proposed method is competitive when addressing complicated structural systems with different ranges of uncertainty. |
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