A sequential approximate programming strategy for reliability-based structural optimization
Although reliability-based structural optimization (RBSO) is recognized as a rational structural design philosophy that is more advantageous to deterministic optimization, most common RBSO is based on straightforward two-level approach connecting algorithms of reliability calculation and that of des...
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| Published in: | Computers & structures Vol. 84; no. 21; pp. 1353 - 1367 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Oxford
Elsevier Ltd
01.08.2006
Elsevier Science |
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| ISSN: | 0045-7949, 1879-2243 |
| Online Access: | Get full text |
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| Abstract | Although reliability-based structural optimization (RBSO) is recognized as a rational structural design philosophy that is more advantageous to deterministic optimization, most common RBSO is based on straightforward two-level approach connecting algorithms of reliability calculation and that of design optimization. This is achieved usually with an outer loop for optimization of design variables and an inner loop for reliability analysis. A number of algorithms have been proposed to reduce the computational cost of such optimizations, such as performance measure approach, semi-infinite programming, and mono-level approach. Herein the sequential approximate programming approach, which is well known in structural optimization, is extended as an efficient methodology to solve RBSO problems. In this approach, the optimum design is obtained by solving a sequence of sub-programming problems that usually consist of an approximate objective function subjected to a set of approximate constraint functions. In each sub-programming, rather than direct Taylor expansion of reliability constraints, a new formulation is introduced for approximate reliability constraints at the current design point and its linearization. The approximate reliability index and its sensitivity are obtained from a recurrence formula based on the optimality conditions for the most probable failure point (MPP). It is shown that the approximate MPP, a key component of RBSO problems, is concurrently improved during each sub-programming solution step. Through analytical models and comparative studies over complex examples, it is illustrated that our approach is efficient and that a linearized reliability index is a good approximation of the accurate reliability index. These unique features and the concurrent convergence of design optimization and reliability calculation are demonstrated with several numerical examples. |
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| AbstractList | Although reliability-based structural optimization (RBSO) is recognized as a rational structural design philosophy that is more advantageous to deterministic optimization, most common RBSO is based on straightforward two-level approach connecting algorithms of reliability calculation and that of design optimization. This is achieved usually with an outer loop for optimization of design variables and an inner loop for reliability analysis. A number of algorithms have been proposed to reduce the computational cost of such optimizations, such as performance measure approach, semi-infinite programming, and mono-level approach. Herein the sequential approximate programming approach, which is well known in structural optimization, is extended as an efficient methodology to solve RBSO problems. In this approach, the optimum design is obtained by solving a sequence of sub-programming problems that usually consist of an approximate objective function subjected to a set of approximate constraint functions. In each sub-programming, rather than direct Taylor expansion of reliability constraints, a new formulation is introduced for approximate reliability constraints at the current design point and its linearization. The approximate reliability index and its sensitivity are obtained from a recurrence formula based on the optimality conditions for the most probable failure point (MPP). It is shown that the approximate MPP, a key component of RBSO problems, is concurrently improved during each sub-programming solution step. Through analytical models and comparative studies over complex examples, it is illustrated that our approach is efficient and that a linearized reliability index is a good approximation of the accurate reliability index. These unique features and the concurrent convergence of design optimization and reliability calculation are demonstrated with several numerical examples. |
| Author | Xu, Lin Jiang, Lei Cheng, Gengdong |
| Author_xml | – sequence: 1 givenname: Gengdong surname: Cheng fullname: Cheng, Gengdong email: chenggd@dlut.edu.cn organization: State Key Laboratory for Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116023, China – sequence: 2 givenname: Lin surname: Xu fullname: Xu, Lin organization: State Key Laboratory for Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116023, China – sequence: 3 givenname: Lei surname: Jiang fullname: Jiang, Lei organization: Design Technology and Solutions, Intel Corporation RA3-254, 2501 NW 229th Avenue, Hillsboro, OR 97124, USA |
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| Keywords | Accurate reliability index Approximate reliability index Reliability-based structural optimization Concurrent convergence Computational efficiency Sequential approximate programming Recurrence Rupture Structural reliability Taylor series Modeling Optimization Sequential method Series expansion Optimality criterion Deterministic approach Structural analysis Linearization |
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| SubjectTerms | Accurate reliability index Approximate reliability index Computational efficiency Computational techniques Concurrent convergence Exact sciences and technology Fracture mechanics (crack, fatigue, damage...) Fundamental areas of phenomenology (including applications) Mathematical methods in physics Physics Reliability-based structural optimization Sequential approximate programming Solid mechanics Static elasticity (thermoelasticity...) Structural and continuum mechanics |
| Title | A sequential approximate programming strategy for reliability-based structural optimization |
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