Single-loop system reliability-based topology optimization considering statistical dependence between limit-states |
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Authors: | Tam H Nguyen Junho Song Glaucio H Paulino |
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Affiliation: | (1) Dept. of Civil and Environmental Engineering, Univ. of Illinois, Urbana, IL 61801, USA |
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Abstract: | This paper presents a single-loop algorithm for system reliability-based topology optimization (SRBTO) that can account for
statistical dependence between multiple limit-states, and its applications to computationally demanding topology optimization
(TO) problems. A single-loop reliability-based design optimization (RBDO) algorithm replaces the inner-loop iterations to
evaluate probabilistic constraints by a non-iterative approximation. The proposed single-loop SRBTO algorithm accounts for
the statistical dependence between the limit-states by using the matrix-based system reliability (MSR) method to compute the
system failure probability and its parameter sensitivities. The SRBTO/MSR approach is applicable to general system events
including series, parallel, cut-set and link-set systems and provides the gradients of the system failure probability to facilitate
gradient-based optimization. In most RBTO applications, probabilistic constraints are evaluated by use of the first-order
reliability method for efficiency. In order to improve the accuracy of the reliability calculations for RBDO or RBTO problems
with high nonlinearity, we introduce a new single-loop RBDO scheme utilizing the second-order reliability method and implement
it to the proposed SRBTO algorithm. Moreover, in order to overcome challenges in applying the proposed algorithm to computationally
demanding topology optimization problems, we utilize the multiresolution topology optimization (MTOP) method, which achieves
computational efficiency in topology optimization by assigning different levels of resolutions to three meshes representing
finite element analysis, design variables and material density distribution respectively. The paper provides numerical examples
of two- and three-dimensional topology optimization problems to demonstrate the proposed SRBTO algorithm and its applications.
The optimal topologies from deterministic, component and system RBTOs are compared with one another to investigate the impact
of optimization schemes on final topologies. Monte Carlo simulations are also performed to verify the accuracy of the failure
probabilities computed by the proposed approach. |
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