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A constraints-shifting sequential method for reliability-based design optimization of engineering structures
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DOI：10.1007/s00158-026-04405-8.png)
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Abstract
En 中文
Reliability-based design optimization (RBDO) remains challenging in engineering applications due to its prohibitive computational cost. This paper proposes a constraints-shifting sequential method (CSS) to efficiently decouple RBDO into a series of reliability assessment and optimization processes. In CSS, the constraints are iteratively shifted to reduce the feasible region by the corresponding shifting vectors. The computation of shifting vectors avoids the inverse most probable point (MPP) solving process, as they are determined directly from samples near the real limit state functions (LSFs) and the standard deviations of the input random variables. In each cycle, Genetic Algorithm (GA) is used to search for the optimal solution in reduced feasible region, and the failure probabilities of probabilistic constraints are estimated at current optimal solution. The shifting operations proceed iteratively on unsatisfied probabilistic constraints until all constraints are satisfied and the RBDO solution is reached. To alleviate the computational burden, polynomial chaos expansion (PCE) is used to approximate the objective function and LSFs. A local variation function (LVF) is developed to refine the PCE models of LSFs, while the PCE model of objective is updated by the historical optimal solutions. The performance of the proposed CSS is demonstrated through four examples of varying complexity, including a high‑dimensional problem and a real‑world engineering application, where its accuracy and computational efficiency are compared against existing RBDO methods.
Keywords:
Reliability-based design optimization
Constraints-shifting
Sequential scheme
Adaptive PCE
Genetic algorithm
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