Abstract This contribution presents a general approach for solving structural design problems formulated as a class of nonlinear constrained optimization problems. A Two-Phase approach based on Bayesian model updating is considered for obtaining the optimal designs. Phase I generates samples (designs) uniformly distributed over the feasible design space, while Phase II obtains a set of designs lying in the vicinity of the optimal solution set. The equivalent model updating problem is solved by the transitional Markov chain Monte Carlo method. The proposed constraint-handling approach is direct and does not require special constraint-handling techniques. The population-based stochastic optimization algorithm generates a set of nearly optimal solutions uniformly distributed over the vicinity of the optimal solution set. The set of optimal solutions provides valuable sensitivity information. In addition, the proposed scheme is a useful tool for exploration of complex feasible design spaces. The general approach is applied to an important class of problems. Specifically, reliability-based design optimization of structural dynamical systems under stochastic excitation. Numerical examples are presented to evaluate the effectiveness of the proposed design scheme.

中文翻译：

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用于约束设计优化的一般两阶段马尔可夫链蒙特卡罗方法：应用于随机结构优化

摘要 本文提出了一种解决结构设计问题的通用方法，该问题被表述为一类非线性约束优化问题。考虑基于贝叶斯模型更新的两阶段方法来获得最佳设计。阶段 I 生成均匀分布在可行设计空间上的样本（设计），而阶段 II 获得一组位于最佳解决方案集附近的设计。等效模型更新问题由过渡马尔可夫链蒙特卡罗方法解决。建议的约束处理方法是直接的，不需要特殊的约束处理技术。基于群体的随机优化算法生成一组近乎最优的解，均匀分布在最优解集的附近。这组最佳解决方案提供了宝贵的灵敏度信息。此外，所提出的方案是探索复杂可行设计空间的有用工具。一般方法适用于一类重要的问题。具体而言，随机激励下结构动力系统的基于可靠性的设计优化。数值例子被提出来评估所提出的设计方案的有效性。