随机动力荷载激励下建筑结构的基于可靠度优化设计

The research focuses on reliability-based optimal design of structures subjected to stochatic dynamic loadings, where the uncertainties in external dynamic loading and structural properties are both considered.The topics that will be fully investigated include:(1)reliability analysis of linear strctures considering uncertainties in structural properties and external dynamic loadings. (2)application of two global optimization algorithms, simulated annealing and subset simulation, in reliability-based optimal design of strcuturs subjected to stochastic dynamic loadings.In simulated annealing,the optimiazation problem is converted into the problem of populating a suitable constrcuted probability density function,which has the largest value at the globla optial design.In subset simulation,the optimization problem is translated into the problem of sampling uniform distribution in a sequence of nested subsets (in the space of design variables), which gradually shrink to the region around the global optimal design.(3)compuation cost reduction in reliability-based optimal design. To reduce the computational cost and enhance the compuational efficiency of the reliability-based optimization algorithm, the idea of 'mininum computational cost' is examined. It is noted that the purpose of reliability analysis in reliability-based optimal design is to provide a reliable judgement on the reliability constraint, i.e., the relationship between the failure probability at the examined design and the failure probability threshold. Besides, a range can be specified so that it has high probability of containing the actual value of the failure probability at the examined design, based on the estimators for the failure probability and its coefficient of vairation. With the above two observations, the 'minimum' computational cost is defined such that the corresponding range excludes the failure probability threshold, which means that the judgement on the reliability constraint can be made plausibly.

项目的研究对象为随机动力荷载激励下建筑结构的基于可靠度优化设计。研究内容包括：(1) 线性结构系统的可靠度分析。其中的不确定性来源综合考虑外界随机动力荷载和结构模型参数失真；(2)模拟退火算法及子空间模拟法在研究对象中的应用及比较。作为全局优化方法，模拟退火优化算法将优化问题转化为根据构造的概率密度函数进行随机取样的问题，而子空间模拟法将优化问题转化为在一系列逐渐收缩且靠近全局最优解的空间区域中随机取样的问题。项目通计划通过计算实例应用，比较两种方法在涉及设计变量较多情况下的性能。(3)基于可靠度的优化设计中计算成本的控制研究。为降低计算成本，提高优化设计的计算效率，项目计划考察"极大可能区间"的思想：即根据可靠度分析估计的安全失效概率及其变异系数，估计备选设计对应安全失效概率所在的极大可能区间。针对备选设计进行的可靠度分析所需的最低计算成本需使容许安全失效概率在其提供的极大可能区间之外。

项目针对随机动力荷载激励下建筑结构的基于可靠度优化设计进行研究。建筑结构的基于可靠度优化设计，提供了一种兼顾结构可靠性和经济合理性的科学的设计方法。其一方面将概率论和数理统计理论引入结构设计，利用可靠度或失效概率，科学和定量地衡量结构性能指标得到保证的可靠程度；另一方面力求以最低费用满足结构的性能要求，以实现最佳的社会经济效益。.项目的研究成果主要有：（1）针对随机动力荷载激励下线性结构系统的基于可靠度优化设计，提出了基于过渡马尔可夫链蒙特卡罗方法的全局优化算法。通过在满足所有约束条件的决策变量的可行域上构造合适的概率密度函数，原始的优化问题可转变为根据构造的概率密度函数取样的问题。研究采用过渡马尔可夫链蒙特卡罗方法解决取样问题，以确保马尔可夫链的状态点的稳态概率分布较快地到达要求的概率分布。同时，研究采用区域分解法来估计备选决策变量的可靠度，以检验其是否满足可靠度约束条件，即其对应的失效概率是否小于要求的限值。为提高优化算法的计算效率，研究提出“最小计算成本”的概念，即针对备选决策变量的可靠度分析的计算成本，只需确保可靠度约束条件的检验结果可靠即可。提出的基于可靠度优化设计算法通过实例验证，具备较好的性能。（2）针对随机风荷载激励下线性结构系统的首次穿越可靠度问题，提出了高效数值模拟算法。研究从该可靠度问题对应的失效区域的几何分析入手，发现整体失效区域可由一系列高维二次基本失效区域的并集表示，且基本失效区域间存在旋转对称性。同时，基于梯度投影法，提出了高维二次基本失效区域设计点的求解算法，并以此改进了之前提出的针对首次穿越可靠度问题的数值模拟算法。改进的数值模拟算法的精度和提高的计算效率，通过实例得到了验证。