摘要
工程结构中存在大量的不确定因素，如外部荷载、结构尺寸、材料参数等，可靠度优化（RBDO）可以充分考虑不确定因素对结构性能的影响，合理平衡产品性能和产品可靠度之间的关系。常用的可靠度优化求解方法有双循环法、单循环法和解耦法。序列优化与可靠度评定法（SORA）具有较高的求解效率和稳定性，成为应用最广泛的解耦算法之一。然而，基于最小性能目标点（MPTP）解耦的SORA法不能避免一次二阶矩（FORM）带来的近似误差，并且SORA法使用失效面平移近似替代真实可靠度边界，会降低SORA法的计算精度和稳定性，导致SORA法在求解复杂功能函数可靠度优化问题时性能表现不佳。
为了克服基于MPTP点算法的内在缺陷，本文采用分位点代替MPTP点进行解耦，提出了基于分位点移动的解耦法。该方法在概率空间基于分位点对RBDO问题进行解耦，采用蒙特卡洛法（MCS）计算分位点，不需要计算MPTP点，避免了FORM近似误差。为使该方法可以应用于实际工程问题，对目标函数和功能函数建立Kriging代理模型，并采用了高效的样本点更新策略，使样本点较大概率的分布在利于RBDO求解的区域，样本点利用率高，代理模型准确。
传统的SORA法使用近似边界替代真实的可靠度边界，当近似边界误差较大时，就会导致SORA法提前收敛或振荡，本文通过对近似边界进行修正，提出了基于共轭惩罚边界的SORA法。由于SORA法采用失效面平移近似替代真实可靠度约束，会引入多余区域进入可行域内或丢失一部分可行域，本文通过保存所有
迭代步的可靠度信息和边界惩罚，将多余可行域剔除，将丢失的区域拉入可行域内，避免了由于近似边界误差导致的SORA法振荡和提前收敛问题，提高了SORA法的整体性能。
对于一些复杂功能函数，MPTP点随均值变化规律性较差，使得基于MPTP点解耦的SORA法性能不佳，本文提出了基于共轭惩罚边界的分位点移动解耦法。该方法使用在概率空间变化相对缓和连续的分位点代替MPTP点进行解耦，并对近似边界进行修正，提高了解耦法求解复杂功能函数的能力。
关键词：可靠度优化；解耦法；序列优化与可靠度评定；分位点；边界修正；Kriging 代理模型
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Decoupled Methods for Reliability-Based Design Optimization based on
Quantiles and Boundary Penalty
Abstract
There are a lot of uncertainties in practical engineering, such as external load, structural size, material properties, etc. Reliability-based design optimization (RBDO) considers the influence of uncertainties on structural performance, which can balance the relationship between structural performance and str
uctural reliability properly. The problems of RBDO can generally be solved by double-loop methods, single-loop methods or decoupled methods. The sequence optimization and reliability assessment method (SORA) is a widely used decoupled method due to its good efficiency and stability. However most research on SORA is based on minimum performance target point (MPTP) , which may cause the unavoidable error of the first order reliability methods (FORM). Moreover, SORA uses the failure surface to replace the true reliability boundary, and this approximation will reduce accuracy and stability of SORA. As a result, SORA has poor performance in solving RBDO with complex performance functions. To overcome the intrinsic shortcomings of MPTP based methods, this paper presents a new decoupled method based on quantiles instead of MPTP, which decouples RBDO in probability space using quantiles. Quantiles are obtained by Monte Carlo Method (MCS) without using MPTPs which can avoid the approximate error of FORM. In order to apply this method to practical engineer problems, the objective function and constraint functions are replaced by Kriging models. The efficient sample point updating strategies are adopted to make the sample points distribute in the region significant for solving RBDO problems, and the sample point utilization is high and Kriging model is accurate.
The conventional SORA uses approximate boundaries to replace real reliability constraints, which may
lead to convergence premature or oscillation of SORA when the approximate boundary error is large. This paper proposes a conjugate boundary penalty based SORA method to modified approximate boundaries. The approximate boundary may cause superfluous area or missing area of the feasible region. This paper adopts the whole reliability information technology and boundary penalty strategies to modify these two kinds of areas to improve the performance of SORA.
For complex performance functions, MPTP has a poor relation with the mean values of random variables, which causes the MPTP-based methods have a bad robustness. In this paper, the conjugate boundary penalty based decoupled method using quantiles is proposed. The quantile, which is more stable and continuous than MPTP, is used to decouple RBDO.
And the boundary penalty strategies are also used to modified the approximate boundaries. The modified decoupled method using quantiles can solve RBDO problems with multiple design points and complex performance functions efficiently and accurately.
Key Words：Reliability-based Optimization Design, Decoupled Method; Sequential Optimization and Reliability Assessment, Quantile; Boundary Penalty; Kriging Model
目录
摘要............................................................................................................................. I Abstract ............................................................................................................................. II 1 绪论 (1)
1.1 研究背景与意义 (1)
1.2 国内外研究进展 (2)
1.2.1 结构可靠度分析 (2)
1.2.2 结构可靠度优化 (5)
1.2.3 代理模型 (6)
1.3 本文主要研究内容 (7)
2 可靠度优化理论与Kriging代理模型 (9)
2.1 Monte Carlo模拟法 (9)
2.2 逆可靠度分析方法 (10)
2.3 序列优化与可靠度评定法（SORA） (13)
2.4 Kriging代理模型 (15)
2.5 小结 (16)
3 基于分位点移动的可靠度优化解耦法 (17)
trunc函数怎么切除小数点后几位
3.1 概率空间中基于分位点的解耦法 (17)
3.2 基于MCS和RBDO问题的Kriging样本点更新策略 (20)
3.3 算例分析 (22)
3.3.1 高非线性可靠度优化算例 (23)
3.3.2 高非线性多MPTP点可靠度优化问题 (25)
3.3.3 减速器可靠度优化算例 (27)
3.3.4 开孔曲筋板可靠度优化算例 (29)
3.4 小结 (31)
4 基于共轭惩罚边界的SORA法 (33)
4.1 解耦法近似边界分析 (33)
4.1.1 近似可行域扩大 (34)
4.1.2 近似可行域缩小 (36)
4.2 基于共轭惩罚边界的SORA法 (37)
4.2.1 保存全部可靠度信息技术 (38)
4.2.2 边界惩罚技术 (39)
4.3 算例分析 (41)
4.3.1 线性约束可靠度优化算例 (42)
4.3.2 高非线性可靠度优化算例 (43)
4.3.3 三杆桁架可靠度优化算例 (45)
4.3.4 减速器可靠度优化算例 (47)
4.4 小结 (49)
5 基于共轭惩罚边界的分位点移动解耦法 (51)
5.1 基于共轭惩罚边界的分位点移动解耦法 (51)
5.2 算例分析 (53)
5.2.1 多设计点可靠度优化算例1 (53)
5.2.2 多设计点可靠度优化算例2 (55)
5.2.3 MPTP变化剧烈可靠度优化算例 (56)
5.3 小结 (58)
结论 (59)
参考文献 (60)
攻读硕士学位期间发表学术论文情况 (65)
致谢 (66)
大连理工大学学位论文版权使用授权书 (67)

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