基于贝叶斯可信可靠性的安全系数量化方法
A SAFETY FACTOR QUANTIFICATION METHOD BASED ON BAYESIAN CREDIBLE RELIABILITY
-
摘要: 针对航空航天结构设计中传统经验安全系数取值过于保守、缺乏科学量化依据的问题, 提出了一种基于贝叶斯可信可靠性的安全系数量化方法. 首先建立了安全系数量化的解析框架, 将安全系数与概率模型中的可靠度相联系. 在此基础上, 推导非概率模型中安全系数与可靠度的映射关系, 据此在安全系数与应力分布参数平面上构建量化方法. 随后基于贝叶斯理论对结构应力和强度进行可信建模, 通过设置先验分布并进行后验更新, 获得不同可信度水平下的不确定性区间, 并用于非概率可信可靠度计算. 利用实际样本数据, 可动态更新不确定性模型参数, 并同步更新安全系数, 由此形成一种动态的安全系数量化方案. 最后利用典型杆和机翼结构的数值算例验证了所提方法在工程问题中的适用性. 文中讨论了可信可靠度指标和样本数量对安全系数选取的影响, 并揭示了可信可靠性方法在结构减重方面的有效性. 结果表明, 该方法能够有效克服传统经验安全系数的保守性问题, 为航空航天领域先进结构的轻量化设计提供新的依据和指导.Abstract: To address the issues of overly conservative and insufficiently quantified safety factor selection grounded in traditional experience in aerospace structural design, this paper proposes a safety factor quantification method based on Bayesian credible reliability. Building on the analytical framework that relates safety factors to reliability in probabilistic models, the mapping between safety factors and reliability is derived for non-probabilistic models, thereby establishing a safety factor quantification method on the plane of safety factor versus stress distribution parameters. According to Bayesian theory, credible modeling is performed for structural stress and material strength. By specifying prior distributions and incorporating Bayesian posterior updating, uncertainty intervals at different credibility levels are obtained and employed to compute non-probabilistic credible reliability. Furthermore, the uncertainty model parameters are dynamically updated utilizing actual sample data to subsequently calibrate safety factors, thereby establishing a dynamic quantification method for safety factors. Numerical case studies of a typical rod and a wing structure systematically validate the engineering applicability of the proposed method, and discuss the influence of credible reliability indicators and sample size on safety factor selection in structural design, revealing the effectiveness of the credible reliability method in structural weight reduction. The numerical results demonstrate that the proposed method can effectively mitigate the conservatism of traditional experience-based safety factors, offering new foundations and guidance for the lightweight design of advanced structures in the aerospace field.
下载: