基于经验频率分布的偏态概率模型可靠度计算方法研究  

Research on reliability calculation method of skew probability model based on empirical frequency distribution

作　　者：冉志红 董国华 杨子富 林帆 RAN Zhihong;DONG Guohua;YANG Zifu;LIN Fan(School of Architecture and Planning,Yunnan University,Kunming 650091,China)

机构地区：[1]云南大学建筑与规划学院,云南昆明650091

出　　处：《四川建筑科学研究》2024年第1期52-59,共8页Sichuan Building Science

基　　金：国家自然科学基金项目(51968074)。

摘　　要：在既有结构可靠度计算中,经验频率分布较容易通过简单的序列计算得到。利用经验频率分布回归得到的正态概率模型或偏态概率模型可以计算相关统计参数、失效概率和可靠指标。大量的计算和比较分析得出,偏态概率模型在工程实践中具有更好的适应性。数值计算结果也进一步表明,用正态分布进行近似,其可靠指标的误差较大,甚至会影响既有结构的评估结果。提出了基于Azzalini偏态分布函数的参数估计方法,并利用失效概率作为联系纽带,建立了偏态分布下失效概率与可靠指标之间的函数关系。以某较为复杂的功能函数为例,展示了所提出的基于经验频率分布的偏态概率模型可靠度计算方法,该方法具有步骤清晰、目标明确、精度较高的优点,能够适用于更加广泛的实际既有工程结构可靠度的评估。In the reliability calculation of existing structures,the empirical frequency distribution can be easily obtained by simple sequence calculation.By using the normal probability model or skew probability model obtained by empirical frequency distribution regression,the relevant statistical parameters,failure probability and reliability index can be calculated.Through a large number of calculations and comparative analysis,the skew probability model has better adaptability in engineering practice,and the numerical calculation results further show that the approximation with the normal distribution will lead to a large error in the reliability index,and even affect the evaluation results of existing structures.A parameter estimation method based on Azzalini skew distribution function was proposed,and the functional relationship between failure probability and reliability index under skew distribution was established by using failure probability as a link.Taking a complex functional function as an example,it is shown that the reliability calculation method based on empirical frequency distribution for skew probability model proposed in this paper has the advantages of clear calculation steps,clear calculation objectives and high calculation accuracy,and can be applied to the reliability evaluation of existing engineering structures.

关 键 词：工程结构可靠度 经验频率分布 偏态概率模型 既有结构评估 

分 类 号：TP114.3[自动化与计算机技术—控制理论与控制工程]