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摘要:
针对传统结构可靠性试验的验证多是基于载荷应力和结构强度相互独立的假设问题，从应力和强度数据的相关性分析与度量出发，在二者均为正态随机变量的前提下，建立了一种基于Copula函数相关应力-强度干涉模型的结构可靠性加严试验验证方案设计方法。该方法结合Copula函数和应力-强度干涉模型实现相关条件下原可靠性指标与加严条件下可靠性指标的转化，适用于小样本情况下基于传统成败型试验方法评估其可靠性。研究结果表明：相比独立假设，应力和强度呈负相关时，会增加试验样本量且样本量随负相关程度减弱而减少；呈正相关时，会减少试验样本量且样本量随正相关程度增强而减少。
Abstract:The traditional test verification of structural reliability is generally based on the independence assumption between loading stress and structural strength. Stating with the correlation analysis of stress and strength, we propose a hardened test method of structural reliability verification based on the stress-strength interference model with Copula correlation when loading and strength both follow the normal distribution. The method combines Copula functions with stress-strength interference model to achieve the transformation of the original reliability index and reliability index under the hardened condition, and the reliability is estimated by the traditional binomial distribution test under the condition of small sample. Compared with the independence assumption, the results show that the negative correlation between stress and strength leads to the increase of sample size and the sample size decreases with the decrease of negative correlation; the positive correlation leads to the decrease of sample size and the sample size decreases with the increase of positive correlation.
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图 1 不同θ下可靠度-生存系数变化
Figure 1. Variation of reliability-survival coefficient with different θ
图 2 试验样本量与相关程度参数的关系
Figure 2. Relationship between test sample size and correlation coefficient
表 1 独立与相关情况下试验样本量的比较
Table 1. Comparison of test sample size between independent and correlative conditions
k RL=0.998 RL=0.996 RL=0.994 相关 独立 相关 独立 相关 独立 1.2 97 64 57 39 41 29 1.3 39 24 24 16 18 13 1.4 19 11 13 8 10 7 1.5 10 6 7 5 6 4 
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