【摘要】：不完備概率信息條件下變量聯(lián)合分布函數(shù)的確定及其對結(jié)構(gòu)系統(tǒng)可靠度的影響還缺少系統(tǒng)地研究,該文目的在于研究表征變量間相關(guān)性的Copula函數(shù)對結(jié)構(gòu)系統(tǒng)可靠度的影響規(guī)律。首先,簡要介紹了變量聯(lián)合分布函數(shù)構(gòu)造的Copula函數(shù)方法。其次,提出了并聯(lián)系統(tǒng)失效概率計算方法,并推導(dǎo)了相應(yīng)的計算公式。最后以幾種典型Copula函數(shù)為例研究了Copula函數(shù)類型對結(jié)構(gòu)并聯(lián)系統(tǒng)可靠度的影響規(guī)律。結(jié)果表明:表征變量間相關(guān)性的Copula函數(shù)類型對結(jié)構(gòu)系統(tǒng)可靠度具有明顯的影響,不同Copula函數(shù)計算的系統(tǒng)失效概率存在明顯的差別,這種差別隨構(gòu)件失效概率的減小而增大。當(dāng)并聯(lián)系統(tǒng)的失效區(qū)域位于Copula函數(shù)尾部時,Copula函數(shù)的尾部相關(guān)性對系統(tǒng)可靠度有明顯的影響,計算的失效概率比沒有尾部相關(guān)性的Copula函數(shù)的失效概率大。當(dāng)組成并聯(lián)系統(tǒng)的兩構(gòu)件功能函數(shù)間正相關(guān)時,系統(tǒng)失效概率隨相關(guān)系數(shù)的增大而增加;當(dāng)構(gòu)件功能函數(shù)間負相關(guān)時,系統(tǒng)失效概率隨相關(guān)系數(shù)的增大而減小。此外,無論構(gòu)件失效概率和變量間相關(guān)系數(shù)如何變化,Copula函數(shù)計算的失效概率都位于系統(tǒng)失效概率的上下限內(nèi)。
[Abstract]:Under the condition of incomplete probability information, the determination of joint distribution function of variables and its influence on the reliability of structural systems are not systematically studied. The purpose of this paper is to study the influence of Copula function, which characterizes the correlation between variables, on the reliability of structural systems. Firstly, the Copula function method of joint distribution function is introduced briefly. Secondly, the failure probability calculation method of parallel system is proposed, and the corresponding formula is deduced. Finally, several typical Copula functions are taken as examples to study the influence of Copula function types on the reliability of parallel structure systems. The results show that the type of Copula function, which characterizes the correlation between variables, has an obvious influence on the reliability of structural system, and the system failure probability calculated by different Copula functions has obvious differences, and the difference increases with the decrease of failure probability of components. When the failure region of the parallel system is located at the tail of the Copula function, the tail correlation of the Copula function has an obvious effect on the reliability of the system, and the calculated failure probability is larger than that of the Copula function without the tail correlation. The failure probability of the system increases with the increase of the correlation coefficient, and decreases with the increase of the correlation coefficient when the functional functions of the two components of the parallel system are positively correlated with each other. In addition, the failure probability calculated by the Copula function is within the upper and lower limits of the failure probability of the system, regardless of the variation of the component failure probability and the correlation coefficient between variables.
【作者單位】： 武漢大學(xué)水資源與水電工程科學(xué)國家重點實驗室;武漢大學(xué)水工巖石力學(xué)教育部重點實驗室;新加坡國立大學(xué)土木與環(huán)境工程系;
【基金】：國家杰出青年科學(xué)基金項目(51225903) 國家自然科學(xué)基金項目(51329901) 高等學(xué)校博士學(xué)科點專項科研基金項目(20120141110009)
【分類號】：TU312.3

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