【摘要】：現(xiàn)有的不確定性傳播分析方法大都假設(shè)各輸入變量相互獨立,然而實際工程中,很多變量間具有相關(guān)性,特別是多維相關(guān)性問題廣泛存在實際工程中.為此,本文提出了一種基于vine copula函數(shù)的結(jié)構(gòu)不確定性傳播分析方法,為復(fù)雜多維相關(guān)問題的不確定性傳播分析提供了一種有效工具.首先,根據(jù)隨機變量的樣本由vine copula構(gòu)造輸入變量的聯(lián)合概率密度函數(shù);其次,先由Rosenblatt變換將相關(guān)變量轉(zhuǎn)換成獨立變量,再由降維積分法計算響應(yīng)的前四階原點矩;最后,由最大熵原理計算響應(yīng)的概率密度函數(shù).算例分析表明,本文方法在計算精度和計算效率方面具有較好的綜合性能,能夠用于變量間具有相關(guān)性的復(fù)雜工程問題的不確定性傳播分析.
[Abstract]:Most of the existing methods of uncertainty propagation analysis assume that the input variables are independent of each other. However, in practical engineering, many variables have correlation, especially the multi-dimensional correlation problem exists widely in practical engineering. Therefore, this paper presents a structural uncertainty propagation analysis method based on vine copula function, which provides an effective tool for the uncertainty propagation analysis of complex multi-dimension related problems. Firstly, the joint probability density function of input variable is constructed by vine copula according to the sample of random variable. Secondly, the correlation variable is transformed into independent variable by Rosenblatt transform, and then the first four order origin moments of response are calculated by dimension reduction integration method. The probability density function of the response is calculated by the maximum entropy principle. The numerical examples show that the proposed method has better comprehensive performance in terms of computational accuracy and efficiency, and can be used to analyze the uncertainty propagation of complex engineering problems with correlation among variables.
【作者單位】： 湖南大學(xué)機械與運載工程學(xué)院汽車車身先進設(shè)計制造國家重點實驗室;中航工業(yè)貴陽萬江航空機電有限公司;
【基金】：國家自然科學(xué)基金重大項目(批準(zhǔn)號:51490662);國家自然科學(xué)基金重點項目(批準(zhǔn)號:11232004)資助 國家重點研發(fā)計劃項目(批準(zhǔn)號:2016YFD0701105)
【分類號】：O211
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本文編號：2147762