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  本文關(guān)鍵詞：結(jié)構(gòu)不確定分析中的全局及區(qū)域靈敏度研究　出處：《西北工業(yè)大學(xué)》2016年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 全局靈敏度分析 區(qū)域靈敏度分析 解析解 相關(guān)變量 概率盒 擴展Monte Carlo法 隨機森林 廣義方差

【摘要】：各類廣泛存在的不確定性影響著飛機結(jié)構(gòu)系統(tǒng)的性能,因此研究這些不確定性如何影響輸出性能對于提高飛機結(jié)構(gòu)產(chǎn)品質(zhì)量、簡化模型以及減小決策失誤率都有重要意義。本文圍繞結(jié)構(gòu)不確定分析中的全局及區(qū)域靈敏度理論展開研究工作,主要內(nèi)容如下:1.對輸入變量相關(guān)情況下全局靈敏度指標之間的關(guān)系進行探究比較,為輸入變量相關(guān)情況下的輸出性能設(shè)計提供指導(dǎo)。首先以不含交叉項和包含交叉項的二次多項式輸出模型為例,解析推導(dǎo)了相關(guān)正態(tài)輸入變量情況下基于協(xié)方差分解的全局靈敏度指標,包括總貢獻、結(jié)構(gòu)貢獻和相關(guān)貢獻。然后,理論推導(dǎo)了傳統(tǒng)基于方差的指標與基于協(xié)方差分解的全局靈敏度指標之間的關(guān)系,從特殊二次多項式模型的研究結(jié)果對一般模型做出推斷,并從高維模型分解的角度對所推斷的結(jié)論進行了驗證,最后詳細討論了不同靈敏度指標的優(yōu)缺點�；谒茖�(dǎo)的解析結(jié)論進行變量相關(guān)情況下的參數(shù)影響分析,并結(jié)合機翼三盒段等具體算例驗證了所得結(jié)論。2.建立了輸入變量的不確定性為概率盒描述時的全局靈敏度指標,并提出了相應(yīng)的擴展Monte Carlo高效求解算法。在所建立的指標中以主指標下界和總指標上界作為概率盒描述輸入變量不確定性時的全局靈敏度指標,提供了一種非精確概率描述時全局靈敏度分析的新思路。所發(fā)展的求解方法通過抽取合適的樣本顯式表達出靈敏度指標與分布參數(shù)的函數(shù)關(guān)系,進而將雙層優(yōu)化過程解耦為單層過程,并用同一組樣本完成指標優(yōu)化計算。最后通過無頭鉚釘模型和十桿結(jié)構(gòu)兩個工程問題驗證了所提指標的有效性和求解算法的高效性。3.為了衡量輸入變量的各取值區(qū)域?qū)敵鲂阅艿挠绊?發(fā)展了基于隨機森林的區(qū)域靈敏度分析方法。定義了擾動重要性指標函數(shù),該函數(shù)本質(zhì)上衡量了輸入變量減縮到子區(qū)域后對輸出變異性的總貢獻。發(fā)展了相應(yīng)的區(qū)域算法,該算法可以與原始隨機森林的擾動重要性分析共用一組樣本。通過考慮擾動重要性指標與Sobol總效應(yīng)指標的關(guān)系,對所發(fā)展的基于隨機森林的區(qū)域靈敏度指標計算方法進行嚴謹?shù)臄?shù)學(xué)分析,從而說明了所提方法的合理性。最后結(jié)合單側(cè)襟翼不對稱運動失效模型和多指標系統(tǒng)進一步闡釋了所提區(qū)域分析方法在工程中的應(yīng)用價值。4.針對結(jié)構(gòu)系統(tǒng)中需要綜合考慮多個輸出性能的情況,研究了多維輸出情況下的區(qū)域靈敏度分析問題。首先采用多元統(tǒng)計學(xué)中的廣義方差描述多維輸出模型的變異性,并詳細闡述了廣義方差的幾何意義,它既包含每一維輸出的不確定信息,也在一定程度上包含了各輸出量之間的相關(guān)信息。提出了相應(yīng)的區(qū)域靈敏度指標,即廣義方差比函數(shù),并發(fā)展了單層Monte Carlo法和稀疏網(wǎng)格法高效求解所提指標。
[Abstract]:Various kinds of uncertainties affect the performance of aircraft structure system, so it is studied how these uncertainties affect the output performance to improve the quality of aircraft structure products. It is important to simplify the model and reduce the error rate of decision making. This paper focuses on the global and regional sensitivity theory in structural uncertainty analysis. The main contents are as follows: 1. To explore and compare the relationship between the global sensitivity indicators in the case of input variables correlation. To provide guidance for the output performance design in the case of input variables correlation. Firstly, take the quadratic polynomial output model without crossover and with crossover as an example. The global sensitivity index based on covariance decomposition in the case of correlated normal input variables is derived analytically, including total contribution, structural contribution and correlation contribution. The relationship between the traditional variance-based index and the global sensitivity index based on covariance decomposition is derived theoretically, and the general model is inferred from the research results of the special quadratic polynomial model. At last, the advantages and disadvantages of different sensitivity indexes are discussed in detail. Based on the derived analytical conclusions, the parameter influence analysis is carried out under the condition of variable correlation. Combined with the three box section of the wing and other specific examples to verify the conclusion. 2. The uncertainty of the input variables is the global sensitivity index of the probability box description. The corresponding extended Monte is proposed. In the established index, the lower bound of the main index and the upper bound of the total index are used as the global sensitivity index to describe the uncertainty of the input variables in the probability box. A new method of global sensitivity analysis for imprecise probabilistic description is presented. The developed method can express the function relationship between sensitivity index and distribution parameters by taking appropriate samples. Furthermore, the two-layer optimization process is decoupled into single-layer process. Finally, through two engineering problems of headless rivet model and ten-bar structure, the validity of the proposed index and the efficiency of the algorithm. 3. In order to measure the input variables, the index optimization calculation is completed with the same set of samples. The effect of the value area on the output performance. The regional sensitivity analysis method based on stochastic forest is developed, and the disturbance importance index function is defined. This function essentially measures the total contribution of input variables to the output variability after they are reduced to a sub-region, and develops the corresponding region algorithm. The algorithm can share a set of samples with the disturbance importance analysis of the original random forest. The relationship between the disturbance importance index and the Sobol total effect index is considered. A rigorous mathematical analysis of the developed regional sensitivity index method based on stochastic forest is carried out. The rationality of the proposed method is illustrated. Finally, the application value of the proposed region analysis method in engineering is further explained with the failure model of asymmetrical motion of single flaps and the multiple index system. 4. In view of the structural system, the application value of the proposed method in engineering is further explained. Multiple output performance needs to be considered comprehensively. In this paper, the problem of region sensitivity analysis under multidimensional output is studied. Firstly, the variation of multidimensional output model is described by generalized variance in multivariate statistics, and the geometric meaning of generalized variance is expounded in detail. It not only contains the uncertain information of each one dimensional output, but also contains the relevant information among the outputs to a certain extent. The corresponding region sensitivity index, the generalized variance ratio function, is proposed. The single layer Monte Carlo method and sparse mesh method are developed to solve the proposed index efficiently.
【學(xué)位授予單位】：西北工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：V214

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