结构不确定分析中的全局及区域灵敏度研究

发布时间：2018-01-09 01:25

本文关键词：结构不确定分析中的全局及区域灵敏度研究　出处：《西北工业大学》2016年硕士论文　论文类型：学位论文

【摘要】：各类广泛存在的不确定性影响着飞机结构系统的性能,因此研究这些不确定性如何影响输出性能对于提高飞机结构产品质量、简化模型以及减小决策失误率都有重要意义。本文围绕结构不确定分析中的全局及区域灵敏度理论展开研究工作,主要内容如下:1.对输入变量相关情况下全局灵敏度指标之间的关系进行探究比较,为输入变量相关情况下的输出性能设计提供指导。首先以不含交叉项和包含交叉项的二次多项式输出模型为例,解析推导了相关正态输入变量情况下基于协方差分解的全局灵敏度指标,包括总贡献、结构贡献和相关贡献。然后,理论推导了传统基于方差的指标与基于协方差分解的全局灵敏度指标之间的关系,从特殊二次多项式模型的研究结果对一般模型做出推断,并从高维模型分解的角度对所推断的结论进行了验证,最后详细讨论了不同灵敏度指标的优缺点。基于所推导的解析结论进行变量相关情况下的参数影响分析,并结合机翼三盒段等具体算例验证了所得结论。2.建立了输入变量的不确定性为概率盒描述时的全局灵敏度指标,并提出了相应的扩展Monte Carlo高效求解算法。在所建立的指标中以主指标下界和总指标上界作为概率盒描述输入变量不确定性时的全局灵敏度指标,提供了一种非精确概率描述时全局灵敏度分析的新思路。所发展的求解方法通过抽取合适的样本显式表达出灵敏度指标与分布参数的函数关系,进而将双层优化过程解耦为单层过程,并用同一组样本完成指标优化计算。最后通过无头铆钉模型和十杆结构两个工程问题验证了所提指标的有效性和求解算法的高效性。3.为了衡量输入变量的各取值区域对输出性能的影响,发展了基于随机森林的区域灵敏度分析方法。定义了扰动重要性指标函数,该函数本质上衡量了输入变量减缩到子区域后对输出变异性的总贡献。发展了相应的区域算法,该算法可以与原始随机森林的扰动重要性分析共用一组样本。通过考虑扰动重要性指标与Sobol总效应指标的关系,对所发展的基于随机森林的区域灵敏度指标计算方法进行严谨的数学分析,从而说明了所提方法的合理性。最后结合单侧襟翼不对称运动失效模型和多指标系统进一步阐释了所提区域分析方法在工程中的应用价值。4.针对结构系统中需要综合考虑多个输出性能的情况,研究了多维输出情况下的区域灵敏度分析问题。首先采用多元统计学中的广义方差描述多维输出模型的变异性,并详细阐述了广义方差的几何意义,它既包含每一维输出的不确定信息,也在一定程度上包含了各输出量之间的相关信息。提出了相应的区域灵敏度指标,即广义方差比函数,并发展了单层Monte Carlo法和稀疏网格法高效求解所提指标。
[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.
【学位授予单位】：西北工业大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：V214

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