复杂结构的不确定性传递及重要性分析研究

发布时间：2018-05-17 17:28

  本文选题：重要性测度 + 区域重要性　； 参考：《西北工业大学》2015年博士论文

【摘要】：航空及机械等复杂工程结构系统中广泛存在各种各样的不确定性。针对复杂结构的特点,研究这些不确定性对输出性能的影响,预测复杂结构系统在不确定性环境下的风险评估和可靠性模型的不确定性传递具有重要的意义。为了提高复杂结构在不确定性环境下的性能,在已有研究的基础上,本文展开以下研究:1)在结构可靠性分析和设计中,往往存在部分不确定性分布特征不明确而仅知其不确定参数的边界,因此基于凸集非概率模型的不确定性描述得到广泛关注。为了有效分析凸集非概率输入变量对可靠性工程中所关心的结构系统失效的影响,在矩独立重要性测度的基础上,扩展了其在非概率可靠性分析中的工程应用,建立了基于凸模型非概率可靠性的矩独立重要性测度。针对凸集非概率输入变量对非概率可靠性贡献表达式的特点,将态相关参数(State Dependent Parameter,SDP)方法和主动学习Kriging(Active learning Kriging,ALK)方法建立代理模型的优点推广到该重要性测度的计算当中,并以实际算例验证了所提重要性测度的合理性,所推导的非概率可靠性重要性测度的普遍适用性以及所建求解方法的可行性。2)为研究输入变量分布参数对基于失效概率的重要性测度的影响程度,建立一个基于失效概率的重要性测度对输入变量分布参数的灵敏度分析体系。该参数灵敏度首先分析各个不确定性分布参数对基于失效概率的重要性测度不确定性传递,得到重要性测度后在分布参数处求导。针对复杂结构模型,将重要性分析中高效的ALK方法引入到基于失效概率的重要性测度参数的灵敏度分析中,解决了传统的MC求解中计算量过于庞大的困难,大大提高了计算效率。3)为了降低复合随机振动系统动力学输出的失效概率,引入了基于失效概率主重要性测度指标和总重要性测度指标,通过控制重要性程度高的输入变量的不确定性来降低失效概率。结合复合随机振动系统动力学输出的特点,采用ALK方法能在不减少精确度的条件下大幅减少计算量。其次从随机结构无条件动力可靠度的表达式出发,利用条件概率密度函数的解析变换,给出了一种衡量基本随机变量对动力可靠性影响的矩独立重要性测度指标。基于态相关参数模型,提出了求解矩独立重要性测度指标的态相关参数(SDP)法。与直接Monte-Carlo法对比,所提方法可以在保证计算精度的同时大幅度提高计算效率,适用于分析复合随机振动系统的非线性可靠性响应。4)将基于均值和方差的区域重要性指标进一步推广到复合随机结构结构系统,分别定义了输入变量的任意取值区域对输出动力学可靠度及动力学可靠性测度主贡献的区域重要性指标,为复杂结构动力学可靠性设计工程提供更多的有用信息。另外,本文还针对当前基于输出动力学可靠性测度主贡献的区域重要性指标定义中的问题,根据了其表达式的特点建立了所提各种指标高效的求解方法。5)针对同时含有主、客观混合不确定性的结构系统,考虑到主客观变量含有非概率变量的情况,提出了新的主客观重要性测度。所提指标体系能够很好的度量含非概率变量情况下主客观输入变量对结构可靠度的影响,为主、客观混合不确定性情况下减缩模型维度和减少输出响应的不确定性提供指导。同时建立了主、客观混合不确定性从主观输入变量向输出性能可靠度的传递过程,给出了两种重要性测度的基本求解方法和实现步骤。针对所提出的主、客观变量重要性测度指标求解中存在的问题,建立了两种主、客观输入变量重要性分析算法,并采用数值和工程算例验证了其效率和精度,满足实际复杂工程结构的需要。
[Abstract]:There are various uncertainties in the complex engineering structure systems such as aviation and machinery. In view of the characteristics of complex structures, it is important to predict the impact of these uncertainties on the output performance and to predict the risk assessment and the uncertainty transmission of the reliability model in the uncertain environment. The performance of complex structures in the uncertain environment has been studied on the basis of the existing research. 1) in structural reliability analysis and design, there are often some uncertainties in the uncertain distribution characteristics and only the boundary of the uncertain parameters. Therefore, the uncertainty description based on the non probabilistic model of convex sets has been widely concerned. In order to effectively analyze the effect of the non probabilistic input variable on the failure of the structural system in the reliability engineering, the engineering application in the non probabilistic reliability analysis is extended on the basis of the moment independent importance measure, and a moment independent importance measure based on the non probabilistic reliability of the convex model is established. The characteristics of the contribution expression to the non probabilistic reliability contribution are presented. The advantages of the State Dependent Parameter (SDP) method and the active learning Kriging (Active learning Kriging, ALK) method are extended to the calculation of the importance measure, and the reasonableness of the importance measure is verified by a practical example. The generalized applicability of the importance measure of non probabilistic reliability and the feasibility of the proposed solution method.2) to study the influence degree of the input variable distribution parameters on the importance measure based on the failure probability, a sensitivity analysis system based on the importance measure of the failure probability on the input variable distribution parameters is established. The sensitivity first analyzes the uncertainty transfer of the uncertainty distribution parameters to the importance measure based on the failure probability, and obtains the guidance after the importance measure. For the complex structure model, the efficient ALK method in the importance analysis is introduced to the sensitivity analysis of the importance measure parameters based on the failure probability, and the solution is solved. In order to reduce the failure probability of the dynamic output of the composite random vibration system, the failure probability of the dynamic output of the composite random vibration system is reduced. In order to reduce the failure probability of the dynamic output of the composite random vibration system, the index of the main importance measure based on the failure probability and the measure of the total importance are introduced, and the uncertainty of the input variable of high importance is reduced to reduce the uncertainty of the MC. In combination with the characteristics of the dynamic output of the composite random vibration system, the ALK method can be used to reduce the amount of calculation without reducing the accuracy. Secondly, based on the expression of the unconditional dynamic reliability of the random structure and the analytical change of the conditional probability density function, a measure of the basic random variable pair motion is given. Based on the state dependent parameter model, the state dependent parameter (SDP) method for solving the moment independent importance measure is proposed. Compared with the direct Monte-Carlo method, the proposed method can greatly improve the calculation efficiency while ensuring the calculation precision, and is suitable for the analysis of the composite random vibration system. In the nonlinear reliability response.4), the regional importance index based on mean and variance is further extended to the composite stochastic structural system. The regional gravity index for the main contribution of the arbitrary value area of the input variable to the output dynamic reliability and the dynamic reliability measure is defined respectively, which is set up for the dynamic reliability of the complex structure. The project provides more useful information. In addition, this paper also aims at the problem of the current regional importance index definition based on the main contribution of the output dynamic reliability measurement. According to the characteristics of the expression, the paper establishes a method of solving all kinds of indexes high efficiency.5) for the structure system with both main and objective mixed uncertainty. Considering that the subjective and objective variables contain non probabilistic variables, a new subjective and objective importance measure is proposed. The proposed index system can well measure the influence of the subjective and objective input variables on the structural reliability under the case of non probability variables, and the uncertainty of the model dimension and the output response are reduced under the objective mixed uncertainty. At the same time, the transfer process of the objective mixed uncertainty from the subjective input variable to the output reliability is established, and the basic solution methods and the implementation steps of the two importance measures are given. Two kinds of main and objective inputs are established to solve the existing problems in the solution of the importance measure index of the subjective and objective variables. Variable importance analysis algorithm is applied, and numerical and engineering examples are used to verify its efficiency and accuracy, so as to meet the needs of practical complex engineering structures.
【学位授予单位】：西北工业大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TB114.3
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本文编号：1902230