认知不确定性下可靠性灵敏度分析的新指标

传统的可靠性灵敏度指标只考虑了随机不确定性,当结构中还存在认知不确定性时,该指标难以反映出基本变量中认知不确定性对结构可靠性评估结果的影响程度.针对这一问题,引入概率包络来表达结构中的随机不确定性和认知不确定性,在此基础上建立了可靠性灵敏度分析的新指标——认知灵敏度系数,给出了其定义和代表的意义,并基于证据理论提出了认知灵敏度系数的计算方法.算例分析表明,认知灵敏度系数可以反映出基本变量中认知不确定性对结构可靠性评估结果的不确定性的影响程度,从而为有针对性地提高可靠性评估结果的准确性提供依据.另外,基于证据理论的认知灵敏度系数的计算方法适用于极限状态函数为单调、非单调的结构,以及变量服从正态、非正态的结构,具有普适性.     

Epistemic uncertainty quantification in flutter analysis using evidence theory

Aimed at evaluating the structural stability and flutter risk of the system, this paper manages to quantify epistemic uncertainty in flutter analysis using evidence theory, including both parametric uncertainty and method selection uncertainty, on the basis of information from limited experimental data of uncertain parameters. Two uncertain variables of the actuator coupling system with unknown probability distributions, that is bending and torsional stiffness, which are both described with multiple intervals and the basic belief assignment(BBA) extricated from the modal test of actuator coupling systems, are taken into account. Considering the difference in dealing with experimental data by different persons and the reliability of various information sources, a new combination rule of evidence––the generalized lower triangular matrices method is formed to acquire the combined BBA. Finally the parametric uncertainty and the epistemic uncertainty of flutter analysis method selection are considered in the same system to realize quantification. A typical rudder of missile is selected to examine the present method, and the dangerous range of velocity as well as relevant belief and plausibility functions is obtained. The results suggest that the present method is effective in obtaining the lower and upper bounds of flutter probability and assessing flutter risk of structures with limited experimental data of uncertain parameters and the belief of different methods.     

Sealing reliability modeling of aviation seal based on interval uncertainty method and multidimensional response surface

Many variables affect the sealing performance, and their distribution characteristics are difficult to obtain with probabilistic methods owing to the high cost involved. Numerous problems in engineering are similar due to the appearance of small-sample parameters. In this study, the sealing reliability of an aviation seal was defined as the research object, and an interval uncertainty method and multidimensional response surface were proposed to calculate the sealing reliability.Based on this, we first analyzed the failure mechanism of the aviation seal and established a leakage rate model. Then, based on the non-probabilistic interval model, an interval uncertainty method was proposed to construct the analytical model. With reference to the limit state equation from the structural reliability theory, the multidimensional response surface was used for fast calculation.Then, we chose the single-cylinder gas steering gear used in aircraft as the case study, its sealing reliability in working and non-working statuses were calculated, and the results were verified with the actual maintenance records. By analyzing the sensitivity of some variables, we can improve the sealing reliability of the aviation seal by improving the surface roughness only if the cost allows.Finally, we consider that the method proposed in this study realizes the application of smallsample uncertainty analysis in reliability analysis, and could provide a feasible way to solve the similar problems in engineering with multidimensional and small-sample parameters.     

结构非概率可靠性灵敏度分析方法

 结构非概率可靠性的灵敏度分析对工程中非概率问题的分析预测和优化具有重要的指导作用。基于结构非概率可靠性指标理论,提出了结构非概率可靠性的灵敏度分析方法。针对极限状态函数为线性的情况,推导出了非概率可靠性灵敏度的解析解。在此基础上,结合函数线性化理论,提出了求解极限状态函数为非线性情况的非概率可靠性灵敏度的近似解析方法。基于求解非概率可靠性指标的优化方法,并结合差分理论,提出了求解非概率可靠性灵敏度的优化方法。给出了算例分析,结果表明了所提方法的可行性。     

结构的概率-非概率混合可靠性模型

将影响结构可靠性分析的不确定性因素用概率和非概率两种方式模拟。并基于结构可靠性分析中的概率可靠性模型和非概率集合可靠性模型,提出一种新的结构可靠性分析的概率-非概率混合模型。该模型首先通过将功能函数进行非概率可靠性分析,然后将标准化区间变量空间所有区域的可靠度进行求和计算,从而给出结构的可靠度。并根据相同的不确定信息,由混合可靠性模型与概率可靠性模型得到的结果是相等的,证明了方法的有效性。最后,通过一个典型结构和一个机翼下壁加筋板与传统概率可靠性模型进行比较,表明该混合模型对于结构的分析和设计更为合理,能够更好地保证结构的安全性。     

A new structural reliability analysis method in presence of mixed uncertainty variables

For structures with both random and fuzzy uncertainty, this paper presents a novel method for determining the membership function in fuzzy reliability with the Automatic Updating Extreme Response Surface (AUERS) method. In the proposed method, fuzzy variables are initially converted into a value domain under the given cut level and the extreme point in the domain where the reliability reaches its extreme value is considered. Second, the Particle Swarm Optimization (PSO) algorithm is used to determine the extreme point according to the extreme responses for different sets of random sample inputs. A kriging response surface is subsequently constructed between the random variables and the corresponding extreme points. An automatic updating strategy is then introduced based on the Relative Mean Square Predicted Error (RMSPE) before performing every iteration of reliability analysis. By adding new sample points, the approximate quality of the kriging response surface is improved. Finally, reliability analysis is used to determine the reliability bound under the given cut level. The proposed method assures the accuracy and computation efficiency of the mixed uncertainty reliability analysis results while it prevents the solution from becoming trapped in a local optimum, which occurs in classical optimization methods. Two example analyses are used to demonstrate the validity and advantages of the proposed method.     

航空发动机套齿动态装配间隙非概率优化设计

为解决航空发动机套齿动态装配间隙的响应问题,在考虑动态变形和参数不确定性的情况下,将1种非概率区间分析方法与Kriging响应面模型及响应面优化方法相结合,对套齿初始装配间隙进行了可靠性优化设计。以某刚性套齿联轴器作为数值算例,在确定性设计的基础上,考虑机械载荷、热载荷、材料参数的分散性,运用区间分析方法得到了动态装配间隙的响应范围,利用非概率可靠性指标对初始装配间隙进行了优化设计。与确定性设计相比,优化设计提高了结构的可靠性;与概率设计相比,优化设计降低了对不确定参数的信息要求。验证了非概率方法解决装配对象不确定性结构响应问题的可行性与适用性。     

A new structural reliability index based on uncertainty theory

The classical probabilistic reliability theory and fuzzy reliability theory cannot directly measure the uncertainty of structural reliability with uncertain variables,i.e.,subjective random and fuzzy variables.In order to simultaneously satisfy the duality of randomness and subadditivity of fuzziness in the reliability problem,a new quantification method for the reliability of structures is presented based on uncertainty theory,and an uncertainty-theory-based perspective of classical Cornell reliability index is explored.In this paper,by introducing the uncertainty theory,we adopt the uncertain measure to quantify the reliability of structures for the subjective probability or fuzzy variables,instead of probabilistic and possibilistic measures.We utilize uncertain variables to uniformly represent the subjective random and fuzzy parameters,based on which we derive solutions to analyze the uncertainty reliability of structures with uncertainty distributions.Moreover,we propose the Cornell uncertainty reliability index based on the uncertain expected value and variance.Experimental results on three numerical applications demonstrate the validity of the proposed method.     

含缺陷结构非概率可靠性分析方法研究

将基于分段描述的结构非概率可靠性模型引入含缺陷结构的可靠性分析,结合断裂判据,并用分段描述模型刻画未确知变量,实现了非概率的断裂力学分析,克服了概率断裂力学方法对原始数据要求高的局限和未确知信息区间均匀分布模型过于保守的缺陷,有效解决了含裂纹结构在小样本、贫信息场合的可靠性评定问题.通过算例,对文中方法的可行性和有效性...     

概率盒全局灵敏度和活跃子空间跨层降维

航空航天仿真系统中的不确定性通常是多源的、混合的,并且系统参数的维数众多。针对高维混合不确定性量化问题,提出一种结合概率盒全局灵敏度和活跃子空间的跨层降维方法。在随机和认知不确定的概率盒表征基础上,使用不确定性缩减法分析参数的全局灵敏度继而进行参数筛选;基于输出梯度协方差矩阵的特征分解,使用活跃子空间法对参数进行降维;构造出一种概率盒表征下的参数筛选和跨层降维方法。最后以NASA多学科不确定性量化挑战问题为例,通过概率盒全局灵敏度分析进行第1层次的参数筛选,原有的21维输入参数减为13维;随后采用活跃子空间进行第2层次的参数降维,维数进一步降至一维。研究结果表明,所提出的方法能够对混合不确定性参数进行灵敏度排序,还能够有效降低模型输入参数的维度,为高维系统混合不确定性量化和进一步的优化工作奠定了基础。     

考虑多工况性能可靠性的航空发动机循环设计方法

为实现航空发动机总体性能设计方法由传统的确定性设计向不确定性概率设计转变,提出基于分布式协同响应面法思想的航空发动机多工况性能可靠性循环优化设计方法:建立了引入非确定性部件性能的航空发动机性能仿真模型,通过试验设计、非设计点性能仿真试验等步骤,构建了各典型工况下发动机推力与耗油率性能可靠度关于设计点循环参数的分布式响应面模型,并以此构建多工况性能协同响应面模型进行循环参数优化设计,最终获得循环参数非劣解集并通过随机试验进行验证。结果表明,通过多工况性能可靠性循环优化设计方法获得的循环参数非劣解集均能使发动机在多个典型工况下的总体性能同时达到不低于97.5%的高可靠度,为设计人员根据实际情况选取循环参数提供依据。      

超椭球凸集合可靠性综合指标定义及求解方法

针对失效域与超椭球凸集合发生干涉与不发生干涉两种情况下,超椭球凸集合非概率可靠性与非概率可靠度两种指标各自存在的不足,将两指标相结合提出多个超椭球凸集合描述时的可靠性综合指标定义,并提出将改进的有限步长迭代法(MLSA)与Monte-Carlo法结合来求解综合指标的方法.MLSA是在有限步长迭代法的基础上提出的,根据增...     

Methods and advances in the study of aeroelasticity with uncertainties

Uncertainties denote the operators which describe data error, numerical error and model error in the mathematical methods. The study of aeroelasticity with uncertainty embedded in the subsystems, such as the uncertainty in the modeling of structures and aerodynamics, has been a hot topic in the last decades. In this paper, advances of the analysis and design in aeroelasticity with uncertainty are summarized in detail. According to the non-probabilistic or probabilistic uncer- tainty, the developments of theories, methods and experiments with application to both robust and probabilistic aeroelasticity analysis are presented, respectively. In addition, the advances in aeroelastic design considering either probabilistic or non-probabilistic uncertainties are introduced along with aeroelastic analysis. This review focuses on the robust aeroelasticity study based on the structured singular value method, namely the ~t method. It covers the numerical calculation algo- rithm of the structured singular value, uncertainty model construction, robust aeroelastic stability analysis algorithms, uncertainty level verification, and robust flutter boundary prediction in the flight test, etc. The key results and conclusions are explored. Finally, several promising problems on aeroelasticity with uncertainty are proposed for future investigation.     

Safety estimation of structural systems via interval analysis

Considering that the uncertain information has serious influences on the safety of structural systems and is always limited, it is reasonable that the uncertainties are generally described as interval sets. Based on the non-probabilistic set-theoretic theory, which is applied to measuring the safety of structural components and further combined with the branch-and-bound method for the probabilistic reliability analysis of structural systems, the non-probabilistic branch-and-bound method for determining the dominant failure modes of an uncertain structural system is given. Meanwhile, a new system safety measuring index obtained by the non-probabilistic set-theoretic model is investigated. Moreover, the compatibility between the classical probabilistic model as well as the proposed interval-set model will be discussed to verify the physical meaning of the safety measure in this paper. Some numerical examples are utilized to illustrate the validity and feasibility of the developed method.     

A novel method for importance measure analysis in the presence of epistemic and aleatory uncertainties

For structural systems with both epistemic and aleatory uncertainties, research on quantifying the contribution of the epistemic and aleatory uncertainties to the failure probability of the systems is conducted. Based on the method of separating epistemic and aleatory uncertainties in a variable, the core idea of the research is firstly to establish a novel deterministic transition model for auxiliary variables, distribution parameters, random variables, failure probability, then to propose the improved importance sampling(IS) to solve the transition model. Furthermore,the distribution parameters and auxiliary variables are sampled simultaneously and independently;therefore, the inefficient sampling procedure with an ‘‘inner-loop' for epistemic uncertainty and an‘‘outer-loop' for aleatory uncertainty in traditional methods is avoided. Since the proposed method combines the fast convergence of the proper estimates and searches failure samples in the interesting regions with high efficiency, the proposed method is more efficient than traditional methods for the variance-based failure probability sensitivity measures in the presence of epistemic and aleatory uncertainties. Two numerical examples and one engineering example are introduced for demonstrating the efficiency and precision of the proposed method for structural systems with both epistemic and aleatory uncertainties.     

基于截尾概率-非概率混合模型的可靠性优化算法

针对工程中截尾概率变量与非概率变量同时存在的情况,给出一种新的截尾概率与非概率混合可靠性模型。在该混合可靠性模型基础上,按照可靠性指标(RIA)法给出双层嵌套可靠性优化模型,并采用改进搜索策略后的ST-Powell优化算法在外层搜索设计变量的最优值,内层采用能保证收敛的改进的有限步长迭代法求解混合可靠性指标。数值算例表明,改进搜索策略后的ST-Powell优化算法的全局寻优性得到显著提升;改进搜索策略后的ST-Powell优化算法与改进的有限步长迭代法相结合求解双层嵌套混合可靠性优化模型的正确性得到验证,且对于非线性程度较高的极限状态函数同样能够得到满足截尾概率与非概率混合可靠性模型指标要求的最优解,并对工程结构算例具有很好的适应性。     

一种基于Kriging和Monte Carlo的主动学习可靠度算法

机械结构可靠性分析时,常常会采用代理模型拟合隐式功能函数来解决计算量大的问题,但由于试验设计方案需要同时考虑代理模型的拟合精度和可靠度计算精度的问题。因此,为了能够充分使用较少的样本信息,最大化可靠度计算精度,本文充分发挥Kriging预测的随机特性,提出一种主动学习可靠度计算方法。首先,类似于优化问题中改善函数的选点方式,提出一种基于Kriging预测的学习函数,基于Monte Carlo法生成大量的候选样本点,找出学习函数最小值对应的样本点作为最佳取样点。其次,推导和提出了一种学习停止的条件,保证了Monte Carlo样本点预测符号的正确性且学习次数明显减小。最后,通过2个数值算例分析结果表明,该算法相比其他方法需要更少的样本数量,得到的可靠度计算精度更高,验证了本文算法的正确性和高效性。     

α-l型区间可靠性分析方法及其工程应用

在区间非概率可靠性模型的基础上,以区间长度l和区间下限α为结构系统变量的输入参数,重新定义了一种新的可靠性指标,分析得到了这种可靠性分析方法的判定依据;在此基础上,在线性和非线性条件下讨论了结构可靠度的计算方法.以某型飞机防冰引气管结构为例,进一步探讨了所提方法在共振可靠性分析当中的工程应用.     

涡轮冷却叶片寿命可靠性分析参数化仿真平台

目前,涡轮冷却叶片等复杂结构的多模式寿命可靠性分析中存在各功能模块的集成与管理不成体系、参数化联合调用技术不完善的工程应用问题。针对这些问题,完善了随机不确定性下涡轮冷却叶片多模式寿命可靠性分析的工程化方法,搭建了多模式寿命可靠性分析的参数化、多软件联合仿真平台,为某型号叶片寿命可靠性分析提供合理的工程化方法及高效便捷的自动化实现工具。主要工作包括：一建立了不确定性环境下含孔、肋及空腔复杂结构网格划分和结构有限元仿真的参数化方法,实现了随机变量不同取值下仿真的自动执行,解决了可靠性理论方法应用至复杂工程结构的瓶颈问题;二在经回归处理的概率寿命曲线中考虑温度插值及多失效模式串联系统,拓展了概率寿命曲线的应用范围,使得所建涡轮叶片寿命可靠性模型更符合实际;三提出了可靠性分析数字模拟过程中嵌入包括有限元结构分析和疲劳寿命极限状态面两方面的双层自适应代理模型方法,该自适应策略可在保证寿命可靠性分析精度的基础上提高效率。通过所建平台在某型号叶片上的算例分析及与蒙特卡洛法参考解的对比,验证了所提多模式系统寿命可靠性分析工程化方法的高效和准确性及仿真平台的实用性。     

机载武器作战使用可靠性综合验证

为减少机载武器可靠性验证试验样本量和降低验证试验风险,通过对机载武器作战使用可靠性验证的工程需求、试验方案、统计模型、验证方法等进行研究,提出了一种利用研制试验数据和定型飞行试验数据的作战使用可靠性综合验证方法。针对机载武器的特点,根据变动统计理论,考虑性能验证与可靠性验证的要求,综合利用研制试验数据和定型飞行试验数据,给出作战使用可靠性综合验证方案,进而制定设计定型飞行试验方案。实例表明,在不改变生产方风险和使用方风险的情况下,该方法可有效地验证机载武器挂飞可靠性和自主飞行可靠性指标,显著地减少定型飞行试验样本量,大幅节约研制成本,并缩短研制周期。