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.     

基于领域专家知识的发动机模糊可靠性分配方法

提出了一种基于多领域专家知识的发动机模糊可靠性分配方法,以降低决策者主观偏好以及分配过程中模糊和不确定因素对分配结果的影响.基于对影响发动机可靠性因素的分析,建立了发动机模糊可靠性分配的数学模型,并以三角模糊数代替常规层次分析法中的标度,提出了一种模糊评判矩阵方法来确定影响可靠性因素的权重.在可靠性分配过程中,充分考虑多领域专家的意见和产品开发过程的风险性.以应用实例对提出方法的有效可行性进行了验证.     

Hybrid uncertainty-based design optimization and its application to hybrid rocket motors for manned lunar landing

Design reliability and robustness are getting increasingly important for the general design of aerospace systems with many inherently uncertain design parameters. This paper presents a hybrid uncertainty-based design optimization (UDO) method developed from probability theory and interval theory. Most of the uncertain design parameters which have sufficient information or experimental data are classified as random variables using probability theory, while the others are defined as interval variables with interval theory. Then a hybrid uncertainty analysis method based on Monte Carlo simulation and Taylor series interval analysis is developed to obtain the uncer-tainty propagation from the design parameters to system responses. Three design optimization strategies, including deterministic design optimization (DDO), probabilistic UDO and hybrid UDO, are applied to the conceptual design of a hybrid rocket motor (HRM) used as the ascent propulsion system in Apollo lunar module. By comparison, the hybrid UDO is a feasible method and can be effectively applied to the general design of aerospace systems.     

分布参数为模糊变量的结构体系模糊可靠性分析方法及应用

 随机模型的分布参数是由随机试验结果进行统计推断而得出的，往往难以准确预知，将其描述为模糊变量是可行的。将模糊数学理论与可靠性分析相结合，对分布参数为模糊变量的结构体系模糊可靠性进行了分析，具体推导了两种失效模式间的模糊相关系数和二阶联合模糊失效概率的求解公式，求出了失效模式间不相关和相关两种情况下，结构体系模糊失效概率在各λ水平截集下的区间解，估算出了结构体系的模糊失效概率，并对加筋板结构的模糊可靠性进行了分析。通过算例表明该方法更符合工程实际，是有效可行的。     

Sensitivity analysis for probabilistic anti-resonance design of aeronautical hydraulic pipelines

In an uncertainty scheme, reliability and global sensitivity analysis is studied in this work, to provide helpful information for probabilistic anti-resonance design of vibration systems.Discussions show that the resonance failure problem can be viewed as a series system, in which input uncertainties are modeled by random variables. In order to quantitatively measure the contributions of input variables to the system reliability, a global sensitivity index is proposed, the properties of which are also discussed. Then the proposed index is tested with an aeronautical hydraulic pipeline system, which is under the excitation of pump vibration and at a risk of resonance failure. Sensitivity results under different failure criteria and variation coefficients are obtained and studied, from which significant and insignificant input variables can be identified.The proposed method provides a relatively new insight for anti-resonance design of engineering structures.     

基于模糊贝叶斯的导弹武器系统可靠性和可用性分析

综合考虑了装备、保障系统、管理和人员、保障方案等要素,提出了一种基于模糊贝叶斯的导弹武器系统可靠性和可用性分析方法,将先验信息和样本数据有效融合,采用模糊随机变量来处理数据的不确定。通过算例分析,验证了模型的有效性。结论表明,该方法所得的评估结果符合装备的实际情况。     

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.     

用摄动法研究几何尺寸为随机量时轮盘的可靠性

几何尺寸和材料性质等的随机性都影响结构的可靠性。本文提出用建立在二阶摄动法基础上的概率有限元来分析轮盘的几何形状不确定时的随机应力场和可靠性，研究用摄动方法处理问题的基本思路，推导随机应力场和可靠度的计算公式，用简单算例分析讨论了几何尺寸对可靠性的影响规律，算例结果与ＭｏｎｔｅＣａｒｌｏ模拟结果的对比表明本文的方法有效，理论正确。     

基于失效概率的涡轮后机匣全局灵敏度分析

涡轮后机匣是航空发动机安全的关键部件，但是其具有工况复杂、不确定性因素多的缺点。为了探究输入随机变量的不确定性对涡轮后机匣结构失效概率的影响，建立参数化有限元模型进行确定性分析。考虑材料性能、几何参数及外部载荷的不确定性，对涡轮后机匣两种典型失效模式：强度失效以及刚度失效建立极限状态函数；通过构造自适应Kriging 代理模型并结合重要抽样方法评估涡轮后机匣结构失效概率，利用基于失效概率的全局灵敏度方法对涡轮后机匣结构可靠度的不确定性来源进行分析，对各输入随机变量重要性进行排序，构建一种涡轮后机匣全局灵敏度分析框架。结果表明：涡轮后机匣在两种失效模式以及系统失效模式下，发动机推力以及线性膨胀系数对结构失效概率影响最为显著，应对其重点考虑；内外机匣长度以及材料弹性模量对涡轮后机匣结构失效概率影响较小，可对其适当忽略。     

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.