基于自适应Kriging代理模型的交叉熵重要抽样法

对于复杂失效域和小失效概率耦合的可靠性分析问题，本文提出了一种交叉熵重要抽样（CE-IS）方法结合自适应Kriging （AK）代理模型的求解方法（CE-IS-AK）。所提方法基于交叉熵原理，用混合高斯模型逐步逼近最优重要抽样密度函数，并采用AK模型协助逼近过程中混合高斯模型的参数的更新，从而提高了CE-IS方法的计算效率。另外，本文还改进了CE-IS方法的收敛准则，避免了方法的冗余迭代，扩大了方法的适用范围。由于在CE-IS方法中引入了AK模型，因此，本文方法所构建的重要抽样函数在保证精度的基础上提高了效率。相较于AK-MCS方法，本文方法中引入了重要抽样的思想，因此在Kriging训练点数目基本相同的情况下，大幅缩减小失效概率计算时样本池规模，并且由于利用了混合高斯模型，因而对多失效域具有较好的适用性。算例分析也证明了本文所提方法的优越性。     

计算涡轮叶片结构可靠度的自适应重要抽样法

为直接准确地计算系统结构可靠度，提出了自适应重要抽样方法，由极限状态面失效区确定的最初抽样区开始，用与随机变量联合概率密度函数成比例的抽样密度，自适应递增调整抽样，使抽样区稍大于失效区，以减少安全区的追加抽样，提高抽样效率，并将其应用于航空发动机涡轮叶片的结构可靠性分析，在获得相同的准确计算结果时，所需计算量显著减少。     

涡轮轴低周疲劳寿命可靠性分析及优化设计方法研究

为保障涡轮轴在多种不确定性因素影响下的可靠性和寿命性能,建立了涡轮轴低周疲劳寿命可靠性分析与优化设计方法.搭建了涡轮轴结构分析、可靠性分析和可靠性优化设计的参数化平台,实现了设计参数的不同访问值处结构分析和可靠性分析的自主调用.提出了改进Monte Carlo结合自适应Kriging的算法(A-MCS-AK),通过多点...     

航空发动机限寿件疲劳可靠度计算新方法

针对目前的航空发动机限寿件（ELLP）疲劳可靠性分析中的小失效概率事件以及其极限状态函数具有较强非线性的特点，提出了一种具有自更新机制的半径外自适应重要抽样（AUMCROAIS）疲劳可靠性分析方法。该方法首先利用蒙特卡罗自适应重要抽样（MCAIS）快速逼近真实设计验算点（MPP）附近，随后以近似设计验算点为中心进行极坐标抽样，并依次构造主动学习函数，对近极限状态函数和抽样半径进行最优选取，从而实现最优抽样半径的更新，通过不断的更新确定出最优抽样半径，加速失效概率计算的收敛。本方法提高了设计验算点的收敛速度同时保证了计算精度，解决了小失效概率事件以及强非线性极限状态函数可靠度计算难题，最后以某型发动机压气机轮盘为对象应用本方法，并与传统的蒙特卡罗仿真（MCS）方法、蒙特卡罗半径外自适应重要抽样法（MCROAIS）和一阶可靠性方法（FORM）进行了对比，验证了本方法的高效率、鲁棒性和仿真精度。     

Efficient adaptive Kriging for system reliability analysis with multiple failure modes under random and interval hybrid uncertainty

In the field of the system reliability analysis with multiple failure modes, the advances mainly involve only random uncertainty. The upper bound of the system failure probability with multiple failure modes is usually employed to quantify the safety level under Random and Interval Hybrid Uncertainty(RI-HU). At present, there is a lack of an efficient and accurate method for estimating the upper bound of the system failure probability. This paper proposed an efficient Kriging model based on nume...     

An efficient algorithm for calculating Profust failure probability

For efficiently estimating the Profust failure probability based on probability input variables and fuzzy-state assumption, a General Performance Function(GPF) expression is established under the strict mathematical derivation for the Profust reliability model. By constructing the GPF,the calculation of the Profust failure probability can be transformed into the calculation of the traditional failure probability. Then various existing methods for the traditional failure probability can be used to estimate the Profust failure probability. Due to the high efficiency of the Adaptive Kriging(AK) model and the universality of the Monte Carlo Simulation(MCS), AK inserted MCS(abbreviated as AK-MCS) has been proven to be an efficient method for estimating the failure probability. Therefore, the AK-MCS combined with the GPF(abbreviated as AK-MCS + GPF)is proposed for estimating Profust failure probability. The proposed method greatly reduces the computational cost while ensuring the accuracy. Finally, four examples are given to validate the proposed AK-MCS + GPF. The results of the examples show the rationality and the efficiency of the proposed AK-MCS + GPF.     

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。     

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。     

基于交叉熵和空间分割的全局可靠性灵敏度分析

基于失效概率的全局灵敏度分析可以度量各个基本随机变量的不确定性对失效概率的影响程度,对如何降低结构的失效概率具有指导意义。基于交叉熵方法和空间分割提出一种新全局可靠性灵敏度分析方法。该方法采用交叉熵法自适应的确定重要抽样密度函数,有效地回避了传统重要抽样中设计点位置和个数求解的困难。基于评估失效概率所使用的样本,利用空间分割方法计算各个输入随机变量的全局可靠性灵敏度指标,能够提高样本的利用率和计算效率。文中利用一个数值算例和两个工程算例验证了所提方法的计算效率和精度。     

小失效概率情况下的全局可靠性灵敏度分析的高效方法

针对目前很多算法都无法准确、高效地计算小失效概率（10^-4,甚至更小）情况下的全局可靠性灵敏度问题,本文提出了一种高效求解小失效概率情况下的全局可靠性灵敏度新算法。所提算法通过扩大标准差构造重要抽样密度函数来进行空间分割（SP）,再与无迹变换（UT）结合,利用函数在分割后的子空间内非线性程度的降低和无迹变换方法可以高效计算低非线性程度函数的前二阶矩,来高效准确地计算小失效概率情况下的全局可靠性灵敏度。所提算法的优点有：重要抽样密度函数的选择可以使得空间分割时向重要区域偏移,并且在分割区域内功能函数的复杂性被降低,从而可以利用无迹变换方法高效计算失效概率,进而高效求得全局可靠性灵敏度。与已有的算法相比,算例说明了本文所提方法的优势。     

可靠性全局灵敏度求解的Meta-IS-AK算法

可靠性全局灵敏度（GRS）可以衡量输入变量对结构系统失效概率的平均影响,但目前仍然缺乏具有广泛适应性的高效算法。针对此问题,本文将在元重要抽样和可靠性全局灵敏度的贝叶斯算法基础上建立一种新的高效算法。所提算法首先利用已有的贝叶斯算法,将可靠性全局灵敏度转换成由无条件失效概率及输入变量失效域条件下的概率密度函数（PDF）表达的形式,然后分3步来完成算法的组织。第1步是利用元重要抽样的迭代策略抽取失效域的重要抽样样本;第2步是在已有的元重要抽样法中嵌入自适应Kriging模型,高效计算出无条件失效概率;第3步是利用Metropolis-Hastings准则,将失效域的重要抽样样本转化成为原始密度函数在失效域的样本点,进而同时求得各个输入变量在失效域中的条件概率密度函数,并最终求得可靠性全局灵敏度。由于所提算法充分利用了已有的可靠性全局灵敏度贝叶斯算法的维度独立性、元重要抽样法对隐式多失效域的适应性以及元重要抽样法中嵌入式Kriging模型的高效性,因此所提算法具有广泛的适用范围和较高的效率,该结论得到了算例结果的充分验证。     

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。     

基于Kriging模型梯度解析解的改进一次二阶矩方法

改进一次二阶矩（AFOSM）法是一种基于功能函数梯度的结构可靠性分析方法，鉴于其对隐式函数的梯度较难求解，提出了一种基于Kriging模型梯度解析解的AFOSM方法，利用Kriging代理模型的解析表达式推导得到功能函数对输入变量的梯度解析解，为AFOSM中设计点的确定提供高精度的梯度信息。通过Kriging与AFOSM的结合，很好地解决了基于有限元模型的隐式情况下梯度计算量相当大、可靠性分析难的问题。数值与工程算例验证了所提Kriging梯度解析解的较高精确性，同时验证了所提基于Kriging解析解的AFOSM结构可靠性分析方法的正确性与较高精度。     

Kriging模型在固体火箭发动机装药可靠性分析中的应用

基于Kriging方法对固体火箭发动机装药结构可靠性进行了分析.首先,采用拉丁超立方抽样技术得到了随机参数样本点;然后,利用样本点数据对黏弹性有限元模型的装药进行了结构力学分析;最后,通过Kriging模型得到了八面体剪应变的函数近似响应面,并结合失效判据对失效函数进行了可靠性计算.为了验证Kriging模型在可靠性计算中的有效性,其计算结果与Monte-Carlo方法进行了比较,得到了十分接近的可靠度.      

A Bayesian approach for integrating multilevel priors and data for aerospace system reliability assessment

This paper investigates Bayesian methods for aerospace system reliability analysis using various sources of test data and expert knowledge at both subsystem and system levels. Four scenarios based on available information for the priors and test data of a system and/or subsystems are studied using specific Bayesian inference techniques. This paper proposes the Bayesian melding method for integrating subsystem-level priors with system-level priors for both system- and subsystem-level reliability analysis. System and subsystem reliability outcomes are compared under different scenarios. Computational challenges for posterior inferences using the sophisticated Bayesian melding method are addressed using Markov Chain Monte Carlo (MCMC) and adaptive Sampling Importance Re-sampling (SIR) methods. A case study with simulation results illustrates the applications of the proposed methods and provides insights for aerospace system reliability analysis using available multilevel information.     

基于自适应代理模型的结构动力可靠度分析方法

结构动力可靠度分析对于衡量结构的安全状态和工作性能具有重要的指导意义。采用一种同时考虑 动态激励载荷和材料力学性能参数随机性的动力可靠度计算高效方法,通过建立不确定性材料力学性能参数 与条件动力可靠度之间的 Kriging代理模型,推导动力可靠度的解析表达式;提出一个新的学习函数来构建自 适应的 Kriging代理过程,通过复合材料飞行器蒙皮骨架结构在随机振动载荷和随机材料力学性能参数共同作 用下的动力可靠度分析对所提方法的准确性与高效性进行验证。结果表明:所提方法不仅能够避免使用代理 模型对动力可靠度求解时由于使用数值积分所引入的误差,同时能够使用尽可能少的计算成本获得准确的动 力可靠度结果。     

矩独立重要性分析的Kriging代理模型方法

结构重要性分析是结构不确定性分析的重要研究内容之一。作为一种矩独立的重要性测度指标,基于失效概率的重要性测度能够有效地反映输入变量的不确定性对结构失效概率的影响。然而,相比于其他形式的重要性测度,对基于失效概率的矩独立重要性测度进行高效准确的求解仍然存在一定的困难。基于此,结合Kriging代理模型提出了一种高效的矩独立重要性分析的新方法。所提方法首先通过较少的实验设计样本构建能够充分近似真实输入输出响应函数的Kriging代理模型,进而通过数值模拟策略对所构建的Kriging模型进行分析,最终求解得到各个输入变量基于失效概率矩独立重要性测度的主效应和总效应,给出各个输入变量对于失效概率的影响程度排序。相比于现有方法,所提方法由于引入Kriging代理模型极大地降低了对响应函数的计算次数,同时保证了重要性分析的计算精度。两个工程应用实例结果表明了所提方法在计算效率和计算精度方面的优势,体现了所提方法良好的适用性。     

Stochastic structural optimization using particle swarm optimization, surrogate models and Bayesian statistics

This paper focuses on a method to solve structural optimization problems using particle swarm optimization (PSO), surrogate models and Bayesian statistics. PSO is a random/stochastic search algorithm designed to find the global optimum. However, PSO needs many evaluations compared to gradient-based optimization. This means PSO increases the analysis costs of structural optimization. One of the methods to reduce computing costs in stochastic optimization is to use approximation techniques. In this work, surrogate models are used, including the response surface method (RSM) and Kriging. When surrogate models are used, there are some errors between exact values and approximated values. These errors decrease the reliability of the optimum values and discard the realistic approximation of using surrogate models. In this paper, Bayesian statistics is used to obtain more reliable results. To verify and confirm the efficiency of the proposed method using surrogate models and Bayesian statistics for stochastic structural optimization, two numerical examples are optimized, and the optimization of a hub sleeve is demonstrated as a practical problem.     

Safety lifetime analysis method for multi-mode time-dependent structural system

It is important to determine the safety lifetime of Multi-mode Time-Dependent Structural System (MTDSS). However, there is still a lack of corresponding analysis methods. Therefore, this paper establishes MTDSS safety lifetime model firstly, and then proposes a Kriging surrogate model based method to estimate safety lifetime. The first step of proposed method is to construct the Kriging model of MTDSS performance function by using extremum learning function. By identifying possible extremum mode of MTDSS, the performance function of MTDSS can be equivalently transformed into the one of Single-mode Time-Dependent Structure (STDS). The second step is to use the Advanced First Failure Instant Learning Function (AFFILF) to train the Kriging model constructed in the first step, so that the convergent Kriging model can identify the possible First Failure Instant (FFI) of STDS. Then safety lifetime can be searched quickly by dichotomy search. By using AFFILF, the minimum instant that the state is not accurately identified by the current Kriging model is selected as the training point, which avoids the unnecessary calculation which may be introduced into the existing First Failure Instant Learning Function (FFILF). In addition, the Candidate Sample Pool (CSP) reduction strategy is also adopted. By adaptively deleting the random candidate sample points whose FFI have been accurately identified by the current Kriging model, the training efficiency is further improved. Three cases show that the proposed method is accurate and efficient.     

Light weight optimization of stratospheric airship envelope based on reliability analysis

A stratospheric airship is an essential flight vehicle in the aviation field. In this paper, optimal design approach of stratospheric airships is developed to optimize envelope shape considering three failure modes and multidisciplinary analysis models, and could also reduce the mass of a stratospheric airship to be deployed at a specific location. Based on a theoretical analysis, three failure modes of airships including bending wrinkling failure, hoop tearing failure and bending kink failure, are given to describe and illustrate the failure mechanism of stratospheric airships. The results show that the location, length and size of the local uniform load and the large fineness ratio are easier to lead to bending wrinkling failure and bending kink failure. The small fineness ratio and the increasing differential pressure are more prone to cause hoop tearing failure for an airship hull. The failure probability is sensitive to the wind field. From an optimization design, the reliability analysis is essential to be carried out based on the safety of the airship. The solution in this study can provide economical design recommendations.