联合分布函数构造的Copula函数方法及结构可靠度分析

不完备概率信息条件下变量联合分布函数的确定及其对结构可靠度的影响还缺少系统地研究。为此,提出了基于Copula函数的变量联合概率分布函数构造方法,并分析了不同Copula函数类型对结构可靠度的影响规律。首先,简要介绍了基于Copula函数的变量联合分布函数构造方法。其次,提出了构件失效概率计算的直接积分方法。最后以构件可靠度问题为例研究了Copula函数的类型对结构可靠度的影响规律。结果表明:不完备概率信息条件下构件可靠度是不唯一的,表征变量间相关性的Copula函数类型对构件可靠度具有明显的影响,不同Copula函数计算的构件失效概率存在明显的差别,这种差别随构件可靠指标的增大(或失效概率的减小)而增大。Copula函数尾部相关性对结构可靠度具有重要的影响。当功能函数的失效区域位于Copula函数尾部时,计算的失效概率明显比没有尾部相关性的Copula函数的失效概率大。基于功能函数的均值和标准差计算的可靠指标不能反映Copula函数的类型对结构可靠度的影响,而基于功能函数实际分布求得的失效概率则可以有效反映不同Copula函数对结构可靠度的影响。     

2D-C/SiC复合材料面内剪切性能统计及强度B基准值

针对2D-C/SiC复合材料进行大子样面内剪切实验,研究材料面内剪切模量和强度的分布规律及强度B基准值。运用线性回归结合假设检验的方法,确定2D-C/SiC复合材料面内剪切力学性能的分布规律及参数,对比两种不同经验失效概率得到统计结果;通过观察试样最窄净截面微CT照片及断口电镜扫描照片,解释材料面内剪切强度分散性微观机制,基于分布规律,最终计算得到2D-C/SiC复合材料面内剪切强度威布尔B基准值。结果表明:强度和模量均同时服从威布尔、正态和对数正态分布,且理论模型与实验结果吻合良好,两种经验失效概率不影响力学性能分布规律;面内剪切强度分散性与最窄净截面致密度和界面脱粘长度有关;2D-C/SiC复合材料面内剪切强度威布尔B基准值为80.41MPa。     

基于贝叶斯理论的结构动力可靠度更新方法与分析

通过一种基于结构动力测试数据和贝叶斯理论的方法来更新结构可靠度。该方法考虑了结构可能受到的激励和结构模型及其参数的不确定性,利用结构在服役期间的动力测试数据,通过贝叶斯概率方法对结构参数进行了识别。利用拉普拉斯渐近估计解法,对仅根据设计条件得到的结构可靠度进行了更新。对受随机动荷载作用的某桁架结构在三种情况下的可靠度进行了计算:一为仅考虑荷载的随机性,二为考虑荷载的随机性和结构模型参数的先验分布,三为考虑荷载的随机性和结构模型参数的更新分布。比较了实际结构和有限元模型更新后的自振频率和振型,并对更新的可靠度计算结果进行了分析。结果表明,与确定性名义模型的失效概率相比,测点处自由度的更新失效概率与真实值较为接近;未测试自由度的更新失效概率可能与真实值差别较大;增加测点数不一定改善失效概率的更新效果。     

基于Copula函数的2.5MW风电齿轮箱齿轮可靠性分析

针对2.5 MW风电齿轮箱齿轮可靠性分析时,需考虑其接触疲劳和弯曲疲劳失效的相关性问题,根据风场长年监测数据,利用雨流计数法得到了其载荷谱,利用Romax Designer软件建立了2.5 MW风电齿轮箱的传动系统模型;利用其齿轮部件分析模块计算并统计得到了各齿轮的接触应力与弯曲应力分布;应用应力—强度干涉模型并基于Copula函数建立了考虑接触疲劳和弯曲疲劳相关性的齿轮疲劳可靠性计算模型;应用蒙特卡罗法对应力和疲劳强度抽样,并利用离差平方和最小值原理和MATLAB优化工具箱估计了Copula函数的参数,并计算出各齿轮的疲劳可靠度.研究结果为改进2.5 MW风电齿轮箱设计、提高其可靠性提供理论依据.     

基于Copula函数的并联结构系统可靠度分析

不完备概率信息条件下变量联合分布函数的确定及其对结构系统可靠度的影响还缺少系统地研究,该文目的在于研究表征变量间相关性的Copula函数对结构系统可靠度的影响规律。首先,简要介绍了变量联合分布函数构造的Copula函数方法。其次,提出了并联系统失效概率计算方法,并推导了相应的计算公式。最后以几种典型Copula函数为例研究了Copula函数类型对结构并联系统可靠度的影响规律。结果表明:表征变量间相关性的Copula函数类型对结构系统可靠度具有明显的影响,不同Copula函数计算的系统失效概率存在明显的差别,这种差别随构件失效概率的减小而增大。当并联系统的失效区域位于Copula函数尾部时,Copula函数的尾部相关性对系统可靠度有明显的影响,计算的失效概率比没有尾部相关性的Copula函数的失效概率大。当组成并联系统的两构件功能函数间正相关时,系统失效概率随相关系数的增大而增加;当构件功能函数间负相关时,系统失效概率随相关系数的增大而减小。此外,无论构件失效概率和变量间相关系数如何变化,Copula函数计算的失效概率都位于系统失效概率的上下限内。     

基于伪寿命分布的电主轴极小子样可靠性研究

在分析和研究了电主轴性能退化失效机理的前提下,选取合适的性能退化特征量,在此条件下设计电主轴可靠性实验方案,并在该方案的指导下进行电主轴可靠性实验。在研究了基于伪寿命分布的退化数据可靠性评估方法的基本原理基础上,应用该方法结合电主轴实验样本的可靠性实验数据,综合虚拟增广样本法对其可靠性进行评估。最终获得失效分布函数、分布密度函数及其曲线,以及一系列可靠性指标,包括可靠度函数及其曲线、失效率函数及其曲线、平均寿命及部分可靠寿命等。     

基于小样本失效数据的机械可靠性评估

"高可靠,少失效"的机械产品或系统特征使得可靠性评估变得愈发困难。针对这一问题,提出了一种基于三参数威布尔分布的小样本失效数据的机械可靠性评估方法。在确定寿命分布模型的基础上对小样本失效数据采用灰色估计法进行三参数估计,并进行拟合优度检验,进而通过蒙特卡洛抽样得到的子样作为参数的贝叶斯先验分布。在此基础上通过贝叶斯公式计算三参数后验分布,继而得到系统的可靠度、失效率等可靠性指标,更加准确地对小样本失效数据的机械可靠性进行评估。实际算例验证了方法的有效性。     

面向维修的机械系统可靠度预测与仿真研究

机电产品在服役期间因零件失效而产生故障,重组维修破坏了原有的系统可靠性模型,因而需要对设备可靠性问题重新进行研究和评价。基于机电系统中零件的失效时间分布密度函数,研究了在重组维护过程中机电系统服役期间零件年龄结构的分布规律,发展了机电系统可靠性数学模型。通过仿真研究,探讨了系统服役期间年龄结构、可靠度和失效率的发展规律,定量地研究了失效时间分布密度函数的参数对系统可靠度的影响。这对于评估机械系统的可靠性和全生命周期的失效率,制定合理的维修策略具有重要意义。     

预应力CFRP加固钢筋混凝土受弯构件的抗力概率模型研究

预应力CFRP 加固混凝土结构技术因其在材料性能利用方面的优越性能已成为CFRP 加固的热点方向,其中预应力CFRP 加固结构的可靠性是这一方向研究的重要内容。该文分析了影响预应力CFRP 板加固钢筋混凝土受弯构件承载力的主要变量的概率特征,考虑CFRP 板尺寸效应和应力分布的影响,采用Weibull 分布推导了CFRP 板的极限强度概率分布函数,根据预应力CFRP 张拉工艺,分析了预应力损失随机变量,建立了在不同失效模式(破坏形态)下的受弯构件抗力概率模型,并开展了参数敏感性分析,获得各个失效模式下抗力概率模型的主要影响因素。研究结果表明:抗力概率模型是预应力CFRP 加固结构的失效概率计算与可靠度校准的重要内容之一,各参数的影响规律与各失效模式的破坏形式密切相关。     

性能退化量分布LED可靠性评估

针对LED可靠性评估的方法大部分均基于样品伪寿命这一现象,提出基于退化量分布的LED可靠性评估方法。先依据指数模型预测后续时刻的退化量,再通过β分布统示法求出各时刻的累积失效概率,然后根据加速模型确定常应力下LED的可靠度函数。以国内某型LED灯具为实验对象,求出该型灯具寿命估计值为77100h,验证方法的实用性、有效性。     

A New Adaptive Response Surface Model for Reliability Analysis of 2.5D C/SiC Composite Turbine Blade

In order to calculate the failure probability of complex structures such as a 2.5D/SiC composites turbine blade and improve the structure safety, a new adaptive model of Response Surface (RS) analysis has been developed in this paper, which can improve the computational efficiency of structural failure problem while ensure the accuracy. The Gaussian Process Regression (GPR) theory was used to establish the RS and reconstruct the performance function of structure. And, an Adaptive Latin hypercube Sampling (ALHS) strategy was adopted in the process of establishing and correcting the RS. Finally the Direct Simulation Monte Carlo(DSMC)was utilized to calculate the failure probability of the performance function replacing the complex structure. Two numerical examples were calculated to validate the accuracy and computational efficiency of the proposed method. Additionally the finite element stress analysis results of 2.5D C/SiC composite turbine blade were used to structural reliability analysis by the proposed method. The approach in this paper provides a new way to evaluate the risk of the complex structures.     

Fracture behavior and mechanism of 2D C/SiC-BCx composite at room temperature

2D C/SiC composite was modified with partial BC_x matrix by low pressure chemical vapor infiltration technique (LPCVI), which was named as 2D C/SiC-BC_x composite. The flexural fracture behavior, mechanism, and strength distribution of 2D C/SiC-BC_x composite are investigated. The results indicate that the flexural strength, fracture toughness, and fracture work are 442.1 MPa, 22.84 MPa m^1/2, and 19.2 kJ m⁻², respectively. The flexural strength of C/SiC-BC_x composite decrease about 20% than that of C/SiC composite. However, the fracture toughness and fracture work increase about 19% and 18.5%, respectively. The properties varieties between C/SiC-BC_x composite and C/SiC composite can be attributed to the weak-bonding interface between BC_x/SiC matrices according to the results of detailed microstructure analysis. The strength distribution of 2D C/SiC-BC_x composite follows as Normal distribution or Weibull distribution with σ_u = 0, and m = 8.1393. The mean value of flexural strength for 2D C/SiC-BC_x composite is 443 MPa obtained by theory calculation, which is consistent with experiment result (442.1 MPa) very well.     

Oxidation behavior of 3D Hi–Nicalon/SiC composite

Oxidation behavior of a three dimensional (3D) Hi–Nicalon/SiC composite with CVD SiC coating was investigated in the simulated air using a thermogravimetric analysis (TGA) device. Below 1100 °C, the oxidation kinetics was controlled by gas diffusion through the defects in the SiC matrix and coating and resulted in the consumption of PyC interphase. The residual flexural strength did have not a remarkable fluctuation and the relationship between the residual strength to temperature and weight change to temperature of the 3D Hi–Nicalon/PyC/SiC composite indicated the same regularity. Above 1200 °C, the oxidation kinetics was controlled by oxygen diffusion through the SiO₂ scale formed on the SiC coating and matrix. And the residual flexural strength of the composites was governed by the strength degradation of the Hi–Nicalon fiber. After oxidation, the fracture displacement in flexural tests increased with the weight loss increasing and the fracture mode showed a non-brittle pattern.     

Hazard maps and global probability as a way to transfer standard fracture results to reliable design of real components

Design and lifetime prediction of structural and mechanical components require the assessment of the global probability of failure to be determined from stress and strain distributions obtained by FEM, as well as calculation of hazard maps in order to facilitate redesign and recognition of critical parts to be inspected regularly. The so-called generalized probabilistic local approach (GPLA), developed by the authors, allows the primary failure cumulative distribution function (PFCDF) owning to a certain failure type to be determined for a given material from experimental data and used subsequently for probabilistic design. The approach ensures a realistic safety margin provided that the failure criterion represented by an adequate generalized parameter (GP) and the corresponding failure criterion is properly recognized as a reference variable to be considered in the failure assessment. The way in which the results of such a reliability analysis are interpreted encompasses a variety of concepts under which failure can be understood and may be classified as global probability of failure and hazard maps, the former providing the conclusive failure probability for definitive design, and the latter representing, presumably, a risk of local failure that facilitates the possible component redesign but without providing the global probability of failure. In order to promote the implementation of the methodology proposed, an application is exemplary presented for the particular case of experimental results of glass plates. A finite element subroutine is developed for calculation of hazard maps and global probabilities of failure.     

2.5维C/SiC复合材料经向拉伸性能

将微观尺度的强度预测模型与单胞尺度有限元模型相结合, 建立了2.5维C/SiC复合材料的双尺度强度预测模型。该模型首先计算微观尺度的应力-应变曲线以及最终失效时的力学性能, 然后将其带入单胞模型, 对不同边界条件下单胞模型的弹性模量进行折减, 统计单胞模型的平均应力与应变, 最后得到单胞尺度的应力-应变关系和最终失效时的力学性能。通过2.5维C/SiC复合材料常温和高温条件下的经向单轴拉伸试验, 得到了2.5维C/SiC复合材料经向拉伸过程的应力-应变曲线以及最终失效时的力学性能。结果表明, 理论分析结果与实验值基本一致, 验证了该方法的有效性。     

二维编织陶瓷基复合材料偏轴拉伸力学性能预测

基于二维编织C/SiC复合材料的细观结构,建立了碳纤维丝/热解碳界面/SiC基体和纤维束/表层SiC基体两种尺度下的细观单胞模型,通过有限元方法计算碳纤维丝/热解碳界面/SiC基体模型的等效弹性常数和强度,然后代入纤维束/表层SiC基体模型中计算,并引入Tsai-Wu失效准则,考虑不同失效模式的损伤,建立了二维编织C/SiC复合材料的渐进损伤模型,模拟了其偏轴拉伸应力-应变行为。针对该模型,阐述了二维编织C/SiC复合材料单胞模型在复杂应力状态下其纤维束的损伤过程。数值模拟结果与实验数据吻合较好,验证了模型的有效性,为该种材料的力学性能分析提供了一种有效方法。     

Comparison of Fatigue Life Between C/SiC and SiC/SiC Ceramic-Matrix Composites at Room and Elevated Temperatures

In this paper, the comparison of fatigue life between C/SiC and SiC/SiC ceramic-matrix composites (CMCs) at room and elevated temperatures has been investigated. An effective coefficient of the fiber volume fraction along the loading direction (ECFL) was introduced to describe the fiber architecture of preforms. Under cyclic fatigue loading, the fibers broken fraction was determined by combining the interface wear model and fibers statistical failure model at room temperature, and interface/fibers oxidation model, interface wear model and fibers statistical failure model at elevated temperatures in the oxidative environments. When the broken fibers fraction approaches to the critical value, the composites fatigue fracture. The fatigue life S–N curves and fatigue limits of cross-ply, 2D and 3D C/SiC and SiC/SiC composites at room temperature, 550 °C in air, 750 °C in dry and humid condition, 800 °C in air, 1000 °C in argon and air, 1100 °C, 1300 °C and 1500 °C in vacuum, have been predicted. At room temperature, the fatigue limit of 2D C/SiC composite with ECFL of 20 % lies between 0.78 and 0.8 tensile strength; and the fatigue limit of 2D SiC/SiC composite with ECFL of 20 % lies between 0.75 and 0.85 tensile strength. The fatigue limit of 2D C/SiC composite increases to 0.83 tensile strength with ECFL increasing from 20 to 22.5 %, and the fatigue limit of 3D C/SiC composite is 0.85 tensile strength with ECFL of 37 %. The fatigue performance of 2D SiC/SiC composite is better than that of 2D C/SiC composite at elevated temperatures in oxidative environment.     

1500℃高温氧化环境下C/SiC复合材料结构的热/力联合试验

针对高超声速飞行器新型超高温结构力/热/氧化关键性能参量试验测试的迫切需求,自行设计并建立了可实现在高达1 500℃极端高温氧化环境下进行结构断裂性能测试的辐射式热/力联合试验系统,并对耐高温C/SiC复合材料结构在1 500℃等高温氧化环境下的断裂强度以及出现断裂时的时间点等关键性能参数进行了试验测试,当试验温度从1 000℃上升至1 500℃,C/SiC复合材料试验件的断裂强度下降了47.5%,断裂时间缩短50.1%。本极端高温载荷试验系统为高超声速飞行器结构热强度研究提供了重要的氧化环境下的热/力联合试验测试手段。研究结果表明:通过高温预加载可以明显提高C/SiC复合材料结构的断裂强度,增幅为38%,承载时间提高61.1%。试验结果为高超声速飞行器复合材料部件在极端热环境下的安全可靠性设计以及强度性能的改进提供了重要依据。     

Reliability Bounds based on Universal Generating Function and Discrete Stress-strength Interference Model

A method for estimating the component reliability is proposed when the probability density functions of stress and strength can not be exactly determined. For two groups of finite experimental data about the stress and strength,an interval statistics method is introduced. The processed results are formulated as two interval-valued random variables and are graphically represented by using two histograms. The lower and upper bounds of component reliability are proposed based on the universal generating function method and are calculated by solving two discrete stress-strength interference models. The graphical calculations of the proposed reliability bounds are presented through a numerical example and the confidence of the proposed reliability bounds is discussed to demonstrate the validity of the proposed method. It is showed that the proposed reliability bounds can undoubtedly bracket the real reliability value. The proposed method extends the exciting universal generating function method and can give an interval estimation of component reliability in the case of lake of sufficient experimental data. An application example is given to illustrate the proposed method.     

Simulation of Degraded Properties of 2D plain Woven C/SiC Composites under Preloading Oxidation Atmosphere

In this paper, a numerical model which incorporates the oxidation damage model and the finite element model of 2D plain woven composites is presented for simulation of the oxidation behaviors of 2D plain woven C/SiC composite under preloading oxidation atmosphere. The equal proportional reduction method is firstly proposed to calculate the residual moduli and strength of unidirectional C/SiC composite. The multi-scale method is developed to simulate the residual elastic moduli and strength of 2D plain woven C/SiC composite. The multi-scale method is able to accurately predict the residual elastic modulus and strength of the composite. Besides, the simulated residual elastic moduli and strength of 2D plain woven C/SiC composites under preloading oxidation atmosphere show good agreements with experimental results. Furthermore, the preload, oxidation time, temperature and fiber volume fractions of the composite are investigated to show their influences upon the residual elastic modulus and strength of 2D plain woven C/SiC composites.