基于改进MCMC方法的有限元模型修正研究

针对马尔可夫链蒙特卡罗(MCMC)模型修正方法在待修正参数维数较高时不易收敛和计算效率低下的问题,建立了融合自适应算法和相关向量机的快速模型修正方法。基于广义无偏见先验分布,推导了待修正参数的后验分布;在标准MCMC方法的基础上,引入延缓拒绝算法以提高新样本接受概率;引入自适应算法以自主调整建议分布的带宽。通过相关向量机建立待修正参数与有限元模型理论计算值之间的回归模型,以提高模型修正的计算效率。数值模拟和试验结构的模型修正结果表明,该方法的收敛速度较快,计算效率优于传统的一阶优化模型修正方法,为解决不确定性模型修正中的计算效率提供了一种新手段。     

一类基于改进Weibull分布模型电力电缆寿命评估方法

对电缆的剩余寿命进行评估是电缆寿命管理的关键环节,以往电缆寿命评估的方法中有Arrhenius方法和Weibull分布模型.对这两种方法分别进行分析,特别是确定Arrhenius模型中激活能的计算,以及应用Weibull分布模型对电缆寿命进行评估.最后以实际电缆的状态监测数据,对简化的Arrhenius模型进行仿真,说明所提出的方法是有效的.     

一类基于改进Weibull分布模型的电力电缆寿命评估方法

对电缆的剩余寿命进行评估是电缆寿命管理的关键环节,以往电缆寿命评估的方法中有Arrhenius方法和Weibull分布模型。对这两种方法分别进行分析,特别是确定Arrhenius模型中激活能的计算,以及应用Weibull分布模型对电缆寿命进行评估。最后以实际电缆的状态监测数据,对简化的Arrhenius模型进行仿真,说明所提出的方法是有效的。     

一种基于改进MCMC算法的模型修正方法

标准马尔可夫链蒙特卡罗(MCMC)算法不易收敛、拒绝率高,使其应用受到限制。在贝叶斯方法中引入最大熵值法来估计参数的后验概率密度函数最大值,进而将布谷鸟算法中新鸟巢更新的思想融入Metropolis-Hasting(MH)抽样算法得到改进的MH抽样算法,同时使用支持向量机(SVM)建立待修正参数与有限元模型输出之间的代理模型,以提高模型修正的计算效率。分别使用三自由度线性系统和平面桁架模型来验证本文方法的有效性,结果表明:修正后样本的马尔可夫链混合性能好,停滞概率低,修正后参数相对误差均小于2%。     

竞争失效场合Weibull产品的可靠性分析

在竞争失效场合下,建立了Weibull产品的具有二项移走的逐步Ⅱ型截尾寿命试验模型.针对一般近似算法在小样本情形下精度较低的问题,以Gamma分布综合产品的先验信息,采用Gibbs抽样建立了参数的Bayes估计.利用Bootstrap方法、Bayes后验分布法分别构造了参数的置信区间.最后,利用随机模拟方法对估计结果进行了比较,结果表明在小样本情形下,Bayes比MLEs估计效果更好.     

结构可靠性分析的模拟重要抽样方法

提出了一种基于Kriging模拟的重要抽样方法用以结构可靠度计算。对于含有隐式极限状态方程的问题,重要抽样方法将大部分的计算时间用于结构有限元分析,这使得重要抽样的计算效率被大大降低了。而Kriging方法能够较好地模拟高度非线性的极限状态方程,并以此模拟计算代替真实的结构分析,其主要目的是为了减少蒙特卡罗方法的计算量。将此方法用于两个框架结构可靠度分析的实例,表明了该方法的有效性和较高的计算效率。     

基于Weibull模型的C/C复合材料销钉剪切强度分布及本构关系

针对C/C复合材料销钉力学性能各向异性的特点,开展基于Weibull分布模型的C/C销钉剪切强度分布及本构关系研究,探讨不同剪切方向对C/C销钉剪切强度和剪切本构的影响规律。基于两参数Weibull分布模型,采用最小二乘法获得不同剪切方向上剪切强度的分布规律;根据C/C复合材料损伤失效机制,采用基于Weibull分布的弹性损伤模型表征材料的剪切本构关系,并通过试验数据获取损伤模型中的参数。结果表明:通过Kolmogorov-Smirnov拟合优度检验,两参数Weibull分布模型能较好地表征C/C销钉剪切强度的分布规律;沿45°方向剪切的C/C销钉,其剪切强度最高;随着剪切角度的增大销钉剪切刚度逐渐降低,从0°方向上的19.46 kN/mm下降到90°方向上的12.70 kN/mm。      

人的可靠性模型的回归分析

根据回归分析理论,提出了建立人的可靠性单变量模型的一般方法。并在试验的基础上,利用子样试验数据,构造了小型人群的动作可靠性的单变量模型。     

基于MCMC算法的粗集料粒径分布推断研究

运用机器视觉对振动盘掉落的粗集料进行数据采集,得到了动态集料的‘伪三维’图像。针对图像信息不能准确表达集料真实三维情况,引入贝叶斯统计推断的思想对集料进行粒径分布的推断,选取等效Feret短径作为图像特征,由于集料在大粒径情况下其Feret短径与实际粒径误差较大,故增加了等效椭圆短径作为第二特征。为获得准确的后验分布和高效的工程计算能力,采用了MCMC算法,解决了传统贝叶斯统计推断在高维计算不足的问题,从而得到了集料粒径分布的后验分布。实验结果表明：该方法的针对合格集料的粒径分布测量误差保持在±2.5%以内,不合格集料误差保持在±3.5%以内。     

一种基于Bayes方法的随机模型修正方法

提出了一种随机模型的修正方法用以估计结构参数的统计特性.基于Bayes方法的参数估计原理,将需要修正的结构参数的均值和方差看作符合一定先验概率分布的随机变量,根据核密度估计原理构建得到似然函数,进而使用基于差分进化的MCMC方法估计参数的后验概率密度,并根据最大后验概率密度准则估计结构参数的均值和方差.同时使用Kriging方法建立了结构输入和输出之间的代理模型,保证计算精度的同时极大地节约了计算时间.数值算例验证了本方法的可行性.     

RELIABILITY ANALYSIS AND MAINTENANCE POLICY OF RADIATORS FOR A LARGE FLEET OF BUSES

Parts in an engineering system are subject to deterioration caused by friction, impact, metal fatigue, etc. which occur when the system is in operation, and also due to ageing of its plastic and rubber parts and rusting of metal parts. In order to ensure that a system functions properly, it is important to perform maintenance which rectifies the faults in its parts as time passes. In this paper the authors use Weibull analysis to investigate the failure pattern of radiators in the cooling system of different bus types in a large public transportation company, and work out from a costing point of view that regular preventive maintenance is not recommended but overhaul of the radiators should be done once in several years when the bus undergoes a major overhaul. In this analysis, the renewal function of the Weibull distribution has to be computed. A table for the renewal function has been computed as well. The manpower requirement for the maintenance of radiators for the bus fleet is also investigated. © 1997 John Wiley & Sons, Ltd.     

Life-Test Sampling Plans for Two-Parameter Weibull Populations

In this paper, we give variables sampling plans for items whose failure times are distributed as either extreme-value variates or Weibull variates (the logarithms of which are from an extreme-value distribution). Tables applying to acceptance regions and operating characteristics for sample size n, ranging from 3 to 18, are given. The tables allow for Type II censoring, with censoring number r ranging from 3 to n. In order to fix the maximum time on test, the sampling plan also allows for Type I censoring.

Acceptance/rejection is based upon a statistic incorporating best linear invariant estimates, or, alternatively, maximum likelihood estimates of the location and scale parameters of the underlying extreme value distribution. The operating characteristics are computed using an approximation discussed by Fertig and Mann (1980).     

Bayesian estimation of mixed Weibull distributions

Estimation of mixed Weibull distribution by maximum likelihood estimation and other methods is frequently difficult due to unstable estimates arising from limited data. Bayesian techniques can stabilize these estimates through the priors, but there is no closed-form conjugate family for the Weibull distribution. This paper reduces the number of numeric integrations required for using Bayesian estimation on mixed Weibull situations from five to two, thus making it a more feasible approach to the typical user. It also examines the robustness of the Bayesian estimates under a variety of different prior distributions. It is found that Bayesian estimation can improve accuracy over the MLE for situations with low mixture ratios so long as the prior on the weak subpopulation's characteristic life has an expected value less than or equal to the true characteristic life.     

A study of a storage reliability estimation problem

Storage reliability, which describes the failure or deterioration of items in a dormant state, is considered in this paper. The study presented here is focused on the estimation of the storage reliability after a certain amount of storage time. We start with simple non-parametric estimation of the current reliability and then study the problem of parametric estimation based on a simple Weibull distribution assumption. Both maximum likelihood estimation and graphical techniques are considered in this case. The study is useful for planning a storage environment and making a decision about the maximum length of storage. Furthermore, the information can be used in the design and improvement of products for which the storage is an important part of the product's life cycle. A numerical example is provided to enlighten the idea.