紊流激励下基于贝叶斯统计推断的颤振边界预测方法研究

提出将贝叶斯统计推断方法推广应用于大气紊流激励下飞行器结构的颤振分析,对含不确定性因素影响的模态参数识别与颤振边界预测进行研究。在采用自然激励技术从结构在大气紊流激励下的响应中提取自由衰减信号后,基于贝叶斯统计推断,通过马尔科夫链蒙特卡罗(Markov chain Monte Carlo, MCMC)算法对结构模态参数的后验概率密度函数进行采样识别,并利用Z-W(Zimmerman-Weissenburger)颤振裕度法获取颤振速度概率分布,预测颤振边界并分析其不确定性。进行了数值仿真研究,对大气紊流激励下的结构响应数据进行分析,验证了所提出方法的有效性。     

一种新的预测蛋白质二级结构的模型-贝叶斯神经网络

提出了一种新的基于贝叶斯神经网络（BNN）的蛋白质二级结构预测方法。计算结果表明,BNN的性能优于反向神经网络（BPNN）,平均Q3精度在四组交叉证实数据集与测试数据集下分别提高了3．65％和4．01％;还提出了一种有效缩短马尔可夫链蒙特卡罗（MCMC）模拟过程中“burn in”阶段的交叉证实初值选取方法。     

基于贝叶斯方法的包装企业供应商评价与选择模型

目的建立基于贝叶斯方法的供应商选择模型。方法建立一个供应商选择动态过程,将供应商的历史信息与供应商提供的自身信息联系起来;利用贝叶斯方法对供应商达成采购企业目标的能力进行评判和修订,并进一步评估供应商风险。结果贝叶斯方法为包装企业评价和选择供应商提供了规避风险的有效手段,可以提高包装企业的竞争力。结论基于风险视角下的供应商选择与评价模型,是保证包装企业在控制供应商风险的前提下对供应商进行选择评价的重要工具。     

基于模块化贝叶斯推理的随机非线性模型修正EI北大核心CSCD

为同时考虑多种不确定因素对非线性结构模型修正的影响,提出了一种基于模块化贝叶斯推理的随机非线性模型修正方法。为了描述具有时变特性的非线性动力响应,提取结构动力响应主分量的瞬时加速度幅值作为非线性指标,基于贝叶斯方法,将整个模型修正过程分为3个相互独立的模块:首先建立非线性模型的高斯过程替代模型记为模块一;同时,为考虑模型误差对非线性结构随机模型修正的影响,将设计变量作为输入,模型误差作为输出,建立关于模型误差的高斯过程替代模型,记为模块二;最后,结合贝叶斯推理方法与模块一和模块二中的高斯过程模型,利用过渡马尔可夫链蒙特卡罗(transitional Markov Chain Monte Carlo,TMCMC)随机采样方法估计待修正参数后验概率密度函数,实现基于模块化贝叶斯推理的随机非线性模型修正研究。采用三跨连续梁桥数值算例来验证所提出的随机非线性模型修正方法的准确性,并对比了不同噪声水平、不同程度模型误差条件下的模型修正结果。研究结果表明,基于模块化贝叶斯推理的随机非线性模型修正方法能够有效地实现非线性结构的随机模型修正,并具有较好的鲁棒性。     

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%。     

基于改进SCAM算法的结构物理参数识别贝叶斯方法

针对贝叶斯估计中逐分量自适应Metropolis(single component adaptive Metropolis,SCAM)算法易生成重复性样本,导致抽样效率低、结果误差大等问题,重新定义了提议分布方差的表达式,提出了改进的SCAM算法,使得抽样样本序列构成的马尔可夫链相对稳定。进而将贝叶斯理论与改进的SCAM算法相结合,求解结构物理参数的后验边缘概率分布、最优估计值以识别和估计结构损伤,通过理论分析和结构数值模拟算例验证了改进的SCAM算法的有效性。结果表明,改进的SCAM算法既提高了抽样效率,又提高了计算结果准确性,可应用于物理参数识别及损伤识别与评估等工作。     

基于加速度频响函数小波变换的贝叶斯模型修正EI北大核心CSCD

针对频响函数的似然函数推导复杂以及马尔科夫链蒙特卡罗(Markov chain Monte Carlo,MCMC)算法不易收敛、样本拒绝率高的问题,提出一种基于小波变换和改进MCMC算法的贝叶斯模型修正法。首先,引入模态参与变异系数准则选取激励点位置、模态动能法选取测点位置;然后,构造Kriging模型,计算加速度频响函数并进行小波变换,提取小波总能量作为Kriging模型输出,并通过粒子群算法优化Kriging模型相关系数;最后,为提高采样效率,以延缓拒绝策略为基础,当候选样本被拒绝时,引入天牛须搜索算法产生新的候选样本,以此估计待修正参数的后验概率分布。分别使用车辆三自由度系统和空间桁架模型验证所提方法,结果表明:修正后获得的马尔科夫链整体性能较好,样本接受率提高,各参数的相对误差基本保持在1%以内且具有良好的抗噪性。     

基于模糊数学的测试用例优化技术研究

为了缩短软件测试周期,测试用例的生成是关键.在模糊综合评判数学模型和马尔可夫使用链模型的基础上,提出了基于模糊数学的测试用例优化的方法.通过实例证明了这一技术的实用性和有效性.     

计量中回归模型参数值及其不确定度评估

针对计量领域中广泛应用的数据回归处理方法,阐述了在基于正态分布噪声条件下,最小二乘法与贝叶斯推断法用于回归模型参数估计以及相应不确定度评估的过程。GUM系列不确定度评估准则中没有明确指出如何对回归参数进行不确定度评估,同时有些回归模型也无法唯一地转化为相应的测量方程。通过计量校准的实例说明了如何处理相应参数的确定等问题,以此说明2种方法的相同与不同之处。最小二乘方法计算简单直接且便于使用;而基于贝叶斯推断的方法则能充分利用计量校准中的经验和历史数据等信息,但由于其参数后验分布计算通常较为复杂,需采用马尔科夫链-蒙特卡罗(MCMC)法通过数值计算得到关注参数的结果。     

多方程线性模型系统的贝叶斯预报分析

多方程线性模型系统的贝叶斯预报分析是贝叶斯线性模型理论的重要组成部分。通过模型系统的统计结构,证明了矩阵正态-Wishart分布是模型参数的共轭先验分布;根据模型的样本似然函数和参数的先验分布推导了参数的后验分布;然后,从数学上严格推断了模型的预报分布密度函数,证明了模型预报分布为矩阵t分布。研究结果表明：由于参数先验分布的作用辟,样本的预报分布与其原统计分布有着本质性的差异,前者为矩阵正态分布,而后者为矩阵t分布。     

Reliability Analysis for Degradation of Locomotive Wheels using Parametric Bayesian Approach

This paper undertakes a reliability study using a Bayesian survival analysis framework to explore the impact of a locomotive wheel's installed position on its service lifetime and to predict its reliability characteristics. The Bayesian Exponential Regression Model, Bayesian Weibull Regression Model and Bayesian Log‐normal Regression Model are used to analyze the lifetime of locomotive wheels using degradation data and taking into account the position of the wheel. This position is described by three different discrete covariates: the bogie, the axle and the side of the locomotive where the wheel is mounted. The goal is to determine reliability, failure distribution and optimal maintenance strategies for the wheel. The results show that: (i) under specified assumptions and a given topography, the position of the locomotive wheel could influence its reliability and lifetime; (ii) the Bayesian Log‐normal Regression Model is a useful tool. Copyright © 2013 John Wiley & Sons, Ltd.     

Logistic 组稀疏回归模型的 Bayes 建模及变分推断

在工程应用中,如数据挖掘、成本预测以及风险预测等,Logistic 回归是一类十分重要的预测方法．当前,大部分 Logistic 回归方法都是基于优化准则而设计,这类回归方法具有参数调试过程繁琐、模型解释性差、估计子没有置信区间等缺点．本文从 Bayes 概率角度研究 Logistic 组稀疏性回归的建模与推断问题．具体来说,首先利用高斯-方差混合公式提出 Logistic 组稀疏回归的 Bayes 概率模型;其次,通过变分 Bayes 方法设计出一个高效的推断算法．在模拟数据上的实验结果表明,本文所提出的方法具有较好的预测性能．     

结构物理参数识别的贝叶斯估计马尔可夫蒙特卡罗方法

从结构动力特征方程出发,以结构主模态参数为观测量,推得结构物理参数线性回归模型。对该模型应用贝叶斯估计理论得到物理参数后验联合分布,再结合马尔可夫蒙特卡罗抽样方法给出各个物理参数的边缘概率分布和最优估计值,而提出了基于结构主模态参数的结构物理参数识别贝叶斯估计马尔可夫蒙特卡罗方法。对五层剪切型结构的数值研究表明,此方法能够利用少数主模态参数给出结构质量和刚度参数的概率分布和最优识别值,而且在主模态参数较准确时识别误差很小。     

A fast Bayesian approach using adaptive densifying approximation technique accelerated MCMC

A novel algorithm is presented in this study to improve the efficiency and accuracy of Bayesian approach for fast sampling of posterior distributions of the unknown structure parameters. This algorithm can save a computational cost by resolving the efficiency problem in Bayesian identifications. In this algorithm, an approximation model based on the radial basis function is first used to replace the actual joint posterior distribution of the unknown parameters. An adaptive densifying technique is then introduced to increase the accuracy of the approximation model by reconstructing them with densified samples. Finally, the marginal posterior distributions for each parameter with fine accuracy can be efficiently achieved using the Markov Chain Monte Carlo method based on the present densified approximation model. Two numerical examples are investigated to demonstrate that the present algorithm can achieve significant computational gains without sacrificing the accuracy.     

Investigation of time and weather effects on crash types using full Bayesian multivariate Poisson lognormal models

Previous research shows that various weather elements have significant effects on crash occurrence and risk; however, little is known about how these elements affect different crash types. Consequently, this study investigates the impact of weather elements and sudden extreme snow or rain weather changes on crash type. Multivariate models were used for seven crash types using five years of daily weather and crash data collected for the entire City of Edmonton. In addition, the yearly trend and random variation of parameters across the years were analyzed by using four different modeling formulations. The proposed models were estimated in a full Bayesian context via Markov Chain Monte Carlo simulation. The multivariate Poisson lognormal model with yearly varying coefficients provided the best fit for the data according to Deviance Information Criteria. Overall, results showed that temperature and snowfall were statistically significant with intuitive signs (crashes decrease with increasing temperature; crashes increase as snowfall intensity increases) for all crash types, while rainfall was mostly insignificant. Previous snow showed mixed results, being statistically significant and positively related to certain crash types, while negatively related or insignificant in other cases. Maximum wind gust speed was found mostly insignificant with a few exceptions that were positively related to crash type. Major snow or rain events following a dry weather condition were highly significant and positively related to three crash types: Follow-Too-Close, Stop-Sign-Violation, and Ran-Off-Road crashes. The day-of-the-week dummy variables were statistically significant, indicating a possible weekly variation in exposure. Transportation authorities might use the above results to improve road safety by providing drivers with information regarding the risk of certain crash types for a particular weather condition.     

An Efficient Sampling Technique for Bayesian Inference With Computationally Demanding Models

In the environmental sciences, a large knowledge base is typically available on an investigated system or at least on similar systems. This makes the application of Bayesian inference techniques in environmental modeling very promising. However, environmental systems are often described by complex, computationally demanding simulation models. This strongly limits the application of Bayesian inference techniques, because numerical implementation of these techniques requires a very large number of simulation runs. The development of efficient sampling techniques that attempt to approximate the posterior distribution with a relatively small parameter sample can extend the range of applicability of Bayesian inference techniques to such models. In this article a sampling technique is presented that tries to achieve this goal. The proposed technique combines numerical techniques typically applied in Bayesian inference, including posterior maximization, local normal approximation, and importance sampling, with copula techniques for the construction of a multivariate distribution with given marginals and correlation structure and with low-discrepancy sampling. This combination improves the approximation of the posterior distribution by the sampling distribution and improves the accuracy of results for small sample sizes. The usefulness of the proposed technique is demonstrated for a simple model that contains the major elements of models used in the environmental sciences. The results indicate that the proposed technique outperforms conventional techniques (random sampling from simpler distributions or Markov chain Monte Carlo techniques) in cases in which the analysis can be limited to a relatively small number of parameters.     

基于贝叶斯推理时空交互式多视角目标跟踪

本文针对多摄像机视频跟踪的应用场景,在贝叶斯推理的框架下,提出了一种具有分布式时空交互计算特点的目标跟踪算法.本文首先利用贝叶斯网络对拓扑确定的多摄像机系统进行建模,并对待估状态(目标位置)高阶联合后验概率密度函数进行时空的递推,最后借助序列蒙特卡洛(粒子滤波)逼近后验概率密度函数,并采用高效的数据传送机制高效求解出跟...     

Complex system reliability modelling with Dynamic Object Oriented Bayesian Networks (DOOBN)

Nowadays, the complex manufacturing processes have to be dynamically modelled and controlled to optimise the diagnosis and the maintenance policies. This article presents a methodology that will help developing Dynamic Object Oriented Bayesian Networks (DOOBNs) to formalise such complex dynamic models. The goal is to have a general reliability evaluation of a manufacturing process, from its implementation to its operating phase. The added value of this formalisation methodology consists in using the a priori knowledge of both the system's functioning and malfunctioning. Networks are built on principles of adaptability and integrate uncertainties on the relationships between causes and effects. Thus, the purpose is to evaluate, in terms of reliability, the impact of several decisions on the maintenance of the system. This methodology has been tested, in an industrial context, to model the reliability of a water (immersion) heater system.     

A Bayesian model averaging method for software reliability modeling and assessment

The software reliability modeling is of great significance in improving software quality and managing the software development process. However, the existing methods are not able to accurately model software reliability improvement behavior because existing single model methods rely on restrictive assumptions and combination models cannot well deal with model uncertainties. In this article, we propose a Bayesian model averaging (BMA) method to model software reliability. First, the existing reliability modeling methods are selected as the candidate models, and the Bayesian theory is used to obtain the posterior probabilities of each reliability model. Then, the posterior probabilities are used as weights to average the candidate models. Both Markov Chain Monte Carlo (MCMC) algorithm and the Expectation–Maximization (EM) algorithm are used to evaluate a candidate model's posterior probability and for comparison purpose. The results show that the BMA method has superior performance in software reliability modeling, and the MCMC algorithm performs better than EM algorithm when they are used to estimate the parameters of BMA method.