桥梁结构物理参数识别的双单元子结构法

为了解决大型桥梁结构局部区域的健康监测问题,提出了一种用于桥梁结构物理参数识别的双单元子结构法。该方法是一种基于有限元的时域系统识别方法,其一次仅能识别出两个相邻单元的物理参数。将桥梁结构划分为若干个单元,选取任意两相邻单元为研究对象,建立其状态方程和观测方程。应用广义卡尔曼滤波,可得到该两相邻单元的质量、刚度和阻尼等物理参数。以一座三跨连续梁桥为例进行仿真分析,识别出不同信噪比情况下其子结构的物理参数。结果表明参数识别精度高,收敛速度快,从而验证了方法的有效性。     

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。     

基于Gibbs抽样的马尔科夫蒙特卡罗方法在结构物理参数识别及损伤定位中的研究

通过对结构动力特征方程进行的一系列变化,得到了线性结构识别模型,并由贝叶斯更新理论得到其后验分布形式.利用结构的模态参数,并考虑其随机性,应用基于Gibbs抽样的马尔科夫蒙特卡罗方法对线性结构识别模型中各参数的条件后验分布进行了抽样,成功地实现了结构物理参数识别及损伤定位.数值算例表明:Gibbs抽样结果可以以不同的方...     

考虑参数更新的大跨桥梁温差极值分布估计方法研究

为了建立可靠的大跨桥梁全寿命温差极值分布模型,提出采用广义帕累托分布（Generalized Pareto Distribution,GPD）对超阈值温差的统计特征进行描述,并给出了超阈值温差样本相关性的去除方法和最优阈值的确定方法。为了融合温差分布的先期经验信息和不断递增的温差监测样本,建立了考虑参数更新的贝叶斯估计方法,利用Gibbs抽样对贝叶斯后验分布进行计算,进而得到准确的基于广义帕累托分布的温差极值分布模型。最后利用九堡大桥长期监测温差数据进行了验证。研究结果表明,广义帕累托分布能够对超阈值温差样本的尾部统计特征进行准确描述,提出的考虑参数更新的温差极值分布贝叶斯估计方法能够对广义帕累托分布的参数进行可靠估计,估计的统计模型比极大似然估计计算的结果更接近真实情况。研究结果可为大跨桥梁温差特性分析提供参考。     

基于UKF模型更新的混合试验方法

在混合试验中,将结构划分为物理子结构和数值子结构两部分。对遭遇强震下大型结构的混合试验,很难保证数值子结构仍处于弹性阶段。为确保数值子结构模型的准确性,提出基于Unscented Kalman filter (UKF) 模型更新混合试验方法。该方法假定数值子结构与物理子结构恢复力模型相同,在混合试验进行中利用物理子结构试验观测数据,采用UKF方法在线识别物理子结构模型参数,实时更新数值子结构模型参数。通过数值模拟,应用UKF方法对单自由度结构非线性模型进行在线参数识别,验证UKF方法性能;通过对弹簧试件实际试验,验证该混合试验方法的有效性。结果表明,基于UKF模型更新混合试验方法较传统混合试验方法精度更高。     

基于贝叶斯估计的动载荷识别方法

为了降低测量误差等不确定性因素对识别结果的影响,建立基于贝叶斯估计理论的动力学系统载荷识别方法。首先,根据动力学系统运动方程,利用贝叶斯理论,推导载荷和误差参数的联合后验分布,进而得到载荷和误差参数的边缘概率分布;然后,采用马尔可夫蒙特卡罗方法,估计动力学系统所受的载荷,并利用仿真算例与基于奇异值分解的载荷识别方法进行对比;最后,利用实验数据,进一步验证本方法的有效性。结果表明,该方法在一定程度上减小了不确定性因素造成的识别误差,对于提高动载荷识别精度具有一定的参考意义。     

基于子空间法与子结构法时变结构连接处的物理参数在线辨识

结构系统连接处的物理参数对于系统建模具有极其重要的影响,如何准确合理地辨识出结构系统连接处的物理参数一直是人们研究的热点,也一个存在相当大难度的问题。一般利用传统的子结构法进行参数辨识,还仅局限于针对非运动状态下系统结构连接处的物理参数识别问题。文中在传统子结构法的基础上,提出一种计算结构系统在运动状态下连接处时变物理参数在线辨识方法,这种方法分两步对系统进行辨识。首先利用子空间法实时辨识出时变结构系统的特征值与特征向量,然后利用辨识出的特征值与特征向量以子结构法为基础在线辨识出连接处的物理参数。通过改变子空间法的Hankel矩阵的分解方法提高计算速度。文中仅用响应数据形成子空间法的脉冲响应矩阵。通过仿真分析验证方法的有效性。     

基于静动力凝聚及扩展卡尔曼滤波的连续梁桥损伤识别

以卡尔曼滤波算法为代表的物理参数识别方法在结构损伤识别方面得到广泛应用,但限于状态方程的复杂性,大部分应用集中在具有平动自由度的剪切型建筑结构模型,且一般需要较完备的激励和响应信息。利用静力凝聚方法消去转动自由度以建立力学模型,并提出考虑Rayleigh阻尼的动力凝聚方法,实现了较复杂连续梁桥有限元模型的等效简化。针对桥梁检测及健康监测需求,提出了利用锤击产生自由振动的激励方式进行连续梁桥扩展卡尔曼滤波在线损伤识别方法,从而克服了传统方法需要复杂激励信号的不足。以一座三跨连续梁桥为例进行了仿真分析,识别出了不同位置的刚度和阻尼物理参数,参数识别结果具有较高精度和抗噪性,收敛速度快,证明该方法有效可行。     

环境激励下基于快速贝叶斯FFT的实桥模态参数识别

近年来,贝叶斯理论逐步应用于工程结构的模态参数识别、有限元模型修正及状态评估等方面。基于快速贝叶斯FFT的模态参数识别方法是针对某一共振频率带的单个模态,通过一个四维的数值优化问题得到模态参数的最佳估计,并通过对数似然函数关于模态参数的二阶导数求得Hessian矩阵,使得基于贝叶斯的参数识别方法可以快速高效地进行。为了评估该方法在实际桥梁结构模态参数识别应用中的可行性及优越性,运用快速贝叶斯FFT方法对环境激励下一刚构-连续组合梁桥的竖向加速度响应进行了分析处理,识别了其模态参数的最佳估计,并根据模态参数的变异系数评估了其后验的不确定性。识别结果与随机子空间识别结果的对比表明,两种方法识别的频率和振型基本吻合,阻尼识别结果的差异仍然较大。     

基于贝叶斯理论嵌套抽样的结构物理参数识别研究EI北大核心CSCD

基于贝叶斯估计的结构物理参数识别中,传统马尔可夫蒙特卡洛抽样(MCMC)在解决高维密度函数问题时往往存在抽样效率低、不收敛等问题。采用嵌套抽样方法代替传统的马尔可夫蒙特卡洛抽样,解决了结构物理参数识别中高维后验联合概率密度函数问题。首先从结构加速度时程响应时程出发,建立了后验联合概率密度函数,然后重新定义了结构参数先验分布与似然函数,实现了基于嵌套抽样的结构物理参数识别。采用该方法分别对10层剪切结构数值模型与3层RC框架结构振动台试验模型进行识别,得到了结构刚度及阻尼比等参数,并与试验现象进行了对比。结果表明,该方法可以解决贝叶斯公式高维后验联合概率密度函数问题,且能高效识别结构物理参数,同时也验证了该方法在真实结构物理参数识别与结构损伤识别中的适用性与可靠性。     

基于Novozhilov理论薄壁弯箱位移参数的动态Bayes估计

基于Novozhilov理论推导了薄壁弯箱结构的有限曲条控制方程,并首次建立了薄壁弯箱位移参数的动态Bayes误差函数,推导了参数的动态Bayes均值和方差表达式,提出步长的一维自动搜索方案后,并结合共轭梯度法推导了薄壁弯箱位移参数的动态Bayes估计公式,同时给出了具体计算步骤。通过算例分析,总结了薄壁弯箱位移参数先验信息准确性判定方法及位移参数动态Bayes估计的其它重要结论。     

Advanced Scientific Computing in BASIC With Applications in Chemistry,Biology, and Pharmacology

Tuning and calibration are processes for improving the representativeness of a computer simulation code to a physical phenomenon. This article introduces a statistical methodology for simultaneously determining tuning and calibration parameters in settings where data are available from a computer code and the associated physical experiment. Tuning parameters are set by minimizing a discrepancy measure while the distribution of the calibration parameters are determined based on a hierarchical Bayesian model. The proposed Bayesian model views the output as a realization of a Gaussian stochastic process with hyper-priors. Draws from the resulting posterior distribution are obtained by the Markov chain Monte Carlo simulation. Our methodology is compared with an alternative approach in examples and is illustrated in a biomechanical engineering application. Supplemental materials, including the software and a user manual, are available online and can be requested from the first author.     

Bayesian Analysis of Step‐Stress Accelerated Life Test with Exponential Distribution

In this article, we propose a general Bayesian inference approach to the step‐stress accelerated life test with type II censoring. We assume that the failure times at each stress level are exponentially distributed and the test units are tested in an increasing order of stress levels. We formulate the prior distribution of the parameters of life‐stress function and integrate the engineering knowledge of product failure rate and acceleration factor into the prior. The posterior distribution and the point estimates for the parameters of interest are provided. Through the Markov chain Monte Carlo technique, we demonstrate a nonconjugate prior case using an industrial example. It is shown that with the Bayesian approach, the statistical precision of parameter estimation is improved and, consequently, the required number of failures could be reduced. Copyright © 2011 John Wiley & Sons, Ltd.     

Bayesian State Space Modeling of Physical Processes in Industrial Hygiene

Abstract

Exposure assessment models are deterministic models derived from physical–chemical laws. In real workplace settings, chemical concentration measurements can be noisy and indirectly measured. In addition, inference on important parameters such as generation and ventilation rates are usually of interest since they are difficult to obtain. In this article, we outline a flexible Bayesian framework for parameter inference and exposure prediction. In particular, we devise Bayesian state space models by discretizing the differential equation models and incorporating information from observed measurements and expert prior knowledge. At each time point, a new measurement is available that contains some noise, so using the physical model and the available measurements, we try to obtain a more accurate state estimate, which can be called filtering. We consider Monte Carlo sampling methods for parameter estimation and inference under nonlinear and non-Gaussian assumptions. The performance of the different methods is studied on computer-simulated and controlled laboratory-generated data. We consider some commonly used exposure models representing different physical hypotheses. Supplementary materials for this article are available online.     

A probabilistic-based airframe integrity management model

This paper proposes a lognormal distribution model to relate crack-length distribution to fatigue damage accumulated in aging airframes. The fatigue damage is expressed as fatigue life expended (FLE) and is calculated using the strain-life method and Miner's rule. A two-stage Bayesian updating procedure is constructed to determine the unknown parameters in the proposed semi-empirical model of crack length versus FLE. At the first stage of the Bayesian updating, the crack closure model is used to simulate the crack growth based upon generic but uncertain physical properties. The simulated crack-growth results are then used as data to update the uninformative prior distributions of the unknown parameters of the proposed semi-empirical model. At the second stage of the Bayesian updating, the crack-length data collected from field inspections are used as evidence to further update the posteriors from the first stage of the Bayesian updating. Two approaches are proposed to build the crack-length distribution for the fleet based on individual posterior crack distribution of each aircraft. The proposed distribution model of the crack length can be used to analyze the reliability of aging airframes by predicting, for instance, the probability that a crack will reach an unacceptable length after additional flight hours.     

A sequential constant‐stress accelerated life testing scheme and its Bayesian inference

In the analysis of accelerated life testing (ALT) data, some stress‐life model is typically used to relate results obtained at stressed conditions to those at use condition. For example, the Arrhenius model has been widely used for accelerated testing involving high temperature. Motivated by the fact that some prior knowledge of particular model parameters is usually available, this paper proposes a sequential constant‐stress ALT scheme and its Bayesian inference. Under this scheme, test at the highest stress is firstly conducted to quickly generate failures. Then, using the proposed Bayesian inference method, information obtained at the highest stress is used to construct prior distributions for data analysis at lower stress levels. In this paper, two frameworks of the Bayesian inference method are presented, namely, the all‐at‐one prior distribution construction and the full sequential prior distribution construction. Assuming Weibull failure times, we (1) derive the closed‐form expression for estimating the smallest extreme value location parameter at each stress level, (2) compare the performance of the proposed Bayesian inference with that of MLE by simulations, and (3) assess the risk of including empirical engineering knowledge into ALT data analysis under the proposed framework. Step‐by‐step illustrations of both frameworks are presented using a real‐life ALT data set. Copyright © 2008 John Wiley & Sons, Ltd.     

Bayesian Analysis in Partially Accelerated Life Tests for Weighted Lomax Distribution

Accelerated life testing has been widely used in product life testing experiments because it can quickly provide information on the lifetime distributions by testing products or materials at higher than basic conditional levels of stress, such as pressure, temperature, vibration, voltage, or load to induce early failures. In this paper, a step stress partially accelerated life test (SS-PALT) is regarded under the progressive type-II censored data with random removals. The removals from the test are considered to have the binomial distribution. The life times of the testing items are assumed to follow length-biased weighted Lomax distribution. The maximum likelihood method is used for estimating the model parameters of length-biased weighted Lomax. The asymptotic confidence interval estimates of the model parameters are evaluated using the Fisher information matrix. The Bayesian estimators cannot be obtained in the explicit form, so the Markov chain Monte Carlo method is employed to address this problem, which ensures both obtaining the Bayesian estimates as well as constructing the credible interval of the involved parameters. The precision of the Bayesian estimates and the maximum likelihood estimates are compared by simulations. In addition, to compare the performance of the considered confidence intervals for different parameter values and sample sizes. The Bootstrap confidence intervals give more accurate results than the approximate confidence intervals since the lengths of the former are less than the lengths of latter, for different sample sizes, observed failures, and censoring schemes, in most cases. Also, the percentile Bootstrap confidence intervals give more accurate results than Bootstrap-t since the lengths of the former are less than the lengths of latter for different sample sizes, observed failures, and censoring schemes, in most cases. Further performance comparison is conducted by the experiments with real data.     

Application of Bayesian Methods for Age‐Dependent Reliability Analysis

In this article, the authors present a general methodology for age‐dependent reliability analysis of degrading or ageing components, structures and systems. The methodology is based on Bayesian methods and inference—its ability to incorporate prior information and on ideas that ageing can be thought of as age‐dependent change of beliefs about reliability parameters (mainly failure rate), when change of belief occurs not only because new failure data or other information becomes available with time but also because it continuously changes due to the flow of time and the evolution of beliefs. The main objective of this article is to present a clear way of how practitioners can apply Bayesian methods to deal with risk and reliability analysis considering ageing phenomena. The methodology describes step‐by‐step failure rate analysis of ageing components: from the Bayesian model building to its verification and generalization with Bayesian model averaging, which as the authors suggest in this article, could serve as an alternative for various goodness‐of‐fit assessment tools and as a universal tool to cope with various sources of uncertainty. The proposed methodology is able to deal with sparse and rare failure events, as is the case in electrical components, piping systems and various other systems with high reliability. In a case study of electrical instrumentation and control components, the proposed methodology was applied to analyse age‐dependent failure rates together with the treatment of uncertainty due to age‐dependent model selection. Copyright © 2013 John Wiley & Sons, Ltd.