模态参数不确定性分析的贝叶斯方法研究

在结构损伤诊断和参数识别中,实测结构模态参数不可避免地存在误差。本文将模态参数视为随机变量,采用贝叶斯方法对模态参数的不确定性进行分析。分析中选用高斯联合概率密度函数作为先验密度函数,通过多次独立的模态参数测试,得到传递函数的条件概率密度函数和模态参数的后验估计表达式,再利用拉普拉斯渐近方法求解边缘概率密度函数,得到模态参数的最大后验估计。在钢筋混凝土框架结构的模态试验中,利用本文方法给出了结构模态参数的估计值,结果表明,本文方法具有良好的收敛性。     

正态相关变量主客观不确定性分离和参数影响分析

针对主观和客观不确定性同时存在且输入变量相关的结构系统,研究分析了分布参数的主观不确定性对系统输出响应的影响. 首先采用正交变换进行了相关输入变量情况下主、客观不确定性的分离,通过引入独立标准正态空间辅助变量,使得分布参数的主观不确定性能够从输入变量客观不确定性中分离,进而分析分布参数的主观不确定性对输出响应的主效应指标. 其次验证了分布参数对模型输出响应期望影响的一阶方差贡献与主、客观不确定性分离后其对响应量一阶方差贡献的相等关系. 算例结果表明了文中所用主、客观不确定性分离方法的合理性和有效性.      

贝叶斯神经网络建模预测方法及其应用

针对神经网络建模时,其模型的复杂性难以控制而且缺乏分析结果的工具,以及贝叶斯方法可以通过定义一些超参数的模糊先验来控制模型参数复杂性,并且可对任何感兴趣的变量产生后验预测分布,使得置信区间的计算成为可能.研究了贝叶斯神经网络的建模预测问题,通过融入模型参数的先验知识,在给定数据样本及模型假设下进行后验概率的贝叶斯推理,使用马尔可夫链蒙特卡罗算法来优化模型控制参参数,实现了对神经网络模型中不同部分复杂度的控制,获得了模型参数的后验分布及预测分布.通过动调陀螺仪漂移数据建模应用分析结果证明此方法可以达到较好的建模预测效果.     

AN SEPARATION OF THE ALEATORY AND EPISTEMIC UNCERTAINTIES WITH CORRELATED NORMAL VARIABLES AND ANALYSIS OF THE INFLUENCE OF PARAMETERS

针对主观和客观不确定性同时存在且输入变量相关的结构系统,研究分析了分布参数的主观不确定性对系统输出响应的影响. 首先采用正交变换进行了相关输入变量情况下主、客观不确定性的分离,通过引入独立标准正态空间辅助变量,使得分布参数的主观不确定性能够从输入变量客观不确定性中分离,进而分析分布参数的主观不确定性对输出响应的主效应指标. 其次验证了分布参数对模型输出响应期望影响的一阶方差贡献与主、客观不确定性分离后其对响应量一阶方差贡献的相等关系. 算例结果表明了文中所用主、客观不确定性分离方法的合理性和有效性.     

基于高精度模态综合法的螺栓连接组合结构不确定模型更新

由于螺栓结构中存在复杂的微观特征,数值模型中无法避免的会引入不确定性。针对螺栓设计中参数不确定性量化问题,一种基于高精度模态综合法的螺栓连接组合结构随机模型更新方法被提出。首先考虑高阶剩余模态的影响,推导了适用于螺栓组合结构弹性交界面的高精度模态综合法;之后,在贝叶斯推理框架下,通过组合结构的自振频率和振型的概率分布,建立螺栓连接参数的后验概率密度函数,并借助DRAM(delayed rejection adaptive metropolis)抽样方法量化参数的不确定性。数值算例表明,针对各子结构之间自振频率差别较大的结构,与模态综合法相比,本研究方法在较少子结构模态参与的情形下,也可以保证良好的模型更新结果。     

钢筋混凝土柱抗弯承载力的概率模型与校准分析

为了克服传统确定性抗弯承载力模型和校准方法无法合理考虑不确定性所存在的缺陷,分别建立了钢筋混凝土(RC)柱的概率抗弯承载力模型与概率校准方法。首先,基于RC柱正截面受弯承载力的基本假定,结合偏心受压RC柱的截面内力平衡条件,分别建立了大(小)偏心受压RC柱的确定性抗弯承载力模型;然后,综合考虑固有不确定性和认知不确定性的影响,分别建立了大(小)偏心受压RC柱概率抗弯承载力模型的解析表达式,进而结合贝叶斯理论和MCMC法确定了概率模型参数的后验分布信息,从而建立了RC柱的概率抗弯承载力模型;最后,基于概率抗弯承载力模型所确定的概率密度函数、置信区间和置信水平,提出了传统确定性抗弯承载力模型的概率校准方法。研究结果表明,所建立的概率抗弯承载力模型不仅可以合理描述RC柱抗弯承载力的概率分布特性,而且可以校准传统确定性抗弯承载力模型的计算精度和置信水平。     

基于随机加权的捷联惯组历次测试数据验前分布研究

针对捷联惯性测量组合(捷联惯组)历次测试数据小样本的特点,在总体分布参数形式未知的情况下,根据已有的先验信息,提出了通过随机加权法,获得捷联惯组历次测试数据总体参数的验前分布。结合当前样本信息,利用贝叶斯方法得到捷联惯组历次测试数据的验后分布。将统计推断建立在验后分布基础之上,可以减小小样本情况下的统计分析误差。     

一种基于Gauss von Mises分布模型的非线性量测更新方法

基于状态空间模型的许多传统滤波算法都基于Rn空间中的高斯分布模型,但当状态向量中包含角变量或方向变量时,难以达到理想的效果。针对J.T.Horwood等提出的nS?R流形上的Gauss Von Mises(GVM)多变量概率密度分布,扩展了狄拉克混合逼近方法,给出了联合分布的GVM逼近方法,推导了后验分布的GVM参数计算公式,设计了量测更新状态估计算法。将J.T.Horwood等的时间更新算法与所提出的量测更新算法相结合,可实现基于GVM分布的递推贝叶斯滤波器(GVMF)。仿真结果表明,当状态向量符合GVM概率分布模型时,GVMF对角变量的估计明显优于传统的扩展卡尔曼滤波器。     

基于贝叶斯方法的模态参数识别的不确定度分析

振动模态分析和模态参数识别是动态测试的一个重要研究方向。模态参数在模型的修正、响应的预测、系统的健康检测及控制等方面有着重要的作用。但动态测试的不确定度分析,尤其是模态参数的不确定度的研究还十分缺乏。本文主要基于贝叶斯方法,通过傅立叶变换(FFT)建立时域数据和频域数据之间的对应关系。根据共振频带内的多个模态的响应数据得到相对应的模态参数,优化得到模态参数的最佳估计值,评定模态参数识别的不确定度。在固支梁的模态实验中,加速度传感器采集环境激励中的振动数据,运用贝叶斯法进行处理得到模态参数的最佳估计值。在此基础上,通过模态参数的最佳估计值,以及仪器的检定报告数据,结合合成不确度分析方法,系统分析了模态参数识别的不确定度。     

基于变量修正分布的混凝土结构长期变形预测

由于随机因素的影响,混凝土结构长期变形通常表现出很强的离散性,Bayesian理论提供了改善这种离散性的方法。基于Bayesian理论的混凝土结构长期变形预测方法的核心是引入短期变形构造似然函数,通过修正先验概率得到长期变形的后验概率分布。但是对于实际结构而言,在施工之前短期变形及其标准差无法获取,这就使得这种方法在开展时机和实际应用方面存在一定的限制性。为了改善这种限制性,在随机变量修正分布的基础上,结合拉丁超立方抽样技术,采用CEB-FIP(MC90)模型建立了钢筋混凝土梁长期变形的随机分析模型。采用该模型进行混凝土梁长期变形随机分析,得到基于变量修正分布的混凝土梁长期变形预测结果,并分别与先验预测结果和Bayesian预测结果进行比较。研究结果表明,基于变量修正分布的预测结果与Bayesian预测结果十分接近,比先验预测结果不确定性降低50%左右,与试验结果吻合良好。     

Uncertainty quantification of a graphite nitridation experiment using a Bayesian approach

In this paper, a stochastic system based Bayesian approach is applied to estimate different model parameters and hence quantify the uncertainty of a graphite nitridation experiment. The Bayesian approach is robust due to its ability to characterize modeling uncertainties associated with the underlying system and is rigorous due to its exclusive foundation on the axioms of probability theory. We choose an experiment by Zhang et al. [1] whose main objective is to measure the reaction efficiency for the active nitridation of graphite by atomic nitrogen. To obtain the primary physical quantity of interest, we need to model and estimate the uncertainty of a number of other physical processes associated with the experimental setup. We use the Bayesian method to obtain posterior probability distributions of all the parameters relevant to the experiment while taking into account uncertainties in the inputs and the modeling errors. We use a recently developed stochastic simulation algorithm which allows for efficient sampling in the high-dimensional parameter space. We show that the predicted reaction efficiency of the graphite nitridation and its uncertainty is ∼3.1 ± 1.0 × 10⁻³ that is slightly larger than the ones deterministically obtained by Zhang et al. [1].     

Resampling strategies to improve surrogate model‐based uncertainty quantification: Application to LES of LS89

Uncertainty quantification (UQ) is receiving more and more attention for engineering applications particularly from robust optimization. Indeed, running a computer experiment only provides a limited knowledge in terms of uncertainty and variability of the input parameters. These experiments are often computationally expensive, and surrogate models can be constructed to address this issue. The outcome of an uncertainty quantification study is, in this case, directly correlated to the surrogate's quality. Thus, attention must be devoted to the design of experiments to retrieve as much information as possible. This work presents 2 new strategies for parameter space resampling to improve a Gaussian process surrogate model. These techniques indeed show an improvement of the predictive quality of the model with high‐dimensional analytical input functions. Finally, the methods are successfully applied to a turbine blade large‐eddy simulation application: the aerothermal flow around the LS89 blade cascade.     

Rigorous model-based uncertainty quantification with application to terminal ballistics—Part II. Systems with uncontrollable inputs and large scatter

This Part II of this series is concerned with establishing the feasibility of an extended data-on-demand (XDoD) uncertainty quantification (UQ) protocol based on concentration-of-measure inequalities and martingale theory. Specific aims are to establish the feasibility of the protocol and its basic properties, including the tightness of the predictions afforded by the protocol. The assessment is based on an application to terminal ballistics and a specific system configuration consisting of 6061-T6 aluminum plates struck by spherical 440c stainless steel projectiles at ballistic impact speeds in the range of 2.4–2.8 km/s. The system's inputs are the plate thickness, plate obliquity and impact velocity. The perforation area is chosen as the sole performance measure of the system. The objective of the UQ analysis is to certify the lethality of the projectile, i.e., that the projectile perforates the plate with high probability over a prespecified range of impact velocities, plate thicknesses and plate obliquities. All tests were conducted at Caltech's Small Particle Hypervelocity Range (SPHIR), which houses a two-stage gas gun. A feature of this facility is that the impact velocity, while amenable to precise measurement, cannot be controlled precisely but varies randomly according to a known probability density function. In addition, due to a competition between petalling and plugging mechanisms for the material system under consideration, the measured perforation area exhibits considerable scatter. The analysis establishes the feasibility of the XDoD UQ protocol as a rigorous yet practical approach for model-based certification of complex systems characterized by uncontrollable inputs and noisy experimental data.     

Uncertainty quantification in LES of channel flow

In this paper, we present a Bayesian framework for estimating joint densities for large eddy simulation (LES) sub‐grid scale model parameters based on canonical forced isotropic turbulence direct numerical simulation (DNS) data. The framework accounts for noise in the independent variables, and we present alternative formulations for accounting for discrepancies between model and data. To generate probability densities for flow characteristics, posterior densities for sub‐grid scale model parameters are propagated forward through LES of channel flow and compared with DNS data. Synthesis of the calibration and prediction results demonstrates that model parameters have an explicit filter width dependence and are highly correlated. Discrepancies between DNS and calibrated LES results point to additional model form inadequacies that need to be accounted for. Copyright © 2016 John Wiley & Sons, Ltd.     

基于区间分析的工程结构不确定性研究现状与展望

随机分析方法、模糊分析方法是已经广泛使用的工程结构不确定性分析方法, 近年来区间分析方法逐渐为人们所熟知并成为是一种新的工程结构不确定性分析方法,它主要用来研究具有区间特性的工程结构. 区间分析方法在统计信息不足以描述不确定参数的概率分布或隶属函数、工程单位仅提供不确定参数的区间范围而想获得结构响应的区间范围时就发挥了其优点. 综述了区间分析方法及其在工程结构不确定性分析中的应用状况, 将基于区间分析的工程结构不确定性问题研究归结为以下4个方面: 不确定性结构系统的区间有限元分析; 基于区间的非概率可靠性分析; 工程结构区间反演分析; 基于区间参数的结构优化设计. 分析评价了国内外在这几个方面的研究成果及其最新进展, 同时指出目前研究中存在的问题和研究的方向.      

Multiple hot-film sensor array calibration and skin friction measurement

A method for the calibration of closely spaced multiple hot-film sensor (MHFS) arrays of nickel-on-polyimide-substrate type was presented in this paper. The hot-film sensors were calibrated individually and in situ against the values of the wall-shear stresses determined from boundary-layer velocity profiles (developed on the front portion of a circular cylinder) through a specially designed wall-mounted hot-wire probe. The accuracy and feasibility of the present method was examined through the subsequent measurements of the skin-friction distributions on a circular cylinder (including the removal and bonding of the calibrated MHFS from a 10-cm diameter calibration cylinder and onto the surface of a 8-cm diameter test cylinder) and comparison of their consistency with the published results. The present MHFS calibration method is important in the non-intrusive multipoint measurements of the mean skin friction along the surfaces of two-dimensional aerodynamic objects of interest.     

基于非嵌入多项式混沌的爆轰不确定度量化

固体炸药爆轰是极为复杂的极端物理和化学过程,发生在极小的时间尺度和极小的空间尺度内,产生极高的爆压和极快的爆速,给理论研究和实验带来巨大的挑战,数值模拟成为极为重要的研究手段。验证、确认和不确定度量化综合了实验和数值模拟的优点。针对圆筒试验问题,使用基于全张量积的多元非嵌入多项式混沌方法,给出了初始密度和JWL参数不确定时、圆筒位置和速度的期望、方差以及置信区间。结果发现试验数据均落在置信区间内。最后,使用信息熵方法给出实验不确定度量化,从而确认了模型的有效性。     

基于自适应和投影Wiener混沌的圆筒实验不确定度量化

由于炸药爆轰现象的复杂性和人们对它的认知缺陷，其表征爆轰流体力学过程的物理数学模型具有较强的不确定性，要降低基于爆轰建模与模拟的数值结果做出决策的风险，量化和评估不确定输入对爆轰系统输出结果的影响尤为重要。本文中针对具有高维随机变量的爆轰问题的不确定度量化，使用自适应基函数的Wiener混沌方法、耦合旋转变换和投影方法，减少截断空间的长度。针对输入变量相关性，使用Rosenblatt变换使其相互独立。针对不符合标准正态分布的变量使用等概率原则，将它化为标准正态分布。最后，使用自主研发的具有完全知识产权的爆轰数值模拟软件LAD2D, 研究了具有高维不确定参数的圆筒实验的不确定度量化，给出期望、标准差、置信区间等统计信息，所得问题与实验数据比对，从而确认了模型的有效性。