贝叶斯方法在大跨度斜拉桥模态参数识别中的应用研究

为研究大跨度斜拉桥模态参数的不确定性,将遗传算法引入传统快速贝叶斯傅里叶变换法中,并采用高信噪比渐进估计值约束遗传算法的参数搜索空间,发展了一种大跨度桥梁的贝叶斯模态参数识别方法。利用悬臂梁数值模拟验证该方法的识别效率与精度;依托苏通大桥实测加速度数据应用上述方法开展大跨度斜拉桥的模态参数识别。在此基础上,探讨频带宽度系数对模态参数识别精度和不确定性的影响,并分析模态参数后验概率密度函数（PDF）的分布特征。结果表明,所提方法可有效识别大跨度斜拉桥的各阶模态参数;频率和振型的不确定性较低,而阻尼比的不确定性较高;将频带宽度系数限制在5～10有利于保证识别误差与不确定性的平衡;模态参数后验PDF符合高斯分布。     

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。     

小样本结构参数不确定性量化及传递分析的信息扩散方法

如何准确估计不确定性参数的概率密度函数是结构不确定性分析的一个重要环节。而这一环节常因实测数据有限而难以实现。为此,提出基于信息扩散理论的小样本结构参数不确定性量化及传递分析方法。首先基于有限样本数据,采用信息扩散理论估计不确定性参数服从的概率密度函数,进而采用接受-拒绝法生成随机数并进行统计分析得到不确定性参数的均值和标准差。其次,根据不确定性参数量化结果,基于响应面模型快速计算参数不确定性引起的结构响应变异程度。最后,以4自由度弹簧—质量系统和钢板材料参数不确定性量化及传递分析试验来验证所提方法的可行性及可靠性。分析结果表明:所提方法在概率分布未知、实测数据大于20个的情况下可有效地量化参数的不确定性及其引起的结构响应的变异程度。     

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。     

水力发电机组轴系不确定性量化及参数敏感性分析

当前关于水力发电机组轴系的研究主要基于确定性的框架,但在实际工程中,不确定性因素对机组轴系的影响不容忽视。鉴此,将在不确定性框架下对水力发电机组轴系结构固有特性和动态响应开展不确定性量化和参数的全局敏感性分析。首先,建立一个包含不确定参数的水力发电机组轴系动力学模型。然后,基于广义多项式混沌方法构建不确定结构参数与输出变量之间的关系,并结合最大熵原理,求得系统随机输出的具体概率分布表达式。另外,通过对多项式混沌展开系数的简单后处理获得了不确定输入参数对轴系结构固有频率和振动响应不确定性贡献的量化指标。同时,不确定性量化及敏感性分析的可靠性也用暴力Monte-Carlo模拟进行验证。在所提出的不确定性框架下水力发电机组轴系不确定性及参数敏感性研究对水力发电机组的设计、优化和运行具有重要指导意义。     

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。     

桥梁车辆荷载识别的贝叶斯方法研究

基于贝叶斯推理提出了一种可实现误差模式选择的桥梁车辆荷载识别方法。该方法通过静力影响线构建车辆荷载与实测响应的关系表达式,并建立修正曲面以消除动力效应造成的识别误差。引入与结构响应大小和车速相关的五种误差模式。根据假设的先验分布推导车辆轴重参数的后验分布,以获得车辆荷载的最优估计值和置信区间,并计算各误差模式的后验概率。分别采用简支梁数值算例和某连续梁桥动载试验,对该方法在不同车速工况下的识别精度和可靠性进行了验证。结果表明,修正曲面可以有效消除车辆动力冲击的影响,提高了荷载识别精度;荷载识别结果以置信区间形式呈现,可量化荷载识别结果的不确定性;贝叶斯方法能够识别出最佳误差模式,进一步提升了荷载识别的鲁棒性。     

基于多分辨率分析的结构物理参数识别贝叶斯估计方法:方法推导与验证

在观测噪声和模型误差等不确定性因素的影响下,结构物理参数识别问题是一个不确定性问题.针对此问题,该文从结构运动微分方程出发,利用小波多分辨率分析原理,建立结构多尺度动力方程,由该方程以结构激励和响应信息在多尺度上的细节信号和最大尺度上的概貌信号为观测量推得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...     

基于贝叶斯功率谱变量分离方法的实桥模态参数识别

工程结构参数识别不可避免地受到测试噪声和模型不确定性的影响,因此在模态参数识别过程中引入贝叶斯方法进行不确定性量化,具有较为重要的意义。通过对自功率谱和互功率谱的统计特性进行分析表明,功率谱迹（自功率谱之和）的概率密度函数与振型无关,因此可以实现振型参数与其它参数（频率、阻尼比、模态激励和预测误差等）的分离。以此变量分离原理为依据,可以实现\     

动态载荷时域识别的联合去噪修正和正则化预优迭代方法

系统响应可表示为单位脉冲响应函数与激励载荷的卷积,将其离散化一组线性方程组,则载荷识别问题即转化为求解线性方程组的反问题。针对响应中带有噪音时载荷识别的困难,提出了联合奇异熵去噪修正和正则化预优的共轭梯度迭代识别方法。一方面对含噪信号进行基于奇异熵的去噪处理,提高反问题求解中输入数据的精度。另一方面利用正则化方法对共轭梯度迭代算法进行预优,改善反问题的非适定性。由于从输入的响应数据去噪和正则化算法两方面同时改善动态载荷识别反问题的求解,因此可以有效地抑制噪声,提高识别精度。通过数值算例分析,表明在不同的噪声水平干扰下,其识别精度均优于常规的正则化方法,能够实现有效稳定地识别动态载荷。最后通过实验研究进一步验证了该方法的正确性和有效性。     

Stochastic optimization using a sparse grid collocation scheme

In computational sciences, optimization problems are frequently encountered in solving inverse problems for computing system parameters based on data measurements at specific sensor locations, or to perform design of system parameters. This task becomes increasingly complicated in the presence of uncertainties in boundary conditions or material properties. The task of computing the optimal probability density function (PDF) of parameters based on measurements of physical fields of interest in the form of a PDF, is posed as a stochastic optimization problem. This stochastic optimization problem is solved by dividing it into two problems—an auxiliary optimization problem to construct stochastic space representations from the PDF of measurement data, and a stochastic optimization problem to compute the PDF of problem parameters. The auxiliary optimization problem is solved using a downhill simplex method, whilst a gradient based approach is employed for solving the stochastic optimization problem. The gradients required for stochastic optimization are defined, using appropriate stochastic sensitivity problems. A computationally efficient sparse grid collocation scheme is utilized to compute the solution of these stochastic sensitivity problems. The implementation discussed, requires minimum intrusion into existing deterministic solvers, and it is thus applicable to a variety of problems. Numerical examples involving stochastic inverse heat conduction problems, contamination source identification problems and large deformation robust design problems are discussed.     

Bayesian time–domain approach for modal updating using ambient data

The problem of identification of the modal parameters of a structural model using measured ambient response time histories is addressed. A Bayesian time–domain approach for modal updating is presented which is based on an approximation of a conditional probability expansion of the response. It allows one to obtain not only the optimal values of the updated modal parameters but also their associated uncertainties, calculated from their joint probability distribution. Calculation of the uncertainties of the identified modal parameters is very important if one plans to proceed in a subsequent step with the updating of a theoretical finite-element model based on modal estimates. The proposed approach requires only one set of response data. It is found that the updated PDF can be well approximated by a Gaussian distribution centered at the optimal parameters at which the updated PDF is maximized. Examples using simulated data are presented to illustrate the proposed method.     

Validation and error estimation of computational models

This paper develops a Bayesian methodology for assessing the confidence in model prediction by comparing the model output with experimental data when both are stochastic. The prior distribution of the response is first computed, which is then updated based on experimental observation using Bayesian analysis to compute a validation metric. A model error estimation methodology is then developed to include model form error, discretization error, stochastic analysis error (UQ error), input data error and output measurement error. Sensitivity of the validation metric to various error components and model parameters is discussed. A numerical example is presented to illustrate the proposed methodology.     

基于全局非线性可分离的最小二乘法的飞机颤振模态参数辨识

本文考虑在输入-输出数据都带有噪声的前提下,将偏差补偿最小二乘算法（CLS）进行推广得到非线性可分离的最小二乘算法（NSLS）。采用适用于噪声环境的非线性可分离的最小二乘算法可准确地辨识飞机的颤振模态参数,该算法结合传递函数模型,将带噪声系统的辨识问题转化为非线性可分离的最小二乘问题。利用该算法,两噪声的方差值和传递函数中的模型参数可分离地估计出来。最后利用试飞试验数据辨识飞机的系统参数,验证了该方法的有效性。     

Monte Carlo filters for identification of nonlinear structural dynamical systems

The problem of identification of parameters of nonlinear structures using dynamic state estimation techniques is considered. The process equations are derived based on principles of mechanics and are augmented by mathematical models that relate a set of noisy observations to state variables of the system. The set of structural parameters to be identified is declared as an additional set of state variables. Both the process equation and the measurement equations are taken to be nonlinear in the state variables and contaminated by additive and (or) multiplicative Gaussian white noise processes. The problem of determining the posterior probability density function of the state variables conditioned on all available information is considered. The utility of three recursive Monte Carlo simulation-based filters, namely, a probability density function-based Monte Carlo filter, a Bayesian bootstrap filter and a filter based on sequential importance sampling, to solve this problem is explored. The state equations are discretized using certain variations of stochastic Taylor expansions enabling the incorporation of a class of non-smooth functions within the process equations. Illustrative examples on identification of the nonlinear stiffness parameter of a Duffing oscillator and the friction parameter in a Coulomb oscillator are presented. This paper is dedicated to Prof R N Iyengar of the Indian Institute of Science on the occasion of his formal retirement.     

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。     

Identification of physical parameters of a flexible structure from noisy measurement data

We focus on an inverse problem for identifying physical parameters such as Young's modulus and air and structural damping coefficients in the mathematical model of cantilevered beams subject to random disturbance, using dynamic noisy data measured on its vibration taken in a nondestructive manner. First, we describe mathematical models of the cantilevered beam by an Euler-Bernoulli type partial differential equation including parameters to be identified and the measurement equation, taking vibration data including the observation noise. Second, the identification problem using random dynamic data is divided into an estimation problem obtaining the (modal) state estimate and a least-squares problem determining unknown parameters, and then the unknown parameters are determined recursively by using the pair of algorithms alternately. Finally, in order to verify the efficacy of the proposed identification algorithm, simulation studies and experiments are shown.     

Probabilistic learning for modeling and quantifying model-form uncertainties in nonlinear computational mechanics

Recently, a novel nonparametric probabilistic method for modeling and quantifying model-form uncertainties in nonlinear computational mechanics was proposed. Its potential was demonstrated through several uncertainty quantification (UQ) applications in vibration analysis and nonlinear computational structural dynamics. This method, which relies on projection-based model order reduction to achieve computational feasibility, exhibits a vector-valued hyperparameter in the probability model of the random reduced-order basis and associated stochastic projection-based reduced-order model. It identifies this hyperparameter by formulating a statistical inverse problem, grounded in target quantities of interest, and solving the corresponding nonconvex optimization problem. For many practical applications, however, this identification approach is computationally intensive. For this reason, this paper presents a faster predictor-corrector approach for determining the appropriate value of the vector-valued hyperparameter that is based on a probabilistic learning on manifolds. It also demonstrates the computational advantages of this alternative identification approach through the UQ of two three-dimensional nonlinear structural dynamics problems associated with two different configurations of a microelectromechanical systems device.     

An adaptive algorithm for nonlinear system identification

There are several methods — fixed, adaptive, recursive — for the identification of linear and bilinear systems from input-output measurements that are noisy. However, literature is rather scarce as far as such techniques are concerned for the identification of nonlinear systems. The objective of this paper, therefore, is to suggest an iterative technique for the identification of nonlinear system parameters from measurements that are noisy. This technique requires the transformation of a nonlinear system in the state variable form into an input-output autoregressive moving average exogenous (armax) model. The pseudo linear regression algorithm, which has been extensively used for the identification of linear systems, can then be used to identify the nonlinear system parameters. Using this technique simulation studies were carried out which, indeed, confirm the efficacy of the method.