基于物理参数贝叶斯更新的桥梁剩余强度估计研究

考虑系统参数的随机性,将基于广义卡尔曼滤波的子结构法与贝叶斯更新方法相结合,提出了桥梁结构基于贝叶斯更新物理参数的剩余强度估计两步法:第一步,将子结构法与广义卡尔曼滤波算法相结合,成功识别出子结构及其相邻单元的物理参数;第二步,视识别出的结构物理参数为更新信息,对以蒙特卡罗仿真实验结果作为先验分布的参数进行贝叶斯更新并分别基于蒙特卡罗仿真参数和贝叶斯更新物理参数对结构进行了剩余强度估计。数值算例表明:基于贝叶斯更新物理参数估计得到的结构剩余强度明显低于基于蒙特卡罗仿真参数估计得到的结构剩余强度。该方法为测量响应信息不完备条件以及小样本抽样情况下桥梁结构剩余强度估计提供了一个较好的解决思路。     

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。     

基于贝叶斯理论的拉杆转子模态特性确认

为了更真实地反映航空发动机高压转子拉杆结构的振动特性,对基于非线性弹塑性滑动模型中不确定参数的变化范围和规律进行研究,提出了基于贝叶斯理论的有限元模型模态特性确认方法。运用贝叶斯理论构建模态特性似然函数,通过马尔可夫蒙特卡罗方法求解不确定参数的后验概率分布,并建立基于稀疏网格配点法的替代模型,减少了蒙特卡罗方法的计算量,使该方法能够适用于大型复杂高压转子结构。以实际的航空发动机高压转子为例,确定高压转子结构特征频率的变化范围和规律,通过与实验模态特征频率对比,证明了该方法的有效性。     

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...     

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。     

样本数目对岩土体参数联合分布模型识别精度的影响

目前样本数目对岩土体参数联合概率分布模型识别精度的影响还缺少研究。该文提出了样本数目对岩土体参数联合分布模型识别精度的影响分析方法,给出了基于蒙特卡洛模拟的统计量AIC值变异性模拟步骤,定义了描述岩土体参数联合概率分布模型识别精度的正确识别概率,采用蒙特卡洛模拟方法分别研究了样本数目对岩土体参数最优边缘分布函数和最优Copula函数识别精度的影响规律。结果表明:基于有限岩土体参数数据估计的边缘分布函数和Copula函数的AIC值存在较大的变异性。岩土体参数样本数目对最优边缘分布函数和Copula函数的识别精度具有重要的影响,边缘分布函数和Copula函数的正确识别概率随样本数目的增加而增大。岩土体参数变异系数对最优边缘分布函数的识别精度影响相对较小,岩土体参数间相关系数对最优Copula函数的识别精度影响较大。此外,岩土体参数二维分布模型识别比一维边缘分布模型识别需要更多的数据。因此,为了提高岩土体参数联合概率分布模型的识别精度,建议尽可能多地收集岩土体参数试验数据。     

基于MCMC稳态模拟的Weibull共享异质性模型及其可靠性应用

针对传统假设中个体寿命独立同分布的不足，构建了贝叶斯Weibull共享异质性模型，提出了对寿命服从Weibull分布的产品，运用基于Gibbs抽样的马尔可夫链蒙特卡罗(Markov chain Monte Carlo, MCMC)方法动态模拟出参数后验分布的马尔可夫链，在异质性因子的先验分布为Gamma分布时，给出随机截尾条件下，参数在Weibull共享异质性模型中的贝叶斯估计，提高了计算的精度。借助数据仿真说明了利用WinBUGS (Bayesian inference using Gibbs samp     

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。     

高斯流场中单自由度线性体系非高斯振动响应试验研究

对于风湍流等高斯分布流速场中的线性结构体系,当考虑荷载中脉动流速二次项的影响时,理论上其振动响应将呈现非高斯分布特性。基于调试得到的不同粗糙工况高斯流场,开展了单自由度线性体系顺流向振动响应测试,研究了单自由度线性体系加速度响应的非高斯分布特性,分析了粗糙度对响应非高斯成分的影响,讨论了三种常见非高斯概率密度逼近方法对响应的拟合效果。试验结果表明:试验高斯流场中单自由度线性体系的顺流向加速度响应主要呈现出尖峰非高斯分布特征,且随着紊流度的提高,响应非高斯性有增强的趋势;响应的非高斯概率密度宜采用高斯混合模型方法进行拟合。     

Modified moment-matching method for estimating pointing parameters in the presence of atmospheric turbulence

An accurate pointing system is required in free-space optical (FSO) communication links. Low energy-transmission efficiency caused by pointing errors would decline the communication system's performance. The statistics of the detected signal or return signal values could be used to estimate the pointing parameters, whereas atmospheric turbulence brings in serious challenges. A modified moment-matching estimation method is presented in this paper. The irradiance fluctuation caused by the atmospheric turbulence is considered, and the probability density function (PDF) in a weak turbulence condition is assumed to be lognormal. This modified approach is evaluated with wave-propagation simulation data and shows significant improvement over the conventional approach. The estimation accuracy and the properties of this new approach are also discussed. Although our method is based on lognormal irradiance PDF under a weak turbulence condition, the irradiance PDF would tend to be lognormal with aperture averaging effect under moderate to strong turbulence, and the ideas can be extended with appropriate PDF models to satisfy different conditions.     

Toward Robust Classifiers for PDF Malware Detection

Malicious Portable Document Format (PDF) files represent one of the largest threats in the computer security space. Significant research has been done using handwritten signatures and machine learning based on detection via manual feature extraction. These approaches are time consuming, require substantial prior knowledge, and the list of features must be updated with each newly discovered vulnerability individually. In this study, we propose two models for PDF malware detection. The first model is a convolutional neural network (CNN) integrated into a standard deviation based regularization model to detect malicious PDF documents. The second model is a support vector machine (SVM) based ensemble model with three different kernels. The two models were trained and tested on two different datasets. The experimental results show that the accuracy of both models is approximately 100%, and the robustness against evasive samples is excellent. Further, the robustness of the models was evaluated with malicious PDF documents generated using Mimicus. Both models can distinguish the different vulnerabilities exploited in malicious files and achieve excellent performance in terms of generalization ability, accuracy, and robustness.     

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.     

Adaptive non‐linear control for cancer therapy through a Fokker–Planck observer

In recent years, many efforts have been made to present optimal strategies for cancer therapy through the mathematical modelling of tumour‐cell population dynamics and optimal control theory. In many cases, therapy effect is included in the drift term of the stochastic Gompertz model. By fitting the model with empirical data, the parameters of therapy function are estimated. The reported research works have not presented any algorithm to determine the optimal parameters of therapy function. In this study, a logarithmic therapy function is entered in the drift term of the Gompertz model. Using the proposed control algorithm, the therapy function parameters are predicted and adaptively adjusted. To control the growth of tumour‐cell population, its moments must be manipulated. This study employs the probability density function (PDF) control approach because of its ability to control all the process moments. A Fokker–Planck‐based non‐linear stochastic observer will be used to determine the PDF of the process. A cost function based on the difference between a predefined desired PDF and PDF of tumour‐cell population is defined. Using the proposed algorithm, the therapy function parameters are adjusted in such a manner that the cost function is minimised. The existence of an optimal therapy function is also proved. The numerical results are finally given to demonstrate the effectiveness of the proposed method.Inspec keywords: physiological models, cancer, patient treatment, probability, stochastic processes, tumours, Fokker‐Planck equation, statistical analysis, cellular biophysicsOther keywords: adaptive nonlinear control, cancer therapy, Fokker‐Planck observer, tumour cell growth behavior, mathematical modelling, tumour‐cell population dynamics, optimal control theory, stochastic Gompertz model, empirical data, statistical methods, logarithmic function, probability density function, nonlinear stochastic observer     

Short-term instability in stochastic systems

Dynamic systems with lumped parameters which experience random temporal variations are considered in this paper. These variations may lead to “short-term” dynamic instability that is reflected in the system’s response as alternating periods of zero or almost zero response and rare short outbreaks. As long as it may be impractical to preclude completely such outbreaks for a designed system, the corresponding response should be analyzed to evaluate the system’s reliability.Results of such analyses are presented separately for cases of slow and rapid parameter variations. Linear models of the systems are studied in the former case using parabolic approximation (PA) for the variations in the vicinity of their peaks together with Krylov-Bogoliubov (KB) averaging for the transient response. This results in a solution for the response probability density function (PDF).The case of rapid broadband parameter variations is studied using theory of Markov processes. The system is assumed to operate beyond its stochastic instability threshold-although only slightly-and its nonlinear model is used accordingly. The analysis is based on solution of the Fokker-Planck-Kolmogorov (FPK) partial differential equation for stationary PDF of the response. Several such PDFs are analyzed; they are found to have integrable singularities at the origin indicating an intermittent nature of the response.     

Probability density evolution method for dynamic response analysis of structures with uncertain parameters

Probability density evolution method is proposed for dynamic response analysis of structures with random parameters. In the present paper, a probability density evolution equation (PDEE) is derived according to the principle of preservation of probability. With the state equation expression, the PDEE is further reduced to a one-dimensional partial differential equation. The numerical algorithm is studied through combining the precise time integration method and the finite difference method with TVD schemes. The proposed method can provide the probability density function (PDF) and its evolution, rather than the second-order statistical quantities, of the stochastic responses. Numerical examples, including a SDOF system and an 8-story frame, are investigated. The results demonstrate that the proposed method is of high accuracy and efficiency. Some characteristics of the PDF and its evolution of the stochastic responses are observed. The PDFs evidence heavy variance against time. Usually, they are much irregular and far from well-known regular distribution types. Additionally, the coefficients of variation of the random parameters have significant influence on PDF and second-order statistical quantities of responses of the stochastic structure.The support of the Natural Science Funds for Distinguished Young Scholars of China (Grant No.59825105) and the Natural Science Funds for Innovative Research Groups of China (Grant No.50321803) are gratefully appreciated.     

Uncertainty quantification models for micro‐scale squeeze‐film damping

Two squeeze‐film gas damping models are proposed to quantify uncertainties associated with the gap size and the ambient pressure. Modeling of gas damping has become a subject of increased interest in recent years due to its importance in micro‐electro‐mechanical systems (MEMS). In addition to the need for gas damping models for design of MEMS with movable micro‐structures, knowledge of parameter dependence in gas damping contributes to the understanding of device‐level reliability. In this work, two damping models quantifying the uncertainty in parameters are generated based on rarefied flow simulations. One is a generalized polynomial chaos (gPC) model, which is a general strategy for uncertainty quantification, and the other is a compact model developed specifically for this problem in an early work. Convergence and statistical analysis have been conducted to verify both models. By taking the gap size and ambient pressure as random fields with known probability distribution functions (PDF), the output PDF for the damping coefficient can be obtained. The first four central moments are used in comparisons of the resulting non‐parametric distributions. A good agreement has been found, within 1%, for the relative difference for damping coefficient mean values. In study of geometric uncertainty, it is found that the average damping coefficient can deviate up to 13% from the damping coefficient corresponding to the average gap size. The difference is significant at the nonlinear region where the flow is in slip or transitional rarefied regimes. Copyright © 2010 John Wiley & Sons, Ltd.     

Assignment of probability distributions for parameters in the 1996 performance assessment for the Waste Isolation Pilot Plant. Part 1: description of process

A managed process was used to consistently and traceably develop probability distributions for parameters representing epistemic uncertainty in four preliminary and the final 1996 performance assessment (PA) for the Waste Isolation Pilot Plant. Between 67 probability density functions (PDFs) in the 1989 PA and 236 PDFs in the 1996 PA were assigned by a parameter development team, using a process described in a companion paper. In the five iterative PAs conducted, the most commonly used distributions were the uniform PDF and piecewise-uniform PDF (also referred to as a piecewise-linear cumulative distribution function (CDF)). Other distributions used included the truncated normal, truncated Student-t, and triangular PDFs. In a few instances, a discrete delta (piecewise-uniform CDF), beta, and exponential PDF were also used. The PDFs produced for the 24 most important parameters observed in the five iterative PAs are presented. As background, the list of 194 parameters documented in the first 1989 PA through the 1471 parameters documented in the 1996 compliance PA are also provided.