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。     

基于Kriging模型和改进MCMC算法的随机有限元模型修正

针对待修正参数维数较高时,标准马尔可夫链蒙特卡罗MCMC (Markov Chain Monte Carlo)算法不易收敛、拒绝率高的问题,提出了基于Kriging模型和在MCMC中融合花朵授粉算法的修正方法.首先,以待修正参数作为输入,以应变模态作为输出,建立Kriging模型,通过蝙蝠算法确定Kriging模型的相关系数;然后,采用最大熵的贝叶斯方法估计参数的后验概率密度函数,将花朵授粉算法融入MH (M etropolis-Hasting)抽样算法,提高局部寻优和全局寻优能力;最后,通过三自由度弹簧-质量系统和三维桁架结构的数值算例验证所提模型修正方法,修正后参数相对误差均低于0.86％.结果 表明,所提方法修正后较高维参数的马尔可夫链能够快速收敛且样本接受率也有所提高,该方法也对随机噪声具有一定的鲁棒性.     

矩阵摄动法在汽车车架模态分析中的应用

本文采用以模态迭加原理为基础的实模态分析技术及初参数优选法对汽车车架的模态参数进行了识别,讨论了振动特征值问题中关于非重特征值和重特征值的矩阵摄动法,提出了利用有弹性元件悬挂的结构振动测试数据来得到自由——自由结构的模态参数的摄动修正方法.文中还给出了一些数值例子来说明此方法的应用,同时得到了一些重要结论.     

结构模态参数的时序分析(ARMAV模型)识别法

本文简述了用时间序列分析(ARMAV 模型)识别结构模态参数的原理,对建模方法进行了分析,并对建模分析中至关重要的初值选择问题进行了讨论,提出了一种有效的初值的选取方法;在模拟计算部分中,用 Wilson-θ积分法模拟了一个三个自由度的振动和低信噪比、大阻尼振动和密集模态等复杂情形,对用时序方法(ARMAV 模型)识别模态参数的能力进行了检验;最后通过对实验数据进行有效的预处理后,用时序方法(ARMAV 模型)识别出一个真实结构(圆盘)的第一、二阶模态参数,并得到结构的完整振型.     

拟平稳高斯随机载荷作用下结构的可靠性估计

本文指出,许多随机载荷,诸如大气紊流、地面强风中紊流、路面不平度及海洋波浪产生的随机载荷,均可模型化为拟平稳高斯随机过程或场。在这种随机载荷作用下,线性结构的应力响应是一个拟平稳高斯随机场,可用一个含慢变参数的空间—时间互谱密度函数与一个这些慢变参数的联合概率密度函数来描述。在此情形下,结构的疲劳寿命与首次超越破坏的时间的概率密度函数与可靠性函数可由平稳高斯随机载荷下的相应结果加权平均得到,其权函数为应力响应谱密度函数中的慢变参数的联合概率密度函数。这样,大大地简化了在一大类统计特性缓慢变化的非平稳随机载荷作用下的结构的寿命与可靠性估计问题。     

光纤陀螺基于本征模态函数筛选的阈值滤波算法

为降低光纤陀螺随机噪声,提高其测量精度,利用周期图法辨识光纤陀螺的随机噪声特征参数,针对其噪声特征,提出了基于本征模态函数筛选的微分经验模态分解阈值滤波算法。以本征模态函数和原始信号二者的概率密度函数的空间距离为判别依据,对所有本征模态函数进行筛选,根据已估计的噪声参数计算阈值大小,采用时间序列阈值的方法对筛选出的本征模态函数进行处理。仿真和实验结果表明,该滤波算法能够在跟踪光纤陀螺信号变化的同时,使其零偏不稳定性下降90.35%,角随机游走下降93.75%,对随机噪声有较好的抑制能力。     

基于结构动力学的框架结构固有频率估算方法

对框架结构的一阶固有频率与单门框的一阶固有频率的关系进行了推导,找出一种通过部件模态参数估算整体系统的模态参数的方法．通过ANSYS有限元分析对该估算方法进行了验证,并在石油钻机井架底座的有限元模态分析中应用该方法对系统固有频率进行了估计,误差均不超过1％．结论表明,该方法对于框架串联结构的固有频率估算是方便且可行的．     

在模态分析中如何分析,消除结构参数变化带来的影响

本文提供了在实验模态分析中消除附加质量、刚度和阻尼对复模态参数影响的方法。此外,作者将上述方法予以发展,使它适用于阻尼结构修改后的振动再分析,文中附有数字例题,其结果表明了方法的有效性。     

利用Kriging方法进行结构模型修改

结构模型修改已经演化为一个多学科的研究课题，本文将该问题处理为确定从模态参数到模型参数之间的映射问题，并利用起源于地质统计学的Kriging技术实现该映射。对于一实际钢结构，通过实验测量得到了全部摸态数据，利用部分测量得到的模态数据进行了模型修改的实验研究，实验结果表明，利用修改后模型计算得到的全部摸态数据与测量结果吻合良好，表明该模型修改方法是可行的；同时该方法表现出了与基于神经网络的修改方法的互补特性。     

圆筒试验JWL状态方程参数的贝叶斯标定

在研究数值模拟的输入参数引入的不确定性时,通常需要人为给定每个输入参数的概率分布,且输入参数概率分布的选择可能会对分析结果产生直接影响。利用贝叶斯方法标定了圆筒试验JWL状态方程参数,得到了标定参数的估计值和后验分布,并研究了不同统计模型假设对标定参数的估计值和后验分布的影响。贝叶斯后验分布融合了基准试验的试验数据的信息,因此将其作为不确定度量化分析时输入参数的初始概率分布,可以尽量减少分布选择引入的认知不确定性。     

不完全测量系统鲁棒SGQKF的传递对准滤波器设计和稳定性分析

针对复杂环境下运载体观测信息不完全测量并且存在随机干扰不确定的传递对准问题,研究了不完全测量随机不确定系统的鲁棒稀疏网格求积分(H_∞-SGQKF)的高斯逼近滤波算法。基于非线性离散系统的最优贝叶斯滤波框架和间断观测滤波算法以及不确定性扰动噪声下的H_∞范数的鲁棒SGQKF算法,给出了不完全测量的稀疏网格求积分的高斯逼近滤波算法;通过非线性系统随机稳定性理论,分析并给出了系统估计误差和估计误差方差有界的充分条件,同时给出了系统稳定的不完全测量时的丢包率临界值,证明间断观测条件下的不完全测量H_∞-SGQKF算法是稳定的。通过传递对准仿真试验和某型激光捷联式惯性导航系统的跑车试验对该算法进行了验证。结果表明,该方法比未采用鲁棒的不完全测量的稀疏网格求积分滤波的传递对准精度有所提高,说明不完全测量的鲁棒稀疏网格求积分滤波算法是正确的、稳定的,并且具有鲁棒性能。     

FPK方程的近似闭合解

讨论了FPK方程的近似闭合解问题。假设FPK方程的解具有指数多项式的形式，利用比较系数的方法确定其中待定的常数。计算表明，本方法适用于强非线性系统，在特殊情形下还能求出原方程的精确解。     

正态变量相关情况下可靠性灵敏度分析的新方法

基于独立正态变量情况下可靠性灵敏度分析的线抽样法,提出了一种求解正态相关变量情况下可靠性灵敏度的新方法。在所提方法中,首先将正态相关变量等效变换为正态独立变量,然后利用线抽样方法独立完成等效独立变量情况下失效概率对独立变量的所有分布参数的灵敏度分析,最后依据等效变换前后变量分布参数之间的解析关系和复合函数求导公式,求得...     

Non-stationary response of a van der Pol-Duffing oscillator under Gaussian white noise

This paper investigates the probability density evolution process of a van der Pol-Duffing oscillator under Gaussian white noise. A path integration method is employed with the Gauss–Legendre integration scheme. In the path integration method, the short-time Gaussian approximation scheme is used for computing the one-step transition probability density. Two cases are considered with slight nonlinearity or strong nonlinearity in displacement. The stationary and non-stationary responses of the oscillator are studied. Compared with the simulation result, the path integration method can present a satisfactory probability density function (PDF) solution for each case. Different probability density evolution processes are observed correspondingly. In the case of slight nonlinearity, the PDF undergoes a clockwise motion around the origin. The peak region gradually expands and the PDF eventually forms a circle. By contrast, the strong nonlinearity drives the oscillator to oscillate around the limit cycle. In such a case, the PDF rapidly forms a circle. The circle keeps its shape and develops until the oscillator becomes stationary. More complicated phenomena can be studied by the adopted path integration method.     

随机激励下滞迟系统的稳态响应闭合解

滞迟系统属于一类典型的强非线性系统,滞迟力不仅取决于系统的瞬时变形,还与变形历程有关.虽然滞迟系统的随机振动问题已被广泛研究,但至今尚未得到滞迟系统随机响应概率密度函数的精确闭合解.本文运用迭代加权残值法获得了高斯白噪声激励下Bouc-Wen滞迟系统稳态响应概率密度函数的近似闭合解.首先,运用等效线性化法求出系统的稳态高斯概率密度函数;然后以此构造权函数,应用加权残值法求得了系统指数多项式形式的非高斯概率密度函数;最后引入迭代的过程,逐步优化权函数,提高计算所得结果的精度.以随机地震激励下钢纤维陶粒混凝土结构的稳态响应作为算例,其中Bouc-Wen模型的参数是基于拟静力学试验数据,并应用最小二乘法辨识获得.与Monte Carlo模拟结果相比,等效线性化法得到的结果精度较差;由加权残值法得到的结果能够表现出非线性特征,但其精度依然无法令人满意;采用迭代加权残值法得到的近似闭合解与Monte Carlo模拟的结果吻合非常好;对于较强随机激励情形,采用渐进迭代加权残值法具有较高的求解效率,所获得的理论解析解具有较高的精度.结果表明,所获得的近似闭合解不仅对于土木工程领域具有重要的实际应用价值,而且还可作为检验其他非线性系统随机响应预测方法的精度的标准.     

Joint PDF Closure of Turbulent Premixed Flames

In this paper, a novel model for turbulent premixed combustion in the corrugated flamelet regime is presented, which is based on transporting a joint probability density function (PDF) of velocity, turbulence frequency and a scalar vector. Due to the high dimensionality of the corresponding sample space, the PDF equation is solved with a Monte-Carlo method, where individual fluid elements are represented by computational particles. Unlike in most other PDF methods, the source term not only describes reaction rates, but accounts for “ignition” of reactive unburnt fluid elements due to propagating embedded quasi laminar flames within a turbulent flame brush. Unperturbed embedded flame structures and a constant laminar flame speed (as expected in the corrugated flamelet regime) are assumed. The probability for an individual particle to “ignite” during a time step is calculated based on an estimate of the mean flame surface density (FSD), latter gets transported by the PDF method. Whereas this model concept has recently been published [21], here, a new model to account for local production and dissipation of the FSD is proposed. The following particle properties are introduced: a flag indicating whether a particle represents the unburnt mixture; a flame residence time, which allows to resolve the embedded quasi laminar flame structure; and a flag indicating whether the flame residence time lies within a specified range. Latter is used to transport the FSD, but to account for flame stretching, curvature effects, collapse and cusp formation, a mixing model for the residence time is employed. The same mixing model also accounts for molecular mixing of the products with a co-flow. To validate the proposed PDF model, simulation results of three piloted methane-air Bunsen flames are compared with experimental data and very good agreement is observed.     

基于新型滤波器-HABF的SINS传递对准仿真

传统动基座传递对准主要采用扩展卡尔曼滤波技术。但在动基座传递对准的非线性、非高斯条件下,这种基于模型线性化和高斯假设的滤波方法在估计系统状态及其方差时误差较大且可能发散。混合退火粒子滤波针对非线性、非高斯系统状态的在线估计问题,提出一种新的基于序贯重要性抽样的粒子滤波算法。在滤波算法中,用状态参数分解和退火系数来产生重要性概率密度函数,此概率密度函数综合考虑了转移先验、似然、噪声的统计特性以及最新的观察数据,因此更接近于系统状态的后验概率。实验仿真结果表明,这种基于混合退火粒子滤波器不仅比扩展卡尔曼滤波提高了传递对准的精度,而且又比传统的粒子算法减少了时间。     

Parameters identification of cable stayed footbridges using Bayesian inference

Numerical modeling of actual structural systems is a very complex task mainly due to the lack of complete knowledge on the involved parameters. Simplified assumptions on the uncertain geometry, material properties and boundary conditions make the numerical model response differ from the actual structural response. Improvements of the finite element (FE) models to obtain accurate response predictions can be achieved by vibration based FE model updating which uses experimental measures to minimize the differences between the numerical and experimental modal features (i.e. natural frequencies and mode shapes). Within this context, probabilistic model updating procedures based on the Bayes’ theorem were recently proposed in the literature in order to take into account the uncertainties affecting the structural parameters and their influence on the structural response. In this paper, a novel framework to efficiently estimate the posterior marginal PDF of the selected model parameters is proposed. First, the main dynamic parameters to be used for model updating are identified by ambient vibration tests on an actual structural system. Second, a first numerical FE model is developed to perform initial sensitivity analysis. Third, a surrogate model based on polynomial chaos is calibrated on the initial FE model to significantly reduce computational costs. Finally, the posterior marginal PDFs of the chosen model parameters are estimated. The effectiveness of the proposed method is demonstrated using a FE numerical model describing a curved cable-stayed footbridge located in Terni (Umbria Region, Central Italy).

     

Bayesian System Identification using auxiliary stochastic dynamical systems

Bayesian approaches to statistical inference and system identification became practical with the development of effective sampling methods like Markov Chain Monte Carlo (MCMC). However, because the size and complexity of inference problems has dramatically increased, improved MCMC methods are required. Dynamical systems based samplers are an effective extension of traditional MCMC methods. These samplers treat the posterior probability distribution as the potential energy function of a dynamical system, enabling them to better exploit the structure of the inference problem. We present an algorithm, Second-Order Langevin MCMC (SOL-MC), a stochastic dynamical system based MCMC algorithm, which uses the damped second-order Langevin stochastic differential equation (SDE) to sample a posterior distribution. We design the SDE such that the desired posterior probability distribution is its stationary distribution. Since this method is based upon an underlying dynamical system, we can utilize existing work to develop, implement, and optimize the sampler's performance. As such, we can choose parameters which speed up the convergence to the stationary distribution and reduce temporal state and energy correlations in the samples. We then apply this sampler to a system identification problem for a non-linear hysteretic structure model to investigate this method under globally identifiable and unidentifiable conditions.     

最大熵法在可靠度计算中的应用

在可靠度计算中,任意对立随机变量往往为不同概率分布,不利于可靠度计算。通常采用正态转换法将其转换成具有统一形式的正态分布,以便进行可靠度计算。但是,正态转换并不能保证原有随机变量概率分布特性,从而一定程度上造成可靠度计算误差。针对上述问题,本文提出在可靠度计算中利用最大熵法将任意随机变量概率密度函数转换成近似精度更高且具有统一标准形式的最大熵概率密度函数(MEPDF),然后提出对应的一阶可靠度计算方法进行可靠度求解,最后通过实例分析证明该方法的有效性。