考虑非高斯特性的结构首次失效时间计算

本文发展了一个计算具有非高斯特性的结构首次失效时间的解析方法.该方法利用Hemite矩模型将非高斯结构反应映射为标准高斯过程,由此计算反应的平均超越率、成群超越以及初始状态的影响,并最终给出结构的首次失效时问概率.二次力函数激励下线性单自由度系统的首次失效时间分析说明了该方法的使用过程,同时对该方法的计算结果与Monte Carlo模拟结果进行了对比.     

非高斯结构首次超越分析的概率模型

利用Fleishman近似,通过非高斯结构动力响应的前四阶中心矩,将分布未知的结构响应过程变换为标准高斯随机过程,提出非高斯结构动力响应的平均穿越率计算公式,并考虑初始条件和群穿尺寸的影响,修正平均穿越率的计算,在此基础上,利用传统Poisson模型,建立非高斯结构首次超越分析的概率模型.算例分析表明,本文提出的概率模型可以在结构随机振动分析或试验与检测数据的基础上,分析非高斯结构的首次超越问题,并克服了传统高斯模型所固有的诸多缺点.     

非高斯随机激励下滞迟系统响应与首次穿越失效

针对由有界噪声、泊松白噪声和高斯白噪声共同构成的非高斯随机激励,通过Monte Carlo数值模拟方法研究了此激励作用下双线性滞迟系统和Bouc-Wen滞迟系统这两类经典滞迟系统的稳态响应与首次穿越失效时间。一方面,分析了有界噪声和泊松白噪声这两种分别具有连续样本函数和非连续样本函数的非高斯随机激励,在不同激励参数条件下对双线性滞迟系统和Bouc-Wen滞迟系统的稳态响应概率密度、首次穿越失效时间概率密度及其均值的不同影响;另一方面,揭示了在这类非高斯随机激励荷载作用下,双线性滞迟系统的首次穿越失效时间概率密度将出现与Bouc-Wen滞迟系统的单峰首次穿越失效时间概率密度截然不同的双峰形式。     

非高斯荷载作用下结构微小失效概率的估计方法

本文提出了一个估计非高斯荷载作用下结构体系微小失效概率的有效方法．该方法由两个解耦的分析过程组成：第一个过程由移位广义对数正态分布模型估计结构非高斯反应的边缘分布函数,对于移位广义对数正态分布模型的参数估计采用两水准方法;第二个过程由Copula函数估计结构非高斯反应的联合分布函数,通过该联合分布函数的尾部得到结构体系的微小失效概率．非高斯地震荷载作用下六层抗弯钢框架的微小失效概率算例分析表明,本文所提方法能精确估计结构体系的微小失效概率,其计算效率比目前普遍采用的Monte Carlo模拟方法高5~10倍．     

Improved Response Surface Method for Time-Variant Reliability Analysis of Nonlinear Random Structures Under Non-Stationary Excitations

The problem of time-variant reliability analysis of randomly driven linear/nonlinear vibrating structures is studied. The excitations are considered to be non-stationary Gaussian processes. The structure properties are modeled as non-Gaussian random variables. The structural responses are therefore non-Gaussian processes, the distributions of which are not generally available in an explicit form. The limit state is formulated in terms of the extreme value distribution of the response random process. Developing these extreme value distributions analytically is not easy, which makes failure probability estimations difficult. An alternative procedure, based on a newly developed improved response surface method, is used for computing exceedance probabilities. This involves fitting a global response surface which approximates the limit surface in regions which make significant contributions to the failure probability. Subsequent Monte Carlo simulations on the fitted response surface yield estimates of failure probabilities. The method is integrated with professional finite element software which permits reliability analysis of large structures with complexities that include material and geometric nonlinear behavior. Three numerical examples are presented to demonstrate the method.     

Frequency-domain analysis of non-linear wave effects on offshore platform responses

In this study, the effects of second-order non-linear random waves on the structural response of slender fixed offshore platforms are investigated based on frequency-domain Volterra-series approach and previously proposed correlation function/FFT-based cumulant spectral method. The cumulants of non-Gaussian water particle kinematics are derived and, Morison force is approximated in cubic functional transformations of Gaussian processes. Volterra series is applied to evaluate the power spectra of wave force and induced structural displacement. The more convenient and more efficient power spectral and tri-spectral analyses by cumulant spectral method are presented as well. The thereby estimated variance, skewness and kurtosis excess agree well with time-domain simulation results. It is found that non-linear wave effects result in stronger non-Gaussian behavior of wave force and structural response, especially in seas of finite water depth.     

Random excitation of coupled oscillators with single and simultaneous internal resonances

The primary objective of this paper is to examine the random response characteristics of coupled nonlinear oscillators in the presence of single and simultaneous internal resonances. A model of two coupled beams with nonlinear inertia interaction is considered. The primary beam is directly excited by a random support motion, while the coupled beam is indirectly excited through autoparametric coupling and parametric excitation. For a single one-to-two internal resonance, we used Gaussian and non-Gaussian closures, Monte Carlo simulation, and experimental testing to predict and measure response statistics and stochastic bifurcation in the mean square. The mean square stability boundaries of the coupled beam equilibrium position are obtained by a Gaussian closure scheme. The stochastic bifurcation of the coupled beam is predicted theoretically and experimentally. The stochastic bifurcation predicted by non-Gaussian closure is found to take place at a lower excitation level than the one predicted by Gaussian closure and Monte Carlo simulation. It is also found that above a certain excitation level, the solution obtained by non-Gaussian closure reveals numerical instability at much lower excitation levels than those obtained by Gaussian and Monte Carlo approaches. The experimental observations reveal that the coupled beam does not reach a stationary state, as reflected by the time evolution of the mean square response. For the case of simultaneous internal resonances, both Gaussian and non-Gaussian closures fail to predict useful results, and attention is focused on Monte Carlo simulation and experimental testing. The effects of nonlinear coupling parameters, internal detuning ratios, and excitation spectral density level are considered in both investigations. It is found that both studies reveal common nonlinear features such as bifurcations in the mean square responses of the coupled beam and modal interaction in the neighborhood of internal resonances. Furthermore, there is an upper limit for the excitation level above which the system experiences unbounded response in the neighborhood of simultaneous internal resonances.     

Stochastic non-linear flutter of a panel subjected to random in-plane forces

—An analysis of non-linear flutter of a simply-supported panel exposed to supersonic gas flow and random in-plane forces is presented for two- and three-mode interactions. A first order quasi-steady state aerodynamic piston theory is used to model the aerodynamic loading. The Fokker-Planck equation is used to derive a general moment equation for two- and three-mode interactions. For stability analysis the moment equation is consistent and the mean square stability boundaries of the equilibrium are obtained in terms of the system parameters. The stability boundaries reveal common features to those predicted by the deterministic theory of panel nutter. For the non-linear response the moment equation is found inconsistent and a cumulant-neglect closure is used by setting cumulants of fifth and sixth orders to zero. This first order non-Gaussian closure is carried out to solve for the response statistics in terms of the air-to-plate mass ratio, aerodynamic pressure, modal damping, and in-plane random force spectral density. It is found that the non-Gaussian solution yields higher levels for the response statistics than those obtained by the Gaussian solution. The inclusion of more modes results in a reduction of the response levels and expands the stability region.     

基于区域分解的结构动力学系统首次穿越失效

提出了高斯白噪声激励的线性及非线性结构动力学系统的首次穿越失效概率的估计方法. 对于线性结构动力学系统,失效区域被分解为互斥的基本失效域之和,每个基本失效域可用其设计点完全描述,并以正态分布代替卡方分布估计失效概率中的参数. 对于非线性结构动力学系统,基于Rice穿越理论,将非线性方程转化为与之具有相同平均上穿率的线性化方程,然后利用文中方法对等效线性化方程估计首穿失效概率. 最后给出了线性及非线性结构动力学系统的数值例子,并将所提方法与蒙特卡罗法及重要样本法相比较,模拟结果显示了方法的正确性与有效性.     

泊松白噪声激励下强非线性系统的半解析瞬态解

自然界与工程中都普遍存在着随机扰动, 且大多数呈现出固有的非高斯性质, 若采用高斯激励建模可能会导致巨大的误差. 泊松白噪声作为一种典型且重要的非高斯激励模型, 已引起了广泛的关注. 目前, 泊松白噪声激励下系统的动态特性分析主要集中于稳态响应的研究, 而针对瞬态响应的求解难度仍较大, 需进一步发展. 本文引入径向基神经网络, 提出了一种泊松白噪声激励下单自由度强非线性系统瞬态响应预测的高效半解析方法. 首先将广义Fokker-Plank-Kolmogorov (FPK) 方程的瞬态解表示为一组含时变待定权值系数的高斯径向基神经网络; 然后采用有限差分法离散时间导数项, 并结合随机取样技术构造含时间递推式的损失函数; 最后通过拉格朗日乘子法使得损失函数最小化获得时变最优权值系数. 作为算例, 探究了两个经典强非线性系统, 并采用蒙特卡罗模拟方法对解析结果加以验证. 结果表明: 本文方法所获得的瞬时概率密度函数与蒙特卡罗模拟数据吻合地较好, 并且算法具备较高的计算效率. 在系统响应的整个演化过程中, 本文所提方法能够非常有效地捕捉到系统响应在各个时刻下的复杂非线性特征. 此外, 本文方法所获得的高精度半解析瞬态解, 不仅可作为基准解检验其他非线性随机振动分析方法的精度, 对于结构的优化设计也存在巨大的潜在应用价值.      

非正态概率分布对一次可靠度方法精度影响

一次可靠度方法(FORM)基本原理是将非正态分布基本变量变换为独立标准正态分布,并将功能函数在基本变量的验算点坐标位置线性化,因此功能函数在独立标准正态分布空间的非线性程度将直接影响一次可靠度方法(FORM)的计算精度。功能函数非线性的另一个来源是非正态变量的概率变换。本文通过研究9种非正态分布类型的正态概率变换函数的曲率值,得出了不同非正态分布类型对一次可靠度方法计算精度的影响规律。     

An improved approach for random parametric response of dynamic systems with non-linear inertia

A non-Gaussian closure scheme is developed for determining the stationary response of dynamic systems including non-linear inertia and stochastic coefficients. Numerical solutions are obtained and examined for their validity based on the preservation of moments properties. The method predicts the jump phenomenon, for all response statistics at an excitation level very close to the threshold level of the condition of almost sure stability. In view of the increased degree of non-linearity, resulting from the non-Gaussian closure scheme, the mean square of the response displacement is found to be less than those values predicted by other methods such as the Gaussian closure or the first order stochastic averaging.     

On statistical quasi-linearization

In carrying out the statistical linearization procedure to a non-linear system subjected to an external random excitation, a Gaussian probability distribution is assumed for the system response. If the random excitation is non-Gaussian, however, the procedure may lead to a large error since the response of bother the original non-linear system and the replacement linear system are not Gaussian distributed. It is found that in some cases such a system can be transformed to one under parametric excitations of Gaussian white noises. Then the quasi-linearization procedure, proposed originally for non-linear systems under both external and parametric excitations of Gaussian white noises, can be applied to these cases. In the procedure, exact statistical moments of the replacing quasi-linear system are used to calculate the linearization parameters. Since the assumption of a Gaussian probability distribution is avoided, the accuracy of the approximation method is improved. The approach is applied to non-linear systems under two types of non-Gaussian excitations: randomized sinusoidal process and polynomials of a filtered process. Numerical examples are investigated, and the calculated results show that the proposed method has higher accuracy than the conventional linearization, as compared with the results obtained from Monte Carlo simulations.     

Variations in steepness of the probability density function of beam random vibration

Dynamic behaviour of a beam, subjected to stationary random excitation, has been investigated for the situation in which the response is different from the model of a Gaussian random process. The study was restricted to the case of symmetric non-Gaussian probability density functions of beam vibrations. There are two possible causes of deviations of the system response from the Gaussian model: the first, nonlinear behaviour, concerns the system itself and the second is external when the excitation is not Gaussian. Both cases have been considered in the paper. To clarity the conclusions for each case and to avoid interference of these different types of system behaviour, two beam structures, clamped-clamped and cantilevered, have been studied. A numerical procedure for prediction of the nonlinear random response of a clamped-clamped beam under the Gaussian excitations was based on a linear modal expansion. Monte Carlo simulation was undertaken using Runge–Kutta integration of the generalised coordinate equations. Probability density functions of the beam response were analysed and approximated making use of different theoretical models. An experimental study has been carried out for a linear system of a cantilevered beam with a point mass at the free end. A pseudo-random driving signal was generated digitally in the form of a Fourier expansion and fed to a shaker input. To generate a non-Gaussian excitation a special procedure of harmonic phase adjustment was implemented instead of the random choice. In so doing, the non-Gaussian kurtosis parameter of the beam response was controlled.     

基于不完备频响函数的结构损伤统计识别研究

基于不完备频响函数数据,结合概率统计方法,提出了一种能同时考虑模型参数不确定性和测试噪声影响的结构损伤统计识别方法。首先,基于频响函数某一行向量在不同频率下的幅值数据,利用矩阵拉直运算建立了关于损伤系数的确定性识别方程。其次,假设模型参数误差和测试噪声为零均值的高斯随机变量,根据摄动理论,推导了损伤后结构刚度参数的前二阶矩。随后,利用结构损伤前后的概率分布得到了结构损伤存在概率。最后,通过一个平面桁架结构模型验证了本文方法的有效性。数值算例的研究结果表明,损伤单元的损伤存在概率远大于非损伤单元;测试噪声对识别结果的影响比模型参数不确定性的影响更为显著。     

Response of Systems Under Non-Gaussian Random Excitations

The approach of nonlinear filter is applied to model non-Gaussian stochastic processes defined in an infinite space, a semi-infinite space or a bounded space with one-peak or multiple peaks in their spectral densities. Exact statistical moments of any order are obtained for responses of linear systems jected to such non-Gaussian excitations. For nonlinear systems, an improved linearization procedure is proposed by using the exact statistical moments obtained for the responses of the equivalent linear systems, thus, avoiding the Gaussian assumption used in the conventional linearization. Numerical examples show that the proposed procedure has much higher accuracy than the conventional linearization in cases of strong system nonlinearity and/or high excitation non-Gaussianity. An erratum to this article is available at .     

Inverse stochastic resonance in Hodgkin–Huxley neural system driven by Gaussian and non-Gaussian colored noises

Inverse stochastic resonance (ISR) is the phenomenon of the response of neuron to noise, which is opposite to the conventional stochastic resonance. In this paper, the ISR phenomena induced by Gaussian and non-Gaussian colored noises are studied in the cases of single Hodgkin–Huxley (HH) neuron and HH neural network, respectively. It is found that the mean firing rate of electrical activities depends on the Gaussian or non-Gaussian colored noises which can induce the phenomenon of ISR. The ISR phenomenon induced by Gaussian colored noise is most obvious under the conditions of low external current, low reciprocal correlation rate and low noise level. The ISR in neural network is more pronounced and lasts longer than the duration of a single neuron. However, the ISR phenomenon induced by non-Gaussian colored noise is apparent under low noise correlation time or low departure from Gaussian noise, and the ISR phenomena show different duration ranges under different parameter values. Furthermore, the transition of mean firing rate is more gradual, the ISR lasts longer, and the ISR phenomenon is more pronounced under the non-Gaussian colored noise. The ISR is a common phenomenon in neurodynamics; our results might provide novel insights into the ISR phenomena observed in biological experiments.

     

Understanding the Non-Gaussian Nature of Linear Reactive Solute Transport in 1D and 2D

In the present study, we examine non-Gaussian spreading of solutes subject to advection, dispersion and kinetic sorption (adsorption/desorption). We start considering the behavior of a single particle and apply a random walk to describe advection/dispersion plus a Markov chain to describe kinetic sorption. We show in a rigorous way that this model leads to a set of differential equations. For this combination of stochastic processes, such a derivation is new. Then, to illustrate the mechanism that leads to non-Gaussian spreading, we analyze this set of equations at first leaving out the Gaussian dispersion term (microdispersion). The set of equations now transforms to the telegrapher’s equation. Characteristic for this system is a longitudinal spreading that becomes Gaussian only in the longtime limit. We refer to this as kinetics-induced spreading. When the microdispersion process is included back again, the characteristics of the telegraph equations are still present. Now, two spreading phenomena are active, the Gaussian microdispersive spreading plus the kinetics-induced non-Gaussian spreading. In the long run, the latter becomes Gaussian as well. Another non-Gaussian feature shows itself in the 2D situation. Here, the lateral spread and the longitudinal displacement are no longer independent, as should be the case for a 2D Gaussian spreading process. In a displacing plume, this interdependence is displayed as a ‘tailing’ effect. We also analyze marginal and conditional moments, which confirm this result. With respect to effective properties (velocity and dispersion), we conclude that effective parameters can be defined properly only for large times (asymptotic times). In the two-dimensional case, it appears that the transverse spreading depends on the longitudinal coordinate. This results in ‘cigar-shaped’ contours.     

基于Nataf变换的层递响应面法分析结构可靠度

针对现有的随机响应面法(SRSM)和层递响应面法(CRSM)存在的局限性,本文结合预处理随机Krylov子空间法,建立了基于Nataf变换的向量型层递响应面法,并应用于含非高斯型互相关随机变量的结构可靠度分析。首先,利用预处理随机Krylov子空间的层递基向量近似展开结构的总体节点位移向量,建立向量型层递响应面;然后,根据Nataf变换建立非高斯型互相关随机变量与独立标准正态随机变量之间的关系式,将独立标准正态空间内由Hermite多项式的根组合形成的概率配点变换成非高斯空间内的概率配点,并通过回归分析确定层递响应面的待定系数。计算结果表明,本文建立的CRSM属于向量型响应面法,能较好地处理含非高斯型互相关随机变量的结构可靠度分析问题,计算精度和效率均较高,且具有良好的全域性。     

基于高斯过程分类的结构贝叶斯可靠性分析

贝叶斯可靠性方法是处理不完备信息条件下结构可靠性问题的有效途径之一。在实际应用中,由于可靠性分析的计算量较大,常须采用各种近似替代模型以提高计算效率。传统的替代模型方法是对结构的功能函数予以近似建模。这种方法不易定量考虑模型误差对可靠性分析的影响,且难以应用于诸如功能函数不连续和失效域不连通等情况。为此,本文提出一种基于高斯过程分类的替代模型,直接辨识结构的极限状态曲面,并将其应用于结构贝叶斯可靠性分析之中。分析了替代模型不确定性对可靠性预测结果的影响,给出了失效概率分布参数的方差算式,进而提出了改善模型精度的补充采样准则。通过算例验证了方法的适用性和有被性．