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．     

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.     

非平稳随机激励下结构体系动力可靠度时域解法

将结构动力方程写成状态方程形式,采用精细积分法对其进行数值求解,导出了非平稳激励下结构随机响应的时域显式表达式,该过程的计算量仅相当于两次确定性时程分析的计算量. 基于该显式表达式,结合首次超越失效准则,提出了非平稳随机激励下结构体系动力可靠度的数值模拟算法. 与功率谱方法相比,该方法无需同时在时频域内进行大量数值积分,也无需引入关于响应过程跨越界限次数概率分布, 以及各失效模式相关性等方面的假定. 通过数值算例, 对比了该方法与泊松过程法、马尔可夫过程法、传统蒙特卡罗法的计算精度和计算效率,结果显示该方法具有理想的精度和相当高的效率.      

基于首次超越破坏时间概率的结构动力可靠性分析

对结构非线性动力系统的首次超越破坏(失效)进行研究。首先,采用等效线性化与随机平均方法,推导出了首次超越破坏时间的结构失效概率分布函数,并对单自由度非线性体系的失效概率进行了分析。其次,采用虚拟激励法对多自由度滞变结构体系进行了随机响应计算,结合首次超越准则(双侧界动力界限),研究了随机地震激励下高层结构的各楼层与结构整体可靠度。研究表明:在激励和破坏界限值相同的情况下,非线性体系的首次超越破坏时间概率要比相应线性体系的小;并发现了在随机地震激励下高层结构的薄弱层楼层的位置。该方法对结构的性能设计与控制具有指导意义。     

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。     

结构可靠性分析高效自适应重要抽样方法

提出了一种基于自适应Metropolis算法和快速高斯变换技术的结构可靠性分析高效自适应重要抽样方法. 该方法首先利用自适应Metropolis算法高效生成结构失效域样本, 然后运用自适应宽核密度估计方法构造重要抽样密度函数, 最后采用快速高斯变换加速重要抽样过程中核函数的计算. 与传统方法相比, 自适应Metropolis算法能够在相同计算量下提供更多结构失效域信息从而改善计算精度, 即为求得给定精度问题的解, 可有效减少样本生成过程中的结构分析次数, 提高方法的计算效率; 快速高斯(Gauss)变换大幅降低核密度估计的计算复杂度从而大幅缩减重要抽样的计算耗时. 通过数值算例可以看出该方法具有较高的计算精度和效率.      

随机过程激励下随机结构系统可靠度分析的一种方法

提出了随机过程荷载激励下，具有随机参数的结构系统可靠度分析的一种方法，该方法基于首次超越破坏机制，分析随机过程荷载激励下，结构参数（随机变量）取某一确定向量时的条件失效概率，采用Ｍｏｎｔｅ Ｃａｒｌｏ技术模拟结构参数的随机性，由条件失效概率给出随机结构的无条件失效概率，最后对中方法和程序作了检验，并进行了实际计算。     

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.     

大跨屋盖结构非高斯风场的快速模拟算法研究

针对屋盖结构风压场的非高斯特性,本文提出一种多变量平稳非高斯风压场模拟的新方法。文中首次采用四参数指数函数表达风压过程和高斯过程之间的转换关系,推导出关于指数函数所含参数的非线性方程组,利用双变量联合高斯分布的特性获得相关函数的转换关系。通过上述方法,将非高斯风压场表达为虚拟高斯过程的函数,从而采用谐波合成法生成风压时间序列。工程实例表明,本文算法计算效率和模拟精度高,适合实际工程应用。     

Structural first failure times under non-Gaussian stochastic behavior

An analytical moment-based method for calculating structural first failure times under non-Gaussian stochastic behavior is proposed.In the method,a power series that constants can be obtained from response moments (skewness,kurtosis,etc.) is used firstly to map a non-Gaussian structural response into a standard Gaussian process,then mean up-crossing rates,mean clump size and the initial passage probability of a critical barrier level by the original structural response are estimated,and finally,the formula for calculating first failure times is established on the assumption that corrected up-crossing rates are independent.An analysis of a nonlinear single-degree-of-freedom dynamical system excited by a Gaussian model of load not only demonstrates the usage of the proposed method but also shows the accuracy and efficiency of the proposed method by comparisons between the present method and other methods such as Monte Carlo simulation and the traditional Ganssian model.     

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.     

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.     

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.     

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.

     

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。     

Bifurcation in most probable phase portraits for a bistable kinetic model with coupling Gaussian and non-Gaussian noises

The phenomenon of stochastic bifurcation driven by the correlated non-Gaussian colored noise and the Gaussian white noise is investigated by the qualitative changes of steady states with the most probable phase portraits. To arrive at the Markovian approximation of the original non-Markovian stochastic process and derive the general approximate Fokker-Planck equation (FPE), we deal with the non-Gaussian colored noise and then adopt the uni¯ed colored noise approximation (UCNA). Subsequently, the theoretical equation concerning the most probable steady states is obtained by the maximum of the stationary probability density function (SPDF). The parameter of the uncorrelated additive noise intensity does enter the governing equation as a non-Markovian effect, which is in contrast to that of the uncorrelated Gaussian white noise case, where the parameter is absent from the governing equation, i.e., the most probable steady states are mainly controlled by the uncorrelated multiplicative noise. Additionally, in comparison with the deterministic counterpart, some peculiar bifurcation behaviors with regard to the most probable steady states induced by the correlation time of non-Gaussian colored noise, the noise intensity, and the non-Gaussian noise deviation parameter are discussed. Moreover, the symmetry of the stochastic bifurcation diagrams is destroyed when the correlation between noises is concerned. Furthermore, the feasibility and accuracy of the analytical predictions are verified compared with those of the Monte Carlo (MC) simulations of the original system.