结构非平稳随机响应方差矩阵的直接精细积分计算

对于受演变随机白噪声或有色噪声激励的结构，对其方差矩阵推导了相应的微分Ｌｙａｐｕｎｏｖ方程，并用精细积分方法建立了倍步长与等步长积分格式，使一大类以往难于得到精确解的问题，能迅速地在计算机上得到具有很高精度的解答。并用其它文献上的例题验证了本文给出方法的精确性及极高的计算效率。     

基于离散小波变换的多自由度结构非平稳随机响应计算

将地面运动模拟成非平稳随机过程,基于离散小波变换得到地面运动离散小波系数的统计值,并以此作为输入,推导了多自由度结构和随机响应公式,通过对响应偏谱的计算,得到随时间变化的响应频率特性和名阶谱参数,利用Monte-Carlo法和本文方法进行了计算实例对比,验证了本文方法的正确性。     

结构非平稳随机响应的增维精细时程积分

对于不同形式的均匀调制演变随机激励，给出计算线性多自由度体系非平稳随机响应的增维精细时程积分法。先用虚拟激励法将随机荷载化为确定性荷载，然后把确定性荷载用状态方程表示，进而构造出形式统一的增维精细时程积分格式。算例表明，本文方法不仅与混合型精细时程积分格式具有同样的精度，而且计算效率更高。     

非平稳地震作用下随机结构动力可靠度计算

对非平稳地震作用下的含随机参数结构,建议了一类结构体系动力可靠度的数值模拟求解方法.把结构动力方程写成状态方程形式,采用精细积分法对状态方程进行数值求解,将结构响应表达为一系列随机系数和离散时刻处随机激励乘积的和形式.随机系数为结构随机参数的函数,反映结构随机参数对随机响应的影响.在确定性结构非平稳随机响应时域分析方法的基础上,采用不含交叉项的二次多项式对该随机系数进行重构,获得了结构响应关于结构随机参数和离散时刻处随机激励的显式表达式.基于该显式表达式,利用数值模拟技术可以方便地进行首次超越失效准则下结构体系动力可靠度的求解.对一榀非平稳地震作用下的含随机参数框架进行了结构体系动力可靠度分析,并在计算精度和计算效率上与传统蒙特卡罗法进行了比较,结果显示所提出的方法具有理想的精度和相当高的效率.     

关于非平稳随机过程平稳化处理的一个注记

本文揭示了将非平稳随机过程平稳化所采用的平稳样本函数本质,并明确了什么样非平稳随机过程可以进行平稳化处理,什么样非平稳随机过程不能进行平稳处理,同时提出了确定观察函数和平稳样本函数协方差矩阵方法。     

演变随机激励下线性结构的非平稳响应特性

本文采用复模态分析法,考察了常参数线性阻尼系统在演变随机激励下的非平稳响应特性.得到了响应时变相关函数矩阵的闭式解.所得结果通用于经典阻尼与非经典阻尼情形.方法简便实用,它将非平稳随机响应问题归结为复代数运算.所附算例分别就演变随机激励与相应的突加平稳激励情形,对系统时变均方响应的结果进行了对比.     

非线性系统非平稳随机响应矩计算的Newmark递推算法

利用Ｎｅｗｍａｒｋ离散化格式，结合时变等价线性化步骤，导出了计算非线性系统受白噪声和非白噪声随机激励作用下非平稳响应协方差矩阵的递推算法。该算法计算步骤简单，易于在计算机上实现，计算效率高。算例表明，其所得计算结果和ＭｏｎｔｅＣａｒｌｏ模拟结果符合较好。     

自锚式悬索桥的平稳/非平稳随机地震响应

通过引入均匀调制演变函数,考虑了地震激励幅值的非平稳性。同时考虑了地震动空间效应,包括行波效应、部分相干效应和局部场地效应的影响,对一自锚式混凝土悬索桥结构进行了地震反应分析。计算了平稳/非平稳地面激励下主塔弯矩以及剪力反应。计算结果表明,考虑非平稳因素可使地震反应峰值减小,行波效应和相干效应使结构地震反应增大。     

非白噪声激励的非线性系统非平稳响应的一种计算方法

本文给出了一种计算非线性系统在非白噪声激励下非平稳响应的方法。该方法采用统计线性化和数学归纳法，获得了位移、速度的均方和协方的递推关系。考虑了等效线性化系数的时变性；给出了两个算例，并将计算结果与相应的数字模拟结果［８］进行了比较。结果证明该方法是简单、精确和有效的。     

平稳随机激励下线性随机桁架结构动力响应分析

考虑桁架结构的物理参数、几何尺寸的随机性，利用求解随机变量函数矩的方法和求解随机变量数字特征的代数综合法，从结构平稳随机响应在频域上的表达式出发，导出了随机桁架结构在平稳随机激励下位移响应均方值和应力响应均方值的均值、方差和变异系数的计算表达式。通过算例考察了结构物理参数和几何尺寸的随机性对结构位移响应均方值和应力响应均方值随机变量随机性的影响，并获得了一些有意义的结论。     

A modal correction method for non-stationary random vibrations of linear systems

The computational effort in determining the dynamic response of linear systems is usually reduced by adopting the well-known modal analysis along with modal truncation of higher modes. However, in the case in which the contribution of higher modes is not negligible, modal correction methods have been introduced to improve the accuracy of the dynamic response, for both deterministic and stochastic input. In the latter case the random response is usually corrected via various methods determined as rough extensions of methods originally proposed for deterministic input. Consequently the efficiency of the correction methods is not suitable, from both theoretical and computational points of view. In this paper, a new approach to cope with the non-stationary response of linear systems is presented. The proposed modal correction method provides a correction term determined as a pseudo-stationary contribution of the equation governing either first-order or second-order statistics. Owing to the fact that no truncation criteria are well established for random vibration study, the proposed modal correction method offers a suitable vehicle for determining very accurately the stochastic response of MDOF linear systems under Gaussian stationary and non stationary excitation as evidenced in the numerical applications.     

A method for the random analysis of linear systems subjected to non-stationary multi-correlated loads

The paper shows a procedure for evaluating the correlation matrix and the evolutionary power spectral density matrix of the response of linear structural systems subjected to random non-stationary multi-correlated vector processes. The approach reduces this problem to the solution of some corresponding stationary problems. It is shown that the assumption of a modulating matrix function, whose elements are the sum of exponential functions, allows to transform the initial non-stationary problem into a stationary one. This stationary problem can be solved by well-known unconditionally stable step-by-step numerical procedures in the time domain, and, in closed form, in the frequency domain. The comparison of the results obtained using the proposed approach with those obtained by Monte Carlo Simulations (MCS) has revealed a very good level of accuracy.     

Simulation of multi-dimensional non-gaussian non-stationary random fields

This paper presents a method for simulating multi-dimensional stochastic processes. The target process is specified by its marginal density function which can vary along the indexing set, and by its two point correlation function, which need not be stationary. The polynomial chaos expansion is used to match the marginal densities while the Karhunen–Loève representation is used to fine tune the match of the correlation function. The resulting representation of the process is in the form of a polynomial chaos expansion, which can be readily realized.     

Frequency-based fatigue analysis of non-stationary switching random loads

The service loadings in real systems are not only random, but also non-stationary. The spectral methods based on a frequency-domain characterization of random loads, which have been used in alternative to classical time-domain approaches, cannot be applied to non-stationary loads, because the conventional spectral density spectrum is not able to capture the evolutionary frequency characteristics of non-stationary loads. This clearly restricts the applicability of the existing frequency-based methods only to loads which are stationary. At the same time, it is also very difficult to propose general models valid for all types of load non-stationarity encountered in practice. Therefore, a practical approach is to restrict the analysis to a specific class of non-stationary loads; in this work, we consider particular non-stationary loads (i.e. switching loads), which are piecewise stationary in their variance. A frequency-domain analysis of such loads is proposed, which is based on a combination of the frequency-based analysis of each adjacent stationary segment, which can be either Gaussian or non-Gaussian. Numerically simulated load histories, as well as loads measured on mountain bikes in special tracks, are analysed to validate the proposed methodology. The presented results also show the correlation between load non-stationarity and non-Gaussianity.     

Closed-form solutions for the time-variant spectral characteristics of non-stationary random processes

Spectral characteristics are important quantities in describing stationary and non-stationary random processes. In this paper, the spectral characteristics for complex-valued random processes are evaluated and closed-form solutions for the time-variant statistics of the response of linear single-degree-of-freedom (SDOF) and both classically and non-classically damped multi-degree-of-freedom (MDOF) systems subjected to modulated Gaussian colored noise are obtained. The time-variant central frequency and bandwidth parameter of the response processes of linear SDOF and MDOF elastic systems subjected to Gaussian colored noise excitation are computed exactly in closed-form. These quantities are useful in problems which require the use of complex modal analysis, such as random vibrations of non-classically damped MDOF linear structures, and in structural reliability applications. Monte Carlo simulation has been used to confirm the validity of the proposed solutions.     

Finite element analysis of non-stationary one-dimensional random diffusion problems

A finite element analysis of a class of non-stationary random diffusion problems is considered. By using the one-dimensional heat equation with random initial condition and random external excitation, the statistical numerical formulation is presented. Two typical numerical examples are given for somewhat simplified problems by which the validity of the finite element scheme is discussed. The results obtained by the finite difference scheme are also shown.     

Calculating the variance in Markov-processes with random reward

In this article we present a generalization of Markov Decision Processes with discreet time where the immediate rewards in every period are not deterministic but random, with the two first moments of the distribution given. Formulas are developed to calculate the expected value and the variance of the reward of the process, which formulas generalize and partially correct other results. We make some observations about the distribution of rewards for processes with limited or unlimited horizon and with or without discounting. Applications with risk sensitive policies are possible; this is illustrated in a numerical example where the results are revalidated by simulation.

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Resumen En este artículo se presenta una generalización de los procesos de decisión markovianos en tiempo discreto: las ganancias en el tránsito de un estado a otro no son deterministas sino aleatorias; de las funciones de distribución se suponen conocidos únicamente los dos primeros momentos. Se deducen fórmulas para calcular la esperanza matemática y la varianza de la ganancia total del proceso en horizonte finito o infinito y con o sin descuento. Se hacen algunas observaciones sobre la función de distribución de la ganancia total. Los resultados tienen interés para introducir la noción de riesgo en la búsqueda de políticas óptimas. Este trabajo amplía y corrige resultados de otros autores, ilustrándolo con un ejemplo numérico.

     

Generalization of the multiparticle effective field method to random structure matrix composites

Summary In this paper linearly thermoelastic composite media are treated, which consist of a homogeneous matrix containing a statistically homogeneous random set of ellipsoidal uncoated or coated inclusions. Effective properties (such as compliance, thermal expansion, stored energy) as well as the first statistical moments of stresses in the phases are estimated for the general case of nonhomogeneity of the thermoelastic inclusion properties. The micromechanical approach is based on the generalization of the ``multiparticle effective field' method (MEFM, see [7] for references), previously proposed for the estimation of stress field averages in the phases. The refined version of the MEFM takes into account both the variation of the effective fields acting on each pair of fibers and inhomogeneity of statistical average of stresses inside the inclusions. One considers in detail the connection of the method proposed with numerous related methods. The explicit representations of the effective thermoelastic properties and stress concentration factor are expressed through some building blocks described by numerical solutions for both the one and two inclusions inside the infinite medium subjected to the homogeneous loading at infinity. Just with some additional assumptions (such as an effective field hypothesis) the involved tensors can be expressed through the Green's function, Eshelby tensor and external Eshelby tensor. The dependence of effective properties and stress concentrator factors on the radial distribution function of the inclusion locations is analyzed.     

非负矩阵分解在地震作用下结构随机响应分析中的应用

地震动作为一类典型的非平稳随机过程可由演变谱刻画其能量的时-频分布。然而,演变谱的时-频耦合特性却限制了经典谱表示法的模拟效率。为提高非平稳地震动模拟效率,简化非平稳地震作用下结构随机响应分析,提出了基于非负矩阵分解(nonnegative matrix factorization,NMF)的地震动演变谱解耦方案,使结构在非平稳地震作用下的响应计算简化为各项均匀调制激励下的结构随机响应叠加。分析结果表明,基于非负矩阵分解的地震动演变谱解耦具有良好的精度,快速傅里叶变换技术的引入提高了经典谱表示法的模拟效率,模拟样本自相关函数与目标值吻合良好,非平稳地震作用下结构随机响应频域分析得到简化。     

A nonparametric model of random uncertainties for reduced matrix models in structural dynamics

Random uncertainties in finite element models in linear structural dynamics are usually modeled by using parametric models. This means that: (1) the uncertain local parameters occurring in the global mass, damping and stiffness matrices of the finite element model have to be identified; (2) appropriate probabilistic models of these uncertain parameters have to be constructed; and (3) functions mapping the domains of uncertain parameters into the global mass, damping and stiffness matrices have to be constructed. In the low-frequency range, a reduced matrix model can then be constructed using the generalized coordinates associated with the structural modes corresponding to the lowest eigenfrequencies. In this paper we propose an approach for constructing a random uncertainties model of the generalized mass, damping and stiffness matrices. This nonparametric model does not require identifying the uncertain local parameters and consequently, obviates construction of functions that map the domains of uncertain local parameters into the generalized mass, damping and stiffness matrices. This nonparametric model of random uncertainties is based on direct construction of a probabilistic model of the generalized mass, damping and stiffness matrices, which uses only the available information constituted of the mean value of the generalized mass, damping and stiffness matrices. This paper describes the explicit construction of the theory of such a nonparametric model.