非高斯脉动风压的模拟研究

对于风荷载数值模拟,大多数研究都是假定风荷载为平稳高斯随机过程。然而,在分离流作用的一些局部重要区域,例如建筑物屋盖边缘、屋面转角等,风荷载表现出强烈的非高斯特性。为了能够有效地模拟非高斯脉动风压,本文提出一种模拟非高斯脉动风压的框架。首先,根据风速与风压间的关系,严格推导出脉动风压功率谱密度函数。然后,基于导出的功率谱密度函数、Johnson转换系统和数字滤波理论,提出一种能够快速而有效的生成指定偏度、峰度和功率谱非高斯脉动风压的方法。最后,通过一个一维单变量非高斯脉动风压的模拟算例对该方法的可行性和正确性进行验证。数值结果表明：模拟生成的单样本非高斯脉动风压的统计参数例如偏度和峰度与目标偏度和峰度非常吻合,而且模拟功率谱与目标功率谱两者也吻合得很好。     

基于正交化HHT和随机相位模拟非平稳随机过程

模拟非平稳随机过程已经成为工程中经常遇到的情况,使非平稳过程的大量模拟样本具有相同的统计特性并不容易。基于样本记录正交HHT变换的Hilbert谱提出了非平稳随机过程的模拟方法。首先,利用正交化方法对IMF分量进行处理,避免了传统EMD分解造成的能量泄漏。第二步,把样本的Hilbert谱均值作为随机过程的目标Hilbert谱,通过引入随机相位进行非平稳随机过程的仿真,并且给出了随机过程的统计特性函数。通过对低频地震动记录和高频地铁振动记录的模拟算例表明,模拟的非平稳过程样本与原记录在时频分布上非常接近,具有相同的统计特性。     

基于小波和乘法混合核函数LSSVM的顺风向非高斯空间风压预测

提出了基于Marr小波核函数最小二乘支持向量机(Marr-LSSVM)的顺风向非高斯空间风压预测算法。通过传统高斯核函数(RBF)和多项式核函数(Poly)的乘法运算,提出了Poly*RBF-LSSVM(MK-LSSVM)的空间风压预测算法。运用粒子群优化(PSO)算法,对Marr-LSSVM、传统单核CSK-LSSVM和MK-LSSVM的惩罚参数、核函数参数、权重、尺度因子进行优化,建立基于智能优化的非高斯空间风压预测算法;以30 m和50 m处模拟顺风向风压时程作为输入样本,使用提出的预测算法对40 m处风压时程进行了预测。数值分析表明,Marr-LSSVM、MK-LSSVM比CSK-LSSVM具有明显高的非高斯风压预测性能。     

一种非高斯随机振动过程数值模拟方法

目的 考虑真实随机振动的非高斯特性,提出一种根据已知信息生成与其相符的非高斯随机振动过程的数值模拟方法。方法 基于均值、方差、偏斜度、峭度及功率谱密度函数（或自相关函数）等约束条件,对非高斯随机振动进行模拟。根据功率谱获取非高斯过程的自相关矩阵;通过Hermite多项式的正交性质和多项式混沌展开方法推导出的公式,构造满足标准正态分布随机过程的协方差矩阵,并对其进行谱分解和主成分分析;最后,利用Karhunen-Loeve展开和多项式混沌展开来表示所模拟的非高斯振动过程。结果 随着采样点个数的增加,实测数据与模拟数据之间的误差越来越小,该方法具有较好的模拟精度。结论 应用多项式混沌展开、Karhunen-Loeve展开以及蒙特卡洛等方法,可生成非高斯随机振动过程,并得到准确有效的各项统计参数模拟值。     

非高斯随机振动下包装件时变振动可靠性分析

包装件在流通过程中经常受到非高斯随机振动激励的作用,提出了一种包装件在非高斯随机振动激励条件下的时变可靠性的分析方法。结合多项式混沌扩展和Karhunen-Loeve扩展,提出了基于功率谱(或自相关函数)、均值、方差、偏斜度和峭度信息的非高斯随机振动激励的模拟方法;为减小数值分析量,应用拟蒙特卡洛法,在随机变量空间中合理控制变量的分布模拟非高斯随机振动激励,通过四阶龙格库塔法分析,用较少的随机振动模拟样本准确得到了包装件加速度响应的前四阶矩和自相关函数。基于响应的统计信息,应用该研究提出的多项式混沌扩展、Karhunen-Loeve扩展和拟蒙特卡洛分析,获得包装件加速度响应样本,计算包装件的时变可靠性,用原始蒙特卡洛法验证了计算的准确性;该方法在包装件的可靠性分析、包装系统优化等方面具有重要意义。     

随机动力学响应的高斯相关过程模拟

动力学响应是描述系统振动状态、评估其性能、用于控制等的重要变量,复杂系统的不确定性、随机激励样本的不可测量性等导致传统随机响应时程与统计分析的计算困难,因此需要发展基于系统响应观测的、直接的随机过程概率模型与评估新方法。近年来,人工智能与数据处理技术等领域发展的无确定性系统模型的、直接随机过程概率模型,及其概率评估、系统状态预测等方法为动力学响应的概率分析提供了新思路,特别是具有很好普适性与可分析性的高斯相关过程已具有较完整的理论方法。鉴于此,本文提出针对动力学系统响应的、直接的随机过程概率模型与评估方法,并作探索性研究。先基于高斯白噪声激励动力学系统响应的统计特性分析,说明系统响应的高斯随机过程特性、响应在时间维度上的相关性、及其协方差随时间差的指数衰减特性等;再给出该系统响应的高斯相关过程概率建模与评估方法,包括由响应协方差计算,高斯过程协方差或核函数的拟合,到高斯相关过程概率模型的确定,响应样本过程的直接生成,及其统计评估等,并给出高斯相关过程的贝叶斯更新与系统状态预测有关基本公式。数值结果表明该高斯相关过程的概率建模与响应评估方法的可行性与有效性。     

具有时变功率谱的非高斯随机过程的数值模拟

为了有效地模拟具有目标时变功率谱特征的非高斯随机过程,即非平稳非高斯随机过程。提出了基于目标时变功率谱和目标非高斯概率密度函数,通过建立非高斯与高斯随机过程之间相互转换的非线性平移关系,以及非线性平移前后高斯与非高斯随机过程的功率谱或相关函数的转换关系,将非平稳非高斯随机过程转化为非平稳高斯随机过程的模拟;而非平稳高斯随机过程可通过谱表示进行有效的模拟。为了验证该方法的有效性,进行了具有目标非平稳非高斯特征的脉动风速模拟;模拟结果表明:模拟生成的脉动风速样本的功率谱具有时变特征,且瞬时功率谱和相关函数均与目标相吻合;任意时刻脉动风速样本的概率密度函数与目标非高斯函数相互吻合;因此,模拟的随机样本不仅具有目标时变功率的非平稳特征而且还具有目标概率密度函数的非高斯特征,说明了该非平稳非高斯随机过程模拟方法的有效性。     

非高斯脉动风压的非迭代模拟算法

建立了无需反复迭代的非高斯随机过程模拟算法,避免了反复迭代可能出现不收敛的问题。基于非线性平移过程,详细分析了潜在高斯随机过程与非高斯随机过程的转换关系。通过反证法证明了非高斯随机过程的目标功率谱与边缘概率分布函数需要协调一致,并建立了判断非高斯目标功率谱与边缘概率分布函数是否协调的标准,即潜在高斯目标功率谱是否出现负值。对于目标函数不协调的情况提出了相应的修正方案,建立了模拟单变量非高斯随机过程的非迭代算法。采用该算法对不同斜度的非高斯脉动风压进行了数值模拟分析,并通过相关函数、功率谱、概率密度函数与目标函数的对比验证了该算法的有效性。     

平稳地震动过程的随机函数-谱表示模拟

在平稳随机过程的谱表示基础上,采用随机函数的思想,将谱表达式中的标准正交随机变量表示为基本随机变量的正交函数形式。通过两组随机正交三角函数的构造,实现了非高斯正交随机变量和高斯独立随机变量的随机函数表达。与经典的谱表示方法相比,采用随机函数表达,仅需1~2个基本随机变量即可描述原随机过程的概率特性,而且可以直接由功率谱密度函数生成具有给定概率的非高斯平稳过程和高斯平稳过程的样本函数。最后,结合平稳地震动加速度过程的功率谱密度函数,验证了随机函数-谱表示方法的有效性。     

基于正交化HHT和随机相位模拟非平稳随机过程

模拟非平稳随机过程已经成为工程中经常遇到的情况,使非平稳过程的大量模拟样本具有相同的统计特性并不容易.基于样本记录正交HHT变换的Hilbert谱提出了非平稳随机过程的模拟方法.首先,利用正交化方法对IMF分量进行处理,避免了传统EMD分解造成的能量泄漏.第二步,把样本的Hilbert谱均值作为随机过程的目标Hilbert谱,通过引入随机相位进行非平稳随机过程的仿真,并且给出了随机过程的统计特性函数.通过对低频地震动记录和高频地铁振动记录的模拟算例表明,模拟的非平稳过程样本与原记录在时频分布上非常接近,具有相同的统计特性.     

Simulation of stationary Gaussian/non-Gaussian stochastic processes based on stochastic harmonic functions

A new model is proposed to represent and simulate Gaussian/non-Gaussian stochastic processes. In the proposed model, stochastic harmonic function (SHF) is extended to represent multivariate Gaussian process firstly. Compared with the conventional spectral representation method (SRM), the SHF based model requires much fewer variables and Cholesky decompositions. Then, SHF based model is further extended to univariate/multivariate non-Gaussian stochastic process simulation. The target non-Gaussian process can be obtained from the corresponding underlying Gaussian processes by memoryless nonlinear transformation. For arbitrarily given marginal probability distribution function (PDF), the covariance function of the underlying multivariate Gaussian process can be determined easily by introducing the Mehler’s formula. And when the incompatibility between the target non-Gaussian power spectral density (PSD) or PSD matrix and marginal PDF exists, the calibration of the target non-Gaussian spectrum will be required. Hence, the proposed model can be regarded as SRM to efficiently generate Gaussian/non-Gaussian processes. Finally, several numerical examples are addressed to show the effectiveness of the proposed method.     

Simulation of wind velocity time histories on long span structures modeled as non-Gaussian stochastic waves

A methodology is proposed for efficient and accurate modeling and simulation of correlated non-Gaussian wind velocity time histories along long-span structures at an arbitrarily large number of points. Currently, the most common approach is to model wind velocities as discrete components of a stochastic vector process, characterized by a Cross-Spectral Density Matrix (CSDM). To generate sample functions of the vector process, the Spectral Representation Method is one of the most commonly used, involving a Cholesky decomposition of the CSDM. However, it is a well-documented problem that as the length of the structure – and consequently the size of the vector process – increases, this Cholesky decomposition breaks down numerically. This paper extends a methodology introduced by the second and fourth authors to model wind velocities as a Gaussian stochastic wave (continuous in both space and time) by considering the stochastic wave to be non-Gaussian. The non-Gaussian wave is characterized by its frequency–wavenumber (FK) spectrum and marginal probability density function (PDF). This allows the non-Gaussian wind velocities to be modeled at a virtually infinite number of points along the length of the structure. The compatibility of the FK spectrum and marginal PDF according to translation process theory is secured using an extension of the Iterative Translation Approximation Method introduced by the second and third authors, where the underlying Gaussian FK spectrum is upgraded iteratively using the directly computed (through translation process theory) non-Gaussian FK spectrum. After a small number of computationally extremely efficient iterations, the underlying Gaussian FK spectrum is established and generation of non-Gaussian sample functions of the stochastic wave is straightforward without the need of iterations. Numerical examples are provided demonstrating that the simulated non-Gaussian wave samples exhibit the desired spectral and marginal PDF characteristics.     

谱表示法模拟风场的误差分析

研究了原型谱表示法模拟的非各态历经性多变量风场的统计矩的时域估计值和目标值之间误差的概率描述。基于原型谱表示法的模拟公式，以三变量风场为例，导出了模拟结果的均值、相关函数、功率谱密度函数和根方差等四项统计特征的单样本时域估计表达式，它们是随机变量或随机过程。运用概率论的计算方法，推导出了上述随机变量或过程的前二阶矩的解析表达式，得到了模拟风场的统计特征时域估计的偏度误差和随机误差。将三变量过程的结果加以推广，给出了误差计算的通式。通过算例中统计误差值和理论误差值的对比，验证解析解的正确性。探讨了可能的降低随机误差的方法。求得的误差闭合解将有利于结合误差传播理论进行可靠性分析。     

大跨越输电塔线体系随机脉动风场模拟研究

为在时域内分析大跨越输电塔-线体系风振响应,根据结构体型特征和脉动风场的功率谱特性,考虑输电塔-线分布、平均风剖面变化、功率谱能量与相干性等影响因素,提出了简化作用于输电塔线体系的多变量三维脉动风场(n-V-3D)为多变量一维脉动风场(n-V-1D)分析方法。结合输电塔线体系有限元法风振响应分析的特点,应用谐波叠加法和谱分解的适当修正,建立了脉动风速时程数值模拟方法。实例模拟表明,数据符合统计检验,模拟功率谱与目标谱吻合,从而验证了模拟方法的有效性和模拟脉动风速时程适用性。     

Two dimension-reduction probabilistic models for simulating nonstationary turbulent wind fields

The reasonable modeling of a nonstationary stochastic turbulent wind field is an important basis and premise for the analysis of the wind-induced response and reliability of engineering structures. In the present study, two dimension-reduction probabilistic models are established for simulating the multi-dimensional and multi-variable nonstationary turbulent wind fields based on the double proper orthogonal decomposition (DPOD) and the double spectral representation method (DSRM). Among them, the DPOD, originally used to simulate a stationary turbulent wind field, is extended to a nonstationary one, and the DSRM is a newly proposed method for a nonstationary turbulent wind field with a large number of simulation points. In essence, the DPOD is a discrete method with explicit physical significance and flexible spatial location of simulation points, while the DSRM is a continuous method, of which the simulation efficiency is theoretically independent of the number of simulation points. Furthermore, by introducing the dimension-reduction methods based on random function and POD-FFT (Fast Fourier transform) technique into the DPOD and the DSRM, the nonstationary stochastic turbulent wind field can be effectively described with merely three elementary random variables. Numerical examples of the nonstationary stochastic turbulent wind fields acting on a long-span bridge and a communication tower fully verify the effectiveness and superiority of the proposed methods.     

基于本征正交分解的谱表示法模拟风场的误差

推导了本征正交分解(Proper Orthogonal Decomposition,POD)型谱表示法模拟所得平稳正态脉动风场的偏度误差和随机误差.从POD型谱表示法的模拟公式出发,推导了Ⅳ变量风场模拟结果序列的样本均值、相关函数、功率谱函数和根方差等前二阶矩统计特征的时域估计表达式;并证明了时域估计相关函数是正态过程,功率谱函数为非正态随机过程.进一步,计算上述样本时域估计二阶矩特征的均值和根方差,即得到了POD型谱表示法模拟所得风场的各统计量时域估计的偏度误差和随机误差,并以此给出了误差计算的通式.算例中统计误差和理论误差值的对比验证了所推导的解析解.     

Simulation of higher-order stochastic processes by spectral representation

The Spectral Representation Method is generalized for simulation of asymmetrically nonlinear (skewed higher-order) stochastic processes. This is achieved by deriving new orthogonal increments for the spectral process in the Cramér spectral representation that include wave interactions and satisfy third-order orthogonality properties. These orthogonal increments are derived by introducing two new quantities – the pure power spectrum and the partial bicoherence – that decouple the contributions of single waves and wave interactions in the Fourier-type expansion of a stochastic process. The further extension to fourth and higher-order processes is discussed. Several mathematical examples demonstrate the capabilities of the proposed methodology to generate general third-order stochastic processes. The method is then applied to the generation of turbulent wind velocities characterized from Large Eddy Simulations of the atmospheric boundary layer.     

Filter approach to the stochastic analysis of MDOF wind-excited structures

In this paper, an approach useful for stochastic analysis of the Gaussian and non-Gaussian behavior of the response of multi-degree-of-freedom (MDOF) wind-excited structures is presented. This approach is based on a particular model of the multivariate stochastic wind field based upon a particular diagonalization of the power spectral density (PSD) matrix of the fluctuating part of wind velocity. This diagonalization is performed in the space of eigenvectors and eigenvalues that are called here wind-eigenvalues and wind-eigenvectors, respectively. From the examination of these quantities it can be recognized that the wind-eigenvectors change slowly with frequency while the first wind-eigenvalue dominates all the others in the low-frequency range. It is shown that the wind field can be modeled in a satisfactory way by taking the first wind-eigenvector as constant and by retaining only the first eigenvalue in the calculations. The described model is then used for stochastic analysis in the time domain of MDOF wind-excited structures. This is accomplished by modeling each element of the diagonalized wind-PSD matrix as the velocity PSD function of a set of second-order digital filters with viscous damping driven by white noise of selected intensity. This approach makes it easy to obtain in closed form the statistical moments of every order of the structural response, taking full advantage of the Itô calculus. Moreover, in the proposed approach, it is possible to reduce the computational effort by appropriately selecting the number of wind modes retained in the calculation.