偏斜非高斯随机振动信号幅值概率密度函数研究

偏斜非高斯振动信号幅值概率密度没有明确、简洁的解析表达式。研究概率密度的解析表达式,对于非高斯振动理论研究具有重要意义。针对以上需求,提出了一种基于高斯混合模型的概率密度函数表示方法。首先,通过时间样本序列得到偏斜非高斯振动信号前五阶矩的估计值。其次,根据平稳高斯随机过程各阶矩之间的定量关系,结合二阶高斯混合模型的数学表达式建立方程组,求解得到混合模型中每个高斯分量的均值、标准差和权重系数。然后,将每个高斯分量的参数代入高斯混合模型,得到偏斜非高斯振动信号的幅值概率密度的解析表达式。最后,将所提出的方法应用于仿真非高斯加速度信号和实测非高斯振动应力信号,充分验证了该方法的有效性和适用性。     

非高斯数据的高斯化滤波

在信号检测、图像处理等领域有时需要对非高斯数据进行高斯化滤波处理。给出高斯化滤波定义和它的一般工作机理，重点介绍评估滤波效果的Q-Q图检验方法，然后对比研究了基于概率密度函数及其导数的U滤波和基于概率密度函数反函数的G滤波两种高斯化实现的方法、原理与性能，并给出了一组湖试数据实例。     

物流非高斯振动下的产品损伤分析

公路运输过程中的冲击信号造成了物流随机振动的非高斯特性。为研究冲击成分对产品损伤的影响,对8条中型卡车和重型卡车实测道路信号进行了统计分析。将振动信号分为20%的高强度非高斯信号、60%的中等强度高斯信号和20%的低强度高斯信号。使用有限元软件进行时域振动分析,计算各信号段的损伤占比。结果表明：振动过程中,非高斯信号蕴含了高强度的冲击信号,造成了绝大部分的损伤。中型卡车振动数据冲击幅值大、占比少,相对而言,重型卡车冲击幅值低、占比多。中型卡车高5%的冲击信号造成了90%以上的损伤;重型卡车20%的非高斯信号中除10%的冲击成分外还包含10%的较高幅值振动,其20%的非高斯信号造成的损伤约为80%或更高。在整个运输振动过程中,含量较少的冲击信号主导了损伤的累积。     

基于累积量的非高斯信号AR模型估计

高阶统计量能反映信号的非高斯信息,用高阶统计量对非高斯信号建立AR模型,并建立基于信号高阶统计量的Yule-Walker方程就可以进行AR模型谱估计。与基于二阶统计量的参数估计相比,基于高阶统计量的AR谱估计有更好的精度。     

铁路非高斯随机振动的数字模拟与包装件响应分析

目的研究铁路振动环境的非高斯特性,并分析包装件在非高斯随机振动环境条件下的响应情况。方法结合离散傅里叶变换与EARPG(1)模型,模拟了铁路随机振动信号。根据采集的数据的PSD曲线计算幅值,利用EARPG(1)模型生成了具有尖峰特征的模拟信号,计算了相位并进行了相位整体平移,根据幅值和相位,合成了所需的非高斯随机振动信号。将包装件简化为单自由度系统,分析了包装件在非高斯振动条件下的响应情况。结果铁路随机振动的峭度大于3,偏斜度为0,属于对称超高斯随机振动,提出的模型可准确模拟出铁路振动的非高斯特性,峭度和偏斜度的误差均小于3%,包装系统的固有频率、阻尼比、激励峭度对系统的响应的峭度、均方根均有较大的影响。结论通过合理地选择包装系统的固有频率和阻尼比,可有效减小系统的响应峭度和均方根,提高包装系统的可靠性。     

混合高斯参数估计的动态簇算法

混合高斯概率密度模型可以很好地拟合非高斯样本的概率密度。在各高斯分量概率密度互不重叠的条件下,使用动态簇算法可以快速而精确地估计出混合高斯概率密度模型参数。这是一种基于最小均方差原则的递推算法,在正向推导出各种可能的簇边界后,再根据确定的最末边界值逆向推定各前导簇边界,从而得到混合高斯概率密度模型参数估计值。描述模型及参数估计问题之后,动态簇算法被推导出来。然后深入探讨了该算法的实质及适用条件。最后结合数值仿真实例,分析了动态簇算法的估计性能。     

一种新的非高斯随机振动数值模拟方法

在振动工程领域,采用蒙特卡洛仿真方法求解复杂随机动力学问题时需要精确模拟各种随机振动激励信号。当随机振动激励具有显著的非高斯特征时,用传统的高斯振动去近似将产生较大的分析误差,需要研究精确的非高斯振动数值模拟技术。现有各种非高斯随机模拟方法一般只能模拟具有高峰值特征的随机振动,即超高斯随机振动,并且算法复杂不够直观,需要进行多次反复迭代,模拟精度和效率都有待提高。本文提出了一种新的基于幅值调制和相位重构的非高斯随机振动数值模拟方法,算法简洁直观,并充分利用快速傅里叶变换算法提高模拟效率,不仅可以模拟具有指定统计特性和频谱特性的超高斯随机振动,还能模拟亚高斯随机振动,具有广泛的适应性。数值仿真实验验证了该方法的有效性和精确性。     

小波域高斯混合模型方差估计近红外降噪方法

针对抑制近红外光谱噪声与保留光谱信号细节的矛盾,提出一种基于噪声方差估计的小波域降噪方法.该法对光谱信号小波域高频系数建立了两状态高斯混合模型,用EM算法估计模型系数,推证模型对噪声方差准确估计特性,将估计得到的噪声方差建立了阈值降噪模型.实验建立黄酒近红外光谱快速预测酒精度偏最小二乘模型,对比分析Penalty阈值、...     

高斯流场中单自由度线性体系非高斯振动响应试验研究

对于风湍流等高斯分布流速场中的线性结构体系,当考虑荷载中脉动流速二次项的影响时,理论上其振动响应将呈现非高斯分布特性。基于调试得到的不同粗糙工况高斯流场,开展了单自由度线性体系顺流向振动响应测试,研究了单自由度线性体系加速度响应的非高斯分布特性,分析了粗糙度对响应非高斯成分的影响,讨论了三种常见非高斯概率密度逼近方法对响应的拟合效果。试验结果表明:试验高斯流场中单自由度线性体系的顺流向加速度响应主要呈现出尖峰非高斯分布特征,且随着紊流度的提高,响应非高斯性有增强的趋势;响应的非高斯概率密度宜采用高斯混合模型方法进行拟合。     

非高斯风压峰值因子估计:基于矩的转换过程法的对比研究

建筑围护结构抗风设计需要准确估计非高斯风压极值或者峰值因子。对于非高斯风压峰值因子估计,常用的基于矩的转换过程法有Hermite多项式模型（HPM）、Johnson转换模型（JTM）及平移广义对数正态分布（SGLD）模型。极值通常由母本概率密度函数（PDF）的尾部决定,现阶段对于三种模型基于相同前四阶矩预测的非高斯母本PDF尾部的差别尚不清楚,自然,对于这三种模型预测的极值或者峰值因子的差别尚无答案。为了探明三种模型的异同,从而提供一定的选取原则,该文就三种方法对非高斯风压峰值因子估计效果进行了系统的对比研究。首先从理论上对比了三种方法预测得到的母本PDF的差异和估计的峰值因子差别;其次,选用长时距风洞试验风压数据检验了三种方法对非高斯风压峰值因子的估计效果。结果表明在三种模型都适用的偏度和峰度组合范围内,HPM对非高斯风压峰值因子估计结果相比SGLD模型和JTM模型估计结果更准确。     

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.     

Response probability estimation for randomly excited quasi-linear systems using a neural network approach

A quasi-linear system is referred to as a system linear in properties and subjected to multiplicative random excitations appearing also in the linear terms. It is known that exact solutions for the stationary moments can be obtained analytically for such a quasi-linear system if the excitations are Gaussian white noises. However, the exact response probability, which is non-Gaussian, is not obtainable analytically. In this paper, a neural network approach is proposed to evaluate the stationary response probability for quasi-linear systems under both additive and multiplicative excitations of Gaussian white noises based on the obtained exact statistical moments. Numerical examples show that the procedure yields accurate results if an appropriate form is assumed for the probability density function. The accuracy of the results is substantiated by comparing them with those obtained from Monte Carlo simulations.     

A translation model for non-stationary, non-Gaussian random processes

A model for simulation of non-stationary, non-Gaussian processes based on non-linear translation of Gaussian random vectors is presented. This method is a generalization of traditional translation processes that includes the capability of simulating samples with spatially or temporally varying marginal probability density functions. A formal development of the properties of the resulting process includes joint probability density function, correlation distortion and lower and upper bounds that depend on the target marginal distributions. Examples indicate the possibility of exactly matching a wide range of marginal pdfs and second order moments through a simple interpolating algorithm. Furthermore, the application of the method in simulating statistically inhomogeneous random media is investigated, using the specific case of binary translation with stationary and non-stationary target correlations.     

Higher moments of weighted integrals of non-Gaussian fields

In general, the exact probability distribution of a definite integral of a given non-Gaussian random field is not known. Some information about this unknown distribution can be obtained from the 3rd and 4th moment of the integral. Approximations to these moments can be calculated by discretizing the integral and replacing the integrand by third-degree polynomials of correlated Gaussian variables which reproduce the first four moments and the correlation function of the field correctly. The method described (see Ditlevsen O, Mohr G, Hoffmeyer P. Integration of non-Gaussian fields. Probabilistic engineering mechanics, 1996) based on these ideas is discussed and further developed and used in a computer program which produces fairly accurate approximations to the mentioned moments with no restrictions put on the weight function applied to the field and the correlation function of the field. A pathological example demonstrating the limitations of the method is given.     

Simulation of a non-Gaussian stochastic process based on a combined distribution of the UHPM and the GBD

To simulate non-Gaussian stochastic processes based on the first four moments, various simulation methods are presented, in which the determination of the transformation model and the calculation of the correlation coefficients between non-Gaussian stochastic processes and Gaussian stochastic processes are the critical procedures in these simulation methods. However, some existing simulation methods are limited to specific ranges. Furthermore, their practical applications are affected negatively due to the expensive cost of determining the transformation model and the correlation coefficients between non-Gaussian and Gaussian stochastic processes. Therefore, an accurate and efficient simulation method of a non-Gaussian stochastic process with a broader range is proposed in this article. Since the simulation of non-Gaussian processes and the Nataf transformation of non-Gaussian variables have some similar characteristics, a new combined distribution is proposed based on the unified Hermite polynomial model (UHPM) and the generalized beta distribution (GBD). Then, the combined distribution is employed in the simulation of non-Gaussian stochastic processes, in which the transformation model is deduced by the combined distribution. The correlation coefficient transformation function (CCTF) between the Gaussian and non-Gaussian stochastic processes can be evaluated through the interpolation method. Furthermore, numerical examples are presented to show the accuracy and effectiveness of the proposed simulation method for non-Gaussian stochastic processes.     

混合高斯参数估计的两种EM算法比较

混合高斯模型是一种典型的非高斯概率密度模型,获得广泛应用。其参数的优效估计可以通过最大似然方法获得,但最大似然估计往往因其非线性而难以实现,故期望最大化(Expectation-Maximization,EM)迭代算法成为一种常用的替代方法。常规EM算法性能受迭代初值设置影响大,且不能对模型阶数做出估计。一种名为贪婪EM的改进算法可以克服这两个缺点,获得更为准确的模型参数估计,但其运算量一般会远大于前者。本文对这两种EM算法进行综合研究,深入挖掘两者之间的关系,并基于相同的数值仿真实例,直观地演示比较两者的性能差异。     

Probability distributions of peaks and troughs of non-Gaussian random processes

This paper deals with the development of probability density functions applicable for peaks, troughs and peak-to-trough excursions of a non-Gaussian random process where the response of a non-linear system is represented in the form of Volterra's second-order functional series. The density functions of peaks and troughs are derived in closed form and presented separately. It is found that the probability density function applicable to peaks (and troughs) is equivalent to the density function of the envelope of a random process consisting of the sum of a narrow-band Gaussian process and sine wave having the same frequency. Furthermore, for a non-Gaussian random process for which the skewness of the distribution is less than 1.2, the density function of peaks (and troughs) can be approximately presented in the form of a Rayleigh distribution. The parameter of the Rayleigh distribution is given as a function of parameters representing the non-Gaussian characteristics. The results of comparisons between newly derived density functions and histograms of peaks, troughs and peak-to-trough excursions constructed from data with strong non-linear characteristics show that the distributions well represent the histograms for all cases.     

A simple and efficient methodology to approximate a general non-Gaussian stationary stochastic process by a translation process

Some widely used methodologies for simulation of non-Gaussian processes rely on translation process theory which imposes certain compatibility conditions between the non-Gaussian power spectral density function (PSDF) and the non-Gaussian probability density function (PDF) of the process. In many practical applications, the non-Gaussian PSDF and PDF are assigned arbitrarily; therefore, in general they can be incompatible. Several techniques to approximate such incompatible non-Gaussian PSDF/PDF pairs with a compatible pair have been proposed that involve either some iterative scheme on simulated sample functions or some general optimization approach. Although some of these techniques produce satisfactory results, they can be time consuming because of their nature. In this paper, a new iterative methodology is developed that estimates a non-Gaussian PSDF that: (a) is compatible with the prescribed non-Gaussian PDF, and (b) closely approximates the prescribed incompatible non-Gaussian PSDF. The corresponding underlying Gaussian PSDF is also determined. The basic idea is to iteratively upgrade the underlying Gaussian PSDF using the directly computed (through translation process theory) non-Gaussian PSDF at each iteration, rather than through expensive ensemble averaging of PSDFs computed from generated non-Gaussian sample functions. The proposed iterative scheme possesses two major advantages: it is conceptually very simple and it converges extremely fast with minimal computational effort. Once the underlying Gaussian PSDF is determined, generation of non-Gaussian sample functions is straightforward without any need for iterations. Numerical examples are provided demonstrating the capabilities of the methodology.     

A technique of closure using a polynomial function of Gaussian process

The purpose of the paper is to present a closure technique based on the representation of the non-linear system response process to a random excitation by a polynomial function of Gaussian process. It is shown that for the unimodal and bimodal situations of the Duffing oscillator, the proposed technique can give good approximate response moments as well as the probability density function and power spectral density of the system response.