包装件在非高斯随机载荷下响应特征分析方法研究EI北大核心CSCD

在运输过程中,包装件经常受到非高斯随机振动的作用,在进行包装系统优化时,经常需要重复确定包装件加速度响应的统计特征和振动可靠性,该研究提出一种高效准确确定非高斯随机振动条件下非线性包装件加速度响应统计特征的分析方法。采用非高斯Karhunen-Loeve展开将非高斯随机振动表示为非高斯随机变量的线性组合,用一阶泰勒展开估计包装件加速度响应,确定加速度响应的统计矩参数,根据包装件加速度响应的前四阶矩参数,应用鞍点估计法确定包装件加速度响应的概率密度函数(probability density function, PDF)和累积分布函数(cumulative distribution function, CDF)。由于采用随机变量的线性组合模拟非高斯随机振动激励,避免了随机变量非线性变换,采用一阶泰勒展开估计包装件加速度响应具有良好的准确性,鞍点估计法分析包装件加速度响应的PDF和CDF,避免了大量蒙特卡洛或拟蒙特卡洛分析,提高了分析效率。     

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。     

复合随机振动分析的混合PC-PEM方法

由于加工、制造等原因,实际结构系统往往所具有很多不确定性,准确评估随机系统的动力学行为不仅具有实际意义,而且是近年来结构动力学理论的一个研究热点。本文研究了同时考虑结构模型参数与所受外激励载荷具有不确定性的复合随机振动问题。结构模型参数的不确定性采用随机变量模拟,外激励载荷的不确定性采用随机过程模拟,提出了结构随机振动响应评估的混合混沌多项式-虚拟激励(PC-PEM)方法。数值算例研究了参数不确定性在21杆桁架中的传播,讨论了响应的一阶、二阶统计矩,并同蒙特卡洛方法进行对比表明提出方法的正确性和有效性。本文的工作对于考虑不确定的复杂装备与结构系统的随机振动分析具有很好的借鉴意义。     

泊松白噪声激励下斜拉索的面内随机振动

目前针对斜拉索非线性随机振动的研究已广泛开展,但仅限于高斯随机激励情形。然而,现实中大部分的随机扰动都是非高斯的。若使用高斯激励模型将产生较大误差。假设拉索所受非高斯激励为泊松白噪声,研究了泊松白噪声激励下斜拉索面内随机振动。推导了受泊松白噪声激励的斜拉索面内振动的随机微分方程,建立了支配系统平稳响应概率密度函数的广义FPK方程。提出迭代加权残值法求解了四阶广义FPK方程,得到了系统响应概率密度函数的近似稳态闭合解。考察了垂跨比、阻尼系数以及脉冲到达率对拉索面内随机振动响应的影响。结果表明:拉索的响应随着垂跨比的增大,响应呈现不对称现象愈加明显;随阻尼比增加,系统响应得到显著抑制;当脉冲到达率增大,拉索的响应也随之增大,并逐渐接近于高斯白噪声激励的情形。另外,获得的理论结果与蒙特卡罗模拟的结果吻合地非常好。     

随机振动下包装件加速度响应的非高斯特征

研究了随机振动下包装件加速度响应的频域和时域特征,讨论了包装件跳动及缓冲材料非线性对包装件加速度响应的影响。结果表明:高斯激励下,包装件的跳动是引起包装件加速度响应非高斯性的主要原因。无约束条件下,包装件出现明显跳动,加速度响应概率密度分布呈现非高斯分布;在弹性和固定约束条件下,包装件跳动受到限制,当振动强度较大时,加速度响应分布与高斯分布有一定程度的偏离,在振动强度较小时,加速度响应分布符合高斯分布。     

包装件振动可靠性的不确定度量化及灵敏度分析

研究包装件参数不确定性对振动可靠性变化的影响,并分析振动可靠性指标对各不确定参数的灵敏度。采用Karhunen-Loeve展开将具有一定谱特征的平稳随机振动表示在标准正态随机变量空间中,应用一阶可靠性方法分析线性包装件振动可靠性指标。考虑缓冲材料弹性特性、阻尼特性、产品主体和脆弱部件之间的弹性特性、阻尼特性四个随机参数,对这些参数进行等概率转换,将它们用标准正态随机变量等效表示,根据拉丁超立方采样原则,在四维标准正态随机变量空间采样,应用数值分析研究可靠性指标的变化情况。根据可靠性指标的概率分布选取合理的正交混沌多项式类型,应用非嵌入分析法分析混沌多项式的系数。在获得可靠性指标的多项式混沌展开表达后,采用Sobol法分析可靠性指标的全局灵敏度。给出了一个实例分析,介绍了应用多项式混沌展开对振动可靠性指标进行不确定量化的过程及可靠性指数的分析结果。     

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。     

堆码包装产品响应的非高斯特征

研究随机振动下三层堆码包装产品加速度响应的非高斯特征,讨论引起非高斯响应的原因。试验结果表明:无约束条件下,上层包装件出现明显跳动,产品加速度响应的概率密度分布呈现非高斯分布,中层包装产品响应加速度的概率密度分布与高斯分布有一定程度的偏离,下层包装产品响应加速度较为接近高斯分布;弹性约束条件下,当振动强度较大时,上层包装产品响应加速度的概率密度分布与高斯分布偏离程度较大;在固定约束时,包装件跳动受到限制,各层包装产品响应加速度基本符合高斯分布。     

基于随机函数-谱表示的高阶矩结构动力可靠度分析方法

基于随机函数-谱表示模型,提出了结构响应极值前四阶矩的计算方法 ,发展了非高斯随机激励下的结构动力可靠度分析的高阶矩方法:(1)修正了随机函数单个基本随机变量的离散点集表达式;(2)根据修正的离散点集生成少量的非高斯加速度时程样本并进行结构时程分析,从而估计得到结构响应极值的前四阶矩(均值、标准差、偏度、峰度);(3)提出了四阶矩可靠指标的完整表达,并应用于计算在非高斯随机激励下的结构动力可靠度。最后,以双自由度系统及八层框架结构的动力可靠度分析为算例,验证了本文方法的精确性与高效性:在样本数量明显减少的情形下,本文方法计算的前四阶矩与Monte Carlo模拟结果相比最大相对误差为5.54%,且动力可靠度分析结果几乎一致。     

五自由度强非线性随机振动系统的首次穿越研究

利用基于广义谐和函数的随机平均法,建立了高斯白噪声激励下五自由度强非线性随机振动系统的Pon-tryagin方程及后向Kolmogorov方程。求解这两个高维偏微分方程,得到了系统的平均首次穿越时间、条件可靠性函数以及平均首次穿越时间的条件概率密度。用Monte Carlo数值模拟验证了理论方法的有效性。     

Neumann enriched polynomial chaos approach for stochastic finite element problems

An enrichment scheme based upon the Neumann expansion method is proposed to augment the deterministic coefficient vectors associated with the polynomial chaos expansion method. The proposed approach relies upon a split of the random variables into two statistically independent sets. The principal variability of the system is captured by propagating a limited number of random variables through a low-ordered polynomial chaos expansion method. The remaining random variables are propagated by a Neumann expansion method. In turn, the random variables associated with the Neumann expansion method are utilised to enrich the polynomial chaos approach. The effect of this enrichment is explicitly captured in a new augmented definition of the coefficients of the polynomial chaos expansion. This approach allows one to consider a larger number of random variables within the scope of spectral stochastic finite element analysis in a computationally efficient manner. Closed-form expressions for the first two response moments are provided. The proposed enrichment method is used to analyse two numerical examples: the bending of a cantilever beam and the flow through porous media. Both systems contain distributed stochastic properties. The results are compared with those obtained using direct Monte Carlo simulations and using the classical polynomial chaos expansion approach.     

Reliability‐based topology optimization against geometric imperfections with random threshold model

This paper develops a new reliability‐based topology optimization framework considering spatially varying geometric uncertainties. Geometric imperfections arising from manufacturing errors are modeled with a random threshold model. The projection threshold is represented by a memoryless transformation of a Gaussian random field, which is then discretized by means of the expansion optimal linear estimation. The structural response and their sensitivities are evaluated with the polynomial chaos expansion, and the accuracy of the proposed method is verified by Monte Carlo simulations. The performance measure approach is adopted to tackle the reliability constraints in the reliability‐based topology optimization problem. The optimized designs obtained with the present method are compared with the deterministic solutions and the reliability‐based design considering random variables. Numerical examples demonstrate the efficiency of the proposed method.     

Random response of Duffing oscillator to periodic excitation with random disturbance

This paper discusses the random response of a non-linear Duffing oscillator subjected to a periodic excitation with random phase modulation. Effects of uncertainty in the periodic excitation and level of the system non-linearity on the response moments and non-Gaussian nature of the response caused by both the system non-linearity and the non-Gaussian loading are investigated. Results are presented in terms of the second- and the fourth-order moments as well as the excess factor of the response and some results are compared with those from the Monte Carlo simulation. An iterated linearisation technique is proposed to improve the accuracy of the numerical results for strongly non-linear systems.     

基于结构响应极值前四阶矩的桥墩抗震可靠度

为研究桥墩非线性地震响应下的抗震可靠度,引入随机函数-谱表示模型与高阶矩法,提出了基于结构响应极值前四阶矩的桥墩抗震可靠度分析方法。考虑三线型恢复力模型,建立了桥墩的单墩模型;利用随机函数-谱表示模型生成非平稳地震加速度时程样本并对桥墩进行非线性时程分析,在此基础上,建立了结构响应极值前四阶矩(均值,标准差,偏度和峰度)的计算框架;最后,考虑桥墩位移界限,给出了桥墩位移的功能函数,进而利用高阶矩法计算桥墩抗震可靠指标。通过对桥墩结构分析,验证了该方法的高效性与精确性;计算结果表明:与Monte Carlo模拟结果相比,该方法计算的前四阶矩、抗震可靠指标(失效概率)的最大相对误差分别为0.28%,1.92%(4.92%),该方法为桥墩抗震可靠度评估提供了一种有效的途径。     

A reduced polynomial chaos expansion method for the stochastic finite element analysis

The stochastic finite element analysis of elliptic type partial differential equations is considered. A reduced method of the spectral stochastic finite element method using polynomial chaos is proposed. The method is based on the spectral decomposition of the deterministic system matrix. The reduction is achieved by retaining only the dominant eigenvalues and eigenvectors. The response of the reduced system is expanded as a series of Hermite polynomials, and a Galerkin error minimization approach is applied to obtain the deterministic coefficients of the expansion. The moments and probability density function of the solution are obtained by a process similar to the classical spectral stochastic finite element method. The method is illustrated using three carefully selected numerical examples, namely, bending of a stochastic beam, flow through porous media with stochastic permeability and transverse bending of a plate with stochastic properties. The results obtained from the proposed method are compared with classical polynomial chaos and direct Monte Carlo simulation results.     

An iterative polynomial chaos approach toward stochastic elastostatic structural analysis with non-Gaussian randomness

Stochastic analysis of structure with non-Gaussian material property and loading in the framework of polynomial chaos (PC) is considered. A new approach for the solution of stochastic mechanics problem with random coefficient is presented. The major focus of the method is to consider reduced size of expansion in an iterative manner to overcome the problem of large system matrix in conventional PC expansion. The iterative method is based on orthogonal expansion of stochastic responses and generation of an iterative PC based on the responses of the previous iteration. The polynomials are evaluated using Gram-Schmidt orthogonalization process. The numbers of random variables in PC expansion are reduced by considering only the dominant components of the response characteristics, which is evaluated using Karhunen-Loève (KL) expansion. In case of random material field problem, the KL expansion is used to discretize and simulate the non-Gaussian random field. Independent component analysis (ICA) is carried out on the non-Gaussian KL random variables to minimize statistical dependence. The usefulness of the proposed method in terms of accuracy and computational efficiency is examined. From the numerical analysis of three different types of structural mechanics problems, the proposed iterative method is observed to be computationally more efficient and accurate than conventional PC method for solution of linear elastostatic structural mechanics problems.