含有摇摆装置的双层桥墩结构随机振动分析

基于一种下层含有摇摆装置的双层桥墩结构模型，建立了系统的随机动力学系统模型，其中随机激励选用高斯白噪声模型，自复位恢复力采用经典旗帜形模型。运用广义谐波平衡法将旗帜形滞回力近似分解为幅值依赖的等效拟线性弹性力和拟线性阻尼力，获得原系统的等效随机系统；采用标准随机平均法理论，将等效系统近似为关于幅值的平均伊藤随机微分方程，建立并求解与之对应的Fokker-Planck-Kolmogorov(FPK)方程获得系统的稳态响应。探讨系统参数，如能量耗散系数等对系统稳态响应的影响，并通过Monte Carlo数值模拟加以验证。另外，借助Laplace变换，得到等效系统的转换函数及条件功率谱密度，结合下层幅值的稳态概率密度，得到下层幅值响应的功率谱密度估计。     

一种改进的基于Jacobi椭圆函数的随机平均法

建立了改进的基于Jacobi椭圆函数的随机平均法,用于预测有界噪声激励作用下硬弹簧和软弹簧系统的随机响应。通过引入基于Jacobi椭圆函数的变换,导出关于响应幅值和激励与响应之间相位差的随机微分方程,应用随机平均原理,将响应幅值近似为一个Markov扩散过程,建立其平均的It随机微分方程。响应幅值的稳态概率密度由相应的简化Fokker-Planck-Kolmogorov方程解出;进而得到系统位移和速度的稳态概率密度。以Duffing-Van der Pol振子为例,研究了硬刚度及软刚度情形下的随机响应,通过与Monte Carlo数值模拟结果比较证实了此方法的可行性及精度。由于广义调和函数是基于线性系统的精确解,Jacobi椭圆函数是基于非线性系统的精确解,研究结果表明基于Jacobi椭圆函数的随机平均法得到的结果与Monte Carlo模拟方法更接近。因此与基于广义调和函数的随机平均相比,基于Jacobi椭圆函数更加精确,因为它是基于保守的非线性系统。     

时滞反馈对三稳态van der Pol系统稳态概率密度的影响

利用时滞反馈调节系统随机响应特征是随机动力学与控制重要的课题之一。为解决多稳态随机系统的控制器参数设计问题,针对加性噪声激励下的三稳态van der Pol系统,研究了时滞差分反馈对系统稳态概率密度的影响。利用随机平均法得到系统幅值稳态概率密度函数的解析表达式,随后分别讨论了给定噪声强度情况下时滞和反馈强度对系统稳态概率密度的影响。结果表明,反馈强度和时滞变化均能使系统稳态概率密度曲线的拓扑结构发生改变,从而调节系统稳态响应的幅值分布;转迁集计算的结果对控制参数选择有直接指导作用。     

基于听觉模型和极值点概率密度的断齿故障特征提取方法研究

齿轮断齿故障的重要特征是啮合过程中在断齿处产生碰撞与冲击。考虑到人耳听觉系统对于突发的瞬态声信号具有本能的反应,为提取断齿故障诱发的瞬态冲击响应成分,提出一种基于听觉模型和信号极值点概率密度的特征提取方法。该方法首先对信号进行GT带通滤波、相位调整及极值点提取,然后计算各极值点的幅值概率密度,通过对其求导判断各滤波通道中是否存在瞬态冲击成分,继而提取与之相关的极值点。同时,由于系统振动时会产生与断齿冲击无关的极值点,为准确提取断齿冲击,根据瞬态信号频带连续性和多频段分布特点,设计了相应的提取方法。经实测信号验证表明,所提方法能准确刻画及提取断齿故障特征,可以在含有多种类型的瞬态冲击响应成分中提取出只由断齿故障所诱发的冲击成分,且提取结果精确度较高。     

窄带随机激励带集中质量梁的主参激共振

以受窄带随机激励带集中质量柔性梁为研究对象,采用多尺度法导出系统单模态主参激共振调谐方程组,结合FPK方程分析了力-幅特性下联合概率密度随激励幅值所出现的随机跳跃现象,结果显示:在三值响应范围内存在一外扇形峰及一内火山口峰,随着激励幅值减小,外扇形峰减弱而内火山口峰增强,表明响应逐渐从非平凡稳态响应向平凡稳态响应跳跃。     

考虑负载影响的阶梯形超声变幅杆动力特性

考虑与加工工件表面高频重复撞击对结构动力特性的影响,基于瞬态波传播理论,研究周期激励下阶梯形超声变幅杆重复撞击加工工件的瞬态动力响应,及负载对变幅杆放大特性的影响。首先,建立阶梯形变幅杆力学模型,采用瞬态波响应法分别对接触过程和分离过程动力控制方程进行求解,得到适用于任意级数的阶梯形变幅杆的特征项传递函数,和重复撞击系统的瞬态响应理论解。以工程中常用的三级阶梯形变幅杆为算例,分析了不同外载频率下变幅杆重复撞击动力特性和负载工件对变幅杆聚能效果的影响,得出考虑加工件撞击产生的瞬态响应下的变幅杆放大系数,小于自由振动空载的设计值。可为精细超声加工变幅杆的设计提供更为精确的理论依据     

基于极值点概率密度和听觉模型的瞬态信号提取方法研究

零件间的碰撞会诱发瞬态振动信号成分,所以发现和提取瞬态信号有助于设备故障的识别。人类听觉系统对于突发声音具有本能的敏感性,因此,基于听觉系统的运行机制提出了一种瞬态信号提取方法。提出了信号极值点幅值概率密度曲线中存在小幅值局部波动这一含瞬态成分信号的重要特征,并结合频带连续性和起始同步性做为瞬态信号提取的线索。基于三种线索,首先对信号进行Gammatone带通滤波、相位调整和极值点提取,继而计算各滤波信号极值点的幅值概率密度,并判断各滤波信号中是否存在瞬态成分,根据判断结果提取可能与瞬态成分有关的极值点,但因背景信号和干扰噪声的影响,所提取到的极值点会有一部分与瞬态成分无关,因此,将无关点分为四类并设计了相应的筛选方法。最终,利用筛选后所得极值点生成瞬态信号。数值仿真和实测数据验证的结果表明,所提方法对于瞬态信号提取具有良好的性能,且在干扰噪声和背景信号较强时也可实现较好的提取效果。     

含分数阶导数项的随机Duffing振子的稳态响应分析

本文对一个含有分数阶导数项阻尼的、Gaussian白噪声激励下的Duffing振子进行了稳态响应分析。首先,基于能量平衡理论,运用等效线性化方法,计算等效系统的线性阻尼及自然频率,建立统计意义下的等效线性化系统。然后,利用平均法建立随机Ito方程,得到随机响应的Markovian近似;给出描述振子振幅概率密度函数演化的Fokker-Planck方程,并得到它的稳态解。进一步,对于含有响应振幅的等效线性系统,借助由Laplace变换得到的转换函数,得到原系统的条件功率谱密度,结合振幅的稳态概率密度作为权重函数,给出原系统功率谱密度的估计,以及响应的统计量的估计。数值模拟的结果说明所提出的功率谱密度的近似解析表达式是可靠的,它甚至适用于Duffing振子具有强非线性回复力的情形,因为它可以较好的表现出功率谱密度共振频谱加宽及多峰现象的出现。     

最优有界控制下色噪声驱动多时滞拟线性系统瞬态响应

基于Fokker-Planck-Kolmogorov方程瞬态求解研究了受最优有界控制的色噪声驱动的多时滞拟线性系统的瞬态响应。利用等价变换将时滞系统转化为非时滞系统。在弱扰动假设下应用标准随机平均法得到振幅过程的部分平均It?随机微分方程。由动态规划原理和控制力界值条件得到最优有界控制率从而得到完全平均的Fokker-Planck-Kolmogorov方程。通过原系统的退化线性系统导出一组正交基并在该基空间内进行Galerkin变分得到近似瞬态响应。最后将该方法应用到受最优有界控制率和色噪声共同作用的时滞Duffing-Van Der Pol振子进行理论求解并综合讨论了色噪声、时滞、控制力和共振对系统瞬态响应的影响,采用Monte-Carlo模拟验证了所有理论和计算结果的正确性。     

雨流循环均值-幅值二维联合概率密度的实用算法

在实际工程结构疲劳损伤计算中，经常忽略雨流循环均值，而只考虑幅值的影响。这对计算结果会带来一定的误差，尤其是那些对均值影响比较敏感的材料来说更是如此。若考虑雨流循环均值的影响，在时域计算中可以很方便地实现，但在频域中则必须得到雨流循环均值-幅值二维联合概率密度。本文针对工程中常常遇到的平稳Gauss随机过程，提出由结构响应的PSD得到雨流循环均值-幅值条件概率的简便计算公式，进而结合Dirlik经验公式直接计算出雨流循环均值-幅值二维联合概率密度函数的实用方法。     

First passage problem: a probabilistic dynamic analysis for hot aerospace components

Structures subjected to non-white random excitations with uncertain system parameters affected by surrounding environments are studied. Methods are developed to determine the statistics of dynamic responses such as time-varying mean, standard deviation and autocorrelation functions. Moreover, the first-passage problems with deterministic and stationary/nonstationary random barriers are evaluated. Time-varying (joint) mean crossing rate and the probability density function of the first-passage time for various random barriers are derived.     

Joint distribution of peaks and valleys in a stochastic process

General expressions and numerical results are presented pertaining to the occurrence of two local extrema of a stochastic process at prescribed time values. The extrema may be either peaks or valleys and the process may be either stationary or nonstationary. General formulas are presented for the rates of occurrence, the joint and conditional probability distributions, and the moments of the extreme values. These formulas are relatively simple multiple-integral expressions, but the integrands involve the joint probability density function for six random variables. The procedures are then applied for the special case of a stationary mean-zero Gaussian process for which the calculations are greatly simplified. Numerical results for three different spectral density functions demonstrate that conditioning on either only the existence or both the existence and the value of one peak can have a very significant effect on both the rate of occurrence and the probability distribution of a second peak.     

斜拉索风雨振非平稳风场特性分析

基于小波多尺度分析,提取风雨振实测风速、风向的时变平均值,并建立非平稳风速模型。采用非平稳风速模型,分析了洞庭湖大桥2003年4月初风雨振时实测风速紊流强度、积分尺度、脉动风谱和概率密度等重要风场特性,并将结果与传统的平稳风速模型和基于EMD的非平稳风速模型进行比较,进一步验证采用基于小波分析的非平稳风速模型的合理性。同时,根据Davenport相干系数公式,计算了桥塔和桥面风速记录顺风向脉动风分量的相关性。     

An empirical mode decomposition‐based frequency‐domain approach for the fatigue analysis of nonstationary processes

Mechanical structures in service are often subjected to irregular loads, which are typically idealized as stationary random processes. However, the service loads in real applications are often nonstationary ones, in which case conventional frequency‐domain methods are no longer applicable. Here, a novel frequency‐domain approach based on empirical mode decomposition is developed for the fatigue analysis of nonstationary processes. A simplified approach is introduced to calculate the rainflow cycle distributions of non‐Gaussian intrinsic mode functions. Two typical nonstationary processes in engineering practice are simulated numerically to validate the proposed method. The proposed method is applied to fatigue life estimation of a dynamical structure under nonstationary excitations. Reliable life estimations are obtained within much less computation time than the time‐domain method. The results verify the applicability and effectiveness of the proposed method for the fatigue analysis of nonstationary processes.     

Parametric models of nonstationary Gaussian processes

Three parametric representations are developed for approximating a general nonstationary Gaussian process X(t). The representations: (1) are based on the Bernstein and other interpolation polynomials, spline functions, and an extension of a sampling theorem for stationary processes; (2) consist of finite sums of specified deterministic functions with random amplitudes depending on X(t); and (3) converge to X(t) as the number of these functions increases. However, their convergence rates differ. Numerical results for a nonstationary Ornstein-Uhlenbeck process show that the interpolation polynomials have the slowest rate of convergence. The parametric representations based on spline functions and the extended sampling theorem have similar convergence rates. The paper also presents methods for generating realizations of X(t) based on the three parametric models of this process.     

New integral relations for analytical solutions of parabolic-type equations in noncylindrical domains

The theory of the method of Green’s functions in solving boundary-value problems of nonstationary heat conduction in domains with moving boundaries has been developed. A modification of the thermal-potential method for a uniform law of motion of the boundary has been proposed, which leads to integral relations of a new (simplest) form compared to the existing results; this makes it possible to consider numerous particular cases that are of practical interest for many applications. A number of special features of model representations of nonstationary heat transfer in domains with moving boundaries have been revealed.     

被动声纳方位估计的宽带盲源分离算法

针对实际被动声纳信号宽带非平稳且统计特性无法预知的特点,由宽带卷积混合模型,建立了融合时间延迟结构与非参数化特性的代价函数,通过核密度技术同时估计目标源的概率密度函数和解混矩阵,并对估计的最优解混矩阵与目标源信号求取每个频点内方位能量谱,最后累加所有子带构成宽带方位能量谱。宽带仿真结果与实际海试表明本文方法在方位分辨率和估计精度方面接近最小方差无失真响应（Minimum variance distortionless response, MVDR）和多重信号分类（Multiple signal classification, MUSIC）算法,在弱目标检测方面具有一定优势。     

A solution of direct and converse two-dimensional problems of nonstationary heat conduction with variable boundary conditions using the method of transfer functions

A procedure is developed for determining transfer functions and by employing them to solve direct and converse two-dimensional problems of nonstationary heat conduction with variable boundary conditions for a hollow cylinder.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 17, No. 3, pp. 547–552, September, 1969.     

An efficient simulation method for reliability analysis of linear dynamical systems using simple additive rules of probability

This paper presents a simulation technique for reliability analysis of linear dynamical systems. It is based on simple additive rules of probability (in contrast to other probabilistic approaches such as importance sampling). It is shown that the proposed appoach is identical to a newly developed approach, Importance Sampling using Elementary Events (ISEE) [Au SK, Beck JL. First excursion probabilities for linear sytems by very efficient importance sampling. Probabl Eng Mech 2001;16(3):193–208]. A simple formula for the coefficient of variation of the estimator of the failure probability using the samples is also given. A 10-story building model with nonstationary excitation is utilized to demonstrate the accuracy and efficiency of the proposed method.