地震作用的相关性对结构瞬态响应的影响

地震作用一般分解为水平运动分量和竖向运动分量,在这两个运动分量的作用下,结构发生大变形时,可能会经历由地震运动分量演变的外部激励和参数激励过程。由于运动分量间的相关性,推导出实际上这两个激励过程也是相关的,而且是完全相关的,但在过去的研究中,为了简化分析,常常假设这两个激励过程是完全独立的。该文以高斯白噪声和过滤高斯白噪声过程模拟地震动过程,以某一单层框架结构为研究对象,采用累积矩截断法,分析高斯白噪声和过滤高斯白噪声这两种地震动激励下单层框架结构的非平稳地震响应。同时考虑地震动分量间的相关性,得到更为精细化的结构随机地震响应,并分析这种相关性对结构响应的影响。结果表明：将地震动作用模拟为更接近实际的过滤高斯白噪声过程时,地震作用相关性对结构响应的影响更为明显,更为不可忽略。     

基于子带收敛因子阈值法的轮廓波消噪方法

提出了适用于轮廓波变换消噪中确定子带阈值收敛因子的样本噪声响应法.该方法根据标准高斯白噪声作用在每个子带上的统计特性,得到每个子带的收敛因子;使用该收敛因子对标准的3σ(或4σ)准则进行修正来确定不同尺度不同方向子带的硬阈值;并在轮廓波域进行子带硬阈值处理之后,使用自适应维纳滤波进行后处理.实验结果表明,本文提出的消噪方法,对含有高斯白噪声的图像进行消噪,无论在峰值信噪比方面还是在视觉效果方面均可以取得比较满意的消噪效果;在一定的范围内,采用较小的样本图像计算子带收敛因子,在加快消噪速度和减小内存需求量的同时,仍然可以保持满意的消噪结果.     

一种改进的EEMD方法及其应用研究

针对集成经验模式分解(Ensemble empirical mode decomposition, EEMD)中协助噪声幅值大小需要人为经验确定的不足,基于经验模式分解(Empirical mode decomposition, EMD)二进滤波器特性,讨论了EMD出现模式混淆的原因,研究了EEMD中协助噪声幅值大小的确定原则,提出基于极值点分布特性的改进EEMD方法,通过遍态历经,以极值点分布特性为评价参数,自适应确定EEMD方法中高斯白噪声优化幅值。通过数据仿真,验证了其有效性。最后,应用于转子早期故障诊断中,结果显示可以自适应确定噪声幅值,避免参数人为选择导致分解结果的盲目性,有效抑制了传统EMD方法的模式混淆现象,可有效识别转子早期碰磨引起的故障特征。     

Importance sampling for reliability assessment of dynamic systems under general random process excitation

This paper develops a reliability assessment method for dynamic systems subjected to a general random process excitation. Safety assessment using direct Monte Carlo simulation is computationally expensive, particularly when estimating low probabilities of failure. The Girsanov transformation-based reliability assessment method is a computationally efficient approach intended for dynamic systems driven by Gaussian white noise, and this approach can be extended to random process inputs that can be represented as transformations of Gaussian white noise. In practice, dynamic systems may be subjected to inputs that may be better modeled as non-Gaussian and/or non-stationary random processes, which are not easily transformable to Gaussian white noise. We propose a computationally efficient scheme, based on importance sampling, which can be implemented directly on a general class of random processes — both Gaussian and non-Gaussian, and stationary and non-stationary. We demonstrate that this approach is in fact equivalent to Girsanov transformation when the uncertain inputs are Gaussian white noise processes. The proposed approach is demonstrated on a linear dynamic system driven by Gaussian white noise and Brownian bridge processes, a multi-physics aero-thermo-elastic model of a flexible panel subjected to hypersonic flow, and a nonlinear building frame subjected to non-stationary non-Gaussian random process excitation.     

Approximate representation of the statistics for extreme responses of single degree-of-freedom system excited by non-stationary processes

The objective of this study is to estimate the statistics of the maximum response of a structural system excited by a non-stationary process. To provide basic information for the design of structures, the response of a single degree-of-freedom (SDOF) system subjected to a non-stationary Gaussian white noise is considered. For this purpose, we first derive the probabilistic properties of the maximum values of a non-stationary and zero-mean white noise, whose standard deviation varies temporally under some limited conditions. Then, using the obtained properties, we propose a method to estimate the stochastic properties of the maximum response of a given SDOF system excited by a non-stationary white noise whose time-varying standard deviation is known. The validity of the obtained results is confirmed through Monte Carlo simulation.     

A study of PRML systems by write and read equalization

A new partial response (PR) channel which contains the write equalizer in addition to conventional PR channel is proposed. Our write equalizer outputs DC-free waveforms of two levels. Our read equalizer can reduce high-frequency noise, and what is more, it has little degradation of eye opening. The PR channels in combination with Viterbi decoder give partial response maximum-likelihood (PRML) systems which exhibit a good performance. The bit error rates for several PRML systems are obtained by computer simulation, where a Lorentzian channel with additive white Gaussian noise is assumed. The results shows that PR(1,1,-1,-1) system has an excellent performance in high density recording for a system in which the small transition spacings required by our write equalization is allowed     

Wideband spectrum sensing in unknown white Gaussian noise

The spectrum sensing of a wideband frequency range is studied by dividing it into multiple subbands. It is assumed that in each subband either a primary user (PU) is active or absent in a additive white Gaussian noise environment with an unknown variance. It is also assumed that at least a minimum given number of subbands are vacant of PUs. In this multiple interrelated hypothesis testing problem, the noise variance is estimated and a generalised likelihood ratio detector is proposed to identify possible spectrum holes at a secondary user (SU). Provided that it is known that a specific PU can occupy a subset of subbands simultaneously, a grouping algorithm which allows faster spectrum sensing is proposed. The collaboration of multiple SUs can also be considered in order to enhance the detection performance. The collaborative algorithms are compared in terms of the required exchange information among SUs in some collaboration methods. The simulation results show that the proposed detector outperforms the energy detector in the presence of noise variance mismatch above 2.3 dB. Some involved trade-offs in the spectrum sensing using the proposed detector are discussed.     

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。     

Probabilistic response of nonlinear systems under combined normal and Poisson white noise via path integral method

In this paper the response in terms of probability density function of nonlinear systems under combined normal and Poisson white noise is considered. The problem is handled via a Path Integral Solution (PIS) that may be considered as a step-by-step solution technique in terms of probability density function. A nonlinear system under normal white noise, Poissonian white noise and under the superposition of normal and Poisson white noise is performed through PIS. The spectral counterpart of the PIS, ruling the evolution of the characteristic functions is also derived. It is shown that at the limit when the time step becomes an infinitesimal quantity an equation ruling the evolution of the probability density function of the response process of the nonlinear system in the presence of both normal and Poisson White Noise is provided.     

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.     

用1(1/2)维谱结合小波包能量提取地震动信号特征

针对车辆（轮式车、履带式车）引起的地震动信号中,具有非平稳、非高斯性特征相互重叠的实际情况,研究了地面活动目标产生的地震动信号特性;从理论上说明了1(1/2)维谱可消除车辆引起的地震动信号中的高斯白噪声或有色噪声,在将[112]维谱分析和小波包能量谱相结合的基础上,提出一种特征提取方法,以便区分不同的车辆目标。在时频域构建以[112]维谱和小波包能量谱作为地震动信号的联合特征向量,建立以训练误差为目标的BP神经网络模式分类器;然后对两类车辆信号进行识别。地震动信号的车辆实测数据表明,该方法能够准确和有效地识别车辆引起的地震动信号。     

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。     

The transient characteristics of an underdamped periodic potential system excited by two different kinds of noise

In this paper, the transient characteristics of an underdamped periodic potential system excited by multiplicative Gaussian white noise and additive Lévy noise are studied in terms of the mean first-passage time(MFPT) and the probability density function(PDF) of the first-passage time. The second-order underdamped periodic potential system is equivalent to two first-order stochastic differential equations. The MFPT was obtained by averaging the response value of the first-passage time, and the PDF image of the first-passage time was drawn under different parameter values. It was found that the increase in damping coefficient and stability index will inhibit the particle crossing, while the increase of multiplicative noise intensity, additive noise intensity and skewness parameter will promote the particle crossing to a certain extent.     

自然激励技术在时延相关白噪声激励系统中的应用

工况模态分析(operational modal analysis,OMA)是一种只基于输出数据进行系统模态参数辨识的技术。由于系统所受激励未知,通常假设其为互不相关的白噪声。自然激励技术(natural excitation technique,NExT)正是一种基于该假设的从响应数据中提取自由衰减信号的高效方法。然而对于真实工况,系统所受激励之间互不相关的假设过于严格,例如行驶的车辆等所受激励为时间延迟相关的白噪声。针对这类情况,基于复模态系统讨论NExT理论的适用性。结果表明,NExT是否适用取决于从相关函数中截取的用来进行OMA分析的数据段的位置,当数据段位于Tε区间内,NExT是适用的。在ε已知的情况下,可以基于NExT对系统进行工况模态分析。最后通过仿真进一步验证该结论。     

Nonlinear random vibration of the slender deep-water pier under seismic excitation

The present study investigates the nonlinear random vibration of the deep-water pier exposed to horizontal seismic excitation. First of all, the stochastic dynamic model of the pier is formulated. During the process, the pier is simplified as a cantilever beam fixed on the rock foundation, the seismic excitation is treated as Gaussian white noise, the hydrodynamic pressure is described with the radiation wave theory, and the equation for the nonlinear kinematic of the pier is deduced by the means of Kane’s method. Then, with the application of the stochastic averaging (SA) technique, the Fokker–Plank–Kolmogorov (FPK) equation governing the transient probability density function (PDF) of the amplitude envelope and the backward Kolmogorov (BK) equation for the conditional reliability function (CRF) are derived, respectively. The closed-form stationary PDF can be yielded directly from the reduced FPK equation, while the CRF and the conditional PDF of first-passage time are given after solving the BK equation numerically. Numerical discussions are performed to illustrate the trend of excitation intensity, mass ratio, immersion ratio, and inner and outer hydrodynamic effect on the stationary response and first-passage failure are examined, respectively. It has been shown that increases in the excitation intensity, mass ratio, and immersion ratio can amplify the response and reduce the reliability of the deep-water pier system. The hydrodynamic effect also leads to an amplification of the system response and a reduction in the reliability of the system. Similarly, the presence of inner water can also exacerbate these effects, and this phenomenon becomes more pronounced with increasing immersed ratios. Additionally, the analytical solution is validated by the result obtained by pertained Monte Carlo simulations (MCS). It is noted that this work will be helpful for the optimal seismic design of deep-water piers.     

基于数值子结构方法的低延性RC框架结构抗震性能精细化分析

以抗震设防水平不高、抗震构造措施不足且已经服役多年的低延性钢筋混凝土框架结构1/5缩尺振动台试验模型为研究对象,为捕捉在低强度振动中砌体填充墙与主体框架开裂行为以及框架自身发生开裂导致动力特性变化趋势,采用强度小、持时短的白噪声进行扫频。采用自然激励技术和特征系统实现算法对试验加速度信号分析,识别出试验模型完备模态;采用小波变换提取各阶模态的楼层加速响应并进行分析。研究结果显示：特征系统实现算法适用于低强度振动中的动力特性识别;高阶模态对既有框架结构加速度响应贡献显著。     

随机地震激励作用下自复位结构的平稳响应

自复位结构是一种震后不需修复或仅需少量修复即可继续投入使用的新型抗震结构。目前有关自复位结构地震响应的研究多是在确定性激励下进行,鲜有涉及随机激励环境。假定地震动加速度过程为金井清过滤白噪声模型,研究了随机地震激励下单自由度自复位体系的平稳响应。应用广义谐波平衡技术分解旗帜形的恢复力,建立原系统的等效非线性随机系统。通过Stratonovich-Khasminskii极限定理作随机平均,得到关于幅值的近似一维扩散过程。建立并求解对应的FPK方程,得到关于幅值的稳态概率密度函数并进行参数分析。数值结果表明,能量耗散系数与屈服位移的减小能降低系统响应,同时,随着这两个参数的变化,系统会出现随机P分岔现象。通过蒙特卡罗数值模拟法验证了解析解的有效性。     

Approximate solution of the Fokker–Planck–Kolmogorov equation

The aim of this paper is to present a thorough investigation of approximate techniques for estimating the stationary and non-stationary probability density function (PDF) of the response of nonlinear systems subjected to (additive and/or multiplicative) Gaussian white noise excitations. Attention is focused on the general scheme of weighted residuals for the approximate solution of the Fokker–Planck–Kolmogorov (FPK) equation. It is shown that the main drawbacks of closure schemes, such as negative values of the PDF in some regions, may be overcome by rewriting the FPK equation in terms of log-probability density function (log-PDF). The criteria for selecting the set of weighting functions in order to obtain improved estimates of the response PDF are discussed in detail. Finally, a simple and very effective iterative solution procedure is proposed.     

基于频域形态滤波的低速滚动轴承声发射信号降噪新方法

声发射检测技术以其灵敏度高、频响范围宽、信息量大等优点,为机械故障诊断提供了一条新的检测途径,但应用于旋转机械设备时,容易混入各种有色噪声。当噪声频率与声发射信号重叠时,传统的降噪方法难以满足要求。将形态滤波应用到信号频域,可以有效消除有色噪声的干扰。根据声发射频响特性,对频谱进行拟合平滑高斯白噪声的影响,最后重构到时域。仿真和实际低速轴承信号表明此方法具有较好的降噪效果,有利于信号后续的处理和分析。     

图像噪声方差大小的测量新算法

针对图像中的高斯白噪声,提出了一种利用小波系数分布特征进行噪声估计的算法。根据小波系数的分布特点,利用广义高斯分布模型对小波系数进行拟合,并用广义高斯分布模型参数（尺度和形状参数）提出了一种有效的噪声方差估计算法。实验结果表明,提出的噪声方差估计算法能有效地估计噪声方差大小,同时估计的结果要好于其它相关的算法。这种噪声测量算法具有高精度性和快速性。