基于频率摄动理论对结构健康检测BENCHMARK问题的识别

定义了结构有限元模型中的损伤识别参数,将结构振动特征值摄动和结构有限元理论相结合导出结了构损伤定位以及定量的一阶和二阶摄动识别公式,并给出了两种方程在不适定条件下的优化解法。把该方法用到ASCE结构健康监测工作组提出的Benchmark问题中,成功识别了设定的损伤模式,而且其受模型误差和测量噪声的影响较小。研究表明该方法可以用于大型结构的健康监测问题。     

矩阵摄动和Newmark-β逐步积分相结合的不确定性结构载荷识别

为了反演作用在不确定性结构上的动态激励上下界,在时域内建立了一个矩阵摄动和Newmark-β逐步积分相结合的载荷识别算法。首先依据矩阵摄动理论将动载荷近似表示为中值和摄动量相叠加的一阶泰勒多项式形式,然后引入Newmark-β逐步积分算法对振动学微分方程解耦,推导一个将输入载荷、输出响应和结构特性联系在一起的线性振动离散方程,借助该方程反求出动载荷的中值和摄动量,最终获得动载荷的上下边界。数值算例结果表明,该方法可以高效准确地重建载荷的上下边界,并具有优良的抗噪性能。     

基于模态参数考虑边界条件变异的桥梁结构损伤识别

根据桥梁结构的实际工程特性,分析其边界条件变异、结构损伤及其参数变化,采用约束优化理论,建立以实测和理论模态参数误差平方和最小为目标函数的优化反演问题。基于矩阵摄动理论引入与结构动力方程对应的特征值和特征向量的一阶、二阶摄动量,将优化反演问题简化为非线性最小二乘法优化反演问题。针对桥梁结构边界条件对模态参数影响显著的实际情况,实施桥梁结构边界条件预识别,采用单元模态应变能方法预定位损伤,提出考虑边界条件变异的桥梁结构损伤识别具体流程。以一磁浮轨道梁方案为例,采用数值模拟进行边界条件变异及损伤的识别验证,结果表明:该方法能够有效识别边界条件的变异及构件损伤,识别参数的相对误差最大为12.48%,具有较高的识别精度。     

基于模态数据的长细结构小损伤精确识别研究

本文针对现有的损伤识别方法不能满足部分结构损伤识别精度要求的现状,对结构的小损伤精确识别方法开展研究．以长细结构为研究对象,对具有不同损伤位置和损伤程度的圆柱形的轻阻尼梁结构进行了数值分析和实验研究,应用数值计算方法和实验确定的特征向量和特征频率对长细结构裂缝参数进行识别计算．本文在研究过程中编制了一个创新性的预测程序,通过其一次性生成目标函数图来选择合适的初始参数,从而对识别结果进行分析．研究结果表明,应用本文提出的识别方法,裂缝位置的识别误差可以控制在0.05 %~0.28 %范围内,裂缝深度识别误差低于7 %．     

基于改进灰狼优化算法的结构损伤识别

结合模态柔度矩阵、广义模态柔度矩阵和振型三个识别精度较好的指标,构造新的目标函数求解损伤识别问题。通过Nelson方法求解得到的频率与振型的导数,得到对结构刚度发生变化时更具敏感性的位置,然后在这些位置布置传感器以提取结构信息。针对原有的灰狼算法虽然全局搜索能力强,但是存在局部搜索精度差的问题,本文从初始种群和收敛因子等方面着手,改善灰狼算法的局部搜索能力及收敛速度。最后利用提出的方法,通过识别梁模型及桁架模型中的损伤单元说明本文方法的有效性。     

基于统计损伤理论的冻土蠕变本构模型研究

假定冻土粘塑性微元损伤符合修进的莫尔-库仑准则,损伤变量服从Weibull随机概型分布;基于热力学原理和统计损伤理论,通过推导得到了相关联流动法则下的蠕变损伤耦合本构方程.为了便于研究冻土蠕变和损伤的耦合作用,将提出的本构模型,通过用户子程序嵌入到有限元程序中.最后,对冻土中桩基承载力模型试验进行了数值模拟,结果表明:基于统计损伤理论的冻土蠕变本构模型能较好的模拟冻土蠕变变形的全过程,并且与实测蠕变变形十分吻合,该模型对冻土结构物长期稳定性分析和工程预测具有重要参考意义.     

基于时间序列分析的结构损伤特征提取与预警方法

基于在线监测数据的损伤诊断是结构健康监测的核心课题之一.本文基于时间序列分析ARMA模型探讨了结构损伤特征提取和损伤预警的实现方法.首先对监测数据建立ARMA模型,并基于模型中自回归部分参数,采用主成分分析的方法提出了新的结构损伤特征指标.然后采用t-检验考察该指标在损伤前后是否存在显著性的变化,从而可以有效地实现结构损伤预警.三跨连续梁数值算例表明,本文提出的损伤特征指标对结构的微小损伤具有敏感性,具备结构在线实时损伤预警的应用价值.     

基于频率二阶摄动的结构损伤识别方法

结构损伤的定位和定量是结构健康监测的关键技术之一。本文将矩阵摄动理论、结构振动理论和有限元理论相结合推导出结构固有频率变化的二阶摄动公式,由此公式可以反演结构的损伤位置与损伤程度。该方法仅需要在役结构的固有频率测量值就能识别出结构的损伤位置和损伤程度,而且还可以识别出结构的老化程度。通过数值仿真算例证明了该方法的有效性和实用性。该方法可用于大型结构的损伤识别和健康监测。     

特征值摄动法在利用动响应结构小损伤检测中的应用

目前在使用遗传算法或神经网络方法进行结构动力学损伤检测,需要基于少量的在线测量损伤结构数据和大量的数值仿真数据来实现,其中通过有限元方法来获得仿真数据的巨大计算量是动力学结构损伤检测方法发展中所面临的一个重要问题。本文在建模方面应用近年来提出的调整单元刚度模拟损伤的先进方法,以保证在损伤前后结构自由度数目不变;在此基础上应用特征值摄动法来减少损伤检测中计算量,并通过对复合材料层合板响应信号的小波分析验证了使用一阶矩阵摄动在有效降低计算量的同时,可以获得对损伤检测而言足够准确的响应信号。     

Localization and Degree of Damage Based on Relative Curvature Difference and Frequency Perturbation

This study proposed a damage identification method compared with the existing ones,based on relative curvature difference and frequency perturbation theory,showing sensitivity to local damage by changes in the curvature mode and high recognition accuracy of frequencies.Considering the relative curvature difference as a damage index,numerical simulation is used for a simply supported beam under single and multiple damage conditions for different damage degrees.The damage is located according to the curvature mode curves,and the damage degree is qualitatively determined.Based on the perturbation theory,the damage equations are established by the changes between frequencies before and after damage,and the damage localization and degree are verified and determined.Effectiveness of the proposed method for identifying damage at different conditions is numerically investigated.This method potentially promotes the development of damage identification of beam structures.     

Geometric Singular Perturbation Theory for Systems with Symmetry

Journal of Dynamics and Differential Equations - In this paper we focus on a class of symmetric vector fields in the context of singularly perturbed fast-slow dynamical systems. Our main question...     

结动振动摄动分析的新方法

提出了一种用于结构动力修改的设计灵敏度分析的新方法。它发展了Ｎｅｌｓｏｎ［１］陈［２］等人的方法，较好地解决了结构修改量大时计算精度低之间的矛盾。数值算例表明，本文新方法计算精度高，易于计算机实施。     

A Perturbation Method for Nonlinear Two-Dimensional Maps

A new perturbation method for a weakly nonlinear two-dimensional discrete-time dynamical system is presented. The proposed technique generalizes the asymptotic perturbation method that is valid for continuous-time systems and detects periodic or almost-periodic orbits and their stability. Two equations for the amplitude and the phase of solutions are derived and their fixed points correspond to limit cycles for the starting nonlinear map. The method is applied to various nonlinear (autonomous or not) two-dimensional maps. For the autonomous maps we derive the conditions for the appearance of a supercritical Hopf bifurcation and predict the characteristics of the corresponding limit cycle. For the nonautonomous maps we show amplitude-response and frequency-response curves. Under appropriate conditions, we demonstrate the occurrence of saddle-node bifurcations of cycles and of jumps and hysteresis effects in the system response (cusp catastrophe). Modulated motion can be observed for very low values of the external excitation and an infinite-period bifurcation occurs if the external excitation increases. Analytic approximate solutions are in good agreement with numerically obtained solutions.     

The Asymptotic Perturbation Method for Nonlinear Continuous Systems

We apply the asymptotic perturbation (AP) method to the study of the vibrations of Euler--Bernoulli beam resting on a nonlinear elastic foundation. An external periodic excitation is in primary resonance or in subharmonic resonance in the order of one-half with an nth mode frequency. The AP method uses two different procedures for the solutions: introducing an asymptotic temporal rescaling and balancing the harmonic terms with a simple iteration. We obtain amplitude and phase modulation equations and determine external force-response and frequency-response curves. The validity of the method is highlighted by comparing the approximate solutions with the results of the numerical integration and multiple-scale methods.     

Perturbation Theory for Approximation of Lyapunov Exponents by QR Methods

Motivated by a recently developed backward error analysis for QR methods, we consider the error in the Lyapunov exponents of perturbed triangular systems. We consider the case of stable and distinct Lyapunov exponents as well as the case of stable but not necessarily distinct exponents. We illustrate our analytical results with a numerical example.