基于贝叶斯方法的模态参数识别的不确定度分析

振动模态分析和模态参数识别是动态测试的一个重要研究方向。模态参数在模型的修正、响应的预测、系统的健康检测及控制等方面有着重要的作用。但动态测试的不确定度分析,尤其是模态参数的不确定度的研究还十分缺乏。本文主要基于贝叶斯方法,通过傅立叶变换(FFT)建立时域数据和频域数据之间的对应关系。根据共振频带内的多个模态的响应数据得到相对应的模态参数,优化得到模态参数的最佳估计值,评定模态参数识别的不确定度。在固支梁的模态实验中,加速度传感器采集环境激励中的振动数据,运用贝叶斯法进行处理得到模态参数的最佳估计值。在此基础上,通过模态参数的最佳估计值,以及仪器的检定报告数据,结合合成不确度分析方法,系统分析了模态参数识别的不确定度。     

基于控制响应的时变系统模态参数辨识的改进子空间方法

提出了一种基于系统控制信号激发的响应数据来辨识时变系统模态参数的改进子空间方法。该方法以系统控制响应信号建立系统的状态空间输出方程并构造了一个广义Hankel矩阵,通过对该矩阵做奇异值分解(SVD),用广义能观阵的估计代替输出矩阵,然后利用奇异值矩阵的正交性,有效地降低了噪声敏感性和计算量,从而容易地辨识出等效状态下的系统矩阵,最后采用转换矩阵辨识出时变系统的模态参数。通过理论分析、仿真和实验,讨论了不同信噪比对辨识结果的影响,验证了该方法的有效性。     

A method of online damage identification for structures based on ambient vibration

IntroductionStructuralhealthmonitoringofbridgesandarchitectureshasbeenhighlyinteresting .Whensomebridgesarebuilt,thehealthmonitoringsystemsareinstalled ,whicharemadeupofmanysensors,suchaswindloadingsensors,stresssensorsandaccelerationsensors.Thesesensorscollectagreatdealofinformation .Howtheinformationisusedtoestimatethedamageofbridgestructureandanalyzethedurabilityofbridgestructureisasignificantresearchproblem .Existenceofstructuraldamageswithinstructuresleadstothechangesuchasthevibrationres…     

时域模态参数识别的直接特征系统实现算法

本文提出了一种新的结构模态参数识别算法,称为直接特征系统实现算法(DERA)。直接采用时域多输入多输出数据构成线性时不变离散系统的最小实现,并利用系统矩阵的特征值和特征向量求取模态参数。输入输出数据的直接应用避免了利用脉冲响应函数作原始数据的ERA、PRCE等算法的一些局限。奇异值分解技术的引入使系统的定阶和实现更方便,并具有了更良好的数值稳定性。为验证算法,构造了一个五自由度的弹簧质量系统进行数值模拟。良好的数值结果证明了本算法的有效性,并表明本算法对密集模态仍有较高的识别精度。     

基于Welch法的协方差随机子空间方法的模态参数识别

对工程结构进行环境激励下的模态参数识别具有重要意义, 而随机子空间法作为适合环境激励下模态参数识别的时域方法, 由于噪声和复杂激励的原因, 会产生虚假模态、真实模态遗漏、系统自动定阶难和计算效率等问题, 这些问题阻碍了该方法在实际工程中的广泛应用. 本文提出了基于Welch法的随机子空间方法, 通过Welch法对振动响应在频域进行去噪、降低环境激励和其他不确定性因素影响的处理, 把结构固有模态从噪声和激励频率中突显出来, 形成富含更多结构模态的Toeplitz矩阵, 然后进行奇异值分解和状态矩阵计算, 最后进行特征值分析. 为了实现自动定阶, 对不同奇异值分量构建的状态矩阵得到的特征参数, 进行模糊C均值聚类分析和模态的平均相位偏移分析, 剔除虚假模态, 实现结构模态参数的自动识别. 并把本文所提出方法应用于一座大跨悬索桥的实测加速度响应分析, 和一座七十层的高层建筑的加速度响应分析, 跟频域分解法、传统随机子空间法和基于相关分析的随机子空间法的计算结果进行了比较, 发现基于Welch方法的随机子空间法相比于传统随机子空间法和基于相关分析的随机子空间法, 在避免模态遗漏和计算效率方面有显著提高, 而相对于频域分解法则在自动识别和剔除虚假模态方面有明显优势.      

Modal parameter identification based on ARMAV and state–space approaches

An accurate prediction for the response of civil and mechanical engineering structures subject to ambient excitation requires the information of dynamic properties of these structures including natural frequencies, damping ratios and mode shapes. Since the excitation force is not available as a measured signal, we need to develop techniques which are capable of accurately extracting the modal parameters from output-only data. This article presents the results of modal parameter identification using two time-domain methods as follows: the autoregressive moving average vector (ARMAV) method and the state–space method. These methods directly work with the recorded time signals and allow the analysis of structures where only the output is measured, while the input is unmeasured and unknown. The equivalence between ARMAV and state–space approaches for the problem of modal parameter identification of vibrating systems is shown in the article. Using only the singular value decomposition of a block Hankel matrix of sample covariances, it is shown that these two approaches give identical modal parameters in the case where the block Hankel matrix has full row rank. The time-domain modal identification algorithms have a serious problem of model order determination: when extracting structural modes these algorithms always generate spurious modes. A modal indicator to differentiate spurious and structural modes is presented. Numerical and experimental examples are given to show the effectiveness of the ARMAV or state–space approaches in modal parameter identification using response data only.     

An acceleration for the eigensystem realization algorithm with partial singular values decomposition

The real-time identification of dynamic parameters is important for the control system of spacecraft. The eigensystem realization algorithm (ERA) is currently the typical method for such application. In order to identify the dynamic parameter of spacecraft rapidly and accurately, an accelerated ERA with a partial singular values decomposition (PSVD) algorithm is presented. In the PSVD, the Hankel matrix is reduced to dual diagonal form first, and then transformed into a tridiagonal matrix. The eigenvalues are computed by the bisection method in terms of the Sturm property, and the corresponding eigenvectors are obtained by the inverse iteration method. Finally, the eigenvalues and the eigenvectors are transformed into the singular values and the singular value vectors of the original matrix. An example for space station is presented to demonstrate the efficacy and accuracy of the proposed algorithm.     

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。     

FSDD运行模态参数识别方法中不确定性的计算

运行模态参数识别是一种只利用响应数据进行模态分析的方法。环境激励条件下获得的识别结果会存在随机不确定性,这种不确定程度可以通过模态参数的统计特性进行描述评价。以运行模态分析中的频域空间域分解方法（FSDD）为研究对象,通过对整个模态识别算法进行摄动分析,确定出模态参数对测量误差的灵敏度,实现了模态参数方差的计算。计算过程分为四步：第一步,响应信号功率谱矩阵中噪声方差的估计;第二步,增强功率谱方差的计算;第三步,极点协方差的计算;第四步,模态参数方差的计算。最后通过一个4自由度仿真算例与张家港桥梁实测算例对所给出的方法进行了验证与应用。     

New modal identification method under the non-stationary Gaussian ambient excitation

Based on the multivariate continuous time autoregressive （CAR） model, this paper presents a new time-domain modal identification method of linear time-invariant system driven by the uniformly modulated Gaussian random excitation. The method can identify the physical parameters of the system from the response data. First, the structural dynamic equation is transformed into a continuous time autoregressive model （CAR） of order 3. Second, based on the assumption that the uniformly modulated function is approximately equal to a constant matrix in a very short period of time and on the property of the strong solution of the stochastic differential equation, the uniformly modulated function is identified piecewise. Two special situations are discussed. Finally, by virtue of the Girsanov theorem, we introduce a likelihood function, which is just a con- ditional density function. Maximizing the likelihood function gives the exact maximum likelihood estimators of model parameters. Numerical results show that the method has high precision and the computation is efficient.     

基于二阶系统解耦的精细积分格式下动载荷时域识别

基于模态分析法的载荷识别方法利用模态矩阵获得系统的非耦合形式,推导单自由度系统的载荷识别公式,但要求系统为比例阻尼。在模态模型基础上,对一般系统建立基于二阶系统解耦的动载荷时域识别模型。首先,利用基于Lancaster结构的二阶系统解耦方法推导出系统的非耦合形式;然后,采用精细逐步积分方法,在载荷为阶跃力的假设下,推导出载荷识别数学公式;最后,由系统实时响应反求结构载荷的时间历程。数值算例验证了本文方法针对比例阻尼系统较模态模型具有更高的精度,而且对非比例阻尼系统也有效可行。     

THEORETICAL MODEL AND NUMERICAL METHOD ON ONLINE IDENTIFICATION OF DYNAMICAL CHARACTERISTICS OF STRUCTURAL SYSTEM （Department of Engineering Mechanics, Southeast University, Nanjing 210096, P.R. China）

An online method of identification of dynamic characteristics only using measured ambient response of structural dynamic system is widely focused on. The Ibrahim and ARMA ( AutoRegressive Moving Average ) methods are basic identification methods. A model on dynamic system suffered by random ambient excitation was researched into, and a subspace decomposition methodwas introduced. Robustness and effectiveness of this approach on identification of vibration characteristics are demonstrated on numerical experiment.     

Linear state representations for identification of bilinear discrete-time models by interaction matrices

Bilinear systems can be viewed as a bridge between linear and nonlinear systems, providing a promising approach to handle various nonlinear identification and control problems. This paper provides a formal justification for the extension of interaction matrices to bilinear systems and uses them to express the bilinear state as a linear function of input–output data. Multiple representations of this kind are derived, making it possible to develop an intersection subspace algorithm for the identification of discrete-time bilinear models. The technique first recovers the bilinear state by intersecting two vector spaces that are defined solely in terms of input–output data. The new input–output-to-state relationships are also used to extend the equivalent linear model method for bilinear system identification. Among the benefits of the proposed approach, it does not require data from multiple experiments, and it does not impose specific restrictions on the form of input excitation.     

环境激励下Benchmark结构损伤识别的试验研究

针对结构健康监测中如何利用在线监测数据进行健康诊断的问题,基于时间序列分析提出了一种新的损伤识别方法.首先,获得结构健康状态的监测数据作为参考状态样本,对各数据样本建立ARMA模型并计算模型残差的方差.然后,将未知状态的监测数据作为待检状态样本,代入已建立的参考状态ARMA模型计算新的残差方差.计算发现,损伤前后两状态模型残差方差存在差异.因而,提出以残差方差之比作为损伤敏感特征,并建立基于F分布的假设检验来辨识结构的状态并预警损伤.最后,以Benchmark结构在环境激励下的试验为例,运用本文方法进行了损伤识别研究.结果表明,基于ARMA模型残差方差的损伤敏感特征可准确地区别结构的健康状态和损伤状态,具备结构在线实时损伤识别的应用价值.     

一种桁架结构损伤识别的柔度阵法

利用试验获得的一阶模态参数,提出了一种桁架结构损伤识别的柔度阵法,应用有限元方法柔度阵,建立结构振动特征方程,结构损伤后,引起柔度阵发生改变,从结构振动特征方程出发,对柔度矩阵做关于结构物理参数变化量的一阶泰勒展开,可以确定结构物理参数的变化量,识别结构损伤部位及损伤程度,通过一个桁架结构损伤识别的数值模拟证明了该方法的有效性。     

环境温度影响下基于LSTM神经网络识别结构损伤

环境温度的改变会引起模态参数的变化,其变化程度会掩盖或部分掩盖损伤引起的变化量,导致结构健康监测系统发出假阳性或假阴性的误判,因此,消除温度效应是提高损伤识别精度的关键。本文基于LSTM神经网络提出了一种环境温度影响下识别结构损伤的方法。充分利用LSTM神经网络的非线性映射优势,建立多元温度-模态频率的相关模型,在此基础上采用数据标准化方法消除温度效应,并结合控制图判断模态频率异常变化以确定损伤状况。最后将所提方法在数值模型和实际桥梁中加以应用,结果表明,方法能够有效消除温度效应;结合控制图能识别损伤时刻,并具有一定的抗噪性;在实桥数据分析中仍能表现出较好的损伤敏感性。     

Continuous-Time Bilinear System Identification

The objective of this paper is to describe a new method for identification of a continuous-time multi-input and multi-output bilinear system. The approach is to make judicious use of the linear-model properties of the bilinear system when subjected to a constant input. Two steps are required in the identification process. The first step is to use a set of pulse responses resulting from a constant input of one sample period to identify the state matrix, the output matrix, and the direct transmission matrix. The second step is to use another set of pulse responses with the same constant input over multiple sample periods to identify the input matrix and the coefficient matrices associated with the coupling terms between the state and the inputs. Numerical examples are given to illustrate the concept and the computational algorithm for the identification method.     

Displacement modal identification method of elastic system under operational condition

Modal identification of engineering structure in operation deals with the estimation of modal parameters from vibration data obtained in working conditions rather than laboratory conditions. After one structure destruction during a flight test, it was strongly required to carry out full-scale model testing to acquire the low-frequency vibration acceleration data of the investigated rocket (its structural dynamic properties could be represented by a beam). These vibration data were used to assess the modal properties of the modified structure. In this paper, a new modal identification method based on vibration displacement is suggested. The displacements of the measured points on the rocket are obtained by the integration of the low-frequency vibration accelerations during free flight test. In the method, the data are filtered through wavelet transform. For comparison, several methods are used to extract the modal frequencies of the investigated beam. In terms of the results of standard deviation of identified frequencies, it is believed that the generalized displacement-based modal identification method is more practicable in modal identification for similar problems.     

基于残余力向量法和改进遗传算法的结构损伤识别研究

提出了一种基于残余力向量法和改进遗传算法的结构损伤识别方法。文中首先对残余力向量法和遗传算法的基本理论进行了介绍。在无噪声的情况下,使用任意一阶模态数据,残余力向量法都能够对损伤进行准确定位。但是,振动测试数据中往往包含噪声,导致运用残余力向量法进行损伤识别完全不可行。考虑到这个问题,在常规模态分析的基础上,以节点的残余力向量构造用于遗传搜索优化的目标函数形式,然后利用改进的遗传算法重点进行了噪声条件下的结构损伤定位和定量研究。最后,本文用一个平面桁架模型进行了数值模拟,验证了所提出方法的有效性,并对方法应用中存在的一些问题进行了深入分析,得出了一些有益的结论。     

A model identification method of vibrating structures from incomplete modal information

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