基于Hankel矩阵联合近似对角化的结构模态识别

针对基于二阶盲辨识(second order blind identification,简称SOBI)的模态参数识别方法存在的不足,提出了一种基于Hankel矩阵联合近似对角化(Hankel matrix joint approximate diagonalization,简称HJAD)技术的结构运行模态分析(operational modal analysis,简称OMA)的新方法。该方法通过对随机子空间类模态识别方法常用的Hankel矩阵进行联合近似对角化,以分离各阶模态响应,进行模态识别。与基于SOBI的模态识别方法相比,在具体实施过程中,仅需要在分析数据中添加与实测振动响应对应的时间延迟的数据,实现难度较小。数值算例和物理模型试验的分析结果表明,所提出的基于HJAD技术的结构运行模态分析方法,不仅具有鲁棒性强和计算效率高的优点,还可以克服传统的基于SOBI的模态识别方法的模态识别能力受测点数目限制的问题。     

Matrix of the covariance of covariance of acceleration responses for damage detection from ambient vibration measurements

A new matrix on the covariance of covariance is formed from the auto/cross-correlation function of acceleration responses of a structure under white noise ambient excitation. The components of the covariance matrix are proved to be function of the modal parameters (modal frequency, mode shape, and damping parameter) of the structure. Information from all the vibration modes of the structure limited by the sampling frequency contributes to these components. The formulated covariance matrix contains more information on the vibration modes of the structure that cannot be obtained by the general methods for extracting modal parameters. When the component of the covariance matrix is used for damage detection, it is found more sensitive to local stiffness reduction than the first few modal frequencies and mode shapes obtained from ambient excitation. A simply supported 31 bar plane truss structure is studied numerically where a multiple damage scenario with different noise levels is identified with satisfactory results.     

Identification of modal parameters from ambient vibration data using eigensystem realization algorithm with correlation technique

An effective identification method is developed for the determination of modal parameters of a structure based on the measured ambient response data. In this study, modification to Eigensystem Realization Algorithm with Data Correlation is proposed for modalparameter identification of structural systems subjected to stationary white-noise ambient vibration. By setting up a correlation -function matrix of stationary responses, as well as by introducing an appropriate matrix factorization, modal parameters of a system can be identified effectively through singular -value decomposition and eigenvalue analysis. Numerical simulations using practical excitation data confirm the validity and robustness of the proposed method in identifying modal parameters from stationary ambient vibration data under noisy conditions.     

A modified random decrement technique for modal identification from nonstationary ambient response data only

Modal identification is considered from response data of structural system under nonstationary ambient vibration. In a previous paper, we showed that by assuming the ambient excitation to be nonstationary white noise in the form of a product model, the nonstationary response signals can be converted into free-vibration data via the correlation technique. In the present paper, if the ambient excitation can be modeled as a nonstationary white noise in the form of a product model, then the nonstationary cross random decrement signatures of structural response evaluated at any fixed time instant are shown theoretically to be proportional to the nonstationary cross-correlation functions. The practical problem of insufficient data samples available for evaluating nonstationary random decrement signatures can be approximately resolved by first extracting the amplitude-modulating function from the response and then transforming the nonstationary responses into stationary ones. Modal-parameter identification can then be performed using the Ibrahim time-domain technique, which is effective at identifying closely spaced modes. The theory proposed can be further extended by using the filtering concept to cover the case of nonstationary color excitations. Numerical simulations confirm the validity of the proposed method for identification of modal parameters from nonstationary ambient response data.     

Data processing in subspace identification and modal parameter identification of an arch bridge

A data-processing method concerning subspace identification is presented to improve the identification of modal parameters from measured response data only. The identification procedure of this method consists of two phases, first estimating frequencies and damping ratios and then extracting mode shapes. Elements of Hankel matrices are specially rearranged to enhance the identifiability of weak characteristics and the robustness to noise contamination. Furthermore, an alternative stabilisation diagram in combination with component energy index is adopted to effectively separate spurious and physical modes. On the basis of identified frequencies, mode shapes are extracted from the signals obtained by filtering measured data with a series of band-pass filters. The proposed method was tested with a concrete-filled steel tubular arch bridge, which was subjected to ambient excitation. Gabor representation was also employed to process measured signals before conducting parameter identification. Identified results show that the proposed method can give a reliable separation of spurious and physical modes as well as accurate estimates of weak modes only from response signals.     

一种工作模态参数的在线时域辨识方法

根据环境激励具有随机性以及线性系统在环境激励下各输出点响应之间的相关函数与系统的脉冲响应函数具有相同的数学表达式等特点，给出了在线模态参数识别的理论，并提出了仅根据环境激励响应识别模态参数的新方法。     

基于随机减量技术的模态参数识别方法探讨

大型基础工程结构的特征参数识别通常是通过对环境载荷激励的结构响应进行分析来实现,随机减量(Random Decrement,RD)技术是环境激励下的模态参数识别方法中应用较广的方法。在实际应用中受环境、测量等条件的限制,信号常为含有某些优势频率的非平稳信号,常常导致随机减量技术在识别结构参数尤其是系统阻尼时带来较大误差。为提高随机减量技术在环境激励作用下识别结构参数的准确性,文中从分析随机减量信号频谱中的频率分布特性入手,结合随机减量函数产生的触发条件,给出了一种利用信号频谱的统计特征进行模态参数识别的方法。数值仿真结果表明该函数能准确识别在含有优势频率环境载荷作用下的结构参数。     

环境激励下高桩码头物理模型模态实验

建立高桩码头物理模型,进行环境激励下的模态实验研究.利用特征系统实现算法(eigensystem realizationalgorithm,简称ERA),结合自然激励技术(natural excitation technique,简称NExT),即NExT-ERA模态识别方法编写模态识别程序来识别物理模型的模态参数,并与有限元模型的计算结果进行对比分析.研究结果表明,物理模型实验值与有限元计算结果相比,二者数值接近,误差很小,说明NExT-ERA模态识别方法能够应用于环境激励下高桩码头的模态识别.环境载荷激励下结构的动力响应信号较弱,结构的高阶模态一般无法激出,某些数据识别出的模态参数存在“漏阶”现象,因此结合有限元模型进行分析非常必要.     

随机减量法在斜拉桥拉索模态参数识别中的应用

斜拉桥拉索模态参数(固有频率、阻尼比)在索力测试、拉索减振、实时控制等方面起着重要作用。文中利用随机减量技术从岳阳洞庭桥环境激励下拾取的拉索的加速度响应中分离出自由衰减振动加速度响应信号，将获取的加速度响应信号表达为一理论形式，综合运用参数识别、最优估计理论，识别出拉索的模态参数，与理论值吻合良好。本文方法简单，试验容易实施，具有工程实用价值。数字仿真与工程测试结果表明了方法的有效性和可行性。     

IMPROVED COVARIANCE DRIVEN BLIND SUBSPACE IDENTIFICATION METHOD

An improved covariance driven subspace identification method is presented to identify the weakly excited modes. In this method, the traditional Hankel matrix is replaced by a reformed one to enhance the tdentifiability of weak characteristics. The robustness of eigenparameter estimation to noise contamination is reinforced by the improved Hankel matrix. In combination with component energy index (CEI) which indicates the vibration intensity of signal components, an alternative stabilization diagram is adopted to effectively separate spurious and physical modes. Simulation of a vibration system of multiple-degree-of-freedom and experiment of a frame structure subject to wind excitation are presented to demonstrate the improvement of the proposed blind method. The performance of this blind method is assessed in terms of its capability in extracting the weak modes as well as the accuracy of estimated parameters. The results have shown that the proposed blind method gives a better estimation of the weak modes from response signals of small signal to noise ratio (SNR) and gives a reliable separation of spurious and physical estimates.     

Identification of modal parameters from nonstationary ambient vibration data using the channel-expansion technique

The identification of modal parameters from the response data only is studied for structural systems under nonstationary ambient vibration. In a previous paper by the authors, the modal parameters of a system were identified using the correlation method in conjunction with the curve-fitting technique. This was done by working within the assumption that the ambient excitation is a nonstationary white noise in the form of a product model. In the present paper, the Ibrahim time-domain method (ITD) is extended for modal-parameter identification from the nonstationary ambient response data without any additional treatment of converting the original data into the form of free vibration. The ambient responses corresponding to various nonstationary inputs can be approximately expressed as a sum of exponential functions. In effect, the ITD method can be used in conjunction with the channel-expansion technique to identify the major modes of a structural system. To distinguish the structural modes from the non-structural modes, the concept of mode -shape coherence and confidence factor is employed. Numerical simulations, including one example of using the practical excitation data, confirm the validity and robustness of the proposed method for identification of modal parameters from the nonstationary ambient response.     

Response-only modal identification using random decrement algorithm with time-varying threshold level

Modal Identification from response data only is studied for structural systems under nonstationary ambient vibration. The topic of this paper is the estimation of modal parameters from nonstationary ambient vibration data by applying the random decrement algorithm with time-varying threshold level. In the conventional random decrement algorithm, the threshold level for evaluating randomdec signatures is defined as the standard deviation value of response data of the reference channel. The distortion of randomdec signatures may be, however, induced by the error involved in noise from the original response data in practice. To improve the accuracy of identification, a modification of the sampling procedure in random decrement algorithm is proposed for modal-parameter identification from the nonstationary ambient response data. The time-varying threshold level is presented for the acquisition of available sample time history to perform averaging analysis, and defined as the temporal root-mean-square function of structural response, which can appropriately describe a wide variety of nonstationary behaviors in reality, such as the time-varying amplitude (variance) of a nonstationary process in a seismic record. Numerical simulations confirm the validity and robustness of the proposed modal-identification method from nonstationary ambient response data under noisy conditions.     

USING CROSS—CORRELATION THEORY TO EXTRACT MODAL PARAMETERS IN FREQUENCY—DOMAIN

Conventional modal parameter identifications are usually based on frequency response functions, which require measurements of both the input force and the resulting response. However, in many cases, only response data are available while the actual excitations (such as wind/wave load) are not measurable. Modal parameters estimation must base itself on response-only data. Over the past years, many time-domain modal parameter identification techniques from output-only are proposed. A poly-reference frequency-domain modal identification scheme on response-only is presented. It is based on coupling the cross-correlation theory with conventional frequency-domain modal parameter extraction. An experiment using an airplane model is performed to verify the proposed method.     

Model order determination and noise removal for modal parameter estimation

Given a noisy impulsive response function (IRF) that has been contributed by an unknown number of modes, this article proposes a different approach from the traditional methods for estimating modal parameters from this noisy IRF. The major difference lies in the way of handling noise and choosing the computational model order. Whereas the traditional approach accommodates noise by purposely increasing the computational model order, the proposed approach uses the actual system order as the computational model order and rejects noise prior to performing the modal parameter estimation. The proposed approach includes three steps: (1) model order (or number of modes) determination from the measured IRF—by finding the rank of a Hankel matrix constructed from the measured IRF, (2) noise removal from the measured IRF to obtain a filtered IRF—by implementing Cadzow's algorithm for the structured low rank approximation (SLRA) on the Hankel matrix, and (3) modal parameters estimation from the filtered IRF—by using the complex exponential method (Prony's method). Numerical studies include both synthesized and experimental data. While measured IRFs with mild and strong noise levels are simulated for a 5 degree-of-freedom mass-spring-dashpot system, the modal parameter estimations based on the filtered IRFs are very good for both noise levels. While experimental data are measured from two accelerometers mounted at a cantilever beam, the modal parameters estimated from the filtered IRFs of the two accelerometers are in excellent agreement.     

COMPARATIVE STUDY OF MODAL ANALYSIS TECHNIQUES FOR BRIDGE DYNAMIC CHARACTERISTICS

The purpose of this paper is to present the results of a comparative study of various techniques for evaluating bridge dynamic properties from experimental data. The paper presents a review and synthesis of the work presented in a developed session of the International Modal Analysis Conference of February 2001. Research teams all over the world were invited to participate on a study to compare modal analysis techniques for evaluating the dynamic characteristics of bridges from forced, free and ambient vibration data. The Z24-Bridge, a three-span reinforced concrete bridge in Switzerland, was selected as a case study. The two objectives of the exercise were to compare the modal analysis techniques that are usually employed in the laboratories of the participants and to compare results from typical excitation techniques for large civil engineering structures. A total of six research teams accepted the challenge. The system identification methods that they used ranged from the basic peak-picking method to the advanced subspace identification method. All teams compared at least two excitation types.     

Improved independent component analysis based modal identification of higher damping structures

Structural modal parameter identification under ambient excitation has strong engineering value and theoretical significance. As the most popular tool for solving Blind Source Separation (BSS) problems, Independent Component Analysis (ICA) is able to directly extract the time-domain modal parameters, including frequencies, damping ratios and modal shapes. ICA, however, has a fatal flaw of failing to identify structures with higher damping. To overcome the flaw above, the paper proposes a new method named “ICA + IDT”. Firstly, free vibration response of a structure is obtained from structural outputs under ambient excitation. Inverse damping transfer (IDT) is employed to turn a highly damped signal into a low damping response signal without changing of frequencies and mode shapes. Then, structural modal parameters are extracted from the low damping response signal by ICA. Finally, the identified damping ratios are adjusted to eliminate the impact of IDT. To verify the effectiveness and applicability of IDT + ICA proposed herein, two numerical simulations—mass-spring model and simply supported concrete beam—and an experiment model of three-story steel frame are built, and the analysis results reveal that presented method can identify structures with higher damping effectively.     

Recursive subspace identification for on-line tracking of structural modal parameter

The objective of this paper is to develop an on-line tracking of system parameter estimation and damage detection techniques using response measurements. To avoid the singular-value-decomposition in data Hankel matrix, a new subspace identification algorithm was developed. Seismic response data of a 3-story steel frame with abrupt change of inter-story stiffness from the shaking table test was used to verify the proposed recursive subspace identification (RSI) method by using both input and output measurements. With the implementation of forgetting factor in RSI method the ability of on-line damage detection of the abrupt change of structural stiffness can be enhanced. Then, the recursive stochastic subspace identification (RSSI) algorithm is also developed for continuous structural health monitor of structure by using the output-only measurements. Verification of the proposed RSSI method by using the white noise response data of a 2-story reinforced concrete frame from its low level white noise excitation was used. Discussion of the subspace identification model parameters is also investigated.     

基于贝叶斯运行模态分析法的砂轮架动态特性分析

为了研究砂轮架的固有模态和在工作环境中的谐波模态,运用贝叶斯理论和运行模态分析相结合的模态参数识别技术--分步测试的贝叶斯运行模态分析法对环境状态下的砂轮架进行模态识别,获得了结构的动态特性,包括固有频率、振型以及阻尼特性等,并对外激励和预测误差水平以及信噪比进行了评估;将该模态识别结果与传统试验模态分析结果进行对比,验证了贝叶斯运行模态分析法的应用可行性;进一步在工作环境下对砂轮架进行了振动测试,对比开机前的模态识别结果和开机后砂轮架的功率谱密度图,成功地区分出砂轮架的固有模态和实际工作环境中由结构周期激励引起的谐波模态。     

Enhancement of coherence functions using time signals in Modal Analysis

Experimental Modal Analysis (EMA) and Operational Modal Analysis (OMA) are two widely used techniques in the identification of modal parameters. EMA is synonymous with a laboratory environment requiring complete system shutdown while OMA is implemented in a real environment where the ambient forces cannot be isolated. A new method, namely Impact-Synchronous Modal Analysis (ISMA) utilising the modal extraction techniques commonly used in EMA but performed in the presence of the ambient forces, is proposed. Transfer functions, from where the modal parameters are extracted, are obtained from Fourier transform of cross and auto correlation functions. These functions are estimated quantities and their outcomes are dependable on the averaging techniques used. The coherence functions are commonly used to measure the acceptability of the estimations. Impact-Synchronous Time Averaging is compared against Spectral Averaging while performing Modal Analysis in a situation containing ambient and operating forces. Results showed that while the transfer functions obtained from both the averaging techniques were of similar quality, the Impact-Synchronous Time Averaging indicated better coherence than the Spectral Averaging.     

A framework for blind modal identification using joint approximate diagonalization

In this paper, a second-order statistical method employed in blind source separation (BSS) is adapted for use in modal parameter identification. Modal responses and mode shapes are estimated by the use of second-order blind identification (SOBI) on an expanded and pre-treated dataset. Frequency and damping can be obtained from the modal responses by simple single degree of freedom methods. Using this approach, a class of new non-parametric output-only modal identification algorithms is proposed and examples of its use are provided. It is demonstrated that the proposed methodology provides a novel and robust approach to modal identification. For the example shown, it is deduced that quality of the modal parameters produced by the method is competitive with the state of the art parametric methods.