REFERENCE-BASED STOCHASTIC SUBSPACE IDENTIFICATION FOR OUTPUT-ONLY MODAL ANALYSIS

When performing vibration tests on civil engineering structures, it is often unpractical and expensive to use artificial excitation (shakers, drop weights). Ambient excitation on the contrary is freely available (traffic, wind), but it causes other challenges. The ambient input remains unknown and the system identification algorithms have to deal with output-only measurements. For instance, realisation algorithms can be used: originally formulated for impulse responses they were easily extended to output covariances. More recently, data-driven stochastic subspace algorithms which avoid the computation of the output covariances were developed. The key element of these algorithms is the projection of the row space of the future outputs into the row space of the past outputs. Also typical for ambient testing of large structures is that not all degrees of freedom can be measured at once but that they are divided into several set-ups with overlapping reference sensors. These reference sensors are needed to obtain global mode shapes. In this paper, a novel approach of stochastic subspace identification is presented that incorporates the idea of the reference sensors already in the identification step: the row space of future outputs is projected into the row space of past reference outputs. The algorithm is validated with real vibration data from a steel mast excited by wind load. The price paid for the important gain concerning computational efficiency in the new approach is that the prediction errors for the non-reference channels are higher. The estimates of the eigenfrequencies and damping ratios do not suffer from this fact.     

Modal parameter identification of stay cables from output-only measurements

Stay cables are one of the most critical structural components in modern cable-stayed bridges and the cable tension plays an important role in the construction, control and monitoring of cable-stayed bridges. We propose a time domain and a time-frequency domain approaches for modal parameter identification of stay cables using output-only measurements. The time domain approach uses the subspace algorithm which is improved with a new modal coherence indicator. The time-frequency approach uses the wavelet transform of signals which is improved with a new analyzing wavelet. The wavelet transform is applied to the free response of ambient vibration which is obtained using the random decrement technique. Two experiments of stay cables are presented. The first experiment concerns a stay cable in laboratory where the external load is applied through an impact hammer and the vibratory signals are acquired through four accelerometers. The second experiment concerns the Jinma cable-stayed bridge that connects Guangzhou and Zhaoqing in China. It is a single tower, double row cable-stayed bridge supported by 112 stay cables. Ambient vibration of each stay cable is carried out using accelerometers. From output-only measurements, the modal parameters of stay cables are extracted. Once the eigenfrequencies and the damping coefficients are obtained, the cable forces and the Scruton number are derived. In a continuous monitoring and modal analysis process, the tension forces and Scruton numbers could be used to assess the health of stay cables in cable-stayed bridges.     

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.     

悬臂薄板结构阻尼特性几种测试方法的比较

在振动和噪声控制中,阻尼的测试有着重要的工程及学术意义.在明确阻尼辨识原理的基础上,以悬臂薄板结构为研究对象,搭建了锤击、振动台、压电陶瓷激励三种测试系统,分别采用半功率带宽法和时域自由振动衰减法进行了阻尼测试.并从重复性、测试精度、测试阻尼的频率范围和测试效率等方面,将各种阻尼测试结果进行了比较.最终认为,宜采用振动台扫频激励的方式和半功率带宽法对所研究的薄板进行阻尼测试和辨识.可为悬臂薄板结构后续的响应预估和阻尼优化设计提供重要的参考.     

桥梁工作模态分析中阻尼比识别的离散性研究

准确识别阻尼比一直是桥梁结构模态参数识别的难题。为研究工作模态分析中识别的阻尼比离散性问题,总结了现有的代表性的频域、时域和时频分析的阻尼比识别方法,指出了各种方法导致识别结果不准确的原因。以一个预应力混凝土连续梁桥的工作模态分析为例,分析了阻尼比识别的结果,研究了减小识别的阻尼比离散性的方法。结果表明:相对频率而言,阻尼比识别结果离散程度较高;在混合自由振动响应的情况下,通过增加采样时间,能改善阻尼比识别离散较大的问题,提高识别精度;利用振动水平较低的随机振动响应识别的阻尼比离散性较小。     

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.     

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.     

Experimental investigation of zero phase shift effects for Coriolis flowmeters due to pipe imperfections

Theoretical investigations of a single, straight, vibrating, fluid-conveying pipe have resulted in simple analytical expressions for the approximate prediction of the spatial shift in vibration phase. The expressions have lead to hypotheses for real Coriolis flowmeters (CFMs). To test these, the flexural vibrations of two bent, parallel, non-fluid-conveying pipes are studied experimentally, employing an industrial CFM. Special attention has been paid on the phase shift in the case of zero mass flow, i.e. the zero shift, caused by various imperfections to the “perfect” CFM, i.e. non-uniform pipe damping and mass, and on ambient temperature changes. Experimental observations confirm the hypothesis that asymmetry in the axial distribution of damping will induce zero shifts similar to the phase shifts due to fluid flow. Axially symmetrically distributed damping was observed to influence phase shift at an order of magnitude smaller than the primary effect of mass flow, while small added mass and ambient temperature changes induced zero shifts two orders of magnitude smaller than the phase shifts due to mass flow. The order of magnitude of the induced zero shifts indicates that non-uniform damping, added mass as well as temperature changes could be causes contributing to a time-varying measured zero shift, as observed with some commercial CFMs. The conducted experimental tests of the theoretically based hypotheses have shown that simple mathematical models and approximate analysis allow general conclusions, that may provide a direct insight, and help increasing the benefit of time consuming numerical simulations and laboratory experiments.     

Identification modale sous excitation ambiante : Application à la surveillance des ponts

Vibration measurements on bridges are not recent and many studies were carried out in the past by the LCPC and many French or foreign agencies or companies. What is new today, it is the increase of the number of dynamic tests carried out on bridges for a better assessment of their structural behaviour. The prime objective in a dynamic assessment is the determination – or identification – of the modal characteristics. That includes natural frequencies, damping ratios and mode shapes. The use of tests under ambient vibration is increasingly popular today because they make it possible to measure the structural response in service. The increase in the data acquisition system capacity and data storage also largely supported the development of tests under ambient vibration. The excitation can be induced by wind, pedestrians or vehicles traffic or any other live loads. In this case, identification methods which do not require measurement of the excitation source must be used. After pointing out the objectives and the stakes of bridge dynamic testing, this paper highlights some of these methods and provides some practical applications.     

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.     

Unbalance Response of a Super-Critical Rotor Supported by Foil Bearings—Comparison with Test Results©

This article compares theoretical and experimental results on the unbalance response of a super-critical rotor supported by two kinds of gas foil bearings. Analysis of the super-critical rotor is performed with viscoelastic foil bearings (VEFB) and conventional bump foil bearings and compared with early published experimental data. The vibration orbits obtained by theoretical investigation on the viscoelastic foil bearings (VEFB) and the conventional bump foil bearings are compared with the experimental vibration orbits of the super-critical rotor supported by both foil bearings. A numerical analysis program can calculate the static and dynamic characteristics of the elastically supported gas foil bearing using the measured stiffness and damping of the elastic foundation. After the stiffness and damping of both foil bearings are calculated using the perturbation method, vibration orbits of the flexible rotor modeled by the finite element method are calculated. Vibration orbits calculated by numerical analysis agree well with experimental data when the vibration amplitude is small and the rotating speed is below the bending critical speed. The numerical results also show that the enhanced structural damping of the elastic foundation reduces vibration near the bending critical speed.     

IDENTIFICATION OF PROPORTIONAL AND OTHER SORTS OF DAMPING MATRICES USING A WEIGHTED RESPONSE-INTEGRAL METHOD

One of the available methods for attempting to identify a damping matrix uses a weighted matrix integral of system response functions. Validity of the method is known under a condition called ‘proportional’ damping but has not previously been examined for other sorts of damping. State-space approach and an associated Liapunov equation are introduced for a more general study. It emerges that all sorts of positive-definite damping matrices are in theory open to identification with a weighted matrix integral, though a formal identification result may need to be replaced with a numerical algorithm. Examples relate to simulated vibration response histories under different sorts of damping for a four-element cantilever subjected to half-sine forcing. It is found that error sensitivity and errors arising in extraction of impulse-response histories are apt to obscure identification; moreover that damping identifications can lack uniqueness.     

基于跑车余振的混凝土梁桥阻尼比估算方法

分析了混凝土梁桥跑车余振信号的特点,提出桥梁自由衰减振动分段幅值估算阻尼比的方法,以提高阻尼比的识别精度。该方法通过对结构余振信号分段截取做FFT变换,利用相邻两块数据的幅值求得其阻尼比。仿真分析比较了该方法与传统半功率点法估算结构阻尼比的精度,结果表明该方法在有限衰减数据长度内精度优于传统半功率点法。利用该方法对某混凝土连续刚构桥的跑车余振信号进行阻尼比识别,得到前两阶竖弯频率对应的阻尼比,识别结果稳定,可作为该桥的实际阻尼比。     

VIBRATION CONTROL OF FLUID- FILLED PRISMATIC SHELL WITH ACTIVE CONSTRAINED LAYER DAMPING TREATMENTS

Active constrained layer damping （ACLD） combines the simplicity and reliability of passive damping with the light weight and high efficiency of active actuators to obtain high damping over a wide frequency band. A fluid-filled prismatic shell is set up to investigate the validity and efficiency of ACLD treatments in the case of fluid-structure interaction. By using state subspace identification method, modal parameters of the ACLD system are identified and a state space model is established subsequently for the design of active control laws. Experiments are conducted to the fluid-filled prismatic shell subjected to random and impulse excitation, respectively, For comparison, the shell model without fluid interaction is experimented as well. Experimental results have shown that the ACLD treatments can suppress vibration of the fluid-free and fluid-filled prismatic shell effectively. Under the same control gain, vibration attenuation is almost the same in both cases.     

EXTRACTION OF RITZ VECTORS FROM VIBRATION TEST DATA

Modal parameters obtained from modal testing (such as modal vectors, natural frequencies, and damping ratios) have been used extensively in system identification, finite element model updating, and structural health monitoring. As an alternative to modal vectors, load-dependent Ritz vectors have been shown useful in various areas of structural dynamics such as model reduction and damage detection. The applications of Ritz vectors, however, have been mainly limited in analytical and numerical analyses because of the difficulty to identify them from vibration tests. This paper presents a procedure to extract load-dependent Ritz vectors using a complete flexibility matrix constructed from measured vibration test data. The proposed method cannot only construct the Ritz vectors corresponding to the actual load pattern employed in vibration tests, but also generate Ritz vectors from arbitrary load patterns. Experimental data obtained from the vibration test of a grid-type bridge structure are employed to validate and illustrate the proposed extraction procedure.     

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。     

Finite-element vibration analysis of tapping-mode atomic force microscopy in liquid

Investigation of morphology and mechanical properties of biological specimens using atomic force microscopy (AFM) often requires its operation in liquid environment. Due to the hydrodynamic force, the vibration of AFM cantilevers in liquid shows dramatically different dynamic characteristics from that in air. A good understanding of the dynamics of AFM cantilevers vibrating in liquid is needed for the interpretation of scanning images, selection of AFM operating conditions, and evaluation of sample's mechanical properties. In this study, a finite element (FE) model is used for frequency and transient response analysis of AFM cantilevers in tapping mode (TM) operated in air or liquid. Hydrodynamic force exerted by the fluid on AFM cantilevers is approximated by additional mass and hydrodynamic damping. The additional mass and hydrodynamic damping matrices corresponding to beam elements are derived. With this model, numerical simulations are performed for an AFM cantilever to obtain the frequency and transient responses of the cantilever in air and liquid. The comparison between our simulated results and the experimentally obtained ones shows good agreement. Based on the simulations, different characteristics of cantilever dynamics in air and liquid are discussed.     

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.     

金属橡胶包覆阻尼结构高温力学建模与试验

针对高温管路系统的减振难题,利用等效线性化方法建立了管路金属橡胶包覆阻尼结构的高温力学模型,分析了金属橡胶刚度和响应幅值随温度的变化规律。搭建了高温管路振动测试试验平台,以插入损失为评价指标,对不同环境温度、不同金属橡胶密度的管路包覆阻尼结构减振性能进行了试验验证。试验结果表明,减小金属橡胶密度能有效增加管路减振效果,环境温度对管路金属橡胶包覆阻尼结构的影响较小,说明金属橡胶包覆阻尼结构能很好地在高温环境下工作。     

Modal identification of linear non-proportionally damped systems by wavelet transform

A time-frequency identification technique based on wavelet transform is formulated and applied to free-decay responses of linear systems with non-proportional viscous damping. The Cauchy mother wavelet is used. Frequencies, modal damping ratios and complex mode shapes are identified from output-only free vibration signals. This identification technique has also shown to be effective when the (non-proportional) damping is significant.