IDENTIFICATION OF TIME-VARYING MODAL PARAMETERS USING LINEAR TIME-FREQUENCY REPRESENTATION

A new method of parameter identification based on linear time-frequency representation andHilbert transform is proposed to identify modal parameters of linear time-varying systems frommeasured vibration responses. Using Gabor expansion and synthesis theory measured responses arerepresented in the time-frequency domain and modal components are reconstructed by time-frequencyfiltering. The Hilbert transform is applied to obtain time histories of the amplitude and phase angle ofeach modal component, from which time-varying frequencies and damping ratios are identified. The     

基于电流变阻尼超精密气浮工作台研究

为解决直线气浮系统抗干扰能力较差等问题,针对已开发的超精密直线气浮工作台,设计了电流变剪切模式阻尼器;基于屈服前后平滑过渡的Eyring连续本构模型通过辨识得出电流变剪切阻尼器类稳态模型;从仿真和实验研究了电流变阻尼及高电场强度对直线气浮工作台模态的影响,实验模态结果验证了仿真方法的有效性,同时证实设计的电流变阻尼器及电场强度的提高不会造成模态频率的下降,只会引起阻尼比的大幅度提高,甚至减少模态阶数。     

REAL-TIME MODAL PARAMETER ESTIMATION USING SUBSPACE METHODS: APPLICATIONS

This article describes the underlying theory and hardware implementation of a newly developed algorithm for online modal parameter identification. An online modal parameter estimation algorithm using subspace methods is applied to both model and experimental data for a 4-m laboratory truss structure. Experimental evaluation of this algorithm demonstrates that the technique accomplishes the objective of tracking multiple modes of a complex dynamical system using multiple sensors. The time-varying behaviour is captured in real time via a graphical display of the frequencies and the damping ratios of the system. It is shown that the recursive algorithm provides results similar to the batch algorithm for a time-invariant system. In addition, it is shown that the batch algorithm used to derive the recursive algorithm performs similarly to a newly derived batch algorithm that is closely related to the Eigensystem Realization Algorithm. Details concerning the digital signal processor implementation and off-line monitoring are also presented.     

振动模态固有频率和阻尼比的EMD识别方法

针对机械系统固有频率和阻尼比的识别问题,提出了基于经验模式分解(EMD)的模态参数识别方法.该方法首先对脉冲激励下机械系统的位移响应进行了EMD分解,确定与该系统的各阶模态对应的固有模式函数(IMF),分别对各阶IMF进行希尔伯特变换以得到各自的瞬时幅值和瞬时相位曲线,并对所得曲线进行线性拟合,最后根据拟合曲线的参数来...     

Direct identification of non-proportional modal damping matrix for lumped mass system using modal parameters

Several damping materials have been employed to reduce the vibration of marine structures. In this paper, a new method of identifying system matrices for non-proportional damping structures using modal parameters is proposed. This method has two advantages. First, the mass and stiffness matrices do not need to be calculated using the FEM, so errors due to the inaccuracy of these matrices can be reduced. Second, various indirect methods can be used to identify modal parameters such as natural frequencies, modal damping ratios and mode shapes. Three case studies of lumped mass systems with non-proportional damping are carried out to verify the performance of the proposed method in this study.     

QFT Parameter-Scheduling control design for linear Time-Varying systems based on RBF networks

For most of linear time-varying (LTV) systems, it is difficult to design time-varying controllers in analytic way. Accordingly, by approximating LTV systems as uncertain linear time-invariant, control design approaches such as robust control have been applied to the resulting uncertain LTI systems. In particular, a robust control method such as quantitative feedback theory (QFT) has an advantage of guaranteeing the frozen-time stability and the performance specification against plant parameter uncertainties. However, if these methods are applied to the approximated linear time-invariant (LTI) plants with large uncertainty, the resulting control law becomes complicated and also may not become ineffective with faster dynamic behavior. In this paper, as a method to enhance the fast dynamic performance of LTV systems with bounded time-varying parameters, the approximated uncertainty of time-varying parameters are reduced by the proposed QFT parameter-scheduling control design based on radial basis function (RBF) networks.     

Output-only modal identification based on hierarchical Hough transform

Sparse component analysis (SCA) has been introduced to the output-only modal identification for several years. This paper proposes a new method based on hierarchical Hough transform to extract the modal parameters of mechanical structures. First, the measured system responses are transformed to Time-frequency (TF) domain using Short time Fourier transform (STFT) to get a sparse representation. Then, Hough transform is applied to the TF coefficients hierarchically to identify the hyperplanes and the mixing matrix is calculated. Finally, the modal responses are recovered by using l ₁ -optimization and inverse STFT. From the recovered modal responses, natural frequencies and damping ratios are extracted. Numerical simulation of a 4 Degree-of-freedom (DOF) spring-mass system verifies the validity of the method. Free vibration of a steel cantilever beam is captured by a high-speed camera and then analyzed by the proposed method. The comparison of the estimated natural frequencies and damping ratios illustrates the good performance of the proposed algorithm.     

Natural frequency extraction of a beam-moving mass system with periodic passages using its pseudo-natural frequencies

Wind turbines, helicopters, and turbo-machineries’ rotary motion, along with a variety of nonlinear structures linearized with their periodic limit cycles, may all contain time-periodic terms in their equations of motion even if the equations remain linear. The purpose of this study is to model these systems into a beam-moving mass system. Natural frequencies of the beam are calculated using past work in which pseudo-natural frequencies of a beam-moving mass system were extracted, followed by the homotopy perturbation method. The findings of this study are valuable to the industry, and they decrease error margin in resonance range assessment. This approach indicates that for beam-moving mass systems, extraction of natural frequencies that ignore the moving mass effect can lead to inaccurate results, whereas only a limited amount of physical data are needed obtain accurate calculations. Furthermore, this study used homotopy perturbation for operational modal analysis purposes and not for solving nonlinear equations.     

Identification of the beat characteristics and damping ratios of the Hwacheon World Peace Bell using wavelet transform

In this paper, a new measurement technique is proposed to identify the beat characteristics and modal damping ratios of a Korean bell in the casting field. The beat response caused by the mutual interference of mode pair with very close doublet frequency is unique feature of the Korean bell and should be accurately measured in order to quantitatively estimate the bell sound. However, the conventional method based on a filtering concept such as the Fourier transform has difficulty in extracting the beat frequencies and modal damping ratios because the method should individually decompose the measured signal into each mode. The aim of this paper is to propose an effective measurement method to identify the beat frequencies, mode pairs and modal damping ratios using the continuous wavelet transform in a real striking condition. The proposed method is verified with the Hwacheon World Peace Bell cast in the year 2008, which is the largest bell in Korea. In the future, the proposed method can be applicable to the casting field of the Korean bell to effectively estimate its beat characteristics and damping characteristics.     

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.     

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。     

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.     

Ambient vibration test of building base slab for different ground conditions

It is very important to know the dynamic behavior of base slabs of buildings in earthquake prone areas. The slabs are generally assumed as a rigid diaphragm in structural analysis and design. But their response is considerably affected from ground condition. In this study, the dynamic characteristics of a scaled base slab are determined for different ground conditions. The dimensions of the base slab model are 150 cm long, 100 cm wide and 5 cm thick. This model is designed to be smaller than 20 times from an actual building base. The base slab model is tested for the ground conditions of sand, gravel and clay–silt mixture by ambient vibration test. The dynamic characteristics, such as natural frequencies, modal damping ratios, mode shapes, are identified from collected signals by Operational Modal Analysis method. The first five modes are taken into consideration to compare the effect of ground conditions on the dynamic characteristics. It is observed that the natural frequencies, mode shapes and modal damping ratios are considerably affected from ground conditions. The highest natural frequency is obtained for the gravel ground case. The lowest natural frequency is identified for the clay–silt mixture ground case. The mode shapes changed randomly in each case. But the main modal behaviors are vertical mode and bending modes.     

基于实验数据的PCB组件模型修正和阻尼选择

基于三维CAD模型建立了某航空电子设备PCB组件的有限元仿真模型。通过有限元模态分析结果与实验模态分析结果的对比,验证了有限元模型的正确性。在此基础上进行了3种不同阻尼设置下的随机振动分析,并进行了实物的随机振动实验。分别比较了仿真和实验得到的均方根(RMS)值和功率谱密度(PSD)响应。最后得出结论:常数阻尼比0.01并叠加模态阻尼时的仿真结果与实验数据最接近;模态分析时应覆盖激励谱的全部频率。     

Effects of Joint Controller on Analytical Modal Analysis of Rotational Flexible Manipulator

Modal analysis is a fundamental and important task for modeling and control of the flexible manipulator. However, almost all of the traditional modal analysis methods view the flexible manipulator as a...     

Dynamic Stability Analysis of Linear Time-varying Systems via an Extended Modal Identification Approach

The problem of linear time-varying(LTV) system modal analysis is considered based on time-dependent state space representations, as classical modal analysis of linear time-invariant systems and current LTV system modal analysis under the ‘‘frozen-time' assumption are not able to determine the dynamic stability of LTV systems.Time-dependent state space representations of LTV systems are first introduced, and the corresponding modal analysis theories are subsequently presented via a stabilitypreserving state transformation. The time-varying modes of LTV systems are extended in terms of uniqueness, and are further interpreted to determine the system's stability. An extended modal identification is proposed to estimate the time-varying modes, consisting of the estimation of the state transition matrix via a subspace-based method and the extraction of the time-varying modes by the QR decomposition. The proposed approach is numerically validated by three numerical cases, and is experimentally validated by a coupled moving-mass simply supported beam experimental case. The proposed approach is capable of accurately estimating the time-varying modes, and provides a new way to determine the dynamic stability of LTV systems by using the estimated time-varying modes.     

On the computation of the slow dynamics of nonlinear modes of mechanical systems

A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the first step, a multiharmonic analysis of the autonomous system is performed to directly compute the amplitude-dependent characteristics of the considered nonlinear mode. In the second step, these modal properties are used to construct a two-dimensional reduced order model (ROM) that facilitates the efficient computation of steady-state and unsteady dynamics provided that nonlinear modal interactions are absent.The proposed methodology is applied to several nonlinear mechanical systems ranging form single degree-of-freedom to Finite Element models. Unsteady vibration phenomena such as approaching behavior towards an equilibrium point or limit cycles, and resonance passages are studied regarding the effect of various nonlinearities such as cubic springs, unilateral contact and friction. It is found that the proposed ROM facilitates very fast and accurate analysis of the slow dynamics of nonlinear systems. Moreover, the ROM concept offers a huge parameter space including additional linear damping, stiffness and near-resonant forcing.     

半挂牵引车车架模态分析

建立了以板壳单元为基本单元的半挂牵引车车架有限元分析模型,应用NASTRAN有限元分析软件对车架进行了模态分析。计算了该车架在自由状态下的模态参数,并分析了其振动特性和对整车性能的影响。计算结果与试验结果对比分析表明,所建立的有限元模型和分析方法是可行的,可为车架结构的进一步改进提供依据。     

Experimental modal test of the spiral bevel gear wheel using the PolyMAX method

To verify the effectiveness and correctness of free modal analysis results from a Spiral bevel gear (SBG) wheel by using Finite element method (FEM), an experimental platform was constructed through the free-hanging support of the SBG wheel. The experiment used the hammer knock percussion for excitation and a three-directional acceleration sensor as signal acquisition equipment and utilized the LMS modal analysis module. The geometric model of the SBG wheel was constructed using an eight-node octagon instead of the SBG wheel outer contour. The experiment then extracted the modal parameters of the wheel using the PolyMAX method and obtained the first- and second-order natural frequencies, damping ratios, and mode shapes of the SBG wheel at 0-7 kHz during the experimental modal test. The results of the experimental test were compared with those of the FEM free modal analysis. The first- and second-order natural frequency error rates by FEM were 0.25 % and 0.45 %, respectively. The experimental modal test result verified the rationality of the model by FEM, thus showing that the result of modal analysis by FEM is reliable and providing a basis for the dynamic characteristic analysis of SBG.     

半挂牵引车车架模态分析

建立了以板壳单元为基本单元的半挂牵引车车架有限元分析模型，应用NASTRAN有限元分析软件对车架进行了模态分析。计算了该车架在自由状态下的模态参数，并分析了其振动特性和对整车性能的影响。计算结果与试验结果对比分析表明，所建立的有限元模型和分析方法是可行的，可为车架结构的进一步改进提供依据。