Output-only modal identification approach for time-unsynchronized signals from decentralized wireless sensor network for linear structural systems

Modal parameter identification is an important content for the research on dynamic behavior of civil engineering structures. For the conventional modal parameter identification techniques, excitation signal and response signal are necessary. But excitations can not be measured for structures under natural loading conditions, or excited by random forces. So, the operational modal parameter identification approaches are developing to identify structural modal parameters by using vibration response signal directly. In this paper, a new method for modal parameter identification depending on ambient excitation response signal is proposed based on independent component analysis (ICA). For modal coordinates independent of each other, ICA can extract modal coordinates of structure and estimate mode shape matrix using vibration response signal directly. The free vibration responses can be obtained by random decrement technique (RDT) from modal coordinates which are random processes, and then the natural frequencies and damping ratios are calculated by Hilbert transform. Numerical simulation results indicate that this method is effective and suitable for output-only structural modal parameter identification.

Output-only modal dynamic identification of frames by a refined FDD algorithm at seismic input and high damping

The ancient masonry city hall in L'Aquila, Italy (Margherita Palace) that was severely damaged during the L'Aquila earthquake in April 2009 has been subjected to ambient vibration tests to determine its dynamic characteristics such as the natural frequencies, mode shapes, and damping ratios. The processing of ambient vibration responses is performed with three output-only identification approaches: (1) the frequency-domain decomposition, (2) random decrement (RD) technique combined with the eigensystem realization algorithm (ERA), and (3) the natural excitation technique (NExT) combined with ERA. Measurements were made in the palace and in the civic tower using 15 sensors in three different configurations, and the ambient vibration tests involved the simultaneous measurements of longitudinal and lateral vibrations. Lateral vibration modes for the civic tower were identified clearly; a total of five modal shapes and frequencies were identified in the frequency range 0 to 7 Hz. The modal identification in the palace was more difficult because of the severe damage; however, the two bending modes in the perpendicular directions were identified. The comparison of the three experimental techniques shows good agreement, confirming the reliability of the three identification methods. The results of the modal identification have been used to update the finite-element model of the palace. DOI: 10.1061/(ASCE)ST.1943-541X.0000494. © 2012 American Society of Civil Engineers. CE Database subject headings: Historic buildings; Masonry; Finite element method; Vibration; Structural analysis; Earthquakes; Italy. Author keywords: Output-only modal identification; Frequency domain decomposition (FDD); Eigensystem realization algorithm (ERA); Random decrement (RD); Masonry structure; Finite-element model; Ambient vibration; Identification; EMA; Operational modal analysis.

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.

The instrumented Canton Tower is a 610 m high-rise structure, which has been considered as a benchmark problem for structural health monitoring (SHM) research. In this paper, an improved automatic modal identification method is presented based on a natural excitation technique in conjunction with the eigensystem realization algorithm (NExT/ERA). In the proposed modal identification method, damping ratio, consistent mode indicator from observability matrices (CMI_O) and modal amplitude coherence (MAC) are used as criteria to distinguish the physically true modes from spurious modes. Enhanced frequency domain decomposition (EFDD), the data-driven stochastic subspace identification method (SSI-DATA) and the proposed method are respectively applied to extract the modal parameters of the Canton Tower under different environmental conditions. Results of modal parameter identification based on output-only measurements are presented and discussed. User-selected parameters used in those methods are suggested and discussed. Furthermore, the effect of environmental conditions on the dynamic characteristics of Canton tower is investigated.

In order to identify the modal parameters of time invariant three-dimensional engineering structures with damping and small nonlinearity, a novel isometric feature mapping (Isomap)-based three-dimensional operational modal analysis (OMA) method is proposed to extract nonlinear features in this paper. Using this Isomap-based OMA method, a low-dimensional embedding matrix is multiplied by a transformation matrix to obtain the original matrix. We find correspondence relationships between the low-dimensional embedding matrix and the modal coordinate response and between the transformation matrix and the modal shapes. From the low-dimensional embedding matrix, the natural frequencies can be determined using a Fourier transform and the damping ratios can be identified by the random decrement technique or natural excitation technique. The modal shapes can be estimated from the Moore–Penrose matrix inverse of the low-dimensional embedding matrix. We also discuss the effects of different parameters (i.e., number of neighbors and matrix assembly) on the results of modal parameter identification. The modal identification results from numerical simulations of the vibration response signals of a cylindrical shell under white noise excitation demonstrate that the proposed method can identify the modal shapes, natural frequencies, and ratios of three-dimensional structures in operational conditions only from the vibration response signals.

In this study the free vibration of circumferentially periodic structures has been analysed using the block Lanczos method in a semi complex domain for extracting real natural frequencies and complex mode shapes. The influence of the number of vectors in the block and also the effect of renumbering of nodes, depending on whether they are internal, adjacent or boundary nodes, on the CPU time are studied. The efficiency of the present method is compared with the subspace iteration schemes.

Structural modal parameter identification with the Power-Exponential window function

The paper summarizes the dynamic-based assessment of a reinforced concrete arch bridge, dating back to the 50`s. The outlined approach is based on ambient vibration testing, output-only modal identification and updating of the uncertain structural parameters of a finite element model. The Peak Picking and the Enhanced Frequency Domain Decomposition techniques were used to extract the modal parameters from ambient vibration data and a very good agreement in both identified frequencies and mode shapes has been found between the two techniques. In the theoretical study, vibration modes were determined using a 3D Finite Element model of the bridge and the information obtained from the field tests combined with a classic system identification technique provided a linear elastic updated model, accurately fitting the modal parameters of the bridge in its present condition. Hence, the use of output-only modal identification techniques and updating procedures provided a model that could be used to evaluate the overall safety of the tested bridge under the service loads.

Accurate and timely identification of modal parameters of long-span bridges is important for bridge health monitoring and wind tunnel tests. Wavelet analysis is one of the most advantageous methods for identification because of its good localization characteristics in both time and frequency domain. In recent years, the wavelet method has been applied more frequently in parameter identification of linear and nonlinear systems. In this article, based on wavelet ridges and wavelet skeleton, the improved modal parameter identification method was studied. To find the appropriate time-frequency resolution, an optimal wavelet basis design principle based on minimum Shannon entropy was proposed. Aiming at endpoint effect in wavelet transform, a prediction continuation method based on support vector machine (SVM) was proposed, which can effectively suppress the endpoint effect of the extended samples. In view of the fact that the ridges of metric matrices obtained by the traditional crazy climber algorithm cannot fully reflect the distribution of ridges of modulus value matrices of wavelet coefficients, an improved high-precision crazy climber algorithm was put forward to accurately identify the position of the ridge of wavelet coefficients. Finally, taking a long-span cable-stayed bridge and a long-span suspension bridge as the engineering background, improved continuous wavelet transform (CWT) was applied to modal parameter identification of bridge under ambient excitation. The modal parameters such as modal frequency, damping ratio, and mode shape were obtained. Compared with the calculation value of the numerical simulation of long-span cable-stayed bridge and wind tunnel test of long-span suspension bridge, the reliability of CWT for modal parameter identification of long-span bridges under ambient excitation was verified.

Characterization of identification errors and uses in localization of poor modal correlation

This work aims to study the dynamics of 3D plates under uniform and nonuniform temperature distributions in the framework of the space-fractional generalized thermoelasticity (S-FGT) approach. The quadratic eigenvalue problem is obtained, which means that the thermoelastic damping plays a meaningful role due to the plate’s thermal energy absorption. The plate’s complex frequency spectrum and mode shapes (free ends) under two different temperature distributions are considered for different values of the fractional continua order α and the length scale parameter l. For the first four frequencies, the fractional modes closest to the experimental results and the classical modes are presented with the absolute differences between them. For the nonuniform temperature distribution case, the mode shape analysis is performed assuming that modulus of elasticity, thermal expansion, and specific heat parameters are functions of the temperature. The primary outcomes of the paper can be stated as follows: 1) the S-FGT approach analysis gives more reliable results than the classical (local) theory; 2) the peak point of the out-of-plane mode amplitude is shifted toward the warmed zone; 3) a mode shifting is observed for the uniform temperature distribution in contrast to the nonuniform temperature distribution; 4) the fractional order derivative and length scale parameter depend on temperature, similar to other material properties such as elastic modulus, specific heat, and coefficients of thermal expansion; 5) a decrease in the fractional order is observed, while temperature increases for the fixed length scale parameter. These novelties indicate that the S-FGT approach establishes a new model for analyzing materials under heating, and the results may be beneficial for designing thermal structures.

This paper proposes a rail defect location method based on a single mode extraction algorithm (SMEA) of ultrasonic guided waves. Simulation analysis and verification were conducted. The dispersion curves of a CHN60 rail were obtained using the semi-analytical finite element method, and the modal data of the guided waves were determined. According to the inverse transformation of the excitation response algorithm, modal identification under low-frequency and high-frequency excitation was realized, and the vibration displacements at other positions of a rail were successfully predicted. Furthermore, an SMEA for guided waves is proposed, through which the single extraction results of four modes were successfully obtained when the rail was excited along different excitation directions at a frequency of 200 Hz. In addition, the SMEA was applied to defect location detection, and the single reflection mode waveform of the defect was extracted. Based on the group velocity of the mode and its propagation time, the distance between the defect and the excitation point was measured, and the defect location was predicted as a result. Moreover, the SMEA was applied to locate the railhead defect. The detection mode, the frequency, and the excitation method Were selected through the dispersion curves and modal identification results, and a series of signals of the sampling nodes were obtained using the three-dimensional finite element software ANSYS. The distance between the defect and the excitation point was calculated using the SMEA result. When compared with the structure of the simulated model, the errors obtained were all less than 0.5 m, proving the efficacy of this method in precisely locating rail defects, thus providing an innovated solution for rail defect location.

Operational modal analysis (OMA) is essential for long-term health monitoring of offshore wind turbines (OWTs), helping identifying changes in structural dynamic characteristics. OMA has been applied under parked or idle states for OWTs, assuming a linear and time-invariant dynamic system subjected to white noise excitations. The impact of complex operating environmental conditions on structural modal identification therefore requires systematic investigation. This paper studies the applicability of OMA based on covariance-driven stochastic subspace identification (SSI-COV) under various non-white noise excitations, using a DTU 10 MW jacket OWT model as a basis for a case study. Then, a scaled (1:75) 10 MW jacket OWT model test is used for the verification. For pure wave conditions, it is found that accurate identification for the first and second FA/SS modes can be achieved with significant wave energy. Under pure wind excitations, the unsteady servo control behavior leads to significant identification errors. The combined wind and wave actions further complicate the picture, leading to more scattered identification errors. The SSI-COV based modal identification method is suggested to be reliably applied for wind speeds larger than the rated speed and with sufficient wave energy. In addition, this method is found to perform better with larger misalignment of wind and wave directions. This study provides valuable insights in relation to the engineering applications of in situ modal identification techniques under operating conditions in real OWT projects.

A complex Rayleigh's Quotient is defined and explored as a means of estimating natural frequencies and damping in structures containing dissipative elements. The complex modulus or structural damping model is used to characterize the damping elements, leading to complex stifrhess matrices. Estimates of the resulting complex mode shapes are then used in the Complex Rayleigh Quotient to produce the desired estimates of a complex natural frequency, from which natural frequencies and damping may be determined. Demonstrations of the application to both discrete and continuous systems are given, and suggest that the method is an effective means of providing satisfactory estimates of frequencies and loss factors for damped systems. Introduction In this paper, an approximate method for predicting natural frequencies and damping in structures is considered. The Complex Rayleigh Quotient is suggested for use in the analysis of structures whose components have out of phase displacements. The method produces an estimate of the complex natural frequency for the system from a quotient of terms similar in form to Rayleigh's Quotient. The terms in this quotient are developed from approximations to the complex modes of the system. The system damping may then be estimated from the ratio of imaginary to real parts of the complex frequency. The form of the Complex Rayleigh Quotient is first considered for discrete linear damped systems, modeled with a complex stiffness (i.e., a structural damping model). A two degree of freedom system is used to illustrate the method, which is then applied through an iterative process to a five degree of freedom system. The Complex Rayleigh Quotient is then applied to continuous systems, and is illustrated with constrained layer damping treatments of various configurations.. Approximate complex solutions for constraining layer displacements are * Professor of Aerospace Engineering and Engineering Mechanics; Fellow: AIAA, ASME. Formerly Graduate Student; now Technical Manager, Vibration and Acoustics Section, Wright Laboratories. found by solving the constraining layer equations after approximating the deflections of the underlying structure by the corresponding undamped mode shape(s). Results from using this approach are compared with an exact solution. If real-valued approximations to the mode shapes are used, the Complex Rayleigh Quotient method is found to be equivalent to the Modal Strain Energy approach. It is demonstrated, for both discrete and continous systems, that the Complex Rayleigh Quotient produces a better estimate of the loss factor than does the Modal Strain Energy approach Ravleigh's Quotient Rayleigh's Quotient, based on the principle that a conservative system vibrating at a natural frequency has maximum system kinetic energy equal to the maximum system potential energy, is a popular means of estimating frequencies in linear undamped vibratory' systems More detailed treatments are available' Rayleigh's Quotient is obtained by setting expressions for maximum kinetic and maximum strain energy equal to each other, then solving for the natural frequency, fl. To apply Rayleigh's Quotient to a general system consisting of N individual components, estimates of the mode shape are used to estimate the maximum kinetic energies, Q Ta and maximum strain energies, Un , of each component of the system. The form of Rayleigh's Quotient then becomes: