A synthesis of peak picking method and wavelet packet transform for structural modal identification

Large scale tests with progressive damage on a prestressed concrete highway bridge have been performed to investigate the sensitivity of several damage detection, localization, and quantification methods based on modal parameters. To investigate the quality of modal parameters, the data set of one damage step was analyzed by several output-only identification techniques. Although the bridge was severely cracked, natural frequencies as well as mode shapes display only minor changes. However, the relative changes of mode shapes are larger than those observed for natural frequencies. A novel damage indicator, called mode shape area index, based on changes of mode shapes, has been developed and found as the most sensitive damage detection approach. Damage detection or localization via changes of the flexibility matrix performed better than natural frequencies or mode shapes alone. The application of the direct stiffness calculation and a sensitivity-based model update technique showed results having a high level of ambiguity about the location and quantification of damage also at the highest damage level. Evaluating the information collected in this study the test results indicate that an early stage damage identification in prestressed concrete bridges is hardly possible because of the nearly complete recovery of stiffness after closing of cracks in prestressed concrete and the effect of environmental parameters on modal data.

Automated identification and long-term tracking of modal parameters for a super high-rise building

sAircrafts with high Mach speeds are exposed to severe thermal load, which affect the performance of aircraft components. Although several experimental studies have been performed on the mechanical behavior of aircraft structures subjected to high temperatures, the experimental research on dynamic characteristics of structures under thermal load is limited. In this work, a series of laboratory modal tests have been carried out on carbon fiber reinforced silicon carbide matrix (C/SiC) composite plates under various radiant-heating conditions. High temperatures are achieved using quartz lamps, and their dynamic responses are measured using a scanning laser vibrometer. The modal parameters are evaluated by PolyMAX at several static temperature distributions. The temperatures are acquired by both full-field noncontacting infrared thermography and contacting thermocouples. The flat plates are with both free and constrained boundary conditions and the high temperature modal survey are performed for two kinds of thickness. The stiffened plate with free boundary condition is further studied as a more practical structure. Both the changes of the modal frequency and modal shape as temperature rises are presented. The effects of the thermal loads on the modal characteristics are investigated by test. The results show that the thermal stresses have a much greater effect on the modal characteristics than the change of the material properties due to heating. The test results could provide technical material for the limited database of high-temperature modal testing results.

Experimental method for modal parameter identification of civil engineering structures based on improved wavelet transform

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.

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.

In vibration based modal identification of railways bridges, if the mass of the train is not negligible as compared to that of the bridge, the modal parameters of the train-bridge system becomes time-varying, making modal identification challenging. In this study, a method is developed to identify such time-varying modes of a train-bridge system using moving train induced vibration data. The method utilizes the continuous but gradual variation in the modal parameters to perform a window-wise identification of these parameters. In each time window, an auto-regressive model of the system is first identified, which is then used to identify the modes in that window using the Eigensystem Realization Algorithm. A damage index, based on damage locating vectors, to detect damage location using such identified time-varying modes is also discussed. The proposed time-varying modal identification and damage detection methods are illustrated using laboratory experimental data from a two span continuous steel bridge, as well as a damaged version of the bridge, excited using a moving laboratory scale model train.KeywordsTime varying systemAuto regressive modelEigensystem realization algorithmDamage locating vectorMoving train laboratory experiment

Damage detection based on measured vibration data has received intensive studies recently. Frequently, the damage to a structure may be reflected by a change of some system parameters, such as a degradation of the stiffness. In this paper, we apply a method to nondestructively locate and estimate the severity of damage in corrosion pipeline for which a few natural frequencies or mode shapes are available. The method is based on the strain modal sensitivity ratio (SMSR) and the orthogonality conditions sensitivities (OCS) applied to vibration features identified during the monitoring of the pipeline. The advantage of these methods is that it only requires measuring few modal parameters. The SMSR-based and OCS-based damage detection methods are illustrated using computer-simulated and laboratory testing data. The results show that the current method provides a precise indication of both the location and the extent of corrosion pipeline.

Performing forced vibration tests on full-scale structures is the most reliable way of determining the relevant modal parameters in structural dynamics, such as modal frequencies, mode shapes, modal damping, and modal masses. This study describes the modal identification of a double-level curved cable-stayed bridge with separate deck systems for pedestrians and vehicles via forced vibration tests. The steady-state structural responses to sinusoidal excitations produced by an electrodynamic shaker are recorded under varying excitation frequencies, and the frequency response functions are established. The measured frequency response functions are curve fitted to estimate the modal parameters. The numerical simulation of frequency response function–based modal parameter identification of an elastically multi-supported continuous beam structure is carried out, and the emphasis has been placed on the evaluation of the effect of an additional shaker mass, excitation frequency step and range, multi-mode vibration, and noise on identification results. Finally, the modal parameters for the first lateral mode of a double-level curved cable-stayed bridge are identified by forced vibration experiments, and the results are compared with those from ambient vibration tests and free vibration tests. The effect of the unmeasured wind excitation on identification is discussed. It is shown that the effect of ambient vibration is minor for wind velocity of 3–5 m/s. The damping ratios identified by forced and free vibration tests are comparable, while those from ambient vibration are subject to large variations. The modal mass obtained from forced vibration tests is in good agreement with finite element prediction, which provides design basis for mass-type dampers.

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.

<p>FE model updating has mostly been performed relying upon natural frequencies and mode shapes. These modal parameters only provide global information about the structure, which leads to important uncertainties. The recent development of fiber optic strain sensors has made it possible to include modal strains in FE model updating. In this paper, it is investigated how including modal strains in FE model updating allows complementing the global information on natural frequencies and mode shapes by the local information in modal strains. Including modal strains can be of major benefit for identification of local damage. With the additional information obtained using modal strains, local uncertainties in FE model updating can be effectively reduced. The benefit of including modal strains in FE model updating is illustrated using modal data from numerical simulations on a reinforced concrete (RC) beam.</p>

Modal analysis has developed into a major technology for the study of structural dynamics in the past several decades. Through it, complex structural dynamics phenomena can be represented in terms of structural invariants, i.e., the modal parameters: natural frequencies, damping ratios and mode shapes. Operational Modal Analysis (OMA) deals with the estimation of modal parameters on vibration data measured for operational conditions, when the excitation on the structure is not measured. In this work, OMA is performed on a wind turbine blade undergoing wind tunnel testing. These tests included different wind speeds, pitch angles and also different health conditions of the blade, where masses of different magnitude were fixed to the blade on different locations to emulate damage conditions. In order to monitor the modal parameters across multiple days of varied tests in the wind tunnel, the Polymax modal parameter estimator was implemented, coupled with an Automated Modal Analysis methodology. This methodology included an automatic modal parameter selection technique, using a Machine Learning (ML) clustering algorithm, coupled with a modal tracking procedure which applied statistical thresholds on the modal parameters’ values. The tracking procedure searches for modes similar to the ones calculated for healthy conditions. The results show how the modal parameters of the wind turbine blade vary with the different measured conditions in the wind tunnel. Moreover, a damage detection methodology is implemented to differentiate between the healthy and damaged conditions on the blade, by leveraging an anomaly detection algorithm using the Multivariate Gaussian Distribution (MGD). This algorithm takes as input the modal parameters calculated by the previous Automated Modal Analysis methodology and detects statistical deviations among them which could indicate the presence of damage. All steps of this work contribute to developing an automatic framework able to detect damages on a wind turbine blade, and therefore perform Structural Health Monitoring (SHM) for different operational conditions.

Structural damage and its extent can be detected by vibration-based techniques to avoid failure or to minimize maintenance. Among different damage identification techniques, modal curvature approaches are widely researched and applied one. On the contrary, wavelet transformation (WT) methods are gaining popularity in damage identification of real life buildings because of their suitability for non-stationary signals and non-dependency on baseline data. This paper presents a novel approach utilizing complex continuous wavelet to effectively locate change in physical properties of reinforced concrete (RC) buildings by virtue of variation in frequency and mode shapes due to small change in mass and stiffness. In this paper, the effect of variation of mass and stiffness of a building on the modal parameters is established analytically using theequation of motion for a multi-degree freedom system under forced vibration condition. A 3-D finite element model was developed for predicting the modal frequencies and mode shapes of the scaled down six storey RC building and the effect of addition of mass on a particular level of structure on the modal parameters was studied. Further, acceleration time histories were recorded with variation in mass on 3rd story of building using wireless tri-axial accelerometers and the time histories were processed to arrive at Curvature Damage Factor and wavelet coefficients for identification of the additional load on the particular floor. Vibration responses from all floors of RC building in ambient and loaded conditions were analyzed for frequency response spectra (FRS). Mode shapes were drawn for unloaded case and loaded cases. It was observed that the modal frequency of building decreases with the increase in mass at floors. It is observed that CDF approach could detect the change in mass in both numerical and experimental results. However, CDF algorithm could not detect the addition of load in case 1, 2 and 3, i.e. when load was less than 25 kg, i.e. only 2.6% of floor mass (960 kg). The acquired data for the above stated load cases were analyzed using complex Gaussian ‘cgau5’ wavelet in MATLAB toolbox to determine the singularity in the signal in terms of wavelet coefficient modulus. It is observed that the WT approach is able to precisely locate the change in physical parameters of the RC model building. However, it is seen that additional load could not be detected in case where only 9 kg, i.e. 0.93% of the total floor mass, was placed on 3rd floor. From the research work, it is observed that CDF technique is inefficient in damage detection and always demand prior baseline information, which is usually difficult to obtain in practice. However, the wavelet transform-based approach more accurately detects the location of change without relying on intact state vibration data.

Modal parameter identification via ambient vibration is popular but faces challenges from uncertainties due to unknown inputs and low signal‐to‐noise ratio. Bayesian methods are gaining increasing attention for operational modal identification due to their ability to quantify uncertainties. However, improvements in computational efficiency are needed, particularly when addressing numerous modes and degrees of freedom. To address this challenge, this study proposes an innovative approach, termed the “Bayesian spectral decomposition” method (BSD), employing the decompose‐and‐conquer strategy. This novel method, operating within the frequency domain, identifies each mode individually by exploiting their inherent separated modal characteristics. For each mode, the response spectrum matrix undergoes an eigenvalue decomposition, yielding crucial eigenvalues (incorporating frequency and damping information) and eigenvectors (containing mode shape information). Subsequently, statistical properties of the eigenvalues and eigenvectors are utilized to establish likelihood functions for Bayesian parameter identification. By combining prior information, the posterior probability distribution functions of modal parameters are derived. The optimal solution is then obtained by resolving the maximum posterior probability distribution function problem. To further quantify the uncertainty of modal parameters, Gaussian distributions are employed to approximate the posterior probability distribution functions. The adoption of the decomposition approach circumvents the joint identification of all modal parameters, substantially reducing the parameter dimensions for optimization. Consequently, this strategy leads to decreased computational complexity and significantly improved computational stability. The effectiveness of the BSD is confirmed through simulated data generated from an 8‐story shear building as well as measured data collected from both an experimental shear frame and the Canton Tower. The results demonstrate that the proposed method achieves high accuracy in identifying modal parameters, greatly improves computational efficiency, and effectively quantifies the uncertainties in modal parameters.

Complex modal testing is employed for parameter identification of a four-axis active magnetic bearing system. In the test, magnetic bearings are used as exciters while the system is in operation. The experimental results show that the directional frequency response function, which is properly defined in the complex domain, is a powerful tool for identification of bearing as well as modal parameters.