Mode isolation: a new algorithm for modal parameter identification.

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 eigensystem realization algorithm based data-driven approach for extracting electromechanical oscillation dynamic patterns from synchrophasor measurements in bulk power grids

This work is placed on the scope of characterization and modeling of structures and the central objective is to establish a computer code capable to provide models for structures of interest from practical experimentation, to be used to refine the computer models a posteriori. To realize that project, the experimental modal analysis was applied in the Eigensystem Realization Algorithm – ERA. As well as most of the techniques of identification of dynamic of systems, the ERA also creates the compute modes, being necessary the application of procedures for filtering the real modes before the noises and/or computers modes. In this work, two techniques for the distinction were used: Modal Amplitude Coherence (MAC) and Modal Singular Value (MSV). Beside this, a novel approach to help interpret and filter based in MSV deviation was proposed and tested, producing good results. To achieve this, a computer code that receives experimental data and returns the global properties of the system, i.e., the natural frequencies, the damping factors and the mode shapes was developed. The preliminary results, developed in the know structure, indicate the code has the potential to handle with complex geometries.

The Alfred Zampa Memorial Bridge (AZMB), a newly built long-span suspension bridge, is located 32km northeast of San Francisco on interstate Highway I-80. A set of dynamic field tests were conducted on the AZMB in November 2003, just before the bridge opening to traffic. These tests provided a unique opportunity to identify the modal properties of the bridge in its as-built condition with no previous traffic loads or seismic excitation. A benchmark study on modal identification of the AZMB is performed using three different state-of-the-art system identification algorithms based on ambient, as well as forced vibration measurements. These system identification methods consist of: (1) the multiple-reference natural excitation technique combined with the eigensystem realization algorithm; (2) the data-driven stochastic subspace identification method; and (3) the enhanced frequency domain decomposition method. Overall, the modal parameters identified using these system identification methods are found to be in very good agreement for each type of tests (ambient and forced vibration tests). For most vibration modes, the natural frequencies and mode shapes identified using the two different types of test data also match very well. However, the modal damping ratios identified from forced vibration test data are, in general, higher than those estimated from ambient vibration data. The identified natural frequencies and mode shapes are finally compared with their analytical counterparts from a three-dimensional finite-element model of the AZMB. The modal properties of the AZMB presented in this paper can be used as baseline in future health monitoring studies of this bridge.

The present paper combined the natural environment excitation technology (NExT) with the eigen system realization algorithm (ERA) to identify the modal parameters of a suspension bridge. Firstly, the critical parameters in NExt–ERA, such as record length, window length, and ranks of the Hankel matrix, and their influence on identification accuracy have been discussed. Subsequently, based on the acceleration series obtained from the Xihoumen Bridge Health Monitoring System, 3015 sets of modal frequencies and modal damping ratios of the Xihoumen Bridge were identified under 7 sets of wind speeds by the NExt–ERA. Finally, the probability distribution and confidence interval of the structural modal damping ratios were analyzed. Besides, the dependence of identified frequencies damping ratios on wind speed was also discussed. The results show that at the same wind speed, the mean value, and variance of the torsional and lateral mode damping ratios are larger than those of the vertical mode, but this difference gradually decreases with the increment of wind speed. The modal damping ratios along three directions under different wind speeds all follow the generalized extreme value distribution, but wind speed affects the tailing properties of probability distribution of the vertical and torsional mode damping ratios. The estimated damping ratios could provide references for structural design and vibration control of similar long-span bridges.

Study on applicability of two modal identification techniques in irrelevant cases is made in this paper. The following techniques are considered: peak picking based on correlation analysis (PP-CA), dedicated for ambient vibrations and eigensystem realization algorithm (ERA), formulated for free-decay vibrations investigation. Irrelevant cases are found when analyzed signals are different than recommended to a given technique. The study is conducted on examples of two real structures: masonry tower and steel railway bridge. Both cases are diverse in age, material, excitation and vibrations energy. The signals measured on the tower are suitable for the PP-CA technique (ambient vibrations), while the signals measured on the bridge are suitable for the ERA (free-decay vibrations). However, both methods have been applied to both systems. Natural frequencies, mode shapes and damping ratios are identified and the effectiveness of the irrelevant technique is assessed in relation to the results obtained by the relevant method in each case.

Accurate estimation of structural parameters such as the natural frequencies, modal shapes and damping ratios is important for both numerical modelling and structural health monitoring, and ambient vibration analysis is usually used for the estimation. Although the Eigensystem Realization Algorithm (ERA) is widely used, the results are known to depend on the selection of the calculation parameters. In this study, first the sensitivity of the calculation parameters of the NExT-ERA method for the full-scale measurement data of a 2,4MW wind turbine is studied to provide reference for practical application of the method. Small initial model order resulted in unstable estimation of the damping ratios, while higher values gave robust results. The optimum value for the initial model order was 400 to 600, which was much larger than the recommendation in the literature as four times the model order. The optimal values for the correlation length parameter are 3500 to 4000 for the 1st modes, and 100 to 350 for the 2nd modes, which corresponds to the length of the free decay process seen in the cross- correlation function. Higher number of points used for FFT gave lower damping ratios for the 1st mode in both fore-aft and side-side directions. The effect of the number of the FFT points is smaller in 2nd mode, which may be due to difference of the length of data required to capture the characteristics of the system. The structural parameters estimated with NExT-ERA method agreed well with the results of the previously conducted forced vibration test except for the fore-aft 1st mode damping ratio, of which value was especially small compared to other modes.

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.

With complex structures, comparison of independently derived sets of experimental modal parameters is an excellent way to increase confidence in the results. This paper presents modal identification results using the Eigensystem Realization Algorithm (ERA) on frequency response functions from the modal test of the Space Station Resource Node. The Resource Node is the first U.S-built structure for the International Space Station. The modal test was conducted by the NASA Marshall Space Flight Center (MSFC) in January 1997 for the Boeing Company, who designed and built the Node. The ERA-calculated parameters are compared with independent results obtained by the MSFC test team using commercial software. There was excellent correlation of mode shapes between the two sets of results for the first 21 vibration modes of the structure up to 35Hz. From 35 to 50 Hz, about 60 percent of 25 additional modes had excellent correlation. Natural frequencies and damping factors of most modes agreed within 0.1 Hz and 0.2 percent, respectively.

Dynamic monitoring of an offshore jacket platform based on RTK-GNSS measurement by CF-CEEMDAN method

Characteristic value decomposition: A unifying paradigm for data-driven modal analysis

Damage identification methods for engineering structures based on vibration parameters have the advantages of easy detection and high precision; however, structural strain information is more sensitive to structural damage than displacement information. Traditional resistance strain sensors have low accuracy and poor stability when measuring structural strains. Therefore, this paper uses a highly sensitive polyvinylidene fluoride dynamic strain sensor to identify structural damage in a thin plate. The polyvinylidene fluoride sensor is used to obtain structural strain response information, and structural modal parameters are identified using operational modal identification methods based on the natural excitation technique and the eigensystem realization algorithm. This paper uses a damage index based on mode shape and flexibility. A new damage index based on the LU decomposition of the flexibility matrix is used to identify the damage of the thin plate structure. The effectiveness of the modal identification methods and the new damage index is validated via an elastic thin plate experiment. The results show that the modal identification method and the new damage index proposed in this paper can identify damage in a thin plate structure. Sensor comparison experiments also show that compared with a resistance strain sensor, the polyvinylidene fluoride sensor has higher damage sensitivity, better damage recognition and the ability to recognize farther from the sensor.

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.

An algorithm to estimate multiple-input, multiple-output, time-series models for structural system identification using short time histories is presented. The method uses order overspecification to reduce estimation bias and automatically sorts identified system modes from computational modes. The system natural frequencies, damping factors, mode shapes, and modal participation factors are estimated and can be used to reconstruct singleinput, single-output models for every input-output pair. Experimental data from a large cantilevered flexible truss are used to demonstrate the technique. Modal estimates are comparable to those obtained using accepted methods such as the eigensystem realization algorithm.

This project investigates the structural dynamics and vibration of a model that closely approximates real-world conditions. Obtaining model incorporates the critical parameters of density, stiffness, and damping to effectively simulate mode shapes and floor displacements under natural frequencies, by varying these factors, the project aims to minimize mode shapes, thus optimize structural performance. The study demonstrates the importance of considering different kinds of damping in structural models and highlights the practical applications of our model in selecting appropriate materials and dampers. Future research can enhance this model through occupancy load, environmental forces and other factors, so as to further improve its accuracy and relevance to real situations.