Modal Identification Techniques Research Articles

The use of operational modal analysis in the process of modal parameters identification in a rotating machine supported by roller bearings

This paper investigates the use of conventional operational modal analysis (OMA) techniques for modal parameters identification of a rotating system supported by roller bearings. Although largely applied in civil engineering, in-depth studies on different types of systems are still limited in the literature. The novel of the paper is to address such issue by applying conventional OMA methods, such as enhanced frequency domain decomposition (EFDD) and stochastic subspace identification (SSI-data), to identify the modal parameters of a rotating machine, investigating the challenging particularities of these systems due to their inherent operating conditions, especially regarding the presence of harmonic forces, eventually closed-spaced modes, and non-proportional damping due to the bearings. The results presented in the experimental tests showed that, with the use of specific tools, in comparison with traditional experimental modal analysis (EMA), the used OMA methods have managed to successfully identify the modal parameters of a roller bearing supported rotor.

Modal identification of concrete dams under natural excitation

Historically, the dynamic testing of concrete dams has been associated with experimental modal analysis (EMA) and the performance of forced vibrations tests. Nevertheless, this type of tests requires the use of a heavy equipment and the interruption of the regular operation of the structure. An alternative to EMA relies on the application of operational modal analysis (OMA), through the performance of ambient vibration tests, and thus, it is essential to investigate if the application of OMA to concrete dams can provide good results with high levels of accuracy. In this context, this work addresses the performance of ambient vibration tests on concrete dams with quite diverse geometrical attributes and on the application of state-of-art output-only modal identification methods, to gain awareness of the issues that may occur during the application of OMA methods to signals with such low amplitudes (of the order of micro g), such as those that are usually recorded when dealing with these massive structures. More specifically, the paper describes the ambient vibration tests executed on six very different concrete dams. The most relevant modal properties are estimated through the application of modern output-only modal identification techniques, stressing the good level of accuracy achieved, which is quantified through the calculation of modal properties’ uncertainties. Finally, a novel approach considering the uncertainties estimated is used to study the effect of noise on the quality of modal estimates and to qualify the adequacy of sensors to perform these tests on dams.

Modal Parameter Identification Based on Hilbert Vibration Decomposition in Vibration Stability of Bridge Structures

Modal parameters are important parameters for the dynamic response analysis of structures. An output‐only modal parameter identification technique based on Hilbert Vibration Decomposition (HVD) is developed herein for structural modal parameter identification to (1) obtain the Free Decay Response (FDR) of a structure through free vibration or ambient vibration tests, (2) decompose the FDR into modal responses using HVD, and (3) calculate the instantaneous frequencies and instantaneous damping ratios of the modal responses to obtain the modal frequencies and modal damping ratios. A series of numerical examples are examined to demonstrate the efficiency and highlight the superiorities of the proposed method relative to the empirical model decomposition‐based (EMD‐based) method. The robustness of the proposed method to noises is also investigated and proved to be positive effect. The proposed method is proved to be efficient in modal parameter identification for both linear and nonlinear systems, with better frequency resolution, and it can be applied to systems with closely spaced modes and low‐energy mode.

Estimation of Damping for a Double-Layer Grid Using Input-Output and Output-Only Modal Identification Techniques

In large civil engineering structures, the output-only modal identification is the most applicable technique for estimating the modal parameters such as damping. However, due to no measurement and control of excitation force, the identified parameters obtained by output-only technique have more uncertainty than those derived from the input-output technique. Given the different nature and uncertainties of the two modal identification techniques, in the present study, the damping related to the first 12 modes of a double-layer grid developed from the ball joint system were identified via the two techniques and compared with each other. For this purpose, a double-layer grid was constructed by pipes and balls with free-free boundary conditions provided for both input-output and output-only experiments. Exciting the grid, its acceleration response was measured at appropriate degrees of freedom. Then, by using these data and performing modal analysis, involving four different methods of input-output and five different methods of output-only, the natural frequencies and damping ratios of the desired modes were extracted. The results indicated that despite the good agreement between the modal damping of the grid, as identified by different methods of input-output together and by different methods of output-only together, the results of input-output and output-only methods were different with each other. The damping values through the input-output modal identification methods were on average 65% higher than the corresponding values of the output-only modal identification methods.

A review of operational modal analysis techniques for in-service modal identification

Vibrations are the root cause of many mechanical and civil structure failures. Dynamic characteristics of a structure must be extracted to better understand structural vibrational problems. Modal analysis is used to determine the dynamic characteristics of a system like natural frequencies, damping ratios and mode shapes. Some of the applications of modal analysis include damage detection, design of a structure/machine for dynamic loading conditions and structural health monitoring. The techniques used for modal analysis are experimental modal analysis (EMA), operational modal analysis (OMA) and a less known technique called impact synchronous modal analysis (ISMA), which is a new development. EMA is performed in simulated controlled environment, while OMA and ISMA are performed when the system is in operation. Although EMA is the oldest modal analysis technique, there is an increasing interest in operational modal analysis techniques in recent years. In this paper, operational modal analysis techniques OMA and ISMA are reviewed with their development over the years and their pros and cons discussed.

Bayesian operational modal analysis of a long-span cable-stayed sea-crossing bridge

Sea-crossing bridges have attracted considerable attention in recent years as an increasing number of projects have been constructed worldwide. Situated in the coastal area, sea-crossing bridges are subjected to a harsh environment (e.g. strong winds, possible ship collisions, and tidal waves) and their performance can deteriorate quickly and severely. To enhance safety and serviceability, it is a routine process to conduct vibration tests to identify modal properties (e.g. natural frequencies, damping ratios, and mode shapes) and to monitor their long-term variation for the purpose of early-damage alert. Operational modal analysis (OMA) provides a feasible way to investigate the modal properties even when the cross-sea bridges are in their operation condition. In this study, we focus on the OMA of cable-stayed bridges, because they are usually long-span and flexible to have extremely low natural frequencies. It challenges experimental capability (e.g. instrumentation and budgeting) and modal identification techniques (e.g. low frequency and closely spaced modes). This paper presents a modal survey of a cable-stayed sea-crossing bridge spanning 218 m+620 m+218 m. The bridge is located in the typhoon-prone area of the northwestern Pacific Ocean. Ambient vibration data was collected for 24 h. A Bayesian fast Fourier transform modal identification method incorporating an expectation-maximization algorithm is applied for modal analysis, in which the modal parameters and associated identification uncertainties are both addressed. Nineteen modes, including 15 translational modes and four torsional modes, are identified within the frequency range of [0, 2.5 Hz].

A dynamic vehicle-bridge model based on the modal identification results of an existing EN57 train and bridge spans with non-ballasted tracks

This paper addresses the methodology of the bridge-vehicle dynamic model definition based on the free response measurements of an existing train and existing bridge spans. In the case of the railway vehicle, the methodology uses the impulse excitations of a single car by means of the wedge method. In the case of the bridge spans, free responses are collected after the passages of trains. The global modal parameters (frequencies and modal damping) of both structures are identified using two modal identification techniques, i.e., the eigensystem realization algorithm (ERA) and the peak picking method (PP). A simplified single-suspension model of the vehicle with 11 global dof’s is proposed that can be useful in the bridge-vehicle interaction analysis. Two steel spans having non-ballasted tracks are the bridge structures. Field tests are conducted to identify the modal parameters and validate the numerical models. Finally, numerical simulations of the train passing over the bridges are compared with the in situ measurements performed under operating conditions.

A validated robust and automatic procedure for vibration analysis of bridge structures using MEMS accelerometers

Abstract Today, short- and long-term structural health monitoring (SHM) of bridge infrastructures and their safe, reliable and cost-effective maintenance has received considerable attention. From a surveying or civil engineer’s point of view, vibration-based SHM can be conducted by inspecting the changes in the global dynamic behaviour of a structure, such as natural frequencies (i. e. eigenfrequencies), mode shapes (i. e. eigenforms) and modal damping, which are known as modal parameters. This research work aims to propose a robust and automatic vibration analysis procedure that is so-called robust time domain modal parameter identification (RT-MPI) technique. It is novel in the sense of automatic and reliable identification of initial eigenfrequencies even closely spaced ones as well as robustly and accurately estimating the modal parameters of a bridge structure using low numbers of cost-effective micro-electro-mechanical systems (MEMS) accelerometers. To estimate amplitude, frequency, phase shift and damping ratio coefficients, an observation model consisting of: (1) a damped harmonic oscillation model, (2) an autoregressive model of coloured measurement noise and (3) a stochastic model in the form of the heavy-tailed family of scaled t-distributions is employed and jointly adjusted by means of a generalised expectation maximisation algorithm. Multiple MEMS as part of a geo-sensor network were mounted at different positions of a bridge structure which is precalculated by means of a finite element model (FEM) analysis. At the end, the estimated eigenfrequencies and eigenforms are compared and validated by the estimated parameters obtained from acceleration measurements of high-end accelerometers of type PCB ICP quartz, velocity measurements from a geophone and the FEM analysis. Additionally, the estimated eigenfrequencies and modal damping are compared with a well-known covariance driven stochastic subspace identification approach, which reveals the superiority of our proposed approach. We performed an experiment in two case studies with simulated data and real applications of a footbridge structure and a synthetic bridge. The results show that MEMS accelerometers are suitable for detecting all occurring eigenfrequencies depending on a sampling frequency specified. Moreover, the vibration analysis procedure demonstrates that amplitudes can be estimated in submillimetre range accuracy, frequencies with an accuracy better than 0.1 Hz and damping ratio coefficients with an accuracy better than 0.1 and 0.2 % for modal and system damping, respectively.

Evaluation of natural periods and modal damping ratios for seismic design of building structures

A comprehensive technique for identification of modal properties (i.e. natural periods and equivalent modal damping ratios) of building structures is presented. The proposed identification technique employs a combination of multiple system identification methods; it utilizes the benefits and suppresses the shortcomings of each method to provide a succinct set of modal properties for building structures. Using the proposed modal identification technique, modal properties of 80 buildings with a total of 896 distinct seismic event and building direction records were identified. Simplified and practical equations for modal quantities along with the variation of such parameters for different structural system types, building height, and amplitude of excitation are studied and presented. A critical assessment of other similar studies and results are presented.

Study on applicability of two modal identification techniques in irrelevant cases

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.

A strategy for decoupling of nonlinear systems using the inverse sub-structuring method and the parametric modal identification technique

The inverse sub-structuring method has been proposed and further developed for multi-component systems to predict the component-level frequency response functions (FRFs) only by the system-level FRFs. The previous methods are all based on the assumption that the system is linear. However, nonlinear systems are more common in engineering practices. This study aims to extend the linear inverse sub-structuring method for nonlinear systems, which can be applied to predict the FRFs of nonlinear substructure only from the system-level FRFs of the coupled nonlinear system. The formulations for nonlinear systems whose nonlinearity is previously known and only displacement-dependent is derived and verified by both lumped parameter models and FEA study. It should be noted that the nonlinear systems with known nonlinearity type and its location, and the nonlinearity can be modeled as a single nonlinear element between two coordinates. The results of the predicted nonlinear FRFs for the component are compared with those directly by measured, showing good agreement. The suggested new nonlinear inverse sub-structuring method is helpful for nonlinear component dynamics identification and/or nonlinear system vibration control.

Post‐installation adaptation of offshore wind turbine controls

AbstractThe cost of offshore wind energy can be reduced by incorporating control strategies to reduce the support structures' load effects into the structural design process. While effective in reducing the cost of support structures, load‐reducing controls produce potentially costly side effects in other wind turbine components and subsystems. This paper proposes a methodology to mitigate these side effects at the wind farm level. The interaction between the foundation and the surrounding soil is a major source of uncertainty in estimating the safety margins of support structures. The safety margins are generally closely correlated with the modal properties (natural frequencies, damping ratios). This admits the possibility of using modal identification techniques to reassess the structural safety after installing and commissioning the wind farm. Since design standards require conservative design margins, the post‐installation safety assessment is likely to reveal better than expected structural safety performance. Thus, if load‐reducing controls have been adopted in the structural design process, it is likely permissible to reduce the use of these during actual operation. Here, the probabilistic outcome of such a two‐stage controls adaptation is analyzed. The analysis considers the structural design of a 10 MW monopile offshore wind turbine under uncertainty in the site‐specific soil conditions. Two control strategies are considered in separate analyses: (a) tower feedback control to increase the support structure's fatigue life and (b) peak shaving to increase the support structure's serviceability capacity. The results show that a post‐installation adaptation can reduce the farm‐level side‐effects of load‐reducing controls by up to an order of magnitude.

Damping estimation of a double layer grid with ball joint system by output-only modal identification

Modal parameters of large civil engineering structures such as modal damping ratios (MDRs) are determined mainly by output-only modal identification. In this paper, MDRs of a double layer grid were obtained using output-only modal identification. For this purpose, a double layer grid constructed from ball-joint system was tested. Doing some random tapping on the structure, the acceleration response in multiple locations was measured. The acquired data was processed using output-only modal identification to arrive at MDRs. The MDRs corresponding to the first eight modes of the grid were extracted by five output-only modal identification techniques; namely enhanced frequency domain decomposition (EFDD), curve-fit frequency domain decomposition (CFDD) and three different methods of data-driven stochastic subspace identification. To determine the appropriate model order used in SSI methods, a sensitivity analysis was carried out and the resulting number of order was 200. The proper frequency resolution of 1600 was also determined to estimate the MDRs of the grid by EFDD and CFDD. The results showed that the MDRs of the grid, obtained from different methods, are in good agreement with each other. The grid has very low MDRs, as the MDRs of the modes measured from different methods varied from 0.06% to 0.11%.

A Toolbox for Analyzing and Testing Mode Identification Techniques and Network Equivalent Models

During the last decade the dynamic properties of power systems have been altered drastically, due to the emerge of new non-conventional types of loads as well as to the increasing penetration of distributed generation. To analyze the power system dynamics and develop accurate models, measurement-based techniques are usually employed by academia and power system operators. In this regard, in this paper an identification toolbox is developed for the derivation of measurement-based equivalent models and the analysis of dynamic responses. The toolbox incorporates eight of the most widely used mode identification techniques as well as several static and dynamic network equivalencing models. First, the theoretical background of the mode identification techniques as well as the mathematical formulation of the examined equivalent models is presented and analyzed. Additionally, multi-signal analysis methods are incorporated in the toolbox to facilitate the development of robust equivalent models. Additionally, an iterative procedure is adopted to automatically determine the optimal order of the derived models. The capabilities of the toolbox are demonstrated using simulation responses, acquired from large-scale benchmark power systems, as well as using measurements recorded at a laboratory-scale active distribution network.

Fisher information-based optimal input locations for modal identification

A method is proposed to determine optimal locations of input forces for experimental modal analysis. The input locations are optimal in a sense that the measured vibration responses, under inputs thus located, contain maximum information about unknown modal parameters of interest. These optimal input locations are obtained by maximizing the trace of the associated Fisher Information Matrix (FIM). Analytical expressions are obtained for the different derivatives involved, by expressing acceleration responses in terms of pseudo-modal responses. A dimensionless scaling is introduced to normalize the effect of different types of modal parameters. An explicit relation is also derived between the FIM and the mode shape components at input locations. It is shown that, in certain experimental scenarios, this relation may be used to directly obtain the optimal input locations from only the mode shapes. An extensive series of numerical simulations, including situations of single/multiple inputs and single/multiple modes of interest, is used to illustrate the proposed approach. It is observed that the modal parameters, identified using any suitable modal identification technique, have the lowest estimation uncertainty when the inputs are optimally located. As an application in damage detection, it is shown that modal parameters estimated from experiments with non-optimally located inputs may lead to incorrect damage localization. The proposed method is also applied to data from experiments performed on a laboratory scale truss model.

Implementation of the Operational Modal Analysis technique in a power transmission shaft

In this paper, we investigate the application of modal identification techniques used in civil structures, in which the excitation forces are not known, and extrapolate them to mechanical elements in operating conditions. A methodology is proposed to identify the modal parameters of a power transmission shaft under rotation. The methodology is based on the comparison of theoretical and experimental results. First, a simulation of the element under study is carried out, using a numerical model based on the Finite Element Method, to evaluate its theoretical dynamic characteristics. Then, an Experimental Modal Analysis (EMA) is performed and the theoretical model is verified by comparing theoretical and experimental results. Moreover, an algorithm based on the non-parametric technique “Peak Pickin” of an Operational Modal Analysis (OMA) is developed and, from the records of accelerations obtained in the bearings, we identify the modal parameters of the shaft. These results are compared with the theoretical values, calculated previously and, thus, verify the effectiveness of the implemented technique.

Reliability of damping ratios inferred from the seismic response of buildings

This paper studies the reliability of damping ratios inferred from the seismic response of buildings employing a modal minimization parametric system identification technique. The reliability of inferred damping ratios is quantified through the use of three metrics: (1) dynamic amplification factors; (2) Arias modal contribution factors; and (3) reliability intervals. Dynamic amplification factors measure the amplification of 1% damped floor acceleration spectral ordinates of the recorded response at the roof in the vicinity of identified modal periods with respect to those of the motion recorded at the base of the building. It is shown that this metric allows to determine if the earthquake produced a minimum dynamic amplification of the first and second modes of the structure, to reliably identify their damping ratios. The Arias modal contribution provides a measure of the intensity of a computed modal response relative to the total predicted structural response. It is argued that only damping ratios from modes with a minimum contribution to the seismic response may be reliably estimated. The third metric corresponds to the reliability intervals of the identified damping ratios, which measure the sensitivity of the objective function to small variations in the damping ratio. It is shown that the objective function is typically significantly less sensitive to variations in damping ratios than to similar variations in modal periods, which leads to larger variability in the results for damping with respect to that obtained in modal periods. Reliability screening tests are developed based on establishing limiting values for these three metrics. It is shown that these screening tests are capable of discriminating inferred damping ratios that are reliable from those that are not, independently from the adopted identification technique, and also reducing the variability of the inferred results.

Dynamics of the small-span railway bridge under moving loads

The paper presents the results of dynamic analysis of the small-span railway bridge, subjected to an action of moving trains. Numerical simulations were performed using three different load models: series of moving forces, series of moving single-mass and double-mass oscillators. The parameters of the vehicle were taken from the existing EN57 train. The parameters of the bridge were taken from the existing steel span of 10,24 m long. In both cases, the dynamic parameters were identified based on free-response measurements using modal identification techniques. Vibrations of the midpoint of the bridge as well as the mass of the oscillator have been analyzed. Numerical results obtained for individual load models were compared with the results of in-situ tests performed under operating conditions.

Modal identification of a high-rise building subjected to a landfall typhoon via both deterministic and Bayesian methods.

Modal identification involves primarily the determination of natural frequencies, damping ratios, mode shapes of a dynamic system, etc. It is usually regarded as an essential task in a wide branch of structural dynamics and civil engineering, such as structural vibration control and damage identification of buildings or bridges. There are many modal identification techniques. Basically, these techniques can be categorized into two groups: deterministic methods and Bayesian approaches. The first group can be used to provide deterministic (or optimal) estimations of modal parameters, but they are unable to quantify the estimation uncertainties. The second group is based on a usage of the Bayesian framework. Compared to the first group, the second group of methods has a typical merit of being able to offer uncertainty information of identified parameters, which is of great interests, or even necessary, for some follow-up studies. In this paper, both a deterministic method, i.e., a combination of spectral analysis, filtering and Random Decrement Technique (RDT), and a Bayesian method, i.e., Bayesian Spectral Density Approach (BSDA), are exploited to experimentally identify the modal parameters of a 303 m high-rise building that was subjected to a landfall typhoon. The validity and efficiency of each method is verified by comparing the two kinds of results. Meanwhile, the identified modal parameters are used for the serviceability assessment of this high-rise building against some frequency-specific criteria.

Modal identification of civil structures via covariance-driven stochastic subspace method.

It is usually of great importance to identify modal parameters for dynamic analysis and vibration control of civil structures. Unlike the cases in many other fields such as mechanical engineering where the input excitation of a dynamic system may be well quantified, those in civil engineering are commonly characterized by unknown external forces. During the last two decades, stochastic subspace identification (SSI) method has been developed as an advanced modal identification technique which is driven by output-only records. This method combines the theory of system identification, linear algebra (e.g., singular value decomposition) and statistics. Through matrix calculation, the so-called system matrix can be identified, from which the modal parameters can be determined. The SSI method can identify not only the natural frequencies but also the modal shapes and damping ratios associated with multiple modes of the system simultaneously, making it of particular efficiency. In this study, main steps involved in the modal identification process via the covariance-driven SSI method are introduced first. A case study is then presented to demonstrate the accuracy and efficiency of this method, through comparing the corresponding results with those via an alternative method. The effects of noise contaminated in output signals on identification results are stressed. Special attention is also paid to how to determine the mode order accurately.