Modal Identification Techniques Research Articles

Dynamic analysis of the railway bridge span under moving loads

The first part of the paper provides a review of the state of knowledge of the dynamic behaviour of railway bridges under moving loads. Particular attention is paid to developments in modelling railway bridge loading and dynamic vehicle-span (structure) interaction. The most important aspects determining the advancements in this area of knowledge are identified. The contemporary techniques for defining bridge span finite element models used in dynamic analyses are also discussed. The second, practical part of the paper presents the results of numerical simulations of the passage of load along the bridge structure. The railway loads are represented by a series of concentrated forces and a series of single-mass oscillators. Vibration of the bridge span centre and the vehicle mass depending on the speed of travel are considered. The loading parameters are adopted to represent a real railway vehicle - EN57 electrical multiple unit. The structure’s parameters were adopted on the basis of a 30 m long load-relieving span. In both cases modal identification techniques were used to obtain all the required dynamic parameters of the span under analysis on the basis of experimental data.

Boundary behaviours of Leishmania mexicana: A hydrodynamic simulation study

It is well established that the parasites of the genus Leishmania exhibit complex surface interactions with the sandfly vector midgut epithelium, but no prior study has considered the details of their hydrodynamics. Here, the boundary behaviours of motile Leishmania mexicana promastigotes are explored in a computational study using the boundary element method, with a model flagellar beating pattern that has been identified from digital videomicroscopy. In particular a simple flagellar kinematics is observed and quantified using image processing and mode identification techniques, suggesting a simple mechanical driver for the Leishmania beat. Phase plane analysis and long-time simulation of a range of Leishmania swimming scenarios demonstrate an absence of stable boundary motility for an idealised model promastigote, with behaviours ranging from boundary capture to deflection into the bulk both with and without surface forces between the swimmer and the boundary. Indeed, the inclusion of a short-range repulsive surface force results in the deflection of all surface-bound promastigotes, suggesting that the documented surface detachment of infective metacyclic promastigotes may be the result of their particular morphology and simple hydrodynamics. Further, simulation elucidates a remarkable morphology-dependent hydrodynamic mechanism of boundary approach, hypothesised to be the cause of the well-established phenomenon of tip-first epithelial attachment of Leishmania promastigotes to the sandfly vector midgut.

Looseness localization for bolted joints using Bayesian operational modal analysis and modal strain energy

Bayesian operational modal analysis and modal strain energy are employed for determining the damage and looseness of bolted joints in beam structures under ambient excitation. With this ambient modal identification technique, mode shapes of a damaged beam structure with loosened bolted connections are obtained based on Bayesian theory. Then, the corresponding modal strain energy can be calculated based on the mode shapes. The modal strain energy of the structure with loosened bolted connections is compared with the theoretical one without bolted joints to define a damage index. This approach uses vibration-based nondestructive testing of locations and looseness of bolted joints in beam structures with different boundary conditions by first obtaining modal parameters from ambient vibration data. The damage index is then used to identify locations and looseness of bolted joints in beam structures with single or multiple bolted joints. Furthermore, the comparison between damage indexes due to different looseness levels of bolted connections demonstrates a qualitatively proportional relationship.

Dynamic Characterisation and Finite Element Updating of a RC Stadium Grandstand

This paper reports on the dynamic characterisation of a Reinforced Concrete (RC) stadium grandstand module for the Sporting Stadium in Lisbon. To this aim, a three-dimensional (3D) Finite-Element (FE) numerical model, implemented according to the technical drawings of the structure, is first presented to provide preliminary estimates of the expected modal characteristics for the examined structural system. Ambient vibration tests are then carried out on the same grandstand, and used to extract the natural frequencies and vibration modes of the system, according to conventional state-of-the-art output-only modal parameter identification techniques. A sensitivity investigation and FE model updating study is hence presented for the grandstand, giving evidence of the major influencing parameters and key input data for the numerical fitting of the experimental modal testing results.

Modal testing and detection of pretension deviation in a cable dome structure

Pretension deviation may cause stiffness degradation and overstress that can compromise the safety of tensile structures, which can be diagnosed by modal identification. This article presents modal tests on a 1:10 scaled model of a herringbone-ribbed cable dome structure. An optimal sensor placement scheme is proposed to observe the geometric stiffness change induced by pretension deviation. Based on the tests, different output-only modal identification techniques were implemented. A substructure strategy was adopted to overcome the limited measurement quantity and provide localized diagnoses. The experimental results show that operational modal analysis methods based on output-only data can effectively identify major modes of massive structures. The sensitivity of modal characteristics to pretension deviation is also evaluated via experimental comparisons, and modifications are implemented in an analytical finite element model to approximate the test model. The identified modal information can help locate stiffness degradation and thereby pretension loss in tensile structures. A modified modal strain energy method is proposed to detect pretension loss from decentralized testing and is verified by the test results.

Operational modal identification in the presence of harmonic excitation

The dynamic behavior of structures can be studied by the identification of their modal parameters. Classical modal analysis methods are based on the relation between the forces applied to structures (inputs) and their vibration responses (outputs). In real operational conditions it is difficult, or even impossible, to measure the excitation. For this reason, operational modal analysis approaches which consider only output data are proposed. However, most of these output-only techniques are proposed under the assumption of white noise excitation. If additional components, like harmonics for instance, are present in the exciting force, they will not be separated from the natural frequencies. Consequently, this assumption is no longer valid. In this context, an operational modal identification technique is proposed in order to only identify real poles and eliminate spurious ones. It is a method based on transmissibility functions.The objective of the proposed paper is to identify modal parameters in operational conditions in the presence of harmonic excitations. Identification is performed using a method based on transmissibility measurements and then with the classical stochastic subspace identification method, which is based on white noise excitation. These two methods are first applied to numerical examples and then to a laboratory test. Results validate the novel ability of the method based on transmissibility measurements to eliminate harmonics, contrary to the stochastic subspace identification approach.

Identification of coherent trajectories by modal characteristics and hierarchical agglomerative clustering

This paper introduces a novel method to identify coherent generators using the inter-area modal characteristics of power systems. The key idea is to extract the inter-area modes from the simulated data and then to apply a clustering strategy. Thus, the proposed method consists of extracting the phase of the oscillatory modes via a modal identification technique and applying a hierarchical agglomerative clustering technique together with the Elbow's method to gather the phases of each mode, enabling to provide coherent trajectories of generators. The proposed method uses a Taylor-Fourier filtering strategy to remove noises and nonlinearity in the time evolution of coherent generators. Simulated signals with noise added are used for assessing the proposition. Results corroborate the proposed strategy for identifying coherent trajectories in large-scale power systems.

Full-field modal analysis during base motion excitation using high-speed 3D digital image correlation

In recent years, many efforts have been made to exploit full-field measurement optical techniques for modal identification. Three-dimensional digital image correlation using high-speed cameras has been extensively employed for this purpose. Modal identification algorithms are applied to process the frequency response functions (FRF), which relate the displacement response of the structure to the excitation force. However, one of the most common tests for modal analysis involves the base motion excitation of a structural element instead of force excitation. In this case, the relationship between response and excitation is typically based on displacements, which are known as transmissibility functions. In this study, a methodology for experimental modal analysis using high-speed 3D digital image correlation and base motion excitation tests is proposed. In particular, a cantilever beam was excited from its base with a random signal, using a clamped edge join. Full-field transmissibility functions were obtained through the beam and converted into FRF for proper identification, considering a single degree-of-freedom theoretical conversion. Subsequently, modal identification was performed using a circle-fit approach. The proposed methodology facilitates the management of the typically large amounts of data points involved in the DIC measurement during modal identification. Moreover, it was possible to determine the natural frequencies, damping ratios and full-field mode shapes without requiring any additional tests. Finally, the results were experimentally validated by comparing them with those obtained by employing traditional accelerometers, analytical models and finite element method analyses. The comparison was performed by using the quantitative indicator modal assurance criterion. The results showed a high level of correspondence, consolidating the proposed experimental methodology.

Wavenumber-frequency analysis of landslide-generated tsunamis at a conical island. Part II: EOF and modal analysis

In this paper the Empirical Orthogonal Function (EOF) method is applied to extract from the experimental data, related to landslide-tsunamis around the coast of a conical island, the spatial modes that contribute to the wave field. For each mode the wavenumber and the frequency are calculated by analyzing the shape along the coast and the time function. The relevant modes are then compared with those obtained through numerical eigenanalysis of the long wave equation around the considered island. It was possible to associate each EOF mode with some eigenvectors and the corresponding eigenfrequencies, both on the basis of the spatial shape, the wavenumber calculated along the coast and the frequency. Results confirm that landslide-generated waves propagate along the coast as trapped edge waves and the zero-th order mode is the most important. Further of exploring the physics, it is believed that this paper can be of use as some of the most relevant and straightforward techniques for modal identification are applied to the same problem and dataset.

Refined Frequency Domain Decomposition modal dynamic identification from earthquake-induced structural responses

In the present work, earthquake-induced structural responses at heavy damping are considered towards the assessment of current strong-motion output-only modal parameters via a novel refined Frequency Domain Decomposition (rFDD) approach. Classical FDD assumptions of stationary white noise input and light damping no longer hold in such a case, leading to extreme operational conditions for this Frequency-Domain modal dynamic identification technique. The present non-parametric output-only rFDD procedure effectively tackles such issues, through dedicated algorithmic and computational strategies, resulting in a robust identification tool within this challenging identification context. Synthetic earthquake-induced responses are generated from a set of shear-type frames, which are taken as target structural models for the purposes of validation and comparison. Twenty-two “Far-Field” multi-component (NS, WE) seismic base excitations are taken into account from the FEMA P695 strong motion database. In particular, heavy-damped structures (in terms of output-only identification challenge) are considered, raising the modal damping ratios up to 10%. Natural frequencies, mode shapes and modal damping ratios are effectively estimated through the implemented rFDD procedure. The achieved estimates are statistically compared to the target values, by proving the effectiveness of the developed rFDD approach in working with synthetic earthquake-induced responses at concurrent heavy damping. This shall demonstrate a necessary condition for the feasibility of the developed rFDD approach towards Earthquake Engineering and Structural Health Monitoring purposes.

Automated modal tracking in a football stadium suspension roof for detection of structural changes

Considerable efforts have been made towards the development of robust and fully automated vibration-based monitoring systems with the goal of extracting relevant information regarding the dynamic behaviour and health condition of the monitored structure. Satisfactory results have been obtained in this scientific domain by combining accurate measurement systems and fully automated output-only modal identification techniques. In this context, the main objective of this contribution is to demonstrate in a full-scale case study that with the application of sophisticated algorithms for the automatic tracking of modal parameters, it is possible to detect very small structural changes. Apart from describing the main features and capabilities of the autonomous monitoring system implemented to assess the structural condition of a peculiar football stadium suspension roof, this paper also outlines the main results obtained over the course of 4 years of monitoring carried out to assess the dynamic behaviour and the health condition of the roof structure. The routines developed for the online processing of the continuously collected acceleration time series include state-of-the-art processing techniques, such as automated modal identification based on cluster analysis and principal components analyses combined with control charts for removal of environmental or operational effects and detection of structural changes, together with some innovative features in the context of continuous dynamic monitoring, such as the quantification of the uncertainties associated with each modal estimate and the estimation of the contribution of each mode to the measured structural response.

Identification of frame models under unmeasured base motion: experimental validation

Structural Health Monitoring (SHM) is an area of great interest in civil engineering, and in this framework very reliable techniques for modal identification in the linear field are widely used. However, most of them require the knowledge of both forcing actions and structural response (e.g. for transient oscillations, as seismic-induced ones) or long-duration - or even stationary - output-only measures of the response (e.g. in case of wind-induced actions).For a frame structure subject to transient and unmeasured base motion, as considered here, a technique proposed by one of the writers in previous papers requires only the structural response at the floor levels, without any quantitative information on the excitation. It starts from the observation that the ratios between the Fourier transforms of the structural responses at different levels are independent on the base motion characteristics and, therefore, can be expressed as a function of the modal parameters. In particular, the uniqueness of the solution was demonstrated when the structural response is known for at least three different floor levels.To validate the procedure, this paper describes the results of an experimental campaign, that was performed on a laboratory model simulating a three storey shear-type plane frame subject to different types of base motions.

On minimizing the influence of the noise tail of correlation functions in operational modal analysis

In operational modal analysis (OMA) correlation functions are used by all classical time-domain modal identification techniques that uses the impulse response function (free decays) as primary data. However, the main difference between the impulse response and the correlation functions estimated from the operational responses is that the latter present a higher noise level. This is due to statistical errors in the estimation of the correlation function and it causes random noise in the end of the function and this is called the noise tail. This noise might have significant influence on the identification results (random errors) when the noise tail is included in the identification. On the other hand, if the correlation function is truncated too much, then important information is lost. In other to minimize this error, a suitable truncation based on manual inspection of the correlation function is normally used. However, in automated OMA, an automated procedure is needed for the truncation. Based on known theoretical solutions from the literature, a model is proposed in this paper to automatically truncate the correlation function at the point where it starts to get dominated by the noise tail. The accuracy of the proposed truncation procedure is studied using a three degree of freedom simulation case.

Refined FDD modal dynamic identification from earthquake responses with Soil-Structure Interaction

“Non-parametric” structural system identification via a refined Frequency Domain Decomposition (rFDD) algorithm is developed here to evaluate current modal properties of civil engineering buildings subjected to earthquake excitation. Innovatively, the algorithm is expanded to operate under Soil-Structure Interaction (SSI) conditions, in order to deal with both flexible- and fixed-base conditions. At first, the modal dynamic identification technique is explored analytically, by dealing with a variable stiffness and damping foundation system. The standard fixed-base condition (no SSI) may simulate well the response to ambient loadings or weak seismic excitations; rather, a flexible-base model shall better deal with more realistic earthquake-induced structural responses embedding SSI effects. The developed analyses are performed on earthquake-induced synthetic response signals, which are computed from a benchmark linear frame structure under several earthquake excitations and at variable foundation properties. The rFDD expansion originally operates within an OMAX (Operational Modal Analysis with eXogenous input) environment on the base-excited buildings. The OMAX condition comes from the adoption of base excitation records too, which are employed as exogenous input. This aims at detecting also the underlying fixed-base conditions and to quantify the amount of SSI to which the building under analysis is subjected to. The present identification method demonstrates its full effectiveness in detecting both flexible- and fixed-base modal parameters identified based on earthquake excitation, also in the presence of close modes and heavy damping (in terms of identification challenge). This work proves a necessary condition for the effectiveness of the present rFDD-OMAX algorithm as a robust method for inspecting current flexible- and fixed-base strong ground motion modal parameters. This shall help in identifying possible variations of structural features and SSI effects along experienced seismic histories, thus providing an effective tool towards potential Earthquake Engineering and Structural Health Monitoring purposes.

Time-frequency techniques for modal parameters identification of civil structures from acquired dynamic signals

A major trust of modal parameters identification (MPI) research in recent years has been based on using artificial and natural vibrations sources because vibration measurements can reflect the true dynamic behavior of a structure while analytical prediction methods, such as finite element models, are less accurate due to the numerous structural idealizations and uncertainties involved in the simulations. This paper presents a state-of-the-art review of the time-frequency techniques for modal parameters identification of civil structures from acquired dynamic signals as well as the factors that affect the estimation accuracy. Further, the latest signal processing techniques proposed since 2012 are also reviewed. These algorithms are worth being researched for MPI of large real-life structures because they provide good time-frequency resolution and noise-immunity.

Optimal reduction from an initial sensor deployment along the deck of a cable-stayed bridge

The ambient vibration measurement is an output-data-only dynamic testing where natural excitations are represented, for instance, by winds and typhoons. The modal identification involving output-only measurements requires the use of specific modal identification techniques. This paper presents the application of a reliable method (the Stochastic Subspace Identification - SSI) implemented in a general purpose software. As a criterion toward the robustness of identified modes, a bio-inspired optimization algorithm, with a highly nonlinear objective function, is introduced in order to find the optimal deployment of a reduced number of sensors across a large civil engineering structure for the validation of its modal identification. The Ting Kau Bridge (TKB), one of the longest cable-stayed bridges situated in Hong Kong, is chosen as a case study. The results show that the proposed method catches eigenvalues and eigenvectors even for a reduced number of sensors, without any significant loss of accuracy.

Quantifying Distance Overestimation From Global Positioning System in Urban Spaces.

To investigate accuracy of distance measures computed from Global Positioning System (GPS) points in New York City. We performed structured walks along urban streets carrying Globalsat DG-100 GPS Data Logger devices in highest and lowest quartiles of building height and tree canopy cover. We used ArcGIS version 10.1 to select walks and compute the straight-line distance (Geographic Information System-measured) and sum of distances between consecutive GPS waypoints (GPS-measured) for each walk. GPS distance overestimates were associated with building height (median overestimate = 97% for high vs 14% for low building height) and to a lesser extent tree canopy (43% for high vs 28% for low tree canopy). Algorithms using distances between successive GPS points to infer speed or travel mode may misclassify trips differentially by context. Researchers studying urban spaces may prefer alternative mode identification techniques.

Structural Identification for Mobile Sensing with Missing Observations

AbstractThere are many occasions in structural health monitoring (SHM) on which collected data sets contain missing observations. Such instances may occur as a result of failed communications or packet losses in a wireless sensor network or as a result of sensing and sampling methods—for example, mobile sensing. By implementing modified expectation and maximization steps, structural identification using expectation maximization (STRIDE) is capable of processing data in these circumstances and is the first modal identification technique to formally accept data with missing observations. This paper presents the STRIDE algorithm, a statistical perspective of missing data, and new STRIDE equations that account for missing observations. Expectation step (E-step) equations are given explicitly for both partially observed time steps and those not fully observed. The maximization step (M-step) provides state-space parameter updates in terms of available observations and missing-data state-variable statistics. Thi...

Mode Shape Expansion for Lively Pedestrian Bridges through Kriging

AbstractThis paper investigates the use of kriging as a powerful tool for mode shape interpolation in flexible pedestrian bridges. Kriging can be used to interpolate a set of sparse mode shape coordinates obtained through experimental modal identification techniques onto a dense structure geometry, leading to better mode shape visualization and efficient model updating. Kriging does not require a finite-element (FE) model (analytical modes) to be available a priori, as it is purely statistical in nature. Despite this key advantage, kriging has not been adopted for mode shape interpolation due in part to the relative lack of exposure within the modal analysis community and the arbitrariness of the parameter defining the spatial correlation between discrete geometry points. The first objective of this paper is to describe kriging in detail, especially focusing on pedestrian bridges. Second, modifications to the computational procedure for kriging are presented with a new metric to automatically tune the cor...

A Retrospective View of EMM-ARM: Application to Quality Control in Soil-improvement and Complementary Developments

The EMM-ARM (Elasticity Modulus Measurement through Ambient Response Method) is a technique that allows the continuous measurement of the E-modulus of a given material under test, since the instant in which it is cast into the testing mould. The technique has been initially developed in 2008-2009 and it is particularly useful to monitor the hardening process of cement-based materials or any similar materials that can be cast into a mould and endure significant stiffness changes since early ages. EMM-ARM is based on the identification of the resonant frequency of the testing mould, which evolves along time due to the hardening process of the tested material, and then the E-modulus of the tested material can be inferred with basis on the dynamic equations of motion of the testing system. Even though the method has been originally devised to test concrete, it has quickly been extended to other materials such as mortar, cement paste, stabilised soils and even epoxy resins. In the particular case of stabilised soils, the method has been successfully applied to both cement-based stabilization and lime-based stabilization. This paper intends to provide a wide perspective of the several evolutions that EMM-ARM has endured throughout its applications to stabilised soils, namely in regard to: (i) mould geometry and material; (ii) sampling procedures for in-situ application; (iii) excitation and modal identification techniques; (iv) systematic application to several mix formulations and comparative evaluation of hardening kinetics. Indeed, one of the foremost applications of EMM-ARM in the context of soil stabilization is the capability to provide real-time data about the stiffness of the material, allowing the users to take early decisions in regard to the expectable stiffness that a recently improved soil will predictably attain. This readily available information can have strong economic impacts in the case of rejection of a given stabilised layer.