Output-only Modal Analysis Research Articles

Optimal Sensor Placement for Enhanced Efficiency in Structural Health Monitoring of Medium-Rise Buildings.

Output-only modal analysis using ambient vibration testing is ubiquitous for the monitoring of structural systems, especially for civil engineering structures such as buildings and bridges. Nonetheless, the instrumented nodes for large-scale structural systems need to cover a significant portion of the spatial volume of the test structure to obtain accurate global modal information. This requires considerable time and resources, which can be challenging in large-scale projects, such as the seismic vulnerability assessment over a large number of facilities. In many instances, a simple center-line (stairwell case) topology is generally used due to time, logistical, and economic constraints. The latter, though a fast technique, cannot provide complete modal information, especially for torsional modes. In this research, corner-line instrumented nodes layouts using only a reference and a roving sensor are proposed, which overcome this issue and can provide maximum modal information similar to that from 3D topologies for medium-rise buildings. Parametric studies are performed to identify the most appropriate locations for sensor placement at each floor of a medium-rise building. The results indicate that corner locations at each floor are optimal. The proposed procedure is validated through field experiments on two medium-rise buildings.

Smooth mode decomposition: Theory and its applications in full-field output-only modal analysis

Full-field output-only modal analysis (OMA) became popular due to its superior spatiotemporal resolution over traditional sensing methods. It provides rich spatial dynamic information, which is essential for high-fidelity modal models, model updating, and non-intrusive health monitoring. However, the full-field sensory techniques implementation in OMA is hurdled by the excessive storage and computational requirements and the temporal aliasing effect. This paper develops a novel modal decomposition method, called smooth mode decomposition (SMD), to tackle these hurdles by exploiting the spatial dynamics and smoothness of the observed field measurements. SMD imposes the smoothness constraint on the identified mode shapes to resolve a set of orthogonal modes, called the smooth orthogonal modes (SOMs), that maximally represent the original field while also keeping the mode shape as smooth as possible. Since the SMD seeks spatially-smooth modal structures, the requirements on the temporal sampling can be relaxed. Hence, the SMD can be applied to nonuniformly and sub-Nyquist sampled full-field measurement data. Moreover, the SOMs converge to linear normal modes of uniformly distributed parameter systems, which provides a physically meaningful decomposition of the measurement data. Through a series of numerical examples, the SMD is compared to other popular covariance-based OMA methods. These examples demonstrate the merit of the proposed method when the vibration system has nonuniform system parameters and when the data is undersampled. Further, a full-field strain measurement technique, the three-dimensional digital image correlation, is utilized where spatiotemporal displacement measurements are obtained from a vibrating cantilever beam. The SMD is shown to provide accurate mode estimates with undersampled experimental data. Statistically, SMD shows its flexibility and quality in modal identification using temporally randomly captured images, which opens an avenue for alleviating storage and processing requirements for image-based full-field OMA.

Damage identification in beams using burst video-records during free-vibration

In Structural Health Monitoring, computer vision has emerged as a promising approach for dynamic measurement; especially for its full-field characteristic. However, real-world implementations are still sparse due to several reasons. One of them is that vibration-based damage identification methods usually rely on Output-Only Modal-Analysis which, to be accurate, requires very long records with stochastic excitation or relatively long free-vibration records. The first option hinders video taking, storage and processing; specially with high-speed cameras. The second is statistically difficult under common operating conditions. To overcome such difficulties, this paper presents a methodology for damage identification in beams; which is vibration-based and Output-Only, but does not rely on Modal (or other Fourier-based) Analysis. Therefore, it can be fed with very short free-vibration displacement time histories; e.g., extracted from burst video records. The key idea is using the recently developed Synthesis of the Healthy-Structure Model Response, but interpreting the accelerations in free-vibration as an inertial pseudo-loading. The likely problem of high levels of noise is addressed by separating damage detection and localisation (using a statistical approach) from damage quantification (which is physics based). In an experimental example, the methodology showed outstanding detection and localisation performance with low quantification error.

Dynamic displacement estimation and modal analysis of long-span bridges integrating multi-GNSS and acceleration measurements

Compared with acceleration-based modal analysis, displacement can provide a more reliable and robust identification result for output-only modal analysis of long-span bridges. However, the estimated displacements from acceleration records are frequently unavailable due to unrealistic drifts. Aiming at obtaining more accurate and stable results for determining the modal parameters, this study develops a multi-rate weighted data fusion approach for estimating displacement responses in dynamic monitoring of structures based on global navigation satellite system (GNSS) and acceleration measurements. The approach initially derives the local estimations from displacement and acceleration sensors via a Kalman filter algorithm with colored measurement noise, and later uses a weighted fusion criterion of scalar linear minimum variance to fuse the results of local estimations. Then, structural modal pamameters are identified by employing data-driven stochastic subspace identification (SSI) algorithm. The proposed approach is validated in a four degree-of-freedom numerical model and then applied to a long-span bridge in engineering practice. The results illustrate that the proposed approach can reduce the error of GNSS-obtained displacement and expand recognizable frequency range by introducing dynamic displacement component from acceleration measurement.

Robust Synchronization of Ambient Vibration Time Histories Based on Phase Angle Compensations and Kernel Density Function.

The output-only modal analysis is ubiquitously used for structural health monitoring of civil engineering systems. The measurements for such applications require the use of multiple data acquisition systems (DAS) to avoid complicated meshes of cables in high-rise buildings, avoid traffic constriction on a bridge during measurements, or to avoid having limited channels in a single DAS. Nevertheless, such requirements introduce time synchronization problems which potentially lead to erroneous structural dynamic characterization and hence misleading or inconclusive structural health monitoring results. This research aims at proposing a system-identification-based time synchronization algorithm for output-only modal analysis using multiple DAS. A new procedure based on the compensation of the phase angle shifts is proposed to identify and address the time synchronization issue in ambient vibration data measured through multiple DAS. To increase the robustness of the proposed algorithm to the inherent inconsistencies in these datasets, the kernel density function is applied to rank multiple time-shift estimates that are sometimes detected by the algorithm when inaccuracies exist in the data arising from low signal-to-noise ratio and/or presence of colored noise in the ambient excitations. First, the synchronized ambient vibration dataset of a full-scale bridge is artificially de-synchronized and used to present a proof of concept for the proposed algorithm. Next, the algorithm is applied to ambient vibration data of a 30-story, reinforced concrete building, where the synchronization of the data could not be achieved using two DAS despite best efforts. The application of the proposed time synchronization algorithm is shown to both detect and correct the time synchronization discrepancies in the output-only modal analysis.

A methodology for vibro-acoustical Operational Modal Analysis of microsystems

The need for tools to understand, test, model, and predict microsystems performances inspires the wide framework of multidisciplinary research on MEMS sensor technologies. In this work, to dynamically identify these systems, we propose a particular output-only modal analysis (OMA) methodology that includes acoustical excitation via speakers and response measurements through a laser Doppler vibrometer and a microphone. Specifically, we account for the fluid–structure coupling relying on the analytical modal model of the cross-power spectra (CPs) between the structural and the acoustical system outputs, and we apply modal parameter estimation (MPE) techniques from the OMA field. The effectiveness of the methodology is illustrated through the in-plane and out-of-plane flexural mode experimental identification of a high-quality factor quartz tuning fork (QTF), immersed in a fluid environment. This device exhibits a dominant diffusive-velocity contribution in the description of the overall forces exerted by the fluid and, from this point of view, significantly differs from the typical structures analyzed via OMA, where the main effect of the interaction is viscous damping. We point out that the acoustical pressure measurement can be used as a robust reference, instead of the commonly used structural sensors. It results useful for MEMS where, in general, external exciting or measurement components adversely impact the analysis, altering the values of dynamic parameters. In this sense, the use of the vibro-acoustical OMA framework produces a simple and effective methodology for microsystems’ identification.

Output-only modal analysis of the Humen Bridge from video measurement

Abstract Video-based vibration testing is a promising non-contact method for structural health monitoring. This article develops an innovative methodology for estimating the structural modal parameters from videos without recovering the responses of structures. Firstly, an image processing (i.e., Gaussian smoothing) are adopted to smooth frames and alleviate the noises. Secondly, several regions of interest (ROIs) contained the projection area of structure are selected, and edge detection is performed to that to reduce the size of vision data. Then under some assumptions, the reduced vision data can be subjected to the frequency domain decomposition (FDD) similar to the structural modal analysis to identify the modal parameters of structure. Moreover, the structural mode shapes are recovering from such decomposition. The feasibility and accuracy of the proposed method were validated by a field experiment on the Humen Bridge in Guangzhou, China.

Multiple damage detection in a cantilever beam using baseline-free operational modal analysis

Operational Modal Analysis (OMA) or output-only modal analysis allows obtaining modal parameters in operational conditions, i.e., without external excitation. While being more challenging than traditional or Experimental Modal Analysis (EMA), OMA allows to monitor the structural health of a structure in cases where EMA is not practical or feasible. This article presents an introduction to an OMA technique based on Frequency Domain Decomposition (FDD) and its mathematical formalism, and demonstrates its potential for detecting damage in a cantilever beam. A transient dynamic Finite-Element Analysis (FEA) under white noise excitation has been performed in ANSYS Workbench to obtain the acceleration responses of the system. The numerical accelerometers signals along the beam are used for the OMA analysis and multiple cracks are analyzed at different positions along the beam. The technique used for damage detection is Curvature Mode Shape (CMS) analysis, using only the information of the damaged structure, making it a baseline-free method. The technique is shown to be capable of correctly detecting and locating the different damages analyzed.

EFFECTS OF DIFFERENT EXCITATION MECHANISMS IN MACHINE TOOLS WHEN PERFORMING OUTPUT-ONLY MODAL ANALYSIS

Output-only Modal Analysis makes it possible to investigate the dynamic behaviour of machine tools, especially under process conditions. The differences between standstill and process state, which are important to be considered, result from process damping, gyroscopic moments of the rotating spindle, and changes in preloads and clearance in bearing and joints. Output-only Modal Analysis assumes a complete excitation of the structure by white noise characteristics. There are several mechanisms in a machine tool under process conditions that could cause a vibration response. Besides the cutting process itself, the movement of the NC-axes, as well as rotating fans of the control system and auxiliary units, can be excitation sources. This paper investigates to what extent several excitation mechanisms in machine tools fulfill the analysis assumption and in which way the identified modal parameters depend on the boundary conditions of the excitation characteristics.

System identification methods for dynamic models of brain activity

ObjectiveThere is a broad need to better understand the dynamics of neural activity in both space and time. Rigorous modeling methods are needed to improve the analysis of brainwave dynamics. Two system identification algorithms, Output Only Modal Analysis (OMA) and Dynamic Mode Decomposition (DMD), are modified for use on neural dynamics and compared. An example application is included. MethodsThe system identification methods are applied to estimate state space models for neural dynamics. The modeling technique results in a reduced order modal decomposition of the behavior of the brain. The resultant eigenmodes can be non-orthogonal and complex, capturing the emergent space time dynamics. We apply the modeling method to the Database for Emotion Analysis using Physiological Signals (DEAP) and the EEG Motor Movement/Imagery Dataset (EEGMMI) in a biosecurity application. ResultsIt is shown that there are common modes shared among all subjects, regardless of stimuli. Further, the modal decompositions may be used to distinguish subjects from one another in a subject identification biosecurity task. The accuracy of the OMA eigenmode model is 100%, while the accuracy of the DMD eigenmode model is 96%. ConclusionOutput only system identification techniques are an appropriate rigorous modeling method for EEG data. The structured modeling procedure offers new opportunities for cognitive modeling and affective computing.

Robust multi-dataset identification with frequency domain decomposition

Right after its invention in the late nineties, the Frequency Domain Decomposition (FDD) identification technique became very popular in the operational modal analysis community due to its simplicity and robustness. The underlying idea of this technique consists of computing the singular value decomposition of the Power Spectral Densities (PSDs) estimated from the measured vibration responses with the periodogram (also known as “Welch’s”) approach to identify the natural frequencies and mode shape vectors of the tested structural system. When dealing with multi-dataset output-only modal analysis, the classic approach for extracting the global mode shape vectors from all the measured datasets consists of estimating the mode shape parts corresponding to each dataset, and then scaling the different parts with the aid of the reference sensors. In this paper, two new merging approaches are proposed to scale the different mode shape parts. The first consists of (i) re-scaling the different PSDs prior to the identification; (ii) forming a global matrix containing all the re-scaled PSDs; and (iii) applying the FDD approach to the global PSD matrix to estimate the global mode shape vectors. The second merging strategy consists of (i) forming a global matrix containing all the PSDs without any prior re-scaling; (ii) applying the FDD approach to the PSD matrix to estimate the global mode shape vectors; and (iii) re-scaling the different mode shape parts by making use of the reference singular vectors. In order to illustrate the benefits of the two proposed merging approaches with regards to their classic counterpart from a practical perspective, a real-live application example is presented as the last part of the paper.

Laboratory investigation of a bridge scour monitoring method using decentralized modal analysis

Scour is a significant issue for bridges worldwide that influences the global stiffness of bridge structures and hence alters the dynamic behaviour of these systems. For the first time, this article presents a new approach to detect bridge scour at shallow pad foundations, using a decentralized modal analysis approach through re-deployable accelerometers to extract modal information. A numerical model of a bridge with four simply supported spans on piers is created to test the approach. Scour is modelled as a reduction in foundation stiffness under a given pier. A passing half-car vehicle model is simulated to excite the bridge in phases of measurement to obtain segments of the mode shape using output-only modal analysis. Two points of the bridge are used to obtain modal amplitudes in each phase, which are combined to estimate the global mode shape. A damage indicator is postulated based on fitting curves to the mode shapes, using maximum likelihood, which can locate scour damage. The root mean square difference between the healthy and scoured mode shape curves exhibits an almost linear increase with increasing foundation stiffness loss under scour. Experimental tests have been carried out on a scaled model bridge to validate the approach presented in this article.

Evaluating tool point dynamics using output-only modal analysis with mass-change methods

This paper discusses the evaluation of tool point dynamics using output-only modal analysis methods. As compared to the traditional experimental modal analysis procedures that rely on the input and the output, both being known, output-only methods discussed herein can evaluate modal parameters using only the measured response of the tool subjected to unknown impact-based excitations. Since the input is not known, the estimated shapes are unscaled. To correctly scale shapes, we use the mass-change method. We present analytical models to guide the optimal selection of the mass to be added as well as to guide its placement on the tool. Analytical models systematically characterize errors in scaling the eigenvector and errors due to uncertainties in the estimation of the natural frequencies. The model suggests placement of the mass to be added at the anti-node(s) for the mode(s) of interest. These models guide experiments on two tools – a slender boring bar, and an end mill. Tool point frequency response functions (FRFs) reconstructed with the natural frequencies, damping ratios, and scaled mode shapes evaluated with the output-only mass-change method are compared with and found to be in good agreement with FRFs obtained from the traditional experimental modal analysis procedures. Since output-only methods require one less transducer, and since these methods are robust to uncertainties and inconsistencies in the input, output-only methods promise advantages from the industrial point of view.

Output-only Modal Analysis of a Beam Via Frequency Domain Decomposition Method Using Noisy Data

The output data from a structure is the building block for output-only modal analysis. The structure response in the output data, however, is usually contaminated with noise. Naturally, the success of output-only methods in determining the modal parameters of a structure depends on noise level. In this paper, the possibility and accuracy of identifying the modal parameters of a simply supported beam in the presence of noise has been discussed. The output-only modal analysis method with frequency domain decomposition was used and output data with various noise levels were considered. Initially, finite element modal analysis was used to determine the modal parameters for the beam which were afterwards enforced as the reference modal parameters. Then, appropriate input was applied to the beam and the acceleration signals of different nodes were produced through finite element transient analysis. In order to simulate noisy data, noises with different power levels were generated and added to the signals. Finally, the modal parameters were obtained by frequency domain decomposition method. The results showed that the modal parameters corresponding to the first vibration mode could only be identified with acceptable validity at low to moderate noise levels, whereas for higher modes, the modal parameters can be correctly obtained even at high noise levels.

Noise Effects on Modal Parameters Extraction of Horizontal Tailplane by Singular Value Decomposition Method Based on Output Only Modal Analysis

According to the great importance of safety in aerospace industries, identification of dynamic parameters of related equipment by experimental tests in operating conditions has been in focus. Due to the existence of noise sources in these conditions the probability of fault occurrence may increases. This study investigates the effects of noise in the process of modal parameters identification by Output only Modal Analysis (OMA) method using Singular Value Decomposition (SVD) algorithm. The study case is the horizontal tailplane of the aircraft; therefore, at first, the modal parameters of the tailplane are obtained numerically. Then a cantilever beam is used to perform experimental tests with regard to the high aspect ratio of the modeled tailplane. The modal parameters of the beam are obtained nonparametrically by Experimental Modal Analysis (EMA) and OMA. In order to investigate the effects of noise in a controlled manner, the artificial excitation namely the shaker with the random force is used. Then, the effects of noisy measurements on the specifications of the system in EMA and OMA methods are investigated. The results indicate that: 1. The OMA method has more resistance against the noise for extracting natural frequencies. 2. The results of the Modal Assurance Criterion (MAC) values by EMA method, in the condition of noise existence in output data, are worse than the noise existence in input data. 3. The average of MAC values in general condition of EMA method by noisy input & output data is worse than the OMA method.

Modal parameter estimation of a reduced-scale rocket nozzle using blind source separation

In this paper, two blind source separation (BSS) algorithms are used to estimate the modal parameters of a reduced-scale rocket nozzle using only measurements of deformation. The data is gathered using a single high-speed video camera, in combination with fluorescent markers placed on the nozzle lip illuminated by a Nd:YLF pulsed laser strobe. A marker tracking algorithm is used to measure the displacement of each fluorescent marker. The nozzle is excited using a conventional shaker with band-limited white noise input as well as an impact hammer. The results of the two BSS algorithms, namely the second order blind identification algorithm and the complexity pursuit algorithm, are compared to a well-established output-only modal analysis technique, the stochastic subspace identification algorithm, as well as finite element analysis predictions. It was found that both BSS algorithms correctly identified all modes compared to the stochastic subspace identification algorithm and the finite element analysis, and the calculated eigenfrequencies are within 0.1% of measured values. The BSS algorithms facilitate the accurate extraction of modal parameters from output-only measurements with a minimum of user interaction compared to conventional modal analysis algorithms.

Output-only modal identification by in-operation modal appropriation for use with enhanced frequency domain decomposition method

Output-only modal identification or operational modal analysis (OMA) has gained increasing popularity in many fields of engineering. In the context of OMA there is no need to measure the input. Modal parameters of dynamic systems are estimated just based on the output responses. One of the most robust and popular frequency domain methods of OMA is enhanced frequency domain decomposition (EFDD) method. EFDD is widely used as an interesting solution for OMA in a large number of researches, projects, and commercial software. We first assessed the EFDD features considering the design parameters selection and then introduced our recently proposed algorithm named in-operation modal appropriation (INOPMA) for use with EFDD method to improve the identification of modal frequencies and damping ratios and overcome some of the existing drawbacks. Modal identification process starts with EFDD and then INOPMA is applied on derived normalized auto-correlation functions (NACF) to estimate modal damping ratios and natural frequencies. Typical EFDD takes advantage of logarithmic decrement (LD) algorithm and zero crossing (ZC) method at this stage. A simulated four-story shear frame has been employed to perform the evaluation of the proposed method on output-only prediction of ideal natural frequencies and modal damping ratios. The outcomes show that the modal parameters are estimated with much less bias error and variance compared to the typical EFDD procedure. The real data of the heritage court tower ambient vibration test is also used to perform sensitivity analysis of EFDD-INOPMA modal parameter estimation in the presence of measurement noise, and favorable results have been obtained.

Cause investigation of high-mode vortex-induced vibration in a long-span suspension bridge

A significant vortex-induced vibration (VIV) was observed in a suspension bridge under a wind velocity of approximately 6 and 7 m/s, and with a maximum amplitude that exceeded the serviceability limitations. Since the observation of VIV in an operating bridge was an infrequent event, this study investigated the cause of unexpected VIV. A series of wind tunnel tests revealed the main cause of the VIV was temporary screens applied over the guardrails to shield the curing surface during replacement of epoxy-coated pavement. The characteristics of the measured VIV were consistent with those from experimental results in terms of amplitude and lock-in wind speed range. The effect of Scruton numbers on VIV amplitude was examined for several dominant modes with different modal mass and damping ratios. Since the VIV amplitude is sensitive to the inherent damping ratio, the modal damping ratios of the bridge were identified from output-only modal analysis by using the frequency domain decomposition. This approach was efficient in identifying the damping ratios of high modes that were challenging due to weakly excited signals. The damping ratio of the triggered mode for VIV was the lowest among the investigated modes and estimated to be the level of the design-damping ratio.

Time Synchronization for Wireless Sensors Using Low-Cost GPS Module and Arduino

Time synchronisation for wireless sensors is important for a proper interpretation of measurements, particularly for acceleration measurements to estimate mode-shapes correctly. This paper presents a new time synchronisation method working independently on each node without exchanging time-sync packets among nodes. This stand-along operation can make field measurement campaigns very time-efficient without a need of constructing and validating the wireless sensor network. The proposed method firstly time-stamps measurements using the accurate time-source from a GPS module on each node, and secondly re-samples the time-stamped data to get time-synchronised data. The time-stamping method proposed in the study utilises Pulse-Per-Second (PPS) signals and NMEA (National Marine Electronics Association) sentences generated by a low-cost GPS module, and the internal timer/counter unit of Arduino. Error analysis on the proposed time-stamping method was carried out and derived an analytical expression for the maximum variance of time-stamping error of the proposed method. Four experiments have been carried out to observe 1) the long-term operational stability of the GPS module, 2) the accuracy of the PPS signals, 3) the accuracy of the proposed time-stamping method, and 4) the validity of the proposed time-synchronisation method for output-only modal analysis on a laboratory floor structure. The GPS module was found to operate or to resume operating stably for the entire test period of seven days even with the limited field of view to the sky. The relative time errors of two PPS signals from four GPS modules were found to be within +/-400 nsec. The time-stamping error measured by two identical time-stamping Arduinos for common trigger signals was found to have a standard deviation of 40.8 nsec, which agreed well with the maximum value of 42.0 nsec predicted by the error analysis. From the output-only modal analysis, the estimated modal parameters were found to agree well with that from the wired acceleration sensors. The phase angle of the cross spectral density of the two wireless accelerations showed that there was no apparent time-synchronisation error observable. These observations indicated a successful operation of the proposed time-synchronisation method.

Output-only modal analysis of wind turbine tower based on vibration response under emergency stop

The identification technique of output-only modal parameters is proposed for the large wind turbine tower under emergency stop. Compared with the response of regular operating conditions, the immediate tower structural response under emergency stop much more resembles a state of free vibration, which is more appropriate for the modal identification of the wind turbine tower. The vibration response is measured in the nacelle, which is easy to perform in the field modal test. The variational mode decomposition (VMD) is applied to decompose the vibration response into several band-limited intrinsic mode functions. The free responses of decomposed functions are extracted by applying the random decrement technique (RDT). Finally, the modal damping ratio and natural frequency are identified from each free modal response by using the Hilbert transform method. Simulations and a 1.5 MW wind turbine field modal test results verify the effectiveness of the proposed identification method. The main modal parameters of wind turbine, including weak modes, are effectively extracted by using output-only vibration responses under emergency stop. The modal parameter identification method is provided for the large wind turbine structure under the engineering condition.