Robust multi-dataset identification with frequency domain decomposition

Accelerometers on a bridge can be used to extract dynamic properties such as mode shape which are known to be damage-sensitive. However, as bridges are often physically large, this can require a significant number of sensors. In this paper, the concept of re-deploying a small number of sensors is proposed, building up the mode shape from a series of field acceleration measurements. Frequency Domain Decomposition is used to find segments of mode shape in each measurement, using a different train as the source of excitation in each case. In numerical simulations of a simply supported beam, it is shown that a minimum of two accelerometers can be used to construct two points of a mode shape, the first mode being the one most sensitive to excitation. Mode shape amplitudes are calculated in segments which are then stitched together to obtain the global mode shape. In numerical simulations, failure of the support bearings is represented as an increase in rotational spring stiffnesses. This is shown to have a significant effect on the shape of the first mode. The concept was tested in a field trial, before and after the bridge was repaired. The measured mode shape, represented as an envelope of possible shapes, was seen to change significantly when the support system was rehabilitated, and new bearings installed.

Modified frequency and spatial domain decomposition method based on maximum likelihood estimation

Dynamic study is important in order to design, repair and rehabilitation of structures. It has played an important role in the behavior characterization of structures; such as: bridges, dams, high rise buildings etc. There had been substantial development in this area over the last few decades, especially in the field of dynamic identification techniques of structural systems. Frequency Domain Decomposition (FDD) and Time Domain Decomposition are most commonly used methods to identify modal parameters; such as: natural frequency, modal damping and mode shape. The focus of the present research is to study the dynamic characteristics of typical timber masonry walls commonly used in Portugal. For that purpose, a multi-storey structural prototype of such wall has been tested on a seismic shake table at the National Laboratory for Civil Engineering, Portugal (LNEC). Signal processing has been performed of the output response, which is collected from the shaking table experiment of the prototype using accelerometers. In the present work signal processing of the output response, based on the input response has been done in two ways: FDD and Stochastic Subspace Identification (SSI). In order to estimate the values of the modal parameters, algorithms for FDD are formulated and parametric functions for the SSI are computed. Finally, estimated values from both the methods are compared to measure the accuracy of both the techniques.

Motivated by a need to reduce energy consumption in wireless sensors for vibration-based structural health monitoring (SHM) associated with data acquisition and transmission, this paper puts forth a novel approach for undertaking operational modal analysis (OMA) and damage localization relying on compressed vibrations measurements sampled at rates well below the Nyquist rate. Specifically, non-uniform deterministic sub-Nyquist multi-coset sampling of response acceleration signals in white noise excited linear structures is considered in conjunction with a power spectrum blind sampling/estimation technique which retrieves/samples the power spectral density matrix from arrays of sensors directly from the sub-Nyquist measurements (i.e., in the compressed domain) without signal reconstruction in the time-domain and without posing any signal sparsity conditions. The frequency domain decomposition algorithm is then applied to the power spectral density matrix to extract natural frequencies and mode shapes as a standard OMA step. Further, the modal strain energy index (MSEI) is considered for damage localization based on the mode shapes extracted directly from the compressed measurements. The effectiveness and accuracy of the proposed approach is numerically assessed by considering simulated vibration data pertaining to a white-noise excited simply supported beam in healthy and in 3 damaged states, contaminated with Gaussian white noise. Good accuracy is achieved in estimating mode shapes (quantified in terms of the modal assurance criterion) and natural frequencies from an array of 15 multi-coset devices sampling at a 70% slower than the Nyquist frequency rate for SNRs as low as 10db. Damage localization of equal level/quality is also achieved by the MSEI applied to mode shapes derived from noisy sub-Nyquist (70% compression) and Nyquist measurements for all damaged states considered. Overall, the furnished numerical results demonstrate that the herein considered sub-Nyquist sampling and multi-sensor power spectral density estimation techniques coupled with standard OMA and damage detection approaches can achieve effective SHM from significantly fewer noisy acceleration measurements.

A Bayesian approach to global mode shape identification using modal assurance criterion-based discrepancy model

Mobile sensing has emerged as an economically viable alternative to spatially dense stationary sensor networks, leveraging crowdsourced data from today's widespread population of smartphones. Recently, field experiments have demonstrated that using asynchronous crowdsourced mobile sensing data, bridge modal frequencies, and absolute mode shapes (the absolute value of mode shapes, i.e., mode shapes without phase information) can be estimated. However, time‐synchronized data and improved system identification techniques are necessary to estimate frequencies, full mode shapes, and damping ratios within the same context. This paper presents a framework that uses only two time‐synchronous mobile sensors to estimate a spatially dense frequency response matrix. Subsequently, this matrix can be integrated into existing system identification methods and structural health monitoring platforms, including the natural excitation technique eigensystem realization algorithm and frequency domain decomposition. The methodology was tested numerically and using a lab‐scale experiment for long‐span bridges. In the lab‐scale experiment, synchronized smartphones atop carts traverse a model bridge. The resulting cross‐spectrum was analyzed with two system identification methods, and the efficacy of the proposed framework was demonstrated, yielding high accuracy (modal assurance criterion values above 0.94) for the first six modes, including both vertical and torsional. This novel framework combines the monitoring scalability of mobile sensing with user familiarity with traditional system identification techniques.

In this paper, system identification of a cable-stayed bridge in Korea, the Hwamyung Bridge, is performed using vibration responses measured by a wireless sensor system. First, an acceleration based-wireless sensor system is employed for the structural health monitoring of the bridge, and wireless sensor nodes are deployed on a deck, a pylon and several selected cables. Second, modal parameters of the bridge are obtained both from measured vibration responses and finite element (FE) analysis. Frequency domain decomposition and stochastic subspace identification methods are used to obtain the modal parameters from the measured vibration responses. The FE model of the bridge is established using commercial FE software package. Third, structural properties of the bridge are updated using a modal sensitivity-based method. The updating work improves the accuracy of the FE model so that structural behaviors of the bridge can be represented better using the updated FE model. Finally, cable forces of the selected cables are also identified and compared with both design and lift-off test values.

Operational modal analysis (OMA) enables the identification of modal characteristics under operational loads and conditions. Traditional frequency-domain methods cannot directly capture modal changes over time, while existing time-frequency representations are not sufficiently interpretable due to spurious modes and implicit parameter design. This paper develops a new OMA method in time-frequency representation based on frequency-domain decomposition (FDD). Short-time FDD and a convolution-based strategy are proposed to obtain singular values and local mode shape similarity, respectively, which are further fused into mode indicators by a fuzzy-based strategy mimicking the modal assurance criterion. The method provides not only a global view of the modal characteristics over time and frequency but also estimates of the modal parameters. It is applicable to strongly nonstationary responses under time-varying loads and conditions. All the parameters explicitly affect the time-frequency representation, and the interpretability is enhanced by including physical information from the user’s prior knowledge in selecting parameters and peak bands. The proposed method is validated based on a study of railway sleepers under train passage. The rigid-body motions and bending modes are identified at frequencies up to 6,500 Hz in laboratory tests and 4,500 Hz in field tests at speeds up to 200 km/h. The identified natural frequencies and mode shapes agree with experimental modal analysis (EMA). The proposed method outperforms EMA in terms of broad frequency range and low measurement cost and can be potentially applied to structural health monitoring under operational conditions.

Signal processing of flutter flight test data enables verification of aircraft flutter design, and the signal from a flutter flight test excited by atmospheric turbulence is a particularly important form of the flutter test. Owing to the randomness of atmospheric turbulence excitation, multi-channel analysis of turbulence responses at various positions in the same component can improve the analytical accuracy of flutter signal processing. The relationship between the maximum singular value of the multi-channel turbulence response power spectral density matrix and the system self-power spectral density function is elucidated herein using a frequency domain decomposition method. However, there is a contradiction in the power spectral density function between the spectral line density and the spectral line smoothing calculated based on the periodogram of the frequency domain decomposition. By applying an autoregressive spectral model, the power spectral density function of the turbulence response is calculated to achieve spectral line smoothing and sufficient spectral line density. Additionally, the power spectral density function is then used to construct the power spectral density function matrix of the multi-channel turbulence response, and the maximum singular value curve is calculated based on the singular value decomposition of each spectral pin. Finally, the modal parameters of the turbulence response signal are estimated via multi-modal frequency domain fitting. The developed approach is validated based on simulations and flutter flight test turbulence response signals.

Closely spaced modes identification through modified frequency domain decomposition

On the application of blind source separation for damping estimation of bridges under traffic loading

This study presents the use of mode shapes for the identification of damage location. The residual values from curve fitting procedure on mode shape vectors with Chebyshev standard rational series were used to detect the damage along the beam length. The results showed that all the mode shapes for the damaged cases deviated from that of the undamaged case, where the deviation was towards the damage location. The results also showed that the residual from curve fitting procedure for all mode shapes have higher values around the damaged element along the beam length which made it a good indicator for damage location.

In this study, the influence of inerters on the dynamic characteristics of mass-spring chain systems is systematically investigated through both theoretical analysis and numerical simulations. Specifically, the effects of the inerter coefficient on the natural frequencies, mode shape vectors, and frequency response functions (FRFs) are examined. A novel concept, termed the critical inerter coefficient, is introduced to identify a threshold beyond which the dynamic behavior of a vibration system undergoes fundamental change. At this critical value, both the mode shapes and FRFs exhibit significant deviations from those observed in conventional mass-spring chain systems. Moreover, by introducing a new pole-cancellation mechanism, resonance peaks in the FRFs can be effectively eliminated, leading to essential modifications in the dynamic response. The simulation results further reveal that the combined action of dampers and inerters gives rise to frequency response behaviors that are qualitatively different from those in systems employing traditional damping mechanisms. In particular, not only is the resonance peak suppressed, but distinctive dips or bulges emerge in the FRFs near the natural frequency. Building on these findings, the analysis is extended to an n -degree-of-freedom ( n -DOF) mass-spring chain system incorporating inerters. A theoretical criterion for determining the critical inerter coefficients is derived, providing analytical insights into the influence of inerters on the natural frequencies, mode shape vectors, and FRFs of n -DOF systems. The theoretical predictions are corroborated through numerical simulations, which also uncover the intricate interaction mechanisms between damping and inerters in these systems. This work advances the understanding of how inerters modify the dynamic behavior of vibration systems and offers a theoretical framework for their utilization in structural vibration control and mitigation strategies.

The paper presents how to identify natural frequencies and mode shapes of structures by Operational Modal Analysis (OMA) technique, in which the Frequency Domain Decomposition (FDD) method is used. This method is an experimental method only base on the data of measuring the dynamic response of the structures under the excitation due to ambient forces and operational loads to determine the vibration characteristics. Measure vibration (acceleration) and determine spectral density matrix, using the singular values decomposition method of spectral density matrix to determine the natural frequencies and mode shapes of structures. The calculation results show that the natural frequencies, the mode shapes form determined by the OMA technique is consistent with the calculation results according to the theory and show the reliability of the method.KeywordsNatural frequencyMode shapeIdentifyEMAOMAFDD

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.