Modal Identification Techniques Research Articles

Estimation of Empirical Response Spectrum and local responses of the Justicia Espada Acuña Mena building using the Mod-ζ(var) method for the 2010 central Chilean mega-earthquake (Mw=8.8)

A novel system identification technique called Mod-ζ (var) is formulated, implemented, and validated to study the seismic response of a 3D R/C shear wall building during the 2010 central Chilean mega-earthquake (Mw = 8.8). The Mod-ζ(var) approach is an evolution of Least-Square modal system identification techniques, where modal parameters are adjusted through small data windows to fit seismic data in the frequency and time domains. This technique offers several advantages over traditional methods, including the estimation of time-variant dynamic properties during seismic events and the reliable assessment of continuous nonlinear modal responses. As a result, the Mod-ζ(var) approach allows for determining empirical response spectra related to each seismic input. The technique can also compute the local response of measured and unmeasured floors as the product between the nonlinear modal responses (obtained from the Mod-ζ(var) approach) and the normalized seismic mode shapes for all building floors, which can be estimated from ambient vibration data. Finally, the seismic floor deformations can be imposed on a FEM to determine relevant engineering quantities such as inter-story drift, inter-story forces, and local demand of structural elements (e.g., drift ratios, curvatures, internal forces, stresses, strains, etc.).

Sensitivity Analysis of Modal Parameters of an RC Joint Subject to Progressive Damage under Cyclic Loads

This paper presents the results of an experimental study that focused on the gradual modification of the modal parameters of reinforced concrete beam–column frames subjected to progressive damage under cyclic loading. As is commonly found in structures of the 1970s, the specimen was characterized by the absence of specific shear reinforcement in the nodal panel. The frame modal parameters were investigated using the ambient vibrations test (AVT) as a modal identification technique. In particular, quasi-static cyclic tests with increasing amplitudes were performed on the reinforced concrete frame specimen and the modal parameters were assessed at various stages of frame degradation. By establishing a correlation between the changes in the modal parameters and the mechanical indicators of the structural damage in the frame, this study aimed to determine whether the ambient vibration tests could offer meaningful insights for evaluating the structural health of this type of structural component. As a result of the damage that occurred in the tested RC frame, the residual experimental value of the first natural frequency of the specimen was found to reduce at 52.7% of the original reference value (undamaged stage). Similarly, the residual value of the frame stiffness was found to be as low as 43.82% of the initial one. Both these results confirmed that changes when monitoring the modal frequencies may provide quantitative indexes to describe the structural health of RC frames. In combination with static tests for a direct measure of the structural stiffness variations, the AVT technique was shown to have interesting potential in detecting the type, level, and distribution of the progressive damage in civil structures. In particular, exponential and polynomial regression curves were defined to describe the decay of the first natural frequency as the structural damage increased in various parts of the frame, and it was shown that the variation in the first natural frequency was determined more by the damage on the beam than by the damage on the joint.

Utilizing data-driven algorithms for blind modal parameter identification of structures from output-only video measurements

In structural dynamics and vibration analysis, modal identification plays a pivotal role in understanding and characterizing the dynamic behavior of complex systems. Traditional modal analysis techniques heavily rely on accurate sensor placement and knowledge of the excitation forces, which may not always be feasible or practical in real-world scenarios. Recently, non-contact video-based modal analysis methods for structures with arbitrary complexity using computer vision techniques have gained much importance. But these methods need to know ahead of time where the structure's natural frequency ranges are, and they use steerable pyramids, which are complicated multi-scale image decomposition filters. To address these issues, a blind modal identification technique is suggested to extract the modal parameters (modal frequency and mode shapes) from the recorded structural vibration video signal. The proposed algorithm for unsupervised machine learning is the Non-Negative Matrix Factorization (NNMF) method, which is combined with the Generalized Complexity Pursuit (GCP) method for blind source separation. The NNMF algorithm is directly applied to the raw pixel-time series made from the video data to get the temporal components, which are then separated using GCP to find the individual modal frequencies and mode shapes. The above algorithm is first validated on a numerical model and then implemented on laboratory scale models (cantilever, single-degree, and multi-degree frame models). Finally, the proposed methodology is implemented on real-world recorded structural vibration videos to determine its noise sensitivity, such as the Tacoma Narrows bridge and the London Millennium footbridge. The modal parameters extracted are compared with those from the available literature for validation. The estimation errors obtained from all the validations are well below 1%, which makes the technique quite suitable and reliable for structural vibration monitoring by identifying and reproducing complex vibration modes.

Research on railway vehicle modal parameter identification method based on drop impact load

This paper investigates the modal parameter identification technique utilizing a drop impact load. A 12-DOF mathematical model of a Railway Vehicle System (RWVS) was constructed, followed by theoretical calculations, simulation analysis, and tests with four different drop impact loads. The responses to these loads were inspected through FFT, and the modal frequencies of the RWVS were determined by the Peak Picking (P-P) method. The simulation demonstrated that four types of drop impact loads can activate the bounce, pitch, and roll modes of the RWVS. The theoretical calculation and simulation analysis revealed that the maximum error of modal frequency identification is no greater than 6.5%. The experimental results verified that the drop impact excitation method can be used to identify the modal parameters of a complex railway vehicle system, which is highly beneficial for the design and verification of the vehicle structure.

The new Subspace-based poly-reference Complex Frequency (S-pCF) for robust frequency-domain modal parameter estimation

Subspace identification has been widely used in modal parameter estimation. The formulation of a parametric subspace-driven modal identification technique is achieved by using the Singular Value Decomposition (SVD) to remove most the uncertainties present in the null space of the system matrices used in the identification process, which leads to a more robust estimation of the modal properties. This idea has been used in the formulation of time domain modal identification techniques like the (time-domain) Eigensystem Realization Algorithm and the Stochastic Subspace identification techniques. In this paper, a subspace implementation of the new poly-reference Complex Frequency (pCF) formulated in Modal Model is proposed. The idea is to combine SVD with the new pCF to derive a new system identification technique that operates in the frequency domain by using either the Frequency Response Function or the Half Spectrum as primary data. Similarly to the ERA, the idea behind the subspace implementation of the pCF is to use different subspaces of the observability and frequency-domain controllability matrices, and carry out eigen-system realizations to estimate the modal properties corresponding to each chosen subspace. In order to illustrate its robustness, the subspace-driven pCF is applied to a simulated and two practical application examples.

Operational Modal Analysis on Bridges: A Comprehensive Review

Structural health monitoring systems have been employed throughout history to assess the structural responses of bridges to both natural and man-made hazards. Continuous monitoring of the integrity and analysis of the dynamic characteristics of bridges offers a solution to the limitations of visual inspection approaches and is of paramount importance for ensuring long-term safety. This review article provides a thorough, straightforward examination of the complete process for performing operational modal analysis on bridges, covering everything from data collection and preprocessing to the application of numerous modal identification techniques in both the time and frequency domains. It also incorporates advanced methods to address and overcome challenges encountered in previous approaches. The paper is distinguished by its thorough examination of various methodologies, highlighting their specific advantages and disadvantages, and providing concrete illustrations of their implementation in practical settings.

Development of a software platform for bridge modal and damage identification based on ambient excitation

Modal and damage identification based on ambient excitation can greatly improve the efficiency of high-speed railway bridge vibration detection. This paper first describes the basic principles of stochastic subspace identification, peak-picking, and frequency domain decomposition method in modal analysis based on ambient excitation, and the effectiveness of these three methods is verified through finite element calculation and numerical simulation. Then the damage element is added to the finite element model to simulate the crack, and the curvature mode difference and the curvature mode area difference square ratio are calculated by using the stochastic subspace identification results to verify their ability of damage identification and location. Finally, the above modal and damage identification techniques are integrated to develop a bridge modal and damage identification software platform. The final results show that all three modal identification methods can accurately identify the vibration frequency and mode shape, both damage identification methods can accurately identify and locate the damage, and the developed software platform is simple and efficient.

Reliable modal estimation of high-rise structures via synergistic usage of multiple stabilization diagram-based operational modal analysis techniques

In operational modal analysis, typically only structural responses are available. Errors and uncertainties may exist in modal estimates, thereby leading to discrepancies in the results by different modal identification approaches even analyzing the same data set. To this end, a synergistic usage of multiple stabilization diagram-based modal identification techniques is presented in this paper to reduce the errors and uncertainties in modal estimates associated with modal identification techniques or modeling ideas. The effectiveness and noise robustness of the synergistic strategy are validated via numerical simulation study of a frame structure. Additionally, the synergistic strategy is further utilized to evaluate the dynamic characteristics of a supertall building with 600 m height during a typhoon event. The application of the synergistic strategy to field measurements reveal that the building natural frequencies varied during the typhoon and exhibited significant amplitude-dependent features. Meanwhile, the damping ratios of the skyscraper for all concerned modes remained roughly stable within a range of [0.16%, 0.94%]. This paper aims to provide a practical way or effective tool to enhance the accuracy and confidence in modal estimation of high-rise buildings, thus further revealing the dynamic characteristics of large-scale structures under severe wind excitations.

Spectral optimization-based modal identification: A novel operational modal analysis technique

In this work, we introduce a novel method, namely Spectral Optimization-based Modal Identification (SOMI) for estimating the modal parameters of structures. SOMI is developed to estimate highly accurate modal damping ratios and mode shapes using the Frequency Domain Decomposition (FDD) principles. The FDD method (and most of the present modal identification techniques), encounters some problems such as modal complexity, lack of accuracy in the case of large damping ratios, and noticeable error in mode shape estimation. In the FDD formulation, the Singular Value Decomposition (SVD) estimation is precise only for lightly damped structures for obtaining the mode shapes and the Power Spectral Density (PSD) function of the modal coordinates. Moreover, the complexity of the mode shapes obtained from the FDD method is significantly biased and should not be used for physical interpretations. The main idea behind the proposed SOMI method is the elimination of the SVD estimation and obtaining the PSD function of the modal coordinates and the mode shapes with the least approximations. Moreover, the modal damping ratio is directly estimated in the frequency domain without any transformation into time domain using two equations derived in this paper. SOMI method uses optimization to make the PSD function of the modal coordinates follow the theoretical equations and estimates highly accurate mode shapes. In this work, the derivations are given for the displacement, velocity, and acceleration signals. The detailed formulation of the proposed method is presented, it is validated with some examples, and its competitive accuracy is compared with the FDD method. The accuracy and robustness of SOMI in noisy conditions are also assessed, with results indicating its effectiveness in handling noise and maintaining accuracy.

Modal Identification of Train Passenger Seats Based on Dynamic Tests and Output-Only Techniques

Railways are one of the most efficient and widely used mass transportation systems for mid-range distances, also being pointed out as the best strategy to reach European Union decarbonisation goals. However, to increase railways attractiveness, it is necessary to improve the quality of the ride, namely its comfort, by decreasing the vibration at the passenger level. This article describes the experimental vibration modal identification of train seats based on a dedicated set of dynamic tests performed on Alfa Pendular and Intercity trains. This work uses two output-only modal identification techniques: the transmissibility functions and the Enhanced Frequency Domain Decomposition (EFDD) method. The last method allows us to clearly distinguish the seat structural movements, particularly the ones related to torsion and bending of the seat frame, from the local vertical foam vibrations. The natural frequencies and mode shapes are validated by matching the results derived from the transmissibility functions and EFDD method. The identified modal parameters are particularly relevant to characterise the vibration transmissibility provided by the foams (local transmissibility) and the vibration transmissibility derived from the metallic seat frame (global transmissibility).

Determining the Dynamic Characteristics of a Multi-Story RC Building Located in Chile: A Comparison of the Results between the Nonparametric Spectral Analysis Method and the Parametric Stochastic Subspace Identification Method

Estimating the dynamic characteristics of instrumented built structures from seismic vibration data collected from built civil structures is essential input information for structural model updating and assessing the health of structures. This study focuses on the earthquake acceleration time histories obtained from several events recorded during its construction phase by accelerometers placed throughout an office building located in Viña del Mar (Chile) to determine its modal features. To this end, the data obtained were analyzed to compare the building’s dynamic properties obtained with two different modal identification techniques. MATLAB programs were developed to implement both methods. The stochastic subspace identification technique for linear systems developed by van Overschee and de Moor was used to study the dynamic properties of the building. In contrast, the nonparametric method employed herein uses correlations and spectral analysis based on the Welch transform in the frequency domain. The investigation demonstrated that both methods identify similar frequencies and that the obtained translational mode shapes exhibit good agreement. Furthermore, the identified frequencies are congruent with the design frequencies.

Rapid Safety Assement and Experimental Derivation of Damage Indexes for In-Service Glass Slabs

The mechanical performance of pedestrian structures attracts the attention of several studies, especially with respect to unfavourable operational conditions or possible damage scenarios. In terms of vibrations, for example, specific customer comfort levels must be satisfied, depending on the class of use, the structural typology, the involved materials, in addition to basic safety requirements. A special consideration should be given to in-service systems that are possibly affected by degradation or even damage, and thus potentially unsafe for pedestrians. In this regard, the availability of standardized non-destructive protocols for a reliable and rapid structural safety assessment may result in efficient support for diagnostic analyses. In this paper, 3 different laminated glass (LG) modular units belonging to 2 different indoor in-service pedestrian systems located in Italy are investigated. Operational Modal Analysis (OMA) procedures and dynamic identification techniques are used to quantify the residual capacity of the examined systems, including damage and material degradation, based on a single triaxial Micro Electro-Mechanical System (MEMS) accelerometer. The experimentally derived performance indicators and calibrated mechanical parameters for the examined structural system are assessed towards traditional design procedures, and further quantified with the support of Finite Element (FE) numerical model updating. A comparative analysis is carried out to explore the structural performance and safety levels of in-service LG slabs in regards to vibration comfort, deflection control and stress analysis.

Design and Validation of a Low-Cost Structural Health Monitoring System for Dynamic Characterization of Structures

Structural Health Monitoring (SHM) is essential to identifying problems that may cause human and material losses produced by disastrous and unexpected structural failures. The dynamic characterization of civil structures adopting SHM systems provides, at a particular moment, accurate information about the current structural response. When considering a proper SHM strategy and affordable economic investment for the maintenance required by structures, it is possible to safeguard the original structural parameters and avoid potential failures. However, traditional SHM systems are not desirable due to the large economic investments involved and demand for exhausting fieldwork. This research presents the design, implementation, and validation of a low-cost SHM system composed of a Wireless Sensor Network (WSN) and a base station in order to identify dynamic properties from the measured structural response. A set of small- and full-scale experimental tests were conducted to validate the WSN system using a wired traditional SHM system. Vibration data recorded through the low-cost SHM system were processed and compared to determine the natural frequencies, mode shapes, and damping properties of different structures by computing modal identification techniques, frequency analysis, and logarithmic decrement. The obtained dynamic characterization results from small- and full-scale experimental testing conclude that the low-cost SHM system can reliably identify the dynamic properties of the tested structures. This proposal provides an inexpensive, functional, and innovative alternative for SHM regarding traditional monitoring systems.

Bayesian Operational Modal Analysis with Genetic Optimization for Structural Health Monitoring of the Long-Span Bridge

Modal parameters, including natural frequencies, damping ratios, and mode shapes, are vital for evaluating the in-service condition of long-span bridges subjected to performance degradation or damages. Operational modal identification techniques requiring only ambient vibration responses are usually utilized to identify the modal parameters of in-service bridges. Due to the measurement incompleteness and modeling errors, uncertainties would inevitably be involved in the identification. The changing operational loads of long-span bridges, e.g. vehicles and winds, could also increase uncertainties. These uncertainty factors could decrease the precision of the operational modal identification and undermine the reliability of structural health monitoring (SHM) for long-span bridges. This study introduces an improved Bayesian modal identification approach using the scaled Fast Fourier Transform data for uncertainty quantification. The proposed method integrates the genetic optimization with the posterior probability density function of modal parameters to ensure the accuracy and robustness of the iteration process. Additionally, an asymptotic estimate interval with the assumption of a high signal-to-noise ratio is defined to improve the computational efficiency. The acceleration responses from a numerical example and a full-scale long-span bridge are adopted to validate the performance of the proposed method. Results show that the improved Bayesian approach can accurately identify the modal parameters and efficiently quantify the uncertainties. The method enhances the reliability of modal tracking for SHM of operational long-span bridges.

Optimal sensor placement techniques for modal identification of historical masonry structures

Since destructive tests are not allowed for historical structures, numerical model updating using accelerometers has gained a lot of attraction in the last decade. Furthermore, another application of structural health monitoring is damage detection for near-real-time monitoring of cultural heritage assets of infrastructures such as masonry bridges. However, high cost is the main problem that discourages the use of large-scale structural health monitoring systems, and a modal pretest analysis is required to plan and optimize the modal tests procedure. For this purpose, various optimal sensor placement (OSP) techniques have been developed to derive the operational modal analysis results with a minimum number of sensors, leading to a lower cost. In this study, various OSP techniques have been applied to optimize sensor placement in two selected case studies. The first case study is a two-span masonry arch bridge in Rhodes, Greece and the second is a stone masonry tower located in Tønsberg, Norway. Baseline finite element models were developed before performing the ambient vibration tests and model updating process. The optimum sensor locations were detected using various techniques, and a comparative study was conducted on the results. Furthermore, the effect of considering soil-structure interaction on the OSP results was investigated.

Single Output and Algebraic Modal Parameters Identification of a Wind Turbine Blade: Experimental Results

This paper describes the evaluation of a single output, online, and time domain modal parameters identification technique based on differential algebra and operational calculus. In addition, an analysis of the frequency response function (FRF) of the system is conducted in a specific set up, emulating its nominal or operational conditions to determine the influence of the non-linearities over the dynamic behavior of the system in those particular magnitudes of deformations; thus, this influence is quantified by a numerical index. This methodology is applied to a wind turbine blade submitted to wind tunnel experiments. The natural frequencies and modal damping ratios of six bending modes associated with the blade are estimated using real-time velocity measurements from one single point of the blade. A comparison with the usual impact hammer modal testing is performed to evaluate and establish the proposed approach’s main contributions. The developed modal parameter identification algorithms are implemented to run into a standard personal computer (PC) where the data acquisition system’s measurements are conditioned and processed. The results show the performance and the fast parametric estimation of the proposed algebraic identification approach.

Modal characteristics and fluid–structure interaction vibration response of submerged impeller

Turbo pump is one of the elements with the most complex flow of liquid rocket engine, and as an important component of turbo pump, an impeller is the weak point affecting its reliability. In this study, a noncontact modal characteristic identification technique was proposed for the liquid oxygen pump impeller. Modal characteristics of the impeller under three different submerged media, air, pure water, and brine with same density as liquid oxygen, were tested based on the noncontact modal identification technology. Submersion state directly affects the modal frequencies and damping ratio. The transient vibration response characteristics of the impeller excited by the unsteady flow field was achieved combining with unsteady flow field analysis and transient dynamic analysis in the whole flow passage of the liquid oxygen pump. Vibration responses at different positions of the impeller show 10X and 20X frequencies, and the amplitude at the root of short blade is significant, which needs to be paid more attention in structural design and fatigue evaluation.

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.

Enhancing the performance of stochastic subspace identification method via energy-oriented categorization of modal components

As an advanced modal identification method, Stochastic Subspace Identification (SSI) technique has been widely used in the engineering field in recent years. However, to apply this technique properly, the characteristics of external force acting on the structural system and the data quality of response signals should meet certain requirements, which sometimes cannot be well satisfied. This may result in some problematic issues, such as mode absences. To improve the working performance of standard SSI method, this study proposes an implementation strategy which is characterized by categorization of modal components in the response into different energy groups for data preprocessing. A numerical case study is presented first, to demonstrate that a key reason for the problematic issues encountered by the standard SSI technique is the imbalanced distribution of energies associated with different modal components of the system response. The proposed method is then detailed. To implement this method, the system response should be first divided into a number of component groups with each group consisting of certain modal components, whose spectral energies are in similar order of magnitude. Then, the standard SSI technique is utilized to identify the modal parameters for each of the above component groups. Measured responses from a real super-tall building are used in the proposed method and other modal identification techniques. The results are compared to validate and evaluate the performance of the proposed method.

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.