Frequency Domain Decomposition Method Research Articles

Fully automated operational modal identification based on scale-space peak picking algorithm and power spectral density estimation

Modal analysis is a fundamental and essential research direction in the field of structural engineering. The ultimate goal is to determine the modal parameters of the structures. However, the existing modal analysis algorithms often require a large number of parameter adjustments and manual intervention during operation, which cannot be fully automated. In order to realize the automatic identification of modal parameters, the automatic operational modal identification method (AOMI) is proposed based on the interpolated power spectral density estimation (IPSE). To achieve more precise spectrum analysis in the low-frequency band, IPSE is employed to perform Fourier transform on the original frequency domain segment with optimized frequency resolution. This enhances the sharpness of the obtained spectrum in the low-frequency range, making peak frequencies more discernible. Subsequently, the scale-space peak picking algorithm is used to automatically obtain the peak of the power spectral density (PSD), thus enabling the automatic identification of the natural frequency. Finally, the frequency domain decomposition method (FDD) is used to identify modal parameters based on the natural frequencies. The effectiveness of AOMI is verified through the modal identification of the old steel truss bridge and the three layer framework. Under the environmental excitation, the frequencies identified by the IPSE method is close to that of FDD, Bayesian fast fourier transform (FFT) and covariance driven stochastic subspace identification (SSI-COV). Furthermore, the PSD obtained through IPSE has sharper peak than that of FDD and the Welch’s method. The damping ratio identification accuracy and modal assurance criterion (MAC) are satisfactory in AOMI, which can improve the automatic performance.

Spillover effects of economic policy uncertainty among the US and BRIC countries: based on time and frequency domain perspectives

ABSTRACT This study examines the static and dynamic spillover effects of economic policy uncertainty (EPU) among US and BRIC countries. We investigate their connectedness both in the time and frequency domains using the spillover index approach and frequency domain decomposition methods. Our results indicate that the countries have significant time-varying characteristic spillover effects, and most of EPU connectedness is generated in the short-term. Furthermore, US domestic emergencies will bring about a sharp increase in spillover indices; in most cases, the US is the major transmitter and receiver of uncertainty spillover while Russia delivers and receives the lowest spillover. These results have implications for policymakers and investors with different time horizons.

Seawater temperature and salinity sensing based on in-fiber Michelson-Fabry-Perrot hybrid interferometer employing frequency domain decomposition method

Seawater temperature and salinity sensing based on in-fiber Michelson-Fabry-Perrot hybrid interferometer employing frequency domain decomposition method

LSTM-Based Approach for Stable Identification of Modal Damping Ratio in Building Structures

Modal parameters are used as safety assessment indicators for evaluating the structural integrity of buildings in various ways. In particular, the modal damping ratio plays a crucial role in accurately predicting the serviceability and safety of buildings, starting from the initial design stage. However, the identification results of the modal damping ratio can become unstable due to measurement time, initial configuration conditions used in the analysis, and nonstationary responses included in the structural response. To address the instability issue, this study proposes a long short-term memory-based frequency domain decomposition (FDD-LSTM) method. The FDD-LSTM method utilizes the acceleration response of the building as input data and the modal damping ratio obtained from the FDD method as output data, constructing an LSTM network model for the relationship between the acceleration response and modal damping ratio. The FDD-LSTM method exhibited a discrepancy of less than 0.02% compared to the reference value of the modal damping ratio obtained through free vibration response. Furthermore, when applied to data acquired from an actual building, the method demonstrated a variance of approximately 5%. The proposed FDD-LSTM method is validated for stability performance using a three-degree-of-freedom numerical analysis model, a 3-story steel frame structure model, and a 117-story high-rise building. The FDD-LSTM method, trained on a large dataset, enables generalized estimation and addresses instability issues related to modal damping ratio.

Generalized adaptive singular spectrum decomposition and its application in fault diagnosis of rotating machinery under varying speed

Rotating machinery fault signals often consist of multiple components with time varying frequencies under variable speed conditions. Spectral overlap exists among these components, making it difficult to independently separate the features of the components. Singular spectrum decomposition (SSD), a singular spectrum analysis-based signal decomposition method, has shown its great potential in suppressing background noise and extracting fault-related components in complex background noise environments. However, SSD is a frequency domain decomposition method with equivalent filtering characteristics, and it is susceptible to the mode mixing when processing signals with spectral overlap. Moreover, the choice of a key parameter in the iteration decomposition process of SSD, the embedding dimension, is determined using an empirical formula, which might cause suboptimal decomposition outcomes. To address these issues, this paper proposes a generalized adaptive singular spectrum decomposition (GASSD) method, which combines generalized demodulation with improved embedding dimension selection for SSD. GASSD incorporates SSD into the framework of adaptive generalized demodulation to separate specific frequency domain features. Firstly, for an effective generalized demodulation analysis, a region block synchronous ridge extraction method is proposed to accurately estimate the instantaneous frequency ridges from the time-frequency plane, which helps construct proper demodulation phase functions. Secondly, to achieve optimal analysis of SSD, a Gini moderation decomposition index is designed to improve the construction of the trajectory matrix by determining an appropriate embedding dimension. Finally, the reliability of the proposed method is demonstrated by analyzing wind turbine generator bearing fault signals and rotor rubbing fault signals.

Identification of damage in steel beam by natural frequency using ANNS models

Beams have played a significant role in engineering applications and they have been commonly used for modelling civil problems. In fact, different models and methods have been developed to identify the damage to the beams. In this paper, the artificial neural network (ANN) model was developed to predict the location, width and depth of the saw-cut of steel beams by the change of natural frequencies. The natural frequencies of a steel beam in different scenarios were identified by the Finite Element Method (FEM). In order to validate the accuracy of FEM model, the natural frequencies of the steel beam in the case of no saw-cut determined by this model were compared with those determined by the Frequency Domain Decomposition (FDD) method. The results indicated that, the combination of FEM method, FDD method and ANN model would have great significance in structure health monitoring.

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.

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.

Structural Damping Ratio Identification through Iterative Frequency Domain Decomposition

The frequency domain decomposition method (FDD) is a commonly used method to identify structural modal parameters and analyze the structural dynamic performance. Although FDD has a high identification accuracy in natural frequencies and mode shapes, damping ratios cannot be identified accurately. The logarithmic decay method to identify the damping ratio in FDD needs the transformation from a narrow frequency band to the time domain, which leads to the loss of the corresponding mode outside the narrow band and add other modes in the narrow band. In this paper, an iterative frequency domain decomposition method (iFDD) is proposed to identify the structural damping ratio in frequency domain. Firstly, the natural frequencies and mode shapes are obtained by the FDD method, and the damping ratios during this identification process are assumed to be unknowns. Then, the natural frequencies, mode shapes, and unknowns are substituted into the output power spectrum formula to construct nonlinear equations. The damping ratios are obtained by solving the equations using iterative optimization methods. Finally, a numerical example and benchmark model are employed to validate the effectiveness of the proposed method. The results showed that the proposed iFDD method can identify the damping ratio precisely in the frequency domain, which is better than the traditional FDD performance.

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).

Extended Tromograph Surveys for a Full Experimental Characterisation of the San Giorgio Cathedral in Ragusa (Italy).

Geophysical surveys are widely used to reconstruct subsoil seismo-stratigraphic structures with a non-invasive approach. In this study the geophysical surveys were carried out with the aim to characterise the San Giorgio Cathedral in Ragusa (Italy) and the area on which it is built from a dynamic point of view. A 3D subsoil model was realised through the integration of two active (i.e., seismic tomography and multichannel analysis of surface waves) and one passive seismic technique (horizontal to vertical spatial ratio). The instrumentation used for the latter method consists of a tromograph (Tromino®), which is also employed for the characterisation of the building, focusing on the façade and the dome, by means of an ambient vibration test, processed through the standard spectral ratio and frequency domain decomposition methods. Integration of the 3D model, showing the distribution of areas with different physicomechanical characteristics, enables identifying anomalies that are likely attributable to the remains of the ancient Byzantine church of San Nicola. Four lower modes mainly involving the two investigated macroelements are identified. The experimental results outline the advantages of the use of the tromograph both for soil and structural characterisation, especially for massive masonry buildings located in areas with high seismic hazard.

Operational and Analytical Modal Analysis of a Bridge Using Low-Cost Wireless Arduino-Based Accelerometers.

Arduino-based accelerometers are receiving wide attention from researchers to make long-term Structural Health Monitoring (SHM) feasible for structures with a low SHM budget. The current low-cost solutions found in the literature share some of the following drawbacks: (1) high noise density, (2) lack of wireless synchronization, (3) lack of automatic data acquisition and data management, and (4) lack of dedicated field tests aiming to compare mode shapes from Operational Modal Analysis (OMA) with those of a digital model. To solve these problems, a recently built short-span footbridge in Barcelona is instrumented using four Low-cost Adaptable Reliable Accelerometers (LARA). In this study, the automatization of the data acquisition and management of these low-cost solutions is studied for the first time in the literature. In addition, a digital model of the bridge under study is generated in SAP2000 using the available drawings and reported characteristics of its materials. The OMA of the bridge is calculated using Frequency Domain Decomposition (FDD) and Covariance Stochastic Subspace Identification (SSI-cov) methods. Using the Modal Assurance Criterion (MAC), the mode shapes of OMA are compared with those of the digital model. Finally, the acquired eigenfrequencies of the bridge obtained with a high-precision commercial sensor (HI-INC) showed a good agreement with those obtained with LARA.

Modal parameter identification and seismic assessment of historical timber structures under near-fault and far-fault ground motions

Timber, one of the oldest structural materials, is an essential material in the construction of traditional structures due to its undeniable advantages. However, wood is sensitive to environmental effects, and hence, historical timber structures experience various degradations and destructions during their service life. This highlights the necessity of investigating the structural responses of such structures using experimental techniques and calibrated finite element models. This paper presents vibration-based system identification of two historical timber structures and an in-depth comparison of the effects of near-fault and far-fault ground motions on seismic responses. Ambient vibration tests were carried out using the operational modal analysis method. Enhanced Frequency Domain Decomposition and Stochastic Subspace Identification methods were used for experimental modal parameters estimation. Also, the initial finite element models were calibrated considering the ambient vibration test results to correctly assess the seismic responses of the selected structures under near-fault and far-fault ground motions. The distributions of maximum amplitudes (displacements, internal forces, and absolute accelerations) under earthquake records with near-fault and far-fault are comparatively presented. All numerical results indicated that both near-fault ground motions and their far-fault counterparts played major roles in terms of the seismic responses of selected historical timber structures. In addition, these results illustrate that both had the potential to increase displacements and, internal forces at load-bearing elements, and leading to notable structural responses and destructive effects.

Numerical Verification on Optimal Sensor Placements for Building Structure Before and After the Stiffness Decrease

Japan and Taiwan are located in an area where earthquakes and typhoons occur very frequently. To ensure the safety of building structures, it is necessary to proceed with structural health identification before and after a disaster. This study proposes the optimal placement of sensors to reduce the number of sensors installed in the mid/high-story building for monitoring and inspection purposes, while simultaneously enhancing the accuracy of the determination of modal frequencies for the building structure. To achieve this goal, the first step is to obtain the reference modal frequencies of the structure. That is to install reference sensors on the structure for recording actual time-histories, then to obtain simulated time-histories using the cubic spline interpolation method. After the actual and simulated time-histories are collected from each structure floor, the Frequency Domain Decomposition (FDD) method is used to enhance the accuracy of reference modal frequencies, and then the Stochastic Subspace Identification (SSI) method is utilized to plot out the stabilization diagram. Several reference modal frequencies shown in the stabilization diagram will be determined. Finally, the Optimal Sensor Placement (OSP) locations for placing acceleration sensors can be obtained using a genetic algorithm. Structural models with different story numbers will then be simulated to obtain OSP locations. The condition of stiffness decrease will also be discussed. A comparison is made before and after stiffness decrease to discover the modal frequencies of the structures under the case of both optimal placement and original placement, ultimately to verify the feasibility of the methods proposed in this study.

Construction and dynamic identification of aeroelastic test models for flexible roofs

The aeroelastic wind tunnel testing of flexible roofs made of hyperbolic paraboloid cable nets is a challenging task for designers and researchers, with very limited documented experiences in the literature. The reduced-scale model construction and its dynamic identification are the main issues to address when approaching this problem, mainly because of (i) the very small mass of the roof, (ii) the strict aeroelastic criteria to satisfy and (iii) a large number of very closely spaced significant natural frequencies. To suggest an approach to follow to investigate the wind—structure interaction for this structural typology, this paper discusses the aeroelastic scaling, the aeroelastic model construction, the dynamic modal identification and the FEM predictive numerical modelling of hyperbolic paraboloid roofs (HPRs) with square, rectangular and circular plan shapes and two different curvatures. Modal identification is especially challenging due to the presence of several closely spaced modes and it is here tackled by different methods such as Welch’s method, random decrement technique (RDT), Empirical mode decomposition with a time-varying filter (TVF-EMD) and frequency domain decomposition method (FDD). The satisfying accuracy of the aeroelastic scaling has been verified by comparing the wind-induced vertical displacements of the prototypes against those of the experimental models. Furthermore, an extensive qualitative investigation of the natural mode shapes has been carried out revealing that test models reproduce most of the prototype modes.

Dynamic Response Identification of a Triple-Single Bailey Bridge Based on Vehicle Traffic-Induced Vibration Analysis

Even though prefabricated steel Bailey bridges have been used for more than 80 years, limited studies of their structural features have been conducted, most of which do not consider their response in operational conditions. This study aimed at determining the modal parameters of a 30.48 m length Triple-Single (TS) Bailey bridge based on traffic-induced vibrations and comparing them with numerical results. Low-cost improvised accelerometers recorded and logged the actual response time histories, while a three-dimensional (3D) numerical model was developed to carry out the relevant dynamic analyses. The identification of modal parameters was based on the Operational Modal Analysis (OMA) process and the Frequency Domain Decomposition (FDD) method. Numerical analysis results are in accordance with the operational dynamic response of the Triple -Single Bailey bridge, confirming that the numerical model can effectively be used for extended dynamic analysis. In addition, the analysis of raw time histories through the OMA process indicates that the response is affected by the connections’ condition, in particular, the eventual looseness of bolts and pins. At least five eigenfrequencies were estimated and matched with relevant mode shapes.

Dynamic Response and Seismic Vulnerabilities of the Historic Tophane-i Amire: Dynamic and Seismic Analysis of a Historic Masonry Building

This study deals with the dynamic characterization of the historic Tophane-i Amire building, located in Istanbul. The domed structure was constructed in the 18th century and is known as the first industrial building in the Ottoman times. It was an arsenal building used for the production of cannons and cannon balls. An ambient vibration survey was conducted with the Enhanced Frequency Domain Decomposition method to identify the dynamic characteristics of the structure. Later, a finite element model of the structure was constructed and numerical dynamic identification was pursued. The obtained experimental and numerical results have been compared and the finite element model of the structure has been tuned to obtain a validated tool to represent the real dynamic behavior of the structure. While the tuned model of the structure is intended to contribute to understanding its structural behavior and evaluate the mechanical properties of masonry, it has also been used for the evaluation of its seismic vulnerabilities. For this purpose, the structure has been analyzed under maximum considered earthquake response spectrum, and stress concentration regions have been determined. The results also serve as data for future structural health monitoring studies related to the structure.

Model parameter estimations of the multi-channel turbulence response from flutter flight tests based on autoregressive spectra

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.

Dictionary learning-based damage detection under varying environmental conditions using only vibration responses of numerical model and real intact State: Verification on an experimental offshore jacket model

Monitoring structural damage is critical for preserving the service life of engineering systems. In varying operational environments, the working loads are changing all the time and they are typically unknown; in such environments, access to damage data is difficult and sometimes even impossible, and generally, intact data of the system is available. From this standpoint, this study aims to propose a novel vibration-based method for damage detection of real systems using Dictionary Learning (DL) based on a FE model and real intact state under different uncertainties such as varying working loads. A Frequency Domain Sparse Representation-based Classification (FDSRC) model is designed via DL to learn the features and damage detection of real systems. The main contribution of this study is the training process of the proposed FDSRC using the raw frequency data of a real intact system and various states of the related Finite Element (FE) model under simple working loads (one working load), which is then tested using the raw frequency data of the various states of the real system under complex working loads (varying working loads), to make more realistic assumptions and simulate the operational conditions. The raw frequency data is generated using the Frequency Domain Decomposition (FDD) method. The performance of the proposed method is validated using real measurements from an experimental offshore jacket model. The results of the study indicate that in the case of changing the working load, the proposed method can achieve higher accuracy than other comparative methods. As a result, the proposed method is robust for structural damage monitoring under different uncertainties.

Resonance measurement and vibration reduction analysis of an office building induced by nearby crane workshop vibration

Tests were conducted on a 6-storey office building and factory building near where abnormal horizontal vibrations often occurred. The floor acceleration responses of the building were measured under the condition of crane operation, which was believed to be one of the sources of the vibration. A one-third octave spectrum and weighted acceleration levels were calculated from the measured floor acceleration time histories to assess human comfort levels. The modal parameters of the building were identified using the frequency domain decomposition method. The field test results indicated that the small crane's excitation frequency during the start and stop operations in the nearby factory was 3.6 Hz, which was the same as the fundamental natural frequency of the building. The resonance phenomenon between the building structure and the crane excitation caused the abnormal horizontal vibration. Finally, the influence of adjusting the excitation frequency, the excitation intensity, and the connection form of the foundation slab on the vibration responses was analyzed. Results showed that when the excitation frequency was adjusted to stagger the natural frequency of the structure by 20%, the acceleration level resulting from the same excitation could be reduced by half. The excitation intensity, the difference between the frequencies of excitation and structure was found to be the key factor influencing the structural resonance response.