Frequency Domain Decomposition Research Articles

Modal identification from turbulence response based on improved frequency domain decomposition

Turbulence excitation is an unavoidable form of excitation in flutter flight tests, and it is also a necessary and effective excitation method in high-speed flights, dives, other high-risk test, and high-frequency modal information mining. However, because the turbulence excitation signals are unmeasurable in the time domain, although the turbulence response contains rich and valuable flutter test information, the randomness and low quality of the data often cause difficulties in modal analysis. Therefore, an improved frequency domain decomposition algorithm for turbulence response processing is proposed in this paper. First, due to the irrelevancy of the atmospheric excitation, the power spectral density function matrix of the multi-channel turbulence response is subjected to singular value decomposition. There is a mathematical relationship between the maximum singular value curve and the system frequency response function. Second, the modal assurance criteria are used to calculate the maximum singular value of a single-degree-of-freedom system. Finally, an orthogonal polynomial method is applied to fit the maximum singular value curve, and the system identification is performed directly in the frequency domain. The simulated data and a certain type of aircraft flutter flight test data are used to verify the proposed method, and the results confirm the effectiveness and engineering applicability of the method developed in this work.

High-resolution frequency domain decomposition for modal analysis of bridges using train-induced free-vibrations

Modal parameters are structural inherent characteristics that can be applied for revealing performance of railway bridges. Free vibration signals generated by a passage of train are commonly utilized to estimate the modal parameters of railway bridges due to their higher signal-to-noise ratios compared to random vibrations caused by ambient loads. However, since free vibration signals rapidly decay over time, the available free-vibration data is typically short-time. When using the fast Fourier transform-based spectral estimation method for modal identification from short-time vibration data, a phenomenon known as spectral leakage occurs, leading to miss-identification of some structural modes. In this study, the classical frequency domain decomposition (FDD) is improved for modal identification of railway bridges, in which the higher resolution auto-power spectral density (PSD) and cross-PSD functions are calculated through the autoregressive (AR) model-based method. The AR model-based method improves both the smoothness and resolution of the PSD functions compared to the fast Fourier transform technique. These AR model-based PSD functions are then employed in the FDD process to facilitate frequency and mode shape identification while avoiding spurious noise modes. The proposed eigenvalue fitting technique is subsequently utilized to estimate damping ratios. Numerical simulation data as well as vibration data from an actual bridge are analyzed to validate the proposed method, with a comparison made to the Welch’s PSD-based method. The results demonstrate that the modified FDD approach enables more effective identification of structural modes, even in the presence of closely-spaced modes.

Development of a low-cost flutter test bed with an EPS foam model for preliminary wing design

This paper discusses a novel, low-cost approach for the design and testing of a flutter test article made out of expanded polystyrene (EPS) foam. The low mass of this test article makes it especially suitable for serving as a test bed for similar low structure-to-fluid mass ratio wing configurations, though it could just as easily be used as the first step in the flutter testing of any structure with complex shape and mechanical properties. The material properties of EPS foam were tested using two different approaches: a 3-point bending test based on ASTM Standards for cellular materials and a new finite element model updating approach that used experimental data collected from simple ground vibration tests (GVT). It was found that the second approach provided material properties that were the most representative of the behavior of the specimen under flutter loads. That information was then used in a computational aeroelastic flutter model of the EPS foam wing. Wind tunnel flutter tests were performed for the EPS foam model. The computational frequency domain decomposition (CFDD) method was used to identify modal parameters and the damping trend extrapolating method was used to predict the critical flutter speed from pre-flutter experimental data. The flutter results from the aeroelastic model were in good agreement with the test data.

Enhancing Wireless Sensor Network in Structural Health Monitoring through TCP/IP Socket Programming-Based Mimic Broadcasting: Experimental Validation

This paper presents the implementation of a synchronous Structural Health Monitoring (SHM) framework utilizing wireless, low-cost, and off-the-shelf components. Vibration-based condition monitoring plays a crucial role in assessing the reliability of structural systems by detecting damage through changes in vibration parameters. The adoption of low-cost Micro-Electro-Mechanical Systems (MEMS) sensors in Wireless Sensor Networks (WSNs) has gained traction, emphasizing the need for precise time synchronization to schedule wake-up times of multiple sensor nodes for data collection. To address this challenge, our proposed method introduces a TCP/IP socket programming-based mimic broadcasting mechanism and a scalable sensing network controlled by a central gateway, leveraging the Raspberry Pi Python platform. The system operates using Internet of Things (IoT) concepts and adopts a star topology, where a packet is transmitted from the gateway to initiate measurements simultaneously on multiple sensor nodes. The sensor node comprises a MEMS accelerometer, a real time clock DS3231 module and Raspberry Pi Zero 2W (RPi0-2W), while the gateway employs a Raspberry Pi 4 (RPi4). To ensure accurate time synchronization, all Pi0-2W nodes were configured as Network Time Protocol (NTP) clients, synchronizing with an RPi4 server using chrony, the reliable implementation of the NTP. Through experimental evaluations, the system demonstrates its effectiveness and reliability in achieving initial time synchronization. This study addresses the challenge of achieving precise time alignment between sensor nodes through the utilization of the Dynamic Time Wrapping (DTW) method for Frequency Domain Decomposition (FDD) applications. The contribution of this research significantly enhances the field by improving the accuracy and reliability of time-aligned measurements, with a specific focus on utilizing low-cost sensors. By developing a practical and cost-effective SHM framework, this work advances the accessibility and scalability of structural health monitoring solutions, facilitating more widespread adoption and implementation in various engineering applications

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.

Adaptive Meta-Learning Probabilistic Inference Framework for Long Sequence Prediction

Long sequence prediction has broad and significant application value in fields such as finance, wind power, and weather. However, the complex long-term dependencies of long sequence data and the potential domain shift problems limit the effectiveness of traditional models in practical scenarios. To this end, we propose an Adaptive Meta-Learning Probabilistic Inference Framework (AMPIF) based on sequence decomposition, which can effectively enhance the long sequence prediction ability of various basic models. Specifically, first, we decouple complex sequences into seasonal and trend components through a frequency domain decomposition module. Then, we design an adaptive meta-learning task construction strategy, which divides the seasonal and trend components into different tasks through a clustering-matching approach. Finally, we design a dual-stream amortized network (ST-DAN) to capture shared information between seasonal-trend tasks and use the support set to generate task-specific parameters for rapid generalization learning on the query set. We conducted extensive experiments on six datasets, including wind power and finance scenarios, and the results show that our method significantly outperforms baseline methods in prediction accuracy, interpretability, and algorithm stability and can effectively enhance the long sequence prediction capabilities of base models. The source code is publicly available at https://github.com/Zhu-JP/AMPIF.

Optimal time decay of the compressible micropolar fluids with discontinuous initial data in 3D

The global existence of weak solutions to Cauchy problem for compressible micropolar fluids with discontinuous initial data has been established in [4]. However, the optimal decay rates of these weak solutions remain an open problem. The current work is to show the optimal decay rates of these weak solutions in Lr-norm with 2<r≤∞ and the optimal decay rates of the first order derivative of the velocity and micro-rotational velocity in L2-norm which are the same as the rates of classical solutions in [20]. In this process, we combine electromagnetic and fluid decomposition, frequency domain decomposition, and construct a series of temporal energy functional to solve complex nonlinear problems with low regularity.

Structural Health Assessment of Kretek II Bridge using Enhanced Frequency Domain Decomposition

The development of infrastructure is growing rapidly in Indonesia. Kretek II bridge is one of the infrastructures built in the country. Dynamics aspects are one of the very important aspects used to validate structural analysis model or being linked to Structural Health Monitoring (SHM) of the bridge. Dynamics properties such as natural frequency, damping ratio, and mode shape also referred as modal parameters. The objective of this research is to determine the modal parameters of Kretek II bridge using Enhanced Frequency Domain Decomposition (EFDD) which is commonly used to extract modal parameters from the acceleration data recorded. Compared to the conventional method, EFDD is very practical and robust in structural health assessment because of its user-friendly uses in the ARTeMIS Modal software. To make sure that the results from EFDD are accurate, numerical modeling is necessary to validate it. This research was conducted using dynamics load test results as data for the modal extraction with EFDD method assisted by ARTeMIS Modal software. Dynamics load test was performed by placing 8 accelerometers in the span and exciting it with impact load from dropped truck on ramp. Modal parameters from the EFDD results are then compared to the numerical modeling results. The first two modes of the EFDD and numerical modeling results consecutively are 3.09 Hz, 3.745 Hz and 3.06 Hz, 3.49 Hz. The EFDD and numerical modeling results are both in agreement with both results having similar mode shape on their first two mode and low error percentage with only 0.89% and 7.17% respectively.

Integrally Bladed Rotor Modal Identification Under Traveling Wave Excitation With High Density Measurement Points

Abstract Vibration testing of an integrally bladed rotor (IBR) is often completed through traveling wave excitation (TWE) bench tests composed of multiple, simultaneously excited inputs. Often, each blade has many output locations. For IBRs with many blades, as often found in the high pressure compressor, the total number of outputs can be several orders of magnitude. Formulation of a full output spectral density matrix from all measurements will then contain an exponential number of values at each frequency bin that can be detrimental to computational resources during the spectral density matrix formulation as well as down-stream system identification algorithms. An online algorithm is proposed for collecting and analyzing TWE data to reduce the large, computationally burdensome datasets into a manageable number of subsets for subsequent system identification. Furthermore, a frequency domain decomposition technique is also proposed for system identification that also attempts to reduce the data size through singular value decomposition. Identified system poles can be averaged from each subset, but mode shapes require stitching each subset together to identify the full mode shape at all output locations. The developed approaches are tested on synthetic TWE data and compared to baseline system identification results obtained using the full spectral density matrix. Results indicate the data subsets accurately compare to the baseline without much loss in accuracy.

Synthetic Aperture Radar Image Despeckling Based on a Deep Learning Network Employing Frequency Domain Decomposition

Synthetic aperture radar (SAR) images are inevitably interspersed with speckle noise due to their coherent imaging mechanism, which greatly hinders subsequent related research and application. In recent studies, deep learning has become an effective tool for despeckling remote sensing images. However, preserving more texture details while removing speckle noise remains a challenging task in the field of SAR image despeckling. Furthermore, most despeckling algorithms are designed specifically for a specific look and seriously lack generalizability. Therefore, in order to remove speckle noise in SAR images, a novel end-to-end frequency domain decomposition network (SAR−FDD) is proposed. The method first performs frequency domain decomposition to generate high-frequency and low-frequency information. In the high-frequency branch, a mean filter is employed to effectively remove noise. Then, an interactive dual-branch framework is utilized to learn the details and structural information of SAR images, effectively reducing speckles by fully utilizing features from different frequencies. In addition, a blind denoising model is trained to handle noisy SAR images with unknown noise levels. The experimental results demonstrate that the SAR−FDD achieves good visual effects and high objective evaluation metrics on both simulated and real SAR test sets (peak signal-to-noise ratio (PSNR): 27.59 ± 1.57 and structural similarity index (SSIM): 0.78 ± 0.05 for different speckle noise levels), demonstrating its strong denoising performance and ability to preserve edge textures.

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

Enhancing response estimation and system identification in structural health monitoring through data-driven approaches

Through the advancement of Data Science methodologies, a new era in output-only identification techniques has been inaugurated, driven by the integration of data-driven methodologies within the realm of Structural Health Monitoring (SHM). This study endeavors to introduce a simplified data-driven approach catering to System Identification (SI) and Response Estimation (RE). This is realized through the utilization of a summation of sine functions, fashioned as a model to harmonize with time domain vibration and acoustic responses. The fidelity of the findings is subsequently authenticated through the application of the Frequency Domain Decomposition (FDD) technique. In addition to the identification process, the proposed approach extends its applicability to predicting time domain responses at novel locations. This augmentation is achieved by harnessing an enhanced methodology founded on the principles of the Dynamic Mode Decomposition (DMD) technique. The veracity of these predicted outcomes is underscored through a comparison with measurements recorded at the same locations, alongside concurrent analysis of DMD-derived results. In order to affirm the efficacy of the proposed methodology, a case study involving a building grappling with enigmatic vibration issues is meticulously selected. The findings underscore that the proposed technique not only adeptly discerns unidentified vibrations without resorting to frequency domain transformation techniques, but also facilitates precise estimation of time domain responses.

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.

Nondestructive Estimation of Neutral Temperature in Rails: A Comparative Study of Machine Learning Strategies

This paper presents the latest findings of a nondestructive evaluation technique currently under development at the University of Pittsburgh to determine the rail neutral temperature (RNT) in continuous welded rails. The technique is based on the extraction of relevant features from rail vibrations and the use of machine learning (ML) to associate these features to the longitudinal stress of the rail of interest. The features contain the spectral information of the vibrations and are pooled together by frequency domain decomposition for input to ML algorithms. Minimum redundancy–maximum relevance and neighboring component analysis are used to identify relevant features to reduce the size of the input vector. In addition, seven algorithms were considered to identify the most accurate model for neutral temperature with respect to the ground truth RNT measured with a strain-gage rosette. The data used in this study were collected from a 5° curved rail on concrete ties. The vibrations were triggered with a hammer and recorded with a few wireless and wired accelerometers attached on the railhead. The results showed that the Gaussian process regressor performs best, and as few as 20 frequencies can be used to predict the RNT with sufficient accuracy.

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.

A digital twin-based framework for damage detection of a floating wind turbine structure under various loading conditions based on deep learning approach

Engineering has many necessary fields, and Structural Health Monitoring (SHM) is one of the most important of them. Sometimes in industrial environments, it is difficult and even impossible to collect data containing different real damages. Therefore, the problem of data acquisition represents a primary challenge in designing damage detection systems. The application of digital twin methods based on simulated models and/or Machine Learning (ML) models is a practical way to solve this problem. In this approach, a digital twin is generated for a compromised structure, utilizing a physics-based model to analyze diverse damage scenarios. Subsequently, an ML model is trained using data extracted from the physics-based model, functioning as the digital twin. This research proposes a method based on a digital twin for detecting damages in structures. The data produced from a Floating Wind Turbine (FWT) model was used to evaluate the performance of the proposed digital twin-based method. For this purpose, the FWT structure was simulated using a numerical model to address the data collection problem in the face of various uncertainties, such as changing loading conditions. In line with the concept of digital twin and to reduce the computational time, a Deep Convolution Long Short-Term Memory Neural Network (DCLSTMNN) model was designed and trained only with the frequency data of various scenarios of the simulated FWT model under constant loads (deterministic loads, including constant wind speed and airy wave model) to learn the damage-sensitive features. Then, to demonstrate the robustness of the proposed model under different uncertainties, the DCLSTMNN model was evaluated using the frequency data of the simulated FWT model under variable loading conditions (including Kaimal wind model and JONSWAP wave theory). Some vibration response components unrelated to the nature of the FWT model were removed using the Complete Ensemble Empirical Mode Decomposition (CEEMD) method. Then, the reconstructed vibration responses were used to create the frequency data using the Frequency Domain Decomposition (FDD) technique. The study results show that the proposed digital twin-based method can detect the location and severity of damage more accurately than other comparable methods despite various uncertainties.

An FDD-based modal parameter-less proportional flexibility-resembling matrix for response-only damage detection

Modal flexibility-based methods are effective tools for vibration-based structural damage detection, including in the output-only case. These methods are typically characterized by two stages: first, the modal parameters are identified, thus obtaining a certain number of modes; second, these modal parameters are used to assemble the modal flexibility matrix. This paper proposes a method for estimating a matrix that approximates a proportional flexibility matrix, termed proportional flexibility-resembling (PFR) matrix, and shows that this matrix can be used for damage detection and localization purposes. This matrix is obtained through signal processing operations to be executed after applying the first steps of the frequency-domain decomposition (FDD) technique—i.e., after the singular value decomposition of the spectral density matrix. The defining aspect of the PFR matrix is that, differently from the traditional formulation of modal flexibility and proportional flexibility matrices, it can be assembled without the need of an explicit identification of the modal parameters. In fact, the matrix is estimated by processing all first singular vectors and also all first singular values in a selected frequency range. In the proposed method, the typical two stage approach of traditional modal flexibility methods is avoided, and the intervention of an operator is limited to setting the values of a few parameters in the initial phase of the process. Numerical simulations and experimental data from a testbed structure were used to show the effectiveness of the proposed approach, and the analyses were performed by considering structures with different damage scenarios and damping properties.

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.

Mutual Interference Mitigation for Automotive FMCW Radar With Time and Frequency Domain Decomposition

Currently, the frequency-modulated continuous-wave (FMCW) millimeter-wave (MMW) radar is a typical choice for automotive and transportation radar systems. As the number of FMCW radars explodes in the current vehicle market and the working frequency is limited in an open window of 76–81 GHz, FMCW radars on the road easily mutually interfere with each other, especially due to their wide bandwidth. Hence, in this article, we rigorously analyze the target echo, i.e., the beat signal, especially the sparsity of the interference signal in the time domain, and the row sparsity of the useful echo signal in the frequency domain. By taking advantage of this feature, we design an interference mitigation optimization problem to extract the target echoes with a row-sparse constraint. A closed-form solution is given in each iteration with specific derivations. Finally, numerical simulations and multiple practical scenes are provided to demonstrate the effectiveness of the proposed method.