Frequency-domain Method Research Articles

Exploring intricate connectivity patterns for cognitive functioning and neurological disorders: incorporating frequency-domain NC method into fMRI analysis.

This study extends the application of the frequency-domain new causality method to functional magnetic resonance imaging analysis. Strong causality, weak causality, balanced causality, cyclic causality, and transitivity causality were constructed to simulate varying degrees of causal associations among multivariate functional-magnetic-resonance-imaging blood-oxygen-level-dependent signals. Data from 1,252 groups of individuals with different degrees of cognitive impairment were collected. The frequency-domain new causality method was employed to construct directed efficient connectivity networks of the brain, analyze the statistical characteristics of topological variations in brain regions related to cognitive impairment, and utilize these characteristics as features for training a deep learning model. The results demonstrated that the frequency-domain new causality method accurately detected causal associations among simulated signals of different degrees. The deep learning tests also confirmed the superior performance of new causality, surpassing the other three methods in terms of accuracy, precision, and recall rates. Furthermore, consistent significant differences were observed in the brain efficiency networks, where several subregions defined by the multimodal parcellation method of Human Connectome Project simultaneously appeared in the topological statistical results of different patient groups. This suggests a significant association between these fine-grained cortical subregions, driven by multimodal data segmentation, and human cognitive function, making them potential biomarkers for further analysis of Alzheimer's disease.

High-efficiency scattering field modeling in metallic components: a machine-learning-inspired approach

We present a highly efficient method for characterizing the scattering field distribution of surface plasmon polaritons in metallic components by combining the eXtended Pseudospectral Frequency-Domain (X-PSFD) method with an iterative, machine-learning-inspired procedure. Shifting away from traditional matrix operations, we utilize the “Adam” optimizer—an effective and swift machine learning algorithm—to solve the scattering field distribution. Our method encompasses the derivation of the associated cost function and gradient differentiation of the field, leveraging spectral accuracy at Legendre collocation points in the Helmholtz equation. We refine the total-field/scattered-field (TF/SF) formulation within the X-PSFD framework for optimized incident field management and employ Chebyshev–Lagrange interpolation polynomials for rapid, accurate computation of broad-band results. To ensure global accuracy, we introduce unique physical boundary conditions at subdomain interfaces. Demonstrating our method’s robustness and computational efficiency, we model perfect electric conductors (PECs) and silver nanocylinders, and we apply our approach to analyze the excited electric field on subtly distorted metallic surfaces, particularly plasmonic structures, thereby validating its wide-ranging effectiveness.

Feasibility of using the frequency-domain electromagnetic method to detect pipeline blockages: Experimental study

The normal function of modern society requires a vast number of buried pipelines with differing specifications, which could become blocked to varying degrees during routine operation. Consequently, a major technical municipal engineering problem is how best to accurately, nondestructively, and efficiently locate blockages in underground pipelines. The frequency-domain electromagnetic (FDEM) method has been widely used in geophysical exploration because of its features of nondestructive examination and high efficiency. Considering the application of FDEM to the problem of locating blockages in underground pipelines, numerical simulations and physical experiments are conducted on different pipeline types with different blocked states, different blockage substances, and different working configurations. Results demonstrate that FDEM is most applicable for the detection of blockages in insulated pipelines, especially when the single-ended charging method is used or when the blockage has reasonable impermeability because the induction signal exhibits a particularly obvious abrupt drop at the blockage position. However, owing to the low resistivity of metals and the current propagating to the surrounding ground, which makes it easier to form more conductive paths than blockages, the FDEM displays no obvious change in signal characteristics at the position of a blockage in a metal pipeline, which means that this method has certain challenges for detecting such blockages.

Ultrasound Shear Elastography With Expanded Bandwidth (USEWEB): A Novel Method for 2D Shear Phase Velocity Imaging of Soft Tissues.

Ultrasound shear wave elastography (SWE) is a noninvasive approach for evaluating mechanical properties of soft tissues. In SWE either group velocity measured in the time-domain or phase velocity measured in the frequency-domain can be reported. Frequency-domain methods have the advantage over time-domain methods in providing a response for a specific frequency, while time-domain methods average the wave velocity over the entire frequency band. Current frequency-domain approaches struggle to reconstruct SWE images over full frequency bandwidth. This is especially important in the case of viscoelastic tissues, where tissue viscoelasticity is often studied by analyzing the shear wave phase velocity dispersion. For characterizing cancerous lesions, it has been shown that considerable biases can occur with group velocity-based measurements. However, using phase velocities at higher frequencies can provide more accurate evaluations. In this paper, we propose a new method called Ultrasound Shear Elastography with Expanded Bandwidth (USEWEB) used for two-dimensional (2D) shear wave phase velocity imaging. We tested the USEWEB method on data from homogeneous tissue-mimicking liver fibrosis phantoms, custom-made viscoelastic phantom measurements, phantoms with cylindrical inclusions experiments, and in vivo renal transplants scanned with a clinical scanner. We compared results from the USEWEB method with a Local Phase Velocity Imaging (LPVI) approach over a wide frequency range, i.e., up to 200-2000 Hz. Tests carried out revealed that the USEWEB approach provides 2D phase velocity images with a coefficient of variation below 5% over a wider frequency band for smaller processing window size in comparison to LPVI, especially in viscoelastic materials. In addition, USEWEB can produce correct phase velocity images for much higher frequencies, up to 1800 Hz, compared to LPVI, which can be used to characterize viscoelastic materials and elastic inclusions.

A Frequency Domain Methodology for Quantitative Evaluation of Diffuse Wavefield With Applications to Seismic Imaging

AbstractAmbient Noise Imaging (ANI) of subsurface structures relies on seismic interferometry of diffuse seismic wavefields. However, the lack of effective methods to quantify and identify highly diffuse waves hampers applications of ANI, particularly in evaluating seismic attenuation and monitoring structural changes with high temporal resolution. Conventional ANI approaches require data normalization, which effectively suppresses the non‐diffuse component with large amplitude but also results in significant loss of amplitude and phase information in the continuous seismic records. In this study, we propose a frequency domain method to quantitatively evaluate the degree of diffuseness of seismic wavefields by analyzing their statistical characteristics of modal amplitudes for stationarity and randomness. Tests on synthetic waveform and field nodal records show that the proposed method can effectively distinguish between diffuse and non‐diffuse waveforms for either single‐ or three‐component data. As an application, we identify a 60‐s‐long diffuse coda of a local M 2.2 earthquake recorded by a dense nodal array on the San Jacinto Fault Zone, and successfully extract high‐quality dispersion curve and Q‐value without performing data normalization. These results are consistent with those obtained by conventional methods that assess the correlation between coherency and the Green's function, and by modeling ballistic waves generated by road traffic. Our proposed method can advance the imaging of subsurface velocity and attenuation structures as well as monitoring temporal changes for scientific studies and engineering applications.

Shaking table model test for seismic response of soft soil site

Soil sites play a crucial role during earthquakes and serve as conduits for the transmission of seismic effects from the bedrock to urban structures. Analyzing the dynamic response of soil sites to seismic waves is crucial as it presents deeper insights into earthquake damage mechanisms. In this study, we prepared a mixture of sawdust and medium sand with a 1:2.5 mass ratio to model soil samples from a soft soil site in Shanghai. The applicability of the scale-factor equation was verified using resonance column tests. A series of shaking table tests were conducted to simulate free-field site responses based on the dimensions, operating frequencies, and vibration modes of the shaking table at the State Key Laboratory of Disaster Reduction in Civil Engineering at Tongji University. Three different types of earthquake waves were selected as the input motions: TCU003 for far-field long-period seismic waves, TCU068 for near-field pulse-type seismic waves, and the El Centro earthquake wave. The Kramer frequency domain method was used to verify the transfer functions of the site seismic responses. Furthermore, discrepancies in the time–frequency distribution of the soft site responses influenced by various types of earthquake waves were assessed and analyzed. The seismic response characteristics of the soft soil sites under varying input intensities were also analyzed. The findings of this study present valuable reference data for the seismic zoning of soft-soil sites and facilitate the determination of seismic input parameters for engineering structures.

The oxymoron of damage assessment in dynamics by static approach

The evaluation of fatigue damage of structural components within dynamic systems subjected to random loads is typically addressed using multibody models wherein one or more components are modeled as flexible using the modal approach. While incorporating flexible elements allows for consideration of their influence on the overall dynamic behavior of the system, certain components are intentionally designed to function as rigid bodies. Consequently, in this case the incorporation of flexible elements within multibody models merely leads to complex and time-consuming analysis. Hence, it would be more pragmatic to realize rigid body multibody models, with components characterized solely by their inertial properties, and subsequently extract the dynamic forces applied to the components to be verified. The assessment of stress can then be carried out by exploiting the principle of superposition of effects in the time domain. In this context, the objective of the present study is to develop this methodology in the frequency domain. This approach not only capitalizes on the simplicity of rigid multibody models but also harnesses the computational capabilities of the frequency-domain method for evaluating fatigue damage in components subjected to random loading conditions. This work, therefore, provides a rapid, effective, and robust method for verifying and designing rigid mechanical components integrated into dynamic systems subjected to random loads.

Apparent Resistivity Variation Imaging Method Based on Magnetic Field Gradient by NGO-LSSVM for the Ground-Airborne Frequency-Domain Electromagnetic Method

Apparent resistivity imaging is a typical rapid imaging method in the ground-airborne frequency-domain electromagnetic method. At present, the apparent resistivity is typically calculated by the measured magnetic field, however, this imaging method exhibits limited capability in recognizing the center of three-dimensional anomalies. Therefore, this paper proposed the calculation of apparent resistivity using magnetic field gradients. To solve the problem of random artificial anomalies that existed during the calculated process, this paper presents a hybrid least square support vector machine (LSSVM) and Northern Goshawk optimization (NGO) to establish the mapping relationship between the magnetic field gradient and apparent resistivity variation. This approach enables accurate prediction of apparent resistivity variations and effectively resolves the challenge of correcting background resistivity. Furthermore, three typical theoretical models and field examples are used to predict the apparent resistivity variation, the imaging results demonstrate that the proposed NGO-LSSVM algorithm is a feasible and efficient tool for predicting the apparent resistivity variation with high accuracy. This study provides a novel and efficient imaging method, which facilitates the application of ground-airborne frequency-domain electromagnetics for high-resolution detection requirements, such as mineral exploration.

A new methodology of non-destructive testing in a set of two parallel immersed plates using time reversal process and leaky Lamb waves

Ultrasound has been identified as a suitable method for inspecting complex structures (such as nuclear reactors), as it can propagate through both liquids and steel elements to be inspected. Leaky Lamb waves have been extensively researched to detect damages in plate-shaped structures, which are waves that reemit bulk waves towards the surrounding fluid. An imaging method based on the time reversal of Lamb waves has been applied in preliminary work to detect the edge of a single immersed plate and a machined notch. In this study, the frequency-domain topological energy method is applied to a set of two parallel immersed plates to succeed in accurately localizing defects represented by the edges of the plates. Firstly, the behaviour of leaky Lamb waves is briefly addressed. A 2D-STFT (two-dimensional Short Time Fourier Transform) is then used to separate the different Lamb modes, which is a powerful tool for tracking the modes involved in the propagation over time. The Fast Topological Imaging Method (FTIM), which allows for faster computations with less data storage, is applied to the case of Lamb waves in a set of parallel plates. Lamb modes can be identified then selected to improve the analysis of the obtained images. An original methodology is proposed based on spots (maxima) analysis for interpreting the results of this topological energy and identifying the edges of the two plates. This process could be applied, in the same manner, to other scattering defects in ultrasound non-destructive testing of plates.

Seismic wave modeling of fluid-saturated fractured porous rock: including fluid pressure diffusion effects of discretely distributed large-scale fractures

Abstract. The scattered seismic waves of fractured porous rock are strongly affected by the wave-induced fluid pressure diffusion effects between the compliant fractures and the stiffer embedding background. To include these poroelastic effects in seismic modeling, we develop a numerical scheme for discretely distributed large-scale fractures embedded in fluid-saturated porous rock. Using Coates and Schoenberg's local-effective-medium theory and Barbosa's dynamic linear slip model characterized by complex-valued and frequency-dependent fracture compliances, we derive the effective viscoelastic compliances in each spatial discretized cell by superimposing the compliances of the background and the fractures. The effective governing equations for fractured porous rocks are viscoelastic anisotropic and numerically solved by the mixed-grid-stencil frequency-domain finite-difference method. The main advantage of our proposed modeling scheme over poroelastic modeling schemes is that the fractured domain can be modeled using a viscoelastic solid, while the rest of the domain can be modeled using an elastic solid. We have tested the modeling scheme in a single fracture model, a fractured model, and a modified Marmousi model. The good consistency between the scattered waves off a single horizontal fracture calculated using our proposed scheme and the poroelastic modeling validates that our modeling scheme can properly capture the fluid pressure diffusion (FPD) effects. In the case of a set of aligned fractures, the scattered waves from the top and bottom of the fractured reservoir are strongly influenced by the FPD effects, and the reflected waves from the underlying formation can retain the relevant attenuation and dispersion information. The proposed numerical modeling scheme can also be used to improve migration quality and the estimation of fracture mechanical characteristics in inversion.

Frequency-domain searching algorithm in deflectometry for measuring the surface of a transparent planar element.

This Letter presents the frequency-domain searching algorithm in deflectometry (FSAD). By encoding specialized multi-frequency fringe patterns and employing a correlation searching algorithm, the limitations of existing frequency-domain methods can be overcome to some extent, thereby separating front and back surface reflections to obtain complete measurement data. The principles of FSAD are described in detail. In the experiment, a piece of window glass with thickness of 10 mm and a square area of 96 × 96 mm is measured to verify the proposed method.

STEWART PLATFORM DYNAMICS MODEL IDENTIFICATION

Context. At the present stage, with the current demands for the accuracy of motion control processes for a moving object on a specified or programmable trajectory, it is necessary to synthesize the optimal structure and parameters of the stabilization system (controller) of the object, taking into account both real controlled and uncontrolled stochastic disturbing factors. Also, in the process of synthesizing the optimal controller structure, it is necessary to assess and consider multidimensional dynamic models, including those of the object itself, its basic components, controlled and uncontrolled disturbing factors that affect the object in its actual motion.
 Objective. The aim of the research, the results of which are presented in this article, is to obtain and assess the accuracy of the Stewart platform dynamic model using a justified algorithm for the multidimensional moving object dynamics identification.
 Method. The article employs a frequency-domain identification method for multidimensional stochastic stabilization systems of moving objects with arbitrary dynamics. The proposed algorithm for multidimensional moving object dynamics model identification is constructed using operations of polynomial and fractional-rational matrices addition, multiplication, Wiener factorization, Wiener separation, and determination of dispersion integrals.
 Results. As a result of the conducted research, the problem of identifying the dynamic model of a multidimensional moving object is formalized, illustrated by the example of a test stand based on the Stewart platform. The outcomes encompass the identification of the dynamic model of the Stewart platform, its transfer function, and the transfer function of the shaping filter. The verification of the identification results confirms the sufficient accuracy of the obtained models.
 Conclusions. The justified identification algorithm allows determining the order and parameters of the linearized system of ordinary differential equations for a multidimensional object and the matrix of spectral densities of disturbances acting on it under operating conditions approximating the real functioning mode of the object prototype. The analysis of the identification results of the dynamic models of the Stewart platform indicates that the primary influence on the displacement of the center of mass of the moving platform is the variation in control inputs. However, neglecting the impact of disturbances reduces the accuracy of platform positioning. Therefore, for the synthesis of the control system, methods should be applied that enable determining the structure and parameters of a multidimensional controller, considering such influences.

Time difference detection based on sliding window all-phase FFT and Kalman filtering for precise flow measurement.

Coriolis mass flowmeter (CMF) measures the mass flow rate by detecting the time difference, typically using frequency domain methods. However, the spectrum leakage is the primary challenge. To address this issue, a new time difference detection method is proposed utilizing sliding window and all-phase fast Fourier transform. The computational complexity is reduced considering the changes in signal frequency. To further improve the stability and response speed of the measured value, a Kalman filtering algorithm based on variance detection is also proposed for post-processing. A transmitter system is developed to validate the proposed methods. The results demonstrate that, for single phase fluids, the accuracy is better than 0.5‰ and the repeatability is better than 0.2‰, thereby offering an improvement in the accuracy of CMF and supporting for industrial applications.

Time-domain sound field reconstruction using a rigid spherical microphone array.

A time-domain approach for interior spherical near-field acoustic holography is proposed to achieve the low-delay reconstruction of time-domain sound fields using a rigid spherical microphone array. This reconstruction encompasses the incident pressure field, the incident radial particle velocity field, and the total pressure field, which includes scattering. The proposed approach derives time-domain radial propagators through the inverse Fourier transform of their frequency-domain counterparts. These propagators are then applied to the array measurements to obtain the time-domain spherical harmonic coefficients of the interior sound field. Given the fact that the time-domain radial propagators possess finite-time support and exhibit significant high-frequency attenuation characteristics, they can be efficiently implemented using finite impulse response (FIR) filters. The proposed approach processes the signal sample-by-sample through these FIR filters, avoiding a series of issues associated with time-frequency transformations in frequency-domain methods. As a result, the approach offers higher accuracy and lower latency in reconstructing non-stationary sound fields compared to its frequency-domain counterpart and thus holds greater potential for real-time applications. Additionally, owing to the scattering effect of the rigid sphere, the approach avoids the impact of spherical Bessel function nulls and does not require the measurement of particle velocities, which renders the measurements cost effective.

Nonlinear aeroelastic analysis of a twin-tail boom UAV with rudder freeplay nonlinearities

The issue of nonlinear structural freeplays in aircraft has always been a significant concern. This study investigates the aeroelastic characteristics of a twin-tail boom Unmanned Aerial Vehicle (UAV) with simultaneous freeplay nonlinearity in its left and right rudders. A comprehensive Limit Cycle Oscillation (LCO) solution route is proposed for complex aircraft with multiple freeplays, which can consider both accuracy and efficiency. For the first time, this study reveals the unique LCO characteristics exhibited by twin-tail boom UAVs with rudder freeplays and provides simulations and explanations of interesting phenomena observed during actual flight. The governing equations are established using the free-interface component mode synthesis method, and the LCOs of the system are mainly solved through the improved time-domain numerical continuation method and frequency-domain numerical continuation method. Furthermore, the study investigates the influence of the left and right rudder freeplay size ratio on the LCO characteristics. The results demonstrate that the twin-tail boom UAV exhibits two stable LCO types: close and differing left and right rudder amplitudes. The proposed method successfully describes the complete LCO behaviors of the system. Overall, this study makes significant contributions to our understanding of the aeroelastic behavior of twin-tail boom UAVs with rudder freeplays.

PPG heart rate extraction algorithm based on the motion artifact intensity Classification and removal framework

When heart rate is extracted by wearable PPG, motion artifact noise causes serious interference. Since the accuracy of PPG heart rate extraction tends to be positively correlated with the complexity of heart rate extraction algorithm, it is challenging to extract heart rate via wearable PPG throughout the day by taking into account both algorithmic complexity and the accuracy of heart rate extraction. In this paper, a PPG heart rate extraction algorithm is proposed under the motion artifact intensity classification and removal (MAICR) framework. Firstly, it evaluates the motion artifact intensity using acceleration time-domain information and PPG frequency-domain information. Then, different heart rate estimation methods are selected according to motion artifact intensity, in ascending order. This corresponds to the use of the frequency-domain direct extraction method, the MNLMS adaptive filtering method, and the joint sparse spectral reconstruction method. Additionally, the overall framework of the algorithm (MAICR) is developed by considering the performance of various methods. Finally, experiments are conducted on the public dataset to demonstrate that the proposed algorithm is applicable to reduce the algorithmic complexity effectively while maintaining the accuracy in heart rate extraction at a certain degree.

Analysis of the exponential stability of a beam-string-beam transmission problem with local damping on the string

We consider a beam-string-beam problem, where two undamped beams are coupled to a locally damped string (first by a damping of frictional type and then by one of Kelvin–Voigt (K–V) type) by transmission conditions. We show that for this structure, the dissipation produced by the frictional part is strong enough to produce an exponential decay of the solution no matter how small is its size, but the semigroup associated with the system is not exponentially stable when we apply a some localized K–V damping on the string, given by a suitable discontinuous function and certain condition under the length of the parts of the structure. However, when we impose hinged conditions on the beams on the interface points, the dissipation produced by a some localized K–V damping, given by a suitable continuous function, is strong enough to produce an exponential decay of the system solution. For the proof of these three results we use a frequency-domain method of semigroup theory, where in the proofs of exponential stability we also use a contradiction argument.

Optimization Analysis of the Shape and Position of a Submerged Breakwater for Improving Floating Body Stability

Submerged breakwaters can be installed underneath floating structures to reduce the external wave loads acting on the structure. The objective of this study was to establish an optimization analysis framework to determine the corresponding shape and position of the submerged breakwater that can minimize or maximize the external forces acting on the floating structure. A two-dimensional frequency-domain boundary element method (FD-BEM) based on the linear potential theory was developed to perform the hydrodynamic analysis. A metaheuristic algorithm, the advanced particle swarm optimization, was newly coupled to the FD-BEM to perform the optimization analysis. The optimization analysis process was performed by calling FD-BEM for each generation, performing a numerical analysis of the design variables of each particle, and updating the design variables using the collected results. The results of the optimization analysis showed that the height of the submerged breakwater has a significant effect on the surface piercing body and that there is a specific area and position with an optimal value. In this study, the optimal values of the shape and position of a single submerged breakwater were determined and analyzed so that the external force acting on a surface piercing body was minimum or maximum.

The higher-order analysis of response for linear structure under non-Gaussian stochastic excitations with known statistical moments and power spectral density

The frequency-domain analysis method is a fundamental component of the random vibration analysis, in which the corresponding moment spectrum of excitations are the prerequisite. Nevertheless, the determination of the higher-order moment spectra for non-Gaussian stochastic excitations continues to pose a significant challenge in the existing research works. This paper introduces an accurate and efficient computational approach for determining higher-order moment spectra of non-Gaussian stochastic excitations with known statistical moments and power spectral density (PSD). Firstly, following the idea of the simulation method of non-Gaussian stochastic processes, the transformation model between the stationary non-Gaussian stochastic process and underlying Gaussian stochastic process is determined based on the known statistical moments, the PSD of the underlying Gaussian stochastic process is determined using the transformation model. Secondly, the approximate higher-order moment spectra models of stationary non-Gaussian stochastic processes are presented by the PSD of the underlying Gaussian process. Subsequently, the higher-order moment spectra models of non-Gaussian excitations are utilized to compute the higher-order moment spectra of response for the linear structure via the auxiliary harmonic excitation generalized method. Finally, three numerical examples are examined to assess the efficiency and accuracy of the proposed approximate models for the higher-order moment spectra of non-Gaussian stochastic processes.

An improved 27-point frequency-domain elastic-wave average-derivative method with applications to a moving point source

Exploration seismology based on moving sources such as high-speed trains has attracted increasingly great attention. It is an important task to perform near-surface seismic imaging and inversion using moving sources. In this context, an accurate and efficient forward-modeling engine for moving sources is crucial. We initially consider a single moving point source. To implement the numerical simulation in terms of a moving point source, two aspects need to be considered: (1) the numerical discretization strategy of the seismic-wave equation and (2) the discrete representation of the moving point source. For the 3D heterogeneous elastic-wave equation, we develop an improved frequency-domain average-derivative numerical method (ADM) by introducing the weighted average of four sets of grid points for the mass-acceleration term. Due to the numerical discretization template, the continuously moving point source is discretized as a series of fixed sources located at different grid points and excited at different times. The corresponding discrete representation of spatio-temporal variation is given by modifying the right-hand side of the resulting linear system of equations. A numerical experiment in a 3D homogeneous half-space model validates the higher computational accuracy of the improved ADM and the feasibility of the numerical simulation scheme for a moving point source. Furthermore, we test the performance of the moving-point-source numerical simulation scheme in the 3D heterogeneous overthrust model. The successful implementation of the 3D frequency-domain numerical simulation for a moving point source establishes a foundation for subsequent practical applications of moving sources in seismic imaging to be performed in the future.