Frequency Domain Approach Research Articles

Polynomial stability of a transmission problem involving Timoshenko systems with fractional Kelvin–Voigt damping

In this work, we study the stability of a one‐dimensional Timoshenko system with localized internal fractional Kelvin–Voigt damping in a bounded domain. First, we reformulate the system into an augmented model and using a general criteria of Arendt–Batty we prove the strong stability. Next, we investigate three cases: The first one when the damping is localized in the bending moment, the second case when the damping is localized in the shear stress, we prove that the energy of the system decays polynomially with rate in both cases. In the third case, the fractional Kelvin–Voigt is acting on the shear stress and the bending moment simultaneously. We show that the system is polynomially stable with energy decay rate of type , provided that the two dampings are acting in the same subinterval. The method is based on the frequency domain approach combined with multiplier technique.

Robust and blind watermarking algorithm for chaotic system encryption based on discrete cosine transform-singular value decomposition

Through comparison with most frequency-domain digital watermarking approaches, the spread transform dither modulation (STDM) method exhibits a good embedding effect and is capable of meeting the requirements of blind extraction. However, the rotating attack is difficult to counter, and the cropping attack is seriously impacted by location factors. In addition, there exist numerous algorithms concentrate solely on the watermarking process, ignoring the image’s security. In these views, our work proposes a two-dimensional hyperchaotic system, the so-named Chebyshev ICMIC cascade map with the Knuth–Durstenfeld method, aiming to enhance the security of digital watermarking systems. The scrambled pixels improve the anticropping attack effect through breaking the location correlation of watermark information. For the purpose of magnifying resistance to rotation attack impact, the radial harmonic Fourier moments subtraction coefficient matrix distribution expectation is appropriately adapted to carry out the rotation correction. The performed experiments reveal that the suggested improved STDM watermarking algorithm demonstrates better robustness and invisibility, resisting more attacks than the existing methodologies. Finally, the feasibility of the proposed methods is proved based on the simulation results.

Stabilization of a coupled wave equation with one localized nonregular fractional Kelvin–Voigt damping with nonsmooth coefficients

In this paper, we study the stabilization of a coupled wave system formed by one localized nonregular fractional viscoelastic damping of Kelvin–Voigt type and localized nonsmooth coefficients. Our main aim is to prove that the ‐semigroup associated with this model is strong stability and decays polynomially at a rate of . By introducing a new system to deal with fractional Kelvin–Voigt damping, we obtain a new equivalent augmented system, so as to show the well‐posedness of the system based on Lumer–Phillips theorem. We achieve the strong stability for the ‐semigroup associated with this new model by using a general criteria of Arendt–Batty and then turn out a polynomial energy decay rate of order with the help of a frequency domain approach.

A Background/Resonant decomposition based method to predict the behavior of 2-dof aeroelastic oscillators

Flutter is known as an important issue when designing flexible structures under environmental loading. The frequency-domain approach is one way to carry out this analysis under aeroelastic and buffeting forces, and consists in the determination of the variance of the response for all wind speeds of the design envelope. Each variance is classically obtained by numerical integration of the response power spectral densities (PSD), using a large number of integration points to capture the sharpness of their resonant peaks. This operation is particularly resource consuming, and considerably restricts the speed of the analysis. This paper presents an alternative semi-analytical method for integrating the PSD of a two degree-of-freedom aeroelastic model, based on the Background/Resonant decomposition of the response spectra. It focuses particularly on the integration of the covariances, that model the intermodal coupling effects in the response. The proposed method is compared to other existing Background/Resonant decomposition formulations, and recovers the Davenport’s approximation when neglecting all aeroelastic effects. It is illustrated on an application under the form of a parametric study, and its accuracy is compared to classical numerical methods. The errors committed on the exact nodal variances are of order of 1%.

Rational inattention in the frequency domain

This paper solves a dynamic rational inattention problem by formulating it in the frequency domain. The main result is a rational inattention version of the classical Wiener-Kolmogorov filter. This filter permits an infinite-dimensional state vector, provides a new line of attack for obtaining closed-form solutions, and can be implemented numerically using a simple iterative algorithm. The frequency-domain approach also sheds new light on why rational inattention produces forward-looking behavior: inattentive agents are willing to accept more uncertainty about the timing of disturbances in exchange for less uncertainty about fluctuations at the most important frequencies.

Stability for Weakly Coupled Wave Equations with a General Internal Control of Diffusive Type

The present paper deals with well-posedness and asymptotic stability for weakly coupled wave equations with a more general internal control of diffusive type. Owing to the semigroup theory of linear operator, the well-posedness of system is proved. Furthermore, we show a general decay rate result. The method is based on the frequency domain approach combined with multiplier technique.

Evaluation of frequency domain parameters of heart rate variability in patients with essential hypertension

Background: The autonomic nervous system (ANS) is crucial for controlling blood pressure and preventing the onset of hypertension. Analyzing heart rate variability (HRV) is a common diagnostic method for evaluating the actions of the ANS. The two domains under which HRV can be evaluated are the time domain method and the frequency domain approach. Aim and Objective: The primary objective of this study was to check the cardiovascular health and cardiac autonomic regulation of patients with essential hypertension by assessing frequency domain parameters of HRV. Materials and Methods: The study included 50 patients with essential hypertension in the age group of 35–55 years and 50 healthy individuals of the same age group were selected as controls. HRV assessment was done using standardized instruments and emWave Pro software. All the individuals went through 5 min HRV assessment in the supine position. The frequency domain parameters were checked for analysis of HRV. Results: Very low frequency, low frequency (LF), and high frequency (HF) were significantly lower in hypertensive patients as compared to healthy individuals. The mean value of the LF/HF ratio (2.01 ± 0.61) in hypertensive patients was significantly higher as compared to normal individuals (0.99 ± 0.17, P < 0.001). Total power was also significantly low in hypertensive individuals (457.40 ± 133.63 ms2) than healthy individuals (457.40 ± 133.63 ms2, P < 0.001). Conclusion: The study indicates that as compared to healthy individuals, in hypertensive patients low total power and high LF/HF ratio are seen which are suggestive of poor cardiovascular health and cardiac autonomic dysregulation in hypertensive individuals.

Energy decay of some boundary coupled systems involving wave\ Euler-Bernoulli beam with one locally singular fractional Kelvin-Voigt damping

<p style='text-indent:20px;'>In this paper, we investigate the energy decay of hyperbolic systems of wave-wave, wave-Euler-Bernoulli beam and beam-beam types. The two equations are coupled through boundary connection with only one localized non-smooth fractional Kelvin-Voigt damping. First, we reformulate each system into an augmented model and using a general criteria of Arendt-Batty, we prove that our models are strongly stable. Next, by using frequency domain approach, combined with multiplier technique and some interpolation inequalities, we establish different types of polynomial energy decay rate which depends on the order of the fractional derivative and the type of the damped equation in the system.</p>

Vertical road profile reconstruction from vehicle embedded-sensors

This paper proposes a method for the reconstruction of the vertical road profile from embedded sensors in a car. The study details the specifications in the time domain to ensure a good tracking of the road variation. To meet these specifications, a frequency domain approach is carried out using a model-based design method with a closed-loop structure and a loop shaping technique. The frequency and time responses of the reconstructor obtained in simulation are presented to illustrate the performances. Note that the road profile used in simulation comes from a test bench recording. Similarly, the measurement of noises used in the simulation recorded from on-board sensors used to control the piloted suspension of a DS7 Crossback.

Stabilization of an interconnected system of Schrödinger and wave equations with boundary coupling

In this paper, we consider the Schrödinger equation coupled by the interface with a wave equation and with a boundary damping. The dissipation is acting on the wave equation through the Neumann boundary condition. We formulate the coupled system as an abstract evolution equation in an appropriate Hilbert space and use linear semigroup theory to show the well-posedness of the system. Then under some assumptions on the geometry of the spatial domain, we prove exponential stability of the solution. The proof of this result is based on a frequency domain approach which consists in verifying that the imaginary axis is included in the resolvent set of the system and analyzing the behavior of the resolvent operator of the system on the imaginary axis. The analysis of the resolvent is carried out by combining contradiction argument with the multipliers technique. This result extends Theorem 3.2 in [13] to multimensional spatial domains.

Stability analysis of some neutral delay-differential equations with a frequency-domain approach

<p style='text-indent:20px;'>Two general schemes of neutral delay differential equations are considered. They represent non delayed systems with delayed, nonlinear feedback control. The stability conditions in terms of system parameters are derived using an approach based on feedback systems, namely, the Nyquist stability criterion. It is also shown that those results coincide with some already found in the literature, and others derived here, which are based on classical tools, that investigate directly the roots of characteristic equation. Finally, some examples are given to illustrate the usefulness of this approach.</p>

Task flexible and high performance ILC: Preliminary analysis of combining a basis function and frequency-domain approach

As the demand for faster and more precise control has exponentially increased, the quality of feedforward (FF) control has become increasingly important. In this sense, iterative learning control (ILC) enables significant performance enhancements by learning the FF signal from previously repeated tasks. This study aims to develop a new framework that potentially creates a breakthrough in the current trade-off between the high performance and task flexibility of ILC. By combining a high-performance but non-flexible frequency-domain ILC (F-ILC) and a task-flexible and good (but not great) performance basis function ILC (B-ILC), both a task-flexible and high-performance ILC (C-ILC) is achieved. The proposed C-ILC framework was validated through a second-order system simulation, showing a task flexibility as high as that of B-ILC and a higher tracking performance then that of the current F-ILC framework.

Power Forecasting in Photovoltaic System using Hybrid ANN and Wavelet Transform based Method

Solar energy is a sustainable, renewable energy which is a part of latest industry standards of operation in line with industry 4.0. Solar power variability leads to fluctuation and uncertainty in Photovoltaic (PV) output power. It is a significant issue with regard to the high penetration of PV power generation. The solar irradiance is affected by weather conditions, and varies with geographical locations. Accurate PV power output forecasting is essential for the planning and scheduling alternate sources of conventional power. In this paper we propose a frequency domain approach for forecasting of short-term PV output power. The wavelet transform allows identification of periodic components with time localization, whereas the Artificial Neural Network (ANN) technique allows us to model the non-linearities in the PV time series. In this paper, PV power data for the city Bareilly, Uttar Pradesh is forecasted. Numerical simulations show that the proposed forecasting method for PV power output, shows a significant increase in accuracy over other similar methods. The root Mean Square Error, Mean Absolute Error for the proposed method are also calculated and compared with state-of-the art methods for PV power forecasting.

Testing for Short-run and Long-Run Asymmetric Causality for two Volatile Series: An Extension of Frequency Domain Approach

Testing for Short-run and Long-Run Asymmetric Causality for two Volatile Series: An Extension of Frequency Domain Approach

Nonlinear Iterative Learning Control: A Frequency-Domain Approach for Fast Convergence and High Accuracy

Iterative learning control (ILC) involves a trade-off between perfect, fast attenuation of iteration-invariant disturbances and amplification of iteration-varying ones. The aim of this paper is to develop a nonlinear ILC framework that achieves fast convergence, robustness, and low converged error values in ILC. To this end, the method includes a deadzone nonlinearity in the learning update, which uses the difference in amplitude characteristics of repeating and varying disturbances to modify the learning gain for each error sample. A criterion for monotonic convergence of the nonlinear ILC algorithm is provided, which is used in combination with system measurements to select suitable design parameters. The proposed algorithm is validated using simulations, in which fast convergence to low error values is demonstrated.

A Frequency-Domain Output-Constrained Active Noise Control Algorithm Based on an Intuitive Circulant Convolutional Penalty Factor

Due to their computational efficiency, least mean square (LMS)–based algorithms are still widely utilized to achieve optimal control in active noise control (ANC) applications. Real-world implementation of advanced ANC functionalities, such as selective cancellation of frequencies, is nonetheless hampered by complexity trade-offs, especially with computationally-expensive frequency-domain approaches. Prevailing time-domain adaptive algorithms – proposed to alleviate complexities from transformation – continue to incur increased complexities while constraining the magnitude of frequency bins in the time-domain filters. To address existing complexities in time-domain approaches, this paper proposes a circulant convolutional penalty factor that assists the extended leaky filtered-reference LMS (FxLMS) algorithm in achieving frequency constraint without any frequency-domain transform. This circulant convolutional penalty factor is readily determined by methods for designing finite response filters, such as frequency sampling. Additionally, the coordinate descent method is adopted to further reduce the proposed algorithm's computations, significantly increasing its feasibility for implementation on conventional real-time processors. Finally, the numerical simulations performed on the measured primary and secondary paths demonstrate the effectiveness of the proposed algorithm.

Time domain boundary element modeling of coupled interaction between ocean wave and elastic bridge pier

High-rising bridge pylons or piers in coastal site are flexible enough to induce obvious interaction effect against ocean waves which could alter the dynamic properties and affect the resultant structural response. This study proposes a time domain boundary element approach to investigate the instantaneous coupled interaction between ocean wave and flexible structure with arbitrary geometry. The boundary element theory is integrated with Euler-Bernoulli element following a time integration scheme. The simple Green function associated with perturbation expansion is employed to build the time-invariant hydrodynamic matrix and Newmark method with additional numerical damping is used to integrate the structural response. The proposed approach is validated against both of a benchmark experiment and a previous frequency-domain approach. The interaction effects on structural dynamic properties as well as simultaneous structural response, wave run-up and surface pressure are characterized. The computational efficiency and stability are discussed. Results show that interaction effect might alter the fundamental period and damping ratio and affects the structural response considerably. The proposed approach shows both favorable accuracy and efficiency and could provide more transient information which is absent in previous frequency domain approaches.

LES-CHT for a Rotating Cavity With Axial Throughflow

Abstract The flow and heat transfer within rotating cavities is often discussed as a conjugate problem; the temperature distribution within the cavity disks drives the large-scale flow structure within the cavity, and the cavity aerodynamics influence the heat transfer to the disks. However, most simulations of rotating cavities only consider the fluid domain in isolation. This is particularly true for turbulence resolving approaches such as large eddy simulation (LES). The large time-scale disparity between the fluid time-steps used in LES and the characteristic solid time-scale complicates the use of LES with conjugate heat transfer (CHT). A further issue is that an under-resolved solid mesh artificially amplifies higher frequency temperature fluctuations from the fluid. This paper addresses these challenges with a new method for LES-CHT where the low frequency temperature fluctuation caused by the large-scale flow structure is accounted for using a multi-scale frequency domain approach. We investigate two cases: axially heated disks made of a low conductivity material, and disks made from a higher conductivity material with a temperature set by radial conduction from the shroud. The formation of small-scale flow structures on both the disk and shroud is dependent on the heating configuration of the cavity—indicating that high-fidelity thermal boundary conditions should be used when simulating rotating cavities. The formation of heating induced vortical flow structures near the disk is particularly interesting, as this is unexpected from the laminar Ekman layer modeling argument usually used to consider this region.

Spectral Acoustic Fingerprints of Sand and Sandstone Sea Bottoms

Modern studies which dealt with the frequency domain analysis showed that a frequency-domain approach has an essential advantage and mentioned an inner qualitative relationship between the subsurface structure and its frequency spectra. This paper deals with the acoustic spectral response of sand and sandstone sediments at the sea bottom. An acoustic data collection campaign was conducted over two sand sites and two sandstone sites. The analysis of the results shows that reflections of acoustic signals from sand and sandstone sea bottom are characterized by various spectral features in the 2.75–6.75 kHz range. The differences in acoustic response of sand and sandstone can be quantified by examining the maximal normalized reflected power, the mean frequency, and the number of crossings at different power levels. The statistical value distribution of these potential classifiers was calculated and analyzed. These classifiers, and especially the roughness of the spectrum quantified by the number of crossings parameter can give information to assess the probability for sand or sandstone based on the reflected spectra and be used for actual distinction between sand and sandstone in sub bottom profiler data collection campaigns.

Learning Control for Motion Coordination in Wafer Scanners: Toward Gain Adaptation

Accurate pattern transfer in wafer scanners necessitates the wafer stage and the reticle stage executing a coordinated motion with the synchronization error in terms of nanometers. In an attempt to cope with this challenging issue, a cross-coupling iterative learning control (ILC) with two inputs and two outputs is proposed and then decomposed into two ILC with the same convergence condition, a master–slave ILC for the reticle stage and an independent ILC for the wafer stage. To handle the inevitable stochastic disturbance, which inhibits the achievable ILC performance, an adaptive gain is involved in the proposed method for the sake of accelerated convergence as well as enhanced robustness. It remains constant or is decreased adaptively along the iteration axis, depending on the proportion that the stochastic term accounts for in the error signal. Moreover, a phase leader is chosen as the learning filter and tuned along with the initial learning gain by a frequency-domain approach. Experimental comparisons with existing close yet distinctive approaches highlight the effectiveness and superiority of the proposed method.