Frequency Domain Approach Research Articles

Time-Optimal Guidance Laws Using a Frequency Domain Approach for Spacecraft Rendezvous

AbstractThis paper proposes a novel approach to solving the time-optimal rendezvous problem for spacecraft in orbit. Initially, the characteristics of the time-optimal rendezvous solution in the in-plane motion of the relative equations of motion are analyzed using the direct collocation method. A time-delay filter is designed in the frequency domain using the analysis results. And then, it transforms the time-optimal control problem into a parameter optimization problem. By solving this optimization problem, the switching times of the bang–bang control profile can be determined. The effectiveness of the proposed method is examined through various simulations, demonstrating its ability to resolve the discontinuities caused by the bang–bang control profile while also being effectively applicable under various boundary conditions. Additionally, the proposed method turns out to be robust against disturbances through real-time application.

Stability and Bifurcations in Time-Delay Systems: A Novel and Efficient Blend of Methods

The goal of this paper is to introduce a hybrid technique, combining two existing methods conveniently, to analyze the stability and bifurcations of equilibrium points and periodic orbits in delay-differential equations of retarded type. One method is called the frequency-domain approach, an analytical tool based on control theory allowing to detect and represent periodic solutions emerging from the Hopf bifurcations, via Fourier series and harmonic balances. The second one, the so-called semi-discretization method, provides a numerical scheme to approximate the monodromy operator of a periodic solution, thus permitting to establish the stability and bifurcations of limit cycles as well as analyzing the equilibrium points. It is shown that a proper combination of these methods provides a straightforward strategy to study both local and global bifurcations in time-delay systems. The usefulness of the proposed approach is shown by three examples, where the results are compared with those given by the software DDE-BIFTOOL.

Strong Stability for a Viscoelastic Transmission Problem under a Nonlocal Boundary Control

The purpose of this paper is to consider a transmission problem of a viscoelastic wave with nonlocal boundary control. It should be noted that the present paper is based on the previous C. G. Gal and M. Warma works, together with H. Atoui and A. Benaissa. Namely, they focused on a transmission problem consisting of a semilinear parabolic equation in a general non-smooth setting with an emphasis on rough interfaces and nonlinear dynamic (possibly, nonlocal) boundary conditions along the interface, where a transmission problem in the presence of a boundary control condition of a nonlocal type was investigated in these papers. Owing to the semigroup theory, we prove the question of well-posedness. For the very rare cases, we combined between the frequency domain approach and the Borichev–Tomilov theorem to establish strong stability results.

Frequency domain identification of passive local modules in linear dynamic networks

We develop a novel frequency-domain approach to address the important open issue of estimating passive local modules within dynamic networks. The method applies an approach based on two stages, a non-parametric and a parametric one. The parametric stage is an extension of the vector fitting technique that incorporates energy consistency conditions as a fundamental component of the identification procedure, forming a path of the passive model in the Sanathanan–Koerner iterations. The approach includes a formulation via linear matrix inequalities to enforce energy-balance conditions resulting in a convex optimization problem. The approach is practical even under weak assumptions on noise, enabling real-world applications. Numerical simulations illustrate the potential of the developed method to effectively estimate local passive modules in dynamic networks.

Stabilization of a locally transmission problems of two strongly-weakly coupled wave systems

In this paper, we embark on a captivating exploration of the stabilization of locally transmitted problems within the realm of two interconnected wave systems. To begin, we wield the formidable Arendt-Batty criteria (Trans. Am. Math. Soc. 306(2) (1988) 837–852) to affirm the resolute stability of our system. Then, with an artful fusion of a frequency domain approach and the multiplier method, we unveil the exquisite phenomenon of exponential stability, a phenomenon that manifests when the waves of the second system synchronize their propagation speeds. In cases where these speeds diverge, our investigation reveals a graceful decay of our system’s energy, elegantly characterized by a polynomial decline at a rate of t − 1 .

Sensitivity of Frequency Domain Near Infrared Spectroscopy for Neurovascular Structure Detection in Biotissue Volume: Numerical Modeling Results.

Through numerical modeling, it has been determined that near infrared spectroscopy with a frequency domain approach can detect neurovascular structures with diameters from 0.5 mm at source-detector distances of 5-8 mm, depending on optical parameters and technical implementation of the method. Among the five classical machine learning methods considered, quadratic discriminant analysis is the most effective for detection. Furthermore, it has been demonstrated that the use of a photomultiplier tube and the registration of both amplitude and phase signal components exhibit the highest sensitivity. Spectroscopy can rival modern ultrasound for detecting arterial vessels. A cross-shaped probe configuration improves sensitivity, and the ratio of reduced scattering coefficient values at different wavelengths is informative for blood-filled vessel detection. These findings are consistent with and significantly extend previous experimental in vivo and in situ studies and could be valuable for intraoperative diagnostic tasks, particularly in neurosurgery.

Estimation of cerebrovascular reactivity amplitude and lag using breath-holding fMRI and the global BOLD signal: Application in diabetes and hypertension.

In this work, we demonstrate a data-driven approach for estimating cerebrovascular reactivity (CVR) amplitude and lag from breathhold (BH) fMRI data alone. Our approach employs a frequency-domain approach that is independent of external recordings. CVR amplitude is estimated from the BOLD frequency spectrum and CVR lag is estimated from the Fourier phase using the global-mean BOLD signal as reference. Unlike referencing to external recordings, these lags are specific to the brain. We demonstrated our method in detecting regional CVR amplitude and lag differences across healthy (CTL), hypertensive (HT) and hypertension-plus-type-2-diabetes (HT + DM) groups of similar ages and sex ratios, with a total N of 49. We found CVR amplitude to be significantly higher in CTL compared to HT + DM, with minimal difference between CTL and HT. Also, voxelwise CVR lag estimated in the Fourier domain is a more sensitive marker of vascular dysfunction than CVR amplitude. CVR lag in HT is significantly shorter than in CTL, with minimal difference between CTL and HT + DM. Our results support the importance of joint CVR amplitude and lag assessments in clinical applications.

Forced vibration characteristics of viscoelastic variable stiffness laminated composite plates using time and frequency domain approaches

The linear forced vibration characteristics of viscoelastic variable stiffness laminated composite plates (VVSLC) are studied using a generalized Maxwell model and finite element method. The integral form of the viscoelastic constitutive relation is converted to the incremental form for finite element formulation based on the Reissner–Mindlin plate theory. The recursive relations are developed to compute the current time-step solution using only the previous time-step solution. The periodic response directly in the time domain is obtained using shooting technique coupled with Newmark’s time integration method. The implementation of shooting technique for Boltzmann integral-based viscoelasticity for curvilinear fibre composite plates is done for the first time in this study. For the comparison purpose, the response/resonance frequency/modal loss factor is also obtained using equivalent complex modulus based viscoelastic correspondence principle. It is observed that the variation in fibre orientation and boundary conditions leads to significant variations in response, stress/moment resultant amplitude and the damping factor of the VVSLC plates. Further, the present time domain based approach is capable of predicting damping factor at all forcing frequencies whereas complex eigenvalue analysis can predict damping factor only at discrete resonance frequency. Based on the detailed studies, it is found that the curvilinear fibre composite plates depict a significant reduction in response/moment resultants compared to straight fibre composite plates.

A bilinear modeling in counts time series with applications

This paper introduces a modified bilinear model for integer-valued time series in which thinning operators are applied in bilinear terms involving the product of the input and state process separately. The proposed model is able to consider overdispersion. Furthermore, it connects a feature of the integer-valued autoregressive conditional heteroskedasticity and integer-valued autoregressive processes. Important properties of the proposed model as well as the sufficient condition for stationarity are derived. After considering some estimation methods based on time domain and frequency domain approaches, simulation studies are conducted to check the performance of the estimates. The analysis of practical cases in social science is accomplished to highlight the usefulness of the proposed model in applications, and the model’s adequacy is provided. Further, the suggested model discusses the problem of data forecasting.

A frequency-domain hydroelastic approach for modeling and stochastic dynamic analysis of pontoon-type floating bridges

In recent years floating bridges have been extensively studied owing to their potential application for crossing wide and deep fjords. An efficient approach for analyzing stochastic hydroelastic responses of floating bridges is valuable for fast assessment of various load effects for preliminary design. This study develops a frequency-domain approach for hydroelastic analysis of pontoon-type floating bridges subjected to wave loads. The frequency-dependent motion equation of the multi-pontoons is established based on the potential flow theory and linearized Morison’s equation for viscous damping. The structural dynamics of the elastic bridge girder are represented utilizing a beam model with excitations transferred from each pontoon. The proposed method is applied to an end-anchored curved floating bridge, with highlights on the verification against a validated time-domain simulation tool. Convincing agreements are found in terms of the eigenvalues, wave excitation loads, and response statistics. The method shows high fidelity with an accurate capture of the linear wave-frequency responses as well as the low-frequency resonances. A further discussion demonstrates that the wave viscous damping restrains low-frequency resonant responses, whereas the hydrodynamic interactions of pontoons induce more resonant peaks in the wave frequency.

Frequency-domain approach to the causal nexus between domestic and international economic policy uncertainties and equity returns of G20 countries

Frequency-domain approach to the causal nexus between domestic and international economic policy uncertainties and equity returns of G20 countries

Time series clustering using fragmented autocorrelations

We propose and study an autocorrelation procedure designed to characterize and compare large sets of long time series. This time-domain procedure is contrasted with a frequency-domain approach that has recently been introduced and discussed in the literature. In both cases, instead of using all the information available from data, which would be computationally very expensive, adequate regularization rules select and summarize the most relevant information suitable for clustering purposes. Essentially, we suggest to use the autocorrelation coefficients of the time series that are only computed around the lags of greatest interest. Then, we study this method in several ways. We argue theoretically that fragmenting the autocorrelation function can have efficiency advantages when comparing time series. By means of a large simulation study, we show that the suggested procedure can condense the relevant information of the time series. We compare its results with those from the frequency domain counterpart. We further illustrate this procedure in a study of the evolution of several stock markets indices and show the effect of recent financial crises on the behaviour of these indices.

Surface light scattering: the capability of precisely measuring the interfacial properties of Newtonian fluids within the capillary wave transition region

This work employs a theoretical power spectrum of the dynamics of surface fluctuations in the frequency domain to elucidate the dissipation of capillary waves of fluids in the near-critical oscillation or transition region, seeking to resolve the problem of large discrepancies in viscosity and surface tension measurements in the region. The frequency-domain analysis approach was suggested, involving the discrete Fourier transform to transform the time domain data to the frequency domain and the fitting algorithm for the power spectrum. A total of three refrigerants, four alkanes and six fatty esters were chosen to examine the approach, with a range of the dimensionless number Y between 1.3 and 101.9. The findings demonstrate that frequency-domain approach is an effective way of dealing with dissipation issues for surface light scattering method when approaching the critical oscillation region, and thus could extend the technique for determining the viscosity and surface tension of Newtonian fluids to a sufficient wide viscosity range.

On the long-term fatigue analysis of marine structures

This paper investigates the performance of several procedures available in literature used to evaluate the multi-dimensional integral associated with long-term fatigue assessment of marine structures. Direct integration methods, Monte Carlo-based approaches and Dimension-Reduction methods are investigated. The focus is on solving the four-dimensional integral for wave-induced fatigue cases when wind-sea and swell waves are simultaneously considered in the analysis. Although the procedures investigated can be used either for time-domain or frequency-domain fatigue approaches, all fatigue analyses performed in this work are restricted to the frequency-domain and are based on idealized stress transfer functions that attempt to mimic the complex behavior of some marine structures. To evaluate the performance of these methodologies, different transfer functions of unimodal and bimodal types are studied. The long-term fatigue damages are calculated using all the investigated methods, and their accuracies and efficiencies are compared. It is found that the efficiency of Monte Carlo Simulation-based methods is problem-dependent and may require many numerical simulations to achieve good accuracy for some cases. Additionally, the Dimension-Reduction methods can lead to highly suitable results with a very low number of integration points and, among all methods investigated, the BDRM (Bivariate Dimension-Reduction Method) stands out due to its excellent performance.

Indirect stabilization of locally weakly coupled second‐order evolution systems of hyperbolic type

The purpose of this work is to investigate the stabilization of locally weakly coupled second‐order evolution equations of hyperbolic type, where only one of the two equations is directly damped. As such system cannot be exponentially stable, we are interested in polynomial energy decay rates. Our main contributions concern strong abstract and polynomial stability properties based on stability properties of two auxiliary problems: the sole damped equation and the second equation with a damping related to the coupling operator. The main novelty is that the polynomial energy decay rates are obtained in different important situations not covered before; let us mention the case of a coupling operator not partially coercive and not necessarily bounded. The main tools are the use of the frequency domain approach combined with new multipliers technique based on the solutions of the resolvent equations of the two auxiliary problems mentioned before. Finally, our abstract framework is illustrated by several concrete examples not treated before.

Economic policy uncertainty and spillovers in selected emerging market economies: time- and frequency-domain approach

Purpose This study aims to investigate the amount and direction of economic policy uncertainty (EPU) spillover among six emerging market economies (EMEs), and to also ascertain arguments on the increased volatilities of uncertainty in most EMEs. Design/methodology/approach This study adopts a recent methodology developed by Baruník and Krehlík’s (2018) methodology to measure pairwise, composite and net spillover. This methodology helps investigate the size and direction of EPU spillover in EMEs. The unique feature of this methodology is its ability to capture frequency domain as well as time-frequency dynamics. Findings Inter-country static spillover connectedness among the EPU of the selected EMEs show that Korea-EPU is the main transmitter and recipient of spillover shocks among the EMEs across all frequency bands. The findings from this study also show evidence of spillover between EPU, GDP and SPX across the EMEs. The time-varying total spillover index analysis shows evidence of overall connectedness across the selected EMEs. Overall connectedness is highest in the short term. We document that global economic and financial events intensify the volatility of the total spillover across the selected EMEs. Originality/value This study extends the literature on studies conducted on EMEs as studies on EPU spillover has mainly focused on advanced economies. To address the limitation of previous empirical studies that were unable to address the amount and direction of spillover from a country to other countries, this study offers new insight on country-specific spillover amounts and causal patterns “to” and “from” the selected EMEs. The findings throw more light on the network connectedness across EMEs and hence aids investors to undertake precise investment decisions and intelligently plan their portfolio diversification strategies. We then introduce two new variables to the analysis and record evidence of high connectedness between EPU, gross domestic product and share price index in all the frequency bands.

A frequency-domain approach for enhanced performance and task flexibility in finite-time ILC

Iterative learning control (ILC) techniques are capable of improving the tracking performance of control systems that repeatedly perform similar tasks by utilizing data from past iterations. The aim of this paper is to achieve both the task flexibility enabled by ILC with basis functions and the performance of frequency-domain ILC, with an intuitive design procedure. The cost function of norm-optimal ILC is determined that recovers frequency-domain ILC, and consequently, the feedforward signal is parameterized in terms of basis functions and frequency-domain ILC. The resulting method has the performance and design procedure of frequency-domain ILC and the task flexibility of basis functions ILC, and are complimentary to each other. Validation on a benchmark example confirms the capabilities of the framework.

A novel high-sensitivity time-domain current differential protection scheme for renewable power transmission system

Integrating large-scale renewable energy sources in modern power systems has altered fault characteristics, resulting in the performance degradation of conventional current differential protection. This paper proposes a novel high-sensitivity time-domain current differential protection scheme. The proposed scheme utilizes the Bergeron model to eliminate the impact of the distributed capacitive current. Furthermore, the Bergeron model error is analyzed theoretically during normal operation, and an algorithm is designed to identify and adjust the α- and β-mode line parameters. Additionally, novel internal fault criteria are presented to mitigate the negative impact of the 0-mode line parameter error. Compared to traditional frequency-domain approaches, the proposed method can more accurately and rapidly distinguish internal and external faults, while reducing the dependency on precise line parameters. Eventually, a VSC-HVDC sending-end grid model consisting of 100% renewable power generations is established using PSCAD/EMTDC software. Simulation results confirm that the proposed protection scheme exhibits exceptional performance in terms of operating speed, sensitivity, and tolerance to fault resistance and noise.

Frequency-Domain Low-Wavenumber Hyperspectral Stimulated Raman Scattering Microscopy.

In recent years, stimulated Raman scattering (SRS) microscopy has experienced rapid technological advancements and has found widespread applications in chemical analysis. Hyperspectral SRS (hSRS) microscopy further enhances the chemical selectivity in imaging by providing a Raman spectrum for each pixel. Time-domain hSRS techniques often require interferometry and ultrashort femtosecond laser pulses. They are especially suited to measuring low-wavenumber Raman transitions but are susceptible to scattering-induced distortions. Frequency-domain hSRS microscopy, on the other hand, offers a simpler optical configuration and demonstrates high tolerance to sample scattering but typically operates within the spectral range of 400-4000 cm-1. Conventional frequency-domain hSRS microscopy is widely employed in biological applications but falls short in detecting chemical bonds with a weaker vibrational energy. In this work, we extend the spectral coverage of picosecond spectral-focusing hSRS microscopy to below 100 cm-1. This frequency-domain low-wavenumber hSRS approach can measure the weaker vibrational energy from the sample and has a strong tolerance to sample scattering. By expanding spectral coverage to 100-4000 cm-1, this development enhances the capability of spectral-domain SRS microscopy for chemical imaging.

On learning time series DAGs: A frequency domain approach

The fields of time series and graphical models emerged and advanced separately. Previous work on the structure learning of continuous and real-valued time series utilizes the time domain, with a focus on either structural autoregressive models or linear (non-)Gaussian Bayesian Networks. In contrast, a novel frequency domain approach is proposed to identify a topological ordering and learn the structure of multivariate time series. In particular, a class of complex-valued Structural Causal Models (cSCM) is defined at each frequency of the Fourier transform of the time series. Assuming that the time series is generated from the transfer function model, it is demonstrated that the topological ordering and the corresponding summary directed acyclic graph can be uniquely identified from cSCM. The performance of the algorithm is investigated using simulation experiments and real datasets.