Numerical solution for fractional-order differential systems with time domain and frequency domain methods

Due to the relative motion between adjacent blade rows the aerodynamic flow fields within turbomachinery are normally dominated by deterministic, periodic phenomena. In the numerical simulation of such unsteady flows (nonlinear) frequency-domain methods are therefore attractive as they are capable of fully exploiting the given spatial and temporal periodicity, as well as capturing or modelling flow nonlinearity. Central to the efficiency and accuracy of such frequency-domain methods is the selection of the frequencies and the circumferential modes to be resolved in simulations. Whilst trivial in the context of the simulation of a single compressor- or turbine-stage, the choice of solution modes becomes substantially more involved in multi-stage configurations. In this work the importance of mode scattering, in the context of the unsteady aerodynamic field, is investigated and quantified. It is shown that scattered modes can substantially impact the unsteady flow field and are essential for the accurate modelling of wake propagation within multistage configurations. Furthermore, an iterative approach is outlined, based on the spectral analysis of the circumferential modes at the interfaces between blade rows, to identify the dominant solution modes that should be resolved in the adjacent blade row. To demonstrate the importance of mode scattering and validate the approach for their identification the unsteady blade row interaction within a 4.5 stage axial compressor is computed using both the harmonic balance method and, based on a full annulus midspan simulation, a time-domain method. Through the inclusion of scattered modes it is shown that the solution quality of the harmonic balance results is comparable to that of the nonlinear time-domain simulation.

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On Frequency-Domain and Time-Domain Input Shaping for Multi-Mode Flexible Structures

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.1591808 ◽

2003 ◽

Vol 125 (3) ◽

pp. 494-497 ◽

Cited By ~ 8

Author(s):

Lucy Y. Pao ◽

Craig F. Cutforth

Keyword(s):

Frequency Domain ◽

Time Domain ◽

Flexible Structures ◽

Design Methods ◽

Input Shaping ◽

Residual Vibration ◽

Know How ◽

Frequency Domain Methods ◽

Multi Mode

The technique of input shaping has been successfully applied to the problem of maneuvering flexible structures without excessive residual vibration. Because a shaper is designed such that vibration is eliminated at the end of the shaped input, a short shaper length means that vibration is eliminated sooner. As different shaper design methods yield different shapers, it is advantageous to know how the shaper lengths of these different methods compare. In this paper we draw comparisons between time-domain input shaping methods and frequency-domain input shaping methods after outlining conditions when non-negative amplitude shapers exist when using frequency-domain methods.

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Sex Differences in Time-Domain and Frequency-Domain Heart Rate Variability Measures of Fatigued Drivers

International Journal of Environmental Research and Public Health ◽

10.3390/ijerph17228499 ◽

2020 ◽

Vol 17 (22) ◽

pp. 8499

Author(s):

Chao Zeng ◽

Wenjun Wang ◽

Chaoyang Chen ◽

Chaofei Zhang ◽

Bo Cheng

Keyword(s):

Heart Rate ◽

Heart Rate Variability ◽

Sex Differences ◽

Frequency Domain ◽

Time Domain ◽

Mental States ◽

Male And Female ◽

Frequency Domain Methods ◽

The Difference ◽

Electrocardiogram Ecg

The effects of fatigue on a driver’s autonomic nervous system (ANS) were investigated through heart rate variability (HRV) measures considering the difference of sex. Electrocardiogram (ECG) data from 18 drivers were recorded during a simulator-based driving experiment. Thirteen short-term HRV measures were extracted through time-domain and frequency-domain methods. First, differences in HRV measures related to mental state (alert or fatigued) were analyzed in all subjects. Then, sex-specific changes between alert and fatigued states were investigated. Finally, sex differences between alert and fatigued states were compared. For all subjects, ten measures showed significant differences (Mann-Whitney U test, p < 0.01) between different mental states. In male and female drivers, eight and four measures, respectively, showed significant differences between different mental states. Six measures showed significant differences between males and females in an alert state, while ten measures showed significant sex differences in a fatigued state. In conclusion, fatigue impacts drivers’ ANS activity, and this impact differs by sex; more differences exist between male and female drivers’ ANS activity in a fatigued state than in an alert state.

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METHODS TO QUANTITATE ATRIAL ELECTRICAL ACTIVITY USING ELECTROGRAMS ACQUIRED DURING ATRIAL FIBRILLATION

Biomedical Engineering Applications Basis and Communications ◽

10.4015/s1016237214300016 ◽

2014 ◽

Vol 26 (06) ◽

pp. 1430001

Author(s):

Edward J. Ciaccio ◽

Angelo B. Biviano ◽

Hasan Garan

Keyword(s):

Atrial Fibrillation ◽

Electrical Activity ◽

Frequency Domain ◽

Time Domain ◽

Periodic Pattern ◽

Spectral Parameters ◽

Domain Method ◽

Frequency Domain Methods ◽

Atrial Electrograms ◽

Fractionated Electrograms

Herein, commonly used quantitative bioengineering methods that have been developed to analyze fractionated electrograms recorded from the surface of the atria during atrial fibrillation (AF) are described. Techniques were categorized as time-domain and frequency-domain methods. The main time-domain method is peak counting. Its variations based on preprocessing and thresholding are discussed. The main frequency-domain method is spectral analysis. Two spectral estimators, the discrete Fourier transform (DFT) and the new spectral estimator (NSE) are described. The ability of each estimator to detect the main periodic component of fractionated atrial electrograms is compared. Several spectral parameters that are used for analysis of atrial electrograms including the dominant frequency (DF), dominant amplitude (DA) and mean spectral profile (MP) are defined. Mean values of these parameters are compared in paroxysmal versus persistent AF fractionated electrograms based upon the results of several studies. Time-domain methods are shown to work best for analysis with deterministic, not fractionated atrial electrograms. For fractionated atrial electrograms, frequency-domain methods are often used. The DF, DA and MP spectral parameters are significantly different in paroxysmal versus longstanding persistent AF recordings. The DF and the DA are significantly higher, and the MP is significantly lower, in persistent AF electrogram recordings. The higher DF and DA parameter values reflect substrate remodeling in persistent AF, which increases the stability of the electrical activation pattern. The lower MP value in persistent AF reflects the lower spectral noise floor, indicative of a less complex and more periodic pattern of electrical activity.

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Non-Linear Time and Frequency Domain Methods for Multi-Row Aeromechanical Analysis

Volume 7: Structures and Dynamics, Parts A and B ◽

10.1115/gt2012-68723 ◽

2012 ◽

Author(s):

M. T. Rahmati ◽

L. He ◽

D. X. Wang ◽

Y. S. Li ◽

R. G. Wells ◽

...

Keyword(s):

Frequency Domain ◽

Time Domain ◽

Computational Models ◽

Linear Time ◽

Navier Stokes ◽

Frequency Domain Method ◽

Domain Method ◽

Frequency Domain Methods ◽

Blade Row ◽

Nonlinear Time Domain

An unsteady Navier-Stokes solution system for aeromechanical analysis of multiple blade row configurations is presented. A distinctive feature of the solver is that unified numerical methods and boundary condition treatments are consistently used for both a nonlinear time-domain solution mode and a frequency-domain one. This not only enables a wider range of physical aeromechanical problems to be tackled, but also provides a consistent basis for validating different computational models, identifying and understanding their relative merits and adequate working ranges. An emphasis of the present work is on a highly efficient frequency-domain method for multi-row aeromechanic analysis. With a new interface treatment, propagations and reflections of pressure waves between adjacent blade rows are modeled within a domain consisting of only a single passage in each blade row. The computational model and methods are firstly described. Then, extensive validations of the frequency-domain method against both experimental data and the nonlinear time-domain solutions are described. Finally the computational analysis and demonstration of the intra-row reflection effects on the rotor aerodynamic damping are presented.

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3D marine magnetotelluric modeling and inversion with the finite-difference time-domain method

Geophysics ◽

10.1190/geo2014-0110.1 ◽

2014 ◽

Vol 79 (6) ◽

pp. E269-E286 ◽

Cited By ~ 13

Author(s):

Sébastien de la Kethulle de Ryhove ◽

Rune Mittet

Keyword(s):

Finite Difference ◽

Frequency Domain ◽

Time Domain ◽

Finite Difference Time Domain ◽

Linear Equations ◽

Time Domain Method ◽

Domain Method ◽

Frequency Domain Methods ◽

Starting Point ◽

Difference Time

Frequency-domain methods, which are typically applied to 3D magnetotelluric (MT) modeling, require solving a system of linear equations for every frequency of interest. This is memory and computationally intensive. We developed a finite-difference time-domain algorithm to perform 3D MT modeling in a marine environment in which Maxwell’s equations are solved in a so-called fictitious-wave domain. Boundary conditions are efficiently treated via convolutional perfectly matched layers, for which we evaluated optimized parameter values obtained by testing over a large number of models. In comparison to the typically applied frequency-domain methods, two advantages of the finite-difference time-domain method are (1) that it is an explicit, low-memory method that entirely avoids the solution of systems of linear equations and (2) that it allows the computation of the electromagnetic field unknowns at all frequencies of interest in a single simulation. We derive a design criterion for vertical node spacing in a nonuniform grid using dispersion analysis as a starting point. Modeling results obtained using our finite-difference time-domain algorithm are compared with results obtained using an integral equation method. The agreement was found to be very good. We also discuss a real data inversion example in which MT modeling was done with our algorithm.

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