Hybrid frequency–time domain models for dynamic response analysis of marine structures

Time-domain models of marine structures based on frequency domain data are usually built upon the Cummins equation. This type of model is a vector integro-differential equation which involves convolution terms. These convolution terms are not convenient for analysis and design of motion control systems. In addition, these models are not efficient with respect to simulation time, and ease of implementation in standard simulation packages. For these reasons, different methods have been proposed in the literature as approximate alternative representations of the convolutions. Because the convolution is a linear operation, different approaches can be followed to obtain an approximately equivalent linear system in the form of either transfer function or state-space models. This process involves the use of system identification, and several options are available depending on how the identification problem is posed. This raises the question whether one method is better than the others. This paper therefore has three objectives. The first objective is to revisit some of the methods for replacing the convolutions, which have been reported in different areas of analysis of marine systems: hydrodynamics, wave energy conversion, and motion control systems. The second objective is to compare the different methods in terms of complexity and performance. For this purpose, a model for the response in the vertical plane of a modern containership is considered. The third objective is to describe the implementation of the resulting model in the standard simulation environment Matlab/Simulink.

The Line Spectral Frequency Model of a Finite-Length Sequence

The line spectral frequency (LSF) of a causal finite length sequence is a frequency at which the spectrum of the sequence annihilates or the magnitude spectrum has a spectral null. A causal finite-length sequencewith (L + 1) samples having exactly L-LSFs, is referred as an Annihilating (AH) sequence. Using some spectral properties of finite-length sequences, and some model parameters, we develop spectral decomposition structures, which are used to translate any finite-length sequence to an equivalent set of AH-sequences defined by LSFs and some complex constants. This alternate representation format of any finite-length sequence is referred as its LSF-Model. For a finite-length sequence, one can obtain multiple LSF-Models by varying the model parameters. The LSF-Model, in time domain can be used to synthesize any arbitrary causal finite-length sequence in terms of its characteristic AH-sequences. In the frequency domain, the LSF-Model can be used to obtain the spectral samples of the sequence as a linear combination of spectra of its characteristic AH-sequences. We also summarize the utility of the LSF-Model in practical discrete signal processing systems.

A fast time-domain algorithm for the assessment of tissue blood flow in laser-Doppler flowmetry

In this study, we derive a fast, novel time-domain algorithm to compute the nth-order moment of the power spectral density of the photoelectric current as measured in laser-Doppler flowmetry (LDF). It is well established that in the LDF literature these moments are closely related to fundamental physiological parameters, i.e. concentration of moving erythrocytes and blood flow. In particular, we take advantage of the link between moments in the Fourier domain and fractional derivatives in the temporal domain. Using Parseval's theorem, we establish an exact analytical equivalence between the time-domain expression and the conventional frequency-domain counterpart. Moreover, we demonstrate the appropriateness of estimating the zeroth-, first- and second-order moments using Monte Carlo simulations. Finally, we briefly discuss the feasibility of implementing the proposed algorithm in hardware.

SC-FDMA versus OFDMA: Sensitivity to Large Carrier Frequency and Timing Offsets on the Uplink

In this paper, we present a comparison between the sensitivity of SC-FDMA and OFDMA schemes to large carrier frequency offsets (CFO) and timing offsets (TO) of different users on the uplink. Our study shows the following observations: 1) In the ideal case of zero CFOs and TOs (i.e., perfect synchronization), the uncoded BER performance of SC-FDMA with frequency domain MMSE equalizer is better than that of OFDMA due to the inherent frequency diversity that is possible in SCFDMA. Also, because of inter-symbol interference in SC-FDMA, the performance of SC-FDMA with MMSE equalizer can be further improved by using low-complexity interference cancellation (IC) techniques. 2) In the presence of large CFOs and TOs, significant multiuser interference (MUI) gets introduced, and hence the performance of SC-FDMA with MMSE equalizer can get worse than that of OFDMA. However, the performance advantage of SC-FDMA with MMSE equalizer over OFDMA (due to the potential for frequency diversity benefit in SC-FDMA) can be restored by adopting multistage IC techniques, using the knowledge of CFOs and TOs of different users at the receiver

Matching sender and receiver: poikilothermy and frequency tuning in a tree cricket

Animals communicate in non-ideal and noisy conditions. The primary method they use to improve communication efficiency is sender-receiver matching: the receiver's sensory mechanism filters the impinging signal based on the expected signal. In the context of acoustic communication in crickets, such a match is made in the frequency domain. The males broadcast a mate attraction signal, the calling song, in a narrow frequency band centred on the carrier frequency (CF), and the females are most sensitive to sound close to this frequency. In tree crickets, however, the CF changes with temperature. The mechanisms used by female tree crickets to accommodate this change in CF were investigated at the behavioural and biomechanical level. At the behavioural level, female tree crickets were broadly tuned and responded equally to CFs produced within the naturally occurring range of temperatures (18 to 27 degrees C). To allow such a broad response, however, the transduction mechanisms that convert sound into mechanical and then neural signals must also have a broad response. The tympana of the female tree crickets exhibited a frequency response that was even broader than suggested by the behaviour. Their tympana vibrate with equal amplitude to frequencies spanning nearly an order of magnitude. Such a flat frequency response is unusual in biological systems and cannot be modelled as a simple mechanical system. This feature of the tree cricket auditory system not only has interesting implications for mate choice and species isolation but may also prove exciting for bio-mimetic applications such as the design of miniature low frequency microphones.

Time-frequency analysis of human motion during rhythmic exercises

Biomechanical signals due to human movements during exercise are represented in time-frequency domain using Wigner Distribution Function (WDF). Analysis based on WDF reveals instantaneous spectral and power changes during a rhythmic exercise. Investigations were carried out on 11 healthy subjects who performed 5 cycles of sun salutation, with a body-mounted Inertial Measurement Unit (IMU) as a motion sensor. Variance of Instantaneous Frequency (I.F) and Instantaneous Power (I.P) for performance analysis of the subject is estimated using one-way ANOVA model. Results reveal that joint Time-Frequency analysis of biomechanical signals during motion facilitates a better understanding of grace and consistency during rhythmic exercise.

Passive vibration isolation of reaction wheel disturbances using a low frequency flexible space platform

Reaction wheel assemblies (RWAs) are momentum exchange devices used in fine pointing control of spacecrafts. Even though the spinning rotor of the reaction wheel is precisely balanced to minimize emitted vibration due to static and dynamic imbalances, precision instrument payloads placed in the neighborhood can always be severely impacted by residual vibration forces emitted by reaction wheel assemblies. The reduction of the vibration level at sensitive payloads can be achieved by placing the RWA on appropriate mountings. A low frequency flexible space platform consisting of folded continuous beams has been designed to serve as a mount for isolating a disturbance source in precision payloads equipped spacecrafts. Analytical and experimental investigations have been carried out to test the usefulness of the low frequency flexible platform as a vibration isolator for RWAs. Measurements and tests have been conducted at varying wheel speeds, to quantify and characterize the amount of isolation obtained from the reaction wheel generated vibration. These tests are further extended to other variants of similar design in order to bring out the best isolation for given disturbance loads. Both time and frequency domain analysis of test data show that the flexible beam platform as a mount for reaction wheels is quite effective and can be used in spacecrafts for passive vibration control. (C) 2011 Elsevier Ltd. All rights reserved.

Low frequency modulation of jets in quasigeostrophic turbulence

Quasigeostrophic turbulence on a beta-plane with a finite deformation radius is studied numerically, with particular emphasis on frequency and combined wavenumber-frequency domain analyses. Under suitable conditions, simulations with small-scale random forcing and large-scale drag exhibit a spontaneous formation of multiple zonal jets. The first hint of wave-like features is seen in the distribution of kinetic energy as a function of frequency; specifically, for progressively larger deformation scales, there are systematic departures in the form of isolated peaks (at progressively higher frequencies) from a power-law scaling. Concomitantly, there is an inverse flux of kinetic energy in frequency space which extends to lower frequencies for smaller deformation scales. The identification of these peaks as Rossby waves is made possible by examining the energy spectrum in frequency-zonal wavenumber and frequency-meridional wavenumber diagrams. In fact, the modified Rhines scale turns out to be a useful measure of the dominant meridional wavenumber of the modulating Rossby waves; once this is fixed, apart from a spectral peak at the origin (the steady jet), almost all the energy is contained in westward propagating disturbances that follow the theoretical Rossby dispersion relation. Quite consistently, noting that the zonal scale of the modulating waves is restricted to the first few wavenumbers, the energy spectrum is almost entirely contained within the corresponding Rossby dispersion curves on a frequency-meridional wavenumber diagram. Cases when jets do not form are also considered; once again, there is a hint of Rossby wave activity, though the spectral peaks are quite muted. Further, the kinetic energy scaling in frequency domain follows a -5/3 power-law and is distributed much more broadly in frequency-wavenumber diagrams. (C) 2015 AIP Publishing LLC.

Evaluation and Minimization of Low-Order Harmonic Torque in Low-Switching-Frequency Inverter-Fed Induction Motor Drives

A low-order harmonic pulsating torque is a major concern in high-power drives, high-speed drives, and motor drives operating in an overmodulation region. This paper attempts to minimize the low-order harmonic torques in induction motor drives, operated at a low pulse number (i.e., a low ratio of switching frequency to fundamental frequency), through a frequency domain (FD) approach as well as a synchronous reference frame (SRF) based approach. This paper first investigates FD-based approximate elimination of harmonic torque as suggested by classical works. This is then extended into a procedure for minimization of low-order pulsating torque components in the FD, which is independent of machine parameters and mechanical load. Furthermore, an SRF-based optimal pulse width modulation (PWM) method is proposed to minimize the low-order harmonic torques, considering the motor parameters and load torque. The two optimal methods are evaluated and compared with sine-triangle (ST) PWM and selective harmonic elimination (SHE) PWM through simulations and experimental studies on a 3.7-kW induction motor drive. The SRF-based optimal PWM results in marginally better performance than the FD-based one. However, the selection of optimal switching angle for any modulation index (M) takes much longer in case of SRF than in case of the FD-based approach. The FD-based optimal solutions can be used as good starting solutions and/or to reasonably restrict the search space for optimal solutions in the SRF-based approach. Both of the FD-based and SRF-based optimal PWM methods reduce the low-order pulsating torque significantly, compared to ST PWM and SHE PWM, as shown by the simulation and experimental results.

Dynamic full-range Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry

We propose a technique for dynamic full-range Fourier-domain optical coherence tomography by using sinusoidal phase-modulating interferometry, where both the full-range structural information and depth-resolved dynamic information are obtained. A novel frequency-domain filtering algorithm is proposed to reconstruct a time-dependent complex spectral interferogram from the sinusoidally phase-modulated interferogram detected with a high-rate CCD camera. By taking the amplitude and phase of the inverse Fourier transform of the complex spectral interferogram, a time-dependent full-range cross-sectional image and depth-resolved displacement are obtained. Displacement of a sinusoidally vibrating glass cover slip behind a fixed glass cover slip is measured with subwavelength sensitivity to demonstrate the depth-resolved dynamic imaging capability of our system. (c) 2007 Society of Photo-Optical Instrumentation Engineers.

Dynamic full-range Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry

We propose a technique for dynamic full-range Fourier-domain optical coherence tomography by using sinusoidal phase-modulating interferometry, where both the full-range structural information and depth-resolved dynamic information are obtained. A novel frequency-domain filtering algorithm is proposed to reconstruct a time-dependent complex spectral interferogram from the sinusoidally phase-modulated interferogram detected with a high-rate CCD camera. By taking the amplitude and phase of the inverse Fourier transform of the complex spectral interferogram, a time-dependent full-range cross-sectional image and depth-resolved displacement are obtained. Displacement of a sinusoidally vibrating glass cover slip behind a fixed glass cover slip is measured with subwavelength sensitivity to demonstrate the depth-resolved dynamic imaging capability of our system. (c) 2007 Society of Photo-Optical Instrumentation Engineers.

Characteristics of low-frequency components of the near-bottom current in the Chinese Pioneer Area

Two deep-sea moorings were deployed respectively in the east area and the west area of Chinese Pioneer Area (CPA) in the tropic east Pacific to monitor the regional deep-sea dynamics below 600 meters above bottom (mab) from July 1997 to Oct. 1999. Results of statistics, spectral estimate and correlation analysis of the low-passed velocity data show that time scales of low-frequency components of the near-bottom currents are 25similar to120 days, in which 51-day period dominates the lower band of the frequency domain. Topographic features have obvious effect on low-frequency currents below 50 mab; modulations of the bottom-intensified sheared mean flow to the low-frequency currents are the dynamic mechanism of the frequency shift that occurs in both the east-area and the west-area.

Measuring morphological features using light-scattering spectroscopy and Fourier-domain low-coherence interferometry.

We present measurements of morphological features in a thick turbid sample using light-scattering spectroscopy (LSS) and Fourier-domain low-coherence interferometry (fLCI) by processing with the dual-window (DW) method. A parallel frequency domain optical coherence tomography (OCT) system with a white-light source is used to image a two-layer phantom containing polystyrene beads of diameters 4.00 and 6.98 mum on the top and bottom layers, respectively. The DW method decomposes each OCT A-scan into a time-frequency distribution with simultaneously high spectral and spatial resolution. The spectral information from localized regions in the sample is used to determine scatterer structure. The results show that the two scatterer populations can be differentiated using LSS and fLCI.

Time domain wave separation using multiple microphones

Methods of measuring the acoustic behavior of tubular systems can be broadly characterized as steady state measurements, where the measured signals are analyzed in terms of infinite duration sinusoids, and reflectometry measurements which exploit causality to separate the forward and backward going waves in a duct. This paper sets out a multiple microphone reflectometry technique which performs wave separation by using time domain convolution to track the forward and backward going waves in a cylindrical source tube. The current work uses two calibration runs (one for forward going waves and one for backward going waves) to measure the time domain transfer functions for each pair of microphones. These time domain transfer functions encode the time delay, frequency dependent losses and microphone gain ratios for travel between microphones. This approach is applied to the measurement of wave separation, bore profile and input impedance. The work differs from existing frequency domain methods in that it combines the information of multiple microphones within a time domain algorithm, and differs from existing time domain methods in its inclusion of the effect of losses and gain ratios in intermicrophone transfer functions.

The Finometer can function as a standalone instrument in blood pressure variability studies and does not require support equipment to determine breathing frequency

Objective: The Finometer (FMS, Finapres Measurement Systems, Amsterdam) records the beat-to-beat finger pulse contour and has been recommended for research studies assessing shortterm changes of blood pressure and its variability. Variability measured in the frequency domain using spectral analysis requires that the impact of breathing be restricted to high frequency spectra (> 0.15 Hz) so data from participants needs to be excluded when the breathing impact occurs in the low frequency spectra (0.04 - 0.15 Hz). This study tested whether breathing frequency can be estimated from standard Finometer recordings using either stroke volume oscillation frequency or spectral stroke volume variability maximum scores. Methods: 22 healthy volunteers were tested for 270s in the supine and upright positions. Finometer recorded the finger pulse contour and a respiratory transducer recorded breathing. Stoke volume oscillation frequency was calculated manually while the stroke volume spectral maximums were obtained using the software Cardiovascular Parameter Analysis (Nevrokard Kiauta, Izola, Slovenia). These estimates were compared to the breathing frequency using the Bland-Altman procedures. Results: Stroke volume oscillation frequency estimated breathing frequency to <±10% 95% levels of agreement in both supine (-7.7 to 7.0%) and upright (-6.7 to 5.4%) postures. Stroke volume variability maximum scores did not accurately estimate breathing frequency. Conclusions: Breathing frequency can be accurately derived from standard Finometer recordings using stroke volume oscillations for healthy individuals in both supine and upright postures. The Finometer can function as a standalone instrument in blood pressure variability studies and does not require support equipment to determine breathing frequency.