Frequency Domain Representation Research Articles

Harnessing data structure for recovery of randomly missing structural vibration responses time history: Sparse representation versus low-rank structure

Randomly missing data of structural vibration responses time history often occurs in structural dynamics and health monitoring. For example, structural vibration responses are often corrupted by outliers or erroneous measurements due to sensor malfunction; in wireless sensing platforms, data loss during wireless communication is a common issue. Besides, to alleviate the wireless data sampling or communication burden, certain accounts of data are often discarded during sampling or before transmission. In these and other applications, recovery of the randomly missing structural vibration responses from the available, incomplete data, is essential for system identification and structural health monitoring; it is an ill-posed inverse problem, however.This paper explicitly harnesses the data structure itself—of the structural vibration responses—to address this (inverse) problem. What is relevant is an empirical, but often practically true, observation, that is, typically there are only few modes active in the structural vibration responses; hence a sparse representation (in frequency domain) of the single-channel data vector, or, a low-rank structure (by singular value decomposition) of the multi-channel data matrix. Exploiting such prior knowledge of data structure (intra-channel sparse or inter-channel low-rank), the new theories of ℓ1-minimization sparse recovery and nuclear-norm-minimization low-rank matrix completion enable recovery of the randomly missing or corrupted structural vibration response data. The performance of these two alternatives, in terms of recovery accuracy and computational time under different data missing rates, is investigated on a few structural vibration response data sets—the seismic responses of the super high-rise Canton Tower and the structural health monitoring accelerations of a real large-scale cable-stayed bridge. Encouraging results are obtained and the applicability and limitation of the presented methods are discussed.

Wideband Spectrum Sensing by Model Order Selection

Spectrum sensing is an essential functionality in cognitive radio (CR) systems allowing us to discover spectrum opportunities and enabling primary user (PU) protection. Wideband spectrum sensing (WS) improves the awareness of the surrounding radio environment by jointly monitoring multiple frequency bands. In this paper we propose a WS approach based on the observation of a frequency domain representation of the received signal and the adoption of model order selection (MOS) to identify the occupied frequency components. We provide a general formulation of the problem valid for any kind of spectral representation and then focus on the case in which discrete Fourier transform (DFT) is used. This choice is motivated by the fact that DFT blocks are available in many wireless systems, such as OFDM receivers and recently proposed software radio architectures. We provide analytical expressions for the maximum probability of correct selection of the occupied sub-bands valid for MOS approaches encompassed within the generalized information criterion (GIC). We then propose a method for designing the selection algorithm to balance overestimation and underestimation. Numerical results show that the MOS scheme derived for DFT can be successfully applied also when more accurate frequency representations, such as multitaper (MT) spectrum estimates, are adopted.

Time-domain diffuse optical tomography using recursive direct method of calculating Jacobian at selected temporal points

An algorithm for time-domain diffuse optical tomography based on the resolution of the time-domain diffusion equation using the finite element method has been developed. An efficient direct method including a recursive approach has been used to obtain the light fluence derivatives with respect to tissue optical properties at precise selected points on the temporal profile resulting in a considerable savings in computation time and memory. The algorithm reconstructs the tissue optical properties in a permissible region or a region-of-interest and the input data for reconstruction comprises selections of points on the temporal curve of the measured pulse. The optical properties have been reconstructed by solving an iterative normalized minimization problem. The algorithm has been applied to a three-dimensional simplified model of a new born baby head and to a three-dimensional model of the mouse (MOBY) for a small animal model. The computation speed and memory usage of the algorithm have been compared with that of other techniques based on continuous wave and frequency domain representations. The effects of using different sizes of time steps and number of time steps on the reconstruction accuracy and the computation time have been reported.

Spectral finite element for vibration analysis of cracked viscoelastic Euler–Bernoulli beam subjected to moving load

In this article, a spectral finite element (SFE) model is presented for vibration analysis of a cracked viscoelastic beam subjected to moving loads. The dynamic shape functions are derived from the exact solution of the governing wave equations and are utilized for frequency-domain representation of a moving load. It is considered with either constant velocity or acceleration; then, the force vector for each spectral element is evaluated. The cracked beam is modeled as two segments connected by a massless rotational spring; thus, the beam dynamic stiffness matrix is extracted in frequency domain by considering compatibility conditions at the crack position. The effects of change in velocity and acceleration of moving load, crack parameters, and viscoelastic material properties on the dynamic response of the SFE beam model are investigated. The accuracy of SFE results is compared with that of finite elements. The results show the ascendency of the SFE model, as compared to FEM, for reducing the number of elements and computational effort, but increasing numerical accuracy.

Efficient Sampling Set Selection for Bandlimited Graph Signals Using Graph Spectral Proxies

We study the problem of selecting the best sampling set for bandlimited reconstruction of signals on graphs. A frequency domain representation for graph signals can be defined using the eigenvectors and eigenvalues of variation operators that take into account the underlying graph connectivity. Smoothly varying signals defined on the nodes are of particular interest in various applications, and tend to be approximately bandlimited in the frequency basis. Sampling theory for graph signals deals with the problem of choosing the best subset of nodes for reconstructing a bandlimited signal from its samples. Most approaches to this problem require a computation of the frequency basis (i.e., the eigenvectors of the variation operator), followed by a search procedure using the basis elements. This can be impractical, in terms of storage and time complexity, for real datasets involving very large graphs. We circumvent this issue in our formulation by introducing quantities called graph spectral proxies, defined using the powers of the variation operator, in order to approximate the spectral content of graph signals. This allows us to formulate a direct sampling set selection approach that does not require the computation and storage of the basis elements. We show that our approach also provides stable reconstruction when the samples are noisy or when the original signal is only approximately bandlimited. Furthermore, the proposed approach is valid for any choice of the variation operator, thereby covering a wide range of graphs and applications. We demonstrate its effectiveness through various numerical experiments.

Characterization and reduction of motion artifacts in photoplethysmographic signals from a wrist-worn device.

Methods for analyzing various motion artifacts in photoplethysmography (PPG) signals, recorded by a wristworn device are reported. The analysis looks both at intrinsic PPG signal properties, through standard deviation, skew and kurtosis, but also at its relationship to five possible motion reference signals, through the correlation coefficient and mutual information. The investigated references include the X, Y, Z accelerometer axes, acceleration magnitude and a different wavelength PPG channel. The latter showed higher correlation to the input PPG signal during movement. A wavelet based motion artifact reduction algorithm is described. The algorithm improves the visibility of the heart rate (HR) components in the frequency domain representation of the signals.

A statistical comparison of EEG time- and time–frequency domain representations of error processing

Successful behavior relies on error detection and subsequent remedial adjustment of behavior. Researchers have identified two electrophysiological signatures of error processing: the time-domain error-related negativity (ERN), and the time–frequency domain increased power in the delta/theta frequency bands (~2–8Hz). The relationship between these two signatures is not entirely clear: on the one hand they occur after the same type of event and with similar latency, but on the other hand, the time-domain ERP component contains only phase-locked activity whereas the time–frequency response additionally contains non-phase-locked dynamics. Here we examined the ERN and error-related delta/theta activity in relation to each other, focusing on within-subject analyses that utilize single-trial data. Using logistic regression, we constructed three statistical models in which the accuracy of each trial was predicted from the ERN, delta/theta power, or both. We found that both the ERN and delta/theta power worked roughly equally well as predictors of single-trial accuracy (~70% accurate prediction). Furthermore, a model including both measures provided a stronger overall prediction compared to either model alone. Based on these findings two conclusions are drawn: first, the phase-locked part of the EEG signal appears to be roughly as predictive of single-trial response accuracy as the non-phase-locked part; second, the single-trial ERP and delta/theta power contain both overlapping and independent information.

Nonparametric directionality measures for time series and point process data.

The need to determine the directionality of interactions between neural signals is a key requirement for analysis of multichannel recordings. Approaches most commonly used are parametric, typically relying on autoregressive models. A number of concerns have been expressed regarding parametric approaches, thus there is a need to consider alternatives. We present an alternative nonparametric approach for construction of directionality measures for bivariate random processes. The method combines time and frequency domain representations of bivariate data to decompose the correlation by direction. Our framework generates two sets of complementary measures, a set of scalar measures, which decompose the total product moment correlation coefficient summatively into three terms by direction and a set of functions which decompose the coherence summatively at each frequency into three terms by direction: forward direction, reverse direction and instantaneous interaction. It can be undertaken as an addition to a standard bivariate spectral and coherence analysis, and applied to either time series or point-process (spike train) data or mixtures of the two (hybrid data). In this paper, we demonstrate application to spike train data using simulated cortical neurone networks and application to experimental data from isolated muscle spindle sensory endings subject to random efferent stimulation.

인공 신경망을 이용한 광대역 과정의 피로 손상 모델 개발

For the frequency-domain spectral fatigue analysis, the probability density function of stress range needs to be estimated based on the stress spectrum only, which is a frequency domain representation of the response. The probability distribution of the stress range of the narrow-band spectrum is known to follow the Rayleigh distribution, however the PDF of wide-band spectrum is difficult to define with clarity due to the complicated fluctuation pattern of spectrum. In this paper, efforts have been made to figure out the links between the probability density function of stress range to the structural response of wide-band Gaussian random process. An artificial neural network scheme, known as one of the most powerful system identification methods, was used to identify the multivariate functional relationship between the idealized wide-band spectrums and resulting probability density functions. To achieve this, the spectrums were idealized as a superposition of two triangles with arbitrary location, height and width, targeting to comprise wide-band spectrum, and the probability density functions were represented by the linear combination of equally spaced Gaussian basis functions. To train the network under supervision, varieties of different wide-band spectrums were assumed and the converged probability density function of the stress range was derived using the rainflow counting method and all these data sets were fed into the three layer perceptron model. This nonlinear least square problem was solved using Levenberg-Marquardt algorithm with regularization term included. It was proven that the network trained using the given data set could reproduce the probability density function of arbitrary wide-band spectrum of two triangles with great success.

Evaluating and Approximating FIR Filters: An Approach Based on Functions of Matrices

Most of the controllers designed for systems with timedelays involve finite impulse response (FIR) filters in their structure, in particular prediction based controllers for systems with input/output delays. We present theory, algorithms and software to evaluate the frequency response, to approximate the filters by stable linear timeinvariant systems and to compute their induced ${\cal L}_{2}$ gain. The approach is based on the theory of functions of matrices. In the approach pole zero cancelations in frequency domain representations are explicitly taken into account.

Axial obliquity control on the greenhouse carbon budget through middle‐ to high‐latitude reservoirs

AbstractCarbon sources and sinks are key components of the climate feedback system, yet their response to external forcing remains poorly constrained, particularly for past greenhouse climates. Carbon‐isotope data indicate systematic, million‐year‐scale transfers of carbon between surface reservoirs during and immediately after the Late Cretaceous thermal maximum (peaking in the Cenomanian‐Turonian, circa 97–91 million years, Myr, ago). Here we calibrate Albian to Campanian (108–72 Myr ago) high‐resolution carbon isotope records with a refined chronology and demonstrate how net transfers between reservoirs are plausibly controlled by ~1 Myr changes in the amplitude of axial obliquity. The amplitude‐modulating terms are absent from the frequency domain representation of insolation series and require a nonlinear, cumulative mechanism to become expressed in power spectra of isotope time series. Mass balance modeling suggests that the residence time of carbon in the ocean‐atmosphere system is—by itself—insufficient to explain the Myr‐scale variability. It is proposed that the astronomical control was imparted by a transient storage of organic matter or methane in quasi‐stable reservoirs (wetlands, soils, marginal zones of marine euxinic strata, and potentially permafrost) that responded nonlinearly to obliquity‐driven changes in high‐latitude insolation and/or meridional insolation gradients. While these reservoirs are probably underrepresented in the geological record due to their quasi‐stable character, they might have provided an important control on the dynamics and stability of the greenhouse climate.

J1630303 ガイド波骨密度推定法に対する多孔質対モデルの組み込み

Ultrasonic densitometry is one of the methods promising as a non-aggression measuring method of a bone density. The ultrasonic method has much possibility theoretically due to use an elastic vibration. However, since the reliability of a measurement results is not enough, the ultrasonic method has not reached a clinical criterion. We aim at the development of a new determination measurement technique for a bone density which uses the guided wave of the ultrasonic in the present study. We conducted the experiment of the guided wave with porous round rods of the same material but different densities. And then we investigated the velocity dispersion of the guided wave with the frequency-domain representation of the semblance lance method, and estimated the bulk velocity of the specimens from the velocity-dispersion characteristics.

Experimental study in the shaking table of the input motion characteristics in the dynamic SSI of a SDOF model

In conventional seismic design the capacity of the system is generally exploited only at the superstructure level. However, soil non-linearity as well as soil-foundation interface non-linearity can be crucial in the seismic response of structures. The results of tests performed on physical models allow the main aspects of these interaction mechanisms to be identified and also provide a benchmark for subsequent theoretical or numerical analyses. The present paper deals with two shaking table tests performed at the University of Bristol’s EERC laboratory. The tests were performed on a physical model consisting of a Leighton Buzzard sand deposit and a one-storey steel model structure. Some of the test results are presented and discussed in terms of acceleration and displacement responses. Both time- and frequency-domain representations were adopted to highlight the influence of the frequency and amplitude of the input motion on the coupled and/or uncoupled response of the tested soil-structure system, as well as the effect of soil non linear behaviour.

Examining thermal transport through a frequency-domain representation of time-domain thermoreflectance data.

Laser-based time-domain thermoreflectance (TDTR) and frequency-domain thermoreflectance (FDTR) techniques are widely used for investigating thermal transport at micro- and nano-scales. We demonstrate that data obtained in TDTR measurements can be represented in a frequency-domain form equivalent to FDTR, i.e., in the form of a surface temperature amplitude and phase response to time-harmonic heating. Such a representation is made possible by using a large TDTR delay time window covering the entire pulse repetition interval. We demonstrate the extraction of frequency-domain data up to 1 GHz from TDTR measurements on a sapphire sample coated with a thin layer of aluminum, and show that the frequency dependencies of both the amplitude and phase responses agree well with theory. The proposed method not only allows a direct comparison of TDTR and FDTR data, but also enables measurements at high frequencies currently not accessible to FDTR. The frequency-domain representation helps uncover aspects of the measurement physics which remain obscured in a traditional TDTR measurement, such as the importance of modeling the details of the heat transport in the metal transducer film for analyzing high frequency responses.

Improved Bandwidth and Noise Resilience in Thermal Impedance Spectroscopy by Mixing PRBS Signals

This paper presents a method of mixing pseudo-random binary sequences (PRBSs) to form a new signal that can be used to obtain the thermal impedance spectrum of power electronic systems. The proposed technique increases the useful frequency range of a PRBS by mixing two identical sequences at different frequencies. The new signal incorporates the frequency responses of both contributions. Mixing can be performed using a number of mathematical operators and analysis reveals that AND is the operator of choice since it has the lowest average input power for the same effectiveness. The bandwidth, frequency-domain representation, and noise resilience of PRBS signals are also reported. It is shown that the noise floor is significantly reduced under the mixed technique, which allows lower impedances to be measured under noisy measurement conditions. For a typical 8-bit PRBS, mixing reduces the noise floor by a factor of 10.5. Simulated and experimental validation are performed and results show the mixed scheme offers increased bandwidth, reduced computation and improved noise resilience compared to single PRBS techniques.

Measuring brain activity cycling (BAC) in long term EEG monitoring of preterm babies

Measuring fluctuation of vigilance states in early preterm infants undergoing long term intensive care holds promise for monitoring their neurological well-being. There is currently, however, neither objective nor quantitative methods available for this purpose in a research or clinical environment. The aim of this proof-of-concept study was, therefore, to develop quantitative measures of the fluctuation in vigilance states or brain activity cycling (BAC) in early preterm infants. The proposed measures of BAC were summary statistics computed on a frequency domain representation of the proportional duration of spontaneous activity transients (SAT%) calculated from electroencephalograph (EEG) recordings. Eighteen combinations of three statistics and six frequency domain representations were compared to a visual interpretation of cycling in the SAT% signal. Three high performing measures (band energy/periodogram: R = 0.809, relative band energy/nonstationary frequency marginal: R = 0.711, g-statistic/nonstationary frequency marginal: R = 0.638) were then compared to a grading of sleep wake cycling based on the visual interpretation of the amplitude-integrated EEG trend. These measures of BAC are conceptually straightforward, correlate well with the visual scores of BAC and sleep wake cycling, are robust enough to cope with the technically compromised monitoring data available in intensive care units, and are recommended for further validation in prospective studies.

Structural model updating using incomplete transfer function of strain data

In this paper a model updating algorithm is presented to estimate structural parameters at the element level utilizing frequency domain representation of the strain data. Sensitivity equations for mass and stiffness parameters estimation are derived using decomposed form of the strain-based transfer functions. The rate of changes of eigenvectors and a subset of measured natural frequencies are used to assemble the sensitivity equation of the strain-based transfer function. Solution of the derived sensitivity equations through the least square method resulted in a robust parameters estimation method. Numerical examples using simulated noise polluted data of 2D truss and frame models confirm that the proposed method is able to successfully update structural models even in the presence of mass modeling errors.

English

Audio Noise Reduction Using Butter Worth Filter     International Journal of Computer & Organization Trends  (IJCOT)             © 2014 by IJCOT Journal Volume - 4 Issue - 2 Year of Publication : 2014 Authors : 

DWT based coding DNA watermarking for DNA copyright protection

DNA watermarking is a technique for copyright protection and ownership authentication of DNA sequences and ensures the security of private genetic information. This paper addresses issues regarding watermarking DNA coding sequences in the frequency domain that confer mutation resistance, amino acid conservation, and security. Multimedia watermarking is designed for robustness and invisibility mainly based on frequency domain representations. However, frequency domain watermarking for a coding DNA sequence is significantly constrained because the transformation and inverse transformation must be performed while completely conserving the amino acid sequence. In this paper, we present a coding DNA watermarking method in a lifting-based discrete wavelet transform (DWT) domain that focuses on the feasibility of frequency domain watermarking for DNA sequences. Our method divides a coding DNA sequence into a number of subsequences and allocates all codons in subsequences to a numerical code using the histogram ranks of the amino acids. Our method then calculates a set of DWT coefficients for subsequences of synonymous codons and finds a subsequence among them with DWT coefficients that are optimal for embedding watermark bits. Finally, our method substitutes this sequence for a subsequence of codons. To secure the watermark, our method generates the binary watermark based on nonlinear congruential – pseudorandom number generator (NC-PRNG) and randomly selects the embeddable position in the DWT domain of the subsequence. We experimentally verified that our method ensures not only amino acid conservation and security but also resists a point mutation rate of approximately 18.5% point mutations.

Quadrature Compressive Sampling for Radar Signals

Quadrature sampling has been widely applied in coherent radar systems to extract in-phase and quadrature (I and Q) components in the received radar signal. However, the sampling is inefficient because the received signal contains only a small number of significant target signals. This paper incorporates the compressive sampling (CS) theory into the design of the quadrature sampling system, and develops a quadrature compressive sampling (QuadCS) system to acquire the I and Q components with low sampling rate. The QuadCS system first randomly projects the received signal into a compressive bandpass signal and then utilizes the quadrature sampling to output compressive I and Q components. The compressive outputs are used to reconstruct the I and Q components. To understand the system performance, we establish the frequency domain representation of the QuadCS system. With the waveform-matched dictionary, we prove that the QuadCS system satisfies the restricted isometry property with overwhelming probability. For K target signals in the observation interval T, simulations show that the QuadCS requires just O(Klog(BT/K)) samples to stably reconstruct the signal, where B is the signal bandwidth. The reconstructed signal-to-noise ratio decreases by 3dB for every octave increase in the target number K and increases by 3dB for every octave increase in the compressive bandwidth. Theoretical analyses and simulations verify that the proposed QuadCS is a valid system to acquire the I and Q components in the received radar signals.