Power Spectral Density Level Research Articles

On the Shaker Simulation of Wind-Induced Non-Gaussian Random Vibration

Gaussian signal is produced by ordinary random vibration controllers to test the products in the laboratory, while the field data is usually non-Gaussian. Two methodologies are presented in this paper for shaker simulation of wind-induced non-Gaussian vibration. The first methodology synthesizes the non-Gaussian signal offline and replicates it on the shaker in the Time Waveform Replication (TWR) mode. A new synthesis method is used to model the non-Gaussian signal as a Gaussian signal multiplied by an amplitude modulation function (AMF). A case study is presented to show that the synthesized non-Gaussian signal has the same power spectral density (PSD), probability density function (PDF), and loading cycle distribution (LCD) as the field data. The second methodology derives a damage equivalent Gaussian signal from the non-Gaussian signal based on the fatigue damage spectrum (FDS) and the extreme response spectrum (ERS) and reproduces it on the shaker in the closed-loop frequency domain control mode. The PSD level and the duration time of the derived Gaussian signal can be manipulated for accelerated testing purpose. A case study is presented to show that the derived PSD matches the damage potential of the non-Gaussian environment for both fatigue and peak response.

Double‐Frequency Microseisms in Ambient Noise Recorded in Mississippi

Abstract This research presents the power spectral density (PSD) of double‐frequency (DF) microseisms of 13 continuous single‐point long‐term ambient noise recordings (LTRs) at five inland and two coastal locations selected in Mississippi and Louisiana states and 234 single‐point short‐term ambient noise recordings (STRs) in northern Mississippi. By correlating PSD of LTRs with the simultaneous ocean data (including significant ocean wave frequency, significant ocean wave height, ocean wind speed, and above‐ocean atmosphere pressure) of the Atlantic Ocean and Gulf of Mexico, as well as local atmosphere pressure and wind speed, DF microseisms observed in northern Mississippi were shown to be shaped by a combined impact of both wave climates of the Atlantic Ocean and Gulf of Mexico. Particle motion analysis and calculation of vibration angle defined separately for LTRs and STRs strengthen this conclusion. The DF and PSD level at DF of STR plots in the horizontal direction versus unconsolidated sediment thickness show significant differences from the plots in the vertical direction, which indicates that the shear‐wave resonance in thick sediments modifies the DF microseisms more obviously in the horizontal than in the vertical direction.

ATSC digital television signal detection with spectral correlation density

In this paper, we consider the problem of spectrum sensing for advanced television systems committee (ATSC) digital television (DTV) signal detection. To exploit the cyclostationarity of the ATSC DTV signals, we employ spectral correlation density (SCD) as the decision statistic and propose an optimal detection algorithm. The major difficulty is in obtaining the probability distribution functions of the SCD. To overcome the difficulty, we probabilistically model the pilot frequency location and employ Gaussian approximation for the SCD distribution. Then, we obtain a practically implementable detection algorithm that outperforms the industry leading systems by 2-3 dB. We also propose various techniques that greatly reduce the system complexity with performance degradation by only a few tenths of decibels. Finally, we show how robust the system is to the estimation errors of the noise power spectral density level and the probability distribution of the pilot frequency location.

CMOS Image Sensor Noise Analysis Through Noise Power Spectral Density Including Undersampling Effect Due to Readout Sequence

This paper presents a noise analysis in the frequency domain using noise power spectral density and considering the undersampling process coming from the native readout circuit sequence of image sensors. It reveals aliasing effect impacting the noise level of the image sensor. Key parameters of the undersampling process, such as sampling period, power spectral density level, and type, are explored. Low-frequency noise and particularly 1/f noise impact show a major impact in results. The new calculation algorithm is implemented in MATLAB software. Two CMOS image sensor technologies are used to perform a comparison between noise estimation and measurements. This comparison shows a very good correlation between estimations and measurements.

Electroelastic modeling and experimental validations of piezoelectric energy harvesting from broadband random vibrations of cantilevered bimorphs

We present electroelastic modeling, analytical and numerical solutions, and experimental validations of piezoelectric energy harvesting from broadband random vibrations. The modeling approach employed herein is based on a distributed-parameter electroelastic formulation to ensure that the effects of higher vibration modes are included, since broadband random vibrations, such as Gaussian white noise, might excite higher vibration modes. The goal is to predict the expected value of the power output and the mean-square shunted vibration response in terms of the given power spectral density (PSD) or time history of the random vibrational input. The analytical method is based on the PSD of random base excitation and distributed-parameter frequency response functions of the coupled voltage output and shunted vibration response. The first of the two numerical solution methods employs the Fourier series representation of the base acceleration history in an ordinary differential equation solver while the second method uses an Euler–Maruyama scheme to directly solve the resulting electroelastic stochastic differential equations. The analytical and numerical simulations are compared with several experiments for a brass-reinforced PZT-5H bimorph under different random excitation levels. The simulations exhibit very good agreement with the experimental measurements for a range of resistive electrical boundary conditions and input PSD levels. It is also shown that lightly damped higher vibration modes can alter the expected power curve under broadband random excitation. Therefore, the distributed-parameter modeling and solutions presented herein can be used as a more accurate alternative to the existing single-degree-of-freedom solutions for broadband random vibration energy harvesting.

Marginal blind deconvolution of adaptive optics retinal images

Adaptive Optics corrected flood imaging of the retina has been in use for more than a decade and is now a well-developed technique. Nevertheless, raw AO flood images are usually of poor contrast because of the three-dimensional nature of the imaging, meaning that the image contains information coming from both the in-focus plane and the out-of-focus planes of the object, which also leads to a loss in resolution. Interpretation of such images is therefore difficult without an appropriate post-processing, which typically includes image deconvolution. The deconvolution of retina images is difficult because the point spread function (PSF) is not well known, a problem known as blind deconvolution. We present an image model for dealing with the problem of imaging a 3D object with a 2D conventional imager in which the recorded 2D image is a convolution of an invariant 2D object with a linear combination of 2D PSFs. The blind deconvolution problem boils down to estimating the coefficients of the PSF linear combination. We show that the conventional method of joint estimation fails even for a small number of coefficients. We derive a marginal estimation of the unknown parameters (PSF coefficients, object Power Spectral Density and noise level) followed by a MAP estimation of the object. We show that the marginal estimation has good statistical convergence properties and we present results on simulated and experimental data.

Temporal Variations in Crustal Scattering Structure near Parkfield, California, Using Receiver Functions

Abstract We investigate temporal variations in teleseismic receiver functions using 11 yr of data at station PKD near Parkfield, California, by stacking power spectral density (PSD) functions within 12-month windows. We find that PSD levels for both radial and transverse components drop by ∼5 dB following the 2003 San Simeon ( M 6.5) earthquake, with a persistent reduction in background levels of ∼2 dB, relative to the pre-2003 levels, after the 2004 Parkfield ( M 6) earthquake, corresponding to an estimated decrease in shear-wave velocity of ∼0.12 and , respectively, or equivalent negative changes in Poisson’s ratio of ∼0.02 and ∼0.01. Our results suggest that the perturbation originates at middle to lower crustal levels, possibly caused by the redistribution of crustal pore fluids, consistent with increased and sustained tremor activity near Parkfield following both earthquakes. This study shows that we can resolve temporal variations in crustal scattering structure near a major seismogenic fault using the receiver function method.

Nonlinear dynamic analysis of an elastic beam isolator sliding on frictional supports

The dynamic behavior of an elastic beam free to slide on two frictional supports is studied under sinusoidal and random excitations. The beam force–deflection relationship, originally expressed in terms of elliptic functions, is approximated by a polynomial fit of eleventh order. The friction force is modeled in terms of the sliding velocity and the end slope angle. Under sinusoidal excitation, the equation of motion of the system is solved numerically and the solution is utilized to estimate the system transmissibility. It is found that when the excitation frequency is increased beyond resonance, the friction at the sliding supports improves the transmissibility. The dependence of the response on initial conditions establishes the basins of attraction for different values of friction coefficient and excitation parameters. The dependence of the safety integrity factor on excitation amplitude level and friction coefficient reveals that the friction extends the stable region. Under random excitation, the system response statistics are estimated from Monte Carlo simulation results for different values of friction coefficient and excitation power spectral density level. The friction is found to result in a significant reduction of the system response mean square.

P‐35: Characterizing Laser Speckle and Its Effect on Target Detection

AbstractIn this study we examine a power spectral density metric for characterizing laser speckle and predicting its effect on target detection. To evaluate the metric, we measured contrast energy thresholds on both a laser speckle background and backgrounds consisting of randomly modulated pixel luminance (i.e., pixel noise). We found that, at the same power spectral density levels, energy thresholds obtained for gratings superimposed on pixel noise were slightly higher than analogous thresholds obtained with laser‐speckle noise. In the discussion section, we outline necessary improvements to the laser speckle power spectral density metric.

The effect of white-noise mask level on sinewave contrast detection thresholds and the critical-band-masking model

It is known that visual noise added to sinusoidal gratings changes the typical U-shaped threshold curve which becomes flat in log-log scale for frequencies below 10c/deg when gratings are masked with white noise of high power spectral density level. These results have been explained using the critical-band-masking (CBM) model by supposing a visual filter-bank of constant relative bandwidth. However, some psychophysical and biological data support the idea of variable octave bandwidth. The CBM model has been used here to explain the progressive change of threshold curves with the noise mask level and to estimate the bandwidth of visual filters. Bayesian staircases were used in a 2IFC paradigm to measure contrast thresholds of horizontal sinusoidal gratings (0.25-8 c/deg) within a fixed Gaussian window and masked with one-dimensional, static, broadband white noise with each of five power density levels. Raw data showed that the contrast threshold curve progressively shifts upward and flattens out as the mask noise level increases. Theoretical thresholds from the CBM model were fitted simultaneously to the data at all five noise levels using visual filters with log-Gaussian gain functions. If we assume a fixed-channel detection model, the best fit was obtained when the octave bandwidth of visual filters decreases as a function of peak spatial frequency.

The Effect of White-Noise Mask Level on Sinewave Contrast Detection Thresholds and the Critical-Band-Masking Model

It is known that visual noise added to sinusoidal gratings changes the typical U-shaped threshold curve which becomes flat in log-log scale for frequencies below 10c/deg when gratings are masked with white noise of high power spectral density level. These results have been explained using the critical-band-masking (CBM) model by supposing a visual filter-bank of constant relative bandwidth. However, some psychophysical and biological data support the idea of variable octave bandwidth. The CBM model has been used here to explain the progressive change of threshold curves with the noise mask level and to estimate the bandwidth of visual filters. Bayesian staircases were used in a 2IFC paradigm to measure contrast thresholds of horizontal sinusoidal gratings (0.25-8 c/deg) within a fixed Gaussian window and masked with one-dimensional, static, broadband white noise with each of five power density levels. Raw data showed that the contrast threshold curve progressively shifts upward and flattens out as the mask noise level increases. Theoretical thresholds from the CBM model were fitted simultaneously to the data at all five noise levels using visual filters with log-Gaussian gain functions. If we assume a fixed-channel detection model, the best fit was obtained when the octave bandwidth of visual filters decreases as a function of peak spatial frequency.

A low complexity multicarrier PAR reduction approach based on subgradient optimization

We introduce a novel subgradient optimization-based framework for iterative peak-to-average power ratio (PAR) reduction for multicarrier systems, such as wireless orthogonal frequency division multiplexing (OFDM) and wireline discrete multitone (DMT) very high-speed digital subscriber line (DMT-VDSL) systems. The proposed approach uses reserved or unused tones to minimize the peak magnitude of the DMT symbol vector where these tone values are iteratively updated through a subgradient search. The algorithms obtained through this framework have very simple update rules, and therefore, low computational complexities in general. Since the approach is based on the direct update of some frequency domain parameters, the power spectral density (PSD) level constraints that exist in the communications standards can easily be incorporated into the algorithms. This feature also enables simple compensation for the effects of transmit filter on PAR. Furthermore, we can locate the Active Set PAR reduction method for real baseband signals as a special case of the subgradient approach and provide its natural extension to handle complex baseband DMT signals. In addition to the peak level cost function, we also introduce the K -peak energy cost function which is also used to develop effective subgradient algorithms as illustrated by the simulation examples.

Prediction of Upper Tolerance Limit of Acceleration Power Spectrum Density of Satellite Panel under Diffused Acoustic Field Excitation

Severe vibroacoustic random vibration is easily induced to satellite structure during the flight. Design specification of acoustically induced random vibration for satellite and equipment component is based on the acceleration power spectral density (PSD) at the mount interface. Ground acoustic test is conducted to verify the structural design and abnormal function of equipments. The response of a satellite structure under acoustic test can be predicted by Statistical Energy Analysis. In addition to the mean energy vibration level obtained by SEA, upper tolerance limit of vibration response in PSD needs to be predicted for conservative design purposes. This paper deals with the upper tolerance limit of PSD acceleration level of a satellite plate under high frequency diffused acoustic excitation. The upper tolerance limit is derived based on the statistical distribution of the vibroacoustic response together with the theoretical description of response variance. The upper tolerance limit for the acceleration PSD level obtained by Statistical Energy Analysis is compared with the experiment result. The result from the comparison shows that the upper tolerance limit presented in this paper yields good estimate of PSD upper tolerance level for conservative design. The effect of PSD estimation error in experiment on variance is also discussed.

Comparison of fast Fourier transformation and autoregressive modelling as a diagnostic tool in analysis of lower extremity venous signals

In this study, we have compared the efficacy of autoregressive modelling (ARM) and fast Fourier transformation (FFT) of Doppler signals from lower extremity veins of healthy volunteers in various physiologic situations. Compared to FFT, ARM produced smooth spectra and less spectral broadening both in sonograms and power spectra. However, faulty positioning of the peaks along the time axis in FFT-derived power spectral density curves show that FFT is not a suitable method if these graphs are to be used as a diagnostic tool. Analysis of ARM-based venous sonograms and power spectral density graphs revealed that FFT should not be used in signals with high power spectral density levels and low-frequency bandwidth within limited segments of time.

Hydromagnetic Wave Excitation Upstream of an Interplanetary Traveling Shock

Using data of the Highly Suprathermal Time-Of-Flight sensor of the Charge, Element, and Isotope Analysis System on board the Solar and Heliospheric Observatory spacecraft located at Lagrangian point L1 near Earth, we have measured proton spectra in the energy range 60 keV-2 MeV associated with the Bastille Day coronal mass ejection of 2000 July 14-16. For the same event, the power spectral densities of the magnetic field fluctuations in the solar wind have been measured with the magnetometer on board the Advanced Composition Explorer in the frequency range from about 0.05 mHz to 0.5 Hz. Within 0.11 AU upstream of the main shock, the flux of protons in the energy range 150 keV-2 MeV decreases much more rapidly with distance from the shock than is expected from diffusion in typical solar wind magnetic turbulence. In the same upstream region, the excitation of hydromagnetic waves in the frequency range 0.25-3 mHz and with power spectral density levels of up to 100 times the typical levels in the ambient solar wind is observed.

A novel approach to solve DSL network data rate problems

Digital subscriber line (DSL) is a service that offers much faster Internet connection than a standard dial up connection. Crosstalk is a major impairment in DSL telecommunication networks. It degrades the upstream and downstream data rates and risks the DSL service providers ability to meet their service level agreement requirements. A novel approach to solve the upstream and downstream data rate problems is presented in this paper. The approach considered is to control the power spectral density and aggregate power level of the DSL access multiplexer.

Influence of Aliasing in Time and Frequency Electrochemical Noise Measurements

This paper points out the importance of anti‐aliasing filtering in the analog‐to‐digital conversion performed in electrochemical noise (EN) measurements. This operation is currently implemented in spectrum analyzers, but it is generally ignored in data acquisition systems based on acquisition cards in personal computers or on digital voltmeters. It is shown that without filtering, aliasing occurs and leads to fallacious amplitudes of the EN, that is, too‐high standard deviations in the time domain and too‐high power spectral density levels in the frequency domain. In particular the white noises, which are commonly encountered in localized corrosion at low sampling rates, always have a wrong amplitude when measured without filtering. Anti‐aliasing filtering may be carried out with analog filters or a combination of analog and digital filters. A comparison of two different digital filters, which are easily implementable in personal computers, shows that the slope of the filter roll‐off has to be high enough to avoid aliasing for all types of EN and to obtain a good overlapping of the power spectral densities measured at various sampling rates. © 2000 The Electrochemical Society. All rights reserved.

STOCHASTIC DYNAMICS OF SYSTEMS WITH FRICTION-INDUCED VIBRATION

This paper presents linear and non-linear phenomenological models of interfacial forces between a rotating disc and a rigid pin in contact with the disc. The models are developed based on experimental results which revealed that both normal and frictional forces were essentially random non-Gaussian processes. The characteristics of these forces are different when the disc reverses its rotation. When the disc rotates clockwise, the sprag-slip phenomenon occurs due to so-called kinematic constraint instability. Furthermore, in view of the time variations of contact forces, the boundary conditions of the pin become time varying and its natural frequency becomes time-dependent. The interfacial forces appear in the pin's equation of motion as multiplicative and non-homogeneous terms. In the non-linear model, the normal force appears as multiplicative of velocity terms up to cubic order. The pin's dynamic behavior was studied using the method of stochastic averaging. For the non-linear model, the problem of noise-induced transition was examined for clockwise and counter-clockwise cases. The pin amplitude extrema were found to be more complex for the case of clockwise rotation than those for the counter-clockwise case. For the linear model, the complete probabilistic description of the pin's dynamic behavior is derived in a closed form in terms of disc speed and friction power spectral density level.

Very low frequency (0.2–10.0 Hz) seismoacoustic noise below the seafloor

The sources and propagation of VLF (0.2 → 10 Hz) ambient noise on and within the deep ocean crust at Deep Sea Drilling Project (DSDP) Hole 534B in the Blake Bahama Basin are shown to be related to the surface sea state and local lithology. This study represents the first experiment where ambient noise is measured simultaneously at several depths below the seafloor. The low‐frequency microseism power spectral density (PSD) peak at 0.3 Hz is nearly invariant with depth between 0 and 100 m below the seafloor. PSD levels of the peak are 65 and 75 dB (rel 1 (nm/s2)2/Hz) for the vertical and horizontal components, respectively, and both horizontal and vertical components of the ocean bottom seismometer and borehole array compare favorably. Above 0.5 Hz the noise levels decrease with depth and increasing frequency. At 1.0 Hz, 100 m below the seafloor the noise level is 10 and 20 dB below the levels observed at the seafloor for vertical and horizontal components, respectively. There is evidence that amplification in some frequency bands may make deeper sites noisier than shallower sites in the same well. Temporal variation of the noise shows nonlinear interaction of local water‐borne gravity waves to be the dominant source mechanism and that the passing of a local storm generates interface waves and increases the noise level (∼10 dB) from 0.3 to 1.5 Hz and 5 to 64 Hz. Between 1.5 and 5 Hz the spectrum is not strongly affected by the passing storm, indicating that the ocean wave spectrum may be saturated.

Advantage of Monitoring Skin Vibration as an Index of Arteriovenous Fistular Blood Flow

Monitoring of the skin vibration is disturbed little by environmental noise. Therefore, the skin vibration is more relevant than bruit on the skin by means of monitoring the fistular blood flow. Frequency analysis of the skin vibration generated by an internal arteriovenous fistula indicated two peaks of power spectral density (PSD), one in the frequency range of 4-10 Hz and the other from 100-300 Hz. The analysis of the skin vibration generated by an external fistula, however, showed only one peak in the range of 4-10 Hz and a moderate flat PSD level in the range of 100-300 Hz. The PSD level in the range of 100-300 Hz decreased dramatically or disappeared when the fistular blood flow diminshed or ceased. Therefore, the optimal frequency for monitoring skin vibration may be the range of 100-300 Hz.