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NASA NTRS1995

On the joint spectral density of bivariate random sequences

For univariate random sequences, the power spectral density acts like a probability density function of the frequencies present in the sequence. This dissertation extends that concept to bivariate random sequences. For this purpose, a function called the joint spectral density is defined that represents a joint probability weighing of the frequency content of pairs of random sequences. Given a pair of random sequences, the joint spectral density is not uniquely determined in the absence of any constraints. Two approaches to constraining the sequences are suggested: (1) assume the sequences are the margins of some stationary random field, (2) assume the sequences conform to a particular model that is linked to the joint spectral density. For both approaches, the properties of the resulting sequences are investigated in some detail, and simulation is used to corroborate theoretical results. It is concluded that under either of these two constraints, the joint spectral density can be computed from the non-stationary cross-correlation.

Aalfs, David D.↗
NASA NTRS1975

Spectral characteristics of digital phase-modulated signals

The power spectral density of two-level digital phase modulated signals is determined using various polar pulse shaping functions, the only restriction being that the pulses are independent and do not overlap. Rectangular pulses and pulses having finite rise and decay times are considered. It is shown that a substantial improvement in terms of minimizing spectral occupancy on a power basis over a given frequency band can be achieved by using linear and raised cosine pulse shaping functions. Further, the rate of decrease of the power spectral density is given for the asymptotic limit as f goes to infinity. The use of these and possibly other well chosen pulse shaping functions can then provide an additional aid to overall efficient spectrum utilization and management.

Mcgregor, D. N.↗
NASA NTRS2004

Signal Processing Variables for Optimization of Flaw Detection in Composites Using Ultrasonic Guided Wave Scanning

This study analyzes the effect of signal processing variables on the ability of the ultrasonic guided wave scan method at NASA Glenn Research Center to distinguish various flaw conditions in ceramic matrix composites samples. In the ultrasonic guided wave scan method, several time- and frequency-domain parameters are calculated from the ultrasonic guided wave signal at each scan location to form images. The parameters include power spectral density, centroid mean time, total energy (zeroth moment), centroid frequency, and ultrasonic decay rate. A number of signal processing variables are available to the user when calculating these parameters. These signal processing variables include 1) the time portion of the time-domain waveform processed, 2) integration type for the properties requiring integrations, 3) bounded versus unbounded integrations, 4) power spectral density window type, 5) and the number of time segments chosen if using the short-time fourier transform to calculate ultrasonic decay rate. Flaw conditions examined included delamination, cracking, and density variation.

Roth, Don J.↗
NASA NTRS1992

Spectrum characteristics of Denver and Philadelphia ground clutter and the problem of distinguishing wind shear targets from moving clutter

Spectral analysis of 1991 wind shear flight data has provided information about the power spectral density, spectral width, and velocity of ground clutter detected by the wind shear radar at several major airports. Ground clutter must be recognized and separated from weather targets before wind shear can be computed. Information will be presented characterizing and comparing ground clutter and weather target spectra. The information includes (1) spectral widths of stationary ground clutter seen at various scan and tilt angles, (2) power spectral density and velocity of moving ground clutter relative to the stationary ground clutter, and (3) spectral widths and velocities of weather targets. A summary of numerical results in the form of histograms and example numerical results in the form of spectral plots are presented.

Mackenzie, Anne I.↗
NASA NTRS1973

Effects of vibration and shock on the performance of gas-bearing space-power Brayton cycle turbomachinery. Part 3: Sinusoidal and random vibration data reduction and evaluation, and random vibration probability analysis

The random vibration response of a gas bearing rotor support system has been experimentally and analytically investigated in the amplitude and frequency domains. The NASA Brayton Rotating Unit (BRU), a 36,000 rpm, 10 KWe turbogenerator had previously been subjected in the laboratory to external random vibrations, and the response data recorded on magnetic tape. This data has now been experimentally analyzed for amplitude distribution and magnetic tape. This data has now been experimentally analyzed for amplitude distribution and frequency content. The results of the power spectral density analysis indicate strong vibration responses for the major rotor-bearing system components at frequencies which correspond closely to their resonant frequencies obtained under periodic vibration testing. The results of amplitude analysis indicate an increasing shift towards non-Gaussian distributions as the input level of external vibrations is raised. Analysis of axial random vibration response of the BRU was performed by using a linear three-mass model. Power spectral densities, the root-mean-square value of the thrust bearing surface contact were calculated for specified input random excitation.

Tessarzik, J. M.↗
NASA NTRS1972

Lumped parameter analysis of a stringer reinforced plate excited by band limited noise

The maximum root-mean-square response of a square clamped plate, subjected to a stationary random excitation, was determined both theoretically and empirically. For the tests, a 40 x 40 x 1/4 aluminum sheet was milled out to provide a thin waffle plate with 9 panels. The plate was acoustically excited, with the frequency range limited between 25 Hz and 500 Hz. The root-mean-square power of the random excitations, 149 decibels, was nearly constant for all natural frequencies of the plate system. Strain gage readings at 14 points were plotted as power spectral densities and root-mean-square displacements. A modal damping ratio matrix was determined from the response curves. Damping ratios were found to be a function of frequency, but not of location on the plate. For comparisons with the theoretical response, the plate was subdivided into 14 modes and anlayzed as a damped, lumped parameter system by use of an approximate normal-mode method. This method gave the best predictions of the power spectral densities for the lower frequencies. That prediction errors increased for the higher frequencies is attributed to improper assumptions for mass distribution and the insufficient number of lumped mass points.

Bilyeu, D. J.↗
NASA NTRS1995

Basic principles and recent observations of rotationally sampled wind

The concept of rotationally sampled wind speed is described. The unusual wind characteristics that result from rotationally sampling the wind are shown first for early measurements made using an 8-point ring of anemometers on a vertical plane array of meteorological towers. Quantitative characterization of the rotationally sampled wind is made in terms of the power spectral density function of the wind speed. Verification of the importance of the new concept is demonstrated with spectral analyses of the response of the MOD-OA blade flapwise root bending moment and the corresponding rotational analysis of the wind measured immediately upwind of the MOD-OA using a 12-point ring of anemometers on a 7-tower vertical plane array. The Pacific Northwest Laboratory (PNL) theory of the rotationally sampled wind speed power spectral density function is tested successfully against the wind spectrum measured at the MOD-OA vertical plane array. A single-tower empirical model of the rotationally sampled wind speed is also successfully tested against the measurements from the full vertical plane array. Rotational measurements of the wind velocity with hotfilm anemometers attached to rotating blades are shown to be accurate and practical for research on winds at the blades of wind turbines. Some measurements at the rotor blade of a MOD-2 turbine using the hotfilm technique in a pilot research program are shown. They are compared and contrasted to the expectations based upon application of the PNL theory of rotationally sampled wind to the MOD-2 size and rotation rate but without teeter, blade bending, or rotor induction accounted for. Finally, the importance of temperature layering and of wind modifications due to flow over complex terrain is demonstrated by the use of hotfilm anemometer data, and meteorological tower and acoustic doppler sounder data from the MOD-2 site at Goodnoe Hills, Washington.

Connell, James R.↗
NASA NTRS1985

A relation between the short time variations of cosmic rays and geomagnetic field change

An event is reported of approx. 37 min periodicity in cosmic ray intensity observed at Akeno(38 deg 47 N, 138 deg 30 E. 900m above s.l., cutoff 10.4 GV) during 1300 approx. 1900 UT on April 25th, 1984, just a day before Forbush decrease of April 26th. This event seemed to be followed by the periodic variations of the geomagnetic field observed at Kakioka (36 deg 23 N, 140 deg 18 E). The regression coefficient between them was obtained approx. 0.07%/10nT. It is shown that in general the power spectral density of cosmic rays in the frequency of 0.0001 approx. 0.001Hz correlates positively with the fluctuations of geomagnetic field (Dst field) around approx. 1.2x0.0001Hz. From the analysis of 47 days data (April 14th to June 13th, 1984) the regression curve was obtained as y=0.275x sup 0.343 with the correlation coefficient of 0.48, where x and y mean Fourier components of Dst field summed over 1.04 approx. 1.39x0.001Hz and cosmic ray power spectral density averaged over 0.0001 approx. 0.001Hz.

Saki, T.↗
NASA NTRS2007

Self-consistent Model of Magnetospheric Ring Current and Propagating Electromagnetic Ion Cyclotron Waves. 2. Wave Induced Ring Current Precipitation and Thermal Electron Heating

This paper continues presentation and discussion of the results from our new global self-consistent theoretical model of interacting ring current ions and propagating electromagnetic ion cyclotron waves [Khazanov et al., 2006]. To study the effects of electromagnetic ion cyclotron wave propagation and refraction on the wave induced ring current precipitation and heating of the thermal plasmaspheric electrons, we simulate the May 1998 storm. The main findings after a simulation can be summarized as follows. Firstly, the wave induced ring current precipitation exhibits quite a lot of fine structure, and is highly organized by location of the plasmapause gradient. The strongest fluxes of about 4 x 10(exp 6) (cm(raised dot) s(raised dot) sr(raised dot) (sup -1)) are observed during the maill and early recovery phases of the storm. The very interesting and probably more important finding is that in a number of cases the most intense precipitating fluxes are not connected to the most intense waves in simple manner. The characteristics of the wave power spectral density distribution over the wave normal angle are extremely crucial for the effectiveness of the ring current ion scattering. Secondly, comparison of the global proton precipitating patterns with the results from RAM [Kozyra et al., 1997a] reveals that although we observe a qualitative agreement between the localizations of the wave induced precipitations in the models, there is no quantitative agreement between the magnitudes of the fluxes. The quantitative differences are mainly due to a qualitative difference between the characteristics of the wave power spectral density distributions over the wave normal angle in RAM and in our model. Thirdly, the heat fluxes to plasmaspheric electrons caused by Landau resonate energy absorption from electromagnetic ion cyclotron waves are observed in the postnoon-premidnight MLT sector, and can reach the magnitude of 10(exp 11) eV/(cm(sup 2)(raised dot)s). The Coulomb energy degradation of the RC H(+) and O(+) ions maximizes at about 10(exp 11) (eV/(cm(sup 2) (raised dot) s), and typically leads to electron energy deposition rates of about 2(raised dot) 10(exp 10) (eV/(cm(sup 2)(raised dot)s) which are observed during two periods; 32-48 hours, and 76-86 hours after 1 May, 0000 UT. The theoretically derived spatial structure of the thermal electron heating caused by interaction of the ring current with the plasmasphere is strongly supported by concurrent and conjugate plasma measurements from the plasmasphere, ring current, and topside ionosphere [Gurgiolo et al., 2005]. Finally, the wave induced intense electron heating has a structure of the spot-like patches along the most enhanced density gradients in the plasmasphere boundary layer and can be a possible driver to the observed but still not explained small-scale structures of enhanced emissions in the stable auroral red arcs.

Khazanov, G. V.↗
NASA NTRS2006

Self-Consistent Model of Magnetospheric Ring Current and Propagating Electromagnetic Ion Cyclotron Waves: Waves, Precipitating Ring Current Ions, and Thermal Electron Heating - 2

This paper is dedicated to further presentations and discussions of the results from our new global self-consistent theoretical model of interacting ring current ions and electromagnetic ion cyclotron waves [Khazanov et al., 2006; here referred to as Paper 1]. In order to adequately take into account the wave propagation and refraction in a multi-ion plasmasphere, we explicitly include the ray tracing equations in our previous self-consistent model and use the general form of the wave kinetic equation [for details see Paper 1]. To demonstrate the effects of the EMIC wave propagation and refraction on the RC proton precipitations and heating of the thermal plasmaspheric electrons we simulate the May 1998 storm. The main findings of our simulation can be summarized as follows. Firstly, the wave induced precipitations have a quite fine structure, and are highly organized by location of the plasmapause gradient. The strongest fluxes of about 4 (raised dot) 10(exp 6) [(cm (raised dot) s (raised dot) sr)(sup -l)] are observed during the main and early recovery phases of the storm. The very interesting and probably more important finding is that in a number of cases the most intense precipitating fluxes are not simply connected to the most intense EMIC waves. The character of the EMIC wave power spectral density distribution over the equatorial wave normal angle is an extremely crucial for the effectiveness of the RC ion scattering. Secondly, comparison of the global proton precipitating patterns with the results from other ring current model [Kozyra et al., 1997] reveals that although we observe a qualitative agreement between localizations of the wave induced fluxes in the models, there is no quantitative agreement between the magnitudes of these fluxes. These differences are mainly due to a qualitative difference between the characters of the EMIC wave power spectral density distributions over the equatorial wave normal angle. Finally, the two energy sources to the plasmaspheric electrons are considered; (i) the heat fluxes caused by the EMIC wave energy absorption due to Landau resonance, and (ii) the heat fluxes due to Coulomb energy degradation of the RC o(+) ions. The heat fluxes caused by the EMIC wave energy absorption due to Landau resonance are observed in the postnoon-premidnight MLT sector, and maximize at the magnitude of 10l1 (eV/(cm(sup 2)(raised dot) s) at L=3.25, MLT=22 at 3400 UT after 1 May, 0000 UT. The greatest Coulomb energy deposition rates are about 2 (raised dot) 10(sup 10)(eV/(cm(sup 2)(raised dot) s) and observed during two periods; 32-48 hours, and 76-86 hours after 1 May, 0000 UT. The theoretically derived spatial structure of the thermal electron heating caused by interaction of the RC with plasmasphere is strongly supported by concurrent and conjugate plasma measurements from the plasmasphere, the RC, and the topside ionosphere [Gurgiolo et al., 20051.

Khazanov, G. V.↗
DOE OSTI2021

Model-based real-time surface heat flux and temperature estimation for the DIII-D tokamak

A control-oriented model for monitoring of wall power flux densities on the DIII-D tokamak has been successfully implemented and validated experimentally. Future reactors will have to withstand severe steady state high heat flux loads on plasma-facing components (PFCs). Due to the difficulty of directly-measuring local heat fluxes on these components, monitoring and protection of PFCs during the plasma discharge can benefit from simplified physics-based real-time (RT) functional models to estimate and guide heat load control. As a first step into the development, a control-oriented model for monitoring of wall power flux densities and temperatures on DIII-D tokamak has been successfully implemented. The paper discusses the experimental demonstration and comparison of the 2-D model-based wall heat flux algorithm on the DIII-Dinner wall limiter (IWL) against infra-red camera heat flux measurements for limited plasma configurations. The paper also reports on the benchmarking of the field line tracing environment, SMITER, developed at ITER organization on DIII-D tokamak against experimental IR diagnostic data and the derivation of the component shaping weighting factors for the 2-D model-based approach. Here, the extension of the model-based approach for surface temperature estimation on the DIII-D IWL is also presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1991

Limits on the isolation of stochastic vibration for microgravity space experiments

The limitations on the isolation of stochastic vibrations for microgravity space experiments are explored. These limitations result from the restricted interior space available for vibration isolation. A one-degree-of-freedom representation of the experiment-spacecraft system is used, and an ideal vibration actuator is assumed. A kinematic representation results, and the problem becomes one of finding the minimum acceleration trajectory within a pair of stochastic walls. The wall motion is characterized by an ergodic, stationary, zero-mean, Gaussian random process with known power spectral density. The geometry of the wall trajectories is defined in terms of their significant extrema and zero crossings. This geomemtry is used in defining a composite trajectory that has a mean square acceleratiaon lower than that on the optimal path satisfying the stochastic wall inequality constraints. The optimal control problem is solved on a return path yielding the mean square acceleration in terms of the distributions of significant maxima and first-passage time of the wall process. The methodology is applied to a microgravity isolation problem to find the lower bounds on root-mean-square acceleration given the disturbance power spectral density.

Knospe, C. R.↗
NASA NTRS1978

Acoustic scattering from locally homogeneous turbulence

An equation is derived for acoustic scattering from the velocity and temperature fields of a drifting blob of air turbulence. The equation is solved for scattering from the mean and turbulent portions of both fields, and the time autocorrelation and power spectral density of the received signal are calculated. The mean velocity and temperature fields, as well as the corresponding turbulence intensity distributions, are allowed to be spatially nonuniform. The turbulent fields are required to be only locally homogeneous and locally stationary. It is shown that the common practice of representing antenna patterns by either truncating the flow or tapering the strength of the flow is, at least in the case of the transmitting pattern, not a bad approximation. Spectral broadening of the receiver signal due to convection of the small scattering eddies by macroeddies and by the mean flow in modeled, and the broadening by macroeddy convection is seen to render negligible the broadening which arises from the drift of the target flow through the antenna beam. The analysis reveals that only for target flows having a high degree of spatial uniformity and/or symmetry does the received positive-frequency power spectral density turn out to be symmetrical about a center frequency.

Ramsey, V. W.↗
NASA NTRS1990

Dynamic Power Spectral Analysis of Solar Measurements from Photospheric, Chromospheric, and Coronal Sources

An important aspect in the power spectral analysis of solar variability is the quasistationary and quasiperiodic nature of solar periodicities. In other words, the frequency, phase, and amplitude of solar periodicities vary on time scales ranging from active region lifetimes to solar cycle time scales. Here, researchers employ a dynamic, or running, power spectral density analysis to determine many periodicities and their time-varying nature in the projected area of active sunspot groups (S sub act). The Solar Maximum Mission/Active Cavity Radiometer Irradiance Monitor (SMM/ACRIM) total solar irradiance (S), the Nimbus-7 MgII center-to-wing ratio (R (MgII sub c/w)), the Ottawa 10.7 cm flux (F sub 10.7), and the GOES background x ray flux (X sub b) for the maximum, descending, and minimum portions of solar cycle 21 (i.e., 1980 to 1986) are used. The technique dramatically illustrates several previously unrecognized periodicities. For example, a relatively stable period at about 51 days has been found in those indices which are related to emerging magnetic fields. The majority of solar periodicities, particularly around 27, 150 and 300 days, are quasiperiodic because they vary in amplitude and frequency throughout the solar cycle. Finally, it is shown that there are clear differences between the power spectral densities of solar measurements from photospheric, chromospheric, and coronal sources.

Bouwer, S. D.↗
DOE OSTI2023

Analytical harmonic vibrational frequencies with VV10-containing density functionals: Theory, efficient implementation, and benchmark assessments

VV10 is a powerful nonlocal density functional for long-range correlation that is used to include dispersion effects in many modern density functionals, such as the meta-generalized gradient approximation (mGGA), B97M-V, the hybrid GGA, ωB97X-V, and the hybrid mGGA, ωB97M-V. While energies and analytical gradients for VV10 are already widely available, this study reports the first derivation and efficient implementation of the analytical second derivatives of the VV10 energy. The additional compute cost of the VV10 contributions to analytical frequencies is shown to be small in all but the smallest basis sets for recommended grid sizes. Here, this study also reports the assessment of VV10-containing functionals for predicting harmonic frequencies using the analytical second derivative code. The contribution of VV10 to simulating harmonic frequencies is shown to be small for small molecules but important for systems where weak interactions are important, such as water clusters. In the latter cases, B97M-V, ωB97M-V, and ωB97X-V perform very well. The convergence of frequencies with respect to the grid size and atomic orbital basis set size is studied, and recommendations are reported. Finally, scaling factors to allow comparison of scaled harmonic frequencies with experimental fundamental frequencies and to predict zero-point vibrational energy are presented for some recently developed functionals (including r2SCAN, B97M-V, ωB97X-V, M06-SX, and ωB97M-V).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1983

High frequency, high power capacitor development

A program to develop a special high energy density, high power transfer capacitor to operate at frequency of 40 kHz, 600 V rms at 125 A rms plus 600 V dc bias for space operation. The program included material evaluation and selection, a capacitor design was prepared, a thermal analysis performed on the design. Fifty capacitors were manufactured for testing at 10 kHz and 40 kHz for 50 hours at Industrial Electric Heating Co. of Columbus, Ohio. The vacuum endurance test used on environmental chamber and temperature plate furnished by Maxwell. The capacitors were energized with a special power conditioning apparatus developed by Industrial Electric Heating Co. Temperature conditions of the capacitors were monitored by IEHCo test equipment. Successful completion of the vacuum endurance test series confirmed achievement of the main goal of producing a capacitor or reliable operation at high frequency in an environment normally not hospitable to electrical and electronic components. The capacitor developed compared to a typical commercial capacitor at the 40 kHz level represents a decrease in size and weight by a factor of seven.

White, C. W.↗