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NASA NTRSDate not supplied

Exercising Prediction Validation Methods for Analysis of Quiet Supersonic Overflight

En route noise certification procedures for quiet supersonic aircraft are in development under the International Civil Aviation Organization for a proposed standard that could enable civil supersonic overland flight. While these quiet supersonic aircraft do not exist yet, methods are being developed and evaluated using existing N-wave empirical datasets and low-boom simulation datasets. One potential aspect of future certification methods is the ability to use a validated prediction model to predict the certification noise level under reference day weather conditions. Methods to validate predictions, such as the two-sample t-test, Fisher’s combined probability test, two-sample Kolmogorov-Smirnov test, and equivalence testing, have been exercised and modified for this application. While some methods compare mean values, others compare values across the distribution, and a combination of methods can be used. The methods were applied to a subset of an N-wave dataset to demonstrate the applicability and identify potential areas for improvement. Atmospheric turbulence variability was included as a factor in these analyses through KZKFourier propagation simulations with parameters matching actual flights and weather conditions. Results are presented for six noise metrics (PL, ASEL, BSEL, DSEL, ESEL, and ISBAP), and plans to expand the analyses are discussed.

sonic boom↗

NASA NTRS1985

Statistical methods for astronomical data with upper limits. I - Univariate distributions

The statistical treatment of univariate censored data is discussed. A heuristic derivation of the Kaplan-Meier maximum-likelihood estimator from first principles is presented which results in an expression amenable to analytic error analysis. Methods for comparing two or more censored samples are given along with simple computational examples, stressing the fact that most astronomical problems involve upper limits while the standard mathematical methods require lower limits. The application of univariate survival analysis to six data sets in the recent astrophysical literature is described, and various aspects of the use of survival analysis in astronomy, such as the limitations of various two-sample tests and the role of parametric modelling, are discussed.

Feigelson, E. D.↗

NASA NTRS1994

Searching for hard X-ray directivity during the rise, peak, and decay phases of solar flares

We have identified 72 large solar flares (peak counting rates more than 1000 counts/s) observed by Hard X-ray Burst Spectroscopy (HXRBS) on-board the Solar Maximum Mission (SMM). Using a database of these flares, we have studied hard X-ray (50-850 keV) spectral center-to-limb variation and its evolution with time. The major results are the following: (1) During the rise phase, the center-to-limb spectral variation is small, with a hardness of delta delta = 0.02 +/- 0.25, and a statistical significance of 0.1 sigma. (2) During the peak phase, the center-to-limb variation is delta delta = 0.13 +/- 0.13, with a statistical significance of 1 sigma. (3) During the decay phase, the center-to-limb variation changes to softening. The softness is relatively large with delta delta = -0.25 +/- 0.21, and a statistical significance of 1.2 sigma. (4) The linear least-squares fits to the spectral center-to-limb variations do not have slopes significantly different from zero during all those three phases. (5) The center events and limb events spectral distributions are shown to be not different by using Kolmogorov-Smirnov two-samples test. (6) The fraction of events detected near the limb is marginally consistent with that expected from isotropically emitting flares. (7) On average, flares evolve as soft-hard-soft. These results suggest that there is no statistically significant evidence for hard X-ray directivity during the rise, peak, and decay phases of solar flares. The hard X-ray radiation pattern at those energies is almost isotropic during all those phases. This lack of directivity (or anisotropy) found in this study is not in agreement with the results discovered by Vestrand et al. (1987) in which they found energetic photon source is anisotropic, using SMM Gamma-Ray Spectrometer (GRS) data at a much higher energy band of 0.3-1 MeV. If we want to interpret the results of Vestrand et al. (1987) and our present results in a self-consistent way, we must conclude that at energies of greater than 50 keV, the Compton backscattering suppresses the hard X-ray anisotropy sufficiently so that no significant directivity can be measured during the rise, peak, and decay phases of solar flares. during the rise, peak, and decay phases of solar flares.

Li, Peng↗

NASA NTRSDate not supplied

Copula-based Method to Generate Consistent Surface Pressures Under Uncertainty

This paper establishes a method to create surface pressure databases that allow for uncertainty quantification. Aerodynamic databases are critical products for launch vehicles and other aeronautical systems, and surface pressure databases are one such database that constains large quantities of data. The focus of this work is the relationship between the integrated force and moment data base and the surface pressure database. In particular, the work attempts to provide a method that maintains consistency between these two databases when accounting for uncertainty. The integrated force and moment database and surface pressure databases are constructed from CFD data which is high-density but low-trust. However, the force and moment database will often also include data from high-trust but low-density sources such as from wind tunnel experiments. This means that the quantified uncertainty of the force and moment database is higher quality as it includes this high fidelity wind tunnel data. This motivates the idea to use the force and moment database uncertainty when constructing the surface pressure database uncertainty. The method utilizes the statistical idea of a copula in order to generate surface pressures that match with uncertain integrated force and moment distributions as well as being consistent with known CFD data. This statistical consistency is quantified by using the Maximum Mean Discrepancy two-sample test. The predictive error of the method is also approximated using leave-one-out error estimation and the good overall performance of the method is presented using probability boxes in a simulated uncertainty scenario.

SLS↗

NASA NTRS2017

Updated MISR Dark Water Research Aerosol Retrieval Algorithm - Part 1: Coupled 1.1 km Ocean Surface Chlorophyll a Retrievals with Empirical Calibration Corrections

As aerosol amount and type are key factors in the 'atmospheric correction' required for remote-sensing chlorophyll alpha concentration (Chl) retrievals, the Multi-angle Imaging SpectroRadiometer (MISR) can contribute to ocean color analysis despite a lack of spectral channels optimized for this application. Conversely, an improved ocean surface constraint should also improve MISR aerosol-type products, especially spectral single-scattering albedo (SSA) retrievals. We introduce a coupled, self-consistent retrieval of Chl together with aerosol over dark water. There are time-varying MISR radiometric calibration errors that significantly affect key spectral reflectance ratios used in the retrievals. Therefore, we also develop and apply new calibration corrections to the MISR top-of-atmosphere (TOA) reflectance data, based on comparisons with coincident MODIS (Moderate Resolution Imaging Spectroradiometer) observations and trend analysis of the MISR TOA bidirectional reflectance factors (BRFs) over three pseudo-invariant desert sites. We run the MISR research retrieval algorithm (RA) with the corrected MISR reflectances to generate MISR-retrieved Chl and compare the MISR Chl values to a set of 49 coincident SeaBASS (SeaWiFS Bio-optical Archive and Storage System) in situ observations. Where Chl(sub in situ) less than 1.5 mg m(exp -3), the results from our Chl model are expected to be of highest quality, due to algorithmic assumption validity. Comparing MISR RA Chl to the 49 coincident SeaBASS observations, we report a correlation coefficient (r) of 0.86, a root-mean-square error (RMSE) of 0.25, and a median absolute error (MAE) of 0.10. Statistically, a two-sample Kolmogorov- Smirnov test indicates that it is not possible to distinguish between MISR Chl and available SeaBASS in situ Chl values (p greater than 0.1). We also compare MODIS-Terra and MISR RA Chl statistically, over much broader regions. With about 1.5 million MISR-MODIS collocations having MODIS Chl less than 1.5 mg m(exp -3), MISR and MODIS show very good agreement: r = 0.96, MAE = 0.09, and RMSE = 0.15. The new dark water aerosol/Chl RA can retrieve Chl in low-Chl, case I waters, independent of other imagers such as MODIS, via a largely physical algorithm, compared to the commonly applied statistical ones. At a minimum, MISR's multi-angle data should help reduce uncertainties in the MODIS-Terra ocean color retrieval where coincident measurements are made, while also allowing for a more robust retrieval of particle properties such as spectral single-scattering albedo.

Limbacher, James A.↗

NASA NTRS1994

Two-sample discrimination of Poisson means

This paper presents a statistical test for detecting significant differences between two random count accumulations. The null hypothesis is that the two samples share a common random arrival process with a mean count proportional to each sample's exposure. The model represents the partition of N total events into two counts, A and B, as a sequence of N independent Bernoulli trials whose partition fraction, f, is determined by the ratio of the exposures of A and B. The detection of a significant difference is claimed when the background (null) hypothesis is rejected, which occurs when the observed sample falls in a critical region of (A, B) space. The critical region depends on f and the desired significance level, alpha. The model correctly takes into account the fluctuations in both the signals and the background data, including the important case of small numbers of counts in the signal, the background, or both. The significance can be exactly determined from the cumulative binomial distribution, which in turn can be inverted to determine the critical A(B) or B(A) contour. This paper gives efficient implementations of these tests, based on lookup tables. Applications include the detection of clustering of astronomical objects, the detection of faint emission or absorption lines in photon-limited spectroscopy, the detection of faint emitters or absorbers in photon-limited imaging, and dosimetry.

Lampton, M.↗

NASA NTRS1978

Performance evaluation of the SAO VLG-11 atomic hydrogen masers

A new generation of frequency standards, the VLG-11 hydrogen maser, has been designed and built at the Smithsonian Astrophysical Observatory (SAO). A comprehensive series of environmental and short-term stability tests on three VLG-11 masers has been completed and evaluated. The test results reported here show substantial improvements over previous hydrogen masers in measured sensitivity to variations in ambient temperature, barometric pressure, and magnetic fields. The maser frequency stability, as represented by the two-sample (Allan) variance, has been measured for averaging times ranging from 1 to 100,00 seconds. The variance is lower than 1 x 10 to the -15th for averaging intervals between 1400 and 20,000 seconds. For times shorter than 4000 seconds, the measured stability data agree remarkably well with theoretical values calculated from thermal noise mechanisms and the 'noise within the linewidth' regime is clearly discernable in the data.

Levine, M. W.↗

NASA NTRS1984

The system design of a rubidium maser frequency standard

The Rubidium Maser Frequency Standard is a precision frequency source with excellent short-term stability. A type PBR-II Rb maser frequency standard was developed by the Beijing Institute of Radio Metrology and Measurement (BIRMM). The time-domain frequency stability (two-sample variance) of this frequency standard is less than 1/5 times 10 to the 13th power for t=10ms yields 1.0s, fh=1.0 KHz. Two PBR-II frequency standards were used as reference frequency sources in a frequency stability measurement system. Some important system characteristics for the PBR-II Rb maser frequency standard such as phase noise and frequency stability transfer characteristics are discussed. Furthermore, the design of the frequency standard for optimum frequency stability of the output signal; the choice of a voltage controlled crystal oscillator for the frequency standard; the design of the phase-locked loop; and the frequency stability test results on the PBR-II are discussed.

Xiong, C. X.↗

NASA NTRS1985

Statistical analysis of astronomical data containing upper bounds - General methods and examples drawn from X-ray astronomy

Statistical procedures taken from the field of survival analysis have been adapted to astronomical usage and have been applied to a sample of stars in the B-V color range between 0.1 and 0.5 with measured soft X-ray luminosities and projected equatorial velocities. The two-sample problem and linear regression problem with arbitrarily censored data were studied. A new method for determining the linear regression between two random variables in the presence of arbitrary censoring has been developed which can also be used for a likelihood-ratio test for the independence of two random variables and for principal-component analysis in the presence of arbitrary censoring. The required numerical computations can be carried out straightforwardly and rapidly.

Schmitt, J. H. M. M.↗