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NASA NTRS2015

Predicting the Redshift 2 H-Alpha Luminosity Function Using [OIII] Emission Line Galaxies

Upcoming space-based surveys such as Euclid and WFIRST-AFTA plan to measure Baryonic Acoustic Oscillations (BAOs) in order to study dark energy. These surveys will use IR slitless grism spectroscopy to measure redshifts of a large number of galaxies over a significant redshift range. In this paper, we use the WFC3 Infrared Spectroscopic Parallel Survey (WISP) to estimate the expected number of H-alpha emitters observable by these future surveys. WISP is an ongoing Hubble Space Telescope slitless spectroscopic survey, covering the 0.8 - 1.65 micrometers wavelength range and allowing the detection of H-alpha emitters up to z approximately equal to 1.5 and [OIII] emitters to z approximately equal to 2.3. We derive the H-alpha-[OIII] bivariate line luminosity function for WISP galaxies at z approximately equal to 1 using a maximum likelihood estimator that properly accounts for uncertainties in line luminosity measurement, and demonstrate how it can be used to derive the H-alpha luminosity function from exclusively fitting [OIII] data. Using the z approximately equal to 2 [OIII] line luminosity function, and assuming that the relation between H-alpha and [OIII] luminosity does not change significantly over the redshift range, we predict the H-alpha number counts at z approximately equal to 2 - the upper end of the redshift range of interest for the future surveys. For the redshift range 0.7 less than z less than 2, we expect approximately 3000 galaxies per sq deg for a flux limit of 3 x 10(exp −16) ergs per sec per sq cm (the proposed depth of Euclid galaxy redshift survey) and approximately 20,000 galaxies per sq deg for a flux limit of approximately 10(exp −16) ergs per sec per sq cm (the baseline depth of WFIRST galaxy redshift survey).

Redshift↗
NASA NTRS1988

Neptune radio emission - Predictions based on planetary scaling laws

In this paper a prediction is advanced concerning Neptune's low-frequency radio emission based on the radiometric Bode's law for radio planets in combination with the magnetostrophic scaling law for magnetized planets. The total emitted radio power is predicted to be about 1.6 x 10 to the 7th W, very nearly the same as that predicted and observed for Uranus. Possible emission spectral shapes, based on Saturn and earth-like models, are shown. Using these models, the radio emission frequency range is predicted to extend from approximately 100 to just over 1000 kHz, with a spectral peak between 350 and 500 kHz. If radiation is beamed approximately in the sunward direction, Neptune should be detectable by the planetary radio astronomy experiment onboard the Voyager spacecraft sometime between 45 and 90 days before closest approach. This detection is likely to represent the first direct evidence of a Neptune magnetic field. Possible implications for Neptune's magnetosphere with regard to the time of first detection are discussed.

Desch, Michael D.↗
NASA NTRS2010

Hybrid Decompositional Verification for Discovering Failures in Adaptive Flight Control Systems

Adaptive flight control systems hold tremendous promise for maintaining the safety of a damaged aircraft and its passengers. However, most currently proposed adaptive control methodologies rely on online learning neural networks (OLNNs), which necessarily have the property that the controller is changing during the flight. These changes tend to be highly nonlinear, and difficult or impossible to analyze using standard techniques. In this paper, we approach the problem with a variant of compositional verification. The overall system is broken into components. Undesirable behavior is fed backwards through the system. Components which can be solved using formal methods techniques explicitly for the ranges of safe and unsafe input bounds are treated as white box components. The remaining black box components are analyzed with heuristic techniques that try to predict a range of component inputs that may lead to unsafe behavior. The composition of these component inputs throughout the system leads to overall system test vectors that may elucidate the undesirable behavior

Thompson, Sarah↗
NASA NTRS2000

45 Km Horizontal Path Optical Link Experiment

Mountain-top to mountain-top optical link experiments have been initiated at JPL, in order to perform a systems level evaluation of optical communications. Progress made so far is reported. ne NASA, JPL developed optical communications demonstrator (OCD) is used to transmit a laser signal from Strawberry Peak (SP), located in the San Bernadino mountains of California. This laser beam is received by a 0.6 m aperture telescope at JPL's Table Mountain Facility (TMF), located in Wrightwood, California. The optical link is bi-directional with the TMF telescope transmitting a continuous 4-wave (cw) 780 run beacon and the OCD sending back a 840 nm, 100 - 500 Mbps pseudo noise (PN) modulated, laser beam. The optical link path is at an average altitude of 2 km above sea level, covers a range of 46.8 km and provides an atmospheric channel equivalent to approx. 4 air masses. Average received power measured at either end fall well within the uncertainties predicted by link analysis. The reduction in normalized intensity variance (sigma(sup 2, sub I)) for the 4-beam beacon, compared to each individual beam, at SP, was from approx. 0.68 to 0.22. With some allowance for intra-beam mis-alignment, this is consistent with incoherent averaging. The sigma(sup2, sub I) measured at TMF approx. 0.43 +/- 0.22 exceeded the expected aperture averaged value of less than 0.1, probably because of beam wander. The focused spot sizes of approx. 162 +/- 6 microns at the TMF Coude and approx. 64 +/- 3 microns on the OCD compare to the predicted size range of 52 - 172 microns and 57 - 93 microns, respectively. This is consistent with 4 - 5 arcsec of atmospheric "seeing". The preliminary evaluation of OCD's fine tracking indicates that the uncompensated tracking error is approx. 3.3 micro rad compared to approx. 1.7 micro rad observed in the laboratory. Fine tracking performance was intermittent, primarily due to beacon fades on the OCD tracking sensor. The best bit error rates observed while tracking worked were 1E-5 to 1E-6.

Biswas, A.↗
NASA NTRS1998

Predicting lettuce canopy photosynthesis with statistical and neural network models

An artificial neural network (NN) and a statistical regression model were developed to predict canopy photosynthetic rates (Pn) for 'Waldman's Green' leaf lettuce (Latuca sativa L.). All data used to develop and test the models were collected for crop stands grown hydroponically and under controlled-environment conditions. In the NN and regression models, canopy Pn was predicted as a function of three independent variables: shootzone CO2 concentration (600 to 1500 micromoles mol-1), photosynthetic photon flux (PPF) (600 to 1100 micromoles m-2 s-1), and canopy age (10 to 20 days after planting). The models were used to determine the combinations of CO2 and PPF setpoints required each day to maintain maximum canopy Pn. The statistical model (a third-order polynomial) predicted Pn more accurately than the simple NN (a three-layer, fully connected net). Over an 11-day validation period, average percent difference between predicted and actual Pn was 12.3% and 24.6% for the statistical and NN models, respectively. Both models lost considerable accuracy when used to determine relatively long-range Pn predictions (> or = 6 days into the future).

Non-NASA Center↗
NASA NTRS1973

Electrochemical carbon dioxide concentrator: Math model

A steady state computer simulation model of an Electrochemical Depolarized Carbon Dioxide Concentrator (EDC) has been developed. The mathematical model combines EDC heat and mass balance equations with empirical correlations derived from experimental data to describe EDC performance as a function of the operating parameters involved. The model is capable of accurately predicting performance over EDC operating ranges. Model simulation results agree with the experimental data obtained over the prediction range.

Marshall, R. D.↗
NASA NTRS1988

Planetary scaling laws and predictions for Neptune

This paper offers a prediction concerning Neptune's low-frequency radio emission based on the radiometric Bode's law in combination with a recent prediction for Neptune's global magnetic field strength. The latter is based on a dynamo scaling relation derived from the magnetospheric balance condition within planetary cores. The radio emission frequency range is predicted to extend from approximately 100 to 1000 kHz, with a spectral peak between 350 and 500 kHz. A crude estimate of the emission spectral shape, based on Saturn and earth-like models, is shown. If radiation is beamed approximately in the sunward direction, Neptune should be detectable by the Planetary Radio Astronomy experiment onboard the Voyager spacecraft sometime between 45 and 60 days before closest approach.

Desch, Michael D.↗
NASA NTRS1961

Some Recent Studies in Structural Dynamics of Rotor Aircraft

This paper presents a summary of four recent studies relating to the structural-dynamics problems of rotor-powered aircraft. The first study concerns the measurement by means of dynamic models of the forces and moments at the hubs of various rotor configurations. The results of this study show that the periodic components of the forces and moments are highly dependent on both the rotor configuration and the flight condition. The second study treats the problem of resonance amplifications of rotor-blade stress and shows that by using multiple flapping hinges or flex-joints it is possible to control the natural frequencies of the rotor blade so that conditions of resonance between the frequencies of the aerodynamic input forces and the natural frequencies of the lower blade modes are avoided for all rotor speeds. Two studies of the stability of rotor aircraft axe also discussed. One of these involves the mechanical instability or ground resonance of rotorcraft wherein the rotor support in each of two mutually perpendicular directions in the rotor plane is represented as a multiple-degree-of-freedom system in contrast to the system having a "single" degree of freedom normally used in helicopter analysis. The consideration of the rotor support system as a two-degree-of-freedom system predicts additional unstable ranges of rotor speed not predicted by former analyses. The other instability treated is propeller whirl for which the significant motions are the pitching and yawing motions of the propeller disk which are coupled together by gyroscopic forces. The effect of the significant variables on the instability is presented and shows that the speed at which the instability occurs can be increased by increasing the relative stiffness of the propeller in the pitch and yaw directions or by increasing the effective structural damping of the nacelle.

George W Brooks↗
NASA NTRS1971

Propellant thermal stratification

The term thermal stratification is used to express nonuniform heat distribution within the bulk propellant. The nonuniform distribution of heat results in significant temperature variations in booster propulsion propellants and causes an undesirable increase in the self-pressurization rate of cryogen storage systems. A semiempirical prediction method has been developed for high gravity environments and is adequate for design purposes; model accuracy is somewhat limited to similarity in tank geometries, and additional work is needed to extend the correlation range. Several low gravity environment models that cover a broad range of predicted results have been developed. There are no applicable data by which any of these models may be selected in preference over the others.

Winstead, T. W.↗
NASA NTRS2015

Temperature Sensitivity of an Atomic Vapor Cell-Based Dispersion-Enhanced Optical Cavity

Enhancement of the response of an optical cavity to a change in optical path length, through the use of an intracavity fast-light medium, has previously been demonstrated experimentally and described theoretically for an atomic vapor cell as the intracavity resonant absorber. This phenomenon may be used to enhance both the scale factor and sensitivity of an optical cavity mode to the change in path length, e.g. in gyroscopic applications. We study the temperature sensitivity of the on-resonant scale factor enhancement, S(sub o), due to the thermal sensitivity of the lower-level atom density in an atomic vapor cell, specifically for the case of the Rb-87 D(sub 2) transition. A semi-empirical model of the temperature-dependence of the absorption profile, characterized by two parameters, a(sub o)(T) and gamma(sub a)(T) allows the temperature-dependence of the cavity response, S(sub o)(T) and dS(sub o)/dT to be predicted over a range of temperature. We compare the predictions to experiment. Our model will be useful in determining the useful range for S(sub o), given the practical constraints on temperature stability for an atomic vapor cell.

Myneni, K.↗
NASA NTRS1984

Measuring EUV Line Emission from the Hot Interstellar Medium

In the local interstellar medium, the presence of hot gas was inferred from measurements of oxygen VI absorption in the ultraviolet, and from diffuse emission in the extreme ultraviolet (EUV) and soft X-ray regions. A spectrometer that is very sensitive to gas in this temperature range is described. The spectrometer uses an array of plane ruled gratings at grazing incidence in the extreme off plane mount. A set of Kirkpatrick-Baez mirrors focuses the conically diffracted light on to one of two microchannel plate detectors. The field of view of the instrument is 0.2 deg by 12 deg. The predicted sensitivity ranges from 50 to 200 ph/(sq cm sec str) with a resolving power of 15 to 50 over the 50 to 700 angstrom wavelength band.

Labov, S.↗
NASA NTRS1995

Ultraviolet radiation from evolved stellar populations. 2: The ultraviolet upturn phenomenon in elliptical galaxies

We discuss the far-ultraviolet upturn phenomenon (UVX) observed in elliptical galaxies and spiral galaxy bulges. Our premise is the UV radiation from these systems emanates primarily from extreme horizontal branch (EHB) stars and their progeny. We derive the broad-band UV colors 1500-V and 2500-V for globular clusters and elliptical galaxies from the available satellite data and investigate color-color and color-line strength correlation. Clusters can be bluer than any galaxy in 15-V and 25-V, implying larger hot star populations, but galaxies are significantly bluer than clusters in 15-25 at a given 15-V. We attribute this primarily to the effect of metal abundance on the mid-UV (2500 A) light. These redder colors of the galaxies also imply that the UVX in galaxies is not produced by metal-poor subpopulations similar to the clusters. We devlop a simple spectral synthesis formulation for all phases of single star evolution from the zero-age main sequence (ZAMS) to the white dwarf cooling track that requires only one or two parameters for each choice of age and abundance. We provide the ingredients necessary for constructing models with arbitrary horizontal branch (HB) morphologies in the age range 2 less than t less than 20 Gyr and for six metallicities in the range -2.26 less than (Fe/H) less than 0.58; we also consider the efect of enhanced Y in metal-rich models. The maximum lifetime UV output is produced by EHB stars with (M(sub env))(sup 0) approximately 0.02 solar mass and can be up to 30 times higher than for post-asymptotic giant branch (P-AGB) stars. The ultraviolet output of old populations is governed primarily by the distribution of (M(sub env))(sup 0)P(M(sub env))(sup 0), on the ZAHB. The UV output is not very sensitive to (Fe/H) or to Y, but it can change very rapidly with (M(sub env))(sup 0). Thus it is extremely sensitive to the precise nature of giant-branch mass loss. Our models use simple descriptions of P(M(sub env))(sup 0) to bracket the colors produced from any real distribution of stars. Our models accurately predict the range of UV colors observed for the globular clusters, given known constraints on their age, abundances, and HB morphologies. We find that models with (Fe/H) greater than or = 0 that do not contain EHB stars cannot reproduce the colors of most of the galaxies. The models also predict that the fraction of the far-UV light from P-AGB stars, which are spatially resolvable in nearby galaxies, is approximately 70% and approximately 20% for moderate UVX and strong UVX systems, respectively. We find that 25-V, but not 15-V, is sensitive to the age and abundance, though these cannot always be cleanly distinguished. The galaxy colors place limits of (Fe/H) greater than -0.5 and less than 15% on the contribution of globular cluster-type populations to the V light. Galaxy colors are consistent with solar-abundance models with ages in the range 6-14 Gyr. We discuss several implications of the observations and the models, including the question of light metal versus iron peak enhancements in galaxies, whether the UV color-Mg(sub 2) correlation is continuous or discrete, effects of helium abundnace on the UVX, and the key question of whether red giant branch mass loss can be large enough to produce the necessary EHB population in the strong UVX galaxies.

Dorman, Ben↗
NASA NTRS1999

MOLA-derived Roughness Data Used to Predict Surface Scattering for Mars Subsurface Radar Sounding

The Mars Express orbiter, to be launched by the European Space Agency in 2003, will carry a low-frequency radar sounding instrument, MARSIS (Mars Advanced Radar for Subsurface and Ionospheric Sounding). The primary goal of MARSIS is to map the distribution of water, both solid and (if present) liquid, in the upper several km of the martian crust. Detecting discontinuities in the crust, such as an ice-water transition, presents many challenges for a Mars orbital radar sounder. One challenge that must be overcome is the presence of radar scattering (echoes) from the surface of Mars, expected to be detected by the sounder antennas at the same time as any echoes aris-ing from subsurface interfaces. As the transmitted spherical wavefront spreads within the crust of Mars,. it also interacts with surface topography at off-nadir positions, creating a "clutter" signal that can mask the subsurface echoes. The MARSIS instrument will utilize Doppler filtering to limit the off-nadir clutter in the along-track direction, and a nadir-null secondary antenna to identify strong off-nadir clutter from the cross-track direction. To evaluate the effects of off-nadir surface clutter and the capability of these schemes to reduce the clutter, it is necessary to predict the range of scattering behavior that may be expected from martian surface topography. In this paper, we utilize Mars Orbital Laser Altimeter (MOLA) data from the current Mars Global Surveyor mission to characterize the topographic roughness of a variety of martian terrain types, at scales relevant to the MARSIS clutter problem. Segments of MOLA altimetry profiles are reduced to the topographic parameters rms slope and fractal dimension, which then are used as inputs to a near-nadir radar scattering model to predict the strength of the clutter signal. Additional information is contained in the original extended abstract.

Plaut, J. J.↗
NASA NTRS1996

Turbulence Scales, Rise Times, Caustics, and the Simulation of Sonic Boom Propagation

The general topic of atmospheric turbulence effects on sonic boom propagation is addressed with especial emphasis on taking proper and efficient account of the contributions of the portion oi the turbulence that is associated with extremely high wavenumber components. The recent work reported by Bart Lipkens in his doctoral thesis is reexamined to determine whether the good agreement between his measured rise times with the 1971 theory of the author is fortuitous. It is argued that Lipken's estimate of the distance to the first caustic was a gross overestimate because of the use of a sound speed correlation function shaped like a gaussian curve. In particular, it is argued that the expected distance to the first caustic varies with the kinematic viscosity nu and the energy epsilon dissipated per unit mass per unit time, and the sound speed c as : d(sub first caustic) = nu(exp 7/12) c(exp 2/3)/ epsilon(exp 5/12)(nu x epsilon/c(exp 4))(exp a), where the exponent a is greater than -7/12 and can be argued to be either O or 1/24. In any event, the surprising aspect of the relationship is that it actually goes to zero as the viscosity goes to zero with s held constant. It is argued that the apparent overabundance of caustics can be grossly reduced by a general computational and analytical perspective that partitions the turbulence into two parts, divided by a wavenumber k(sub c). Wavenumbers higher than kc correspond to small-scale turbulence, and the associated turbulence can be taken into account by a renormalization of the ambient sound speed so that the result has a small frequency dependence that results from a spatial averaging over of the smaller-scale turbulent fluctuations. Selection of k(sub c). can be made so large that only a very small number of caustics are encountered if one adopts the premise that the frequency dispersion of pulses is caused by that part of the turbulence spectrum which lies in the inertial range originally predicted by Kolmogoroff. The acoustic propagating wave's dispersion relation has the acoustic wavenumber being of the form k = (omega/c) + F(omega), where c is a spatially averaged sound speed and where, for mechanical turbulence, the extra term F(omega) must depend on only the angular frequency omega, the sound speed c, and the turbulent energy dissipation epsilon per unit fluid mass and per unit time. If the turbulence is weak, then the quantity F(omega) has to be of second order in the portions of the turbulent fluid velocity in the inertial range, so, following Kolmogoroff's reasoning, it must vary with epsilon as epsilon(exp 2/3). Simple dimensional analysis then reveals that F(omega) is K epsilon(exp 2/3) c(exp -7/3) omega(exp l/3), K being a universal dimensionless complex constant.

Pierce, Allan D.↗
NASA NTRS1980

The reverse laser drilling of transparent materials

Within a limited range of incident laser-beam intensities, laser drilling of a sapphire wafer initiates on the surface of the wafer where the laser beam exits and proceeds upstream in the laser beam to the surface where the laser beam enters the wafer. This reverse laser drilling is the result of the constructive interference between the laser beam and its reflected component on the exit face of the wafer. Constructive interference occurs only at the exit face of the sapphire wafer because the internally reflected laser beam suffers no phase change there. A model describing reverse laser drilling predicts the ranges of incident laser-beam intensity where no drilling, reverse laser drilling, and forward laser drilling can be expected in various materials. The application of reverse laser drilling in fabricating feed-through conductors in silicon-on-sapphire wafers for a massively parallel processer is described.

Anthony, T. R.↗
NASA NTRS2000

Estimates of Ground Temperature and Atmospheric Moisture from CERES Observations

A method is developed to retrieve surface ground temperature (Tg) and atmospheric moisture using clear sky fluxes (CSF) from CERES-TRMM observations. In general, the clear sky outgoing long-wave radiation (CLR) is sensitive to upper level moisture (q(sub h)) over wet regions and Tg over dry regions The clear sky window flux from 800 to 1200 /cm (RadWn) is sensitive to low level moisture (q(sub j)) and Tg. Combining these two measurements (CLR and RadWn), Tg and q(sub h) can be estimated over land, while q(sub h) and q(sub t) can be estimated over the oceans. The approach capitalizes on the availability of satellite estimates of CLR and RadWn and other auxiliary satellite data. The basic methodology employs off-line forward radiative transfer calculations to generate synthetic CSF data from two different global 4-dimensional data assimilation products. Simple linear regression is used to relate discrepancies in CSF to discrepancies in Tg, q(sub h) and q(sub t). The slopes of the regression lines define sensitivity parameters that can be exploited to help interpret mismatches between satellite observations and model-based estimates of CSF. For illustration, we analyze the discrepancies in the CSF between an early implementation of the Goddard Earth Observing System Data Assimilation System (GEOS-DAS) and a recent operational version of the European Center for Medium-Range Weather Prediction data assimilation system. In particular, our analysis of synthetic total and window region SCF differences (computed from two different assimilated data sets) shows that simple linear regression employing (Delta)Tg and broad layer (Delta)q(sub l) from 500 hPa to surface and (Delta)q(sub h) from 200 to 500 hPa provides a good approximation to the full radiative transfer calculations, typically explaining more than 90% of the 6-hourly variance in the flux differences. These simple regression relations can be inverted to "retrieve" the errors in the geophysical parameters. Uncertainties (normalized by standard deviation) in the monthly mean retrieved parameters range from 7% for (Delta)T to about 20% for (Delta)q(sub t). Our initial application of the methodology employed an early CERES-TRMM data set (CLR and Radwn) to assess the quality of the GEOS2 data. The results showed that over the tropical and subtropical oceans GEOS2 is, in general, too wet in the upper troposphere (mean bias of 0.99 mm) and too dry in the lower troposphere (mean bias of -4.7 mm). We note that these errors, as well as a cold bias in the Tg, have largely been corrected in the current version of GEOS-2 with the introduction of a land surface model, a moist turbulence scheme and the assimilation of SSTM/I total precipitable water.

Wu, Man Li C.↗
NASA NTRS2000

Estimates of Ground Temperature and Atmospheric Moisture from CERES Observations

A method is developed to retrieve surface ground temperature (T(sub g)) and atmospheric moisture using clear sky fluxes (CSF) from CERES-TRMM observations. In general, the clear sky outgoing longwave radiation (CLR) is sensitive to upper level moisture (q(sub l)) over wet regions and (T(sub g)) over dry regions The clear sky window flux from 800 to 1200/cm (RadWn) is sensitive to low level moisture (q(sub t)) and T(sub g). Combining these two measurements (CLR and RadWn), Tg and q(sub h) can be estimated over land, while q(sub h) and q(sub l) can be estimated over the oceans. The approach capitalizes on the availability of satellite estimates of CLR and RadWn and other auxiliary satellite data. The basic methodology employs off-line forward radiative transfer calculations to generate synthetic CSF data from two different global 4-dimensional data assimilation products. Simple linear regression is used to relate discrepancies in CSF to discrepancies in T(sub g), q(sub h) and q(sub l). The slopes of the regression lines define sensitivity parameters that can be exploited to help interpret mismatches between satellite observations and model-based estimates of CSF. For illustration, we analyze the discrepancies in the CSF between an early implementation of the Goddard Earth Observing System Data Assimilation System (GEOS-DAS) and a recent operational version of the European Center for Medium-Range Weather Prediction data assimilation system. In particular, our analysis of synthetic total and window region SCF differences (computed from two different assimilated data sets) shows that simple linear regression employing Delta(T(sub g)) and broad layer Delta(q(sub l) from .500 hPa to surface and Delta(q(sub h)) from 200 to .300 hPa provides a good approximation to the full radiative transfer calculations. typically explaining more than 90% of the 6-hourly variance in the flux differences. These simple regression relations can be inverted to "retrieve" the errors in the geophysical parameters. Uncertainties (normalized by standard deviation) in the monthly mean retrieved parameters range from 7% for Delta(T(sub g)) to about 20% for Delta(q(sub l)). Our initial application of the methodology employed an early CERES-TRMM data set (CLR and Radwn) to assess the quality of the GEOS2 data. The results showed that over the tropical and subtropical oceans GEOS2 is, in general, too wet in the upper troposphere (mean bias of 0.99 mm) and too dry in the lower troposphere (mean bias of -4.7 min). We note that these errors, as well as a cold bias in the T(sub g). have largely been corrected in the current version of GEOS-2 with the introduction of a land surface model, a moist turbulence scheme and the assimilation of SSM/I total precipitable water.

Wu, Man Li C.↗
NASA NTRS2012

Uncertainty Quantification for Polynomial Systems via Bernstein Expansions

This paper presents a unifying framework to uncertainty quantification for systems having polynomial response metrics that depend on both aleatory and epistemic uncertainties. The approach proposed, which is based on the Bernstein expansions of polynomials, enables bounding the range of moments and failure probabilities of response metrics as well as finding supersets of the extreme epistemic realizations where the limits of such ranges occur. These bounds and supersets, whose analytical structure renders them free of approximation error, can be made arbitrarily tight with additional computational effort. Furthermore, this framework enables determining the importance of particular uncertain parameters according to the extent to which they affect the first two moments of response metrics and failure probabilities. This analysis enables determining the parameters that should be considered uncertain as well as those that can be assumed to be constants without incurring significant error. The analytical nature of the approach eliminates the numerical error that characterizes the sampling-based techniques commonly used to propagate aleatory uncertainties as well as the possibility of under predicting the range of the statistic of interest that may result from searching for the best- and worstcase epistemic values via nonlinear optimization or sampling.

Crespo, Luis G.↗