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NASA NTRS1996

Variational Methods in Sensitivity Analysis and Optimization for Aerodynamic Applications

Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Ibrahim, A. H.↗

NASA NTRS1993

An adjoint sensitivity study of blocking in a two-layer isentropic model

This paper presents a new methodology for adjoint sensitivity analysis, previously developed in general terms by Cacuci, into a form directly applicable 10 meteorological problems. This technique is illustrated by examining the sensitivity of a blocking index in a two-layer isentropic model. The index represents a response function for the sensitivity analysis that unlike previous meteorological applications, is an operator and not a functional, and thus extends the scope of adjoint sensitivity to general operator-type responses depending on time and/or space. The sensitivity of the blocking index to perturbations introduced into the model atmosphere, as well as to model parameters, is discussed. The methodology of generalized adjoint sensitivity analysis described in this paper constitutes a prototype for further applications in the atmospheric and/or oceanic sciences.

Zou, X.↗

NASA NTRS1974

On the passage of radiation through inhomogeneous, moving media. XI - Nonlinear effects on ray paths in the geometrical optics approximation

Study illustrating how the presence of a high-intensity pulse of radiation can distort its own passage through a plane differentially shearing medium. It is demonstrated that the distortion is a sensitive function of the precise, and detailed, variation of the medium's refractive index by considering a couple of simple examples which are worked out numerically. In view of the high-intensity pulses observed from pulsars (approximately 10 to the 30th ergs per pulse), it is believed that the present calculations are of more than academic interest in helping unravel the fundamental properties of pulse production in, and propagating through, differentially sheared media - such as pulsars' magnetospheres within the so-called speed-of-light circle.

Lee, M. A.↗

NASA NTRS2016

Mid and Thermal Infrared Remote Sensing at the Jet Propulsion Laboratory

The mid and thermal infrared (MTIR) for the Earth surface is defined between 3 and 14µm. In the outer solar system, objects are colder and their Planck response shifts towards longer wavelengths. Hence for these objects (e.g. icy moons, polar caps, comets, Europa), the thermal IR definition usually stretches out to 50µm and beyond. Spectroscopy has been a key part of this scientific exploration because of its ability to remotely determine elemental and mineralogical composition. Many key gas species such as methane, ammonia, sulfur, etc. also have vibrational bands which show up in the thermal infrared spectrum above the background response. Over the past few decades, the Jet Propulsion Laboratory has been building up a portfolio of technology to capture the MTIR for various scientific applications. Three recent sensors are briefly reviewed: The airborne Hyperspectral thermal emission spectrometer (HyTES), the ECOsystem Spaceborne Thermal Radiometer Experiment on Space Station (ECOSTRESS) and Mars Climate Sounder (MCS)/DIVINER. Each of these sensors utilize a different technology to provide a remote sensing product based on MTIR science. For example, HyTES is a push-brooming hyperspectral imager which utilizes a large format quantum well infrared photodetector (QWIP). The goal is to transition this to a new complementary barrier infrared photodetector (CBIRD) with a similar long wave cut-off and increased sensitivity. ECOSTRESS is a push-whisk Mercury Cadmium Telluride (MCT) based high speed, multi-band, imager which will eventually observe and characterize plant/vegetation functionality and stress index from the International Space Station (ISS) across the contiguous United States (CONUS). MCS/DIVINER utilizes thermopile technology to capture the thermal emission from the polar caps and shadow regions of the moon. Each sensor utilizes specific JPL technology to capture unique science. similar long wave cut-off and increased sensitivity. ECOSTRESS is a push-whisk Mercury Cadmium Telluride (MCT) based high speed, multi-band, imager which will eventually observe and characterize plant/vegetation functionality and stress index from the International Space Station (ISS) across the contiguous United States (CONUS). MCS/DIVINER utilizes thermopile technology to capture the thermal emission from the polar caps and shadow regions of the moon. Each sensor utilizes specific JPL technology to capture unique science.

Johnson, William R.↗

NASA NTRS1991

Calculated sensitivities of several optical radiometric indices for vegetation canopies

The present study employs a radiative transfer model for a vegetation canopy to compute several quantities used in remote sensing applications and to determine the sensitivity of these radiometric quantities to several of the important problem parameters. Attention is given to the ratio of near IR to visible reflected intensities in the nadir direction, the ratio of the fraction of incident energy reflected in the near IR to that in the visible, the normalized difference between the near IR and visible nadir-reflected intensities, and the visible intensity transmitted in a given downward direction. A realistic radiative transfer model is proposed for calculating these radiometric quantities. With these models, the sensitivity of the reflected and transmitted quantities to various canopy and illumination conditions are then determined. The sensitivity of the calculated quantities are presented as a function of the leaf area index of the canopy, and, for the reflected quantities, also as a function of the fraction of visible light absorbed in the canopy.

Shultis, J. K.↗

NASA NTRS1980

Polar nephelometer for atmospheric particulate studies

A unique polar nephelometer was designed and constructed for the measurement of atmospheric particulate characteristics. The nephelometer produces visible light from a self-contained laser to irradiate an air sample drawn into the instrument. The light scattered from the particulates and molecules in the sample is detected as a function of scattering angle for each of four different incident light polarizations. These measurements are used to determine the particulate scattering matrix which is a function of the size, shape, and index of refraction of the particles. The region of sensitivity for the measurements corresponds to the size range of particles that strongly affects visible radiative transfer in the atmosphere, which is the primary application for the derived information.

Hansen, M. Z.↗

NASA NTRS2000

Effect of head-down-tilt bed rest and hypovolemia on dynamic regulation of heart rate and blood pressure

Adaptation to head-down-tilt bed rest leads to an apparent abnormality of baroreflex regulation of cardiac period. We hypothesized that this "deconditioning response" could primarily be a result of hypovolemia, rather than a unique adaptation of the autonomic nervous system to bed rest. To test this hypothesis, nine healthy subjects underwent 2 wk of -6 degrees head-down bed rest. One year later, five of these same subjects underwent acute hypovolemia with furosemide to produce the same reductions in plasma volume observed after bed rest. We took advantage of power spectral and transfer function analysis to examine the dynamic relationship between blood pressure (BP) and R-R interval. We found that 1) there were no significant differences between these two interventions with respect to changes in numerous cardiovascular indices, including cardiac filling pressures, arterial pressure, cardiac output, or stroke volume; 2) normalized high-frequency (0.15-0.25 Hz) power of R-R interval variability decreased significantly after both conditions, consistent with similar degrees of vagal withdrawal; 3) transfer function gain (BP to R-R interval), used as an index of arterial-cardiac baroreflex sensitivity, decreased significantly to a similar extent after both conditions in the high-frequency range; the gain also decreased similarly when expressed as BP to heart rate x stroke volume, which provides an index of the ability of the baroreflex to alter BP by modifying systemic flow; and 4) however, the low-frequency (0.05-0.15 Hz) power of systolic BP variability decreased after bed rest (-22%) compared with an increase (+155%) after acute hypovolemia, suggesting a differential response for the regulation of vascular resistance (interaction, P < 0.05). The similarity of changes in the reflex control of the circulation under both conditions is consistent with the hypothesis that reductions in plasma volume may be largely responsible for the observed changes in cardiac baroreflex control after bed rest. However, changes in vasomotor function associated with these two conditions may be different and may suggest a cardiovascular remodeling after bed rest.

Non-NASA Center↗

NASA NTRS2011

Defining the Relationship Between Biomarkers of Oxidative and Inflammatory Stress and the Risk for Atherosclerosis in Astronauts During and After Long-Duration Spaceflight

Future human space travel will primarily consist of long-duration missions aboard the International Space Station (ISS) or exploration class missions to Mars, its moons, or nearby asteroids. These missions will expose astronauts to increased risk of oxidative and inflammatory damage primarily from radiation, but also from psychological stress, reduced physical activity, diminished nutritional status, and, in the case of extravehicular activity, hyperoxic exposure. There is evidence that increased oxidative damage and inflammation can accelerate the development of atherosclerosis. PURPOSE The purpose of this proposal is to identify biomarkers of oxidative and inflammatory stress and to correlate them to indices of atherosclerosis risk before, during, and after long-duration spaceflight. METHODS To meet the objectives of the study, we will study astronauts before, during, and up to 5 years after long-duration missions aboard ISS. Biomarkers of oxidative and inflammatory stress, some of which we have previously shown to be elevated with spaceflight, will be measured before, during, and after spaceflight. Arterial structure will be monitored using ultrasound to measure carotid intima-medial thickness before, during, and after weightlessness. Carotid intima-medial thickness has been shown to be a better indicator than Framingham Risk scores for prediction of atherosclerosis. Arterial function will be monitored using brachial flow-mediated dilation before flight and after landing. Brachial flow-mediated dilation is a good index of endothelium-dependent vasodilation, which is a sensitive predictor of atherosclerotic risk. This is the first study to propose assessing atherosclerotic risk using biochemical, structural, and functional measures before, during, and immediately after spaceflight and structural functional measures for up to 5 years after landing. EXPECTED RESULTS We hypothesize that these biomarkers of oxidative and inflammatory stress will be increased with spaceflight and will correlate with increased carotid intima-medial thickness in- and postflight and with decreased flow-mediated dilation after the mission. Furthermore, we hypothesize that measures of oxidative stress will return to baseline after flight, but that biomarkers of inflammatory stress and vascular indices of atherosclerosis risk will remain elevated.

Lee, Stuart M. C.↗

NASA NTRS1979

Accuracy of RGD approximation for computing light scattering properties of diffusing and motile bacteria

The study tests the accuracy of the Rayleigh-Gans-Debye (RGD) approximation against a rigorous scattering theory calculation for a simplified model of E. coli (about 1 micron in size) - a solid spheroid. A general procedure is formulated whereby the scattered field amplitude correlation function, for both polarized and depolarized contributions, can be computed for a collection of particles. An explicit formula is presented for the scattered intensity, both polarized and depolarized, for a collection of randomly diffusing or moving particles. Two specific cases for the intermediate scattering functions are considered: diffusing particles and freely moving particles with a Maxwellian speed distribution. The formalism is applied to microorganisms suspended in a liquid medium. Sensitivity studies revealed that for values of the relative index of refraction greater than 1.03, RGD could be in serious error in computing the intensity as well as correlation functions.

Kottarchyk, M.↗

NASA NTRS1981

A sensitivity model for energy consumption in buildings. Part 1: Effect of exterior environment

A simple analytical model is developed for the simulation of seasonal heating and cooling loads of any class of buildings to complement available computerized techniques which make hourly, daily, and monthly calculations. An expression for the annual energy utilization index, which is a common measure of rating buildings having the same functional utilization, is derived to include about 30 parameters for both building interior and exterior environments. The sensitivity of a general class building to either controlled or uncontrolled weather parameters is examined. A hypothetical office type building, located at the Goldstone Space Communication Complex, Goldstone, California, is selected as an example for the numerical sensitivity evaluations. Several expressions of variations in local outside air temperature, pressure, solar radiation, and wind velocity are presented.

Lansing, F. L.↗

NASA NTRS1982

A climate index derived from satellite measured spectral infrared radiation

The vertical infrared radiative emitting structure (VIRES) climate index, based on radiative transfer theory and derived from the spectral radiances typically used to retrieve temperature profiles, is introduced. It is assumed that clouds and climate are closely related and a change in one will result in a change in the other. The index is a function of the cloud, temperature, and moisture distributions. It is more accurately retrieved from satellite data than is cloudiness per se. The VIRES index is based upon the shape and relative magnitude of the broadband weighting function of the infrared radiative transfer equation. The broadband weighting curves are retrieved from simulated satellite infrared sounder data (spectral radiances). The retrieval procedure is described and the error error sensitivities of the method investigated. Index measuring options and possible applications of the VIRES index are proposed.

Abel, M. D.↗

NASA NTRS1992

Prediction and measurement of soil bidirectional reflectance

The present model for soil bidirectional reflectance distribution functions in the visible and reflective IR ranges is based on a representation of soil surfaces by a collection of opaque spheres atop a Lambertian horizontal surface. The model is not sensitive to increases in the sphere area index beyond a value of 0.4. Observed soil reflectance factor data for a tilled field are noted to be consistent with those predicted by the model's expression of soil reflectance as a function of the horizontal area obscured by a sphere, the amount of surface in shadow, and relative brightness of a sphere, and the fraction of diffuse illumination.

Irons, James R.↗

NASA NTRS2015

Empirical Relationships Between Optical Properties and Equivalent Diameters of Fractal Soot Aggregates at 550 Nm Wavelength.

Soot aggregates (SAs)-fractal clusters of small, spherical carbonaceous monomers-modulate the incoming visible solar radiation and contribute significantly to climate forcing. Experimentalists and climate modelers typically assume a spherical morphology for SAs when computing their optical properties, causing significant errors. Here, we calculate the optical properties of freshly-generated (fractal dimension Df = 1.8) and aged (Df = 2.6) SAs at 550 nm wavelength using the numericallyexact superposition T-Matrix method. These properties were expressed as functions of equivalent aerosol diameters as measured by contemporary aerosol instruments. This work improves upon previous efforts wherein SA optical properties were computed as a function of monomer number, rendering them unusable in practical applications. Future research will address the sensitivity of variation in refractive index, fractal prefactor, and monomer overlap of SAs on the reported empirical relationships.

deuterium fluorides↗

NASA NTRS2002

Pulmonary venous flow determinants of left atrial pressure under different loading conditions in a chronic animal model with mitral regurgitation

BACKGROUND: The aim of our study was to quantitatively compare the changes and correlations between pulmonary venous flow variables and mean left atrial pressure (mLAP) under different loading conditions in animals with chronic mitral regurgitation (MR) and without MR. METHODS: A total of 85 hemodynamic conditions were studied in 22 sheep, 12 without MR as control (NO-MR group) and 10 with MR (MR group). We obtained pulmonary venous flow systolic velocity (Sv) and diastolic velocity (Dv), Sv and Dv time integrals, their ratios (Sv/Dv and Sv/Dv time integral), mLAP, left ventricular end-diastolic pressure, and MR stroke volume. We also measured left atrial a, x, v, and y pressures and calculated the difference between v and y pressures. RESULTS: Average MR stroke volume was 10.6 +/- 4.3 mL/beat. There were good correlations between Sv (r = -0.64 and r = -0.59, P <.01), Sv/Dv (r = -0.62 and r = -0.74, P <.01), and mLAP in the MR and NO-MR groups, respectively. Correlations were also observed between Dv time integral (r = 0.61 and r = 0.57, P <.01) and left ventricular end-diastolic pressure in the MR and NO-MR groups. In velocity variables, Sv (r = -0.79, P <.001) was the best predictor of mLAP in both groups. The sensitivity and specificity of Sv = 0 in predicting mLAP 15 mm Hg or greater were 86% and 85%, respectively. CONCLUSION: Pulmonary venous flow variables correlated well with mLAP under altered loading conditions in the MR and NO-MR groups. They may be applied clinically as substitutes for invasively acquired indexes of mLAP to assess left atrial and left ventricular functional status.

Pulmonary Veins/physiopathology↗

NASA NTRS1980

Sensitivity of the optimal preliminary design of a transport to operational constraints and performance index

Constrained parameter optimization was used to perform the optimal preliminary design of a medium range transport configuration. The impact of choosing a performance index was studied and the required fare for a 15 percent return-on-investment was proposed as a figure-of-merit. A number of design constants and constraint functions were systematically varied to document the sensitivities of the optimal design to a variety of economic and technological assumptions. Additionally, a comparison is made for each of the parameter variations between the baseline configuration and the optimally redesigned configuration.

Sliwa, S. M.↗

NASA NTRS2010

Utilizing In Situ Directional Hyperspectral Measurements to Validate Bio-Indicator Simulations for a Corn Crop Canopy

Two radiative transfer canopy models, SAIL and the two-layer Markov-Chain Canopy Reflectance Model (MCRM), were coupled with in situ leaf optical properties to simulate canopy-level spectral band ratio vegetation indices with the focus on the photochemical reflectance index in a cornfield. In situ hyperspectral measurements were made at both leaf and canopy levels. Leaf optical properties were obtained from both sunlit and shaded leaves. Canopy reflectance was acquired for eight different relative azimuth angles (psi) at three different view zenith angles (Theta (sub v)), and later used to validate model outputs. Field observations of photochemical reflectance index (PRI) for sunlit leaves exhibited lower values than shaded leaves, indicating higher light stress. Canopy PRI expressed obvious sensitivity to viewing geometry, as a function of both Theta (sub v) and psi . Overall, simulations from MCRM exhibited better agreements with in situ values than SAIL. When using only sunlit leaves as input, the MCRM-simulated PRI values showed satisfactory correlation and RMSE, as compared to in situ values. However, the performance of the MCRM model was significantly improved after defining a lower canopy layer comprised of shaded leaves beneath the upper sunlit leaf layer. Four other widely used band ratio vegetation indices were also studied and compared with the PRI results. MCRM simulations were able to generate satisfactory simulations for these other four indices when using only sunlit leaves as input; but unlike PRI, adding shaded leaves did not improve the performance of MCRM. These results support the hypothesis that the PRI is sensitive to physiological dynamics while the others detect static factors related to canopy structure. Sensitivity analysis was performed on MCRM in order to better understand the effects of structure related parameters on the PRI simulations. Leaf area index (LAI) showed the most significant impact on MCRM-simulated PRI among the parameters studied. This research shows the importance of hyperspectral and narrow band sensor studies, and especially the necessity of including the green wavelengths (e.g., 531 nm) on satellites proposing to monitor carbon dynamics of terrestrial ecosystems.

Cheng, Yen-Ben↗

NASA NTRS1972

Procedure for estimating stability and control parameters from flight test data by using maximum likelihood methods employing a real-time digital system

A maximum likelihood parameter estimation procedure and program were developed for the extraction of the stability and control derivatives of aircraft from flight test data. Nonlinear six-degree-of-freedom equations describing aircraft dynamics were used to derive sensitivity equations for quasilinearization. The maximum likelihood function with quasilinearization was used to derive the parameter change equations, the covariance matrices for the parameters and measurement noise, and the performance index function. The maximum likelihood estimator was mechanized into an iterative estimation procedure utilizing a real time digital computer and graphic display system. This program was developed for 8 measured state variables and 40 parameters. Test cases were conducted with simulated data for validation of the estimation procedure and program. The program was applied to a V/STOL tilt wing aircraft, a military fighter airplane, and a light single engine airplane. The particular nonlinear equations of motion, derivation of the sensitivity equations, addition of accelerations into the algorithm, operational features of the real time digital system, and test cases are described.

Grove, R. D.↗

NASA NTRS2008

Validation of a Remote Sensing Based Index of Forest Disturbance Using Streamwater Nitrogen Data

Vegetation disturbances are known to alter the functioning of forested ecosystems by contributing to export ('leakage') of dissolved nitrogen (N), typically nitrate-N, from watersheds that can contribute to acidification of acid-sensitive streams, leaching of base cations, and eutrophication of downstream receiving waters. Yet, at a landscape scale, direct evaluation of how disturbance is linked to spatial variability in N leakage is complicated by the fact that disturbances operate at different spatial scales, over different timescales, and at different intensities. In this paper we explore whether data from synoptic streamwater surveys conducted in an Appalachian oak-dominated forested river basin in western MD (USA) can be used to test and validate a scalable, synthetic, and integrative forest disturbance index (FDI) derived from Landsat imagery. In particular, we found support for the hypothesis that the interannual variation in spring baseflow total dissolved nitrogen (TDN) and nitrate-N concentrations measured at 35 randomly selected stream stations varied as a linear function of the change in FDI computed for the corresponding set of subwatersheds. Our results demonstrate that the combined effects of forest disturbances can be detected using synoptic water quality data. It appears that careful timing of the synoptic baseflow sampling under comparable phenological and hydrometeorological conditions increased our ability to identify a forest disturbance signal.

Eshleman, Keith N.↗