Variable time optimal control
Computational algorithms and techniques for solving variable time optimal control problems
NUMERICAL ANALYSIS↗
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Structural Tailoring of Advanced Turboprops (STAT). Theoretical manual
This manual describes the theories in the Structural Tailoring of Advanced Turboprops (STAT) computer program, which was developed to perform numerical optimizations on highly swept propfan blades. The optimization procedure seeks to minimize an objective function, defined as either direct operating cost or aeroelastic differences between a blade and its scaled model, by tuning internal and external geometry variables that must satisfy realistic blade design constraints. The STAT analyses include an aerodynamic efficiency evaluation, a finite element stress and vibration analysis, an acoustic analysis, a flutter analysis, and a once-per-revolution (1-p) forced response life prediction capability. The STAT constraints include blade stresses, blade resonances, flutter, tip displacements, and a 1-P forced response life fraction. The STAT variables include all blade internal and external geometry parameters needed to define a composite material blade. The STAT objective function is dependent upon a blade baseline definition which the user supplies to describe a current blade design for cost optimization or for the tailoring of an aeroelastic scale model.
Brown, K. W.↗
The ground truth analysis of rain gauge data for the TRMM project
As a part of the Tropical Rainfall Measuring Missioin (TRMM) ground truth program to determine the diurnal variability of the area wide rain rates, the rain rate PDFs, and their effect on the area integral algorithm, rain rate data have been collected from a network of gages located in the area near the Cape Canaveral and Kennedy Space Center, in the period beginning in September 1987. In the preliminary statistical analysis, based on the rain rates derived from the eleven gages, the seasonal diurnal rainfall and network averaged rain rates are determined. The analysis was performed in two steps: determination of the hourly and daily rain accumulations and rain rates; and computation of the fraction of hourly and daily rain rates that exceed a particular threshold, and analysis of the hourly and daily rain rate PDFs for the network. The results indicate that there are diurnal and seasonal variations in the components which determine the network rain rate PDFs.
Kowalewsky, Karen J.↗
Long-Term, Non-Anthropogenic Groundwater Storage Changes Simulated by Three Global-Scale Hydrological Models
This study examined long-term, natural (i.e., excluding anthropogenic impacts) variability of groundwater storage worldwide. Groundwater storage changes were estimated by forcing three global-scale hydrological models with three 50+ year meteorological datasets. Evaluation using in situ groundwater observations from the U.S. and terrestrial water storage derived from the Gravity Recovery and Climate Experiment (GRACE) satellites showed that these models reasonably represented inter-annual variability of water storage, as indicated by correlations greater than 0.5 in most regions. Empirical orthogonal function analysis revealed influences of the El Niño Southern Oscillation (ENSO) on global groundwater storage. Simulated groundwater storage, including its global average, exhibited trends generally consistent with that of precipitation. Global total (natural) groundwater storage decreased over the past 5-7 decades with modeled rates ranging from 0.01 to 2.18 mm year-1. This large range can be attributed in part to groundwater’s low frequency (inter-decadal) variability, which complicates identification of real long-term trends even within a 50+ year time series. Results indicate that non-anthropogenic variability in groundwater storage is substantial, making knowledge of it fundamental to quantifying direct human impacts on groundwater storage.
Groundwater storage↗
Long-Term, Non-Anthropogenic Groundwater Storage Changes Simulated by Three Global-Scale Hydrological Models
This study examined long-term, natural (i.e., excluding anthropogenic impacts) variability of groundwater storage worldwide. Groundwater storage changes were estimated by forcing three global-scale hydrological models with three 50+ year meteorological datasets. evaluation using in situ groundwater observations from the U.S. and terrestrial water storage derived from the Gravity Recovery and Climate experiment (GRACe) satellites showed that these models reasonably represented inter-annual variability of water storage, as indicated by correlations greater than 0.5 in most regions. Empirical orthogonal function analysis revealed influences of the El Niño Southern Oscillation (ENSO) on global groundwater storage. simulated groundwater storage, including its global average, exhibited trends generally consistent with that of precipitation. Global total (natural) groundwater storage decreased over the past 5–7 decades with modeled rates ranging from 0.01 to 2.18 mm year−1. this large range can be attributed in part to groundwater’s low frequency (inter-decadal) variability, which complicates identification of real long-term trends even within a 50+ year time series. Results indicate that non-anthropogenic variability in groundwater storage is substantial, making knowledge of it fundamental to quantifying direct human impacts on groundwater storage.
Bailing Li↗
Functional Data Analysis of Spaceflight-Induced Changes in Coordination and Phase in Head Pitch Acceleration During Treadmill Walking
Astronauts returning from spaceflight experience neurovestibular disturbances during head movements and attempt to mitigate them by limiting head motion. Analyses to date of the head movements made during walking have concentrated on amplitude and variability measures extracted from ensemble averages of individual gait cycles. Phase shifts within each gait cycle can be determined by functional data analysis through the computation of time-warping functions. Large, localized variations in the timing of peaks in head kinematics may indicate changes in coordination. The purpose of this study was to determine timing changes in head pitch acceleration of astronauts during treadmill walking before and after flight. Six astronauts (5M/1F; age = 43.5+/-6.4yr) participated in the study. Subjects walked at 1.8 m/sec (4 mph) on a motorized treadmill while reading optotypes displayed on a computer screen 4 m in front of their eyes. Three-dimensional motion of the subject s head was recorded with an Inertial Measurement Unit (IMU) device. Data were recorded twice before flight and four times after landing. The head pitch acceleration was calculated by taking the time derivative of the pitch velocity data from the IMU. Data for each session with each subject were time-normalized into gait cycles, then registered to align significant features and create a mean curve. The mean curves of each postflight session for each subject were re-registered based on their preflight mean curve to create time-warping functions. The root mean squares (RMS) of these warping functions were calculated to assess the deviation of head pitch acceleration mean curves in each postflight session from the preflight mean curve. After landing, most crewmembers exhibited localized shifts within their head pitch acceleration regimes, with the greatest deviations in RMS occurring on landing day or 1 day after landing. These results show that the alteration of head pitch coordination due to spaceflight may be assessed using an analysis of time-warping functions.
Miller, Christopher↗
A Strategic Approach to Medical Care for Exploration Missions
Exploration missions will present significant new challenges to crew health, including effects of variable gravity environments, limited communication with Earth-based personnel for diagnosis and consultation for medical events, limited resupply, and limited ability for crew return. Providing health care capabilities for exploration class missions will require system trades be performed to identify a minimum set of requirements and crosscutting capabilities, which can be used in design of exploration medical systems. Medical data, information, and knowledge collected during current space missions must be catalogued and put in formats that facilitate querying and analysis. These data are used to inform the medical research and development program through analysis of risk trade studies between medical care capabilities and system constraints such as mass, power, volume, and training. Medical capability as a quantifiable variable is proposed as a surrogate risk metric and explored for trade space analysis that can improve communication between the medical and engineering approaches to mission design. The resulting medical system design approach selected will inform NASA mission architecture, vehicle, and subsystem design for the next generation of spacecraft.
Canga, Michael A.↗
Long term monitoring of methane in the atmosphere by multiplex gas chromatography
Methane is of interest in the study of the Earth's atmosphere because of its implication in the future global warming of the surface. This warming is produced by the absorption of infrared energy by trace gases. It has been estimated that in the next 40 to 50 years, methane could contribute 20 to 25 pct. as much atmospheric warming as that expected from carbon dioxide increases. Studies to examine sources, sinks, and cycles of methane will require analytical methods capable of continuous unattended measurement with temporal resolution of an hour or less for weeks at a time. Gas chromatography (GC) is one of the most practical methods available to conduct the analysis of air, but limitations in this technique still exist which can be alleviated with multiplex GC (MGC). MGC is a technique where many samples are pseudo-randomly introduced to the chromatograph without regard to the length of time required for an analysis. The resulting data must then be reduced using computational methods such as cross correlation. In the technique reported, a tube packed with silver oxide was used at the inlet of the GC column to create concentration pulses of methane in a sample stream of air. By using only one carrier, i.e., ambient air, an effective and accurate method to monitor the variations in concentration of methane in the atmosphere over long periods of time was developed. Methane in ambient air was monitored for an eight day period and an interesting temporal variability was found. This work has shown the utility of a relatively simple MGC for the analysis of a real environmental sample.
Valentin, Jose R.↗
A variable conductance heat pipe/radiator for the lunar surface magnetometer.
The device was developed to supplement the existing cooling system of the Apollo 16 Lunar Surface Magnetometer (LSM). Analysis and tests showed that two such devices, inserted by an astronaut into receptacles on opposite sides of the electronics package, would reduce the diurnal temperature variation by about 40% and thereby would considerably increase the reliability of 50,000 welded connections. The LSM design constraints, selection of a variable conductance technique, heat pipe/radiator design features, and thermal performance are discussed.
Kirkpatrick, J. P.↗
A Path to Improving Simulated Properties of Low Clouds over the Beaufort Sea using Airborne In Situ Observations of Subgrid-Scale Variability
Arctic low clouds influence the evolution of the Arctic system through their effects on radiative fluxes, boundary layer mixing, stability, turbulence, humidity, and precipitation. Unfortunately, atmospheric models and retrospective analysis (reanalysis) products struggle to accurately simulate the occurrence and properties of low clouds in the Arctic. One of the main reasons for this problem are the possible unrealistic assumptions that models/reanalyses make about the subgrid-scale (SGS) variability of meteorological properties, as well as the relationship between SGS variability and grid-scale (GS) cloud properties. We utilize cloud and thermodynamic data of low level (primarily) liquid clouds collected from two aircraft campaigns conducted over the Beaufort Sea to better understand and characterize this problem. Examining data from the September 2014 Arctic Radiation-IceBridge Sea and Ice Experiment (ARISE) airborne campaign reveals that GS cloud water variability is closely related with SGS distribution of total water (i.e. water vapor + cloud water). Multiple models/reanalyses use SGS supersaturated total water (relative to GS saturation) as a threshold for partitioning available water for condensation, and indeed we find significant correlation between GS cloud water and SGS supersaturation. However, we also find that the assumption of a static threshold of 100% saturation to be unrealistic. Empirical calculations from the ARISE data show a large sensitivity of this threshold to GS relative humidity, and so a microphysical parameterization allowing the threshold to vary according to GS thermodynamic properties may result in more realistic GS cloud water values. Finally, to determine how sensitive the ARISE-derived results are to that particular campaign, we include additional data from the First International Satellite Cloud Climatology Project (ISCCP) Regional Experiment (FIRE)–Arctic Cloud Experiment (ACE) conducted in 1998. The inclusion of the second dataset will help with demonstrating the robustness of the results and their utility in improving the representation of Arctic clouds in models and reanalyses.
J Brant Dodson↗
A Path to Improving Simulated Properties of Low Clouds over the Beaufort Sea using Airborne In Situ Observations of Subgrid-Scale Variability
Arctic low clouds influence the evolution of the Arctic system through their effects on radiative fluxes, boundary layer mixing, stability, turbulence, humidity, and precipitation. Unfortunately, atmospheric models and retrospective analysis (reanalysis) products struggle to accurately simulate the occurrence and properties of low clouds in the Arctic. One of the main reasons for this problem are the possible unrealistic assumptions that models/reanalyses make about the subgrid-scale (SGS) variability of meteorological properties, as well as the relationship between SGS variability and grid-scale (GS) cloud properties. We utilize cloud and thermodynamic data of low level (primarily) liquid clouds collected from two aircraft campaigns conducted over the Beaufort Sea to better understand and characterize this problem. Examining data from the September 2014 Arctic Radiation-IceBridge Sea and Ice Experiment (ARISE) airborne campaign and the 1998 First International Satellite Cloud Climatology Project (ISCCP) Regional Experiment (FIRE)–Arctic Cloud Experiment (ACE) reveals that GS cloud water variability is closely related with SGS distribution of total water (i.e. water vapor + cloud water). We investigate two related approaches to prediction of GS cloud properties from SGS variability: the critical saturation ratio method, and the critical relative humidity method. We find significant correlation between GS cloud water and SGS supersaturation when the critical saturation ratio is set at 100%, as well as a notable relationship between GS cloud water and the width of the SGS total water distribution. Critical relative humidity also compares well with GS cloud water. However, we also find that the assumptions of a static critical saturation ratio of 100% to be unrealistic, as well as a fixed SGS distribution width. Empirical calculations from the ARISE data show a large sensitivity of these SGS variables to GS relative humidity, and so a SGS parameterization allowing them to vary according to GS thermodynamic properties may result in more realistic GS cloud water values.
J. Brant Dodson↗
A Path to Improving Simulated Properties of Low Clouds over the Beaufort Sea using Airborne In Situ Observations of Subgrid-Scale Variability
Arctic low clouds influence the evolution of the Arctic system through their effects on radiative fluxes, boundary layer mixing, stability, turbulence, humidity, and precipitation. Unfortunately, atmospheric models and retrospective analysis (reanalysis) products struggle to accurately simulate the occurrence and properties of low clouds in the Arctic. One of the main reasons for this problem are the possible unrealistic assumptions that models/reanalyses make about the subgrid-scale (SGS) variability of meteorological properties, as well as the relationship between SGS variability and grid-scale (GS) cloud properties. We utilize cloud and thermodynamic data of low level (primarily) liquid clouds collected from two aircraft campaigns conducted over the Beaufort Sea to better understand and characterize this problem. Examining data from the September 2014 Arctic Radiation-IceBridge Sea and Ice Experiment (ARISE) airborne campaign and the 1998 First International Satellite Cloud Climatology Project (ISCCP) Regional Experiment (FIRE)–Arctic Cloud Experiment (ACE) reveals that GS cloud water variability is closely related with SGS distribution of total water (i.e. water vapor + cloud water). We examine the influence of three assumed SGS parameters on the estimation of GS cloud water: the width of the SGS PDF of total water (ΔQT), the shape of the SGS PDF, and the critical saturation ratio (Scrit), which partitions the SGS PDF into water that is available or not for conversion to cloud water. Both Scrit and ΔQT influence predicted GS cloud water strongly. ARISE and FIRE-ACE disagree somewhat in the details, but both campaigns support the possibility that more realistic representations of these two parameters may lead to more realistic GS cloud water. In particular, both parameters are sensitive to GS relative humidity, and so we examine the effects of allowing these quantities to vary as an empirically-derived linear function of GS relative humidity. In contrast, the shape of the PDF has little effect on the predicted cloud water – a surprising result that merits additional investigation.
J Brant Dodson↗
The primer vector in linear, relative-motion equations
Primer vector theory is used in analyzing a set of linear, relative-motion equations - the Clohessy-Wiltshire equations - to determine the criteria and necessary conditions for an optimal, N-impulse trajectory. Since the state vector for these equations is defined in terms of a linear system of ordinary differential equations, all fundamental relations defining the solution of the state and costate equations, and the necessary conditions for optimality, can be expressed in terms of elementary functions. The analysis develops the analytical criteria for improving a solution by (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of (1) fixed-end conditions, two-impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized rendezvous problem. A sequence of rendezvous problems is solved to illustrate the analysis and the computational procedure.
Source record↗
Uncertainty Analysis of Decomposing Polyurethane Foam
Sensitivity/uncertainty analyses are necessary to determine where to allocate resources for improved predictions in support of our nation's nuclear safety mission. Yet, sensitivity/uncertainty analyses are not commonly performed on complex combustion models because the calculations are time consuming, CPU intensive, nontrivial exercises that can lead to deceptive results. To illustrate these ideas, a variety of sensitivity/uncertainty analyses were used to determine the uncertainty associated with thermal decomposition of polyurethane foam exposed to high radiative flux boundary conditions. The polyurethane used in this study is a rigid closed-cell foam used as an encapsulant. Related polyurethane binders such as Estane are used in many energetic materials of interest to the JANNAF community. The complex, finite element foam decomposition model used in this study has 25 input parameters that include chemistry, polymer structure, and thermophysical properties. The response variable was selected as the steady-state decomposition front velocity calculated as the derivative of the decomposition front location versus time. An analytical mean value sensitivity/uncertainty (MV) analysis was used to determine the standard deviation by taking numerical derivatives of the response variable with respect to each of the 25 input parameters. Since the response variable is also a derivative, the standard deviation was essentially determined from a second derivative that was extremely sensitive to numerical noise. To minimize the numerical noise, 50-micrometer element dimensions and approximately 1-msec time steps were required to obtain stable uncertainty results. As an alternative method to determine the uncertainty and sensitivity in the decomposition front velocity, surrogate response surfaces were generated for use with a constrained Latin Hypercube Sampling (LHS) technique. Two surrogate response surfaces were investigated: 1) a linear surrogate response surface (LIN) and 2) a quadratic response surface (QUAD). The LHS techniques do not require derivatives of the response variable and are subsequently relatively insensitive to numerical noise. To compare the LIN and QUAD methods to the MV method, a direct LHS analysis (DLHS) was performed using the full grid and timestep resolved finite element model. The surrogate response models (LIN and QUAD) are shown to give acceptable values of the mean and standard deviation when compared to the fully converged DLHS model.
Hobbs, Michael L.↗
An Outburst Scenario for the X-ray Spectral Variability in 3C 111
We present a combined Suzaku and Swift BAT broad-band E=0.6-200 keV spectral analysis of three 3C 111 observations obtained in 2010. The data are well described with an absorbed power-law continuum and a weak (R approximately equal to 0.2) cold reflection component from distant material. We constrain the continuum cutoff at E(sub C) approximately equal to 150- 200 keV, which is in accordance with X-ray Comptonization corona models and supports claims that the jet emission is only dominant at much higher energies. Fe XXVI Ly alpha emission and absorption lines are also present in the first and second observations, respectively. The modelling and interpretation of the emission line is complex and we explore three possibilities. If originating from ionized disc reflection, this should be emitted at r(sub in) greater than or equal to 50 r(sub g) or, in the lamp-post configuration, the illuminating source should be at a height of h greater than or equal to 30 r(sub g) over the black hole. Alternatively, the line could be modeled with a hot collisionally ionized plasma with temperature kT = 22.0(sup +6.1)(sub −3.2) keV or a photo-ionized plasma with logXi=4.52(sup +0.10)(sub −0.16) erg per second cm, and column density N(sub H) greater than 3×10(sup 23) per square centimeter. However, the first and second scenarios are less favored on statistical and physical grounds, respectively. The blue-shifted absorption line in the second observation can be modelled as an ultra-fast outflow (UFO) with ionization parameter logXi=4.47(sup +0.76) (sub −0.04) erg per second cm, column density NH=(5.3(sup +1.8)(sub −1.3))×10(sup 22) per square centimeter and outflow velocity v(sub out) = 0.104+/-0.006c. Interestingly, the parameters of the photoionized emission model remarkably match those of the absorbing UFO, supporting the possibility that the same material could be responsible for both emission and absorption. We suggest an outburst scenario in which an accretion disc wind, initially lying out of the line of sight and observed in emission, then crosses our view to the source and it is observed in absorption as a mildly-relativistic UFO.
Outburst↗
Multi-Scale Fractal Analysis of Image Texture and Pattern
Fractals embody important ideas of self-similarity, in which the spatial behavior or appearance of a system is largely independent of scale. Self-similarity is defined as a property of curves or surfaces where each part is indistinguishable from the whole, or where the form of the curve or surface is invariant with respect to scale. An ideal fractal (or monofractal) curve or surface has a constant dimension over all scales, although it may not be an integer value. This is in contrast to Euclidean or topological dimensions, where discrete one, two, and three dimensions describe curves, planes, and volumes. Theoretically, if the digital numbers of a remotely sensed image resemble an ideal fractal surface, then due to the self-similarity property, the fractal dimension of the image will not vary with scale and resolution. However, most geographical phenomena are not strictly self-similar at all scales, but they can often be modeled by a stochastic fractal in which the scaling and self-similarity properties of the fractal have inexact patterns that can be described by statistics. Stochastic fractal sets relax the monofractal self-similarity assumption and measure many scales and resolutions in order to represent the varying form of a phenomenon as a function of local variables across space. In image interpretation, pattern is defined as the overall spatial form of related features, and the repetition of certain forms is a characteristic pattern found in many cultural objects and some natural features. Texture is the visual impression of coarseness or smoothness caused by the variability or uniformity of image tone or color. A potential use of fractals concerns the analysis of image texture. In these situations it is commonly observed that the degree of roughness or inexactness in an image or surface is a function of scale and not of experimental technique. The fractal dimension of remote sensing data could yield quantitative insight on the spatial complexity and information content contained within these data. A software package known as the Image Characterization and Modeling System (ICAMS) was used to explore how fractal dimension is related to surface texture and pattern. The ICAMS software was verified using simulated images of ideal fractal surfaces with specified dimensions. The fractal dimension for areas of homogeneous land cover in the vicinity of Huntsville, Alabama was measured to investigate the relationship between texture and resolution for different land covers.
Emerson, Charles W.↗
A Catchment-Based Approach to Modeling Land Surface Processes in a GCM: Model Structure - Part 1
A new strategy for modeling the land surface component of the climate system is described. The strategy is motivated by an arguable deficiency in most state-of-the-art land surface models (LSMs), namely the disproportionately higher emphasis given to the formulation of one-dimensional, vertical physics relative to the treatment of horizontal heterogeneity in surface properties -- particularly subgrid soil moisture variability and its effects on runoff generation. The new strategy calls for the partitioning of the continental surface into a mosaic of hydrologic catchments, delineated through analysis of high-resolution surface elevation data. The effective "grid" used for the land surface is therefore not specified by the overlying atmospheric grid. Within each catchment, the variability of soil moisture is related to characteristics of the topography and to three bulk soil moisture variables through a well-established model of catchment processes. This modeled variability allows the partitioning of the catchment into several areas representing distinct hydrological regimes, wherein distinct (regime-specific) evaporation and runoff parameterizations are applied. Care is taken to ensure that the deficiencies of the catchment model in regions of little to moderate topography are minimized.
Koster, Randal D.↗
Quantitative Evaluation of MODIS Fire Radiative Power Measurement for Global Smoke Emissions Assessment
Satellite remote sensing is providing us tremendous opportunities to measure the fire radiative energy (FRE) release rate or power (FRP) from open biomass burning, which affects many vegetated regions of the world on a seasonal basis. Knowledge of the biomass burning characteristics and emission source strengths of different (particulate and gaseous) smoke constituents is one of the principal ingredients upon which the assessment, modeling, and forecasting of their distribution and impacts depend. This knowledge can be gained through accurate measurement of FRP, which has been shown to have a direct relationship with the rates of biomass consumption and emissions of major smoke constituents. Over the last decade or so, FRP has been routinely measured from space by both the MODIS sensors aboard the polar orbiting Terra and Aqua satellites, and the SEVIRI sensor aboard the Meteosat Second Generation (MSG) geostationary satellite. During the last few years, FRP has steadily gained increasing recognition as an important parameter for facilitating the development of various scientific studies and applications relating to the quantitative characterization of biomass burning and their emissions. To establish the scientific integrity of the FRP as a stable quantity that can be measured consistently across a variety of sensors and platforms, with the potential of being utilized to develop a unified long-term climate data record of fire activity and impacts, it needs to be thoroughly evaluated, calibrated, and validated. Therefore, we are conducting a detailed analysis of the FRP products from MODIS to evaluate the uncertainties associated with them, such as those due to the effects of satellite variable observation geometry and other factors, in order to establish their error budget for use in diverse scientific research and applications. In this presentation, we will show recent results of the MODIS FRP uncertainty analysis and error mitigation solutions, and demonstrate their implications for biomass burning emissions assessment.
Ichoku, Charles↗