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NASA NTRS1994

The dynamical evolution of poor clusters of galaxies: Growth and properties of the first-ranked galaxy

We report N-body simulations of the dynamical evolution of isolated clusters of 50 galaxies containing a dark matter component that comprises 90% of the cluster mass. For our adopted physical scaling, the line-of-sight velocity dispersion of the cluster is 310 km/s and the initial core radius is 250 kpc. Our results are applicable to (1) present-day poor clusters, (2) the small systems that may have merged to produce present-day rich clusters, and (3) virialized subclumps within larger systems, in between major substructure merger events. We have evolved a total of 10 cluster models, using N = 40,000 particles per model. The models are fully self-consistent in that each galaxy is represented as an extended structure containing many particles and the gravitational potential arises from the particles alone. Dark matter is apportioned between the galaxy halos and a smoothly distributed common group halo, the intracluster background (ICB). The percentage of cluster mass initially in the ICB, Beta, is chosen to be 50, 75, or 90. Increasing Beta has the effect of removing mass from dark halos around galaxies and distributing it throughout the cluster. The initial conditions were constructed by randomly sampling a King distribution with W(sub 0) = 6. The galaxies are also King models; the masses of the galaxies follow a Schechter distribution function.

Bode, Paul W.↗
NASA NTRS1960

An Exploratory Statistical Analysis of a Planet Approach-Phase Guidance Scheme Using Angular Measurements with Significant Error

An exploratory analysis of vehicle guidance during the approach to a target planet is presented. The objective of the guidance maneuver is to guide the vehicle to a specific perigee distance with a high degree of accuracy and minimum corrective velocity expenditure. The guidance maneuver is simulated by considering the random sampling of real measurements with significant error and reducing this information to prescribe appropriate corrective action. The instrumentation system assumed includes optical and/or infrared devices to indicate range and a reference angle in the trajectory plane. Statistical results are obtained by Monte-Carlo techniques and are shown as the expectation of guidance accuracy and velocity-increment requirements. Results are nondimensional and applicable to any planet within limits of two-body assumptions. The problem of determining how many corrections to make and when to make them is a consequence of the conflicting requirement of accurate trajectory determination and propulsion. Optimum values were found for a vehicle approaching a planet along a parabolic trajectory with an initial perigee distance of 5 radii and a target perigee of 1.02 radii. In this example measurement errors were less than i minute of arc. Results indicate that four corrections applied in the vicinity of 50, 16, 15, and 1.5 radii, respectively, yield minimum velocity-increment requirements. Thrust devices capable of producing a large variation of velocity-increment size are required. For a vehicle approaching the earth, miss distances within 32 miles are obtained with 90-percent probability. Total velocity increments used in guidance are less than 3300 feet per second with 90-percent probability. It is noted that the above representative results are valid only for the particular guidance scheme hypothesized in this analysis. A parametric study is presented which indicates the effects of measurement error size, initial perigee, and initial energy on the guidance requirements. Measurement error size significantly affects both guidance accuracy and velocity-increment expenditure. The initial trajectory, as given by its perigee and energy, affects the velocity-increment expenditure but not final guidance accuracy.

Friedlander, Alan L.↗
NASA NTRS2001

General Aviation Aircraft Reliability Study

This reliability study was performed in order to provide the aviation community with an estimate of Complex General Aviation (GA) Aircraft System reliability. To successfully improve the safety and reliability for the next generation of GA aircraft, a study of current GA aircraft attributes was prudent. This was accomplished by benchmarking the reliability of operational Complex GA Aircraft Systems. Specifically, Complex GA Aircraft System reliability was estimated using data obtained from the logbooks of a random sample of the Complex GA Aircraft population.

Pettit, Duane↗
NASA NTRS1994

Search Space Characterization for a Telescope Scheduling Application

This paper presents a technique for statistically characterizing a search space and demonstrates the use of this technique within a practical telescope scheduling application. The characterization provides the following: (i) an estimate of the search space size, (ii) a scaling technique for multi-attribute objective functions and search heuristics, (iii) a "quality density function" for schedules in a search space, (iv) a measure of a scheduler's performance, and (v) support for constructing and tuning search heuristics. This paper describes the random sampling algorithm used to construct this characterization and explains how it can be used to produce this information. As an example, we include a comparative analysis of an heuristic dispatch scheduler and a look-ahead scheduler that performs greedy search.

Bresina, John↗
NASA NTRS2000

Combined dietary and exercise intervention for control of serum cholesterol in the workplace

PURPOSE: To elucidate a potential combined dietary and exercise intervention affect on cardiovascular risk reduction of the National Aeronautics and Space Administration Headquarters employees. DESIGN: A nonexperimental, longitudinal, clinical-chart review study (1987 to 1996) of an identified intervention group and a reference (not a control) group. SETTING: The study group worked in an office environment and participated in the annual medical examinations. SUBJECTS: An intervention group of 858 people with initially elevated serum cholesterol, and a reference group of 963 people randomly sampled from 10% of the study group. MEASURES: Serum cholesterol data were obtained for both groups, respectively, from pre- and postintervention and annual examinations. The reference group was adjusted by statistical exclusion of potential intervention participants. Regression equations (cholesterol vs. study years) for the unadjusted/adjusted reference groups were tested for statistical significance. INTERVENTION: An 8-week individualized, combined dietary and exercise program was instituted with annual follow-ups and was repeated where warranted. RESULTS: Only the unadjusted (but not the adjusted) reference group with initial mean total serum cholesterol levels above 200 mg/dL shows a significant 9-year decline trend and significant beta coefficient tests. An intervention effect is suggested. Mean high density lipoprotein cholesterol rose slightly in the intervention group but was maintained in the reference group. CONCLUSION: With potential design limitations, the NASA intervention program focusing on a high risk group may be associated to some degree, if not fully, with an overall cardiovascular risk profile improvement.

Occupational Health Services↗
NASA NTRS1999

Transduction-like gene transfer in the methanogen Methanococcus voltae

Strain PS of Methanococcus voltae (a methanogenic, anaerobic archaebacterium) was shown to generate spontaneously 4.4-kbp chromosomal DNA fragments that are fully protected from DNase and that, upon contact with a cell, transform it genetically. This activity, here called VTA (voltae transfer agent), affects all markers tested: three different auxotrophies (histidine, purine, and cobalamin) and resistance to BES (2-bromoethanesulfonate, an inhibitor of methanogenesis). VTA was most effectively prepared by culture filtration. This process disrupted a fraction of the M. voltae cells (which have only an S-layer covering their cytoplasmic membrane). VTA was rapidly inactivated upon storage. VTA particles were present in cultures at concentrations of approximately two per cell. Gene transfer activity varied from a minimum of 2 x 10(-5) (BES resistance) to a maximum of 10(-3) (histidine independence) per donor cell. Very little VTA was found free in culture supernatants. The phenomenon is functionally similar to generalized transduction, but there is no evidence, for the time being, of intrinsically viral (i.e., containing a complete viral genome) particles. Consideration of VTA DNA size makes the existence of such viral particles unlikely. If they exist, they must be relatively few in number;perhaps they differ from VTA particles in size and other properties and thus escaped detection. Digestion of VTA DNA with the AluI restriction enzyme suggests that it is a random sample of the bacterial DNA, except for a 0.9-kbp sequence which is amplified relative to the rest of the bacterial chromosome. A VTA-sized DNA fraction was demonstrated in a few other isolates of M. voltae.

Methanococcus/genetics/growth & development/metabo↗
NASA NTRS2004

Perceptual learning through optimization of attentional weighting: human versus optimal Bayesian learner

Human performance in visual detection, discrimination, identification, and search tasks typically improves with practice. Psychophysical studies suggest that perceptual learning is mediated by an enhancement in the coding of the signal, and physiological studies suggest that it might be related to the plasticity in the weighting or selection of sensory units coding task relevant information (learning through attention optimization). We propose an experimental paradigm (optimal perceptual learning paradigm) to systematically study the dynamics of perceptual learning in humans by allowing comparisons to that of an optimal Bayesian algorithm and a number of suboptimal learning models. We measured improvement in human localization (eight-alternative forced-choice with feedback) performance of a target randomly sampled from four elongated Gaussian targets with different orientations and polarities and kept as a target for a block of four trials. The results suggest that the human perceptual learning can occur within a lapse of four trials (<1 min) but that human learning is slower and incomplete with respect to the optimal algorithm (23.3% reduction in human efficiency from the 1st-to-4th learning trials). The greatest improvement in human performance, occurring from the 1st-to-2nd learning trial, was also present in the optimal observer, and, thus reflects a property inherent to the visual task and not a property particular to the human perceptual learning mechanism. One notable source of human inefficiency is that, unlike the ideal observer, human learning relies more heavily on previous decisions than on the provided feedback, resulting in no human learning on trials following a previous incorrect localization decision. Finally, the proposed theory and paradigm provide a flexible framework for future studies to evaluate the optimality of human learning of other visual cues and/or sensory modalities.

Non-NASA Center↗
NASA NTRS2007

Potential of VIIRS Data for Regional Monitoring of Gypsy Moth Defoliation: Implications for Forest Threat Early Warning System

A NASA RPC (Rapid Prototyping Capability) experiment was conducted to assess the potential of VIIRS (Visible/Infrared Imager/Radiometer Suite) data for monitoring non-native gypsy moth (Lymantria dispar) defoliation of forests. This experiment compares defoliation detection products computed from simulated VIIRS and from MODIS (Moderate Resolution Imaging Spectroradiometer) time series products as potential inputs to a forest threat EWS (Early Warning System) being developed for the USFS (USDA Forest Service). Gypsy moth causes extensive defoliation of broadleaved forests in the United States and is specifically identified in the Healthy Forest Restoration Act (HFRA) of 2003. The HFRA mandates development of a national forest threat EWS. This system is being built by the USFS and NASA is aiding integration of needed satellite data products into this system, including MODIS products. This RPC experiment enabled the MODIS follow-on, VIIRS, to be evaluated as a data source for EWS forest monitoring products. The experiment included 1) assessment of MODIS-simulated VIIRS NDVI products, and 2) evaluation of gypsy moth defoliation mapping products from MODIS-simulated VIIRS and from MODIS NDVI time series data. This experiment employed MODIS data collected over the approximately 15 million acre mid-Appalachian Highlands during the annual peak defoliation time frame (approximately June 10 through July 27) during 2000-2006. NASA Stennis Application Research Toolbox software was used to produce MODIS-simulated VIIRS data and NASA Stennis Time Series Product Tool software was employed to process MODIS and MODIS-simulated VIIRS time series data scaled to planetary reflectance. MODIS-simulated VIIRS data was assessed through comparison to Hyperion-simulated VIIRS data using data collected during gypsy moth defoliation. Hyperion-simulated MODIS data showed a high correlation with actual MODIS data (NDVI R2 of 0.877 and RMSE of 0.023). MODIS-simulated VIIRS data for the same date showed moderately high correlation with Hyperion-simulated VIIRS data (NDVI R2 of 0.62 and RMSE of 0.035), even though the datasets were collected about a half an hour apart during changing weather conditions. MODIS products (MOD02, MOD09, and MOD13) and MOD02-simulated VIIRS time series data were used to generate defoliation mapping products based on image classification and image differencing change detection techniques. Accuracy of final defoliation mapping products was assessed by image interpreting over 170 randomly sampled locations found on Landsat and ASTER data in conjunction with defoliation map data from the USFS. The MOD02-simulated VIIRS 400-meter NDVI classification produced a similar overall accuracy (87.28 percent with 0.72 Kappa) to the MOD02 250-meter NDVI classification (86.71 percent with 0.71 Kappa). In addition, the VIIRS 400-meter NDVI, MOD02 250-meter NDVI, and MOD02 500-meter NDVI showed good user and producer accuracies for the defoliated forest class (70 percent) and acceptable Kappa values (0.66). MOD02 and MOD02-simulated VIIRS data both showed promise as data sources for regional monitoring of forest disturbance due to insect defoliation.

Spruce, Joseph P.↗
NASA NTRS2008

The Integrated Medical Model: Statistical Forecasting of Risks to Crew Health and Mission Success

The Integrated Medical Model (IMM) helps capture and use organizational knowledge across the space medicine, training, operations, engineering, and research domains. The IMM uses this domain knowledge in the context of a mission and crew profile to forecast crew health and mission success risks. The IMM is most helpful in comparing the risk of two or more mission profiles, not as a tool for predicting absolute risk. The process of building the IMM adheres to Probability Risk Assessment (PRA) techniques described in NASA Procedural Requirement (NPR) 8705.5, and uses current evidence-based information to establish a defensible position for making decisions that help ensure crew health and mission success. The IMM quantitatively describes the following input parameters: 1) medical conditions and likelihood, 2) mission duration, 3) vehicle environment, 4) crew attributes (e.g. age, sex), 5) crew activities (e.g. EVA's, Lunar excursions), 6) diagnosis and treatment protocols (e.g. medical equipment, consumables pharmaceuticals), and 7) Crew Medical Officer (CMO) training effectiveness. It is worth reiterating that the IMM uses the data sets above as inputs. Many other risk management efforts stop at determining only likelihood. The IMM is unique in that it models not only likelihood, but risk mitigations, as well as subsequent clinical outcomes based on those mitigations. Once the mathematical relationships among the above parameters are established, the IMM uses a Monte Carlo simulation technique (a random sampling of the inputs as described by their statistical distribution) to determine the probable outcomes. Because the IMM is a stochastic model (i.e. the input parameters are represented by various statistical distributions depending on the data type), when the mission is simulated 10-50,000 times with a given set of medical capabilities (risk mitigations), a prediction of the most probable outcomes can be generated. For each mission, the IMM tracks which conditions occurred and decrements the pharmaceuticals and supplies required to diagnose and treat these medical conditions. If supplies are depleted, then the medical condition goes untreated, and crew and mission risk increase. The IMM currently models approximately 30 medical conditions. By the end of FY2008, the IMM will be modeling over 100 medical conditions, approximately 60 of which have been recorded to have occurred during short and long space missions.

Fitts, M. A.↗
NASA NTRS2009

Land-Use and Land-Cover Change around Mobile Bay, Alabama from 1974-2008

This document summarizes the major findings of a Gulf of Mexico Application Pilot project led by NASA Stennis Space Center (SSC) in conjunction with a regional collaboration network of the Gulf of Mexico Alliance (GOMA). NASA researchers processed and analyzed multi-temporal Landsat data to assess land-use and land-cover (LULC) changes in the coastal counties of Mobile and Baldwin, AL between 1974 and 2008. Our goal was to create satellite-based LULC data products using methods that could be transferable to other coastal areas of concern within the Gulf of Mexico. The Mobile Bay National Estuary Program (MBNEP) is the primary end-user, however, several other state and local groups may benefit from the project s data products that will be available through NOAA-NCDDC s Regional Ecosystem Data Management program. Mobile Bay is a critical ecologic and economic region in the Gulf of Mexico and to the entire country. Mobile Bay was designated as an estuary of national significance in 1996. This estuary receives the fourth largest freshwater inflow in the United States. It provides vital nursery habitat for commercially and recreationally important fish species. It has exceptional aquatic and terrestrial bio-diversity, however, its estuary health is influenced by changing LULC patterns, such as urbanization. Mobile and Baldwin counties have experienced a population growth of 1.1% and 20.5% from 2000-2006. Urban expansion and population growth are likely to accelerate with the construction and operation of the ThyssenKrupp steel mill in the northeast portion of Mobile County. Land-use and land-cover change can negatively impact Gulf coast water quality and ecological resources. The conversion of forest to urban cover types impacts the carbon cycle and increases the freshwater and sediment in coastal waters. Increased freshwater runoff decreases salinity and increases the turbidity of coastal waters, thus impacting the growth potential of submerged aquatic vegetation (SAV), which is critical nursing ground for many Gulf fish species. A survey of Mobile Bay SAV showed widespread decreases since the 1940s. Prior to our project, coastal environmental managers in Baldwin and Mobile counties needed more understanding of the historical LULC for properly assessing the impacts of urbanization. In particular, more information on the location and extent of changing urbanization LULC patterns was needed to aid LULC planning and to assess predictions of future LULC patterns. Our products will assist the coastal environmental managers and land-use planners in making better community growth planning decisions. Our project also will help to establish a historical baseline of LULC distributions, which is a fundamental need in any stewardship plan. The primary research objective of our project was to produce historic and current geospatial LULC change products across a 34-year time frame. A multi-decadal coastal LULC change product was the major project deliverable. The geographic extent and nature of change was quantified and assessed for the upland herbaceous, barren, open water, urban, upland forest, woody wetland, and non-woody wetlanddominated land cover types. We focused on regional analyses of decadal-scale urban expansion and watershed-scaled analyses of LULC change for multiple areas of concern to the Mobile Bay NEP (Figure A). We used the following dates to derive LULC classification products from Landsat data: 1974, 1979, 1984, 1988, 1991, 1996, 2001, 2005, and 2008. We assessed the accuracy of our products using randomly sampled locations and digital geospatial reference data including field survey data, high resolution orthorectified aerial photography, high resolution multispectral and panchromatic satellite data displays (from QuickBird and Corona sensors), digital elevation model data, and National Wetlands Inventory wetland cover type data. NOAA s Coastal Change Assessment Program s (C-CAP) and National Land Cover Database (NLCD) procts were used for qualitative comparison in assessing map accuracy. We calculated an average overall classification accuracy of 87% with similar overall accuracies for the older (MSS) and newer (TM and ETM) Landsat LULC products.

Ellis, Jean↗
NASA NTRS2008

The CME Flare Arcade and the Width of the CME in the Outer Corona

Moore, Sterling, & Suess (2007, ApJ, 668, 1221) present evidence that (1) a CME is typically a magnetic bubble, a low-beta gplasmoid with legs h having roughly the 3D shape of a light bulb, and (2) in the outer corona the CME plasmoid is in lateral pressure equilibrium with the ambient magnetic field. They present three CMEs observed by SOHO/LASCO, each from a very different source located near the limb. One of these CMEs came from a compact ejective eruption from a small part of a sunspot active region, another came from a large quiet-region filament eruption, and the third CME, an extremely large and fast one, was produced in tandem with an X20 flare arcade that was centered on a huge delta sunspot. Each of these CMEs had more or less the classic lightbulb silhouette and attained a constant heliocentric angular width in the outer corona. This indicates that the CME plasmoid attained lateral magnetic pressure balance with the ambient radial magnetic field in the outer corona. This lateral pressure balance, together with the standard scenario for CME production by the eruption of a sheared-core magnetic arcade, yields the following simple estimate of the strength B(sub Flare) of the magnetic field in the flare arcade produced together with the CME: B(sub Flare) 1.4(theta CME/theta Flare)sup 2 G, where theta (sub CME) is the heliocentric angular width of the CME plasmoid in the outer corona and theta (sub Flare) is the heliocentric angular width of the full-grown flare arcade. Conversely, theta (sub CME) approximately equal to (R(sub Sun)sup -1(phi(sub Flare)/1.4)sup 1/2 radians, where Flare is the magnetic flux covered by the full-grown flare arcade. In addition to presenting the three CMEs of Moore, Sterling, & Suess (2007) and their agreement with this relation between CME and Flare, we present a further empirical test of this relation. For CMEs that erupt from active regions, the co-produced flare arcade seldom if ever covers the entire active region: if AR is the total magnetic flux of the active region, Flare . AR, and we predict that CME. (R(sub Sun))sup -1(theta AR/1.4)sup 1/2 radians. For a random sample of 31 CMEs that erupted from active regions within 30 of the limb, for each CME we have measured CME from LASCO/C3 and have measured AR from a SOHO/MDI magnetogram of the source active region when it was within 30 of disk center. We find that each CME obeys the above predicted inequality, none having width greater than half of the upper bound given by theta(sub AR). Thus, an active region's magnetic flux content, together with its location on the solar disk, largely determines whether the active region can possibly produce a CME that is wide enough to intercept the Earth.

Moore, Ron↗
NASA NTRS2011

A New Aerodynamic Data Dispersion Method for Launch Vehicle Design

A novel method for implementing aerodynamic data dispersion analysis is herein introduced. A general mathematical approach combined with physical modeling tailored to the aerodynamic quantity of interest enables the generation of more realistically relevant dispersed data and, in turn, more reasonable flight simulation results. The method simultaneously allows for the aerodynamic quantities and their derivatives to be dispersed given a set of non-arbitrary constraints, which stresses the controls model in more ways than with the traditional bias up or down of the nominal data within the uncertainty bounds. The adoption and implementation of this new method within the NASA Ares I Crew Launch Vehicle Project has resulted in significant increases in predicted roll control authority, and lowered the induced risks for flight test operations. One direct impact on launch vehicles is a reduced size for auxiliary control systems, and the possibility of an increased payload. This technique has the potential of being applied to problems in multiple areas where nominal data together with uncertainties are used to produce simulations using Monte Carlo type random sampling methods. It is recommended that a tailored physics-based dispersion model be delivered with any aerodynamic product that includes nominal data and uncertainties, in order to make flight simulations more realistic and allow for leaner spacecraft designs.

Pinier, Jeremy T.↗
NASA NTRS2012

Pilot Test of a Novel Method for Assessing Community Response to Low-Amplitude Sonic Booms

A pilot test of a novel method for assessing residents annoyance to sonic booms was performed. During a two-week period, residents of the base housing area at Edwards Air Force Base provided data on their reactions to sonic booms using Smartphone-based interviews. Noise measurements were conducted at the same time. The report presents information about data collection methods and about test participants reactions to low-amplitude sonic booms. The latter information should not be viewed as definitive for several reasons. It may not be reliably generalized to the wider U.S. residential population (because it was not derived from a representative random sample) and the sample itself was not large.

Fidell, Sanford↗
NASA NTRS2013

Estimated Probability of a Cervical Spine Injury During an ISS Mission

Introduction: The Integrated Medical Model (IMM) utilizes historical data, cohort data, and external simulations as input factors to provide estimates of crew health, resource utilization and mission outcomes. The Cervical Spine Injury Module (CSIM) is an external simulation designed to provide the IMM with parameter estimates for 1) a probability distribution function (PDF) of the incidence rate, 2) the mean incidence rate, and 3) the standard deviation associated with the mean resulting from injury/trauma of the neck. Methods: An injury mechanism based on an idealized low-velocity blunt impact to the superior posterior thorax of an ISS crewmember was used as the simulated mission environment. As a result of this impact, the cervical spine is inertially loaded from the mass of the head producing an extension-flexion motion deforming the soft tissues of the neck. A multibody biomechanical model was developed to estimate the kinematic and dynamic response of the head-neck system from a prescribed acceleration profile. Logistic regression was performed on a dataset containing AIS1 soft tissue neck injuries from rear-end automobile collisions with published Neck Injury Criterion values producing an injury transfer function (ITF). An injury event scenario (IES) was constructed such that crew 1 is moving through a primary or standard translation path transferring large volume equipment impacting stationary crew 2. The incidence rate for this IES was estimated from in-flight data and used to calculate the probability of occurrence. The uncertainty in the model input factors were estimated from representative datasets and expressed in terms of probability distributions. A Monte Carlo Method utilizing simple random sampling was employed to propagate both aleatory and epistemic uncertain factors. Scatterplots and partial correlation coefficients (PCC) were generated to determine input factor sensitivity. CSIM was developed in the SimMechanics/Simulink environment with a Monte Carlo wrapper (MATLAB) used to integrate the components of the module. Results: The probability of generating an AIS1 soft tissue neck injury from the extension/flexion motion induced by a low-velocity blunt impact to the superior posterior thorax was fitted with a lognormal PDF with mean 0.26409, standard deviation 0.11353, standard error of mean 0.00114, and 95% confidence interval [0.26186, 0.26631]. Combining the probability of an AIS1 injury with the probability of IES occurrence was fitted with a Johnson SI PDF with mean 0.02772, standard deviation 0.02012, standard error of mean 0.00020, and 95% confidence interval [0.02733, 0.02812]. The input factor sensitivity analysis in descending order was IES incidence rate, ITF regression coefficient 1, impactor initial velocity, ITF regression coefficient 2, and all others (equipment mass, crew 1 body mass, crew 2 body mass) insignificant. Verification and Validation (V&V): The IMM V&V, based upon NASA STD 7009, was implemented which included an assessment of the data sets used to build CSIM. The documentation maintained includes source code comments and a technical report. The software code and documentation is under Subversion configuration management. Kinematic validation was performed by comparing the biomechanical model output to established corridors.

Brooker, John E.↗
NASA NTRS2013

LEGEND, a LEO-to-GEO Environment Debris Model

LEGEND (LEO-to-GEO Environment Debris model) is a three-dimensional orbital debris evolutionary model that is capable of simulating the historical and future debris populations in the near-Earth environment. The historical component in LEGEND adopts a deterministic approach to mimic the known historical populations. Launched rocket bodies, spacecraft, and mission-related debris (rings, bolts, etc.) are added to the simulated environment. Known historical breakup events are reproduced, and fragments down to 1 mm in size are created. The LEGEND future projection component adopts a Monte Carlo approach and uses an innovative pair-wise collision probability evaluation algorithm to simulate the future breakups and the growth of the debris populations. This algorithm is based on a new "random sampling in time" approach that preserves characteristics of the traditional approach and captures the rapidly changing nature of the orbital debris environment. LEGEND is a Fortran 90-based numerical simulation program. It operates in a UNIX/Linux environment.

Liou, Jer Chyi↗
NASA NTRS2013

Probabilistic Modeling of the Renal Stone Formation Module

The Integrated Medical Model (IMM) is a probabilistic tool, used in mission planning decision making and medical systems risk assessments. The IMM project maintains a database of over 80 medical conditions that could occur during a spaceflight, documenting an incidence rate and end case scenarios for each. In some cases, where observational data are insufficient to adequately define the inflight medical risk, the IMM utilizes external probabilistic modules to model and estimate the event likelihoods. One such medical event of interest is an unpassed renal stone. Due to a high salt diet and high concentrations of calcium in the blood (due to bone depletion caused by unloading in the microgravity environment) astronauts are at a considerable elevated risk for developing renal calculi (nephrolithiasis) while in space. Lack of observed incidences of nephrolithiasis has led HRP to initiate the development of the Renal Stone Formation Module (RSFM) to create a probabilistic simulator capable of estimating the likelihood of symptomatic renal stone presentation in astronauts on exploration missions. The model consists of two major parts. The first is the probabilistic component, which utilizes probability distributions to assess the range of urine electrolyte parameters and a multivariate regression to transform estimated crystal density and size distributions to the likelihood of the presentation of nephrolithiasis symptoms. The second is a deterministic physical and chemical model of renal stone growth in the kidney developed by Kassemi et al. The probabilistic component of the renal stone model couples the input probability distributions describing the urine chemistry, astronaut physiology, and system parameters with the physical and chemical outputs and inputs to the deterministic stone growth model. These two parts of the model are necessary to capture the uncertainty in the likelihood estimate. The model will be driven by Monte Carlo simulations, continuously randomly sampling the probability distributions of the electrolyte concentrations and system parameters that are inputs into the deterministic model. The total urine chemistry concentrations are used to determine the urine chemistry activity using the Joint Expert Speciation System (JESS), a biochemistry model. Information used from JESS is then fed into the deterministic growth model. Outputs from JESS and the deterministic model are passed back to the probabilistic model where a multivariate regression is used to assess the likelihood of a stone forming and the likelihood of a stone requiring clinical intervention. The parameters used to determine to quantify these risks include: relative supersaturation (RS) of calcium oxalate, citrate/calcium ratio, crystal number density, total urine volume, pH, magnesium excretion, maximum stone width, and ureteral location. Methods and Validation: The RSFM is designed to perform a Monte Carlo simulation to generate probability distributions of clinically significant renal stones, as well as provide an associated uncertainty in the estimate. Initially, early versions will be used to test integration of the components and assess component validation and verification (V&V), with later versions used to address questions regarding design reference mission scenarios. Once integrated with the deterministic component, the credibility assessment of the integrated model will follow NASA STD 7009 requirements.

kidney stones↗
NASA NTRS2014

Exact and Approximate Probabilistic Symbolic Execution

Probabilistic software analysis seeks to quantify the likelihood of reaching a target event under uncertain environments. Recent approaches compute probabilities of execution paths using symbolic execution, but do not support nondeterminism. Nondeterminism arises naturally when no suitable probabilistic model can capture a program behavior, e.g., for multithreading or distributed systems. In this work, we propose a technique, based on symbolic execution, to synthesize schedulers that resolve nondeterminism to maximize the probability of reaching a target event. To scale to large systems, we also introduce approximate algorithms to search for good schedulers, speeding up established random sampling and reinforcement learning results through the quantification of path probabilities based on symbolic execution. We implemented the techniques in Symbolic PathFinder and evaluated them on nondeterministic Java programs. We show that our algorithms significantly improve upon a state-of- the-art statistical model checking algorithm, originally developed for Markov Decision Processes.

Symbolic Execution↗
NASA NTRS2015

Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating each component weight during the nonlinear propagation stage an approximation of the true pdf can be successfully reconstructed. Particle filtering (PF) methods have gained popularity recently for solving nonlinear estimation problems due to their straightforward approach and the processing capabilities mentioned above. The basic concept behind PF is to represent any pdf as a set of random samples. As the number of samples increases, they will theoretically converge to the exact, equivalent representation of the desired pdf. When the estimated qth moment is needed, the samples are used for its construction allowing further analysis of the pdf characteristics. However, filter performance deteriorates as the dimension of the state vector increases. To overcome this problem Ref. [5] applies a marginalization technique for PF methods, decreasing complexity of the system to one linear and another nonlinear state estimation problem. The marginalization theory was originally developed by Rao and Blackwell independently. According to Ref. [6] it improves any given estimator under every convex loss function. The improvement comes from calculating a conditional expected value, often involving integrating out a supportive statistic. In other words, Rao-Blackwellization allows for smaller but separate computations to be carried out while reaching the main objective of the estimator. In the case of improving an estimator's variance, any supporting statistic can be removed and its variance determined. Next, any other information that dependents on the supporting statistic is found along with its respective variance. A new approach is developed here by utilizing the strengths of the adaptive Gaussian sum propagation in Ref. [2] and a marginalization approach used for PF methods found in Ref. [7]. In the following sections a modified filtering approach is presented based on a special state-space model within nonlinear systems to reduce the dimensionality of the optimization problem in Ref. [2]. First, the adaptive Gaussian sum propagation is explained and then the new marginalized adaptive Gaussian sum propagation is derived. Finally, an example simulation is presented.

state estimation↗