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NASA NTRS2019

Terrestrial Single-Station Analog for Constraining the Martian Core and Deep Interior: Implications for InSight

We used a terrestrial single-station seismometer to quantify the uncertainty of InSight (INterior explorations using Seismic Investigations, Geodesy and Heat Transport) data for determining Martian core size. To mimic Martian seismicity, we formed a catalog using 917 terrestrial earthquakes, from which we randomly selected events. We stacked ScS amplitudes on modeled arrival times and searched for where ScS produced coherent seismic amplitudes. A core detection was defined by a coherent peak with small offset between predicted and user-selected arrival times. Iterating the detection algorithm with varying signal-to-noise (SNR) ranges and quantity of events determined the selection frequency of each model and quantified core depth uncertainty. Increasing the quantity of events reduced core depth uncertainty while increasing the recovery rate, while increasing event SNR had little effect. Including ScS2 multiples increased the recovery rate and reduced core depth uncertainty when we used low quantities of events. The most-frequent core depths varied by back azimuth, suggesting our method is sensitive to the presence of mantle heterogeneities. When we added 1° in source distance errors, core depth uncertainty increased by up to 11 km and recovery rates decreased by <5%. Altering epicentral distances by 25% added ~35 km of uncertainty and reduced recovery rates to <50% in some cases. From these experiments, we estimate that if InSight can detect five events with high location precision (< 10% epicentral distance errors), that there is at least an 88% chance of core depth recovery using ScS alone with uncertainty in core depth approaching 18 km and decreasing as more events are located.

Angela G Marusiak↗

NASA NTRS2005

An information maximization model of eye movements

We propose a sequential information maximization model as a general strategy for programming eye movements. The model reconstructs high-resolution visual information from a sequence of fixations, taking into account the fall-off in resolution from the fovea to the periphery. From this framework we get a simple rule for predicting fixation sequences: after each fixation, fixate next at the location that minimizes uncertainty (maximizes information) about the stimulus. By comparing our model performance to human eye movement data and to predictions from a saliency and random model, we demonstrate that our model is best at predicting fixation locations. Modeling additional biological constraints will improve the prediction of fixation sequences. Our results suggest that information maximization is a useful principle for programming eye movements.

NASA Discipline Neuroscience↗

NASA NTRS2010

Kriging as a Means of Improving WAAS Availability

The Wide Area Augmentation System (WAAS), an augmentation of the Global Positioning System (GPS), provides safe and reliable use of GPS signals for airline navigation over much of North America. Currently the largest source of positioning error in the system is signal delay caused by the ionosphere. To allow the user to take account of such error, WAAS computes and broadcasts ionospheric vertical delays at a set of regularly-spaced grid points. In addition, WAAS computes and broadcasts a safety-critical integrity bound at each ionospheric grid point (IGP) called the Grid Ionospheric Vertical Error (GIVE). GIVEs are constructed to be sufficiently large to protect the user against positioning error due to the presence of ionospheric irregularity. In the initial operating capability (IOC) of WAAS, the vertical delay estimate at each IGP is determined from a planar fit of neighboring slant delay measurements, projected to vertical using an obliquity factor specified by the standard thin-shell model of the ionosphere. In WAAS Follow-On (WFO) Release 3, however, the vertical delay will be estimated by an established, geo-statistical technique known as kriging. Compared to the planar fit model, the kriging model is found, in general, to match better the observed random structure of the vertical delay. This paper presents the kriging methodology that will be used to estimate the vertical delay and its uncertainty at each IGP, and it assesses the subsequent improvement in WAAS availability enabled by kriging.

GPS↗

NASA NTRS1991

Quantification of uncertainties in coupled material degradation processes - High temperature, fatigue and creep

This paper describes the development of methodology that provides for quantification of uncertainties in lifetime strength of aerospace materials subjected to a number of diverse effects. A probabilistic material degradation model, in the form of a randomized multifactor interaction equation, has been postulated for lifetime strength degradation of structural components of aerospace propulsion systems. The model includes effects that typically reduce lifetime strength and may include temperature, mechanical fatigue, creep and others. The paper also includes the analysis of experimental data from the open literature for Inconel 718. These data are used to provide an initial check for model validity, as well as for calibration of the model's empirical material constants. The model validity check and calibration is carried out for three effects, namely, high temperature, mechanical fatigue and creep.

Boyce, L.↗

NASA NTRS2006

Estimating Random Errors Due to Shot Noise in Backscatter Lidar Observations

In this paper, we discuss the estimation of random errors due to shot noise in backscatter lidar observations that use either photomultiplier tube (PMT) or avalanche photodiode (APD) detectors. The statistical characteristics of photodetection are reviewed, and photon count distributions of solar background signals and laser backscatter signals are examined using airborne lidar observations at 532 nm using a photon-counting mode APD. Both distributions appear to be Poisson, indicating that the arrival at the photodetector of photons for these signals is a Poisson stochastic process. For Poisson-distributed signals, a proportional, one-to-one relationship is known to exist between the mean of a distribution and its variance. Although the multiplied photocurrent no longer follows a strict Poisson distribution in analog-mode APD and PMT detectors, the proportionality still exists between the mean and the variance of the multiplied photocurrent. We make use of this relationship by introducing the noise scale factor (NSF), which quantifies the constant of proportionality that exists between the root-mean-square of the random noise in a measurement and the square root of the mean signal. Using the NSF to estimate random errors in lidar measurements due to shot noise provides a significant advantage over the conventional error estimation techniques, in that with the NSF uncertainties can be reliably calculated from/for a single data sample. Methods for evaluating the NSF are presented. Algorithms to compute the NSF are developed for the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) lidar and tested using data from the Lidar In-space Technology Experiment (LITE). OCIS Codes:

Liu, Zhaoyan↗

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 NTRS2015

Data Applicability of Heritage and New Hardware For Launch Vehicle Reliability Models

Bayesian reliability requires the development of a prior distribution to represent degree of belief about the value of a parameter (such as a component's failure rate) before system specific data become available from testing or operations. Generic failure data are often provided in reliability databases as point estimates (mean or median). A component's failure rate is considered a random variable where all possible values are represented by a probability distribution. The applicability of the generic data source is a significant source of uncertainty that affects the spread of the distribution. This presentation discusses heuristic guidelines for quantifying uncertainty due to generic data applicability when developing prior distributions mainly from reliability predictions.

Al Hassan, Mohammad↗

NASA NTRS2015

Improving AIRS Radiance Spectra in High Contrast Scenes Using MODIS

The Atmospheric Infrared Sounder (AIRS) on the EOS Aqua Spacecraft was launched on May 4, 2002. AIRS acquires hyperspectral infrared radiances in 2378 channels ranging in wavelength from 3.7-15.4 microns with spectral resolution of better than 1200, and spatial resolution of 13.5 km with global daily coverage. The AIRS is designed to measure temperature and water vapor profiles for improvement in weather forecast accuracy and improved understanding of climate processes. As with most instruments, the AIRS Point Spread Functions (PSFs) are not the same for all detectors. When viewing a non-uniform scene, this causes a significant radiometric error in some channels that is scene dependent and cannot be removed without knowledge of the underlying scene. The magnitude of the error depends on the combination of non-uniformity of the AIRS spatial response for a given channel and the non-uniformity of the scene, but is typically only noticeable in about 1% of the scenes and about 10% of the channels. The current solution is to avoid those channels when performing geophysical retrievals. In this effort we use data from the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument to provide information on the scene uniformity that is used to correct the AIRS data. For the vast majority of channels and footprints the technique works extremely well when compared to a Principal Component (PC) reconstruction of the AIRS channels. In some cases where the scene has high inhomogeneity in an irregular pattern, and in some channels, the method can actually degrade the spectrum. Most of the degraded channels appear to be slightly affected by random noise introduced in the process, but those with larger degradation may be affected by alignment errors in the AIRS relative to MODIS or uncertainties in the PSF. Despite these errors, the methodology shows the ability to correct AIRS radiances in non-uniform scenes under some of the worst case conditions and improves the ability to match AIRS and MODIS radiances in non-uniform scenes.

spatial↗

NASA NTRS2016

Taxi-Out Time Prediction for Departures at Charlotte Airport Using Machine Learning Techniques

Predicting the taxi-out times of departures accurately is important for improving airport efficiency and takeoff time predictability. In this paper, we attempt to apply machine learning techniques to actual traffic data at Charlotte Douglas International Airport for taxi-out time prediction. To find the key factors affecting aircraft taxi times, surface surveillance data is first analyzed. From this data analysis, several variables, including terminal concourse, spot, runway, departure fix and weight class, are selected for taxi time prediction. Then, various machine learning methods such as linear regression, support vector machines, k-nearest neighbors, random forest, and neural networks model are applied to actual flight data. Different traffic flow and weather conditions at Charlotte airport are also taken into account for more accurate prediction. The taxi-out time prediction results show that linear regression and random forest techniques can provide the most accurate prediction in terms of root-mean-square errors. We also discuss the operational complexity and uncertainties that make it difficult to predict the taxi times accurately.

Safe and efficient surface operations↗

NASA NTRS2005

Robust Control Design for Systems With Probabilistic Uncertainty

This paper presents a reliability- and robustness-based formulation for robust control synthesis for systems with probabilistic uncertainty. In a reliability-based formulation, the probability of violating design requirements prescribed by inequality constraints is minimized. In a robustness-based formulation, a metric which measures the tendency of a random variable/process to cluster close to a target scalar/function is minimized. A multi-objective optimization procedure, which combines stability and performance requirements in time and frequency domains, is used to search for robustly optimal compensators. Some of the fundamental differences between the proposed strategy and conventional robust control methods are: (i) unnecessary conservatism is eliminated since there is not need for convex supports, (ii) the most likely plants are favored during synthesis allowing for probabilistic robust optimality, (iii) the tradeoff between robust stability and robust performance can be explored numerically, (iv) the uncertainty set is closely related to parameters with clear physical meaning, and (v) compensators with improved robust characteristics for a given control structure can be synthesized.

Crespo, Luis G.↗

NASA NTRS1979

Carbon monoxide measurement in the global atmospheric sampling program

The carbon monoxide measurement system used in the NASA Global Atmospheric Sampling Program (GASP) is described. The system used a modified version of a commercially available infrared absorption analyzer. The modifications increased the sensitivity of the analyzer to 1 ppmv full scale, with a limit of detectability of 0.02 ppmv. Packaging was modified for automatic, unattended operation in an aircraft environment. The GASP system is described along with analyzer operation, calibration procedures, and measurement errors. Uncertainty of the CO measurement over a 2-year period ranged from + or - 3 to + or - 13 percent of reading, plus an error due to random fluctuation of the output signal + or - 3 to + or - 15 ppbv.

Dudzinski, T. J.↗

NASA NTRS1979

Water vapor differential absorption lidar development and evaluation

A ground-based differential absorption lidar (DIAL) system is described which has been developed for vertical range-resolved measurements of water vapor. The laser transmitter consists of a ruby-pumped dye laser, which is operated on a water vapor absorption line at 724.372 nm. Part of the ruby laser output is transmitted simultaneously with the dye laser output to determine atmospheric scattering and attenuation characteristics. The dye and ruby laser backscattered light is collected by a 0.5-m diam telescope, optically separated in the receiver package, and independently detected using photomultiplier tubes. Measurements of vertical water vapor concentration profiles using the DIAL system at night are discussed, and comparisons are made between the water vapor DIAL measurements and data obtained from locally launched rawinsondes. Agreement between these measurements was found to be within the uncertainty of the rawinsonde data to an altitude of 3 km. Theoretical simulations of this measurement were found to give reasonably accurate predictions of the random error of the DIAL measurements. Confidence in these calculations will permit the design of aircraft and Shuttle DIAL systems and experiments using simulation results as the basis for defining lidar system performance requirements

Browell, E. V.↗

NASA NTRS1991

Collisional cascading - The limits of population growth in low earth orbit

Random collisions between made-made objects in earth orbit will lead to a significant source of orbital debris, but there are a number of uncertainties in these models, and additional analysis and data are required to fully characterize the future environment. However, the nature of these uncertainties are such that while the future environment is uncertain, the fact that collisions will control the future environment is less uncertain. The data that already exist is sufficient to show that cascading collisions will control the future debris environment with no, or very minor increases in the current low-earth-orbit population. Two populations control this process: explosion fragments and expended rocket bodies and payloads. Practices are already changing to limit explosions in low earth orbit; it is necessary to begin limiting the number of expended rocket bodies and payloads in orbit.

Kessler, Donald J.↗

NASA NTRS2002

Eulerian Mapping Closure Approach for Probability Density Function of Concentration in Shear Flows

The Eulerian mapping closure approach is developed for uncertainty propagation in computational fluid mechanics. The approach is used to study the Probability Density Function (PDF) for the concentration of species advected by a random shear flow. An analytical argument shows that fluctuation of the concentration field at one point in space is non-Gaussian and exhibits stretched exponential form. An Eulerian mapping approach provides an appropriate approximation to both convection and diffusion terms and leads to a closed mapping equation. The results obtained describe the evolution of the initial Gaussian field, which is in agreement with direct numerical simulations.

He, Guowei↗

NASA NTRSDate not supplied

Adding GPU Support to the Markov Chain Monte Carlo Code Catmip

In geophysics, we are confronted with many under-determined inverse problems. For example, all of our observations of earthquakes are made at the Earth’s surface. So, when we try to infer how slip during an earthquake evolves in space and time, we find that there are many potential slip histories that are consistent with our limited observations and our understanding of earthquake physics. One way to approach these problems is with Bayesian analysis which allows us to infer the ensemble of all potential slip models that satisfy the observations and our prior knowledge of earthquake physics. In Bayesian analysis, our prior knowledge is known as the prior probability density function or prior PDF, the fit to the data is known as the data likelihood, and the target PDF that satisfies both the prior PDF and data likelihood is known as the posterior PDF. However, simulating the posterior PDF typically requires using Markov Chain Monte Carlo (MCMC) to draw tens of billions of random realizations of earthquake slip models, which may not be computationally feasible. To make this and similar geophysical inversions computationally tractable, we developed the Cascading Adaptive Transitional Metropolis In Parallel (CATMIP) algorithm. CATMIP is an efficient parallel Markov Chain Monte Carlo (MCMC) sampler that is used for model fitting and uncertainty quantification in geophysics. Example use cases are earthquake rupture modeling, determining mineral composition on Mars, reconstructing the history of ocean salinity, and historical earthquake relocation. CATMIP employs many parallel instances of the Metropolis algorithm for sampling in a transitioning framework. Transitioning is a process in which a set of random samples at equilibrium with a known probability density function (PDF) are used as seeds for the Markov chains to sample successive target PDFs that incrementally move the distribution from the starting seeds to the final desired PDF that describes the relative plausibility of potential values for the model parameters. The algorithm is implemented as a Master-Worker model employing MPI for communication. The worker processes are loosely coupled with global parameters periodically optimized by the master process. This provides a very high amount of parallelism with little communication between updates. During the presentation we will discuss the history of the algorithm and elaborate the earthquake rupture modeling use case for the CATMIP package. Our first step toward GPU optimization was to optimize the code for the CPU. CPU profiling revealed that most of the compute time is spent in calls to level 2 BLAS routines and calls to GSL random number generators. We revised the algorithm to employ level 3 BLAS routines instead. In our presentation we will describe how this was accomplished. Adding GPU support to CATMIP consisted mostly of replacing the calls to GSL with calls to GPU vendor-provided library routines. A small number of loops were directly implemented in CUDA. In the presentation will provide implementation details. Finally, we will discuss methods for profiling and opportunities for further optimizing GPU execution. By creating a code with the flexibility to run on either a CPU or GPU architecture, CATMIP can be used on systems ranging from large CPU-based HPC environments to single servers with GPU acceleration and everything in between.

HECC↗

NASA NTRS1989

Review of probabilistic analysis of dynamic response of systems with random parameters

The various methods that have been studied in the past to allow probabilistic analysis of dynamic response for systems with random parameters are reviewed. Dynamic response may have been obtained deterministically if the variations about the nominal values were small; however, for space structures which require precise pointing, the variations about the nominal values of the structural details and of the environmental conditions are too large to be considered as negligible. These uncertainties are accounted for in terms of probability distributions about their nominal values. The quantities of concern for describing the response of the structure includes displacements, velocities, and the distributions of natural frequencies. The exact statistical characterization of the response would yield joint probability distributions for the response variables. Since the random quantities will appear as coefficients, determining the exact distributions will be difficult at best. Thus, certain approximations will have to be made. A number of techniques that are available are discussed, even in the nonlinear case. The methods that are described were: (1) Liouville's equation; (2) perturbation methods; (3) mean square approximate systems; and (4) nonlinear systems with approximation by linear systems.

Kozin, F.↗

NASA NTRS2023

Real Options Analysis for Valuation of Climate Adaptation Pathways With Application to Transit Infrastructure

Climate change and sea level rise (SLR) are expected to increase the frequency and intensity of coastal flood events, posing risks to coastal communities and infrastructure. While regional climate adaptation investments can provide substantive flood protection, existing plans often neglect uncertainty in future climate conditions and adaptation performance, consequently neglecting the option value of flexibly implementing proposed projects. Addressing this gap, we develop and employ a generalizable real options analysis (ROA) valuation framework that considers how uncertainty in adaptation project costs, SLR, flood severity, and flood losses inform the full range of adaptation performance outcomes. We further propose and apply a novel, computationally efficient flood loss sampling algorithm to estimate the consequences of randomly arriving coastal flood events. We apply this ROA framework to assess the option value of flexibly timing adaptation investments over time, investigating an adaptation pathway proposed by the City of Boston from the perspective of the regional transit system manager. Our results suggest that flexible implementation can provide significant option value in the near-to mid-term(>30 years), with highest option values under low-probability, high consequence scenarios. Our results also suggest adaptation pathway performance in the latter half of the 21stcenturyis most sensitive to uncertainty in sea level rise, flood loss estimates, and flood frequency, underscoring the importance of uncertainty quantification in the long-term valuation of adaptation investments.

Michael V. Martello↗

NASA NTRSDate not supplied

Use of three-cornered hat error estimates in MERRA-2 to guide an improved reanalysis-Part 1

The three-cornered hat (3CH) method estimates the uncertainties of three different co-located model or observational data sets (Anthes and Rieckh, 2018; Sjoberg et al., 2021). Rieckh et al. (2021) used the 3CH method to compare the random error statistics of different global forecast and reanalysis models, as well as radio occultation (RO) and radiosonde observations. That study showed that the MERRA-2 reanalysis, while having smaller errors in the stratosphere than its predecessor MERRA, had larger errors in the troposphere than many of the other data sets analyzed. The MERRA-2 errors were particularly large in the tropics. In a collaborative effort between UCAR’s COSMIC (Constellation Observing System for Meteorology, Ionosphere and Meteorology) program and NASA’s Global Modeling and Assimilation Office (GMAO), we carried out further 3CH error diagnostics to help isolate the causes of these larger errors and help guide the development of an improved reanalysis. This presentation summarizes random error statistics associated with MERRA-2, ECMWF’s ERA5 reanalysis, and COSMIC-2 (C2) RO observations. We compute 3CH error variance estimates of refractivity, as well as temperature and specific humidity using UCAR’s COSMIC Data Analysis and Archive Center (CDAAC) improved 1D-variational (1D-Var) retrieval (wetPf2) over 15 latitude bands from 45S to 45N. The 1D-Var retrievals of specific humidity and temperature for C2 use NCEP’s Global Forecast System (GFS) as the background. Anthes et al. (2021) showed that it gives accurate estimates of temperature and specific humidity in the tropics and subtropics, even in the challenging environment of intense Hurricane Dorian (2019). This presentation confirms the previous results that MERRA-2 has significantly larger errors in the tropics and subtropics than either C2 or ERA5. Its errors are larger between 30S and 30N compared to 30-45 N-S latitudes, and are also larger over land compared to oceans. Most of the MERRA-2 refractivity errors come from specific humidity, except over land below 3 km where temperature errors are large. These results suggest that moist convection and atmospheric boundary layer physics in MERRA-2 may be responsible for a significant part of the higher uncertainties. These results are being used to guide GMAO in developing an improved next-generation reanalysis, as shown in a companion presentation submitted to this conference (El Akkraoui et al., 2021), which extends this study and describes improvements to MERRA-2 leading to the next GMAO reanalysis.

Jeremiah Sjoberg↗