Engineering PapersSearch

SEARCH · Engineering Papers

Results for “Probability Distribution Function”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3

A generative artificial intelligence framework for long-time plasma turbulence simulations

Generative deep learning techniques are employed in a novel framework for the construction of surrogate models capturing the spatiotemporal dynamics of 2D plasma turbulence. The proposed Generative Artificial Intelligence Turbulence (GAIT) framework enables the acceleration of turbulence simulations for long-time transport studies. GAIT leverages a convolutional variational auto-encoder and a recurrent neural network to generate new turbulence data from existing simulations, extending the time horizon of transport studies with minimal computational cost. The application of the GAIT framework to plasma turbulence using the Hasegawa–Wakatani (HW) model is presented, evaluating its performance via various analyses. Very good agreement is found between the GAIT and the HW models in the spatiotemporal Fourier and Proper Orthogonal Decomposition spectra, the flow topology characterized by the Okubo–Weiss parameter, and the time autocorrelation function of turbulent fluctuations. Excellent agreement has also been obtained in the probability distribution function of particle displacements and the effective turbulent diffusivity. In-depth analyses of the latent space of turbulent states, choice of hyperparameters and alternative deep learning models for the time prediction are presented. Our results highlight the potential of Artificial Intelligence-based surrogate models to overcome the computational challenges in turbulence simulation, which can be extended to other situations such as geophysical fluid dynamics.

Artificial intelligence

The Solar Wind and Geomagnetic Activity as a Function of Time Relative to Corotating Interaction Regions

Corotating interaction regions during the declining phase of the solar cycle are the cause of recurrent geomagnetic storms and are responsible for the generation of high fluxes of relativistic electrons. These regions are produced by the collision of a high-speed stream of solar wind with a slow-speed stream. The interface between the two streams is easily identified with plasma and field data from a solar wind monitor upstream of the Earth. The properties of the solar wind and interplanetary magnetic field are systematic functions of time relative to the stream interface. Consequently the coupling of the solar wind to the Earth's magnetosphere produces a predictable sequence of events. Because the streams persist for many solar rotations it should be possible to use terrestrial observations of past magnetic activity to predict future activity. Also the high-speed streams are produced by large unipolar magnetic regions on the Sun so that empirical models can be used to predict the velocity profile of a stream expected at the Earth. In either case knowledge of the statistical properties of the solar wind and geomagnetic activity as a function of time relative to a stream interface provides the basis for medium term forecasting of geomagnetic activity. In this report we use lists of stream interfaces identified in solar wind data during the years 1995 and 2004 to develop probability distribution functions for a variety of different variables as a function of time relative to the interface. The results are presented as temporal profiles of the quartiles of the cumulative probability distributions of these variables. We demonstrate that the storms produced by these interaction regions are generally very weak. Despite this the fluxes of relativistic electrons produced during those storms are the highest seen in the solar cycle. We attribute this to the specific sequence of events produced by the organization of the solar wind relative to the stream interfaces. We also show that there are large quantitative differences in various parameters between the two cycles.

McPherron, Robert L.

Space Radiation Risk Assessment for Future Lunar Missions

For lunar exploration mission design, radiation risk assessments require the understanding of future space radiation environments in support of resource management decisions, operational planning, and a go/no-go decision. The future GCR flux was estimated as a function of interplanetary deceleration potential, which was coupled with the estimated neutron monitor rate from the Climax monitor using a statistical model. A probability distribution function for solar particle event (SPE) occurrence was formed from proton fluence measurements of SPEs occurred during the past 5 solar cycles (19-23). Large proton SPEs identified from impulsive nitrate enhancements in polar ice for which the fluences are greater than 2 10(exp 9) protons/sq cm for energies greater than 30 MeV, were also combined to extend the probability calculation for high level of proton fluences. The probability with which any given proton fluence level of a SPE will be exceeded during a space mission of defined duration was then calculated. Analytic energy spectra of SPEs at different ranks of the integral fluences were constructed over broad energy ranges extending out to GeV, and representative exposure levels were analyzed at those fluences. For the development of an integrated strategy for radiation protection on lunar exploration missions, effective doses at various points inside a spacecraft were calculated with detailed geometry models representing proposed transfer vehicle and habitat concepts. Preliminary radiation risk assessments from SPE and GCR were compared for various configuration concepts of radiation shelter in exploratory-class spacecrafts.

Kim, Myung-Hee Y.

The Impacts of an Observationally-Based Cloud Fraction and Condensate Overlap Parameterization on a GCM's Cloud Radiative Effect

It has been shown that the details of how cloud fraction overlap is treated in GCMs has substantial impact on shortwave and longwave fluxes. Because cloud condensate is also horizontally heterogeneous at GCM grid scales, another aspect of cloud overlap should in principle also be assessed, namely the vertical overlap of hydrometeor distributions. This type of overlap is usually examined in terms of rank correlations, i.e., linear correlations between hydrometeor amount ranks of the overlapping parts of cloud layers at specific separation distances. The cloud fraction overlap parameter and the rank correlation of hydrometeor amounts can be both expressed as inverse exponential functions of separation distance characterized by their respective decorrelation lengths (e-folding distances). Larger decorrelation lengths mean that hydrometeor fractions and probability distribution functions have high levels of vertical alignment. An analysis of CloudSat and CALIPSO data reveals that the two aspects of cloud overlap are related and their respective decorrelation lengths have a distinct dependence on latitude that can be parameterized and included in a GCM. In our presentation we will contrast the Cloud Radiative Effect (CRE) of the GEOS-5 atmospheric GCM (AGCM) when the observationally-based parameterization of decorrelation lengths is used to represent overlap versus the simpler cases of maximum-random overlap and globally constant decorrelation lengths. The effects of specific overlap representations will be examined for both diagnostic and interactive radiation runs in GEOS-5 and comparisons will be made with observed CREs from CERES and CloudSat (2B-FLXHR product). Since the radiative effects of overlap depend on the cloud property distributions of the AGCM, the availability of two different cloud schemes in GEOS-5 will give us the opportunity to assess a wide range of potential cloud overlap consequences on the model's climate.

Oreopoulos, Lazaros

Inter-Calibrating the CERES SW Instrument Fluxes Using Deep Convective Clouds(DCC) Within the Same Sun-Synchronous Orbit

The NASA CERES EBAF product provides the scientific community observed TOA fluxes to monitor the Earth’s energy imbalance and to validate climate models. To provide a seamless EBAF 24-year record, the CERES instrument calibration must be stable and consistent across satellite records. Once the Terra and Aqua spacecraft are decommissioned at the end of 2025, the CERES project will rely on CERES instrument observations on the SNPP and NOAA-20 1:30 PM sun-synchronous orbits. The SNPP and NOAA-20 satellite orbit placement will prevent any time matched observations for inter-calibration efforts. The future Libera instrument, which will continue the CERES record and scheduled for launch in 2028 onboard the NOAA-22 satellite, will also need to be inter-calibrated without the aid of time-matched observations. Deep convective clouds (DCC) are the most Lambertian, brightest, tropical Earth invariant targets located at the tropopause making them ideal to radiometrically scale the CERES SW observed radiance to a common reference. The SNPP, NOAA-20 and future NOAA-22 satellites are in the same 16-day repeatable orbits, allowing the DCC targets to be observed with the same angular configuration. The empirically derived SNPP CERES SW channel Bidirectional Reflectance Distribution Function (BRDF) can be easily be applied to the NOAA-20 CERES SW channel radiances since they observe the nearly the same DCC systems. The DCC BRDF corrected radiances are analyzed collectively into radiance probability distribution functions (PDF). By comparing the PDF statistics, the SNPP and NOAA-20 CERES SW channel can be inter-calibrated. The inter-calibration coefficients are validated with the CERES instrument calibration team coefficients to optimize the methodology.

David Doelling

Observation of Kolmogorov turbulence due to multiscale vortices in dusty plasma experiments

We report the experimental observation of fully developed Kolmogorov turbulence originating from self-excited vortex flows in a three-dimensional (3D) dust cloud. The characteristic -5/3 scaling of 3D Kolmogorov turbulence is consistent in both the spatial and temporal energy spectra within a statistical variation of experimental data. Additionally, the 2/3 scaling in the second-order structure function further supports the presence of Kolmogorov turbulence. We also identified a slight deviation in the tails of the probability distribution functions for velocity gradients, a reflection of intermittency. The experiment showed the formation of a dust cloud in the diffused plasma region away from the electrodes. The dust rotation was observed in multiple experimental campaigns under different discharge conditions at different spatial locations and background plasma environments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Determination of a Limited Scope Network's Lightning Detection Efficiency

This paper outlines a modeling technique to map lightning detection efficiency variations over a region surveyed by a sparse array of ground based detectors. A reliable flash peak current distribution (PCD) for the region serves as the technique's base. This distribution is recast as an event probability distribution function. The technique then uses the PCD together with information regarding: site signal detection thresholds, type of solution algorithm used, and range attenuation; to formulate the probability that a flash at a specified location will yield a solution. Applying this technique to the full region produces detection efficiency contour maps specific to the parameters employed. These contours facilitate a comparative analysis of each parameter's effect on the network's detection efficiency. In an alternate application, this modeling technique gives an estimate of the number, strength, and distribution of events going undetected. This approach leads to a variety of event density contour maps. This application is also illustrated. The technique's base PCD can be empirical or analytical. A process for formulating an empirical PCD specific to the region and network being studied is presented. A new method for producing an analytical representation of the empirical PCD is also introduced.

Rompala, John T.

Extinction-to-Backscatter Ratios of Lofted Aerosol Layers Observed During the First Three Months of CALIPSO Measurements

Case studies from the first three months of the Cloud and Aerosol Lidar and Infrared Pathfinder Spaceborne Observations (CALIPSO) measurements of lofted aerosol layers are analyzed using transmittance [Young, 1995] and two-wavelength algorithms [Vaughan et al., 2004] to determine the aerosol extinction-to-backscatter ratios at 532 and 1064 nm. The transmittance method requires clear air below the layer so that the transmittance through the layer can be determined. Suitable scenes are selected from the browse images and clear air below features is identified by low 532 nm backscatter signal and confirmed by low depolarization and color ratios. The transmittance and two-wavelength techniques are applied to a number of lofted layers and the extinction-to-backscatter ratios are compared with values obtained from the CALIPSO aerosol models [Omar et al., 2004]. The results obtained from these studies are used to adjust the aerosol models and develop observations based extinction-to-backscatter ratio look-up tables and phase functions. Values obtained by these techniques are compared to Sa determinations using other independent methods with a goal of developing probability distribution functions of aerosol type-specific extinction to backscatter ratios. In particular, the results are compared to values determined directly by the High Spectral Resolution Lidar (HSRL) during the CALIPSO CloudSat Validation Experiments (CCVEX) and Sa determined by the application of the two-wavelength lidar Constrained Ratio Aerosol Model-fit (CRAM) retrieval approach [Cattrall et al., 2005; Reagan et al., 2004] to the HSRL data. The results are also compared to values derived using the empirical relationship between the multiple-scattering fraction and the linear depolarization ratio by using Monte Carlo simulations of water clouds [Hu et al., 2006].

Omar, Ali H.

Evolution of in-medium baryon-baryon scattering cross sections and stiffness of dense nuclear matter from Bayesian analyses of FOPI proton-flow excitation functions

Within a Bayesian statistical framework using a Gaussian process (GP) emulator for an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model simulator of heavy-ion reactions with momentum-independent Skyrme interactions, we infer from the proton directed and elliptical flow in mid-central Au + Au reactions, measured at beam energies from 150 to 1200 MeV/nucleon by the FOPI Collaboration, the posterior probability distribution functions (PDFs) of the in-medium baryon-baryon scattering cross section (BBSCS) modification factor 𝑋 (with respect to their free-space values) and the stiffness parameter 𝐾 of dense nuclear matter. Here, we find that the most probable value of 𝑋 evolves from around 0.7 to 1.0 as the beam energy 𝐸 beam /𝐴 increases. On the other hand, the posterior PDF⁡(𝐾) may have dual peaks having roughly the same height or extended shoulders at high 𝐾 values. More quantitatively, the posterior PDF⁡(𝐾) changes from having a major peak around 220 MeV, characterizing a soft EOS in the reaction at 𝐸 beam /𝐴 = 150 MeV, to one that peaks around 320 MeV, indicating a stiff EOS in the reactions at 𝐸 beam /𝐴 higher than about 600 MeV. The transition from soft to stiff happens in mid-central Au + Au reactions at beam energies around 250 MeV/nucleon in which 𝐾 = 220 MeV and 𝐾 = 320 MeV are approximately equally probable. Altogether, the FOPI proton-flow excitation function data indicate a gradual hardening of hot and dense nuclear matter as its density and temperature increase in reactions with higher beam energies.

nuclear matter

Toward the Probabilistic Forecasting of High-latitude GPS Phase Scintillation

The phase scintillation index was obtained from L1 GPS data collected with the Canadian High Arctic Ionospheric Network (CHAIN) during years of extended solar minimum 2008-2010. Phase scintillation occurs predominantly on the dayside in the cusp and in the nightside auroral oval. We set forth a probabilistic forecast method of phase scintillation in the cusp based on the arrival time of either solar wind corotating interaction regions (CIRs) or interplanetary coronal mass ejections (ICMEs). CIRs on the leading edge of high-speed streams (HSS) from coronal holes are known to cause recurrent geomagnetic and ionospheric disturbances that can be forecast one or several solar rotations in advance. Superposed epoch analysis of phase scintillation occurrence showed a sharp increase in scintillation occurrence just after the arrival of high-speed solar wind and a peak associated with weak to moderate CMEs during the solar minimum. Cumulative probability distribution functions for the phase scintillation occurrence in the cusp are obtained from statistical data for days before and after CIR and ICME arrivals. The probability curves are also specified for low and high (below and above median) values of various solar wind plasma parameters. The initial results are used to demonstrate a forecasting technique on two example periods of CIRs and ICMEs.

scintillation

A Probabilistic Wake Vortex Lateral Transport Model Using Data from SFO and DEN

In a previous report, we considered the behavior of the lateral position of vortices as a function of time after vortex formation for Out of Ground Effects (OGE) data for aircraft landing at San Francisco International Airport (SFO). We quantified the spread in lateral position as a function of time and examined how predictable lateral position is under a variety of assumptions. The combination of spread and predictability allowed us to derive probability distribution functions (PDFs) for lateral position given observed crosswind (CW) velocities. In this study, we examine the portability of these PDFs with respect to other landing sites. To this end, we consider OGE data obtained by the Federal Aviation Administration for landings at Denver International Airport (DEN) between 04/05/2006 and 06/03/2006. We consider vortices from both B733 (Boeing 737 models 200-500) and B757 (Boeing 757) aircraft. The data set contains 635 B733 landings and 506 B757 landings. The glide slope altitude for these measurements was 280 m, determined by the average initial vortex observation adjusted for a 3-second delay in the initial observation. The comparable SFO altitude was 158 m. We note that the principal mechanism for lateral transport in the OGE regime is advection by the ambient wind. This implies that a simple crosswind correction may be effective in explaining much of the variation in the lateral transport data. In this study, we again consider the use of ASOS data and average Lidar crosswind data over the vortex altitude range to predict vortex location as a function of time.

Mellman, George R.

Seismic Event Characterization Using Full Moment Tensors on the Hypersphere

Moment tensor solutions provide insights into the deformation that has occurred in the source region of a seismic event and are therefore of great value in identifying different types of seismic sources, such as when monitoring for underground nuclear tests. Despite this utility, inversion of waveforms recorded by seismometers for their full seismic moment tensor is not yet routine, and development of robust methods to classify events based on this information is in its infancy. Here, we assemble an inventory of 1405 full moment tensor solutions that include explosive, earthquake, and collapse events, and investigate the use of anisotropic probability distribution functions on the 5D hypersphere to discriminate between these sources. Using a Bayesian classifier, we obtain optimal success rates of 98.4% across all events and demonstrate that modification of the prior probabilities provides a natural way to alter the balance between not missing desirable events (such as explosions) versus misclassifying large numbers of undesired events (such as earthquakes). The approach is specifically designed to progress from traditional, bipolar event screening metrics to more generalized event identification across multiple types of seismic sources. Despite current databases containing insufficient numbers of events to definitively demonstrate at present, we also find intriguing evidence of subgroupings within individual source populations on the hypersphere, for example, between chemical and nuclear explosions, raising the potential possibility of discriminating between these event types in the future.

Geosciences

Distributed errors in orbit transfer.

Probability distribution errors effect in linear and planar impulse orbital transfers, considering angular orientation and impulsive velocity

IMPULSE ORBITAL TRANSFER

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.

Wear-Out Sensitivity Analysis Project Abstract

During the course of the Summer 2015 internship session, I worked in the Reliability and Maintainability group of the ISS Safety and Mission Assurance department. My project was a statistical analysis of how sensitive ORU's (Orbital Replacement Units) are to a reliability parameter called the wear-out characteristic. The intended goal of this was to determine a worst case scenario of how many spares would be needed if multiple systems started exhibiting wear-out characteristics simultaneously. The goal was also to determine which parts would be most likely to do so. In order to do this, my duties were to take historical data of operational times and failure times of these ORU's and use them to build predictive models of failure using probability distribution functions, mainly the Weibull distribution. Then, I ran Monte Carlo Simulations to see how an entire population of these components would perform. From here, my final duty was to vary the wear-out characteristic from the intrinsic value, to extremely high wear-out values and determine how much the probability of sufficiency of the population would shift. This was done for around 30 different ORU populations on board the ISS.

Harris, Adam

Mountain-Top-to-Mountain-Top Optical Link Demonstration

A mountain-top-to-mountain-top optical link was demonstrated between JPL's Table Mountain Facility (TMF), Wrightwood, California, and Strawberry Peak (SP), Lake Arrowhead, California, during the months of June, August, and September of 2000. The bidirectional laser link was nearly horizontal at an altitude of 2 km and spanned a range of 46.8 km. The 780-nm beacon laser transmitted from TMF comprised eight co-propagating mutually incoherent laser beams. The normalized variance or scintillation index (SI) of the individual beacon lasers measured by recording the signal received through 8.50-cm-diameter spotting telescopes on three different nights (June 28-30, 2000) was 1.05 +/- 0.2, 1.76 +/- 0.6, and 0.96 +/- 0.24, respectively. These measurements agreed with values predicted by a heuristic model. The SI of the signal received at SP was found to decrease progressively with an increasing number of beams, and a factor of 3 to 3.5 reduction was achieved for all eight beams. The beam divergence determined by mapping out the point spread function of a few of the individual laser footprints received at SP was 85 to 150 microrad, compared to a design goal of 120 microrad. The 852-nm communications laser beam received at TMF through a 60-cm-diameter telescope on the nights of August 4 and September 14 and 15, 2000, yielded SI values of 0.23 +/- 0.04, 0.32 +/- 0.01, and 0.49 +/- 0.18, respectively, where the reduction was attributed to aperture averaging. The probability distribution functions of the received signal at either end, mitigated by multi-beam averaging in one direction and by aperture averaging in the other direction, displayed lognormal behavior. Consequently, the measured fade statistics showed good agreement with a lognormal model.

Biswas, A.

Probabilistic simulation of long term behavior in polymer matrix composites

A methodology to compute cumulative probability distribution functions (CDF) of fatigue life for different ratios, r of applied stress to the laminate strength based on first ply failure criteria has been developed and demonstrated. Degradation effects due to long term environmental exposure and mechanical cyclic loads are considered in the simulation process. A unified time-stress dependent multi-factor interaction equation model developed at NASA Lewis Research Center has been used to account for the degradation/aging of material properties due to cyclic loads. Fast probability integration method is used to perform probabilistic simulation of uncertainties. Sensitivity of fatigue life reliability to uncertainties in the primitive random variables are computed and their significance in the reliability based design for maximum life is discussed. The results show that the graphite/epoxy (0/+45/90) deg laminate with ply thickness 0.125 in. has 500,000 cycles life for applied stress to laminate strength ratio of 0.6 and a reliability of 0.999. Also, the fatigue life reliability has been found to be most sensitive to the ply thickness and matrix tensile strength. Tighter quality controls must therefore be enforced on ply thickness and matrix strength in order to achieve high reliability of the structure.

Shah, A. R.

Statistical Perspectives on Stratospheric Transport

Long-lived tropospheric source gases, such as nitrous oxide, enter the stratosphere through the tropical tropopause, are transported throughout the stratosphere by the Brewer-Dobson circulation, and are photochemically destroyed in the upper stratosphere. These chemical constituents, or "tracers" can be used to track mixing and transport by the stratospheric winds. Much of our understanding about the stratospheric circulation is based on large scale gradients and other spatial features in tracer fields constructed from satellite measurements. The point of view presented in this paper is different, but complementary, in that transport is described in terms of tracer probability distribution functions (PDFs). The PDF is computed from the measurements, and is proportional to the area occupied by tracer values in a given range. The flavor of this paper is tutorial, and the ideas are illustrated with several examples of transport-related phenomena, annotated with remarks that summarize the main point or suggest new directions. One example shows how the multimodal shape of the PDF gives information about the different branches of the circulation. Another example shows how the statistics of fluctuations from the most probable tracer value give insight into mixing between different regions of the atmosphere. Also included is an analysis of the time-dependence of the PDF during the onset and decline of the winter circulation, and a study of how "bursts" in the circulation are reflected in transient periods of rapid evolution of the PDF. The dependence of the statistics on location and time are also shown to be important for practical problems related to statistical robustness and satellite sampling. The examples illustrate how physically-based statistical analysis can shed some light on aspects of stratospheric transport that may not be obvious or quantifiable with other types of analyses. An important motivation for the work presented here is the need for synthesis of the large and growing database of observations of the atmosphere and the vast quantities of output generated by atmospheric models.

Sparling, L. C.