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Disturbance Dynamics in Transitional and Turbulent Flows

In order to expand the predictive capability of single-point turbulence closure models to account for the early-stage transition regime, a methodology for the formulation and calibration of model equations for the ensemble-averaged disturbance kinetic energy and energy dissipation rate is presented. First the decay of laminar disturbances and turbulence in mean shear-free flows is studied. In laminar flows, such disturbances are linear superpositions of modes governed by the Orr-Sommerfeld equation. In turbulent flows, disturbances are described through transport equations for representative mean quantities. The link between a description based on a deterministic evolution equation and a probability based mean transport equation is established. Because an uncertainty in initial conditions exists in the laminar as well as the turbulent regime, a probability distribution must be defined even in the laminar case. Using this probability distribution, it is shown that the exponential decay of the linear modes in the laminar regime can be related to a power law decay of both the (ensemble) mean disturbance kinetic energy and the dissipation rate. The evolution of these mean disturbance quantities is then described by transport equations similar to those for the corresponding turbulent decaying flow. Second, homogeneous shear flow, where disturbances can be described by rapid distortion theory (RDT), is studied. The relationship between RDT and linear stability theory is exploited in order to obtain a closed set of modeled equations. The linear disturbance equations are solved directly so that the numerical simulation yields a database from which the closure coefficients in the ensemble-averaged disturbance equations can be determined.

Grosch, Chester E.↗

Masses and Luminosities of X-Ray Binaries

Using SIM, we will perform narrow-angle observations of several X-ray binaries to determine their orbits, and we will observe about 50 X-ray binary systems in wide-angle mode to measure their distances and proper motions. Sources with mass estimates for the compact component of greater than 3 solar masses are generally called black hole candidates since this mass is above the theoretical neutron star limit. Narrow-angle observations of these sources provide a direct test of the dynamical mass estimates on which the black hole evidence is based. Better measurements of the black hole masses will provide constraints on possible evolutionary paths that lead to black hole formation. When combined with X-ray data, mass measurements may provide additional constraints on the black hole spin. Precise mass determinations of neutron star systems can address the question of whether neutron stars can be significantly more massive than 1.4 solar masses, which would eliminate soft models of the neutron star equations of state. The wide-angle observations will probe the Galactic distribution of X-ray binaries through parallaxes and proper motions. They will also eliminate the uncertainties in the luminosities of individual sources, which is currently up to a full order of magnitude. This will enable more detailed comparisons of X-ray observations to physical models such as advection-dominated accretion flows (ADAFs). We intend to carry out the following measurements: 1) Determine the orbits of two black hole candidates to measure the black hole masses; 2) Obtain precise mass measurements for two neutron star systems to constrain neutron star equations of state; 3) Determine the distances and thus luminosities of selected representatives of various classes of X-ray binaries (black hole candidates, neutron stars, jet sources); 4) In the process of distance determination, proper motions will also be measured, from which the age of the population can be estimated.

Quirrenbach, Andreas↗

Predicting the Earth encounters of (99942) Apophis

Arecibo delay-Doppler measurements of (99942) Apophis in 2005 and 2006 resulted in a five standard-deviation trajectory correction to the optically predicted close approach distance to Earth in 2029. The radar measurements reduced the volume of the statistical uncertainty region entering the encounter to 7.3% of the pre-radar solution, but increased the trajectory uncertainty growth rate across the encounter by 800% due to the closer predicted approach to the Earth. A small estimated Earth impact probability remained for 2036. With standard-deviation plane-of-sky position uncertainties for 2007-2010 already less than 0.2 arcsec, the best near-term ground-based optical astrometry can only weakly affect the trajectory estimate. While the potential for impact in 2036 will likely be excluded in 2013 (if not 2011) using ground-based optical measurements, approximations within the Standard Dynamical Model (SDM) used to estimate and predict the trajectory from the current era are sufficient to obscure the difference between a predicted impact and a miss in 2036 by altering the dynamics leading into the 2029 encounter. Normal impact probability assessments based on the SDM become problematic without knowledge of the object's physical properties; impact could be excluded while the actual dynamics still permit it. Calibrated position uncertainty intervals are developed to compensate for this by characterizing the minimum and maximum effect of physical parameters on the trajectory. Uncertainty in accelerations related to solar radiation can cause between 82 and 4720 Earth-radii of trajectory change relative to the SDM by 2036. If an actionable hazard exists, alteration by 2-10% of Apophis' total absorption of solar radiation in 2018 could be sufficient to produce a six standard-deviation trajectory change by 2036 given physical characterization; even a 0.5% change could produce a trajectory shift of one Earth-radius by 2036 for all possible spin-poles and likely masses. Planetary ephemeris uncertainties are the next greatest source of systematic error, causing up to 23 Earth-radii of uncertainty. The SDM Earth point-mass assumption introduces an additional 2.9 Earth-radii of prediction error by 2036. Unmodeled asteroid perturbations produce as much as 2.3 Earth-radii of error. We find no future small-body encounters likely to yield an Apophis mass determination prior to 2029. However, asteroid (144898) 2004 VD17, itself having a statistical Earth impact in 2102, will probably encounter Apophis at 6.7 lunar distances in 2034, their uncertainty regions coming as close as 1.6 lunar distances near the center of both SDM probability distributions.

Orbit determination↗

Simulation Studies for a Space-Based CO2 Lidar Mission

We report results of initial space mission simulation studies for a laser-based, atmospheric CO2 sounder, which are based on real-time carbon cycle process modelling and data analysis. The mission concept corresponds to the Active Sensing of CO2 Emissions over Nights, Days and Seasons (ASCENDS) recommended by the US National Academy of Sciences' Decadal Survey. As a pre-requisite for meaningful quantitative evaluation, we employ a CO2 model that has representative spatial and temporal gradients across a wide range of scales. In addition, a relatively complete description of the atmospheric and surface state is obtained from meteorological data assimilation and satellite measurements. We use radiative transfer calculations, an instrument model with representative errors and a simple retrieval approach to quantify errors in 'measured' CO2 distributions, which are a function of mission and instrument design specifications along with the atmospheric/surface state. Uncertainty estimates based on the current instrument design point indicate that a CO2 laser sounder can provide data consistent with ASCENDS requirements and will significantly enhance our ability to address carbon cycle science questions. Test of a dawn/dusk orbit deployment, however, shows that diurnal differences in CO2 column abundance, indicative of plant photosynthesis and respiration fluxes, will be difficult to detect

Kawa, S. R.↗

Trajectory-Based Loads for the Ares I-X Test Flight Vehicle

In trajectory-based loads, the structural engineer treats each point on the trajectory as a load case. Distributed aero, inertial, and propulsion forces are developed for the structural model which are equivalent to the integrated values of the trajectory model. Free-body diagrams are then used to solve for the internal forces, or loads, that keep the applied aero, inertial, and propulsion forces in dynamic equilibrium. There are several advantages to using trajectory-based loads. First, consistency is maintained between the integrated equilibrium equations of the trajectory analysis and the distributed equilibrium equations of the structural analysis. Second, the structural loads equations are tied to the uncertainty model for the trajectory systems analysis model. Atmosphere, aero, propulsion, mass property, and controls uncertainty models all feed into the dispersions that are generated for the trajectory systems analysis model. Changes in any of these input models will affect structural loads response. The trajectory systems model manages these inputs as well as the output from the structural model over thousands of dispersed cases. Large structural models with hundreds of thousands of degrees of freedom would execute too slowly to be an efficient part of several thousand system analyses. Trajectory-based loads provide a means for the structures discipline to be included in the integrated systems analysis. Successful applications of trajectory-based loads methods for the Ares I-X vehicle are covered in this paper. Preliminary design loads were based on 2000 trajectories using Monte Carlo dispersions. Range safety loads were tied to 8423 malfunction turn trajectories. In addition, active control system loads were based on 2000 preflight trajectories using Monte Carlo dispersions.

Vause, Roland F.↗

Multitemporal Cross-Calibration of the Terra MODIS and Landsat 7 ETM+ Reflective Solar Bands

In recent years, there has been a significant increase in the use of remotely sensed data to address global issues. With the open data policy, the data from the Moderate Resolution Imaging Spectroradiometer (MODIS) and Enhanced Thematic Mapper Plus (ETM+) sensors have become a critical component of numerous applications. These two sensors have been operational for more than a decade, providing a rich archive of multispectral imagery for analysis of mutitemporal remote sensing data. This paper focuses on evaluating the radiometric calibration agreement between MODIS and ETM+ using the near-simultaneous and cloud-free image pairs over an African pseudo-invariant calibration site, Libya 4. To account for the combined uncertainties in the top-of-atmosphere (TOA) reflectance due to surface and atmospheric bidirectional reflectance distribution function (BRDF), a semiempirical BRDF model was adopted to normalize the TOA reflectance to the same illumination and viewing geometry. In addition, the spectra from the Earth Observing-1 (EO-1) Hyperion were used to compute spectral corrections between the corresponding MODIS and ETM+ spectral bands. As EO-1 Hyperion scenes were not available for all MODIS and ETM+ data pairs, MODerate resolution atmospheric TRANsmission (MODTRAN) 5.0 simulations were also used to adjust for differences due to the presence or lack of absorption features in some of the bands. A MODIS split-window algorithm provides the atmospheric water vapor column abundance during the overpasses for the MODTRAN simulations. Additionally, the column atmospheric water vapor content during the overpass was retrieved using the MODIS precipitable water vapor product. After performing these adjustments, the radiometric cross-calibration of the two sensors was consistent to within 7%. Some drifts in the response of the bands are evident, with MODIS band 3 being the largest of about 6% over 10 years, a change that will be corrected in Collection 6 MODIS processing.

MODIS↗

Clearance Analysis of Node 3 Aft CBM to the Stowed FGB Solar Array

In early 2011, the ISS Vehicle Configuration Office began considering the relocation of the Permanent Multipurpose Module (PMM) to the aft facing Common Berthing Mechanism (CBM) on Node 3 to open a berthing location for visiting vehicles on the Node 1 nadir CBM. In this position, computer-aided design (CAD) models indicated that the aft end of the PMM would be only a few inches from the stowed Functional Cargo Block (FGB) port solar array. To validate the CAD model clearance analysis, in the late summer of 2011 the Image Science and Analysis Group (ISAG) was asked to determine the true geometric relationship between the on-orbit aft facing Node 3 CBM and the FGB port solar array. The desired measurements could be computed easily by photogrammetric analysis if current imagery of the ISS hardware were obtained. Beginning in the fall of 2011, ISAG used the Dynamic Onboard Ubiquitous Graphics (DOUG) program to design a way to acquire imagery of the aft face of Node 3, the aft end-cone of Node 1, the port side of pressurized mating adapter 1 (PMA1), and the port side of the FGB out to the tip of the port solar array using cameras on the Space Station Remote Manipulator System (SSRMS). This was complicated by the need to thread the SSRMS under the truss, past Node 3 and the Cupola, and into the space between the aft side of Node 3 and the FGB solar array to acquire more than 100 images from multiple positions. To minimize the number of SSRMS movements, the Special Purpose Dexterous Manipulator (SPDM) would be attached to the SSRMS. This would make it possible to park the SPDM in one position and acquire multiple images by changing the viewing orientation of the SPDM body cameras using the pan/tilt units on which the cameras are mounted. Using this implementation concept, ISAG identified four SSRMS/SPDM positions from which all of the needed imagery could be acquired. Based on a photogrammetric simulation, it was estimated that the location of the FGB solar array could be measured within an accuracy of about 1 in. in each axis relative to the ISS Analysis Coordinate System (ISSACS). In October 2011, a proposed image-acquisition plan was drafted by ISAG and released for review. The ISS Robotics flight control team (ROBO) proposed minor changes to SPDM positions 1 and 4 to meet ISS proximity requirements. The updated image acquisition plan and draft chit were presented to and approved by the Systems Working Group (SWG) November 18 and were sent to the Vehicle Configuration Board (VCB) in early December 2011. Working with ROBO on 3 successive days (February 21, 22, and 23), ISAG collected 161 images of the ISS. Approximately 40 images were collected from each of the four different SSRMS/SPDM positions, with each set mapping the region from the Node 3 end cone, across Node 1, along the forward port side portion of the FGB, and out the port side FGB solar arrays. From this imagery, the best 80 images were selected for use in the analysis. The images were radiometrically enhanced to improve color and contrast and loaded into the FotoG analysis software along with the camera parameters and control data, which consisted of the coordinates for 54 handrail attachment bolts on the aft face of Node 3, in the ISSACS coordinate system. The results of this analysis produced the measured coordinates of 116 points distributed across the face of the FGB solar array panels (see figure 3) along with propagated uncertainty estimates in each coordinate axis. These results were sent to the ISS Vehicle Configuration Office, which sent them to the Configuration Analysis Modeling and Mass Properties (CAMMP) team for comparison with the Russian-provided CAD model for the retracted FGB solar arrays. The CAMMP analysis unexpectedly showed that the measured location of the port FGB solar array was up to 41-in. further outboard than the design and was slightly twisted about its rotational axis. The unexpected comparison results produced some initial concern regarding the accuracy of the photogrammetric measurements. To verify the measured results, ISAG personnel conducted a second analysis using just the imagery of the solar arrays in an arbitrary coordinate system defined by the three corner points of the inboard-most panel, with the design distance between points A1 and A10 as the only scale. The new measurements agreed with the original results to within less than 1 in. RMS in each axis, confirming the original solar array measurements. ISAG produced a final report for the ISS Vehicle Configuration Office documenting an apparent anomaly in the retracted configuration of the port FGB solar arrays. A copy of the measurement report was translated and sent to the Russian Space Agency. During a Vehicle Integrated Performance and Resources (VIPeR) teleconference September 24, 2012, the Russians acknowledged receipt of a translated copy of the ISAG report. The Russian representative stated that the head of the solar array design team claimed that the measured configuration was impossible unless the structure was physically broken. The Russians acknowledged that they had no expertise in photogrammetry, so the analysis technique employed was a "black box" to them, and they did not know how to use the ISAG results. They asked for a single image in which the overextension of the port solar array could be obviously seen. On November 10, 2012, during a face-to-face meeting with their Russian counterparts at JSC, ISAG presented nadir-view imagery of the FGB acquired during Space Shuttle rendezvous. Using the known width of the pressurized portion of the FGB as a scale, this analysis clearly showed that the port FGB solar array was extended outboard further than the Russian design for the retracted solar array.

Liddle, Donn↗

Health Monitoring of a Planetary Rover Using Hybrid Particle Petri Nets

This paper focuses on the application of a Petri Net-based diagnosis method on a planetary rover prototype.The diagnosis is performed by using a model-based method in the context of health management of hybrid systems.In system health management, the diagnosis task aims at determining the current health state of a system and the fault occurrences that lead to this state. The Hybrid Particle Petri Nets (HPPN) formalism is used to model hybrid systems behavior and degradation, and to define the generation of diagnosers to monitor the health states of such systems under uncertainty. At any time, the HPPN-based diagnoser provides the current diagnosis represented by a distribution of beliefs over the health states. The health monitoring methodology is demonstrated on the K11 rover. A hybrid model of the K11 is proposed and experimental results show that the approach is robust to real system data and constraints.

health monitoring↗

Computing Proximity to Threat Along Uncertain Trajectory to Support Urban Air Mobility

Many airspace threats affect the selection of a flight route, such as terrain, physical obstacles, adverse weather, and special-use airspace, among others. Threat avoidance during Urban Air Mobility (UAM) and Low Altitude Mobility (LAM) flights is especially challenging due to their lower cruising altitudes. These operations may be exposed to buildings, towers, trees, terrain undulations, etc., along much of their flight route. Moreover, these low-altitude flights in urban environments are expected to encounter very busy airspace, increasing the workload associated with threat avoidance. The Proximity to Threat (PtT) function aims to support onboard or remote pilots by computing the risk from geospatial threats in the airspace along an aircraft’s flight path. The threats are both static entities and dynamic airspace restrictions that have been modeled and stored in geo-referenced mapping databases. The flight path may be specified by waypoints, airways, or similar discrete route elements or by a time series of closely spaced position and altitude points. Flight path uncertainty can also be taken into account by assuming both the position and altitude to be sampled from two normal distributions, each being specified by a mean and variance. PtT uses this additional information to verify that the flight path remains clear of threats along a wider path or if a position is reached earlier or later than anticipated, assuring the pilot or operator that there will be an available safety margin even if the aircraft deviates due to one or more occurrences of unexpected wind gusts, mechanical failures, airspeed changes, collision avoidance maneuvers, etc. The client can specify an uncertainty confidence level to bound the set of trajectories evaluated for threats so that the confidence level corresponds to the client’s risk tolerance under the expected conditions. PtT can be used as a pre-flight planning tool to determine a safe route through known threats and in-flight to avoid emerging or changing threats. In this report, we present the PtT function, discuss how the trajectory uncertainty is incorporated into the PtT function, and describe the use of this PtT function in a representative scenario.

urban air mobility↗

Understanding Climate Policy Data Needs. NASA Carbon Monitoring System Briefing: Characterizing Flux Uncertainty, Washington D.C., 11 January 2012

Climate policy in the United States is currently guided by public-private partnerships and actions at the local and state levels. This mitigation strategy is made up of programs that focus on energy efficiency, renewable energy, agricultural practices and implementation of technologies to reduce greenhouse gases. How will policy makers know if these strategies are working, particularly at the scales at which they are being implemented? The NASA Carbon Monitoring System (CMS) will provide information on carbon dioxide fluxes derived from observations of earth's land, ocean and atmosphere used in state of the art models describing their interactions. This new modeling system could be used to assess the impact of specific policy interventions on CO2 reductions, enabling an iterative, results-oriented policy process. In January of 2012, the CMS team held a meeting with carbon policy and decision makers in Washington DC to describe the developing modeling system to policy makers. The NASA CMS will develop pilot studies to provide information across a range of spatial scales, consider carbon storage in biomass, and improve measures of the atmospheric distribution of carbon dioxide. The pilot involves multiple institutions (four NASA centers as well as several universities) and over 20 scientists in its work. This pilot study will generate CO2 flux maps for two years using observational constraints in NASA's state-of -the-art models. Bottom-up surface flux estimates will be computed using data-constrained land and ocean models; comparison of the different techniques will provide some knowledge of uncertainty in these estimates. Ensembles of atmospheric carbon distributions will be computed using an atmospheric general circulation model (GEOS-5), with perturbations to the surface fluxes and to transport. Top-down flux estimates will be computed from observed atmospheric CO2 distributions (ACOS/GOSAT retrievals) alongside the forward-model fields, in conjunction with an inverse approach based on the CO2 model of GEOS ]Chem. The forward model ensembles will be used to build understanding of relationships among surface flux perturbations, transport uncertainty and atmospheric carbon concentration. This will help construct uncertainty estimates and information on the true spatial resolution of the top-down flux calculations. The relationship between the top-down and bottom-up flux distributions will be documented. Because the goal of NASA CMS is to be policy relevant, the scientists involved in the flux modeling pilot need to understand and be focused on the needs of the climate policy and decision making community. If policy makers are to use CMS products, they must be aware of the modeling effort and begin to design policies that can be evaluated with information. Improving estimates of carbon sequestered in forests, for example, will require information on the spatial variability of forest biomass that is far more explicit than is presently possible using only ground observations. Carbon mitigation policies being implemented by cities around the United States could be designed with the CMS data in mind, enabling sequential evaluation and subsequent improvements in incentives, structures and programs. The success of climate mitigation programs being implemented in the United States today will hang on the depth of the relationship between scientists and their policy and decision making counterparts. Ensuring that there is two-way communication between data providers and users is important for the success both of the policies and the scientific products meant to support them..

Brown, Molly E.↗

Propagation of Computational Uncertainty Using the Modern Design of Experiments

This paper describes the use of formally designed experiments to aid in the error analysis of a computational experiment. A method is described by which the underlying code is approximated with relatively low-order polynomial graduating functions represented by truncated Taylor series approximations to the true underlying response function. A resource-minimal approach is outlined by which such graduating functions can be estimated from a minimum number of case runs of the underlying computational code. Certain practical considerations are discussed, including ways and means of coping with high-order response functions. The distributional properties of prediction residuals are presented and discussed. A practical method is presented for quantifying that component of the prediction uncertainty of a computational code that can be attributed to imperfect knowledge of independent variable levels. This method is illustrated with a recent assessment of uncertainty in computational estimates of Space Shuttle thermal and structural reentry loads attributable to ice and foam debris impact on ascent.

DeLoach, Richard↗

Homogenizing and Estimating the Uncertainty in NOAA's Long-Term Vertical Ozone Profile Records Measured with the Electrochemical Concentration Cell Ozonesonde

NOAA's program of long-term monitoring of the vertical distribution of ozone with electrochemical concentration cell (ECC) ozonesondes has undergone a number of changes over the 50-year record. In order to produce a homogenous data set, these changes must be documented and, where necessary, appropriate corrections applied. This is the first comprehensive and consistent reprocessing of NOAA's ozonesonde data records that corrects for these changes using the rawest form of the data (cell current and pump temperature) in native resolution as well as a point-by-point uncertainty calculation that is unique to each sounding. The reprocessing is carried out uniformly at all eight ozonesonde sites in NOAA's network with differences in sensing solution and ozonesonde types accounted for in the same way at all sites. The corrections used to homogenize the NOAA ozonesonde data records greatly improve the ozonesonde measurements with an average one sigma uncertainty of +/- 4-6% in the stratosphere and +/- 5-20% in the troposphere. A comparison of the integrated column ozone from the ozonesonde profile with co-located Dobson spectrophotometers total column ozone measurements shows agreement within +/- 5% for >70% of the profiles. Very good agreement is also found in the stratosphere between ozonesonde profiles and profiles retrieved from the Solar Backscatter Ultraviolet (SBUV) instruments.

ozonesonde↗

Compositional and Microstructural Evolution of Olivine During Pulsed Laser Irradiation: Insights Based on a FIB/Field-Emission TEM Study

Introduction: The use of pulsed laser irradiation to simulate the short duration, high-energy conditions characteristic of micrometeorite impacts is now an established approach in experimental space weathering studies. The laser generates both melt and vapor deposits that contain nanophase metallic Fe (npFe(sup 0)) grains with size distributions and optical properties similar to those in natural impact-generated melt and vapor deposits. There remains uncertainty, however, about how well lasers simulate the mechanical work and internal (thermal) energy partitioning that occurs in actual impacts. We are currently engaged in making a direct comparison between the products of laser irradiation and experimental/natural hypervelocity impacts. An initial step reported here is to use analytical TEM is to attain a better understanding of how the microstructure and composition of laser deposits evolve over multiple cycles of pulsed laser irradiation. Experimental Methods: We irradiated pressed-powder pellets of San Carlos olivine (Fo(sub 90)) with up to 99 rastered pulses of a GAM ArF excimer laser. The irradiated surface of the sample were characterized by SEM imaging and areas were selected for FIB cross sectioning for TEM study using an FEI Quanta dual-beam electron/focused ion beam instrument. FIB sections were characterized using a JEOL2500SE analytical field-emission scanning transmission electron microscope (FE-STEM) optimized for quantitative element mapping at less than 10 nm spatial resolutions. Results: In the SEM the 99 pulse pressed pellet sample shows a complex, inhomogeneous, distribution of laser-generated material, largely concentrated in narrow gaps and larger depressions between grains. Local concentrations of npFe0 spherules 0.1 to 1 micrometers in size are visible within these deposits in SEM back-scatter images. Fig. 1 shows bright-field STEM images of a FIB cross-section of a one of these deposits that continuously covers the top and sloping side of an olivine grain. The deposit has 3 microstructurally distinct sub-layers composed of silicate glass with varying modal fractions and size distributions of npFe( sup 0) spherules, along with nanocrystalline silicate material. A relatively thin (50-300 nm) topmost surface layer has a high-concentration of npFe0 spherules 5-20 nm in size. Element mapping shows the layer to be enriched in Fe by a factor of 2.5 relative to the olivine substrate, with Mg and Si depleted by 20% and 10% respectively. This is compositionally complementary to the underlying, middle layer of the deposit that is depleted in Fe, enriched in Mg and has a much lower npFe0 concentration. A third layer of nanocrystalline olivine occurs at the substrate interface. Discussion: The FE-STEM results suggest the topmost layer is a vapor deposit, underlain by a thicker microstructurally complex melt-generated layer. The compositional relations suggest the melt layer was partially vaporized, preferentially losing more volatile elements (e.g., Fe). The vaporized material re-condensed to form the thin, npFe(sup 0)-rich surface deposit during or immediately after the scan cycle. Nanocrystalline olivine that grew within the melt layer as it formed and cooled is similar in volume and microstructure to what we have observed in the impact melt lining of a micrometeorite impact crater in olivine. This suggest the time-temperature relations attained in the laser sample may not be too different from a micrometeorite impact. Our TEM observations, however, do not show evidence for the same level of mechanical dam-age (e.g., fracturing) seen around the natural micrometeorite crater.

Christoffersen, R.↗

Automated Probabilistic Finite Element Model Calibration Tool Based on Uncertainty Quantification and Machine Learning

Qualification and certification of safety critical parts is a hurdle to the adoption of metallic additively manufactured components for aerospace vehicle applications. Challenges include variability in part properties due to inconsistent defect distribution and microstructure. Understanding of the process through finite element modeling (FEM), and process control through in-situ monitoring, may result in significant improvements; however, solutions useful to manufacturers will require large volumes of data and automated data utilization. Toward this end, a generalizable automated FEM calibration paradigm is developed. This paradigm leverages existing and novel tools from machine learning and uncertainty quantification to enable the automatic calibration of FEMs without requiring prior knowledge of the model performance across input parameter space, including meshing and solver settings, which can require time consuming manual model probing or cause noisy and inconsistent predictions. The result is a probabilistic distribution of calibrated and validated FEM input parameters targeting measured data.

Additive manufacturing model calibration finite el↗

High Ice Water Content at Low Radar Reflectivity near Deep Convection: Consistency of In Situ and Remote-Sensing Observations with Stratiform Rain Column Simulations - Part I

Occurrences of jet engine power loss and damage have been associated with flight through fully glaciated deep convection at -10 to -50 degrees Centigrade. Power loss events commonly occur during flight through radar reflectivity (Zeta (sub e)) less than 20-30 decibels relative to Zeta (dBZ - radar returns) and no more than moderate turbulence, often overlying moderate to heavy rain near the surface. During 2010-2012, Airbus carried out flight tests seeking to characterize the highest ice water content (IWC) in such low-radar-reflectivity regions of large, cold-topped storm systems in the vicinity of Cayenne, Darwin, and Santiago. Within the highest IWC regions encountered, at typical sampling elevations (circa 11 kilometers), the measured ice size distributions exhibit a notably narrow concentration of mass over area-equivalent diameters of 100-500 micrometers. Given substantial and poorly quantified measurement uncertainties, here we evaluate the consistency of the Airbus in situ measurements with ground-based profiling radar observations obtained under quasi-steady, heavy stratiform rain conditions in one of the Airbus-sampled locations. We find that profiler-observed radar reflectivities and mean Doppler velocities at Airbus sampling temperatures are generally consistent with those calculated from in situ size-distribution measurements. We also find that column simulations using the in situ size distributions as an upper boundary condition are generally consistent with observed profiles of radar reflectivity (Ze), mean Doppler velocity (MDV), and retrieved rain rate. The results of these consistency checks motivate an examination of the microphysical pathways that could be responsible for the observed size-distribution features in Ackerman et al. (2015).

Rain↗

Copula-based Method to Generate Consistent Surface Pressures Under Uncertainty

This paper establishes a method to create surface pressure databases that allow for uncertainty quantification. Aerodynamic databases are critical products for launch vehicles and other aeronautical systems, and surface pressure databases are one such database that constains large quantities of data. The focus of this work is the relationship between the integrated force and moment data base and the surface pressure database. In particular, the work attempts to provide a method that maintains consistency between these two databases when accounting for uncertainty. The integrated force and moment database and surface pressure databases are constructed from CFD data which is high-density but low-trust. However, the force and moment database will often also include data from high-trust but low-density sources such as from wind tunnel experiments. This means that the quantified uncertainty of the force and moment database is higher quality as it includes this high fidelity wind tunnel data. This motivates the idea to use the force and moment database uncertainty when constructing the surface pressure database uncertainty. The method utilizes the statistical idea of a copula in order to generate surface pressures that match with uncertain integrated force and moment distributions as well as being consistent with known CFD data. This statistical consistency is quantified by using the Maximum Mean Discrepancy two-sample test. The predictive error of the method is also approximated using leave-one-out error estimation and the good overall performance of the method is presented using probability boxes in a simulated uncertainty scenario.

SLS↗

An Inverse Chance-constrained Approach to the Calibration of Robust Models

This paper proposes a strategy to calibrate computational models according to uncertain input-output data. To this end, uncertainty in the data is first quantified by creating adversarial data sets. Samples drawn from such sets are then mapped from the input-output space to the parameter space using an inverse mapping. This mapping minimizes the collective output spread of an ensemble of point predictions while satisfying a set of individual data-matching requirements. The distribution of the resulting parameter points, which often exhibits strong parameter dependencies, is then modeled using sliced-normals. The chance-constrained formulation used to learn this distribution enables the analyst to trade-off a greater likelihood for most of the data against a lower likelihood for some of the data thereby relaxing the conservatism of the calibrated model. This formulation not only neglects the worst-performing quantiles of each adversarial distribution but also eliminates the potentially serious effects that outliers might have on the resulting model. This calibration approach not only has a considerably lower computational cost than the standard forward approach but it also allows for the identification of suitable distribution classes, which in turn yield better calibrated models.

Calibration↗

Uncertainty Quantification and Sensitivity Analysis in Process-Structure-Property Simulations for Laser Powder Bed Fusion Additive Manufacturing

Process variations and process-induced defects like porosity cause significant uncertainty in the microstructure and mechanical behavior of additively manufactured metals. Establishing process-structure-property (PSP) relationships and quantifying uncertainty using experiments alone is costly, especially for structural applications where mechanical allowables must be established for qualification and certification. This work presents a PSP simulation framework for laser powder bed fusion with a focus on uncertainty quantification through probabilistic calibration and multi-fidelity uncertainty propagation. Motivated by phenomenological input parameters related to grain nucleation and growth that are difficult to characterize, a global sensitivity analysis (GSA) is completed. Through GSA, the most important input parameters are identified based on their influence on the statistical distributions of microstructural metrics that influence mechanical behavior, including grain size, morphology, and crystallographic texture. The results provide insight on what experiments are necessary to quantify and control PSP uncertainties, particularly those associated with the more challenging input parameters.

additive manufacturing↗