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NASA NTRSDate not supplied

Simultaneous Development and Robust Optimization of a Microstructure Dependent Material

Recent microstructure characterization techniques combined with Symbolic Regression(SR)analysis has been proven to generate white box plasticity models well suited for incorporation into FEA software.The current work builds upon those efforts and demonstrates the applicability of Sequential Monte-Carlo (SMC) methods within SR analysis to condense model development and robust optimization into a single, co-dependent process. In this project, SMC methods provide a mechanism through which the observed microstructure features and associated variability can be incorporated into the discovery phase of model development and simultaneously recover approximate parameter distributions through SR analysis. The demonstration utilized a data set consisting of tensile test results from a limited number of sample specimens with corresponding EBSD data from which microstructure features were characterized.The maximum threshold stress model in the Visco-Plastic Self-Consistent (VPSC) code developed by Los Alamos National Laboratories was calibrated using mechanical test data.Synthetic volume elements with statistically equivalent microstructure were generated with DREAM3Dbased on the observed EBSD data. VPSC was used to simulate the corresponding tensile test response for each of the synthetic volume elements. The simulated microstructure and tensile test data was used astraining datafor SMC-SR algorithm and the resulting model was validated with data from the original empirical data set.

Karl Garbrecht↗
NASA NTRS2019

Prior biosphere model impact on global terrestrial CO2 fluxes estimated from OCO-2 retrievals

This study assesses the impact of different state of the art global biospheric CO2 flux models, when applied as prior information, on inverse model “top-down” estimates of terrestrial CO2 fluxes obtained when assimilating Orbiting Carbon Observatory 2 (OCO-2) observations. This is done with a series of observing system simulation experiments (OSSEs) using synthetic CO2 column-average dry air mole fraction (XCO2) retrievals sampled at the OCO-2 satellite spatiotemporal frequency. The OSSEs utilized a 4-D variational (4D-Var) assimilation system with the GEOS-Chem global chemical transport model (CTM) to estimate CO2 net ecosystem exchange (NEE) fluxes using synthetic OCO-2 observations. The impact of biosphere models in inverse model estimates of NEE is quantified by conducting OSSEs using the NASA-CASA, CASA-GFED, SiB-4, and LPJ models as prior estimates and using NEE from the multi-model ensemble mean of the Multiscale Synthesis and Terrestrial Model Intercomparison Project as the “truth”. Results show that the assimilation of simulated XCO2 retrievals at OCO-2 observing modes over land results in posterior NEE estimates which generally reproduce “true” NEE globally and over terrestrial TransCom-3 regions that are well-sampled. However, we find larger spread among posterior NEE estimates, when using different prior NEE fluxes, in regions and seasons that have limited OCO-2 observational coverage and a large range in “bottom-up” NEE fluxes. Seasonally averaged posterior NEE estimates had standard deviations (SD) of ∼10 % to ∼50 % of the multi-model-mean NEE for different TransCom-3 land regions with significant NEE fluxes (regions/seasons with a NEE flux ≥0.5 PgC/yr). On a global average, the seasonally averaged residual impact of the prior model NEE assumption on the posterior NEE spread is ∼10 %–20 % of the posterior NEE mean. Additional OCO-2 OSSE simulations demonstrate that posterior NEE estimates are also sensitive to the assumed prior NEE flux uncertainty statistics, with spread in posterior NEE estimates similar to those when using variable prior model NEE fluxes. In fact, the sensitivity of posterior NEE estimates to prior error statistics was larger than prior flux values in some regions/times in the tropics and Southern Hemisphere where sufficient OCO-2 data were available and large differences between the prior and truth were evident. Overall, even with the availability of spatiotemporally dense OCO-2 data, noticeable residual differences (up to ∼20 %–30 % globally and 50 % regionally) in posterior NEE flux estimates remain that were caused by the choice of prior model flux values and the specification of prior flux uncertainties.

Sajeev Philip↗
NASA NTRS2022

A Synopsis of AIRS Global-Mean Clear-Sky Radiance Trends From 2003 to 2020

Atmospheric Infrared Sounder (AIRS) aboard the National Aeronautics and Space Administration (NASA) Aqua satellite has been operating since September 2002. Its information content, superb instrument performance, and dense sampling pattern make the AIRS radiances an invaluable data set for climate studies. The trends of global-mean, nadir-view, clear-sky AIRS radiances from 2003 to 2020 are studied here, together with the counterparts of synthetic radiances based on two reanalyzes, European Centre for Medium-Range Weather Forecasts Reanalysis V5 (ECMWF ERA5) and NASA Goddard Earth Observing System V5.4.1 (GEOS-5.4.1; a reanalysis product without assimilation of hyperspectral radiances such as AIRS). The AIRS observation shows statistically significant negative trends in most of its CO2 channels, positive but non-significant trends in the channels over the window regions, and statistically significant positive trends in some of its H2O channels. The best agreements between observed and simulated radiance trends are seen over the CO2 tropospheric channels, while the observed and simulated trends over the CO2 stratospheric channels are opposite. ERA5 results largely agree with the AIRS observation over the H2O channels. The comparison in the H2O channels helps reveal a data continuity issue in the GEOS-5.4.1. Contributions from individual variables to the radiance trends are also assessed by performing separate simulations. This study provides the first synopsis of the global-mean trend of AIRS radiances over all its thermal-IR channels.

CO2↗
NASA NTRS2016

On the Importance of High Frequency Gravity Waves for Ice Nucleation in the Tropical Tropopause Layer

Recent investigations of the influence of atmospheric waves on ice nucleation in cirrus have identified a number of key processes and sensitivities: (1) ice concentrations produced by homogeneous freezing are strongly dependent on cooling rates, with gravity waves dominating upper tropospheric cooling rates; (2) rapid cooling driven by high-frequency waves are likely responsible for the rare occurrences of very high ice concentrations in cirrus; (3) sedimentation and entrainment tend to decrease ice concentrations as cirrus age; and (4) in some situations, changes in temperature tendency driven by high-frequency waves can quench ice nucleation events and limit ice concentrations. Here we use parcel-model simulations of ice nucleation driven by long-duration, constant-pressure balloon temperature time series, along with an extensive dataset of cold cirrus microphysical properties from the recent ATTREX high-altitude aircraft campaign, to statistically examine the importance of high-frequency waves as well as the consistency between our theoretical understanding of ice nucleation and observed ice concentrations. The parcel-model simulations indicate common occurrence of peak ice concentrations exceeding several hundred per liter. Sedimentation and entrainment would reduce ice concentrations as clouds age, but 1-D simulations using a wave parameterization (which underestimates rapid cooling events) still produce ice concentrations higher than indicated by observations. We find that quenching of nucleation events by high-frequency waves occurs infrequently and does not prevent occurrences of large ice concentrations in parcel simulations of homogeneous freezing. In fact, the high-frequency variability in the balloon temperature data is entirely responsible for production of these high ice concentrations in the simulations.

simulation↗
NASA NTRS2016

Global Estimates of Fine Particulate Matter Using a Combined Geophysical-Statistical Method with Information from Satellites, Models, and Monitors

We estimated global fine particulate matter (PM(sub 2.5)) concentrations using information from satellite-, simulation- and monitor-based sources by applying a Geographically Weighted Regression (GWR) to global geophysically-based satellite-derived PM(sub 2.5) estimates. Aerosol optical depth from multiple satellite products (MISR, MODIS Dark Target, MODIS and SeaWiFS Deep Blue, and MODIS MAIAC) was combined with simulation (GEOS-Chem) based upon their relative uncertainties as determined using ground-based sun photometer (AERONET) observations for 1998−2014. The GWR predictors included simulated aerosol composition and land use information. The resultant PM(sub 2.5) estimates were highly consistent (R(sup 2) equals 0.81) with out-of-sample cross-validated PM(sub 2.5) concentrations from monitors. The global population-weighted annual average PM(sub 2.5) concentrations were 3-fold higher than the 10 micrograms per cubic meter WHO guideline, driven by exposures in Asian and African regions. Estimates in regions with high contributions from mineral dust were associated with higher uncertainty, resulting from both sparse ground-based monitoring, and challenging conditions for retrieval and simulation. This approach demonstrates that the addition of even sparse ground-based measurements to more globally continuous PM(sub 2.5) data sources can yield valuable improvements to PM(sub 2.5) characterization on a global scale.

aerosols↗
NASA NTRSDate not supplied

Linear Mixed-Effects Models for Human-in-the-Loop Tracking Experiment Data

Linear mixed-effects models provide several benefits over more traditional statistical inference tests that are particularly useful for most human-in-the-loop tracking experiment data. However, surprisingly, mixed models are virtually not used for the analysis of tracking experiment data. This paper uses of linear mixed-effects models to analyze combined tracking data from two previous human-in-the-loop roll tracking experiments that compared control behavior metrics collected in both a research aircraft and a motion-base simulator. In the experiments, pilots' behavior under 10 different motion configurations with varying motion filter gains and break frequencies was evaluated and compared to that in the real aircraft. The linear mixed-effects model analysis on the combined dataset confirmed the main statistical outcomes of the individual experiments. The main benefits of mixed models for this type of data were demonstrated by successfully combining data from two experiments that used different experimental conditions and of which one had an additional apparatus and the other a missing participant. Finally, the mixed-model analysis was able to explicitly test for scientifically relevant statistical differences in the dependent measures between the aircraft and simulator, as well as both experiments.

manual control↗
NASA NTRS2010

Estimation of Signal Coherence Threshold and Concealed Spectral Lines Applied to Detection of Turbofan Engine Combustion Noise

Combustion noise from turbofan engines has become important, as the noise from sources like the fan and jet are reduced. An aligned and un-aligned coherence technique has been developed to determine a threshold level for the coherence and thereby help to separate the coherent combustion noise source from other noise sources measured with far-field microphones. This method is compared with a statistics based coherence threshold estimation method. In addition, the un-aligned coherence procedure at the same time also reveals periodicities, spectral lines, and undamped sinusoids hidden by broadband turbofan engine noise. In calculating the coherence threshold using a statistical method, one may use either the number of independent records or a larger number corresponding to the number of overlapped records used to create the average. Using data from a turbofan engine and a simulation this paper shows that applying the Fisher z-transform to the un-aligned coherence can aid in making the proper selection of samples and produce a reasonable statistics based coherence threshold. Examples are presented showing that the underlying tonal and coherent broad band structure which is buried under random broadband noise and jet noise can be determined. The method also shows the possible presence of indirect combustion noise. Copyright 2011 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America.

Miles, Jeffrey Hilton↗
NASA NTRS1996

Annual Research Briefs - 1996, Center for Turbulence Research

Partial contents include: (1) Simulation of jet impingement heat transfer with the k-e-V2 model; (2) A new methodology for turbulence modelers using Direct Numerical Simulation (DNS) database analysis; (3) A particle representation model for the deformation of homogeneous turbulence; (4) Modeling of inhomogeneous compressible turbulence using a two-scale statistical theory; (5) Lewis number effects on partially premixed flames; (6) Conditional moment closure of mixing and reaction in turbulent non-premixed combustion; (7) Dynamic models for LES of turbulent front propagation with a spectral method; (8) Jet noise using large eddy simulation; (9) Towards numerical simulations of trailing-edge aeroacoustics; (10) A model for the onset of vortex breakdown; (11) Compressing an elliptic vortex: transition to turbulence by tumble breakdown; (12) A new method for the adaptive control of vortex-wall interactions; (13) Symmetries in turbulent boundary layer flows; (14) Near-wall models in large eddy simulations of flow behind a backward-facing step; (15) Assessment of the subgrid-scale models at low and high Reynolds numbers; (16) Large-eddy simulations of flow around a NACA 4412 airfoil using unstructured grids; (17) Progress on LES of flow past a circular cylinder; (18) Experimental investigation of flow through an asymmetric plane diffuser; (19) Progress in the large-eddy simulation of an asymmetric plane diffuser; (20) A numerical study of self-similarity in a turbulent plane wake using large-eddy simulation; (21) On the generation of turbulent inflow conditions for boundary layer simulations, and (22) A new class of finite difference schemes.

COMPUTATIONAL FLUID DYNAMICS↗
NASA NTRS1993

Vibration control by limiting the maximum axial forces in space trusses

Proposed here is a method of vibration control based on limiting the maximum axial forces in the active members of an adaptive truss. The actuators simulate elastic rigid-plastic behavior and consume the vibrational energy as work. The method is applicable to both statically determinate as well as indeterminate truss structures. However, for energy efficient control of statistically indeterminate trusses extra actuators may be provided on the redundant bars. An energy formulation relating the various control parameters is derived to get an estimate of the control time. Since the simulation of elastic rigid-plastic behavior requires a piecewise linear control law, a general analytical solution is not possible. Numerical simulation by step-by-step integration is performed to simulate the control of an example truss structure. The problems of application to statically indeterminate trusses and optimal actuator placement are identified for future work.

Chawla, Vikas↗
NASA NTRS2012

Design and Application of the Exploration Maintainability Analysis Tool

Conducting human exploration missions beyond Low Earth Orbit (LEO) will present unique challenges in the areas of supportability and maintainability. The durations of proposed missions can be relatively long and re-supply of logistics, including maintenance and repair items, will be limited or non-existent. In addition, mass and volume constraints in the transportation system will limit the total amount of logistics that can be flown along with the crew. These constraints will require that new strategies be developed with regards to how spacecraft systems are designed and maintained. NASA is currently developing Design Reference Missions (DRMs) as an initial step in defining future human missions. These DRMs establish destinations and concepts of operation for future missions, and begin to define technology and capability requirements. Because of the unique supportability challenges, historical supportability data and models are not directly applicable for establishing requirements for beyond LEO missions. However, supportability requirements could have a major impact on the development of the DRMs. The mass, volume, and crew resources required to support the mission could all be first order drivers in the design of missions, elements, and operations. Therefore, there is a need for enhanced analysis capabilities to more accurately establish mass, volume, and time requirements for supporting beyond LEO missions. Additionally, as new technologies and operations are proposed to reduce these requirements, it is necessary to have accurate tools to evaluate the efficacy of those approaches. In order to improve the analysis of supportability requirements for beyond LEO missions, the Space Missions Analysis Branch at the NASA Langley Research Center is developing the Exploration Maintainability Analysis Tool (EMAT). This tool is a probabilistic simulator that evaluates the need for repair and maintenance activities during space missions and the logistics and crew requirements to support those activities. Using a Monte Carlo approach, the tool simulates potential failures in defined systems, based on established component reliabilities, and then evaluates the capability of the crew to repair those failures given a defined store of spares and maintenance items. Statistical analysis of Monte Carlo runs provides probabilistic estimates of overall mission safety and reliability. This paper will describe the operation of the EMAT, including historical data sources used to populate the model, simulation processes, and outputs. Analysis results are provided for a candidate exploration system, including baseline estimates of required sparing mass and volume. Sensitivity analysis regarding the effectiveness of proposed strategies to reduce mass and volume requirements and improve mission reliability is included in these results.

Stromgren, Chel↗
NASA NTRS1984

The effects of time delay in man-machine control systems: Implications for design of flight simulator Visual-Display-Delay compensation

When human operators are performing precision tracking tasks, their dynamic response can often be modeled by quasilinear describing functions. That fact permits analysis of the effects of delay in certain man machine control systems using linear control system analysis techniques. The analysis indicates that a reduction in system stability is the immediate effect of additional control system delay, and that system characteristics moderate or exaggerate the importance of the delay. A selection of data (simulator and flight test) consistent with the analysis is reviewed. Flight simulator visual-display delay compensation, designed to restore pilot aircraft system stability, was evaluated in several studies which are reviewed here. The studies range from single-axis, tracking-task experiments (with sufficient subjects and trials to establish the statistical significance of the results) to a brief evaluation of compensation of a computer generated imagery (CGI) visual display system in a full six degree of freedom simulation. The compensation was effective, improvements in pilot performance and workload or aircraft handling qualities rating (HQR) were observed. Results from recent aircraft handling qualities research literature, which support the compensation design approach, are also reviewed.

Crane, D. F.↗
NASA NTRS1999

Effects of Space Flight, Clinorotation, and Centrifugation on the Growth and Metabolism of Escherichia Coli

Previous experiments have shown that space flight stimulates bacterial growth and metabolism. An explanation for these results is proposed, which may eventually lead to improved terrestrial pharmaceutical production efficiency. It is hypothesized that inertial acceleration affects bacterial growth and metabolism by altering the transport phenomena in the cells external fluid environment. It is believed that this occurs indirectly through changes in the sedimentation rate acting on the bacteria and buoyancy-driven convection acting on their excreted by-products. Experiments over a broad range of accelerations consistently supported this theory. Experiments at I g indicated that higher concentrations of excreted by products surrounding bacterial cells result in a shorter lag phase. Nineteen additional experiments simulated 0 g and 0.5 g using a clinostat, and achieved 50 g, 180 g, and 400 g using a centrifuge. These experiments showed that final cell density is inversely related to the level of acceleration. The experiments also consistently showed that acceleration affects the length of the lag phase in a non-monotonic, yet predictable, manner. Additional data indicated that E. coli metabolize glucose less efficiently at hypergravity, and more efficiently at hypogravity. A space-flight experiment was also performed. Samples on orbit had a statistically significant higher final cell density and more efficient metabolism than did ground controls. These results. which were similar to simulations of 0 g using a clinostat, support the theory that gravity only affects bacterial growth and metabolism indirectly, through changes in the bacteria's fluid environment.

Brown, Robert B.↗
NASA NTRS2006

A Framework for Performing Multiscale Stochastic Progressive Failure Analysis of Composite Structures

A framework is presented that enables coupled multiscale analysis of composite structures. The recently developed, free, Finite Element Analysis - Micromechanics Analysis Code (FEAMAC) software couples the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) with ABAQUS to perform micromechanics based FEA such that the nonlinear composite material response at each integration point is modeled at each increment by MAC/GMC. As a result, the stochastic nature of fiber breakage in composites can be simulated through incorporation of an appropriate damage and failure model that operates within MAC/GMC on the level of the fiber. Results are presented for the progressive failure analysis of a titanium matrix composite tensile specimen that illustrate the power and utility of the framework and address the techniques needed to model the statistical nature of the problem properly. In particular, it is shown that incorporating fiber strength randomness on multiple scales improves the quality of the simulation by enabling failure at locations other than those associated with structural level stress risers.

Bednarcyk, Brett A.↗
NASA NTRS2007

A Framework for Performing Multiscale Stochastic Progressive Failure Analysis of Composite Structures

A framework is presented that enables coupled multiscale analysis of composite structures. The recently developed, free, Finite Element Analysis-Micromechanics Analysis Code (FEAMAC) software couples the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) with ABAQUS to perform micromechanics based FEA such that the nonlinear composite material response at each integration point is modeled at each increment by MAC/GMC. As a result, the stochastic nature of fiber breakage in composites can be simulated through incorporation of an appropriate damage and failure model that operates within MAC/GMC on the level of the fiber. Results are presented for the progressive failure analysis of a titanium matrix composite tensile specimen that illustrate the power and utility of the framework and address the techniques needed to model the statistical nature of the problem properly. In particular, it is shown that incorporating fiber strength randomness on multiple scales improves the quality of the simulation by enabling failure at locations other than those associated with structural level stress risers.

Bednarcyk, Brett A.↗
NASA NTRS2011

The Various Influences due to Aerosol Depositions

Recently the issue on glacier retreats comes up and many factors should be relevant to the issue. The absorbing aerosols such as dust and black carbon (BC) are considered to be one of the factors. After they deposited onto the snow surface, it will reduce snow albedo (called snow darkening effect) and probably contribute to further melting of glacier. The Goddard Earth Observing System version 5 (GEOS-5) has developed at NASA/GSFC. However, the original snowpack model used in the land surface model in the GEOS-5 did not consider the snow darkening effect. Here we developed the new snow albedo scheme which can consider the snow darkening effect. In addition, another scheme on calculating mass concentrations on the absorbing aerosols in snowpack was also developed, in which the direct aerosol depositions from the chemical transport model in the GEOS-5 were used. The scheme has been validated with the observed data obtained at backyard of the Institute of Low Temperature Science, Hokkaido University, by Dr. Teruo Aoki (Meteorological Research Institute) et al. including me. The observed data was obtained when I was Ph.D.caftdidate. The original GEOS-5 during 2007-2009 over the Himalayas and Tibetan Plateau region showed more reductions of snow than that of the new GEOS-5 because the original one used lower albedo settings. On snow cover fraction, the new GEOS-5 simulated more realistic snow-covered area comparing to the MODIS snow cover fraction. The reductions on snow albedo, snow cover fraction, and snow water equivalent were seen with statistically significance if we consider the snow darkening effect comparing to the results without the snow darkening effect. In the real world, debris cover, inside refreezing process, surface flow of glacier, etc. affect glacier mass balance and the simulated results immediately do not affect whole glacier retreating. However, our results indicate that some surface melting over non debris covered parts of the glacier would be explained by the snow darkening effect. Further discussion and observations are necessary to assess the glacier issue.

Yasunari, Teppei↗
NASA NTRS2012

Incorporation of the Mass Concentration and the New Snow Albedo Schemes into the Global Forecasting Model, GEOS-5 and the Impact of the New Schemes over Himalayan Glaciers

Recently the issue on glacier retreats comes up and many factors should be relevant to the issue. The absorbing aerosols such as dust and black carbon (BC) are considered to be one of the factors. After they deposited onto the snow surface, it will reduce snow albedo (called snow darkening effect) and probably contribute to further melting of glacier. The Goddard Earth Observing System version 5 (GEOS-5) has developed at NASA/GSFC. However, the original snowpack model used in the land surface model in the GEOS-5 did not consider the snow darkening effect. Here we developed the new snow albedo scheme which can consider the snow darkening effect. In addition, another scheme on calculating mass concentrations on the absorbing aerosols in snowpack was also developed, in which the direct aerosol depositions from the chemical transport model in the GEOS-5 were used. The scheme has been validated with the observed data obtained at backyard of the Institute of Low Temperature Science, Hokkaido University, by Dr. Teruo Aoki (Meteorological Research Institute) et aL including me. The observed data was obtained when I was Ph.D. candidate. The original GEOS-5during 2007-2009 over the Himalayas and Tibetan Plateau region showed more reductions of snow than that of the new GEOS-5 because the original one used lower albedo settings. On snow cover fraction, the new GEOS-5 simulated more realistic snow-covered area comparing to the MODIS snow cover fraction. The reductions on snow albedo, snow cover fraction, and snow water equivalent were seen with statistically significance if we consider the snow darkening effect comparing to the results without the snow darkening effect. In the real world, debris cover, inside refreezing process, surface flow of glacier, etc. affect glacier mass balance and the simulated results immediately do not affect whole glacier retreating. However, our results indicate that some surface melting over non debris covered parts of the glacier would be explained by the snow darkening effect. Further discussion and observations are necessary to assess the glacier issue.

Yasunari, Teppei↗
NASA NTRS1983

Compensation for time delay in flight simulator visual-display systems

A piloted aircraft can be viewed as a closed-loop, man-machine control system. When a simulator pilot is performing a precision maneuver, a delay in the visual display of aircraft response to pilot-control input decreases the stability of the pilot-aircraft system. The less stable system is more difficult to control precisely. Pilot dynamic response and performance change as the pilot attempts to compensate for the decrease in system stability, and these changes bias the simulation results by influencing the pilot's rating of the handling qualities of the simulated aircraft. Delay compensation, designed to restore pilot-aircraft system stability, was evaluated in several studies which are reported here. The studies range from single-axis, tracking-task experiments (with sufficient subjects and trials to establish statistical significance of the results) to a brief evaluation of compensation of a computer-generated-imagery (CGI) visual display system in a full six-degree-of-freedom simulation. The compensation was effective - improvements in pilot performance and workload or aircraft handling-qualities rating (HQR) were observed. Results from recent aircraft handling-qualities research literature which support the compensation design approach are also reviewed.

Crane, D. F.↗
NASA NTRS2014

Analytical Assessment of Simultaneous Parallel Approach Feasibility from Total System Error

In a simultaneous paired approach to closely-spaced parallel runways, a pair of aircraft flies in close proximity on parallel approach paths. The aircraft pair must maintain a longitudinal separation within a range that avoids wake encounters and, if one of the aircraft blunders, avoids collision. Wake avoidance defines the rear gate of the longitudinal separation. The lead aircraft generates a wake vortex that, with the aid of crosswinds, can travel laterally onto the path of the trail aircraft. As runway separation decreases, the wake has less distance to traverse to reach the path of the trail aircraft. The total system error of each aircraft further reduces this distance. The total system error is often modeled as a probability distribution function. Therefore, Monte-Carlo simulations are a favored tool for assessing a "safe" rear-gate. However, safety for paired approaches typically requires that a catastrophic wake encounter be a rare one-in-a-billion event during normal operation. Using a Monte-Carlo simulation to assert this event rarity with confidence requires a massive number of runs. Such large runs do not lend themselves to rapid turn-around during the early stages of investigation when the goal is to eliminate the infeasible regions of the solution space and to perform trades among the independent variables in the operational concept. One can employ statistical analysis using simplified models more efficiently to narrow the solution space and identify promising trades for more in-depth investigation using Monte-Carlo simulations. These simple, analytical models not only have to address the uncertainty of the total system error but also the uncertainty in navigation sources used to alert an abort of the procedure. This paper presents a method for integrating total system error, procedure abort rates, avionics failures, and surveillance errors into a statistical analysis that identifies the likely feasible runway separations for simultaneous paired approaches.

Madden, Michael M.↗