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NASA NTRSDate not supplied

On the Probabilistic Analysis of Neural Networks

Neural networks are powerful tools for automated decision-making,seeing increased application in safety-critical domains, such as autonomous driving. Due to their black-box nature and large scale,reasoning about their behavior is challenging. Statistical analysis is often used to infer probabilistic properties of a network, such as its robustness to noise and inaccurate inputs. While scalable, statistical methods can only provide probabilistic guarantees on the quality of their results and may underestimate the impact of low probability inputs leading to undesired behavior of the network.We investigate here the use of symbolic analysis and constraint solution space quantification to precisely quantify probabilistic properties in neural networks. We demonstrate the potential of the proposed technique in a case study involving the analysis of ACAS-Xu, a collision avoidance system for unmanned aircraft control.

neural nets↗
NASA NTRS2020

Monitoring Water-Related Ecosystems with Earth Observation Data in Support of Sustainable Development Goal (SDG) 6 Reporting

Lack of national data on water-related ecosystems is a major challenge to achieving the Sustainable Development Goal (SDG) 6 targets by 2030. Monitoring surface water extent, wetlands, and water quality from space can be an important asset for many countries in support of SDG 6 reporting. We demonstrate the potential for Earth observation (EO) data to support country reporting for SDG Indicator 6.6.1, ‘Change in the extent of water-related ecosystems over time’ and identify important considerations for countries using these data for SDG reporting. The spatial extent of water-related ecosystems, and the partial quality of water within these ecosystems is investigated for seven countries. Data from the Moderate Resolution Imaging Spectroradiometer (MODIS) and Landsat 5, 7, and 8 with Shuttle Radar Topography Mission (SRTM) are used to measure surface water extent at 250 m and 30 m spatial resolution, respectively, in Cambodia, Jamaica, Peru, the Philippines, Senegal, Uganda, and Zambia. The extent of mangroves is mapped at 30 m spatial resolution using Landsat 8 Operational Land Imager (OLI), Sentinel-1, and SRTM data for Jamaica, Peru, and Senegal. Using Landsat 8 and Sentinel 2A imagery, total suspended solids and chlorophyll-a are mapped over time for a select number of large surface water bodies in Peru, Senegal, and Zambia. All of the EO datasets used are of global coverage and publicly available at no cost. The temporal consistency and long time-series of many of the datasets enable replicability over time, making reporting of change from baseline values consistent and systematic. We find that statistical comparisons between different surface water data products can help provide some degree of confidence for countries during their validation process and highlight the need for accuracy assessments when using EO-based land change data for SDG reporting. We also raise concern that EO data in the context of SDG Indicator 6.6.1 reporting may be more challenging for some countries, such as small island nations, than others to use in assessing the extent of water-related ecosystems due to scale limitations and climate variability. Country-driven validation of the EO data products remains a priority to ensure successful data integration in support of SDG Indicator 6.6.1 reporting. Multi-country studies such as this one can be valuable tools for helping to guide the evolution of SDG monitoring methodologies and provide a useful resource for countries reporting on water-related ecosystems. The EO data analyses and statistical methods used in this study can be easily replicated for country-driven validation of EO data products in the future.

water-related ecosystems; surface water extent; ma↗
NASA NTRS2021

Topographic Correction of Geothermal Heat Flux in Greenland and Antarctica

Earth’s thick, polar ice sheets insulate the bedrock beneath them from the colder temperatures at the ice surface. Consequently, the small amount of geothermal heat that Earth’s bedrock releases can have a disproportionate role in controlling ice flow. Geothermal heat flux measurements beneath ice sheets are sparse, and models do not presently account for variable bed topography. Here, we present a simple statistical method for correcting geothermal heat flux models to make them consistent with known subglacial bed topography. This method is based on previous geothermal heat flux measurements across valleys and ridges, and it helps us explore the broader significance of geothermal heat flux variability beneath the Greenland and Antarctic ice sheets. Our method can also be used to estimate the influence of topography on geothermal heat flux in non-ice-covered areas.

William Colgan↗
NASA NTRSDate not supplied

PCB Quality Metrics that Drive Reliability

Risk-based technology infusion is a deliberate and systematic process that defines the analysis and communication methodology by which new technology is applied and integrated into existing and new designs, identifies technology development needs based on trends analysis and facilitates the identification of shortfalls against performance objectives. This presentation at IPC Works Asia Aerospace 2021 Events provides the audience a snapshot of quality variations in printed-wiring-board quality, as assessed, using experiences in processing and risk analysis of PWB structural integrity coupons. The presentation will focus on printed-wiring-board quality metrics used, the relative type and number of non-conformances observed and trend analysis using statistical methods. Trend analysis shows the top five non-conformances observed across PWB suppliers, the root cause(s) behind these non-conformance and suggestions of mitigation plans. The trends are then matched with the current state of the PWB supplier base and its challenges and opportunities. The presentation further discusses the risk-based SMA approaches and methods being applied at GSFC for evaluating candidate printed wiring board technologies that promote the adoption of higher throughput and faster processing technology for GSFC missions.

Printed circuit boards↗
NASA NTRS2021

In Situ Mg/Ca Measurements on Foraminifera: Comparison Between Laser Ablation Inductively Coupled Plasma Mass Spectrometry and Wavelength-Dispersive X-Ray Spectroscopy by Electron Probe Microanalyzer

We present a comparison of two different techniques: Laser Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS) and wavelength-dispersive X-Ray Spectroscopy by electron probe microanalyzer (EPMA) for obtaining Mg/Ca ratios in individual foraminifera shells. The goal is to assess the use of EPMA as an alternative technique for Mg/Ca analyses of single foraminiferal calcite shells. Foraminifera obtained from sediments (benthic, Uvigerina spp.) and from plankton tows (planktonic, Orbulina universa) were analyzed. All specimens were prepared in epoxy mounts and exposed in cross-section such that multiple high-resolution analyses could be completed on the shells using both techniques. We examined our data using statistical methods designed for the assessment and comparison of measurement techniques. In the case of Uvigerina, the mean difference for ratios obtained using EPMA and LA-ICP-MS is very small (−0.046 mmol mol−1) and scale independent. The Limits of Agreement (LoA, the standard deviation of the bias plus the mean bias) is [−0.315, 0.223] mmol mol−1. For samples with ratios lower than 13 mmol mol−1, we found a mean EPMA–LA-ICP-MS bias of −2.44 mmol mol−1 and a corresponding LoA of [−3.85, −1.04] mmol mol−1. For ratios higher than 13 mmol mol−1, there appears to be a scale dependent bias, meaning that the EPMA measured ratios become progressively larger than those of LA-ICP-MS as the Mg/Ca ratio increases, so the mean bias and LoA metrics are not meaningful. Results indicate that it is possible to use EPMA to collect Mg/Ca data, if the ratios are lower than ∼13 mmol mol−1.

EPMA↗
NASA NTRS2021

Maps of Magnetic Field Strength in the OMC-1 Using HAWC+FIR Polarimetric Data

Far-infrared dust polarimetry enables the study of interstellar magnetic fields via tracing of the polarized emission from dust grains that are partially aligned with the direction of the field. The advent of high-quality polarimetric data has permitted the use of statistical methods to extract both the direction and magnitude of the magnetic field. In this work, the Davis–Chandrasekhar–Fermi technique is used to make maps of the plane-of-sky (POS) component of the magnetic field in the Orion Molecular Cloud (OMC-1) by combining polarization maps at 53, 89, 154 and 214 μm from HAWC+/SOFIA with maps of density and velocity dispersion. In addition, maps of the local dispersion of polarization angles are used in conjunction with Zeeman measurements to estimate a map of the strength of the line-of-sight (LOS) component of the field. Combining these maps, information about the threedimensional magnetic field configuration (integrated along the LOS) is inferred over the OMC-1 region. POS magnetic field strengths of up to 2 mG are observed near the BN/KL object, while the OMC-1 bar shows strengths of up to a few hundred μG. These estimates of the magnetic field components are used to produce maps of the mass-to-magnetic-flux ratio (M/Φ)—a metric for probing the conditions for star formation in molecular clouds— and determine regions of sub- and supercriticality in OMC-1. Such maps can provide invaluable input and comparison to MHD simulations of star formation processes in filamentary structures of molecular clouds. Unified Astronomy Thesaurus concepts: Molecular clouds (1072); Giant molecular clouds (653); Interstellar magnetic fields (845); Far infrared astronomy (529)

Jordan A Guerra↗
NASA NTRS2020

Monitoring Water-Related Ecosystems with Earth Observation Data in Support of Sustainable Development Goal (SDG) 6 Reporting

Lack of national data on water-related ecosystems is a major challenge to achieving the Sustainable Development Goal (SDG) 6 targets by 2030. Monitoring surface water extent, wetlands, and water quality from space can be an important asset for many countries in support of SDG 6reporting. We demonstrate the potential for Earth observation (EO) data to support country reporting for SDG Indicator 6.6.1, ‘Change in the extent of water-related ecosystems over time’ and identify important considerations for countries using these data for SDG reporting. The spatial extent of water-related ecosystems, and the partial quality of water within these ecosystems is investigated for seven countries. Data from the Moderate Resolution Imaging Spectroradiometer (MODIS) and Landsat 5, 7, and 8 with Shuttle Radar Topography Mission (SRTM) are used to measure surface water extent at 250 m and 30 m spatial resolution, respectively, in Cambodia, Jamaica, Peru, the Philippines, Senegal, Uganda, and Zambia. The extent of mangroves is mapped at 30 m spatial resolution using Landsat 8 Operational Land Imager (OLI), Sentinel-1, and SRTM data for Jamaica, Peru, and Senegal. Using Landsat 8 and Sentinel 2A imagery, total suspended solids and chlorophyll-a are mapped overtime for a select number of large surface water bodies in Peru, Senegal, and Zambia. All of the EO datasets used are of global coverage and publicly available at no cost. The temporal consistency and long time-series of many of the datasets enable replicability over time, making reporting of change from baseline values consistent and systematic. We find that statistical comparisons between different surface water data products can help provide some degree of confidence for countries during their validation process and highlight the need for accuracy assessments when using EO-based land change data for SDG reporting. We also raise concern that EO data in the context of SDG Indicator 6.6.1reporting may be more challenging for some countries, such as small island nations, than others to use in assessing the extent of water-related ecosystems due to scale limitations and climate variability. Country-driven validation of the EO data products remains a priority to ensure successful data integration in support of SDG Indicator 6.6.1 reporting. Multi-country studies such as this one can be valuable tools for helping to guide the evolution of SDG monitoring methodologies and provide a useful resource for countries reporting on water-related ecosystems. The EO data analyses and statistical methods used in this study can be easily replicated for country-driven validation of EO data products in the future.

Raha Hakimdavar↗
NASA NTRS2020

Advancing Methodologies for Applying Machine Learning and Evaluating Spatiotemporal Models of Fine Particulate Matter (PM 2.5 ) Using Satellite Data Over Large Regions

Reconstructing the distribution of fine particulate matter (PM 2.5 ) in space and time, even far from ground monitoring sites, is an important exposure science contribution to epidemiologic analyses of PM 2.5 health impacts. Flexible statistical methods for prediction have demonstrated the integration of satellite observations with other predictors, yet these algorithms are susceptible to overfitting the spatiotemporal structure of the training datasets. We present a new approach for predicting PM 2.5 using machine-learning methods and evaluating prediction models for the goal of making predictions where they were not previously available. We apply extreme gradient boosting (XGBoost) modeling to predict daily PM 2.5 on a 1 x 1 km 2 resolution for a 13 state region in the Northeastern USA for the years 2000–2015 using satellite-derived aerosol optical depth and implement a recursive feature selection to develop a parsimonious model. We demonstrate excellent predictions of withheld observations but also contrast an RMSE of 3.11 μg/m 3 in our spatial cross-validation withholding nearby sites versus an overfit RMSE of 2.10 μg/m 3 using a more conventional random ten-fold splitting of the dataset. As the field of exposure science moves forward with the use of advanced machine-learning approaches for spatiotemporal modeling of air pollutants, our results show the importance of addressing data leakage in training, overfitting to spatiotemporal structure, and the impact of the predominance of ground monitoring sites in dense urban sub-networks on model evaluation. The strengths of our resultant modeling approach for exposure in epidemiologic studies of PM 2.5 include improved efficiency, parsimony, and interpretability with robust validation while still accommodating complex spatiotemporal relationships.

air pollution↗
NASA NTRS2021

Unsteady Pressure-Sensitive-Paint Shot Noise Reduction

In the study of unsteady Pressure-Sensitive Paint (uPSP) image data sets, pixel intensity values collected by Phantom cameras from multiple perspectives are used to calculate the surface pressure of an experimental model. This paper focuses on mitigation of shot noise which is introduced into the image data set by the cameras. Shot noise impacts the quality of data collected, increasing the system error in its pressure value calculations. This paper characterises statistical methods to reduce shot noise within experimental data by taking an average or weighted average across an area of pixels of their respective counts. Each combined-pixel has a higher total effective intensity value and therefore exhibits reduced noise throughout its time history. This is demonstrated by calculating the standard deviations of the combined pixel values through time, which decrease as the combined pixel area increases. Finally, these methods are compared across experimental wind tunnel conditions to examine their effectiveness at different Mach numbers. Ultimately, the results are used to recommend a blur filter type and size which will be applied to the raw image data prior to processing, as well as a minimum camera resolution for future experiments. Downstream of the filter application, the software to convert the 2D image data sets into surface pressure readings on a 3D grid use a ratio of decimation that assigns multiple pixels to each 3D grid node. This decimation ratio will also be aligned with the size of the blur filter, resulting in a more manageable data set size and compromised spatial resolution. Combined with the effect of the blur filter, the resulting pixel intensity readings will exhibit significantly reduced shot noise, reducing the magnitude of uncertainty and error in the final calculated pressure. For future tests, the camera spatial resolution must be sufficient to capture small flow and model features even after the recommended blur filter is applied. The image data set is taken from a uPSP experiment of the Space Launch System Block 1 cargo vehicle model in September 2019.

Lucy Tang↗
NASA NTRS2021

Unsteady Pressure-Sensitive Paint (UPSP) Shot Noise Reduction

In the study of unsteady Pressure-Sensitive Paint (uPSP) image data sets, pixel intensity values collected by Phantom cameras from multiple perspectives are used to calculate the surface pressure of an experimental model. This paper focuses on mitigation of shot noise which is introduced into the image data set by the cameras. Shot noise impacts the quality of data collected, increasing the system error in its pressure value calculations. This paper characterises statistical methods to reduce shot noise within experimental data by taking an average or weighted average across an area of pixels of their respective counts. Each combined-pixel has a higher total effective intensity value and therefore exhibits reduced noise throughout its time history. This is demonstrated by calculating the standard deviations of the combined pixel values through time, which decrease as the combined pixel area increases. Finally, these methods are compared across experimental wind tunnel conditions to examine their effectiveness at different Mach numbers. Ultimately, the results are used to recommend a blur filter type and size which will be applied to the raw image data prior to processing, as well as a minimum camera resolution for future experiments. Downstream of the filter application, the software to convert the 2D image data sets into surface pressure readings on a 3D grid use a ratio of decimation that assigns multiple pixels to each 3D grid node. This decimation ratio will also be aligned with the size of the blur filter, resulting in a more manageable data set size and compromised spatial resolution. Combined with the effect of the blur filter, the resulting pixel intensity readings will exhibit significantly reduced shot noise, reducing the magnitude of uncertainty and error in the final calculated pressure. For future tests, the camera spatial resolution must be sufficient to capture small flow and model features even after the recommended blur filter is applied. The image data set is taken from a uPSP experiment of the Space Launch System Block 1 cargo vehicle model in September 2019.

Lucy Tang↗
NASA NTRS2021

Measurement Uncertainty Analysis of 6x9 Icing Research Tunnel (IRT)

This paper presents the results of the measurement uncertainty analysis that was performed on the aero-thermal characteristics of the 6- by 9-Foot Icing Research Tunnel (IRT) at the NASA Glenn Research Center. The engineering judgments and statistical methods used to determine the elemental uncertainties are described. Instrumentation uncertainty was quanti ed using MANTUS (Measurement Analysis Tool for Uncertainty in Systems) and instrument speci cation sheets. The Monte Carlo method was used to propagate systematic components of uncertainty in order to quantify the uncertainty of the Variables of Interest (VOI). A detailed description of the Monte Carlo method and the MANTUS tool can be found in the Uncertainty Analysis of the NASA Glenn 8x6 Supersonic Wind Tunnel report [1]. Detailed uncertainty results for test section airspeed and temperature as well as other variables of interest are described within this document.

6x9 Icing Research Tunnel↗
NASA NTRS2021

Refined Mass and Geometric Measurements of the High-mass PSR J0740+6620

We report results from continued timing observations of PSR J0740+6620, a high-mass, 2.8 ms radio pulsar in orbit with a likely ultracool white dwarf companion. Our data set consists of combined pulse arrival-time measurements made with the 100 m Green Bank Telescope and the Canadian Hydrogen Intensity Mapping Experiment telescope. We explore the significance of timing-based phenomena arising from general relativistic dynamics and variations in pulse dispersion. When using various statistical methods, we find that combining∼1.5 yr of additional, high-cadence timing data with previous measurements confirms and improves on previous estimates of relativistic effects within the PSR J0740+6620 system, with the pulsar mass=-+mM2.08p0.070.07 M (68.3% credibility) determined by the relativistic Shapiro time delay. For the first time, we measure secular variation in the orbital period and argue that this effect arises from apparent acceleration due to significant transverse motion. After incorporating contributions from Galactic differential rotation and off-plane acceleration in the Galactic potential, we obtain a model-dependent distance of=-+d1.140.150.17kpc (68.3% credibility). This improved distance confirms the ultracool nature of the white dwarf companion determined from recent optical observations. We discuss the prospects for future observations with next-generation facilities, which will likely improve the precision on mp for J0740+6620 by an order of magnitude within the next few years

Neutron stars↗
NASA NTRSDate not supplied

A Physics of Failure Approach to Evaluate Printed Circuit Board Reliability

Risk based technology infusion is a deliberate and systematic process which defines the analysis and communication methodology by which new technology is applied and integrated into existing and new designs, identifies technology development needs based on trends analysis and facilitates the identification of shortfalls against performance objectives. This presentation at IPC Works Asia Aerospace 2019 Events provides the audience a snapshot of quality variations in printed wiring board quality, as assessed, using experiences in processing and risk analysis of PWB structural integrity coupons. The presentation will focus on printed wiring board quality metrics used, the relative type and number of non-conformances observed and trend analysis using statistical methods. Trend analysis shows the top five non-conformances observed across PWB suppliers, the root cause(s) behind these non-conformance and suggestions of mitigation plans. The trends will then be matched with the current state of the PWB supplier base and its challenges and opportunities. The presentation further discusses the risk based SMA approaches and methods being applied at GSFC for evaluating candidate printed wiring board technologies which promote the adoption of higher throughput and faster processing technology for GSFC missions.

Printed Circuit Boards↗
NASA NTRSDate not supplied

Experiences in the Practice of Design of Experiments at NASA

Statistical design of experiments (DOE) has gained recognition within NASA by spurring innovation and efficiency, and it has demonstrated significant impact. Aerospace research and development benefits DOE techniques by accelerating learning, maximizing knowledge, ensuring strategic resource investment, and informing data-driven decisions. In practice, DOE relies on multidisciplinary collaboration to develop solution strategies that integrate statistical methods with subject-matter expertise to meet challenging research objectives. This presentation shares experiences in the practice of design of experiments at NASA in aeronautics, space exploration, and atmospheric science.

Peter A. Parker↗
NASA NTRS2022

The Origins of Long-Term Variability in Martian Upper Atmospheric Densities

We quantify and interpret the long-term variability of dayside Martian upper thermosphere and lower exosphere densities within 180–275 km altitudes. Atmospheric CO2, N2, O, and Ar densities are from NASA Mars Atmosphere and Volatile EvolutioN (MAVEN) observations during the time period of 2015–2020 near solar minimum. These neutral measurements, together with contemporaneous solar irradiance measurements at Mars, enable disentanglement of the orbital effect (due to the annual Sun-Mars distance change with solar longitude) and the solar extreme ultraviolet (EUV) effect in atmospheric density variations. The relative importance of these two effects, which is obtained using a statistical method of Dominance Analysis, reveals the competition between the indirect effect of solar infrared (via the upward coupling from the middle atmosphere) and the direct effect of solar EUV (due to local heating). Our results show that, unlike the orbital effect which is relatively constant at low altitudes and then decreases with increasing altitude, the solar EUV effect nearly monotonically increases. These two effects are comparable at high altitudes (about 240/270/205 km for CO2/N2/O). This analysis is extended to include long-term exospheric mass density estimates near 400 km from Mars Global Surveyor and Mars Odyssey data, with a focus on representative solar cycle phases of solar minimum and maximum. It is found that near 400 km, the orbital effect is always a key driver regardless of the solar cycle phase, while the solar EUV effect plays a minor role during solar minimum and is greatly enhanced and slightly exceeds the orbital effect during solar maximum.

Xiaohua Fang↗
NASA NTRS2020

Global earth mineral inventory: A data legacy

Minerals contain important clues to understanding the complex geologic history of Earth and other planetary bodies. Therefore, geologists have been collecting mineral samples and compiling data about these samples for centuries. These data have been used to better understand the movement of continental plates, the oxidation of Earth's atmosphere and the water regime of ancient martian landscapes. Datasets found at ‘RRUFF.info/Evolution’ and ‘mindat.org’ have documented a wealth of mineral occurrences around the world. One of the main goals in geoinformatics has been to facilitate discovery by creating and merging datasets from various scientific fields and using statistical methods and visualization tools to inspire and test hypotheses applicable to modelling Earth's past environments. To help achieve this goal, we have compiled physical, chemical and geological properties of minerals and linked them to the above-mentioned mineral occurrence datasets. As a part of the Deep Time Data Infrastructure, funded by the W.M. Keck Foundation, with significant support from the Deep Carbon Observatory (DCO) and the A.P. Sloan Foundation, GEMI (‘Global Earth Mineral Inventory’) was developed from the need of researchers to have all of the required mineral data visible in a single portal, connected by a robust, yet easy to understand schema. Our data legacy integrates these resources into a digestible format for exploration and analysis and has allowed researchers to gain valuable insights from mineralogical data. GEMI can be considered a network, with every node representing some feature of the datasets, for example, a node can represent geological parameters like colour, hardness or lustre. Exploring subnetworks gives the researcher a specific view of the data required for the task at hand. GEMI is accessible through the DCO Data Portal (https://dx.deepcarbon.net/11121/6200-6954-6634-8243-CC). We describe our efforts in compiling GEMI, the Data Policies for usage and sharing, and the evaluation metrics for this data legacy.

data legacy↗
NASA NTRS1978

Cumulative fade statistics and prediction methods associated with the COMSTAR beacon signal at 28.56 GHz

The paper presents cumulative fade statistics for the period April 1977 to March 1978 and reviews the rain attenuation predictive efforts using radar and disdrometer data for the summer of 1977. Attention is given to the receiving and radar systems as well as the disdrometer-raingage system. Discussion of the fade statistics covers the yearly, monthly and time of day statistics. Consideration is given to measured and predicted attenuation events, measured and predicted probability distributions as well as an empirical calibration adjustment. It is noted that in spite of many reasons for noncorrelation, the radar results do correlate well. Finally, it is concluded that the results demonstrate the utility of using radar coupled with disdrometer measurements for predicting individual fade events as well as long term fade distributions associated with satellite communications through rain.

Goldhirsh, J.↗
NASA NTRS2006

Jet Noise Diagnostics Supporting Statistical Noise Prediction Methods

The primary focus of my presentation is the development of the jet noise prediction code JeNo with most examples coming from the experimental work that drove the theoretical development and validation. JeNo is a statistical jet noise prediction code, based upon the Lilley acoustic analogy. Our approach uses time-average 2-D or 3-D mean and turbulent statistics of the flow as input. The output is source distributions and spectral directivity. NASA has been investing in development of statistical jet noise prediction tools because these seem to fit the middle ground that allows enough flexibility and fidelity for jet noise source diagnostics while having reasonable computational requirements. These tools rely on Reynolds-averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) solutions as input for computing far-field spectral directivity using an acoustic analogy. There are many ways acoustic analogies can be created, each with a series of assumptions and models, many often taken unknowingly. And the resulting prediction can be easily reverse-engineered by altering the models contained within. However, only an approach which is mathematically sound, with assumptions validated and modeled quantities checked against direct measurement will give consistently correct answers. Many quantities are modeled in acoustic analogies precisely because they have been impossible to measure or calculate, making this requirement a difficult task. The NASA team has spent considerable effort identifying all the assumptions and models used to take the Navier-Stokes equations to the point of a statistical calculation via an acoustic analogy very similar to that proposed by Lilley. Assumptions have been identified and experiments have been developed to test these assumptions. In some cases this has resulted in assumptions being changed. Beginning with the CFD used as input to the acoustic analogy, models for turbulence closure used in RANS CFD codes have been explored and compared against measurements of mean and rms velocity statistics over a range of jet speeds and temperatures. Models for flow parameters used in the acoustic analogy, most notably the space-time correlations of velocity, have been compared against direct measurements, and modified to better fit the observed data. These measurements have been extremely challenging for hot, high speed jets, and represent a sizeable investment in instrumentation development. As an intermediate check that the analysis is predicting the physics intended, phased arrays have been employed to measure source distributions for a wide range of jet cases. And finally, careful far-field spectral directivity measurements have been taken for final validation of the prediction code. Examples of each of these experimental efforts will be presented. The main result of these efforts is a noise prediction code, named JeNo, which is in middevelopment. JeNo is able to consistently predict spectral directivity, including aft angle directivity, for subsonic cold jets of most geometries. Current development on JeNo is focused on extending its capability to hot jets, requiring inclusion of a previously neglected second source associated with thermal fluctuations. A secondary result of the intensive experimentation is the archiving of various flow statistics applicable to other acoustic analogies and to development of time-resolved prediction methods. These will be of lasting value as we look ahead at future challenges to the aeroacoustic experimentalist.

Bridges, James E.↗