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NASA NTRS2010

Composite Overwrapped Pressure Vessels (COPV): Developing Flight Rationale for the Space Shuttle Program

Introducing composite vessels into the Space Shuttle Program represented a significant technical achievement. Each Orbiter vehicle contains 24 (nominally) Kevlar tanks for storage of pressurized helium (for propulsion) and nitrogen (for life support). The use of composite cylinders saved 752 pounds per Orbiter vehicle compared with all-metal tanks. The weight savings is significant considering each Shuttle flight can deliver 54,000 pounds of payload to the International Space Station. In the wake of the Columbia accident and the ensuing Return to Flight activities, the Space Shuttle Program, in 2005, re-examined COPV hardware certification. Incorporating COPV data that had been generated over the last 30 years and recognizing differences between initial Shuttle Program requirements and current operation, a new failure mode was identified, as composite stress rupture was deemed credible. The Orbiter Project undertook a comprehensive investigation to quantify and mitigate this risk. First, the engineering team considered and later deemed as unfeasible the option to replace existing all flight tanks. Second, operational improvements to flight procedures were instituted to reduce the flight risk and the danger to personnel. Third, an Orbiter reliability model was developed to quantify flight risk. Laser profilometry inspection of several flight COPVs identified deep (up to 20 mil) depressions on the tank interior. A comprehensive analysis was performed and it confirmed that these observed depressions were far less than the criterion which was established as necessary to lead to liner buckling. Existing fleet vessels were exonerated from this failure mechanism. Because full validation of the Orbiter Reliability Model was not possible given limited hardware resources, an Accelerated Stress Rupture Test of a flown flight vessel was performed to provide increased confidence. A Bayesian statistical approach was developed to evaluate possible test results with respect to the model credibility and thus flight rationale for continued operation of the Space Shuttle with existing flight hardware. A non-destructive evaluation (NDE) technique utilizing Raman Spectroscopy was developed to directly measure the overwrap residual stress state. Preliminary results provide optimistic results that patterns of fluctuation in fiber elastic strains over the outside vessel surface could be directly correlated with increased fiber stress ratios and thus reduced reliability.

Kezirian, Michael T.↗

NASA NTRS2011

Integration of Evidence Base into a Probabilistic Risk Assessment

INTRODUCTION: A probabilistic decision support model such as the Integrated Medical Model (IMM) utilizes an immense amount of input data that necessitates a systematic, integrated approach for data collection, and management. As a result of this approach, IMM is able to forecasts medical events, resource utilization and crew health during space flight. METHODS: Inflight data is the most desirable input for the Integrated Medical Model. Non-attributable inflight data is collected from the Lifetime Surveillance for Astronaut Health study as well as the engineers, flight surgeons, and astronauts themselves. When inflight data is unavailable cohort studies, other models and Bayesian analyses are used, in addition to subject matters experts input on occasion. To determine the quality of evidence of a medical condition, the data source is categorized and assigned a level of evidence from 1-5; the highest level is one. The collected data reside and are managed in a relational SQL database with a web-based interface for data entry and review. The database is also capable of interfacing with outside applications which expands capabilities within the database itself. Via the public interface, customers can access a formatted Clinical Findings Form (CLiFF) that outlines the model input and evidence base for each medical condition. Changes to the database are tracked using a documented Configuration Management process. DISSCUSSION: This strategic approach provides a comprehensive data management plan for IMM. The IMM Database s structure and architecture has proven to support additional usages. As seen by the resources utilization across medical conditions analysis. In addition, the IMM Database s web-based interface provides a user-friendly format for customers to browse and download the clinical information for medical conditions. It is this type of functionality that will provide Exploratory Medicine Capabilities the evidence base for their medical condition list. CONCLUSION: The IMM Database in junction with the IMM is helping NASA aerospace program improve the health care and reduce risk for the astronauts crew. Both the database and model will continue to expand to meet customer needs through its multi-disciplinary evidence based approach to managing data. Future expansion could serve as a platform for a Space Medicine Wiki of medical conditions.

Saile, Lyn↗

NASA NTRS2010

Comparison of Postural Recovery Following Short and Long Duration Spaceflights

INTRODUCTION: Post-flight postural ataxia reflects adaptive changes to vestibulo-spinal reflexes and control strategies adopted for movement in weightlessness. Quantitative measures obtained during computerized dynamic posturography (CDP) from US and Russian programs provide insight into the effect of spaceflight duration in terms of both the initial decrements and recovery of postural stability. METHODS: CDP was obtained on 117 crewmembers following Shuttle flights lasting 4-17 days, and on 64 crewmembers following long-duration missions lasting 48-380 days. Although the number and timing of sessions varied, the goal was to characterize postural recovery pooling similar measures from different research and flight medicine programs. This report focuses on eyes closed, head erect conditions with either a fixed or sway-referenced base of support. A smaller subset of subjects repeated the sway-referenced condition while making pitch head movements (+/- 20deg at 0.33Hz). Equilibrium scores were derived from peak-to-peak anterior-posterior sway. Fall probability was modeled using Bayesian statistical methods to estimate parameters of a logit function. RESULTS: The standard Romberg condition was the least sensitive. Longer duration flights led to larger decrements in stability with sway-reference support during the first 1-2 days, although the timecourse of recovery was similar across flight duration with head erect. Head movements led to increased incidence of falls during the first week, with a significantly longer recovery following long duration flights. CONCLUSIONS: The diagnostic assessment of postural instability, and differences in the timecourse of postural recovery between short and long flight durations, are more pronounced during unstable support conditions requiring active head movements.

Wood, S. J.↗

NASA NTRS2010

JSC Safety and Mission Assurance Data Analysis Overview

These slides describe the data analysis methods that are used to determine inputs for probabilistic risk models supporting the Space Shuttle Program. Other applications can follow a similar path probably using different data sources. Statistical approaches are different and not addressed here. Topics included here: 1) Prior Distribution; 2) Likelihood Data; 3) Bayesian Updating; and 4) Uncertainty and Error. Note: This is a high-level discussion and is not intended to be a tutorial.

Roelant, Henk↗

NASA NTRS2011

Visual SLAM Using Variance Grid Maps

An algorithm denoted Gamma-SLAM performs further processing, in real time, of preprocessed digitized images acquired by a stereoscopic pair of electronic cameras aboard an off-road robotic ground vehicle to build accurate maps of the terrain and determine the location of the vehicle with respect to the maps. Part of the name of the algorithm reflects the fact that the process of building the maps and determining the location with respect to them is denoted simultaneous localization and mapping (SLAM). Most prior real-time SLAM algorithms have been limited in applicability to (1) systems equipped with scanning laser range finders as the primary sensors in (2) indoor environments (or relatively simply structured outdoor environments). The few prior vision-based SLAM algorithms have been feature-based and not suitable for real-time applications and, hence, not suitable for autonomous navigation on irregularly structured terrain. The Gamma-SLAM algorithm incorporates two key innovations: Visual odometry (in contradistinction to wheel odometry) is used to estimate the motion of the vehicle. An elevation variance map (in contradistinction to an occupancy or an elevation map) is used to represent the terrain. The Gamma-SLAM algorithm makes use of a Rao-Blackwellized particle filter (RBPF) from Bayesian estimation theory for maintaining a distribution over poses and maps. The core idea of the RBPF approach is that the SLAM problem can be factored into two parts: (1) finding the distribution over robot trajectories, and (2) finding the map conditioned on any given trajectory. The factorization involves the use of a particle filter in which each particle encodes both a possible trajectory and a map conditioned on that trajectory. The base estimate of the trajectory is derived from visual odometry, and the map conditioned on that trajectory is a Cartesian grid of elevation variances. In comparison with traditional occupancy or elevation grid maps, the grid elevation variance maps are much better for representing the structure of vegetated or rocky terrain.

Howard, Andrew B.↗

NASA NTRS2010

Utilization of Hydrologic Remote Sensing Data in Land Surface Modeling and Data Assimilation: Current Status and Challenges

Recent advances in remote sensing technologies have enabled the monitoring and measurement of the Earth's land surface at an unprecedented scale and frequency. The myriad of these land surface observations must be integrated with the state-of-the-art land surface model forecasts using data assimilation to generate spatially and temporally coherent estimates of environmental conditions. These analyses are of critical importance to real-world applications such as agricultural production, water resources management and flood, drought, weather and climate prediction. This need motivated the development of NASA Land Information System (LIS), which is an expert system encapsulating a suite of modeling, computational and data assimilation tools required to address challenging hydrological problems. LIS integrates the use of several community land surface models, use of ground and satellite based observations, data assimilation and uncertainty estimation techniques and high performance computing and data management tools to enable the assessment and prediction of hydrologic conditions at various spatial and temporal scales of interest. This presentation will focus on describing the results, challenges and lessons learned from the use of remote sensing data for improving land surface modeling, within LIS. More specifically, studies related to the improved estimation of soil moisture, snow and land surface temperature conditions through data assimilation will be discussed. The presentation will also address the characterization of uncertainty in the modeling process through Bayesian remote sensing and computational methods.

Kumar, Sujay V.↗

NASA NTRS2010

Physics-Based Methods of Failure Analysis and Diagnostics in Human Space Flight

The Integrated Health Management (IHM) for the future aerospace systems requires to interface models of multiple subsystems in an efficient and accurate information environment at the earlier stages of system design. The complexity of modern aeronautic and aircraft systems (including e.g. the power distribution, flight control, solid and liquid motors) dictates employment of hybrid models and high-level reasoners for analysing mixed continuous and discrete information flow involving multiple modes of operation in uncertain environments, unknown state variables, heterogeneous software and hardware components. To provide the information link between key design/performance parameters and high-level reasoners we rely on development of multi-physics performance models, distributed sensors networks, and fault diagnostic and prognostic (FD&P) technologies in close collaboration with system designers. The main challenges of our research are related to the in-flight assessment of the structural stability, engine performance, and trajectory control. The main goal is to develop an intelligent IHM that not only enhances components and system reliability, but also provides a post-flight feedback helping to optimize design of the next generation of aerospace systems. Our efforts are concentrated on several directions of the research. One of the key components of our strategy is an innovative approach to the diagnostics/prognostics based on the real time dynamical inference (DI) technologies extended to encompass hybrid systems with hidden state trajectories. The major investments are into the multiphysics performance modelling that provides an access of the FD&P technologies to the main performance parameters of e.g. solid and liquid rocket motors and composite materials of the nozzle and case. Some of the recent results of our research are discussed in this chapter. We begin by introducing the problem of dynamical inference of stochastic nonlinear models and reviewing earlier results. Next, we present our analytical approach to the solution of this problem based on the path integral formulation. The resulting algorithm does not require an extensive global search for the model parameters, provides optimal compensation for the effects of dynamical noise, and is robust for a broad range of dynamical models. In the following Section the strengths of the algorithm are illustrated illustrated by inferring the parameters of the stochastic Lorenz system and comparing the results with those of earlier research. Next, we discuss a number of recent results in application to the development of the IHM for aerospace system. Firstly, we apply dynamical inference approach to a solution of classical three tank problems with mixed unknown continuous and binary parameters. The problem is considered in the context of ground support system for filling fuel tanks of liquid rocket motors. It is shown that the DI algorithm is well suited for successful solution of a hybrid version of this benchmark problem even in the presence of additional periodic and stochastic perturbation of unknown strength. Secondly, we illustrate our approach by its application to an analysis of the nozzle fault in a solid rocket motor (SRM). The internal ballistics of the SRM is modelled as a set of one-dimensional partial differential equations coupled to the dynamics of the propellant regression. In this example we are specifically focussed on the inference of discrete and continuous parameters of the nozzle blocking fault and on the possibility of an application of the DI algorithm to reducing the probability of "misses" of an on-board FD&P for SRM. In the next section re-contact problem caused by first stage/upper stage separation failure is discussed. The reaction forces imposed on the nozzle of the upper stage during the re-contact and their connection to the nozzle damage and to the thrust vector control (TVC) signal are obtained. It is shown that transient impact induced torquean be modelled as a response of an effective damped oscillator. A possible application of the DI algorithm to the inference of damage parameters and predicting fault dynamics ahead of time using the actuator signal is discussed. Finally, we formulate Bayesian inferential framework for development of the IHM system for in-flight structural health monitoring (SHM) of composite materials. We consider the signal generated by piezoelectric actuator mounted on composite structure generating elastic waves in it. The signal received by the sensor is than compared with the baseline signal. The possibility of damage inference is discussed in the context of development of the SHM.

Smelyanskiy, Vadim N.↗

NASA NTRS2010

Parameter Estimation with Entangled Photons Produced by Parametric Down-Conversion

We explore the advantages offered by twin light beams produced in parametric down-conversion for precision measurement. The symmetry of these bipartite quantum states, even under losses, suggests that monitoring correlations between the divergent beams permits a high-precision inference of any symmetry-breaking effect, e.g., fiber birefringence. We show that the quantity of entanglement is not the key feature for such an instrument. In a lossless setting, scaling of precision at the ultimate "Heisenberg" limit is possible with photon counting alone. Even as photon losses approach 100% the precision is shot-noise limited, and we identify the crossover point between quantum and classical precision as a function of detected flux. The predicted hypersensitivity is demonstrated with a Bayesian simulation.

Cable, Hugo↗

NASA NTRS2011

Composite Overwrapped Pressure Vessels (COPV): Flight Rationale for the Space Shuttle Program

Each Orbiter Vehicle (Space Shuttle Program) contains up to 24 Kevlar49/Epoxy Composite Overwrapped Pressure Vessels (COPV) for storage of pressurized gases. In the wake of the Columbia accident and the ensuing Return To Flight (RTF) activities, Orbiter engineers reexamined COPV flight certification. The original COPV design calculations were updated to include recently declassified Kevlar COPV test data from Lawrence Livermore National Laboratory (LLNL) and to incorporate changes in how the Space Shuttle was operated as opposed to orinigially envisioned. 2005 estimates for the probability of a catastrophic failure over the life of the program (from STS-1 through STS-107) were one-in-five. To address this unacceptable risk, the Orbiter Project Office (OPO) initiated a comprehensive investigation to understand and mitigate this risk. First, the team considered and eventually deemed unfeasible procuring and replacing all existing flight COPVs. OPO replaced the two vessels with the highest risk with existing flight spare units. Second, OPO instituted operational improvements in ground procedures to signficiantly reduce risk, without adversely affecting Shuttle capability. Third, OPO developed a comprehensive model to quantify the likelihood of occurrance. A fully-instrumented burst test (recording a lower burst pressure than expected) on a flight-certified vessel provided critical understanding of the behavior of Orbiter COPVs. A more accurate model was based on a newly-compiled comprehensive database of Kevlar data from LLNL and elsewhere. Considering hardware changes, operational improvements and reliability model refinements, the mean reliability was determined to be 0.998 for the remainder of the Shuttle Program (from 2007, for STS- 118 thru STS-135). Since limited hardware resources precluded full model validation through multiple tests, additional model confidence was sought through the first-ever Accelerated Stress Rupture Test (ASRT) of a flown flight article. A Bayesian statistical approach was developed to interpret possible test results. Since the lifetime observed in the ASRT exceeded initial estimates by one to two orders of magnitude, the Space Shuttle Program deemed there was significant conservatism in the model and accepted continued operation with existing flight hardware. Given the variability in tank-to-tank original prooftest response, a non-destructive evaluation (NDE) technique utilizing Raman Spectroscopy was developed to directly measure COPV residual stress state. Preliminary results showed that patterns of low fiber elastic strains over the outside vessel surface, together with measured permanent volume growth during proof, could be directly correlated to increased fiber stress ratios on the inside fibers adjacent to the liner, and thus reduced reliability.

Kezirian, Michael T.↗

NASA NTRS2011

Towards Measurement of Confidence in Safety Cases

Arguments in safety cases are predominantly qualitative. This is partly attributed to the lack of sufficient design and operational data necessary to measure the achievement of high-dependability targets, particularly for safety-critical functions implemented in software. The subjective nature of many forms of evidence, such as expert judgment and process maturity, also contributes to the overwhelming dependence on qualitative arguments. However, where data for quantitative measurements is systematically collected, quantitative arguments provide far more benefits over qualitative arguments, in assessing confidence in the safety case. In this paper, we propose a basis for developing and evaluating integrated qualitative and quantitative safety arguments based on the Goal Structuring Notation (GSN) and Bayesian Networks (BN). The approach we propose identifies structures within GSN-based arguments where uncertainties can be quantified. BN are then used to provide a means to reason about confidence in a probabilistic way. We illustrate our approach using a fragment of a safety case for an unmanned aerial system and conclude with some preliminary observations

Denney, Ewen↗

NASA NTRS2004

NASA Tech Briefs, January 2004

Topics covered include: Multisensor Instrument for Real-Time Biological Monitoring; Sensor for Monitoring Nanodevice-Fabrication Plasmas; Backed Bending Actuator; Compact Optoelectronic Compass; Micro Sun Sensor for Spacecraft; Passive IFF: Autonomous Nonintrusive Rapid Identification of Friendly Assets; Finned-Ladder Slow-Wave Circuit for a TWT; Directional Radio-Frequency Identification Tag Reader; Integrated Solar-Energy-Harvesting and -Storage Device; Event-Driven Random-Access-Windowing CCD Imaging System; Stroboscope Controller for Imaging Helicopter Rotors; Software for Checking State-charts; Program Predicts Broadband Noise from a Turbofan Engine; Protocol for a Delay-Tolerant Data-Communication Network; Software Implements a Space-Mission File-Transfer Protocol; Making Carbon-Nanotube Arrays Using Block Copolymers: Part 2; Modular Rake of Pitot Probes; Preloading To Accelerate Slow-Crack-Growth Testing; Miniature Blimps for Surveillance and Collection of Samples; Hybrid Automotive Engine Using Ethanol-Burning Miller Cycle; Fabricating Blazed Diffraction Gratings by X-Ray Lithography; Freeze-Tolerant Condensers; The StarLight Space Interferometer; Champagne Heat Pump; Controllable Sonar Lenses and Prisms Based on ERFs; Measuring Gravitation Using Polarization Spectroscopy; Serial-Turbo-Trellis-Coded Modulation with Rate-1 Inner Code; Enhanced Software for Scheduling Space-Shuttle Processing; Bayesian-Augmented Identification of Stars in a Narrow View; Spacecraft Orbits for Earth/Mars-Lander Radio Relay; and Self-Inflatable/Self-Rigidizable Reflectarray Antenna.

Source record↗

NASA NTRS2011

Obscured AGN

Many obscured AGN show evidence of significant starburst emission dominating below 2 keV. Therefore wide-field X-ray surveys sensitive enough to luminosities below approximately 10^42 ergs per second will result in detections of galaxies with contributions of both obscured AGN and starburst emission. We will discuss Bayesian approaches to assessing the relative contribution of each component, minimizing survey biases and using the resultant posterior probabilities for the AGN and starburst components to determine their evolution.

Ptak, Andrew↗

NASA NTRS2010

Lunar Terrain and Albedo Reconstruction from Apollo Imagery

Generating accurate three dimensional planetary models and albedo maps is becoming increasingly more important as NASA plans more robotics missions to the Moon in the coming years. This paper describes a novel approach for separation of topography and albedo maps from orbital Lunar images. Our method uses an optimal Bayesian correlator to refine the stereo disparity map and generate a set of accurate digital elevation models (DEM). The albedo maps are obtained using a multi-image formation model that relies on the derived DEMs and the Lunar- Lambert reflectance model. The method is demonstrated on a set of high resolution scanned images from the Apollo era missions.

Nefian, Ara V.↗

NASA NTRS2003

Automated Monitoring with a BSP Fault-Detection Test

The figure schematically illustrates a method and procedure for automated monitoring of an asset, as well as a hardware- and-software system that implements the method and procedure. As used here, asset could signify an industrial process, power plant, medical instrument, aircraft, or any of a variety of other systems that generate electronic signals (e.g., sensor outputs). In automated monitoring, the signals are digitized and then processed in order to detect faults and otherwise monitor operational status and integrity of the monitored asset. The major distinguishing feature of the present method is that the fault-detection function is implemented by use of a Bayesian sequential probability (BSP) technique. This technique is superior to other techniques for automated monitoring because it affords sensitivity, not only to disturbances in the mean values, but also to very subtle changes in the statistical characteristics (variance, skewness, and bias) of the monitored signals.

Bickford, Randall L.↗

NASA NTRS2011

Obtaining the Grobner Initialization for the Ground Flash Fraction Retrieval Algorithm

At optical wavelengths and from the vantage point of space, the multiple scattering cloud medium obscures one's view and prevents one from easily determining what flashes strike the ground. However, recent investigations have made some progress examining the (easier, but still difficult) problem of estimating the ground flash fraction in a set of N flashes observed from space In the study by Koshak, a Bayesian inversion method was introduced for retrieving the fraction of ground flashes in a set of flashes observed from a (low earth orbiting or geostationary) satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters, a scalar function of three variables (one of which is the ground flash fraction) was minimized by a numerical method. This method has formed the basis of a Ground Flash Fraction Retrieval Algorithm (GoFFRA) that is being tested as part of GOES-R GLM risk reduction.

Solakiewicz, R.↗

NASA NTRS2011

A Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

A Bayesian inversion method was previously introduced for retrieving the fraction of ground flashes in a set of flashes observed from a (low earth orbiting or geostationary) satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters, a scalar function was minimized by a numerical method. In order to improve this optimization, we introduce a Grobner basis solution to obtain analytic representations of the model parameters that serve as a refined initialization scheme to the numerical optimization. Using the Grobner basis, we show that there are exactly 2 solutions involving the first 3 moments of the (exponentially distributed) data. When the mean of the ground flash optical characteristic (e.g., such as the Maximum Group Area, MGA) is larger than that for cloud flashes, then a unique solution can be obtained.

Solakiewicz, Richard↗

NASA NTRS2012

Thermal Behaviour of Unusual Local-Scale Surface Features on Vesta

On Vesta, the region of the infrared spectrum beyond approximately 3.5 micrometers is dominated by the thermal emission of the asteroid's surface, which can be used to determine surface temperature by means of temperature-retrieval algorithms. The thermal behavior of areas of unusual albedo seen at the local scale can be related to physical properties that can provide information about the origin of those materials. Dawn's Visible and Infrared Mapping Spectrometer (VIR) hyperspectral cubes are used to retrieve surface temperatures, with high accuracy as long as temperatures are greater than 180 K. Data acquired in the Survey phase (23 July through 29 August 2011) show several unusual surface features: 1) high-albedo (bright) and low-albedo (dark) material deposits, 2) spectrally distinct ejecta, 3) regions suggesting finer-grained materials. Some of the unusual dark and bright features were re-observed by VIR in the subsequent High-Altitude Mapping Orbit (HAMO) and Low-Altitude Mapping Orbit (LAMO) phases at increased pixel resolution. To calculate surface temperatures, we applied a Bayesian approach to nonlinear inversion based on the Kirchhoff law and the Planck function. These results were cross-checked through application of alternative methods. Here we present temperature maps of several local-scale features that were observed by Dawn under different illumination conditions and different local solar times. Some bright terrains have an overall albedo in the visible as much as 40% brighter than surrounding areas. Data from the IR channel of VIR show that bright regions generally correspond to regions with lower thermal emission, i.e. lower temperature, while dark regions correspond to areas with higher thermal emission, i.e. higher temperature. This behavior confirms that many of the dark appearances in the VIS mainly reflect albedo variations. In particular, it is shown that during maximum daily insolation, dark features in the equatorial region may rise to temperatures greater than 270 K. However, individual features may show different thermal behaviours, as a result of differences in composition and/or structure (e.g, average grain size of the surface regolith, porosity, etc.). To complement the temperature and near-infrared emissivity derived from the infrared spectra, a separate work is devoted to calculate thermal inertia and other thermal properties using theoretical models which solve the heat equation for airless bodies, and model the distribution of temperatures due to surface roughness variations.

Tosi, F.↗

NASA NTRS2011

Tests of the Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

Satellite lightning imagers such as the NASA Tropical Rainfall Measuring Mission Lightning Imaging Sensor (TRMM/LIS) and the future GOES-R Geostationary Lightning Mapper (GLM) are designed to detect total lightning (ground flashes + cloud flashes). However, there is a desire to discriminate ground flashes from cloud flashes from the vantage point of space since this would enhance the overall information content of the satellite lightning data and likely improve its operational and scientific applications (e.g., in severe weather warning, lightning nitrogen oxides studies, and global electric circuit analyses). A Bayesian inversion method was previously introduced for retrieving the fraction of ground flashes in a set of flashes observed from a satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters (one of which is the ground flash fraction), a scalar function was minimized by a numerical method. In order to improve this optimization, a Grobner basis solution was introduced to obtain analytic representations of the model parameters that serve as a refined initialization scheme to the numerical optimization. In this study, we test the efficacy of the Grobner basis initialization using actual lightning imager measurements and ground flash truth derived from the national lightning network.

Koshak, William↗