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Open-source Numerical Modeling of Solidification Cracking Susceptibility: Application to Refractory Alloy Systems

Introduction. Alloys such as aluminum, nickel-base, and austenitic stainless steels are susceptible to solidification cracking during welding and 3D printing. Compositional optimization is one method used to effectively mitigate solidification cracking of those alloy systems. With the surge in hypersonic and in-space propulsion activities, refractory metals (Nb, Mo, Ta, W, and Re) and their alloy derivatives are increasing in importance due to their extreme high melting point and retention of high-temperature strength; however, their chemistry was most typically optimized to promote ductility during mechanical operations such as drawing and forming. Welding of such alloys has been a challenge due to a number of issues including solidification cracking, atmospheric contamination (O, C, and N), as well as a shift in ductile-to-brittle transition to higher temperature following grain growth induced by welding. Compositional optimization of refractory alloys for solidification cracking resistance in particular is desirable as their usage increases with the advent of advanced manufacturing methods such as 3D printing. This work evaluates the effect of compositional variation in refractory metal systems on the solidification cracking susceptibility with the goals of optimizing existing alloys and joining process techniques, and formulating new alloys with increased solidification cracking resistance. Experimental Procedures. A python code was developed in a Jupyter notebook environment (Michael and Sowards, 2023) to facilitate the calculation of crack susceptibility index proposed by Kou (2015). Composition is entered as a single point, or as a 1-D or 2-D array. The notebook calls pycalphad (Otis and Liu, 2017 and Bocklund et al, 2020) to calculate the evolution of fraction solid as a function of temperature (under either Scheil or equilibrium assumptions) and then evaluates steepness of the fraction solid curve near the terminal stage of solidification to predict solidification cracking resistance. Open source thermodynamic databases available at online repositories are used (van de Walle). The process is setup in an automated fashion to generate plots that show variation in solidification cracking susceptibility according to composition on 1-D line plots or 2-D contour plots. The Jupyter notebook and crack susceptibility algorithm was also integrated with a widely used commercial CALPHAD code for validation and alloy exploration. Results and Discussion. The crack susceptibility model was first validated against a series of refractory alloy compositions evaluated in past work which utilized a specialized Varestraint test built inside a vacuum chamber environment (Lessman and Gold, 1971). The alloys tested in the Varestraint apparatus included T-111 (Ta-8W-2Hf), ASTAR-811C (Ta-8W-1Re-0.7Hf-0.025C), FS-85 (Nb-27Ta-10W-1Zr), T-222 (Ta-9.6W-2.4Hf-0.01C), Ta-10W, B-66 (Nb-5Mo-5V-1Zr), and SCb-291 (Nb-10W-10Ta). The initial test of the model showed a strong correlation with empirical Varestraint data, i.e., a Spearman rank correlation between model predictions and hot cracking measurements was observed to be greater than 0.8. Following the validation, a set of refractory metal binary mixtures was investigated to evaluate sensitivity of Nb, Mo, W, and Ta to C, N, and O content. A series of plots were produced that suggest ppmw ranges of C, N, and O where solidification cracking increases significantly and reaches a maximum. Also comparative ranking of each primary refractory metal to each interstitial was produced. For example C produces greater cracking response in Mo whereas O produces greater cracking response in Ta and Nb. Such compositional values have utility in setting limits on pickup of these interstitial elements during welding and printing rather than using a one-size-fits-all approach. Furthermore, the results have use in determining additive powder recycling requirements, which is especially pertinent for refractory metal powders due to their high cost compared to conventional alloys. Another application created thousands of hypothetical alloys within the nominal specified composition range of two widely used refractory alloys C103 (Nb-10Hf-1Ti) and TZM (Mo-0.5Ti-0.1Zr). The cracking index was calculated for the alloys and results were fed into machine learning regression techniques including Multiple Linear Regression, Ridge Regression, and Lasso Regression to determine relative potency each alloying element had on computed solidification cracking index. A series of linear equations were produced that relate composition of C103 and TZM to solidification cracking index. The crack susceptibility of C103 for example is described by an equation of the form: cracking index ~ O + 0.667*C + 0.635*N + 0.00037*Ta – 0.0008*Hf (in wt.%) From that equation, it is clear that O has strong propensity to induce solidification cracking. Interestingly, Hf is shown to reduce calculated cracking response. Finally, realizing the potential of this method to discover new refractory alloy formulations across the period table that have low solidification cracking sensitivity, the code was applied to new untested alloy systems including W-Zr-C, W-Ta-C, and others. Conclusions. In summary, an open source numerical method has been developed using Python code to calculate Kou’s crack susceptibility index. The method was applied to refractory metals which are inherently difficult to study from a weldability testing standpoint since inert shielding gas is not sufficient and welding is typically done in vacuum, especially in light of findings presented here where oxygen has profound influence on solidification cracking. This work revealed the effect of compositional variations on a series of refractory metals and showed the framework defined here will be useful in 1) the development of new alloys that have improved weldability and 3D printability, 2) placing compositional limits on existing alloys, and 3) ensuring adequate controls of manufacturing processes such as 3D printing where powder reuse is critical. Keywords. pycalphad; Python; refractory metals; solidification cracking. References. B. Bocklund et. al. (2020) http://doi.org/10.5281/zenodo.3630657. S. Kou. (2015) https://doi.org/10.1016/j.actamat.2015.01.034. G.G. Lessmann and R.E. Gold. Welding Journal, issue 1, pp. 1-s – 8-s (1971). F.N. Michael and J.W. Sowards. NASA/TM-20230002218 (2023). R. Otis and Z.-K. Liu. (2017) http://doi.org/10.5334/jors.140. A. Van de Wallle et. al. (2018) https://doi.org/10.1016/j.calphad.2018.04.003.

pycalphad↗
NASA NTRS2006

Genetic Algorithm for Optimization: Preprocessor and Algorithm

Genetic algorithm (GA) inspired by Darwin's theory of evolution and employed to solve optimization problems - unconstrained or constrained - uses an evolutionary process. A GA has several parameters such the population size, search space, crossover and mutation probabilities, and fitness criterion. These parameters are not universally known/determined a priori for all problems. Depending on the problem at hand, these parameters need to be decided such that the resulting GA performs the best. We present here a preprocessor that achieves just that, i.e., it determines, for a specified problem, the foregoing parameters so that the consequent GA is a best for the problem. We stress also the need for such a preprocessor both for quality (error) and for cost (complexity) to produce the solution. The preprocessor includes, as its first step, making use of all the information such as that of nature/character of the function/system, search space, physical/laboratory experimentation (if already done/available), and the physical environment. It also includes the information that can be generated through any means - deterministic/nondeterministic/graphics. Instead of attempting a solution of the problem straightway through a GA without having/using the information/knowledge of the character of the system, we would do consciously a much better job of producing a solution by using the information generated/created in the very first step of the preprocessor. We, therefore, unstintingly advocate the use of a preprocessor to solve a real-world optimization problem including NP-complete ones before using the statistically most appropriate GA. We also include such a GA for unconstrained function optimization problems.

Sen, S. K.↗
NASA NTRS1993

Retrieval of ice thickness from polarimetric SAR data

We describe a potential procedure for retrieving ice thickness from multi-frequency polarimetric SAR data for thin ice. This procedure includes first masking out the thicker ice types with a simple classifier and then deriving the thickness of the remaining pixels using a model-inversion technique. The technique used to derive ice thickness from polarimetric observations is provided by a numerical estimator or neural network. A three-layer perceptron implemented with the backpropagation algorithm is used in this investigation with several improved aspects for a faster convergence rate and a better accuracy of the neural network. These improvements include weight initialization, normalization of the output range, the selection of offset constant, and a heuristic learning algorithm. The performance of the neural network is demonstrated by using training data generated by a theoretical scattering model for sea ice matched to the database of interest. The training data are comprised of the polarimetric backscattering coefficients of thin ice and the corresponding input ice parameters to the scattering model. The retrieved ice thickness from the theoretical backscattering coefficients is compare with the input ice thickness to the scattering model to illustrate the accuracy of the inversion method. Results indicate that the network convergence rate and accuracy are higher when multi-frequency training sets are presented. In addition, the dominant backscattering coefficients in retrieving ice thickness are found by comparing the behavior of the network trained backscattering data at various incidence angels. After the neural network is trained with the theoretical backscattering data at various incidence anges, the interconnection weights between nodes are saved and applied to the experimental data to be investigated. In this paper, we illustrate the effectiveness of this technique using polarimetric SAR data collected by the JPL DC-8 radar over a sea ice scene.

Kwok, R.↗
NASA NTRS1996

From Competence to Efficiency: A Tale of GA Progress

Genetic algorithms (GAs) - search procedures based on the mechanics of natural selection and genetics - have grown in popularity for the solution of difficult optimization problems. Concomitant with this growth has been a rising cacaphony of complaint asserting that too much time must be spent by the GA practitioner diddling with codes, operators, and GA parameters; and even then these GA cassandras continue, and the user is still unsure that the effort will meet with success. At the same time, there has been a rising interest in GA theory by a growing community - a theorocracy - of mathematicians and theoretical computer scientists, and these individuals have turned their efforts increasingly toward elegant abstract theorems and proofs that seem to the practitioner to offer little in the way of answers for GA design or practice. What both groups seem to have missed is the largely unheralded 1993 assembly of integrated, applicable theory and its experimental confirmation. This theory has done two key things. First, it has predicted that simple GAs are severely limited in the difficulty of problems they can solve, and these limitations have been confirmed experimentally. Second, it has shown the path to circumventing these limitations in nontraditional GA designs such as the fast messy GA. This talk surveys the history, methodology, and accomplishment of the 1993 applicable theory revolution. After arguing that these accomplishments open the door to universal GA competence, the paper shifts the discussion to the possibility of universal GA efficiency in the utilization of time and real estate through effective parallelization, temporal decomposition, hybridization, and relaxed function evaluation. The presentation concludes by suggesting that these research directions are quickly taking us to a golden age of adaptation.

Goldberg, David E.↗
NASA NTRS1979

A navigation algorithm for single channel low-cost GPS receiver

A sequential navigation algorithm for a navigator using the Global Positioning System satellites is developed and tested for both noise-free and noisy system models. Data from a six-hour flight from California to Hawaii (C5A aircraft) simulates a true user to test the accuracy of the user's position for a sequential navigation system. For error reduction in the user's position in the sequential navigation system (considering 100 m as a maximum average error tolerated by any low-cost GPS user) an analysis of error sources in the sequential system has led to the use of range-ephemeris rate to translate ranges to a common point in time and to use velocity aiding at the time of a satellite disappearance. To reduce the user's position and velocity errors in a noisy navigation system an 'alpha-beta' two-pole filter is implemented whose optimum alpha is obtained experimentally. A user's position error of 73 m at noise range error of 30.48 (1sigma) is achieved.

Parsiani, H.↗
NASA NTRS2022

Automatic variable selection in ecological niche modeling: A case study using Cassin’s Sparrow (Peucaea cassinii)

MERRA/Max provides a feature selection approach to dimensionality reduction that enables direct use of global climate model outputs in ecological niche modeling. The system accomplishes this reduction through a Monte Carlo optimization in which many independent MaxEnt runs, operating on a species occurrence file and a small set of randomly selected variables in a large collection of variables, converge on an estimate of the top contributing predictors in the larger collection. These top predictors can be viewed as potential candidates in the variable selection step of the ecological niche modeling process. MERRA/Max’s Monte Carlo algorithm operates on files stored in the underlying filesystem, making it scalable to large data sets. Its software components can run as parallel processes in a high-performance cloud computing environment to yield near real-time performance. In tests using Cassin’s Sparrow (Peucaea cassinii) as the target species, MERRA/Max selected a set of predictors from Worldclim’s Bioclim collection of 19 environmental variables that have been shown to be important determinants of the species’ bioclimatic niche. It also selected biologically and ecologically plausible predictors from a more diverse set of 86 environmental variables derived from NASA’s Modern-Era Retrospective Analysis for Research and Applications Version 2 (MERRA-2) reanalysis, an output product of the Goddard Earth Observing System Version 5 (GEOS-5) modeling system. We believe these results point to a technological approach that could expand the use global climate model outputs in ecological niche modeling, foster exploratory experimentation with otherwise difficult-to-use climate data sets, streamline the modeling process, and, eventually, enable automated bioclimatic modeling as a practical, readily accessible, low-cost, commercial cloud service.

John L. Schnase↗
NASA NTRS2011

SPoRT's Participation in the GOES-R Proving Ground Activity

The next generation geostationary satellite, GOES-R, will carry two new instruments with unique atmospheric and surface observing capabilities, the Advanced Baseline Imager (ABI) and the Geostationary Lightning Mapper (GLM), to study short-term weather processes. The ABI will bring enhanced multispectral observing capabilities with frequent refresh rates for regional and full disk coverage to geostationary orbit to address many existing and new forecast challenges. The GLM will, for the first time, provide the continuous monitoring of total lightning flashes over a hemispherical region from space. NOAA established the GOES-R Proving Ground activity several years ago to demonstrate the new capabilities of these instruments and to prepare forecasters for their day one use. Proving Ground partners work closely with algorithm developers and the end user community to develop and transition proxy data sets representing GOES-R observing capabilities. This close collaboration helps to maximize refine algorithms leading to the delivery of a product that effectively address a forecast challenge. The NASA Short-term Prediction Research and Transition (SPoRT) program has been a participant in the NOAA GOES-R Proving Ground activity by developing and disseminating selected GOES-R proxy products to collaborating WFOs and National Centers. Established in 2002 to demonstrate the weather and forecasting application of real-time EOS measurements, the SPoRT program has grown to be an end-to-end research to operations activity focused on the use of advanced NASA modeling and data assimilation approaches, nowcasting techniques, and unique high-resolution multispectral data from EOS satellites to improve short-term weather forecasts on a regional and local scale. Participation in the Proving Ground activities extends SPoRT s activities and taps its experience and expertise in diagnostic weather analysis, short-term weather forecasting, and the transition of research and experimental data to operational decision support systems like NAWIPS, AWIPS, AWIPS2, and Google Earth. Recent SPoRT Proving Ground activities supporting the development and use of a pseudo GLM total lightning product and the transition of the AWG s Convective Initiation (CI) product, both of which were available in AWIPS and AWIPS II environments, by forecasters during the Hazardous Weather Testbed (HWT) Spring Experiment. SPoRT is also providing a suite of SEVIRI and MODIS RGB image products, and a high resolution composite SST product to several National Centers for use in there ongoing demonstration activities. Additionally, SPoRT has involved numerous WFOs in the evaluation of a GOES-MODIS hybrid product which brings ABI-like data sets in front of the forecaster for everyday use. An overview of this activity will be presented at the conference.

Jedlovec, Gary↗
NASA NTRS1989

Multi-version software reliability through fault-avoidance and fault-tolerance

A number of experimental and theoretical issues associated with the practical use of multi-version software to provide run-time tolerance to software faults were investigated. A specialized tool was developed and evaluated for measuring testing coverage for a variety of metrics. The tool was used to collect information on the relationships between software faults and coverage provided by the testing process as measured by different metrics (including data flow metrics). Considerable correlation was found between coverage provided by some higher metrics and the elimination of faults in the code. Back-to-back testing was continued as an efficient mechanism for removal of un-correlated faults, and common-cause faults of variable span. Software reliability estimation methods was also continued based on non-random sampling, and the relationship between software reliability and code coverage provided through testing. New fault tolerance models were formulated. Simulation studies of the Acceptance Voting and Multi-stage Voting algorithms were finished and it was found that these two schemes for software fault tolerance are superior in many respects to some commonly used schemes. Particularly encouraging are the safety properties of the Acceptance testing scheme.

Vouk, Mladen A.↗
NASA NTRS1995

Global electric field determination in the Earth's outer magnetosphere using energetic charged particles

Although many properties of the Earth's magnetosphere have been measured and quantified in the past 30 years since it was discovered, one fundamental measurement (for zeroth order MHD equilibrium) has been made infrequently and with poor spatial coverage - the global electric field. This oversight is due in part to the neglect of theorists. However, there is renewed interest in the convection electric field because it is now realized to be central to many magnetospheric processes, including the global MHD equilibrium, reconnection rates, Region 2 Birkeland currents, magnetosphere ionosphere coupling, ring current and radiation belt transport, substorm injections, and several acceleration mechanisms. Unfortunately the standard experimental methods have not been able to synthesize a global field (excepting the pioneering work of McIlwain's geostationary models) and we are left with an overly simplistic theoretical field, the Volland-Stern electric field model. Single point measurements of the plasmapause were used to infer the appropriate amplitudes of this model, parameterized by K(sub p). Although this result was never intended to be the definitive electric field model, it has gone nearly unchanged for 20 years. The analysis of current data sets requires a great deal more accuracy than can be provided by the Volland-Stern model. The variability of electric field shielding has not been properly addressed although effects of penetrating magnetospheric electric fields has been seen in mid-and low-latitude ionospheric data sets. The growing interest in substorm dynamics also requires a much better assessment of the electric fields responsible for particle injections. Thus we proposed and developed algorithms for extracting electric fields from particle data taken in the Earth's magnetosphere. As a test of the effectiveness of these new techniques, we analyzed data taken by the AMPTE/CCE spacecraft in equatorial orbit from 1984 to 1989.

Eastman, Timothy E.↗
NASA NTRS2000

Filtering in Hybrid Dynamic Bayesian Networks

We implement a 2-time slice dynamic Bayesian network (2T-DBN) framework and make a 1-D state estimation simulation, an extension of the experiment in (v.d. Merwe et al., 2000) and compare different filtering techniques. Furthermore, we demonstrate experimentally that inference in a complex hybrid DBN is possible by simulating fault detection in a watertank system, an extension of the experiment in (Koller & Lerner, 2000) using a hybrid 2T-DBN. In both experiments, we perform approximate inference using standard filtering techniques, Monte Carlo methods and combinations of these. In the watertank simulation, we also demonstrate the use of 'non-strict' Rao-Blackwellisation. We show that the unscented Kalman filter (UKF) and UKF in a particle filtering framework outperform the generic particle filter, the extended Kalman filter (EKF) and EKF in a particle filtering framework with respect to accuracy in terms of estimation RMSE and sensitivity with respect to choice of network structure. Especially we demonstrate the superiority of UKF in a PF framework when our beliefs of how data was generated are wrong. Furthermore, we investigate the influence of data noise in the watertank simulation using UKF and PFUKD and show that the algorithms are more sensitive to changes in the measurement noise level that the process noise level. Theory and implementation is based on (v.d. Merwe et al., 2000).

Andersen, Morten Nonboe↗
NASA NTRS2007

Scope of Gradient and Genetic Algorithms in Multivariable Function Optimization

Global optimization of a multivariable function - constrained by bounds specified on each variable and also unconstrained - is an important problem with several real world applications. Deterministic methods such as the gradient algorithms as well as the randomized methods such as the genetic algorithms may be employed to solve these problems. In fact, there are optimization problems where a genetic algorithm/an evolutionary approach is preferable at least from the quality (accuracy) of the results point of view. From cost (complexity) point of view, both gradient and genetic approaches are usually polynomial-time; there are no serious differences in this regard, i.e., the computational complexity point of view. However, for certain types of problems, such as those with unacceptably erroneous numerical partial derivatives and those with physically amplified analytical partial derivatives whose numerical evaluation involves undesirable errors and/or is messy, a genetic (stochastic) approach should be a better choice. We have presented here the pros and cons of both the approaches so that the concerned reader/user can decide which approach is most suited for the problem at hand. Also for the function which is known in a tabular form, instead of an analytical form, as is often the case in an experimental environment, we attempt to provide an insight into the approaches focusing our attention toward accuracy. Such an insight will help one to decide which method, out of several available methods, should be employed to obtain the best (least error) output. *

Shaykhian, Gholam Ali↗
NASA NTRS1991

Aerodynamic design optimization using sensitivity analysis and computational fluid dynamics

A new and efficient method is presented for aerodynamic design optimization, which is based on a computational fluid dynamics (CFD)-sensitivity analysis algorithm. The method is applied to design a scramjet-afterbody configuration for an optimized axial thrust. The Euler equations are solved for the inviscid analysis of the flow, which in turn provides the objective function and the constraints. The CFD analysis is then coupled with the optimization procedure that uses a constrained minimization method. The sensitivity coefficients, i.e. gradients of the objective function and the constraints, needed for the optimization are obtained using a quasi-analytical method rather than the traditional brute force method of finite difference approximations. During the one-dimensional search of the optimization procedure, an approximate flow analysis (predicted flow) based on a first-order Taylor series expansion is used to reduce the computational cost. Finally, the sensitivity of the optimum objective function to various design parameters, which are kept constant during the optimization, is computed to predict new optimum solutions. The flow analysis of the demonstrative example are compared with the experimental data. It is shown that the method is more efficient than the traditional methods.

Baysal, Oktay↗
NASA NTRS1995

Adaptively Refined Euler and Navier-Stokes Solutions with a Cartesian-Cell Based Scheme

A Cartesian-cell based scheme with adaptive mesh refinement for solving the Euler and Navier-Stokes equations in two dimensions has been developed and tested. Grids about geometrically complicated bodies were generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells were created using polygon-clipping algorithms. The grid was stored in a binary-tree data structure which provided a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations were solved on the resulting grids using an upwind, finite-volume formulation. The inviscid fluxes were found in an upwinded manner using a linear reconstruction of the cell primitives, providing the input states to an approximate Riemann solver. The viscous fluxes were formed using a Green-Gauss type of reconstruction upon a co-volume surrounding the cell interface. Data at the vertices of this co-volume were found in a linearly K-exact manner, which ensured linear K-exactness of the gradients. Adaptively-refined solutions for the inviscid flow about a four-element airfoil (test case 3) were compared to theory. Laminar, adaptively-refined solutions were compared to accepted computational, experimental and theoretical results.

Coirier, William J.↗
NASA NTRS2000

Optimization of Microelectronic Devices for Sensor Applications

The NASA/JPL goal to reduce payload in future space missions while increasing mission capability demands miniaturization of active and passive sensors, analytical instruments and communication systems among others. Currently, typical system requirements include the detection of particular spectral lines, associated data processing, and communication of the acquired data to other systems. Advances in lithography and deposition methods result in more advanced devices for space application, while the sub-micron resolution currently available opens a vast design space. Though an experimental exploration of this widening design space-searching for optimized performance by repeated fabrication efforts-is unfeasible, it does motivate the development of reliable software design tools. These tools necessitate models based on fundamental physics and mathematics of the device to accurately model effects such as diffraction and scattering in opto-electronic devices, or bandstructure and scattering in heterostructure devices. The software tools must have convenient turn-around times and interfaces that allow effective usage. The first issue is addressed by the application of high-performance computers and the second by the development of graphical user interfaces driven by properly developed data structures. These tools can then be integrated into an optimization environment, and with the available memory capacity and computational speed of high performance parallel platforms, simulation of optimized components can proceed. In this paper, specific applications of the electromagnetic modeling of infrared filtering, as well as heterostructure device design will be presented using genetic algorithm global optimization methods.

Cwik, Tom↗
NASA NTRS1992

Global electric field determination in the Earth's outer magnetosphere using charged particles

Although many properties of the Earth's magnetosphere have been measured and quantified in the past 30 years since it was discovered, one fundamental (for a zeroeth order magnetohydrodynamic (MHD) equilibrium) measurement was made infrequently and with poor spatial coverage: the global electric field. This oversight is in part due to the difficulty of measuring a plasma electric field, and in part due to the difficulty of measuring a plasma electric field, and in part due to the neglect of theorists. However, there is renewed interest in the convection electric field, since it has been realized that it is vital for understanding many aspects of the magnetosphere: the global MHD equilibrium, reconnection rates, Region 2 Birkeland currents, magnetosphere-ionosphere coupling, ring current and radiation belt transport, substorm injections, acceleration mechanisms, etc. Unfortunately the standard experimental methods have not been able to synthesize a global field (excepting the pioneering work of McIlwain's geostationary models), and we are left with an overly simplistic theoretical field, the Volland-Stern electric field mode. Again, single point measurements of the plasma pause were used to infer the appropriate amplitudes of the model, parameterized by Kp (Maynard & Chen, JGR 1975). Although this result was never intended to be the definitive electric field model, it has gone nearly unchanged for 15 years. However, the data sets being taken today require a great deal more accuracy than can be provided by the Volland-Stern model. Nor has the variability of the electric field shielding been properly addressed, although effects of penetrating magnetospheric electric fields has been seen in mid- and low-latitude ionospheric data sets. The growing interests in substorm dynamics also requires a much better assessment of the electric fields responsible for particle injections. Thus, we proposed and developed algorithms for extracting electric fields from particle data taken in the earth's magnetosphere. As a test of the effectiveness of these techniques, we analyzed data taken by the AMPTE/CCE spacecraft in equatorial orbit between 1984-1988. Some analytic tools had to be developed before construction of computer algorithms, and they are discussed.

Eastman, T.↗
NASA NTRS1993

Laboratory and theoretical models of planetary-scale instabilities and waves

Research work is proceeding in theoretical, numerical, and experimental geophysical fluid dynamics leading up to a reflight of the GFFC (Geophysical Fluid Flow Cell Experiment) on USML-2. The work is intended not only to generate ideas for future space experiments, but to provide fundamental results concerned with nonlinear and chaotic properties of thermal convection and baroclinic waves in terrestrial and planetary atmospheres. The major efforts are focussed on thermal convection in a rapidly rotating annulus relevant to Jovian atmospheric dynamics, and on the chaotic behavior of baroclinic waves relevant to the Earth's atmosphere. The approach, in preparation for USML-2, is primarily theoretical and numerical. Mechanistic process models are solved numerically in order to identify physical mechanisms that may be observed in the GFFC, and which are important in real geophysical applications. The results from numerical simulations of geophysical fluid flow (subject to rotation and stratification) are compared with previous GFFC experiments on Spacelab-3 and with existing and proposed terrestrial laboratory experiments of various types. Pattern recognition algorithms have been employed to generate low-dimensional descriptions of the highly nonlinear and turbulent numerical simulations. Such empirically truncated descriptions provide for simplified but robust physical interpretations of the dynamics, as well as yielding highly efficient computations of these chaotic flows.

Hart, John E.↗
NASA NTRS2010

Heat Flux and Wall Temperature Estimates for the NASA Langley HIFiRE Direct Connect Rig

An objective of the Hypersonic International Flight Research Experimentation (HIFiRE) Program Flight 2 is to provide validation data for high enthalpy scramjet prediction tools through a single flight test and accompanying ground tests of the HIFiRE Direct Connect Rig (HDCR) tested in the NASA LaRC Arc Heated Scramjet Test Facility (AHSTF). The HDCR is a full-scale, copper heat sink structure designed to simulate the isolator entrance conditions and isolator, pilot, and combustor section of the HIFiRE flight test experiment flowpath and is fully instrumented to assess combustion performance over a range of operating conditions simulating flight from Mach 5.5 to 8.5 and for various fueling schemes. As part of the instrumentation package, temperature and heat flux sensors were provided along the flowpath surface and also imbedded in the structure. The purpose of this paper is to demonstrate that the surface heat flux and wall temperature of the Zirconia coated copper wall can be obtained with a water-cooled heat flux gage and a sub-surface temperature measurement. An algorithm was developed which used these two measurements to reconstruct the surface conditions along the flowpath. Determinations of the surface conditions of the Zirconia coating were conducted for a variety of conditions.

Cuda, Vincent, Jr.↗
NASA NTRS2004

Filtering in Hybrid Dynamic Bayesian Networks

We demonstrate experimentally that inference in a complex hybrid Dynamic Bayesian Network (DBN) is possible using the 2 - T i e Slice DBN (2T-DBN) from [Koller & Lerner, 20001 to model fault detection in a watertank system. In [Koller & Lerner, 20001 a generic Particle Filter (PF) is used for inference. We extend the experiment and perform approximate inference using The Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF). Furthermore, we combine these techniques in a 'non-strict' Rao-Blackwellisation framework and apply it to the watertank system. We show that UKF and UKF in a PF framework outperfom the generic PF, EKF and EKF in a PF framework with respect to accuracy and robustness in terms of estimation RMSE. Especially we demonstrate the superiority of UKF in a PF framework when our beliefs of how data was generated are wrong. We also show that the choice of network structure is very important for the performance of the generic PF and the EKF algorithms, but not for the UKF algorithms. Furthermore, we investigate the influence of data noise in the water[ank simulation. Theory and implementation is based on the theory presented.

Andersen, Morten Nonboe↗