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NASA NTRS1992

Some practicable applications of quadtree data structures/representation in astronomy

Development of quadtree as hierarchical data structuring technique for representing spatial data (like points, regions, surfaces, lines, curves, volumes, etc.) has been motivated to a large extent by storage requirements of images, maps, and other multidimensional (spatially structured) data. For many spatial algorithms, time-efficiency of quadtrees in terms of execution may be as important as their space-efficiency concerning storage conditions. Briefly, the quadtree is a class of hierarchical data structures which is based on the recursive partition of a square region into quadrants and sub-quadrants until a predefined limit. Beyond the wide applicability of quadtrees in image processing, spatial information analysis, and building digital databases (processes becoming ordinary for the astronomical community), there may be numerous further applications in astronomy. Some of these practicable applications based on quadtree representation of astronomical data are presented and suggested for further considerations. Examples are shown for use of point as well as region quadtrees. Statistics of different leaf and non-leaf nodes (homogeneous and heterogeneous sub-quadrants respectively) at different levels may provide useful information on spatial structure of astronomical data in question. By altering the principle guiding the decomposition process, different types of spatial data may be focused on. Finally, a sampling method based on quadtree representation of an image is proposed which may prove to be efficient in the elaboration of sampling strategy in a region where observations were carried out previously either with different resolution or/and in different bands.

Pasztor, L.↗
NASA NTRSDate not supplied

Dynamic Mode Decomposition of Unsteady Pressure-Sensitive Paint Measurements for the NASA Unitary Plan Wind Tunnel Tests

This paper describes the Dynamic Mode Decomposition (DMD) of the pressures on the scale model of the Space Launch System (SLS) Block 1 cargo vehicle with the Unsteady Pressure-Sensitive Paint (uPSP) measurements, which were collected in the Ascent Transient Aerodynamics Tests with the Unitary Plan Wind Tunnel 11-by-11-foot Transonic Wind Tunnel in September 2019 at NASA Ames Research Center. The work described in this paper is a part of NASA’s development of a new state-of-the-art uPSP capability in production wind tunnels. The conventional DMD algorithm is based on the Singular Value Decomposition (SVD) of the data matrix. For the matrix of the uPSP measurements of the SLS ATAT, the number of rows is equal to the number of nodes in the grid of the scale model, and the number of columns is equal to the number of frames in the videos taken with 4 Phantom high-speed cameras. In this paper, it is verified that, for the time series with zero mean value, the DMD is equivalent to the decomposition with the Discrete Fourier Transform (DFT). Considering the uPSP is mainly used in the assessment of the unsteady, aerodynamic phenomena, the DMD of the uPSP measurements can be implemented in two steps: (1) subtract the mean value from the uPSP measurement on each of the grid nodes; (2) apply the Fast Fourier Transform (FFT) on the resulting zero-mean time series. The DMD of the uPSP measurements with FFT has two advantages: (1) the computational complexity of FFT is O(N*logN), where N is the length of the time series; (2) compared to the SVD-based DMD algorithm, the DMD with FFT can be easily implemented in parallel processing. A sample matrix of uPSP measurements, at the size of 341 grid nodes and 128 frames, is generated. Figures 1 and 2 show the eigenvalues and the ratios of the eigenvectors, respectively, of the sample matrix, without and with the mean value removed on each of the grid nodes, computed with the SVD-based DMD and the FFT. The figures demonstrate the equivalence of the SVD-based DMD and the decomposition with DFT/FFT for the time series with zero mean value. The results of DMD of the uPSP measurements of the SLS ATAT in September 2019 are presented in the paper. The DMD modes at different frequencies are shown, the aerodynamic phenomena (e.g. shockwave and vortex shedding) are demonstrated and the correlation of the DMD modes with the test configuration parameter (e.g., the Mach Number) is discussed. Figure 3 shows a software tool to visualize the DMD modes. The code to implement the algorithm described in this paper was written in C, with libraries of FFTW for FFT and MPI/OpenMP for parallel processing, and executed on the NASA Pleiades supercomputer. Funding for this research was provided by the NASA Aerosciences Evaluation and Test Capabilities Project.

Pressure-Sensitive Paint↗
NASA NTRS1993

Parallel O(log n) algorithms for open- and closed-chain rigid multibody systems based on a new mass matrix factorization technique

In this paper, parallel O(log n) algorithms for computation of rigid multibody dynamics are developed. These parallel algorithms are derived by parallelization of new O(n) algorithms for the problem. The underlying feature of these O(n) algorithms is a drastically different strategy for decomposition of interbody force which leads to a new factorization of the mass matrix (M). Specifically, it is shown that a factorization of the inverse of the mass matrix in the form of the Schur Complement is derived as M(exp -1) = C - B(exp *)A(exp -1)B, wherein matrices C, A, and B are block tridiagonal matrices. The new O(n) algorithm is then derived as a recursive implementation of this factorization of M(exp -1). For the closed-chain systems, similar factorizations and O(n) algorithms for computation of Operational Space Mass Matrix lambda and its inverse lambda(exp -1) are also derived. It is shown that these O(n) algorithms are strictly parallel, that is, they are less efficient than other algorithms for serial computation of the problem. But, to our knowledge, they are the only known algorithms that can be parallelized and that lead to both time- and processor-optimal parallel algorithms for the problem, i.e., parallel O(log n) algorithms with O(n) processors. The developed parallel algorithms, in addition to their theoretical significance, are also practical from an implementation point of view due to their simple architectural requirements.

Fijany, Amir↗
NASA NTRS2016

Mapping of Spacecraft Atmosphere Monitor Signal to Major Constituent Abundances

The Spacecraft Atmosphere Monitor (S.A.M.) follows the JPL’s commitment to introduce and develop next-generation instrumentation concepts for sensing the air quality on manned space flights via continuous sampling, measuring, and reporting in 2s intervals on all gaseous pollutants. The S.A.M. will have two modes of operation: the Major Constituent Analysis (MCA) mode and the Trace Gas Analysis (TGA) mode. The MCA mode will report on molecular analytes such as CH4, H2O, N2, O2, Ar, and CO2 while the TGA mode will acquire minute amounts of volatile organic compounds. Both modes assess the composition of the ambient air with twenty full mass spectra per second giving rise to a substantial amount of data to be processed by a set of small footprint software stacks hosted by an on-board computer. Mass spectra will be accumulated as the number of counts recorded in a given mass-to-charge channel and converted into the absolute abundances of detected species using an efficient algorithm. The decomposition algorithm contains four units: peak identification, mass calibration, background and dead time correction, and an abundance analysis unit. The abundance analysis module identifies target species through their characteristic fragmentation patterns in the presence of molecular isobars, such as CO and N2. For example, in order to identify N2 analyte, the code will simultaneously monitor abundance ratios of the 14, 28 and 29 Th signals and will adapt to any instability caused by a decrease in ambient pressure or changes in humidity. This requirement becomes critical for instruments designed to monitor the near real-time quality of cabin air and promptly provide accurate feedbacks.

Nikolic, D.↗
NASA NTRS2011

Receiver Gain Modulation Circuit

A receiver gain modulation circuit (RGMC) was developed that modulates the power gain of the output of a radiometer receiver with a test signal. As the radiometer receiver switches between calibration noise references, the test signal is mixed with the calibrated noise and thus produces an ensemble set of measurements from which ensemble statistical analysis can be used to extract statistical information about the test signal. The RGMC is an enabling technology of the ensemble detector. As a key component for achieving ensemble detection and analysis, the RGMC has broad aeronautical and space applications. The RGMC can be used to test and develop new calibration algorithms, for example, to detect gain anomalies, and/or correct for slow drifts that affect climate-quality measurements over an accelerated time scale. A generalized approach to analyzing radiometer system designs yields a mathematical treatment of noise reference measurements in calibration algorithms. By treating the measurements from the different noise references as ensemble samples of the receiver state, i.e. receiver gain, a quantitative description of the non-stationary properties of the underlying receiver fluctuations can be derived. Excellent agreement has been obtained between model calculations and radiometric measurements. The mathematical formulation is equivalent to modulating the gain of a stable receiver with an externally generated signal and is the basis for ensemble detection and analysis (EDA). The concept of generating ensemble data sets using an ensemble detector is similar to the ensemble data sets generated as part of ensemble empirical mode decomposition (EEMD) with exception of a key distinguishing factor. EEMD adds noise to the signal under study whereas EDA mixes the signal with calibrated noise. It is mixing with calibrated noise that permits the measurement of temporal-functional variability of uncertainty in the underlying process. The RGMC permits the evaluation of EDA by modulating the receiver gain using an external signal. Without the RGMC, samples of calibrated references from radiometers form an ensemble data set of the natural occurring fluctuations within a receiver. By driving the gain of an otherwise stable receiver with an external signal, the conceptual framework and generalization of the mathematics of EDA can be tested. A series of measurements was conducted to evaluate and characterize the performance of the RGMC. Test signals stepped the RGMC across its dynamic range of performance using a radiometer that sampled four noise references; analysis indicates that the RGMC successfully modulated the receiver gain with an external signal. Calibration algorithms applied to four noise references demonstrate the RGMC produced ensemble data sets of the external signal.

Jones, Hollis↗
DOE OSTI2020

α-U and ω-UZr 2 in neutron irradiated U-10Zr annular metallic fuel

Here, to develop metallic fuel with ultra-high burnup of 30%-40%, an annular U-10Zr fuel with 55% smear density was fabricated through a casting route and irradiated at the Advanced Test Reactor at Idaho National Laboratory. The annular fuel design also serves as a demonstration of the feasibility to replace sodium bond with a helium bond to benefit the geological disposal of irradiated fuel, cut the cost of fuel fabrication, and boost the overall metallic fuel economy. This paper reports the results from transmission electron microscopy (TEM) based post-irradiation examination of this fuel type irradiated to a burnup of 3.3% fissions per initial heave metal atoms for initial screening purpose. After irradiation, the initial U-10Zr separated into an a-U annular region and an UZr 2+x center region with nanoscale spinodal decomposed microstructure. Because of the provided large amount of coherent interface areas, the fission gas atoms and vacancies generated in UZr 2+x phase are possibly pinned at the interface areas, leading to 20 times smaller fission gas bubbles than those in the neighboring a-U. The large bubbles in a-U become connected and merged into large pores that provide fast release paths for fission gas which prevents further fuel swelling. The fuel center still has open space to accommodate further fuel swelling from solid fission products at higher burnup. Other neutron irradiation induced phase and microstructure change are also characterized and compared with traditional solid fuel designs.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Sparse Symmetric Format for Tucker Decomposition

Tensor-based methods are receiving renewed attention in recent years due to their prevalence in diverse real-world applications. There is considerable literature on tensor representations and algorithms for tensor decompositions, both for dense and sparse tensors. Many applications in hypergraph analytics, machine learning, psychometry, and signal processing result in tensors that are both sparse and symmetric, making them an important class for further study. Similar to the critical Tensor Times Matrix chain operation (TTM c ) in general sparse tensors, the $\underline{S}$ parse $\underline{S}$ ymmetric $\underline{T}$ ensor $\underline{T}$ imes $\underline{S}$ ame $\underline{M}$ atrix $\underline{c}$ hain (S 3 TTM c ) operation is compute and memory intensive due to high tensor order and the associated factorial explosion in the number of non-zeros. We present the novel Compressed Sparse Symmetric (CSS) format for sparse symmetric tensors, along with an efficient parallel algorithm for the S 3 TTM c operation. We theoretically establish that S 3 TTM c on CSS achieves a better memory versus run-time trade-off compared to state-of-the-art implementations, and visualize the variation of the performance gap over the parameter space. We demonstrate experimental findings that confirm these results and achieve up to 2.72× speedup on synthetic and real datasets. The scaling of the algorithm on different test architectures is also showcased to highlight the effect of machine characteristics on algorithm performance.

42 ENGINEERING↗
NASA NTRS1999

Automated Development of Accurate Algorithms and Efficient Codes for Computational Aeroacoustics

The simulation of sound generation and propagation in three space dimensions with realistic aircraft components is a very large time dependent computation with fine details. Simulations in open domains with embedded objects require accurate and robust algorithms for propagation, for artificial inflow and outflow boundaries, and for the definition of geometrically complex objects. The development, implementation, and validation of methods for solving these demanding problems is being done to support the NASA pillar goals for reducing aircraft noise levels. Our goal is to provide algorithms which are sufficiently accurate and efficient to produce usable results rapidly enough to allow design engineers to study the effects on sound levels of design changes in propulsion systems, and in the integration of propulsion systems with airframes. There is a lack of design tools for these purposes at this time. Our technical approach to this problem combines the development of new, algorithms with the use of Mathematica and Unix utilities to automate the algorithm development, code implementation, and validation. We use explicit methods to ensure effective implementation by domain decomposition for SPMD parallel computing. There are several orders of magnitude difference in the computational efficiencies of the algorithms which we have considered. We currently have new artificial inflow and outflow boundary conditions that are stable, accurate, and unobtrusive, with implementations that match the accuracy and efficiency of the propagation methods. The artificial numerical boundary treatments have been proven to have solutions which converge to the full open domain problems, so that the error from the boundary treatments can be driven as low as is required. The purpose of this paper is to briefly present a method for developing highly accurate algorithms for computational aeroacoustics, the use of computer automation in this process, and a brief survey of the algorithms that have resulted from this work. A review of computational aeroacoustics has recently been given by Lele.

Goodrich, John W.↗
NASA NTRS2001

Three-Dimensional Stereoscopic Tracking Velocimetry and Experimental/Numerical Comparison of Directional Solidification

Measurement of three-dimensional (3-D) three-component velocity fields is of great importance in both ground and space experiments for understanding materials processing and fluid physics. The experiments in these fields most likely inhibit the application of conventional planar probes for observing 3-D phenomena. Here, we present the investigation results of stereoscopic tracking velocimetry (STV) for measuring 3-D velocity fields, which include diagnostic technology development, experimental velocity measurement, and comparison with analytical and numerical computation. STV is advantageous in system simplicity for building compact hardware and in software efficiency for continual near-real-time monitoring. It has great freedom in illuminating and observing volumetric fields from arbitrary directions. STV is based on stereoscopic observation of particles-Seeded in a flow by CCD sensors. In the approach, part of the individual particle images that provide data points is likely to be lost or cause errors when their images overlap and crisscross each other especially under a high particle density. In order to maximize the valid recovery of data points, neural networks are implemented for these two important processes. For the step of particle overlap decomposition, the back propagation neural network is utilized because of its ability in pattern recognition with pertinent particle image feature parameters. For the step of particle tracking, the Hopfield neural network is employed to find appropriate particle tracks based on global optimization. Our investigation indicates that the neural networks are very efficient and useful for stereoscopically tracking particles. As an initial assessment of the diagnostic technology performance, laminar water jets with and without pulsation are measured. The jet tip velocity profiles are in good agreement with analytical predictions. Finally, for testing in material processing applications, a simple directional solidification apparatus is built for experimenting with a metal analog of succinonitrile. Its 3-D velocity field at the liquid phase is then measured to be compared with those from numerical computation. Our theoretical, numerical, and experimental investigations have proven STV to be a viable candidate for reliably measuring 3-D flow velocities. With current activities are focused on further improving the processing efficiency, overall accuracy, and automation, the eventual efforts of broad experimental applications and concurrent numerical modeling validation will be vital to many areas in fluid flow and materials processing.

Lee, David↗
DOE OSTI2026

Multiscale Neural Networks for Approximating Green’s Functions

Neural networks (NNs) have been widely used to solve partial differential equations (PDEs) in the applications of physics, biology, and engineering. One effective approach for solving PDEs with a fixed differential operator is learning Green’s functions. However, Green’s functions are notoriously difficult to learn due to their poor regularity, which typically requires larger NNs and longer training times. In this work, we address these challenges by leveraging multiscale NNs to learn Green’s functions. Through theoretical analysis using multiscale Barron space methods and experimental validation, we show that the multiscale approach significantly reduces the necessary NN size and accelerates training.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2013

RUSHMAPS: Real-Time Uploadable Spherical Harmonic Moment Analysis for Particle Spectrometers

RUSHMAPS is a new onboard data reduction scheme that gives real-time access to key science parameters (e.g. moments) of a class of heliophysics science and/or solar system exploration investigation that includes plasma particle spectrometers (PPS), but requires moments reporting (density, bulk-velocity, temperature, pressure, etc.) of higher-level quality, and tolerates a lowpass (variable quality) spectral representation of the corresponding particle velocity distributions, such that telemetry use is minimized. The proposed methodology trades access to the full-resolution velocity distribution data, saving on telemetry, for real-time access to both the moments and an adjustable-quality (increasing quality increases volume) spectral representation of distribution functions. Traditional onboard data storage and downlink bandwidth constraints severely limit PPS system functionality and drive cost, which, as a consequence, drives a limited data collection and lower angular energy and time resolution. This prototypical system exploit, using high-performance processing technology at GSFC (Goddard Space Flight Center), uses a SpaceCube and/or Maestro-type platform for processing. These processing platforms are currently being used on the International Space Station as a technology demonstration, and work is currently ongoing in a new onboard computation system for the Earth Science missions, but they have never been implemented in heliospheric science or solar system exploration missions. Preliminary analysis confirms that the targeted processor platforms possess the processing resources required for realtime application of these algorithms to the spectrometer data. SpaceCube platforms demonstrate that the target architecture possesses the sort of compact, low-mass/power, radiation-tolerant characteristics needed for flight. These high-performing hybrid systems embed unprecedented amounts of onboard processing power in the CPU (central processing unit), FPGAs (field programmable gate arrays), and DSP (digital signal processing) elements. The fundamental computational algorithm de constructs 3D velocity distributions in terms of spherical harmonic spectral coefficients (which are analogous to a Fourier sine-cosine decomposition), but uses instead spherical harmonics Legendre polynomial orthogonal functions as a basis for the expansion, portraying each 2D angular distribution at every energy or, geometrically, spherical speed-shell swept by the particle spectrometer. Optionally, these spherical harmonic spectral coefficients may be telemetered to the ground. These will provide a smoothed description of the velocity distribution function whose quality will depend on the number of coefficients determined. Successfully implemented on the GSFC-developed processor, the capability to integrate the proposed methodology with both heritage and anticipated future plasma particle spectrometer designs is demonstrated (with sufficiently detailed design analysis to advance TRL) to show specific science relevancy with future HSD (Heliophysics Science Division) solar-interplanetary, planetary missions, sounding rockets and/or CubeSat missions.

Figueroa-Vinas, Adolfo↗
NASA NTRS2004

Increasing the Thermal Stability of Aluminum Titanate for Solid Oxide Fuel Cell Anodes

Solid-oxide fuel cells (SOFCs) show great potential as a power source for future space exploration missions. Because SOFCs operate at temperatures significantly higher than other types of fuel cells, they can reach overall efficiencies of up to 60% and are able to utilize fossil fuels. The SOFC team at GRC is leading NASA's effort to develop a solid oxide fuel cell with a power density high enough to be used for aeronautics and space applications, which is approximately ten times higher than ground transport targets. layers must be able to operate as a single unit at temperatures upwards of 900'C for at least 40,000 hours with less than ten percent degradation. One key challenge to meeting this goal arises from the thermal expansion mismatch between different layers. The amount a material expands upon heating is expressed by its coefficient of thermal expansion (CTE). If the CTEs of adjacent layers are substantially different, thermal stresses will arise during the cell's fabrication and operation. These stresses, accompanied by thermal cycling, can fracture and destroy the cell. While this is not an issue at the electrolyte-cathode interface, it is a major concern at the electrolyte-anode interface, especially in high power anode-supported systems. electrolyte are nearly identical. Conventionally, this has been accomplished by varying the composition of the anode to match the CTE of the yittria-stabilized zirconia (YSZ) electrolyte (approx.10.8x10(exp -6/degC). A Ni/YSZ composite is typically used as a base material for the anode due to its excellent electrochemical properties, but its CTE is about 13.4x10(exp -6/degC). One potential way to lower the CTE of this anode is to add a small percentage of polycrystalline Al2TiO5, with a CTE of 0.68x10(exp -6/degC, to the Ni/YSZ base. However, Al2TiO5 is thermally unstable and loses its effectiveness as it decomposes to Al2O3 and TiO2 between 750 C and 1280 C. be used as additives to increase the thermal stability of Al2TiO5 in SOFC operating conditions without adversely affecting the electrochemical properties of the SOFC anode. Three candidate materials were chosen through an extensive literature review: MgO, Fe2O3, and ZrTiO4. Although all three have been shown to prevent Al2TiO5 decomposition under various conditions, their effectiveness in the temperature range and atmosphere of the SOFC has not yet been evaluated. Several batches of Al2TiO5 with varying amounts of additives were prepared, exposed to reducing and oxidizing atmospheres at elevated temperatures, and the resulting decomposition of Al2TiO5 was measured. The most promising additives were further evaluated with the goal of ultimately preparing low CTE anodes that are chemically compatible to current systems. Adding minor constituents to stabilize Al2TiO5 could ultimately preserve its low CTE for the life of the fuel cell and improve the cell's long-term performance without a drop in anode conductivity. Further, these low CTE filler additions could allow the use of new sulfur tolerant anode materials, improving the viability of SOFCs for future aeronautics and space applications. Every SOFC consists of a cathode and an anode separated by an electrolyte, These three One way to avoid this problem is to design the cell such that the CTEs of the anode and The objective of this summer research project was to evaluate several materials that could

Bender, Jeffrey B.↗
DOE OSTI2020

A fast implicit solver for semiconductor models in one space dimension

Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in semiconductor devices under a low-density assumption. At each implicit time step, the discretized system is formulated as a fixed-point problem, which can then be solved with a variety of methods. A key algorithmic component in all the approaches considered here is a recently developed sweeping algorithm for Vlasov-Poisson systems. A synthetic acceleration scheme has been implemented to accelerate the convergence of iterative solvers by using the solution to a drift-diffusion equation as a preconditioner. The performance of four iterative solvers and their accelerated variants has been compared on problems modeling semiconductor devices with various electron mean-free-path.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2021

Small UAV Flight Planning in Urban Environments

This work proposes a fast algorithm for generating obstacle-free and wind-efficient flight paths at a constant above-ground-level altitude in urban environments because a fast flight path planning algorithm is an essential function or service needed for enabling small unmanned aerial vehicle (sUAV) to operate in urban environments within Class G airspace. The proposed method first converts the 3D path planning problem to a 2D problem by constructing an obstacle map at a given above-ground-level altitude. A quad-tree decomposition is then used to build a search space in terms of obstacle occupancy and wind difference. The wind cost of traveling through each cell is defined based on energy consumption under various wind conditions. A repulsive potential is also adopted to make sure that the flight plans stay away from obstacles. The Theta* search algorithm, a variant of A* algorithm, is applied to mitigate the path angle change constraints introduced by grid-based graphs. With the Theta* and postsmoothing techniques, an obstacle-free, wind efficient, and constant above-ground-level flight plan can be quickly generated for sUAV operations in urban environments while meeting the lateral path angle constraints. The results showed that the path planning algorithm is efficient and can be finished within several seconds. With a proper choice of wind coefficient, the proposed path planning algorithm outperforms the multiple-shooting trajectory optimization method even in an obstacle-free environment. With the flexibility of incorporating other geo-related costs and computation efficiency, the proposed algorithm shows the potential for real-time flight path planning in complex urban environments.

Path planning↗
DOE OSTI2021

Predicting bulge to total luminosity ratio of galaxies using deep learning

ABSTRACT We present a deep learning model to predict the r-band bulge-to-total luminosity ratio (B/T) of nearby galaxies using their multiband JPEG images alone. Our Convolutional Neural Network (CNN) based regression model is trained on a large sample of galaxies with reliable decomposition into the bulge and disc components. The existing approaches to estimate the B/T ratio use galaxy light-profile modelling to find the best fit. This method is computationally expensive, prohibitively so for large samples of galaxies, and requires a significant amount of human intervention. Machine learning models have the potential to overcome these shortcomings. In our CNN model, for a test set of 20 000 galaxies, 85.7 per cent of the predicted B/T values have absolute error (AE) less than 0.1. We see further improvement to 87.5 per cent if, while testing, we only consider brighter galaxies (with r-band apparent magnitude <17) with no bright neighbours. Our model estimates the B/T ratio for the 20 000 test galaxies in less than a minute. This is a significant improvement in inference time from the conventional fitting pipelines, which manage around 2–3 estimates per minute. Thus, the proposed machine learning approach could potentially save a tremendous amount of time, effort, and computational resources while predicting B/T reliably, particularly in the era of next-generation sky surveys such as the Legacy Survey of Space and Time (LSST) and the Euclid sky survey which will produce extremely large samples of galaxies.

Grover, Harsh (ORCID:0000000321338142)↗
NASA NTRS1998

Data Mining and Optimization Tools for Developing Engine Parameters Tools

This project was awarded for understanding the problem and developing a plan for Data Mining tools for use in designing and implementing an Engine Condition Monitoring System. From the total budget of $5,000, Tricia and I studied the problem domain for developing ail Engine Condition Monitoring system using the sparse and non-standardized datasets to be available through a consortium at NASA Lewis Research Center. We visited NASA three times to discuss additional issues related to dataset which was not made available to us. We discussed and developed a general framework of data mining and optimization tools to extract useful information from sparse and non-standard datasets. These discussions lead to the training of Tricia Erhardt to develop Genetic Algorithm based search programs which were written in C++ and used to demonstrate the capability of GA algorithm in searching an optimal solution in noisy datasets. From the study and discussion with NASA LERC personnel, we then prepared a proposal, which is being submitted to NASA for future work for the development of data mining algorithms for engine conditional monitoring. The proposed set of algorithm uses wavelet processing for creating multi-resolution pyramid of the data for GA based multi-resolution optimal search. Wavelet processing is proposed to create a coarse resolution representation of data providing two advantages in GA based search: 1. We will have less data to begin with to make search sub-spaces. 2. It will have robustness against the noise because at every level of wavelet based decomposition, we will be decomposing the signal into low pass and high pass filters.

Dhawan, Atam P.↗
NASA NTRS1998

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes

A code trellis is a graphical representation of a code, block or convolutional, in which every path represents a codeword (or a code sequence for a convolutional code). This representation makes it possible to implement Maximum Likelihood Decoding (MLD) of a code with reduced decoding complexity. The most well known trellis-based MLD algorithm is the Viterbi algorithm. The trellis representation was first introduced and used for convolutional codes [23]. This representation, together with the Viterbi decoding algorithm, has resulted in a wide range of applications of convolutional codes for error control in digital communications over the last two decades. There are two major reasons for this inactive period of research in this area. First, most coding theorists at that time believed that block codes did not have simple trellis structure like convolutional codes and maximum likelihood decoding of linear block codes using the Viterbi algorithm was practically impossible, except for very short block codes. Second, since almost all of the linear block codes are constructed algebraically or based on finite geometries, it was the belief of many coding theorists that algebraic decoding was the only way to decode these codes. These two reasons seriously hindered the development of efficient soft-decision decoding methods for linear block codes and their applications to error control in digital communications. This led to a general belief that block codes are inferior to convolutional codes and hence, that they were not useful. Chapter 2 gives a brief review of linear block codes. The goal is to provide the essential background material for the development of trellis structure and trellis-based decoding algorithms for linear block codes in the later chapters. Chapters 3 through 6 present the fundamental concepts, finite-state machine model, state space formulation, basic structural properties, state labeling, construction procedures, complexity, minimality, and sectionalization of trellises. Chapter 7 discusses trellis decomposition and subtrellises for low-weight codewords. Chapter 8 first presents well known methods for constructing long powerful codes from short component codes or component codes of smaller dimensions, and then provides methods for constructing their trellises which include Shannon and Cartesian product techniques. Chapter 9 deals with convolutional codes, puncturing, zero-tail termination and tail-biting.Chapters 10 through 13 present various trellis-based decoding algorithms, old and new. Chapter 10 first discusses the application of the well known Viterbi decoding algorithm to linear block codes, optimum sectionalization of a code trellis to minimize computation complexity, and design issues for IC (integrated circuit) implementation of a Viterbi decoder. Then it presents a new decoding algorithm for convolutional codes, named Differential Trellis Decoding (DTD) algorithm. Chapter 12 presents a suboptimum reliability-based iterative decoding algorithm with a low-weight trellis search for the most likely codeword. This decoding algorithm provides a good trade-off between error performance and decoding complexity. All the decoding algorithms presented in Chapters 10 through 12 are devised to minimize word error probability. Chapter 13 presents decoding algorithms that minimize bit error probability and provide the corresponding soft (reliability) information at the output of the decoder. Decoding algorithms presented are the MAP (maximum a posteriori probability) decoding algorithm and the Soft-Output Viterbi Algorithm (SOVA) algorithm. Finally, the minimization of bit error probability in trellis-based MLD is discussed.

Lin, Shu↗
NASA NTRS2017

Elastomeric Thermal Insulation Design Considerations in Long, Aluminized Solid Rocket Motors

An all-new sounding rocket was designed at NASA's Marshall Space Flight Center that featured an aft finocyl, aluminized solid propellant grain and silica-filled ethylene-propylene-diene monomer (SFEPDM) internal insulation. Upon the initial static firing of the first of this new design, the solid rocket motor (SRM) case failed thermally just upstream of the aft closure early in the burn time. Subsequent fluid modeling indicated that the high-velocity combustion-product jets emanating from the fin-slots in the propellant grain were likely inducing a strongly swirling flow, thus substantially increasing the severity of the convective environment on the exposed portion of the SFEPDM insulation in this region. The aft portion of the fin-slots in another of the motors were filled with propellant to eliminate the possibility of both direct jet impingement on the exposed SFEPDM and the appearance of strongly swirling flow in the aft region of the motor. When static-fired, this motor's case still failed in the same axial location, and, though somewhat later than for the first static firing, still in less than 1/3rd of the desired burn duration. These results indicate that the extreme material decomposition rates of the SFEPDM in this application are not due to gas-phase convection or shear but rather to interactions with burning aluminum or alumina slag. Further comparisons with between SFEPDM performance in this design and that in other hot-fire tests provide insight into the mechanisms of SFEPDM decomposition in SRM aft domes that can guide the upcoming redesign effort, as well as other future SRM designs. These data also highlight the current limitations of modeling elastomeric insulators solely with diffusion-controlled, gas-phase thermochemistry in SRM regions with significant viscous shear and/or condense-phase impingement or flow.

Martin, Heath T.↗