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NASA NTRS2005

Conservative Patch Algorithm and Mesh Sequencing for PAB3D

A mesh-sequencing algorithm and a conservative patched-grid-interface algorithm (hereafter Patch Algorithm ) have been incorporated into the PAB3D code, which is a computer program that solves the Navier-Stokes equations for the simulation of subsonic, transonic, or supersonic flows surrounding an aircraft or other complex aerodynamic shapes. These algorithms are efficient, flexible, and have added tremendously to the capabilities of PAB3D. The mesh-sequencing algorithm makes it possible to perform preliminary computations using only a fraction of the grid cells (provided the original cell count is divisible by an integer) along any grid coordinate axis, independently of the other axes. The patch algorithm addresses another critical need in multi-block grid situation where the cell faces of adjacent grid blocks may not coincide, leading to errors in calculating fluxes of conserved physical quantities across interfaces between the blocks. The patch algorithm, based on the Stokes integral formulation of the applicable conservation laws, effectively matches each of the interfacial cells on one side of the block interface to the corresponding fractional cell area pieces on the other side. This approach is comprehensive and unified such that all interface topology is automatically processed without user intervention. This algorithm is implemented in a preprocessing code that creates a cell-by-cell database that will maintain flux conservation at any level of full or reduced grid density as the user may choose by way of the mesh-sequencing algorithm. These two algorithms have enhanced the numerical accuracy of the code, reduced the time and effort for grid preprocessing, and provided users with the flexibility of performing computations at any desired full or reduced grid resolution to suit their specific computational requirements.

Pao, S. P.↗

NASA NTRS2020

Comparison of Cloud Detection Algorithms for Sentinel-2 Imagery

Accurate, automated cloud and cloud shadow detection is a key component of the processing needed to prepare optical satellite imagery for scientific analysis. Many existing cloud detection algorithms rely on temperature information to identify clouds, making detection difficult for imagers that lack a thermal band, like Sentinel-2. To get maximum benefit from Sentinel-2 products it is critical to understand which algorithms best identify clouds and their shadows in images. We examined the relative performance of five different cloud-masking algorithms (Sen2Cor, MAJA, LaSRC, Fmask and Tmask) in 6 Sentinel-2 scenes (28 total images) distributed across the Eastern Hemisphere. Expanding on these comparisons, we tested ensemble approaches to improve results. We tested three ensemble approaches to cloud and shadow classification based on the outputs of the five initial algorithms using the cloud masks in: (1) a majority prediction model; (2) a random forests model; and (3) a conditional logic model. Accuracy assessments show a trade-off between omission and commission errors in cloud detection for individual algorithms across all sites, and some algorithms are better at detecting either clouds or cloud shadows. No single algorithm outperforms the others for both clouds and shadows. Aggregating the results from multiple algorithms produces fewer undetected clouds and higher overall accuracy than any single algorithm, with as high as 2.7% improvement over the top-performing algorithm, suggesting an ensemble approach may be the most useful for processing of Sentinel-2 data.

Sentinel-2↗

NASA NTRS2024

Comparison of Multisine Peak Factor Minimization Algorithms for Aircraft System Identification

Two phase-optimized multisine peak factor minimization algorithms are presented and evaluated. The first algorithm minimizes peak factor by iteratively clipping the peaks of generated multisine signals. The second algorithm optimizes peak factor indirectly through minimization of an approximation of the infinity norm of the multisine. Algorithm performance was evaluated as a function of different signal properties, including the number of harmonics, harmonic spacing, and number of snow harmonics (extra harmonics included for further reduction of the peak factor). The two algorithms are compared against results obtained by minimizing peak factor directly using a simplex algorithm, which has been a common approach when designing phase-optimized multisines for system identification flight tests. Sample results show that the clipping and infinity norm algorithms produced multisine signals with comparable peak factors that were lower than that of the simplex algorithm. However, the clipping algorithm runs an order of magnitude faster than the other two algorithms, which also makes it practical to repeat the algorithm multiple times to achieve even lower peak factors.

system identification↗

NASA NTRSDate not supplied

Comparison of Multisine Peak Factor Minimization Algorithms for Aircraft System Identification(Presentation)

flight test↗

NASA NTRS1998

A new frame-based registration algorithm

This paper presents a new algorithm for frame registration. Our algorithm requires only that the frame be comprised of straight rods, as opposed to the N structures or an accurate frame model required by existing algorithms. The algorithm utilizes the full 3D information in the frame as well as a least squares weighting scheme to achieve highly accurate registration. We use simulated CT data to assess the accuracy of our algorithm. We compare the performance of the proposed algorithm to two commonly used algorithms. Simulation results show that the proposed algorithm is comparable to the best existing techniques with knowledge of the exact mathematical frame model. For CT data corrupted with an unknown in-plane rotation or translation, the proposed technique is also comparable to the best existing techniques. However, in situations where there is a discrepancy of more than 2 mm (0.7% of the frame dimension) between the frame and the mathematical model, the proposed technique is significantly better (p < or = 0.05) than the existing techniques. The proposed algorithm can be applied to any existing frame without modification. It provides better registration accuracy and is robust against model mis-match. It allows greater flexibility on the frame structure. Lastly, it reduces the frame construction cost as adherence to a concise model is not required.

NASA Center ARC↗

NASA NTRS2013

Distilling the Verification Process for Prognostics Algorithms

The goal of prognostics and health management (PHM) systems is to ensure system safety, and reduce downtime and maintenance costs. It is important that a PHM system is verified and validated before it can be successfully deployed. Prognostics algorithms are integral parts of PHM systems. This paper investigates a systematic process of verification of such prognostics algorithms. To this end, first, this paper distinguishes between technology maturation and product development. Then, the paper describes the verification process for a prognostics algorithm as it moves up to higher maturity levels. This process is shown to be an iterative process where verification activities are interleaved with validation activities at each maturation level. In this work, we adopt the concept of technology readiness levels (TRLs) to represent the different maturity levels of a prognostics algorithm. It is shown that at each TRL, the verification of a prognostics algorithm depends on verifying the different components of the algorithm according to the requirements laid out by the PHM system that adopts this prognostics algorithm. Finally, using simplified examples, the systematic process for verifying a prognostics algorithm is demonstrated as the prognostics algorithm moves up TRLs.

verification↗

NASA NTRS1989

NETRA: A parallel architecture for integrated vision systems 2: Algorithms and performance evaluation

In part 1 architecture of NETRA is presented. A performance evaluation of NETRA using several common vision algorithms is also presented. Performance of algorithms when they are mapped on one cluster is described. It is shown that SIMD, MIMD, and systolic algorithms can be easily mapped onto processor clusters, and almost linear speedups are possible. For some algorithms, analytical performance results are compared with implementation performance results. It is observed that the analysis is very accurate. Performance analysis of parallel algorithms when mapped across clusters is presented. Mappings across clusters illustrate the importance and use of shared as well as distributed memory in achieving high performance. The parameters for evaluation are derived from the characteristics of the parallel algorithms, and these parameters are used to evaluate the alternative communication strategies in NETRA. Furthermore, the effect of communication interference from other processors in the system on the execution of an algorithm is studied. Using the analysis, performance of many algorithms with different characteristics is presented. It is observed that if communication speeds are matched with the computation speeds, good speedups are possible when algorithms are mapped across clusters.

Choudhary, Alok N.↗

NASA NTRS1989

Parallel algorithms and architecture for computation of manipulator forward dynamics

Parallel computation of manipulator forward dynamics is investigated. Considering three classes of algorithms for the solution of the problem, that is, the O(n), the O(n exp 2), and the O(n exp 3) algorithms, parallelism in the problem is analyzed. It is shown that the problem belongs to the class of NC and that the time and processors bounds are of O(log2/2n) and O(n exp 4), respectively. However, the fastest stable parallel algorithms achieve the computation time of O(n) and can be derived by parallelization of the O(n exp 3) serial algorithms. Parallel computation of the O(n exp 3) algorithms requires the development of parallel algorithms for a set of fundamentally different problems, that is, the Newton-Euler formulation, the computation of the inertia matrix, decomposition of the symmetric, positive definite matrix, and the solution of triangular systems. Parallel algorithms for this set of problems are developed which can be efficiently implemented on a unique architecture, a triangular array of n(n+2)/2 processors with a simple nearest-neighbor interconnection. This architecture is particularly suitable for VLSI and WSI implementations. The developed parallel algorithm, compared to the best serial O(n) algorithm, achieves an asymptotic speedup of more than two orders-of-magnitude in the computation the forward dynamics.

Fijany, Amir↗

NASA NTRS1990

Constraint treatment techniques and parallel algorithms for multibody dynamic analysis

Computational procedures for kinematic and dynamic analysis of three-dimensional multibody dynamic (MBD) systems are developed from the differential-algebraic equations (DAE's) viewpoint. Constraint violations during the time integration process are minimized and penalty constraint stabilization techniques and partitioning schemes are developed. The governing equations of motion, a two-stage staggered explicit-implicit numerical algorithm, are treated which takes advantage of a partitioned solution procedure. A robust and parallelizable integration algorithm is developed. This algorithm uses a two-stage staggered central difference algorithm to integrate the translational coordinates and the angular velocities. The angular orientations of bodies in MBD systems are then obtained by using an implicit algorithm via the kinematic relationship between Euler parameters and angular velocities. It is shown that the combination of the present solution procedures yields a computationally more accurate solution. To speed up the computational procedures, parallel implementation of the present constraint treatment techniques, the two-stage staggered explicit-implicit numerical algorithm was efficiently carried out. The DAE's and the constraint treatment techniques were transformed into arrowhead matrices to which Schur complement form was derived. By fully exploiting the sparse matrix structural analysis techniques, a parallel preconditioned conjugate gradient numerical algorithm is used to solve the systems equations written in Schur complement form. A software testbed was designed and implemented in both sequential and parallel computers. This testbed was used to demonstrate the robustness and efficiency of the constraint treatment techniques, the accuracy of the two-stage staggered explicit-implicit numerical algorithm, and the speed up of the Schur-complement-based parallel preconditioned conjugate gradient algorithm on a parallel computer.

Chiou, Jin-Chern↗

NASA NTRS1990

Evaluating scheduling algorithms for traffic with heterogeneous performance objectives

Two types of network traffic are considered: traffic with deadlines, for which the most important performance objective is based on loss rate, and packets without deadlines, for which the most important performance objective is based on mean delay. An optimal scheduling algorithm is presented to minimize weighted loss rate and weighted mean delay in the queues that form at the switches and at the network access points of a packet-switched network, where weights reflect the relative importance of packets. Although not practical for implementation, the algorithm is intended as a standard for the comparison of the performance of other scheduling algorithms. The algorithm is more general and lower computational complexity than previously published algorithms, enabling performance evaluation of some important scenarios that could not previously have been considered. Using the optimal performance results of this algorithm, the performance of the first-come-first-served, static priority, and earliest deadline first scheduling algorithms is evaluated. The results suggest that network efficiency could be improved by using a more sophisticated heuristic scheduling algorithm rather than one of the aforementioned algorithms.

Peha, Jon M.↗

NASA NTRS1992

A fast, uncoupled, compressible, two-dimensional, unsteady boundary layer algorithm with separation for engine inlets

A finite difference boundary layer algorithm was developed to model viscous effects when an inviscid core flow solution is given. This algorithm solved each boundary layer equation separately, then iterated to find a solution. Solving the boundary layer equations sequentially was 2.4 to 4.0 times faster than solving the boundary layer equations simultaneously. This algorithm used a modified Baldwin-Lomax turbulence model, a weighted average of forward and backward differencing of the pressure gradient, and a backward sweep of the pressure. With these modifications, the boundary layer algorithm was able to model flows with and without separation. The number of grid points used in the boundary layer algorithm affected the stability of the algorithm as well as the accuracy of the predictions of friction coefficients and momentum thicknesses. Results of this boundary layer algorithm compared well with experimental observations of friction coefficients and momentum thicknesses. In addition, when used interactively with an inviscid flow algorithm, this boundary layer algorithm corrected for viscous effects to give a good match with experimental observations for pressures in a supersonic inlet.

Roach, Robert L.↗

NASA NTRS1996

A Fast parallel tridiagonal algorithm for a class of CFD applications

The parallel diagonal dominant (PDD) algorithm is an efficient tridiagonal solver. This paper presents for study a variation of the PDD algorithm, the reduced PDD algorithm. The new algorithm maintains the minimum communication provided by the PDD algorithm, but has a reduced operation count. The PDD algorithm also has a smaller operation count than the conventional sequential algorithm for many applications. Accuracy analysis is provided for the reduced PDD algorithm for symmetric Toeplitz tridiagonal (STT) systems. Implementation results on Langley's Intel Paragon and IBM SP2 show that both the PDD and reduced PDD algorithms are efficient and scalable.

Moitra, Stuti↗

NASA NTRS1998

A Polynomial Time, Numerically Stable Integer Relation Algorithm

Let x = (x1, x2...,xn be a vector of real numbers. X is said to possess an integer relation if there exist integers a(sub i) not all zero such that a1x1 + a2x2 + ... a(sub n)Xn = 0. Beginning in 1977 several algorithms (with proofs) have been discovered to recover the a(sub i) given x. The most efficient of these existing integer relation algorithms (in terms of run time and the precision required of the input) has the drawback of being very unstable numerically. It often requires a numeric precision level in the thousands of digits to reliably recover relations in modest-sized test problems. We present here a new algorithm for finding integer relations, which we have named the "PSLQ" algorithm. It is proved in this paper that the PSLQ algorithm terminates with a relation in a number of iterations that is bounded by a polynomial in it. Because this algorithm employs a numerically stable matrix reduction procedure, it is free from the numerical difficulties, that plague other integer relation algorithms. Furthermore, its stability admits an efficient implementation with lower run times oil average than other algorithms currently in Use. Finally, this stability can be used to prove that relation bounds obtained from computer runs using this algorithm are numerically accurate.

Ferguson, Helaman R. P.↗

NASA NTRS2002

Use of Collocated KWAJEX Satellite, Aircraft, and Ground Measurements for Understanding Ambiguities in TRMM Radiometer Rain Profile Algorithm

Coordinated ground, aircraft, and satellite observations are analyzed from the 1999 TRMM Kwajalein Atoll field experiment (KWAJEX) to better understand the relationships between cloud microphysical processes and microwave radiation intensities in the context of physical evaluation of the Level 2 TRMM radiometer rain profile algorithm and uncertainties with its assumed microphysics-radiation relationships. This talk focuses on the results of a multi-dataset analysis based on measurements from KWAJEX surface, air, and satellite platforms to test the hypothesis that uncertainties in the passive microwave radiometer algorithm (TMI 2a12 in the nomenclature of TRMM) are systematically coupled and correlated with the magnitudes of deviation of the assumed 3-dimensional microphysical properties from observed microphysical properties. Re-stated, this study focuses on identifying the weaknesses in the operational TRMM 2a12 radiometer algorithm based on observed microphysics and radiation data in terms of over-simplifications used in its theoretical microphysical underpinnings. The analysis makes use of a common transform coordinate system derived from the measuring capabilities of the aircraft radiometer used to survey the experimental study area, i.e., the 4-channel AMPR radiometer flown on the NASA DC-8 aircraft. Normalized emission and scattering indices derived from radiometer brightness temperatures at the four measuring frequencies enable a 2-dimensional coordinate system that facilities compositing of Kwajalein S-band ground radar reflectivities, ARMAR Ku-band aircraft radar reflectivities, TMI spacecraft radiometer brightness temperatures, PR Ku-band spacecraft radar reflectivities, bulk microphysical parameters derived from the aircraft-mounted cloud microphysics laser probes (including liquid/ice water contents, effective liquid/ice hydrometeor radii, and effective liquid/ice hydrometeor variances), and rainrates derived from any of the individual ground, aircraft, or satellite algorithms applied to the radar or radiometer measurements, or their combination. The results support the study's underlying hypothesis, particularly in context of ice phase processes, in that the cloud regions where the 2a12 algorithm's microphysical database most misrepresents the microphysical conditions as determined by the laser probes, are where retrieved surface rainrates are most erroneous relative to other reference rainrates as determined by ground and aircraft radar. In reaching these conclusions, TMI and PR brightness temperatures and reflectivities have been synthesized from the aircraft AMPR and ARMAR measurements with the analysis conducted in a composite framework to eliminate measurement noise associated with the case study approach and single element volumes obfuscated by heterogeneous beam filling effects. In diagnosing the performance of the 2a12 algorithm, weaknesses have been found in the cloud-radiation database used to provide microphysical guidance to the algorithm for upper cloud ice microphysics. It is also necessary to adjust a fractional convective rainfall factor within the algorithm somewhat arbitrarily to achieve satisfactory algorithm accuracy.

Smith, Eric A.↗

NASA NTRS2001

Algorithms and Application of Sparse Matrix Assembly and Equation Solvers for Aeroacoustics

An algorithm for symmetric sparse equation solutions on an unstructured grid is described. Efficient, sequential sparse algorithms for degree-of-freedom reordering, supernodes, symbolic/numerical factorization, and forward backward solution phases are reviewed. Three sparse algorithms for the generation and assembly of symmetric systems of matrix equations are presented. The accuracy and numerical performance of the sequential version of the sparse algorithms are evaluated over the frequency range of interest in a three-dimensional aeroacoustics application. Results show that the solver solutions are accurate using a discretization of 12 points per wavelength. Results also show that the first assembly algorithm is impractical for high-frequency noise calculations. The second and third assembly algorithms have nearly equal performance at low values of source frequencies, but at higher values of source frequencies the third algorithm saves CPU time and RAM. The CPU time and the RAM required by the second and third assembly algorithms are two orders of magnitude smaller than that required by the sparse equation solver. A sequential version of these sparse algorithms can, therefore, be conveniently incorporated into a substructuring for domain decomposition formulation to achieve parallel computation, where different substructures are handles by different parallel processors.

Watson, W. R.↗

NASA NTRS2007

A Comparison of Two Skip Entry Guidance Algorithms

The Orion capsule vehicle will have a Lift-to-Drag ratio (L/D) of 0.3-0.35. For an Apollo-like direct entry into the Earth's atmosphere from a lunar return trajectory, this L/D will give the vehicle a maximum range of about 2500 nm and a maximum crossrange of 216 nm. In order to y longer ranges, the vehicle lift must be used to loft the trajectory such that the aerodynamic forces are decreased. A Skip-Trajectory results if the vehicle leaves the sensible atmosphere and a second entry occurs downrange of the atmospheric exit point. The Orion capsule is required to have landing site access (either on land or in water) inside the Continental United States (CONUS) for lunar returns anytime during the lunar month. This requirement means the vehicle must be capable of flying ranges of at least 5500 nm. For the L/D of the vehicle, this is only possible with the use of a guided Skip-Trajectory. A skip entry guidance algorithm is necessary to achieve this requirement. Two skip entry guidance algorithms have been developed: the Numerical Skip Entry Guidance (NSEG) algorithm was developed at NASA/JSC and PredGuid was developed at Draper Laboratory. A comparison of these two algorithms will be presented in this paper. Each algorithm has been implemented in a high-fidelity, 6 degree-of-freedom simulation called the Advanced NASA Technology Architecture for Exploration Studies (ANTARES). NASA and Draper engineers have completed several monte carlo analyses in order to compare the performance of each algorithm in various stress states. Each algorithm has been tested for entry-to-target ranges to include direct entries and skip entries of varying length. Dispersions have been included on the initial entry interface state, vehicle mass properties, vehicle aerodynamics, atmosphere, and Reaction Control System (RCS). Performance criteria include miss distance to the target, RCS fuel usage, maximum g-loads and heat rates for the first and second entry, total heat load, and control system saturation. The comparison of the performance criteria has led to a down select and guidance merger that will take the best ideas from each algorithm to create one skip entry guidance algorithm for the Orion vehicle.

Rea, Jeremy R.↗

NASA NTRS2006

Quantifying Global Uncertainties in a Simple Microwave Rainfall Algorithm

While a large number of methods exist in the literature for retrieving rainfall from passive microwave brightness temperatures, little has been written about the quantitative assessment of the expected uncertainties in these rainfall products at various time and space scales. The latter is the result of two factors: sparse validation sites over most of the world's oceans, and algorithm sensitivities to rainfall regimes that cause inconsistencies against validation data collected at different locations. To make progress in this area, a simple probabilistic algorithm is developed. The algorithm uses an a priori database constructed from the Tropical Rainfall Measuring Mission (TRMM) radar data coupled with radiative transfer computations. Unlike efforts designed to improve rainfall products, this algorithm takes a step backward in order to focus on uncertainties. In addition to inversion uncertainties, the construction of the algorithm allows errors resulting from incorrect databases, incomplete databases, and time- and space-varying databases to be examined. These are quantified. Results show that the simple algorithm reduces errors introduced by imperfect knowledge of precipitation radar (PR) rain by a factor of 4 relative to an algorithm that is tuned to the PR rainfall. Database completeness does not introduce any additional uncertainty at the global scale, while climatologically distinct space/time domains add approximately 25% uncertainty that cannot be detected by a radiometer alone. Of this value, 20% is attributed to changes in cloud morphology and microphysics, while 5% is a result of changes in the rain/no-rain thresholds. All but 2%-3% of this variability can be accounted for by considering the implicit assumptions in the algorithm. Additional uncertainties introduced by the details of the algorithm formulation are not quantified in this study because of the need for independent measurements that are beyond the scope of this paper. A validation strategy for these errors is outlined.

Kummerow, Christian↗

NASA NTRS2007

An Improved Algorithm for Retrieving Surface Downwelling Longwave Radiation from Satellite Measurements

Zhou and Cess [2001] developed an algorithm for retrieving surface downwelling longwave radiation (SDLW) based upon detailed studies using radiative transfer model calculations and surface radiometric measurements. Their algorithm linked clear sky SDLW with surface upwelling longwave flux and column precipitable water vapor. For cloudy sky cases, they used cloud liquid water path as an additional parameter to account for the effects of clouds. Despite the simplicity of their algorithm, it performed very well for most geographical regions except for those regions where the atmospheric conditions near the surface tend to be extremely cold and dry. Systematic errors were also found for scenes that were covered with ice clouds. An improved version of the algorithm prevents the large errors in the SDLW at low water vapor amounts by taking into account that under such conditions the SDLW and water vapor amount are nearly linear in their relationship. The new algorithm also utilizes cloud fraction and cloud liquid and ice water paths available from the Cloud and the Earth's Radiant Energy System (CERES) single scanner footprint (SSF) product to separately compute the clear and cloudy portions of the fluxes. The new algorithm has been validated against surface measurements at 29 stations around the globe for Terra and Aqua satellites. The results show significant improvement over the original version. The revised Zhou-Cess algorithm is also slightly better or comparable to more sophisticated algorithms currently implemented in the CERES processing and will be incorporated as one of the CERES empirical surface radiation algorithms.

Zhou, Yaping↗