SEARCH · Engineering Papers

Results for “approximation algorithm”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,243 records · Page 69

All sources NASA NTRS DOE OSTI

NASA NTRS1993

Flexible Weighting-And-Matching Scheme For Incomplete Data

Method for partial matching of data makes conventional electronic memory addressable via its contents. When implemented by suitable algorithm, method enables computer system containing memory to search memory for datum making exact or best approximate match to datum in query. Advantages are: requires neither long "learning" time nor "retraining" when additional data stored and attaches to each datum relative importance that can change with time without decreasing speed of retrieval. Responses include exact or approximate recollection, indications of ambiguity, avoidance, and even forgetfulness.

Wang, Lui↗

NASA NTRS1994

An implementation of a tree code on a SIMD, parallel computer

We describe a fast tree algorithm for gravitational N-body simulation on SIMD parallel computers. The tree construction uses fast, parallel sorts. The sorted lists are recursively divided along their x, y and z coordinates. This data structure is a completely balanced tree (i.e., each particle is paired with exactly one other particle) and maintains good spatial locality. An implementation of this tree-building algorithm on a 16k processor Maspar MP-1 performs well and constitutes only a small fraction (approximately 15%) of the entire cycle of finding the accelerations. Each node in the tree is treated as a monopole. The tree search and the summation of accelerations also perform well. During the tree search, node data that is needed from another processor is simply fetched. Roughly 55% of the tree search time is spent in communications between processors. We apply the code to two problems of astrophysical interest. The first is a simulation of the close passage of two gravitationally, interacting, disk galaxies using 65,636 particles. We also simulate the formation of structure in an expanding, model universe using 1,048,576 particles. Our code attains speeds comparable to one head of a Cray Y-MP, so single instruction, multiple data (SIMD) type computers can be used for these simulations. The cost/performance ratio for SIMD machines like the Maspar MP-1 make them an extremely attractive alternative to either vector processors or large multiple instruction, multiple data (MIMD) type parallel computers. With further optimizations (e.g., more careful load balancing), speeds in excess of today's vector processing computers should be possible.

Olson, Kevin M.↗

NASA NTRS1996

Wavelet Sparse Approximate Inverse Preconditioners

There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods. Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g. Harwell-Boeing collections. Nonetheless a drawback is that it requires rapid decay of the inverse entries so that sparse approximate inverse is possible. However, for the class of matrices that, come from elliptic PDE problems, this assumption may not necessarily hold. Our main idea is to look for a basis, other than the standard one, such that a sparse representation of the inverse is feasible. A crucial observation is that the kind of matrices we are interested in typically have a piecewise smooth inverse. We exploit this fact, by applying wavelet techniques to construct a better sparse approximate inverse in the wavelet basis. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverse. We emphasize that in this paper we have only presented the idea of wavelet approximate inverses and demonstrated its potential but have not yet developed a highly refined and efficient algorithm.

Chan, Tony F.↗

NASA NTRS1994

Numerical Simulations of Self-Focused Pulses Using the Nonlinear Maxwell Equations

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations. Abstract of a proposed paper for presentation at the meeting NONLINEAR OPTICS: Materials, Fundamentals, and Applications, Hyatt Regency Waikaloa, Waikaloa, Hawaii, July 24-29, 1994, Cosponsored by IEEE/Lasers and Electro-Optics Society and Optical Society of America

Goorjian, Peter M.↗

NASA NTRS1994

Numerical Simulations of Light Bullets, Using the Full Vector, Time Dependent, Nonlinear Maxwell Equations

Goorjian, Peter M.↗

NASA NTRS1995

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that we currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Karr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Goorjian, Peter M.↗

NASA NTRS1994

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

Goorjian, Peter M.↗

NASA NTRS2013

Analytical Algorithms to Quantify the Uncertainty in Remaining Useful Life Prediction

This paper investigates the use of analytical algorithms to quantify the uncertainty in the remaining useful life (RUL) estimate of components used in aerospace applications. The prediction of RUL is affected by several sources of uncertainty and it is important to systematically quantify their combined effect by computing the uncertainty in the RUL prediction in order to aid risk assessment, risk mitigation, and decisionmaking. While sampling-based algorithms have been conventionally used for quantifying the uncertainty in RUL, analytical algorithms are computationally cheaper and sometimes, are better suited for online decision-making. While exact analytical algorithms are available only for certain special cases (for e.g., linear models with Gaussian variables), effective approximations can be made using the the first-order second moment method (FOSM), the first-order reliability method (FORM), and the inverse first-order reliability method (Inverse FORM). These methods can be used not only to calculate the entire probability distribution of RUL but also to obtain probability bounds on RUL. This paper explains these three methods in detail and illustrates them using the state-space model of a lithium-ion battery.

Sankararaman, Shankar↗

NASA NTRS2017

Hybrid Guidance Control for a Hypervelocity Small Size Asteroid Interceptor Vehicle

Near-Earth Objects (NEOs) are comets and/or asteroids that have orbits in proximity with Earth's own orbit. NEOs have collided with the Earth in the past, which can be seen at such places as Chicxulub crater, Barringer crater, and Manson crater, and will continue in the future with potentially significant and devastating results. Fortunately such NEO collisions with Earth are infrequent, but can happen at any time. Therefore it is necessary to develop and validate techniques as well as technologies necessary to prevent them. One approach to mitigate future NEO impacts is the concept of high-speed interceptor. This concept is to alter the NEO's trajectory via momentum exchange by using kinetic impactors as well as nuclear penetration devices. The interceptor has to hit a target NEO at relative velocity which imparts a sufficient change in NEO velocity. NASA's Deep Impact mission has demonstrated this scenario by intercepting Comet Temple 1, 5 km in diameter, with an impact relative speed of approximately 10 km/s. This paper focuses on the development of hybrid guidance navigation and control (GNC) algorithms for precision hypervelocity intercept of small sized NEOs. The spacecraft's hypervelocity and the NEO's small size are critical challenges for a successful mission as the NEO will not fill the field of view until a few seconds before intercept. The investigation needs to consider the error sources modeled in the navigation simulation such as spacecraft initial state uncertainties in position and velocity. Furthermore, the paper presents three selected spacecraft guidance algorithms for asteroid intercept and rendezvous missions. The selected algorithms are classical Proportional Navigation (PN) based guidance that use a first order difference to compute the derivatives, Three Plane Proportional Navigation (TPPN), and the Kinematic Impulse (KI). A manipulated Bennu orbit that has been changed to impact Earth will be used as a demonstrative example to compare the three methods. In addition, a hybrid approach that is a combination between proportional navigation and kinematic impulse will be investigated to find an effective, error tolerant, and power saving approach. A 3-dimension mission scenario for both the asteroid and the interceptor spacecraft software simulator is developed for testing of the controllers. The current result demonstrates that a miss distance magnitude of less than 10m is found using the PN and TPPN guidance laws for small asteroid in the presence of error in the spacecraft states. Moreover, the paper presents these results and also the hybrid control approach simulation results.

asteroid↗

DOE OSTI2021

An adaptive Hessian approximated stochastic gradient MCMC method

Bayesian approaches have been successfully integrated into training deep neural networks. One popular family is stochastic gradient Markov chain Monte Carlo methods (SG-MCMC), which have gained increasing interest due to their ability to handle large datasets and the potential to avoid overfitting. Although standard SG-MCMC methods have shown great performance in a variety of problems, they may be inefficient when the random variables in the target posterior densities have scale differences or are highly correlated. Here, we present an adaptive Hessian approximated stochastic gradient MCMC method to incorporate local geometric information while sampling from the posterior. The idea is to apply stochastic approximation (SA) to sequentially update a preconditioning matrix at each iteration. The preconditioner possesses second-order information and can guide the random walk of a sampler efficiently. Instead of computing and saving the full Hessian of the log posterior, we use limited memory of the samples and their stochastic gradients to approximate the inverse Hessian-vector multiplication in the updating formula. Moreover, by smoothly optimizing the preconditioning matrix via SA, our proposed algorithm can asymptotically converge to the target distribution with a controllable bias under mild conditions. To reduce the training and testing computational burden, we adopt a magnitude-based weight pruning method to enforce the sparsity of the network. Our method is user-friendly and demonstrates better learning results compared to standard SG-MCMC updating rules. The approximation of inverse Hessian alleviates storage and computational complexities for large dimensional models. Numerical experiments are performed on several problems, including sampling from 2D correlated distribution, synthetic regression problems, and learning the numerical solutions of heterogeneous elliptic PDE. The numerical results demonstrate great improvement in both the convergence rate and accuracy.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

CIS Project 22359, Final Technical Report. Discretized Posterior Approximation in High Dimensions

Our primary aim in this work is to understand how to efficiently obtain reliable uncertainty quantification in automatic learning algorithms with limited training datasets. Standard approaches rely on cross-validation to tune hyper parameters. Unfortunately, when our datasets are too small, holdout datasets become unreliable—albeit unbiased—measures of prediction quality due to the lack of adequate sample size. We should not place confidence in holdout estimators under conditions wherein the sample variance is both large and unknown. More poigniantly, our training experiments on limited data (Duersch and Catanach, 2021) show that even if we could improve estimator quality under these conditions, the typical training trajectory may never even encounter generalizable models.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1989

Contact solution algorithms

Two algorithms for obtaining static contact solutions are described in this presentation. Although they were derived for contact problems involving specific structures (a tire and a solid rubber cylinder), they are sufficiently general to be applied to other shell-of-revolution and solid-body contact problems. The shell-of-revolution contact algorithm is a method of obtaining a point load influence coefficient matrix for the portion of shell surface that is expected to carry a contact load. If the shell is sufficiently linear with respect to contact loading, a single influence coefficient matrix can be used to obtain a good approximation of the contact pressure distribution. Otherwise, the matrix will be updated to reflect nonlinear load-deflection behavior. The solid-body contact algorithm utilizes a Lagrange multiplier to include the contact constraint in a potential energy functional. The solution is found by applying the principle of minimum potential energy. The Lagrange multiplier is identified as the contact load resultant for a specific deflection. At present, only frictionless contact solutions have been obtained with these algorithms. A sliding tread element has been developed to calculate friction shear force in the contact region of the rolling shell-of-revolution tire model.

Tielking, John T.↗

NASA NTRS2020

Image Moment-Based Extended Object Tracking for Complex Motions

A novel image moment-based model for shape estimation and tracking of an extended target moving with a complex trajectory is presented. The proposed extended object tracking algorithm is based on multiple noisy measurement points sampled from the target at each time step. The shape of the object, approximated by an ellipse, is estimated using a combination of image moments. Dynamic models of image moments for constant velocity and coordinated turn motions are mathematically derived. An unscented Kalman filter - interacting multiple model (UKF-IMM) method is used to track the object and estimate its shape. A likelihood function based on average log-likelihood is derived for the IMM filter. Simulation results of the proposed UKF-IMM algorithm with the image momentbased models are presented that show the estimation of the shape of the object moving in a complex trajectory. The intersection over union (IoU), and the root mean square errors (RMSEs) of the position and velocity of the centroid of the ellipse are used as metrics. The comparison results of the proposed algorithm with a benchmark algorithm from literature based on the IoU and RMSE metrics are presented.

Extended object tracking↗

NASA NTRS2012

A Comparison of Filter-based Approaches for Model-based Prognostics

Model-based prognostics approaches use domain knowledge about a system and its failure modes through the use of physics-based models. Model-based prognosis is generally divided into two sequential problems: a joint state-parameter estimation problem, in which, using the model, the health of a system or component is determined based on the observations; and a prediction problem, in which, using the model, the stateparameter distribution is simulated forward in time to compute end of life and remaining useful life. The first problem is typically solved through the use of a state observer, or filter. The choice of filter depends on the assumptions that may be made about the system, and on the desired algorithm performance. In this paper, we review three separate filters for the solution to the first problem: the Daum filter, an exact nonlinear filter; the unscented Kalman filter, which approximates nonlinearities through the use of a deterministic sampling method known as the unscented transform; and the particle filter, which approximates the state distribution using a finite set of discrete, weighted samples, called particles. Using a centrifugal pump as a case study, we conduct a number of simulation-based experiments investigating the performance of the different algorithms as applied to prognostics.

prognostics↗

NASA NTRS2017

New-Generation NASA Aura Ozone Monitoring Instrument (OMI) Volcanic SO2 Dataset: Algorithm Description, Initial Results, and Continuation with the Suomi-NPP Ozone Mapping and Profiler Suite (OMPS)

Since the fall of 2004, the Ozone Monitoring Instrument (OMI) has been providing global monitoring of volcanic SO2 emissions, helping to understand their climate impacts and to mitigate aviation hazards. Here we introduce a new-generation OMI volcanic SO2 dataset based on a principal component analysis (PCA) retrieval technique. To reduce retrieval noise and artifacts as seen in the current operational linear fit (LF) algorithm, the new algorithm, OMSO2VOLCANO, uses characteristic features extracted directly from OMI radiances in the spectral fitting, thereby helping to minimize interferences from various geophysical processes (e.g., O3 absorption) and measurement details (e.g., wavelength shift). To solve the problem of low bias for large SO2 total columns in the LF product, the OMSO2VOLCANO algorithm employs a table lookup approach to estimate SO2 Jacobians (i.e., the instrument sensitivity to a perturbation in the SO2 column amount) and iteratively adjusts the spectral fitting window to exclude shorter wavelengths where the SO2 absorption signals are saturated. To first order, the effects of clouds and aerosols are accounted for using a simple Lambertian equivalent reflectivity approach. As with the LF algorithm, OMSO2VOLCANO provides total column retrievals based on a set of predefined SO2 profiles from the lower troposphere to the lower stratosphere, including a new profile peaked at 13 km for plumes in the upper troposphere. Examples given in this study indicate that the new dataset shows significant improvement over the LF product, with at least 50% reduction in retrieval noise over the remote Pacific. For large eruptions such as Kasatochi in 2008 (approximately 1700 kt total SO2/ and Sierra Negra in 2005 (greater than 1100DU maximum SO2), OMSO2VOLCANO generally agrees well with other algorithms that also utilize the full spectral content of satellite measurements, while the LF algorithm tends to underestimate SO2. We also demonstrate that, despite the coarser spatial and spectral resolution of the Suomi National Polar-orbiting Partnership (Suomi-NPP) Ozone Mapping and Profiler Suite (OMPS) instrument, application of the new PCA algorithm to OMPS data produces highly consistent retrievals between OMI and OMPS. The new PCA algorithm is therefore capable of continuing the volcanic SO2 data record well into the future using current and future hyperspectral UV satellite instruments.

OMI↗

NASA NTRS1991

Shock capturing schemes for multidimensional flow

Progress made in the development of a genuinely multidimensional finite volume algorithm for problems in inviscid gas dynamics is presented. The approach entails: (1) the reconstruction of flowfield data using a planar wave pattern in which the strengths and orientations of the component waves are derived independently of the mesh geometry; and (2) the development of a flux formula which provides a numerical approximation to the flux at a finite volume cell face during the passage of waves which are in general oblique to the face. Several algorithms are outlined, and the most recent developments are included. The results of several numerical cases are also included.

Parpia, Ijaz H.↗

DOE OSTI2023

Robust sampling for weak lensing and clustering analyses with the Dark Energy Survey

Recent cosmological analyses rely on the ability to accurately sample from high-dimensional posterior distributions. A variety of algorithms have been applied in the field, but justification of the particular sampler choice and settings is often lacking. Here, we investigate three such samplers to motivate and validate the algorithm and settings used for the Dark Energy Survey (DES) analyses of the first 3 yr (Y3) of data from combined measurements of weak lensing and galaxy clustering. We employ the full DES Year 1 likelihood alongside a much faster approximate likelihood, which enables us to assess the outcomes from each sampler choice and demonstrate the robustness of our full results. We find that the ellipsoidal nested sampling algorithm multinest reports inconsistent estimates of the Bayesian evidence and somewhat narrower parameter credible intervals than the sliced nested sampling implemented in polychord. We compare the findings from multinest and polychord with parameter inference from the Metropolis–Hastings algorithm, finding good agreement. We determine that polychord provides a good balance of speed and robustness for posterior and evidence estimation, and recommend different settings for testing purposes and final chains for analyses with DES Y3 data. Our methodology can readily be reproduced to obtain suitable sampler settings for future surveys.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS1990

The analysis of polar clouds from AVHRR satellite data using pattern recognition techniques

The cloud cover in a set of summertime and wintertime AVHRR data from the Arctic and Antarctic regions was analyzed using a pattern recognition algorithm. The data were collected by the NOAA-7 satellite on 6 to 13 Jan. and 1 to 7 Jul. 1984 between 60 deg and 90 deg north and south latitude in 5 spectral channels, at the Global Area Coverage (GAC) resolution of approximately 4 km. This data embodied a Polar Cloud Pilot Data Set which was analyzed by a number of research groups as part of a polar cloud algorithm intercomparison study. This study was intended to determine whether the additional information contained in the AVHRR channels (beyond the standard visible and infrared bands on geostationary satellites) could be effectively utilized in cloud algorithms to resolve some of the cloud detection problems caused by low visible and thermal contrasts in the polar regions. The analysis described makes use of a pattern recognition algorithm which estimates the surface and cloud classification, cloud fraction, and surface and cloudy visible (channel 1) albedo and infrared (channel 4) brightness temperatures on a 2.5 x 2.5 deg latitude-longitude grid. In each grid box several spectral and textural features were computed from the calibrated pixel values in the multispectral imagery, then used to classify the region into one of eighteen surface and/or cloud types using the maximum likelihood decision rule. A slightly different version of the algorithm was used for each season and hemisphere because of differences in categories and because of the lack of visible imagery during winter. The classification of the scene is used to specify the optimal AVHRR channel for separating clear and cloudy pixels using a hybrid histogram-spatial coherence method. This method estimates values for cloud fraction, clear and cloudy albedos and brightness temperatures in each grid box. The choice of a class-dependent AVHRR channel allows for better separation of clear and cloudy pixels than does a global choice of a visible and/or infrared threshold. The classification also prevents erroneous estimates of large fractional cloudiness in areas of cloudfree snow and sea ice. The hybrid histogram-spatial coherence technique and the advantages of first classifying a scene in the polar regions are detailed. The complete Polar Cloud Pilot Data Set was analyzed and the results are presented and discussed.

Smith, William L.↗