Iterative saddle point techniques.
Iterative solution methods for minimizing convex, differentiable function in Euclidean space
DIFFERENTIAL EQUATION↗
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Results for “randomized methods”
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.
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Sample quadratic variation of sample continuous second order martingales.
Sample continuous second order martingale process, determining existence of limit of stochastic processes using approximation theorems
RANDOM PROCESS↗
Monte Carlo solutions of molecular flow through cylindrical ducts.
Free and near-free molecular flow via cylindrical ducts using Monte Carlo method and high speed digital computer
CHANNEL FLOW↗
Random deflections of a string on an elastic foundation.
The paper is concerned with the problem of a taut string on a random elastic foundation subjected to random loads. The boundary value problem is transformed into an initial value problem by the method of invariant imbedding. Fokker-Planck equations for the random initial value problem are formulated and solved in some special cases. The analysis leads to a complete characterization of the random deflection function.
Sanders, J. L., Jr.↗
Lineaments on Skylab photographs: Detection, mapping, and hydrologic significance in central Tennessee
An investigation was carried out to determine the feasibility of mapping lineaments on SKYLAB photographs of central Tennessee and to determine the hydrologic significance of these lineaments, particularly as concerns the occurrence and productivity of ground water. Sixty-nine percent more lineaments were found on SKYLAB photographs by stereo viewing than by projection viewing, but longer lineaments were detected by projection viewing. Most SKYLAB lineaments consisted of topographic depressions and they followed or paralleled the streams. The remainder were found by vegetation alinements and the straight sides of ridges. Test drilling showed that the median yield of wells located on SKYLAB lineaments were about six times the median yield of wells located by random drilling. The best single detection method, in terms of potential savings, was stereo viewing. Larger savings might be achieved by locating wells on lineaments detected by both stereo viewing and projection.
Moore, G. K.↗
Plasma effects on the spontaneous emission of synchrotron radiation from weakly relativistic electrons
A method for computing the spectral emissivity of spontaneous synchrotron radiation is discussed. The Klimontovich (1967) formalism in plasma kinetic theory is adopted in which an ensemble average of the microscopically emitted power is considered. The present method clarifies the meaning of the random phase approximation which is imposed in several existing theories of synchrotron radiation. Both the effects of dielectric polarization and two-particle correlations are included in the present discussion. The theory is applied to the case of a plasma in thermal equilibrium, for which it is shown that the effect of pair correlations on the emissivity vanishes. On the other hand, the effect of dielectric polarization is studied numerically for a wide range of parameters.
Freund, H. P.↗
SMC X-1 variability observed from HEAO 1
Studies are reported of the slow variability of SMC X-1 and its spectrum. An analysis of red-noise random variability is based on a method discussed by Deeter and Boynton (1982). The 0.7 s X-ray pulsar SMC X-1 is in a 3.89 day eclipsing binary system with a B0 I supergiant companion. Observations of the pulsar were conducted with the aid of the UCSD/MIT instrument on HEAO 1 from 1977 August through 1979 January. A light curve was constructed for the period 1977 September to 1978 December. The apparent tendency of SMC X-1 to be in one of two states, high or low, suggests the acquisition of average spectra separately for each state. The total (steady plus pulsed) emission from SMC X-1 displays a continuum spectrum with a dominant exponential form which implies a temperature of 17 keV for thin thermal bremsstrahlung emission or 5 keV if the other limit of a Wien spectrum is assumed.
Gruber, D. E.↗
Nonlinear analyses of composite aerospace structures in sonic fatigue
This report summarizes the semiannual research progress, accomplishments, and future plans performed under the NASA Langley Research Center Grant No. NAG-1-1358. The primary research effort of this project is the development of analytical methods for the prediction of nonlinear random response of composite aerospace structures subjected to combined acoustic and thermal loads. The progress, accomplishments, and future plates on four sonic fatigue research topics are described. The sonic fatigue design and passive control of random response of shape memory alloy hybrid composites presented in section 4, which is suited especially for HSCT, is a new initiative.
Mei, Chuh↗
Methods for evaluation of the microgravity environment aboard Space Station Freedom
Space Station Freedom will be a platform for microgravity research. For superior microgravity science, the experiment locations must experience very little acceleration in the quasi-steady, structural dynamic, and vibroacoustic frequency ranges. This paper presents the methods that were developed for evaluation of the microgravity environment in the structural dynamic range. An integrated finite element model of the space station was used to conduct analysis for the on-orbit microgravity environment. Methods were developed to evaluate sinusoidal, random, and transient disturbances. Sources of disturbances aboard the Space Station were quantified and forcing functions were assembled. The resulting acceleration levels at the experiment locations due to these disturbances were computed and assessed against the microgravity acceleration requirement curve.
Wetzel, John P.↗
Structural response to discrete and continuous gusts of an airplane having wing bending flexibility and a correlation of calculated and flight results
An analysis is made of the structural response to gusts of an airplane having the degrees of freedom of vertical motion and wing bending flexibility and basic parameters are established. A convenient and accurate numerical solution of the response equations is developed for the case of discrete-gust encounter, an exact solution is made for the simpler case of continuous-sinusoidal-gust encounter, and the procedure is outlined for treating the more realistic condition of continuous random atmospheric turbulence, based on the methods of generalized harmonic analysis. Correlation studies between flight and calculated results are then given to evaluate the influence of wing bending flexibility on the structural response to gusts of two twin-engine transports and one four-engine bomber. It is shown that calculated results obtained by means of a discrete-gust approach reveal the general nature of the flexibility effects and lead to qualitative correlation with flight results. In contrast, calculations by means of the continuous-turbulence approach show good quantitative correlation with flight results and indicate a much greater degree of resolution of the flexibility effects.
Houbolt, John C↗
Progressive Response Surfaces
Response surface functions are often used as simple and inexpensive replacements for computationally expensive computer models that simulate the behavior of a complex system over some parameter space. Progressive response surfaces are ones that are built up progressively as global information is added from new sample points in the parameter space. As the response surfaces are globally upgraded based on new information, heuristic indications of the convergence of the response surface approximation to the exact (fitted) function can be inferred. Sampling points can be incrementally added in a structured fashion, or in an unstructured fashion. Whatever the approach, at least in early stages of sampling it is usually desirable to sample the entire parameter space uniformly. At later stages of sampling, depending on the nature of the quantity being resolved, it may be desirable to continue sampling uniformly over the entire parameter space (Progressive response surfaces), or to switch to a focusing/economizing strategy of preferentially sampling certain regions of the parameter space based on information gained in early stages of sampling (Adaptive response surfaces). Here we consider Progressive response surfaces where a balanced indication of global response over the parameter space is desired.We use a variant of Moving Least Squares to fit and interpolate structured and unstructured point sets over the parameter space. On a 2-D test problem we compare response surface accuracy for three incremental sampling methods: Progressive Lattice Sampling; Simple-Random Monte Carlo; and Halton Quasi-Monte-Carlo sequences. We are ultimately after a system for constructing efficiently upgradable response surface approximations with reliable error estimates.
Romero, V. J.↗
Hoffmann-reflex is delayed during 6 degree head-down tilt with balanced traction
BACKGROUND: Increased spinal height due to the lack of of axial compression on spinal structures in microgravity may stretch the spinal cord, cauda equina, nerve roots, and paraspinal tissues. HYPOTHESIS: Exposure to simulated microgravity causes dysfunction of nerve roots so that the synaptic portion of the Achilles tendon reflex is delayed. METHODS: Six healthy male subjects were randomly divided into two groups with three in each group. The subjects in the first group underwent horizontal bed rest (HBR) for three days. After a two week interval they underwent bed rest in a position of head-down tilt with balanced traction (HDT). So that each subject could serve as his own control, the second group was treated identically but in opposite order. Bilateral F waves and H-reflexes were measured daily (18:30-20:30) on all subjects placed in a prone position. RESULTS: By means of ANOVA, differences between HDT and HBR were observed only in M-latency and F-ratio, not in F-latency, central latency, and H-latency. Differences during the course of the bed rest were observed in M-latency and H-latency only. Tibial H latency was significantly lengthened in HDT group on day 2 and 3, although no significant difference between HDT and HBR was observed. CONCLUSION: The monosynaptic reflex assessed by H-reflex was delayed during 6 degree HDT with traction. The exact mechanism of this delay and whether the change was due to lengthening of the lower part of the vertebrae remain to be clarified.
Randomized Controlled Trial↗
Data transmission system and method
A method of transmitting data packets, where randomness is added to the schedule. Universal broadcast schedules using encoding and randomization techniques are also discussed, together with optimal randomized schedules and an approximation algorithm for finding near-optimal schedules.
Bruck, Jehoshua↗
Phase Retrieval with Signal Bias
The effect of a uniform measurement bias, due to background light, stray light, detector dark current, or detector offset, on phase retrieval wavefront sensing algorithms is analyzed. Simulation results indicate that the root-mean-square error of the retrieved phase can be more sensitive to an unaccounted-for signal bias than to random noise in practical scenarios. Three methods for reducing the impact of signal bias are presented
Thurman, Samuel T.↗
New York Ecological Forecasting: Utilizing NASA Earth Observations to Map Ash Distribution and Inform Emerald Ash Borer Control
Since their first sightings in the U.S. in 2002, emerald ash borer beetles (Agrilus planipennis; EAB) have killed millions of native ash (Fraxinus spp.) trees across 35 states. Infected ash stands frequently exhibit complete mortality, with the predicted result being the functional extinction of native ash in U.S. forests. In August of 2020, EAB was discovered in the 6.1-million-acre Adirondack Park. The team’s partners at the Adirondack Park Invasive Plant Program (APIPP) desired ash tree distribution and EAB susceptibility information to help improve EAB bio-control efficiency and apply the methodology to future invasive programs. To assist, the team mapped ash tree distribution using NASA Earth observations from Landsat 7 Enhanced Thematic Mapper Plus (ETM+) and Shuttle Radar Topography Mission (SRTM), along with hyperspectral imagery from the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS). Field data from the Monitoring and Managing Ash (MaMA) project, iMapInvasives and iNaturalist databases, and the New York State Department of Environmental Conservation (NYSDEC) provided ground truthing for mapping and modeling. Results indicate that for ash detection, the team’s Spectral Angle Mapping (SAM) hyperspectral classification is slightly more sensitive but less accurate than multispectral Random Forest (RF) classification, though neither method was above a ~20% detection rate. End products include maps of ash extent derived from both imagery types, a model forecasting future spread scenarios based on current EAB presence, and outreach materials. These products inform APIPP’s management decisions and facilitate public awareness of EAB’s threat to communities within the region.
Liam Megraw↗
Self-Supervised Anomaly Detection via Neural Autoregressive Flows with Active Learning
Many self-supervised methods have been proposed with the target of image anomaly detection. These methods often rely on the paradigm of data augmentation with predefined transformations such as flipping, cropping, and rotations. However, it is not straightforward to apply these techniques for non-image data, such as time series or tabular data, while the performance of the existing deep approaches has been under our expectation on tasks beyond images. In this work, we propose a novel active learning (AL) scheme that relied on neural autoregressive flows (NAF) for self-supervised anomaly detection, specifically on small-scale data. Unlike other generative models such as GANs or VAEs, flow-based models allow to explicitly learn the probability density and thus can assign accurate likelihoods to normal data which makes it usable to detect anomalies. The proposed NAF-AL method is achieved by efficiently generating random samples from latent space and transforming them into feature space along with likelihoods via invertible mapping. The samples with lower likelihoods are selected and further checked by outlier detection using Mahalanobis distance. The augmented samples incorporating with normal samples are used for training a better detector so as to approach decision boundaries. Compared with random transformations, NAF-AL can be interpreted as a likelihood-oriented data augmentation that is more efficient and robust. Extensive experiments show that our approach outperforms existing baselines on multiple time series and tabular datasets, and a real-world application in advanced manufacturing, with significant improvement on anomaly detection accuracy and robustness over the state-of-the-art.
Zhang, Jiaxin↗
A Galerkin method with two-dimensional Haar basis functions for the computation of the Karhunen–Loève expansion
We study the numerical approximation of a homogeneous Fredholm integral equation of second kind associated with the Karhunen–Loève expansion of Gaussian random fields. We develop, validate, and discuss an algorithm based on the Galerkin method with two-dimensional Haar wavelets as basis functions. The shape functions are constructed from the orthogonal decomposition of tensor-product spaces of one-dimensional Haar functions, and a recursive algorithm is employed to compute the matrix of the discrete eigenvalue system without the explicit calculation of integrals, allowing the implementation of a fast and efficient algorithm that provides considerable reduction in CPU time, when compared with classical Galerkin methods. Numerical experiments confirm the convergence rate of the method and assess the approximation error and the sparsity of the eigenvalue system when the wavelet expansion is truncated. We illustrate the numerical solution of a diffusion problem with random input data with the present method. In this problem, accuracy was retained after dropping the coefficients below a threshold value that was numerically determined. A similar method with scaling functions rather than wavelet functions does not need a discrete wavelet transform and leads to eigenvalue systems with better conditioning but lower sparsity.
97 MATHEMATICS AND COMPUTING↗
A Pattern-Recognition-Based Ensemble Data Imputation Framework for Sensors from Building Energy Systems
Building operation data are important for monitoring, analysis, modeling, and control of building energy systems. However, missing data is one of the major data quality issues, making data imputation techniques become increasingly important. There are two key research gaps for missing sensor data imputation in buildings: the lack of customized and automated imputation methodology, and the difficulty of the validation of data imputation methods. In this paper, a framework is developed to address these two gaps. First, a validation data generation module is developed based on pattern recognition to create a validation dataset to quantify the performance of data imputation methods. Second, a pool of data imputation methods is tested under the validation dataset to find an optimal single imputation method for each sensor, which is termed as an ensemble method. The method can reflect the specific mechanism and randomness of missing data from each sensor. The effectiveness of the framework is demonstrated by 18 sensors from a real campus building. The overall accuracy of data imputation for those sensors improves by 18.2% on average compared with the best single data imputation method.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗