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At least 433 records · Page 24

Fractal Characterization of Hyperspectral Imagery

Two Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) hyperspectral images selected from the Los Angeles area, one representing urban and the other, rural, were used to examine their spatial complexity across their entire spectrum of the remote sensing data. Using the ICAMS (Image Characterization And Modeling System) software, we computed the fractal dimension values via the isarithm and triangular prism methods for all 224 bands in the two AVIRIS scenes. The resultant fractal dimensions reflect changes in image complexity across the spectral range of the hyperspectral images. Both the isarithm and triangular prism methods detect unusually high D values on the spectral bands that fall within the atmospheric absorption and scattering zones where signature to noise ratios are low. Fractal dimensions for the urban area resulted in higher values than for the rural landscape, and the differences between the resulting D values are more distinct in the visible bands. The triangular prism method is sensitive to a few random speckles in the images, leading to a lower dimensionality. On the contrary, the isarithm method will ignore the speckles and focus on the major variation dominating the surface, thus resulting in a higher dimension. It is seen where the fractal curves plotted for the entire bandwidth range of the hyperspectral images could be used to distinguish landscape types as well as for screening noisy bands.

Qiu, Hon-Iie↗

Assessing Risk Due to Small Sample Size in Probability of Detection Analysis Using Tolerance Intervals

Small sample size (e.g.6-30) poses risk in results of probability of detection (POD) analysis using tolerance intervals. This method is also called as the limited sample or LS POD. The analysis is performed either during NDE procedure qualification or for assessment of reliability of an NDE procedure. The risk is primarily due to sampling error. Smaller samples are not likely to be random to the population or representative of the population. The small samples are likely to be biased. Biased samples have smaller standard deviation compared to the population. POD analysis with small biased sample can lead to overestimation of POD. Many sampling schemes are available in statistics to mitigate sampling risk. Primary objective of POD analysis is to determine a decision threshold from signal response measurements of a sample such that it is less than or equal to population decision threshold for 90% POD. Sampling error implies that this NDE reliability condition is violated. One of sampling types is called a representative sample. Representative samples reduce variance in POD estimates but also reduce magnitude of the error. Sampling sensitivity analysis for some sampling types is performed here using repetitive random sampling or Monte Carlo method. Six sampling types are considered for comparison. Some of the sampling types are similar to drawing a representative sample. LS POD model assumes random sampling. Therefore, random sampling is used as a basis for comparison with each sampling type. The sampling types used in the analysis are, A. Nominal and worst-case sampling, B. Worst-case sampling, C. Nominal case sampling, D. Random sampling, E. Random target, and sub-target sampling. F. Nominal target and sub-target sampling. Results of Monte Carlo simulation indicate that type F sampling can mitigate sampling risk and is also more practical to implement. Type A sampling may also mitigate the sampling risk, but it may be less practical to implement.

Ajay M Koshti↗

CORRLA-RS

The CORRLA-RS package provides a suite of statistical methods for sampling multidimensional distributions and to conduct sensitivity and correlation analysis of large scale data in the Rust programming language. The software provides a unique solution to multidimensional constrained sampling problems utilizing a combination of parallelized Markov Chain Monte Carlo methods and traditional rejection sampling. The sensitivity and correlation analysis methods are backed by a high performance randomized singular value decomposition implementation which enables datasets larger than the random access memory (RAM) size to be analyzed. Additionally, CORRLA-RS implements the active subspace identification method using a KD-Tree and the randomized singular value decomposition acting in concert.

Gurecky, William [Oak Ridge National Laboratory (O↗

Mixed-State Entanglement from Local Randomized Measurements

In this work, we propose a method for detecting bipartite entanglement in a many-body mixed state based on estimating moments of the partially transposed density matrix. The estimates are obtained by performing local random measurements on the state, followed by postprocessing using the classical shadows framework. Our method can be applied to any quantum system with single-qubit control. We provide a detailed analysis of the required number of experimental runs, and demonstrate the protocol using existing experimental data [Brydges et al., Science 364, 260 (2019)].

1-dimensional spin chains↗

Analysis/design of strip reinforced random composites /strip hybrids/

Results are described which were obtained by applying advanced analysis methods and composite mechanics to a strip-reinforced random composite square panel with fixed ends. This was done in order to illustrate the use of these methods for the apriori assessment of the composite panel when subjected to complex loading conditions. The panel was assumed to be of E-Glass/Random Composite. The strips were assumed to be of three advanced unidirectional composites to cover a range of low, intermediate, and high modulus stiffness. The panels were assumed to be subjected to complex loadings to assess their adequacy as load-carrying members in auto body, aircraft engine nacelle, and windmill blade applications. The results show that strip hybrid panels can be several times more structurally efficient than the random composite base materials. Some of the results are presented in graphical form and procedures are described for use of these graphs as guides for preliminary design of strip hybrids.

Chamis, C. C.↗

New Approaches in Force-Limited Vibration Testing of Flight Hardware

To qualify flight hardware for random vibration environments the following methods are used to limit the loads in the aerospace industry: (1) Response limiting and notching (2) Simple TDOF model (3) Semi-empirical force limits (4) Apparent mass, etc. and (5) Impedance method. In all these methods attempts are made to remove conservatism due to the mismatch in impedances between the test and the flight configurations of the hardware that are being qualified. Assumption is the hardware interfaces have correlated responses. A new method that takes into account the un-correlated hardware interface responses are described in this presentation.

Random Vibration↗

Scattering Properties of Heterogeneous Mineral Particles with Absorbing Inclusions

We analyze the results of numerically exact computer modeling of scattering and absorption properties of randomly oriented poly-disperse heterogeneous particles obtained by placing microscopic absorbing grains randomly on the surfaces of much larger spherical mineral hosts or by imbedding them randomly inside the hosts. These computations are paralleled by those for heterogeneous particles obtained by fully encapsulating fractal-like absorbing clusters in the mineral hosts. All computations are performed using the superposition T-matrix method. In the case of randomly distributed inclusions, the results are compared with the outcome of Lorenz-Mie computations for an external mixture of the mineral hosts and absorbing grains. We conclude that internal aggregation can affect strongly both the integral radiometric and differential scattering characteristics of the heterogeneous particle mixtures.

minerals↗

SpotSDC: Revealing the Silent Data Corruption Propagation in High-Performance Computing Systems

We report the trend of rapid technology scaling is expected to make the hardware of high-performance computing (HPC) systems more susceptible to computational errors due to random bit flips. Some bit flips may cause a program to crash or have a minimal effect on the output, but others may lead to silent data corruption (SDC), i.e., undetected yet significant output errors. Classical fault injection analysis methods employ uniform sampling of random bit flips during program execution to derive a statistical resiliency profile. However, summarizing such fault injection result with sufficient detail is difficult, and understanding the behavior of the fault-corrupted program is still a challenge. In this article, we introduce SpotSDC, a visualization system to facilitate the analysis of a program's resilience to SDC. SpotSDC provides multiple perspectives at various levels of detail of the impact on the output relative to where in the source code the flipped bit occurs, which bit is flipped, and when during the execution it happens. SpotSDC also enables users to study the code protection and provide new insights to understand the behavior of a fault-injected program. Based on lessons learned, we demonstrate how what we found can improve the fault injection campaign method.

97 MATHEMATICS AND COMPUTING↗

Detection of fatigue cracks by nondestructive testing methods

The effectiveness was assessed of various NDT methods to detect small tight cracks by randomly introducing fatigue cracks into aluminum sheets. The study included optimizing NDT methods calibrating NDT equipment with fatigue cracked standards, and evaluating a number of cracked specimens by the optimized NDT methods. The evaluations were conducted by highly trained personnel, provided with detailed procedures, in order to minimize the effects of human variability. These personnel performed the NDT on the test specimens without knowledge of the flaw locations and reported on the flaws detected. The performance of these tests was measured by comparing the flaws detected against the flaws present. The principal NDT methods utilized were radiographic, ultrasonic, penetrant, and eddy current. Holographic interferometry, acoustic emission monitoring, and replication methods were also applied on a reduced number of specimens. Generally, the best performance was shown by eddy current, ultrasonic, penetrant and holographic tests. Etching provided no measurable improvement, while proof loading improved flaw detectability. Data are shown that quantify the performances of the NDT methods applied.

Anderson, R. T.↗

Alternative Modal Basis Selection Procedures for Nonlinear Random Response Simulation

Three procedures to guide selection of an efficient modal basis in a nonlinear random response analysis are examined. One method is based only on proper orthogonal decomposition, while the other two additionally involve smooth orthogonal decomposition. Acoustic random response problems are employed to assess the performance of the three modal basis selection approaches. A thermally post-buckled beam exhibiting snap-through behavior, a shallowly curved arch in the auto-parametric response regime and a plate structure are used as numerical test articles. The results of the three reduced-order analyses are compared with the results of the computationally taxing simulation in the physical degrees of freedom. For the cases considered, all three methods are shown to produce modal bases resulting in accurate and computationally efficient reduced-order nonlinear simulations.

Przekop, Adam↗

Alternative Modal Basis Selection Procedures For Reduced-Order Nonlinear Random Response Simulation

Three procedures to guide selection of an efficient modal basis in a nonlinear random response analysis are examined. One method is based only on proper orthogonal decomposition, while the other two additionally involve smooth orthogonal decomposition. Acoustic random response problems are employed to assess the performance of the three modal basis selection approaches. A thermally post-buckled beam exhibiting snap-through behavior, a shallowly curved arch in the auto-parametric response regime and a plate structure are used as numerical test articles. The results of a computationally taxing full-order analysis in physical degrees of freedom are taken as the benchmark for comparison with the results from the three reduced-order analyses. For the cases considered, all three methods are shown to produce modal bases resulting in accurate and computationally efficient reduced-order nonlinear simulations.

Przekop, Adam↗

Identifying and Analyzing Uncertainty Structures in the TRMM Microwave Imager Precipitation Product over Tropical Ocean Basins

Despite continuous improvements in microwave sensors and retrieval algorithms, our understanding of precipitation uncertainty is quite limited, due primarily to inconsistent findings in studies that compare satellite estimates to in situ observations over different parts of the world. This study seeks to characterize the temporal and spatial properties of uncertainty in the Tropical Rainfall Measuring Mission Microwave Imager surface rainfall product over tropical ocean basins. Two uncertainty analysis frameworks are introduced to qualitatively evaluate the properties of uncertainty under a hierarchy of spatiotemporal data resolutions. The first framework (i.e. 'climate method') demonstrates that, apart from random errors and regionally dependent biases, a large component of the overall precipitation uncertainty is manifested in cyclical patterns that are closely related to large-scale atmospheric modes of variability. By estimating the magnitudes of major uncertainty sources independently, the climate method is able to explain 45-88% of the monthly uncertainty variability. The percentage is largely resolution dependent (with the lowest percentage explained associated with a 1 deg x 1 deg spatial/1 month temporal resolution, and highest associated with a 3 deg x 3 deg spatial/3 month temporal resolution). The second framework (i.e. 'weather method') explains regional mean precipitation uncertainty as a summation of uncertainties associated with individual precipitation systems. By further assuming that self-similar recurring precipitation systems yield qualitatively comparable precipitation uncertainties, the weather method can consistently resolve about 50 % of the daily uncertainty variability, with only limited dependence on the regions of interest.

Climate↗

Frequency domain analysis of the random loading of cracked panels

The primary effort concerned the development of analytical methods for the accurate prediction of the effect of random loading on a panel with a crack. Of particular concern was the influence of frequency on the stress intensity factor behavior. Many modern structures, such as those found in advanced aircraft, are lightweight and susceptible to critical vibrations, and consequently dynamic response plays a very important role in their analysis. The presence of flaws and cracks can have catastrophic consequences. The stress intensity factor, K, emerges as a very significant parameter that characterizes the crack behavior. In analyzing the dynamic response of panels that contain cracks, the finite element method is used, but because this type of problem is inherently computationally intensive, a number of ways of calculating K more efficiently are explored.

Doyle, James F.↗

The velocity dispersion of the caustic network due to random motion of individual stars in the lensing galaxy

We present a method of computing the velocity distribution of the caustic network due to the random motion of stars in the lensing galaxy. This method is illustrated on the example of the two-point mass lens and then applied to a large sample of stars. We conclude that the proper motion of the stars increases significantly the frequency of the high magnification events in comparison with a static lens configuration with constant stream or constant bulk velocity. The stream velocity is the velocity of the star field relative to the global bulk velocity of the galaxy. We show that the global bulk and the stream velocity of the star field have to be considered separately for any microlensing situation. The higher the surface mass density of the stars in the lensing galaxy, the higher the influence of proper motion of stars on the statistics of high magnification events. The influence of a Gaussian velocity distribution of the stars in the lensing galaxy compared with a constant stream velocity of the stars increases the number of high magnification events by a factor 1.30 +/- 0.06 for a normalized surface density of the stars cr = 0.1 and by a factor 1.7 +/- 0.1 for sigma = 0.5. This means that for some microlensing situations the proper motion of the stars in a lensing galaxy has to be considered for exact microlensing predictions.

Kundik, Tomislav↗

Determination of Nonlinear Stiffness Coefficients for Finite Element Models with Application to the Random Vibration Problem

In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.

Muravyov, Alexander A.↗

Accelerating Ab Initio Simulation via Nested Monte Carlo and Machine Learned Reference Potentials

As a corollary of the rapid advances in computing, ab initio simulation is playing an increasingly important role in modeling materials at the atomic scale. Two strategies are possible, ab initio Monte Carlo (AIMC) and molecular dynamics (AIMD) simulation. The former benefits from exact sampling from the correct thermodynamic distribution, while the latter is typically more efficient with its collective all-atom coordinate updates. In this study, using a relatively simple test model comprised of helium and argon, we show that AIMC can be brought up to, and even above, the performance levels of AIMD via a hybrid nested sampling/machine learning (ML) strategy. Here, ML provides an accurate classical reference potential (up to three-body explicit interactions) that can pilot long collective Monte Carlo moves that are accepted or rejected in toto à la nested Monte Carlo (NMC); this is in contrast to the single move nature of a naive implementation. Our proposed method only requires a small up front expense from evaluating the ab initio energies and forces of (100) random configurations for training. Importantly, our method does not totally rely on the trained, assuredly imperfect, interaction. We show that high performance and exact sampling at the desired level of theory can be realized even when the trained interaction has appreciable differences from the ab initio potential. Remarkably, at the highest levels of performance realized via our approach, a pair of statistically uncorrelated atomic configurations can be generated with (1) ab initio calculations.

74 ATOMIC AND MOLECULAR PHYSICS↗

First-passage problems: A probabilistic dynamic analysis for degraded structures

Structures subjected to random excitations with uncertain system parameters degraded by surrounding environments (a random time history) are studied. Methods are developed to determine the statistics of dynamic responses, such as the time-varying mean, the standard deviation, the autocorrelation functions, and the joint probability density function of any response and its derivative. Moreover, the first-passage problems with deterministic and stationary/evolutionary random barriers are evaluated. The time-varying (joint) mean crossing rate and the probability density function of the first-passage time for various random barriers are derived.

Shiao, Michael C.↗

Scattering by Randomly Oriented Thin Ice Disks with Moderate Equivalent-Sphere Size Parameters

We use the T-matrix method to compute the scattering matrix for randomly oriented circular ice cylinders with diameter-to-length ratios 1 and 20 and surface-equivalent-sphere size parameters up to 12. We show that wavelength-sized, sharp-edged ice plates with extreme diameter-to-length ratios possess the same scattering properties as smooth plate-like spheroids: their phase functions are similar to those of surface-equivalent compact particles, whereas all other elements of the scattering matrix are typical of Rayleigh scattering.

Zakharova, Nadia T.↗