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NASA NTRS2001

Statistical Analysis of Strength Data for an Aerospace Aluminum Alloy

Aerospace vehicles are produced in limited quantities that do not always allow development of MIL-HDBK-5 A-basis design allowables. One method of examining production and composition variations is to perform 100% lot acceptance testing for aerospace Aluminum (Al) alloys. This paper discusses statistical trends seen in strength data for one Al alloy. A four-step approach reduced the data to residuals, visualized residuals as a function of time, grouped data with quantified scatter, and conducted analysis of variance (ANOVA).

Neergaard, L.↗

NASA NTRS2006

Using the Bootstrap Method for a Statistical Significance Test of Differences between Summary Histograms

A new method is proposed to compare statistical differences between summary histograms, which are the histograms summed over a large ensemble of individual histograms. It consists of choosing a distance statistic for measuring the difference between summary histograms and using a bootstrap procedure to calculate the statistical significance level. Bootstrapping is an approach to statistical inference that makes few assumptions about the underlying probability distribution that describes the data. Three distance statistics are compared in this study. They are the Euclidean distance, the Jeffries-Matusita distance and the Kuiper distance. The data used in testing the bootstrap method are satellite measurements of cloud systems called cloud objects. Each cloud object is defined as a contiguous region/patch composed of individual footprints or fields of view. A histogram of measured values over footprints is generated for each parameter of each cloud object and then summary histograms are accumulated over all individual histograms in a given cloud-object size category. The results of statistical hypothesis tests using all three distances as test statistics are generally similar, indicating the validity of the proposed method. The Euclidean distance is determined to be most suitable after comparing the statistical tests of several parameters with distinct probability distributions among three cloud-object size categories. Impacts on the statistical significance levels resulting from differences in the total lengths of satellite footprint data between two size categories are also discussed.

Xu, Kuan-Man↗

NASA NTRS2019

Statistical Hypothesis Testing in Wavelet Analysis: Theoretical Developments and Applications to Indian Rainfall

Statistical hypothesis tests in wavelet analysis are methods that assess the degree to which a wavelet quantity(e.g., power and coherence) exceeds background noise. Commonly, a point-wise approach is adopted in which a wavelet quantity at every point in a wavelet spectrum is individually compared to the critical level of the point-wise test. However, because adjacent wavelet coefficients are correlated and wavelet spectra often contain many wavelet quantities, the point-wise test can produce many false positive results that occur in clusters or patches. To circumvent the point-wise test drawbacks, it is necessary to implement the recently developed area-wise, geometric, cumulative area-wise, and topological significance tests, which are reviewed and developed in this paper. To improve the computational efficiency of the cumulative area-wise test, a simplified version of the testing procedure is created based on the idea that its output is the mean of individual estimates of statistical significance calculated from the geometric test applied at a set of point-wise significance levels. Ideal examples are used to show that the geometric and cumulative area-wise tests are unable to differentiate wavelet spectral features arising from singularity-like structures from those associated with periodicities. A cumulative arc-wise test is therefore developed to strictly test for periodicities by using normalized arc length, which is defined as the number of points composing a cross section of a patch divided by the wavelet scale in question. A previously proposed topological significance test is formalized using persistent homology profiles (PHPs) measuring the number of patches and holes corresponding to the set of all point-wise significance values. Ideal examples show that the PHPs can be used to distinguish time series containing signal components from those that are purely noise. To demonstrate the practical uses of the existing and newly developed statistical methodologies, a first comprehensive wavelet analysis of Indian rainfall is also provided. An R software package has been written by the author to implement the various testing procedures.

Wind speed↗

NASA NTRS1981

Cleanroom software development

The 'cleanroom' software development process is a technical and organizational approach to developing software with certifiable reliability. Key ideas behind the process are well structured software specifications, randomized testing methods and the introduction of statistical controls; but the main point is to deny entry for defects during the development of software. This latter point suggests the use of the term 'cleanroom' in analogy to the defect prevention controls used in the manufacturing of high technology hardware. In the 'cleanroom', the entire software development process is embedded within a formal statistical design, in contrast to executing selected tests and appealing to the randomness of operational settings for drawing statistical inferences. Instead, random testing is introduced as a part of the statistical design itself so that when development and testing are completed, statistical inferences are made about the operation of the system.

Dyer, M.↗

NASA NTRS1985

Unsupervised Classification of Global Radar Units on Venus

Characterization of the Venusian surface in terms of its radar properties was accomplished by application of an unsupervised, linear discriminant algorithm to two Pioneer-Venus (PV) Orbiter radar data sets: the RMS-slope (surface roughness) and reflectivity. Both databases were spatially filtered to the same effective resolution of 100 km prior to classification. A recent supervised classification study using these data was based on presupposed morphologic significance of selected data ranges. The knowledge of both Venusian geology and the geologic significance of the radar data is so limited that the data warrant a more unsupervised approach; for this study a linear discriminant classifier was chosen. This approach is purely statistical, thereby removing any observer bias. Statistical significance of the resulting clusters was evaluated by an ancillary program in which an F test utilizing the Mahalanobis' distance.

Kozak, R. C.↗

NASA NTRS1990

Neural net diagnostics for VLSI test

This paper discusses the application of neural network pattern analysis algorithms to the IC fault diagnosis problem. A fault diagnostic is a decision rule combining what is known about an ideal circuit test response with information about how it is distorted by fabrication variations and measurement noise. The rule is used to detect fault existence in fabricated circuits using real test equipment. Traditional statistical techniques may be used to achieve this goal, but they can employ unrealistic a priori assumptions about measurement data. Our approach to this problem employs an adaptive pattern analysis technique based on feedforward neural networks. During training, a feedforward network automatically captures unknown sample distributions. This is important because distributions arising from the nonlinear effects of process variation can be more complex than is typically assumed. A feedforward network is also able to extract measurement features which contribute significantly to making a correct decision. Traditional feature extraction techniques employ matrix manipulations which can be particularly costly for large measurement vectors. In this paper we discuss a software system which we are developing that uses this approach. We also provide a simple example illustrating the use of the technique for fault detection in an operational amplifier.

Lin, T.↗

NASA NTRS2017

Online Multi-Modal Learning and Adaptive Information Trajectory Planning for Autonomous Exploration

In robotic information gathering missions, scientists are typically interested in understanding variables which require proxy measurements from specialized sensor suites to estimate. However, energy and time constraints limit how often these sensors can be used in a mission. Robots are also equipped with cheaper to use navigation sensors such as cameras. In this paper, we explore a challenging planning problem in which a robot is required to learn about a scientific variable of interest in an initially unknown environment by planning informative paths and deciding when and where to use its sensors. To tackle this we present two innovations: a Bayesian generative model framework to automatically learn correlations between expensive science sensors and cheaper to use navigation sensors online, and a sampling based approach to plan for multiple sensors while handling long horizons and budget constraints. Our approach does not grow in complexity with data and is anytime making it highly applicable to field robotics. We tested our approach extensively in simulation and validated it with real data collected during the 2014 Mojave Volatiles Prospector Mission. Our planning algorithm performs statistically significantly better than myopic approaches and at least as well as a coverage-based algorithm in an initially unknown environment while having added advantages of being able to exploit prior knowledge and handle other intricacies of the real world without further algorithmic modifications.

learning↗

NASA NTRS2000

Assessment of Low Cycle Fatigue Behavior of Powder Metallurgy Alloy U720

The fatigue lives of modem powder metallurgy disk alloys are influenced by variabilities in alloy microstructure and mechanical properties. These properties can vary as functions of variables the different steps of materials/component processing: powder atomization, consolidation, extrusion, forging, heat treating, and machining. It is important to understand the relationship between the statistical variations in life and these variables, as well as the change in life distribution due to changes in fatigue loading conditions. The objective of this study was to investigate these relationships in a nickel-base disk superalloy, U720, produced using powder metallurgy processing. Multiple strain-controlled fatigue tests were performed at 538 C (1000 F) at limited sets of test conditions. Analyses were performed to: (1) assess variations of microstructure, mechanical properties, and LCF failure initiation sites as functions of disk processing and loading conditions; and (2) compare mean and minimum fatigue life predictions using different approaches for modeling the data from assorted test conditions. Significant variations in life were observed as functions of the disk processing variables evaluated. However, the lives of all specimens could still be combined and modeled together. The failure initiation sites for tests performed at a strain ratio R(sub epsilon) = epsilon(sub min)/epsilon(sub max) of 0 were different from those in tests at a strain ratio of -1. An approach could still be applied to account for the differences in mean and maximum stresses and strains. This allowed the data in tests of various conditions to be combined for more robust statistical estimates of mean and minimum lives.

Gabb, Tomothy P.↗

NASA NTRS1993

An approach to estimate the areal rain-rate distribution from spaceborne radar by the use of multiple thresholds

Estimates of rain rate derived from a spaceborne weather radar will be most reliable over an intermediate range of values. In forming an area average of the rain rate, an alternative to the averaging of the high-resolution estimates, irrespective of their individual accuracies, is a multiple threshold approach. The method is based on the fact that the fractional area above a particular rain-rate threshold R(j) is related to the cumulative distribution of rain rates evaluated at R(j). Varying the threshold over the effective dynamic range of the radar yields the cumulative distribution function over this range. To obtain the distribution at all rain rates, a lognormal or gamma test function is selected such that the mean-square error between the test function and the measured values is minimized. Once the unknown parameters are determined, the first-order statistics of the areawide rain-rate distribution can be found. Tests of the method with data from the SPANDAR radar provide comparisons between it and the single threshold and the direct averaging approaches.

Meneghini, R.↗

NASA NTRS1983

Impact resistance of fiber composites: Energy absorbing mechanisms and environmental effects

Energy absorbing mechanisms were identified by several approaches. The energy absorbing mechanisms considered are those in unidirectional composite beams subjected to impact. The approaches used include: mechanic models, statistical models, transient finite element analysis, and simple beam theory. Predicted results are correlated with experimental data from Charpy impact tests. The environmental effects on impact resistance are evaluated. Working definitions for energy absorbing and energy releasing mechanisms are proposed and a dynamic fracture progression is outlined. Possible generalizations to angle-plied laminates are described.

Chamis, C. C.↗

NASA NTRS1985

Impact resistance of fiber composites - Energy-absorbing mechanisms and environmental effects

Chamis, C. C.↗

NASA NTRS1986

Detection of large-scale alignment of Lick counts around Abell clusters

The possible tendency of galaxies to be distributed in an aligned fashion, on sheets or filaments, on scales greater than the Abell radius, has been tested by a variety of statistics. The subject remains controversial because the statistical tests have either not been sensitive to the alignment or capable of unambiguously signalling alignment in a general, clumpy distribution of galaxies. The present approach combines ideas of Bingelli (1982) and Fry and Peebles (1980) in an examination of the cross correlation of Lick counts relative to the preferred direction defined by the cluster. This can substantially reduce the noise, and it is suggested on this basis that alignment has been found on large scales for Lick galaxy counts and Abell cluster positions and their angles.

Argyres, P. C.↗

NASA NTRSDate not supplied

Building a Real-Time Flood Prediction Model for Improving Early Warning Systems in Ellicott City, Maryland

As flood events in the United States grow in frequency and intensity, the use of applied remote sensing analyses is increasingly necessary for effective flood monitoring and warning systems. The NASA DEVELOP National Program partnered with the local government of Howard County, Maryland, to investigate the use of machine learning for advanced flood risk detection, and to test the feasibility of integrating this approach into the county’s flood early warning system. To strengthen the efforts of the Howard County Office of Emergency Management (OEM), the project developed a statistical model capable of hindcasting the two severe flash flood events that devastated Ellicott City and transitioned to a ‘Long Short-Term Memory’ based sequence-to-sequence deep learning model with 8-hour forecast capability. The team combined data inputs from public sources including river and precipitation gauges, NASA and NOAA Earth observations, and numerical weather model products using scripts written in the Google Colaboratory Python scripting environment. In addition to designing the deep learning architecture, the team trained and tested the model, and evaluated its performance using Nash-Sutcliffe Efficiency. The final product, the Sequentially Trained Real-time EstimAted Model (STREAM) predicts stage height for the Hudson Branch gauge in Ellicott City using data products available in near real-time, including the High-Resolution Rapid Refresh model’s accumulated precipitation forecasts supplemented by stream gauge data from the OEM and the U.S. Geological Survey. STREAM was incorporated into an online dashboard in a user-friendly interface capable of triggering the alarms that initiate emergency response protocols up to 8 hours in advance of a predicted severe flood event. The project demonstrated the potential for the integration of open data and Earth observations into a flood risk forecasting tool capable of informing near real-time decision making.

NASA DEVELOP↗

NASA NTRS1997

Adaptation of a Fast Optimal Interpolation Algorithm to the Mapping of Oceangraphic Data

A fast, recently developed, multiscale optimal interpolation algorithm has been adapted to the mapping of hydrographic and other oceanographic data. This algorithm produces solution and error estimates which are consistent with those obtained from exact least squares methods, but at a small fraction of the computational cost. Problems whose solution would be completely impractical using exact least squares, that is, problems with tens or hundreds of thousands of measurements and estimation grid points, can easily be solved on a small workstation using the multiscale algorithm. In contrast to methods previously proposed for solving large least squares problems, our approach provides estimation error statistics while permitting long-range correlations, using all measurements, and permitting arbitrary measurement locations. The multiscale algorithm itself, published elsewhere, is not the focus of this paper. However, the algorithm requires statistical models having a very particular multiscale structure; it is the development of a class of multiscale statistical models, appropriate for oceanographic mapping problems, with which we concern ourselves in this paper. The approach is illustrated by mapping temperature in the northeastern Pacific. The number of hydrographic stations is kept deliberately small to show that multiscale and exact least squares results are comparable. A portion of the data were not used in the analysis; these data serve to test the multiscale estimates. A major advantage of the present approach is the ability to repeat the estimation procedure a large number of times for sensitivity studies, parameter estimation, and model testing. We have made available by anonymous Ftp a set of MATLAB-callable routines which implement the multiscale algorithm and the statistical models developed in this paper.

Menemenlis, Dimitris↗

NASA NTRS1975

Geological mapping in northwestern Saudi Arabia using LANDSAT multispectral techniques

Various computer enhancement and data extraction systems using LANDSAT data were assessed and used to complement a continuing geologic mapping program. Interactive digital classification techniques using both the parallel-piped and maximum-likelihood statistical approaches achieve very limited success in areas of highly dissected terrain. Computer enhanced imagery developed by color compositing stretched MSS ratio data was constructed for a test site in northwestern Saudi Arabia. Initial results indicate that several igneous and sedimentary rock types can be discriminated.

Blodget, H. W.↗

NASA NTRS1975

Geological mapping in northwestern Saudi Arabia using LANDSAT multispectral techniques

Various computer enhancement and data extraction systems using LANDSAT data were assessed and used to complement a continuing geologic mapping program. Interactive digital classification techniques using both the maximum-likelihood and thresholding statistical approaches achieve very limited success in areas of highly dissected terrain. Computer enhanced imagery developed by color compositing stretched MSS ratio data was constructed for a test site in northwestern Saudi Arabia. Initial results indicate that several igneous and sedimentary rock-types can be discriminated.

Blodget, H. W.↗

NASA NTRS1990

Pivotal-Function Assessment Of Reliability Of Software

Approach developed to establish utility of pivotal functions for estimation and prediction of reliability of software. Improved estimates of reliability with statistical confidence obtained when relatively few testing data available. Pivotal functions effective tools for determination of confidence limits for reliability of software and prediction limits for time to next failure. Provides exact confidence and prediction limits regardless of how many bugs found in software.

Hayhurst, Kelly J.↗

NASA NTRS1995

Radio properties of optically selected quasars

Approximately one-quarter (256 objects) of the Large Bright Quasar Survey (LBQS) has been observed with the VLA at 8.4 GHz, resulting in 44 detections (17%) with a median 3 sigma noise limit of 0.29 mJy. Quasars with radio luminosity detectable at this limit are underrepresented at faint absolute blue magnitudes (M(sub B) greater than or equal to -24), an effect which cannot be explained by a potential LBQS selection bias against quasars which have large radio luminosities and small optical luminosities. The radio-loud (8 GHz luminosity greater than 10(exp 25) W/Hz) fraction is observed to change as a function of redshift and M(sub B), for M(sub B) less than -24, although the causal variable is ambiguous. The description most consistent with the available data is that radio-loud fraction is approximately constant over the range -27.5 less than or equal to M(sub B) less than or equal to -24 and increases at brighter absolute magnitudes. The radio-loud fraction as a function of redshift reaches a local maximum at z approximately equal to 1, and, aside from the effects of icreased radio-loud fraction at bright M(sub B), remains roughly constant to redshifts approaching 5. The log R(sub 8.4) distribution (radio-to-optical luminosity ratio) of the current LBQS sample may be bimodal, but the results of statistical tests are ambiguous, requiring a larger sample size to become definite.

Hooper, Eric J.↗