A Liapunov method for the estimation of statistical averages.
Liapunov method for estimating statistical averages of randomly perturbed system
DYNAMICS↗
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Some basic mathematical methods of diffusion theory
An introductory treatment of the fundamentals of diffusion theory is presented, starting with molecular diffusion and leading up to the statistical methods of turbulent diffusion. A multilayer diffusion model, designed to permit concentration and dosage calculations downwind of toxic clouds from rocket vehicles, is described. The concepts and equations of diffusion are developed on an elementary level, with emphasis on atmospheric applications.
Giere, A. C.↗
Robotic Rock Classification
This report describes a three-month research program undertook jointly by the Robotics Institute at Carnegie Mellon University and Ames Research Center as part of the Ames' Joint Research Initiative (JRI.) The work was conducted at the Ames Research Center by Mr. Liam Pedersen, a graduate student in the CMU Ph.D. program in Robotics under the supervision Dr. Ted Roush at the Space Science Division of the Ames Research Center from May 15 1999 to August 15, 1999. Dr. Martial Hebert is Mr. Pedersen's research adviser at CMU and is Principal Investigator of this Grant. The goal of this project is to investigate and implement methods suitable for a robotic rover to autonomously identify rocks and minerals in its vicinity, and to statistically characterize the local geological environment. Although primary sensors for these tasks are a reflection spectrometer and color camera, the goal is to create a framework under which data from multiple sensors, and multiple readings on the same object, can be combined in a principled manner. Furthermore, it is envisioned that knowledge of the local area, either a priori or gathered by the robot, will be used to improve classification accuracy. The key results obtained during this project are: The continuation of the development of a rock classifier; development of theoretical statistical methods; development of methods for evaluating and selecting sensors; and experimentation with data mining techniques on the Ames spectral library. The results of this work are being applied at CMU, in particular in the context of the Winter 99 Antarctica expedition in which the classification techniques will be used on the Nomad robot. Conversely, the software developed based on those techniques will continue to be made available to NASA Ames and the data collected from the Nomad experiments will also be made available.
Hebert, Martial↗
Statistical Practice and Research at NASA
The discipline of statistics has gained recognition within NASA by spurring innovation and efficiency, and it has demonstrated significant impact and value. In aerospace research and development, it accelerates learning, maximizes knowledge, ensures strategic resource investment, and informs rigorous data-driven decisions. In practice, it requires immersive multidisciplinary collaboration to develop solution strategies that integrate statistical methods with subject-matter expertise to address challenging research objectives. This presentation provides an overview of statistical case studies in aeronautics, space exploration, and atmospheric science, and it highlights statistical research motivated by NASA’s challenging applications.
Peter A. Parker↗
Neural networks analysis on SSME vibration simulation data
The neural networks method is applied to investigate the feasibility in detecting anomalies in turbopump vibration of SSME to supplement the statistical method utilized in the prototype system. The investigation of neural networks analysis is conducted using SSME vibration data from a NASA developed numerical simulator. The limited application of neural networks to the HPFTP has also shown the effectiveness in diagnosing the anomalies of turbopump vibrations.
Lo, Ching F.↗
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↗
Evidence of an infrared luminosity indicator for galaxies
To elucidate the nature of infrared-luminous galaxies discovered with the IRAS satellite, the optical and infrared luminosities of 1161 Markarian galaxies and 2146 'normal' galaxies from the CfA redshift survey are compared. Survival analysis statistical methods that take upper limits fully into account are used. It is found that L(IR)/L(B) is statistically correlated with L(60) in both samples, though they differ in the distribution at low luminosities. The derived correlation shows that L(IR)/L(B) provides an indicator for L(60). Since galaxies selected in unbiased IRAS surveys will have higher L(IR)/L(B) than optically selected galaxies, they are therefore also selected for high L(60).
Feigelson, Eric D.↗
Multi-Satellite Estimates of Land-Surface Properties for Determination of Energy and Water Budgets
Using the WETNET database, existing methods for the estimation of surface wetness from SSM/I data have been assessed and further developed. A physical-statistical method for optimal estimation of daily surface heat flux and Bowen ratio on the mesoscale has been developed and tested. This method is based on observations of daytime planetary boundary layer (PBL) growth from operational ravansonde and daytime land-surface temperature amplitude from Geostationary Operational Environmental (GOES) satellites. The mesoscale patterns of these heat fluxes have been compared with an AVHRR-based vegetation index and surface wetness (separately estimated from SSM/I and in situ observations). Cases of the 1988 Midwest drought and a surface/atmosphere moisture gradient (dry-line) in the southern Plains were studied. The analyses revealed significant variations in sensible heat flux (S(sub 0), and Bowen ratio, B(sub 0)) associated with vegetation cover and antecedent precipitation. Relationships for surface heat flux (and Bowen ratio) from antecedent precipitation and vegetation index have been developed and compared to other findings. Results from this project are reported in the following reviewed literature.
Menzel, W. Paul↗
Predicting Slag Generation in Sub-Scale Test Motors Using a Neural Network
Generation of slag (aluminum oxide) is an important issue for the Reusable Solid Rocket Motor (RSRM). Thiokol performed testing to quantify the relationship between raw material variations and slag generation in solid propellants by testing sub-scale motors cast with propellant containing various combinations of aluminum fuel and ammonium perchlorate (AP) oxidizer particle sizes. The test data were analyzed using statistical methods and an artificial neural network. This paper primarily addresses the neural network results with some comparisons to the statistical results. The neural network showed that the particle sizes of both the aluminum and unground AP have a measurable effect on slag generation. The neural network analysis showed that aluminum particle size is the dominant driver in slag generation, about 40% more influential than AP. The network predictions of the amount of slag produced during firing of sub-scale motors were 16% better than the predictions of a statistically derived empirical equation. Another neural network successfully characterized the slag generated during full-scale motor tests. The success is attributable to the ability of neural networks to characterize multiple complex factors including interactions that affect slag generation.
Wiesenberg, Brent↗
Cycom 977-2 Composite Material: Impact Test Results (workshop presentation)
Contents include the following: Ambient (13A) tests of Cycom 977-2 impact characteristics by the Brucenton and statistical method at MSFC and WSTF. Repeat (13A) tests of tested Cycom from phase I at MSFC to expended testing statistical database. Conduct high-pressure tests (13B) in liquid oxygen (LOX) and GOX at MSFC and WSTF to determine Cycom reaction characteristics and batch effect. Conduct expended ambient (13A) LOX test at MSFC and high-pressure (13B) testing to determine pressure effects in LOX. Expend 13B GOX database.
Engle, Carl↗
A general scientific information system to support the study of climate-related data
The development and use of NASA's Pilot Climate Data System (PCDS) are discussed. The PCDS is used as a focal point for managing and providing access to a large collection of actively used data for the Earth, ocean and atmospheric sciences. The PCDS provides uniform data catalogs, inventories, and access methods for selected NASA and non-NASA data sets. Scientific users can preview the data sets using graphical and statistical methods. The system has evolved from its original purpose as a climate data base management system in response to a national climate program, into an extensive package of capabilities to support many types of data sets from both spaceborne and surface based measurements with flexible data selection and analysis functions.
Treinish, L. A.↗
Understanding the relation between wind- and pressure-driven sea level variability
Sea surface adjustment to combined wind and pressure forcing is examined using numerical solutions to the shallow water equations. The experiments use coastal geometry and bottom topography representative of the North Atlantic and are forced by realistic barometric pressure and wind stress fields. The repsonse to pressure is essentially static or close to the inverted barometer solution at periods longer than a few days and dominates the sea level variability, with wind-driven sea level signals being relatively small. With regard to the dynamic signals, wind-driven fluctuations dominate at long periods, as expected from quasi-geostrophic theory. Pressure becomes more important than wind stress as a source of dynamic signals only at periods shorter than approximately three days. Wind- and pressure-driven sea level fluctuations are anticorrelated over most regions. Hence, regressions of sea level on barometric pressure yield coefficients generally smaller than expected for the inverted barometer response known to be the case in the model. In the regions of significant wind-pressure correlation effects, to infer the correct pressure reponse using statistical methods, input fields must include winds as well as pressure. Because of the nonlocal character of the wind response, multivariate statistical models with local wind driving as input are not very successful. Inclusion of nonlocal wind variability over extensive regions is necessary to extract the correct pressure response. Implications of these results to the interpretation of sea level observations are discussed.
Ponte, Rui M.↗
SEE Rate Estimation: Model Complexity and Data Requirements
Statistical Methods outlined in [Ladbury, TNS20071 can be generalized for Monte Carlo Rate Calculation Methods Two Monte Carlo Approaches: a) Rate based on vendor-supplied (or reverse-engineered) model SEE testing and statistical analysis performed to validate model; b) Rate calculated based on model fit to SEE data Statistical analysis very similar to case for CREME96. Information Theory allows simultaneous consideration of multiple models with different complexities: a) Model with lowest AIC usually has greatest predictive power; b) Model averaging using AIC weights may give better performance if several models have similar good performance; and c) Rates can be bounded for a given confidence level over multiple models, as well as over the parameter space of a model.
Ladbury, Ray↗
Reliability approach to rotating-component design
A probabilistic methodology for designing rotating mechanical components using reliability to relate stress to strength is explained. The experimental test machines and data obtained for steel to verify this methodology are described. A sample mechanical rotating component design problem is solved by comparing a deterministic design method with the new design-by reliability approach. The new method shows that a smaller size and weight can be obtained for specified rotating shaft life and reliability, and uses the statistical distortion-energy theory with statistical fatigue diagrams for optimum shaft design. Statistical methods are presented for (1) determining strength distributions for steel experimentally, (2) determining a failure theory for stress variations in a rotating shaft subjected to reversed bending and steady torque, and (3) relating strength to stress by reliability.
Kececioglu, D. B.↗
The effects of multiple repairs on Inconel 718 weld mechanical properties
Inconel 718 weldments were repaired 3, 6, 9, and 13 times using the gas tungsten arc welding process. The welded panels were machined into mechanical test specimens, postweld heat treated, and nondestructively tested. Tensile properties and high cycle fatigue life were evaluated and the results compared to unrepaired weld properties. Mechanical property data were analyzed using the statistical methods of difference in means for tensile properties and difference in log means and Weibull analysis for high cycle fatigue properties. Statistical analysis performed on the data did not show a significant decrease in tensile or high cycle fatigue properties due to the repeated repairs. Some degradation was observed in all properties, however, it was minimal.
Russell, C. K.↗
Advanced probabilistic method of development
Advanced structural reliability methods are utilized on the Probabilistic Structural Analysis Methods (PSAM) project to provide a tool for analysis and design of space propulsion system hardware. The role of the effort at the University of Arizona is to provide reliability technology support to this project. PSAM computer programs will provide a design tool for analyzing uncertainty associated with thermal and mechanical loading, material behavior, geometry, and the analysis methods used. Specifically, reliability methods are employed to perform sensitivity analyses, to establish the distribution of a critical response variable (e.g., stress, deflection), to perform reliability assessment, and ultimately to produce a design which will minimize cost and/or weight. Uncertainties in the design factors of space propulsion hardware are described by probability models constructed using statistical analysis of data. Statistical methods are employed to produce a probability model, i.e., a statistical synthesis or summary of each design variable in a format suitable for reliability analysis and ultimately, design decisions.
Wirsching, P. H.↗
Statistical Analysis of Large Simulated Yield Datasets for Studying Climate Effects
Many studies have been carried out during the last decade to study the effect of climate change on crop yields and other key crop characteristics. In these studies, one or several crop models were used to simulate crop growth and development for different climate scenarios that correspond to different projections of atmospheric CO2 concentration, temperature, and rainfall changes (Semenov et al., 1996; Tubiello and Ewert, 2002; White et al., 2011). The Agricultural Model Intercomparison and Improvement Project (AgMIP; Rosenzweig et al., 2013) builds on these studies with the goal of using an ensemble of multiple crop models in order to assess effects of climate change scenarios for several crops in contrasting environments. These studies generate large datasets, including thousands of simulated crop yield data. They include series of yield values obtained by combining several crop models with different climate scenarios that are defined by several climatic variables (temperature, CO2, rainfall, etc.). Such datasets potentially provide useful information on the possible effects of different climate change scenarios on crop yields. However, it is sometimes difficult to analyze these datasets and to summarize them in a useful way due to their structural complexity; simulated yield data can differ among contrasting climate scenarios, sites, and crop models. Another issue is that it is not straightforward to extrapolate the results obtained for the scenarios to alternative climate change scenarios not initially included in the simulation protocols. Additional dynamic crop model simulations for new climate change scenarios are an option but this approach is costly, especially when a large number of crop models are used to generate the simulated data, as in AgMIP. Statistical models have been used to analyze responses of measured yield data to climate variables in past studies (Lobell et al., 2011), but the use of a statistical model to analyze yields simulated by complex process-based crop models is a rather new idea. We demonstrate herewith that statistical methods can play an important role in analyzing simulated yield data sets obtained from the ensembles of process-based crop models. Formal statistical analysis is helpful to estimate the effects of different climatic variables on yield, and to describe the between-model variability of these effects.
climate↗
Optimum retrieval of precipitable water fields from VAS and surface data
The use of VAS radiances and conventional surface data to determine the optimum resolution and accuracy of low-level precipitable water fields retrieved from geosynchronous satellite observations is examined. VAS retrievals of precipitated water (PW) are compared with various channel selections in the regression algorithm and with the split window algorithm. The split window algorithm and the linear regression algorithm are described. Consideration is given to the sounding-field-of-view (SFOV) resolution; the data reveal that the optimum resolution for the split window algorithm is at 15-60 km resolution, and 30-60 km SFOV resolution is optimal for the regression method. Statistics and images from PW retrieval experiments conducted on July 13, 1981 are presented and utilized to determine optimum channel selection. A fast contouring method for VAS sounding images is proposed.
Chesters, Dennis↗