An alternative to Monte Carlo.
Histogram construction via algebraic Monte Carlo method, determining simultaneous effect of several input statistical variables on output variable
PROBABILITY THEORY↗
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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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A Biomechanical Approach to Assessing Hip Fracture Risk
Bone loss in microgravity is well documented, but it is difficult to quantify how declines in bone mineral density (BMD) contribute to an astronaut's overall risk of fracture upon return. This study uses a biomechanical approach to assessing hip fracture risk, or Factor of Risk (Phi), which is defined as the ratio of applied load to bone strength. All long-duration NASA astronauts from Expeditions 1-18 were included in this study (n=25), while crewmembers who flew twice (n=2) were treated as separate subjects. Bone strength was estimated based on an empirical relationship between areal BMD at the hip, as measured by DXA, and failure load, as determined by mechanical testing of cadaver femora. Fall load during a sideways fall was calculated from a previously developed biomechanical model, which takes into account body weight, height, gender, and soft tissue thickness overlying the lateral aspect of the hip that serves to attenuate the impact force. While no statistical analyses have been performed yet, preliminary results show that males in this population have a higher FOR than females, with a post- flight Phi of 0.87 and 0.36, respectively. FOR increases 5.1% from preflight to postflight, while only one subject crossed the fracture "threshold" of Phi = 1, for a total of 2 subjects with a postflight Phi > 1. These results suggest that men may be at greater risk for hip fracture due largely in part to their relatively thin soft tissue padding as compared to women, since soft tissue thickness has the highest correlation (R(exp 2)= .53) with FOR of all subject-specific parameters. Future work will investigate changes in FOR during recovery to see if baseline risk levels are restored upon return to 1-g activity. While dual x-ray absorptiometry (DXA) is the most commonly used clinical measure of bone health, it fails to provide compartment-specific information that is useful in assessing changes to bone quality as a result of microgravity exposure. Peripheral quantitative computed tomography (pQCT) accomplishes this by imaging transverse "slices" of the long bones. This project was a re-analysis of a 90 day bed rest study to determine if changes to cortical and trabecular compartments could be detected in the distal tibia with statistical significance using a new pQCT image analysis method. Nearly all changes in bone mineral density (BMD) and cross sectional area (CSA) measures were seen with statistical significance, with the exception of a change in cortical BMD. Total bone CSA increased by 1.1 % (p =0.01), cortical CSA decreased by - 5.6% (p<0.001) and trabecular CSA increased by 1.76% (p=0.007); the combination of which suggests bone resorption occurred at the endocortical surface in response to mechanical unloading by bed rest. Furthermore, total BMD and trabecular BMD decreased (-3.8%, p=0.001 and -2.8%, p =0.007, respectively), while decreases in cortical BMD failed to reach significance (-1.2%, p=0.07). Given that compartment-specific changes are seen with significance and are likely to influence bone strength, it is recommended that pQCT remain a standard measure used in bed rest because it provides a unique measure by which to better evaluate the efficacy of countermeasures to microgravity-induced bone loss.
Ellman, Rachel↗
Linear statistical analysis of maneuver optimization techniques
It is shown how a method for maneuver design during the Jovian satellite tour phase of the Galileo mission requires a full-scale redesign of the tour at each maneuver. Software was developed to provide insight into the statistical properties of this process; it is based on the use of linear perturbations to provide trajectory propagation and a least squares representation of the optimization. The result is a Monte Carlo program, making it possible to evaluate the proposed strategy.
Maize, Earl H.↗
Advanced Statistical Methods in Spacecraft Flight Software Cost Estimation: Bayesian Regression and Nonlinear Principal Components Analysis to Support System Engineering in the Early Project Lifecycle
This paper provides an overview of the new features and model updates in the upcoming release of the NASA Analogy Software Cost Tool (ASCoT). ASCoT, hosted within the Online NASA Space Estimation Tools (ONSET) on the One NASA Cost Engineering (ONCE) Database, is a web-based tool that provides a suite of estimation tools to support early lifecycle NASA flight software cost analysis. In addition to the traditional parametric flight software costing method COCOMO II, ASCoT contains a Bayesian linear regression to predict total flight software development cost as a function of total spacecraft cost, as well as four analogic methods: k-Nearest Neighbors (kNN) and Clustering models to predict Effort (in work-months) and total source lines of code (SLOC). These methods are designed to work primarily with system-level inputs such as mission type (orbiter, lander, etc.), mission destination (Earth, Inner Planetary, etc.), and the number of instruments and deployables. Nonlinear principal components analysis (NLPCA) is performed to find the principal features of the data composed of both categorical and numerical variables and is necessary prior to defining our analogic methods. Sensitivity analyses and in- and out-of-sample model performance results are presented for the Bayesian CER and the analogic models.
Johnson, James K.↗
Atmospheric pollution measurement by optical cross correlation methods - A concept
Method combines standard spectroscopy with statistical cross correlation analysis of two narrow light beams for remote sensing to detect foreign matter of given particulate size and consistency. Method is applicable in studies of generation and motion of clouds, nuclear debris, ozone, and radiation belts.
Fisher, M. J.↗
An Analysis Methodology for the Gamma-ray Large Area Space Telescope
The Large Area Telescope (LAT) instrument on the Gamma Ray Large Area Space Telescope (GLAST) has been designed to detect high-energy gamma rays and determine their direction of incidence and energy. We propose a reconstruction algorithm based on recent advances in statistical methodology. This method, alternative to the standard event analysis inherited from high energy collider physics experiments, incorporates more accurately the physical processes occurring in the detector, and makes full use of the statistical information available. It could thus provide a better estimate of the direction and energy of the primary photon.
Morris, Robin D.↗
Estimating maximum instantaneous distortion from inlet total pressure rms and PSD measurements
An inexpensive method is developed to determine the extreme values of instantaneous inlet distortion. This method also provides insight into the basic mechanics of unsteady inlet flow and the associated engine reaction. The analysis is based on fundamental fluid dynamics and statistical methods to provide an understanding of the turbulent inlet flow and quantitatively relate the rms level and power spectral density (PSD) function of the measured time variant total pressure fluctuations to the strength and size of the low pressure regions. The most probable extreme value of the instantaneous distortion is then synthesized from this information in conjunction with the steady state distortion. Results of the analysis show the extreme values to be dependent upon the steady state distortion, the measured turbulence rms level and PSD function, the time on point, and the engine response characteristics. Analytical projections of instantaneous distortion are presented and compared with data obtained by a conventional, highly time correlated, 40 probe instantaneous pressure measurement system.
Melick, H. C., Jr.↗
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↗
Concepts for a theoretical and experimental study of lifting rotor random loads and vibrations. Phase 6-A: Effects of blade torsion, of blade flap bending flexibility and of rotor support flexibility on rotor stability and random response
The effects of lifting rotor blade torsion, blade flap bending flexibility and rotor support flexibility on rotor stability and random response are described. The subjects discussed are: (1) blade representation and method of analysis, (2) random gust response statistics for coupled torsion-flapping rotor blade vibrations, (3) flap bending corrections to the rigid blade analysis of lifting rotors, and (4) effects of rotor support flexibility. The response of linear periodically time varying systems to random excitation is examined.
Hohenemser, K. H.↗
Effects of atmospheric turbulence on microwave and millimeter wave satellite communications systems
A model of the microwave and millimeter wave link in the presence of atmospheric turbulence is presented with emphasis on satellite communications systems. The analysis is based on standard methods of statistical theory. The results are directly usable by the design engineer.
Devasirvatham, D. M. J.↗
Significance testing of rules in rule-based models of human problem solving
Rule-based models of human problem solving have typically not been tested for statistical significance. Three methods of testing rules - analysis of variance, randomization, and contingency tables - are presented. Advantages and disadvantages of the methods are also described.
Lewis, C. M.↗
Contact thermal shock test of ceramics
A novel quantitative thermal shock test of ceramics is described. The technique employs contact between a metal-cooling rod and hot disk-shaped specimen. In contrast with traditional techniques, the well-defined thermal boundary condition allows for accurate analyses of heat transfer, stress, and fracture. Uniform equibiaxial tensile stresses are induced in the center of the test specimen. Transient specimen temperature and acoustic emission are monitored continuously during the thermal stress cycle. The technique is demonstrated with soda-lime glass specimens. Experimental results are compared with theoretical predictions based on a finite-element method thermal stress analysis combined with a statistical model of fracture. Material strength parameters are determined using concentric ring flexure tests. Good agreement is found between experimental results and theoretical predictions of failure probability as a function of time and initial specimen temperature.
Rogers, W. P.↗
Application of impact dampers in vibration control of flexible structures
Impact dampers belong to the category of passive vibration devices used to attenuate the vibration of discrete and continuous systems. An impact damper generally consists of a mass which is allowed to travel freely between two defined stops. Under the right conditions, the vibration of the structure to which the impact damper is attached will cause the mass of the impact damper to strike the structure. Previous analytical and experimental research work on the effect of impact dampers in attenuating the vibration of discrete and continuous systems have demonstrated their effectiveness. It has been shown in this study that impact dampers can increase the intrinsic damping of a lightly-damped flexible structure. The test structure consists of a slender flexible beam supported by a pin-type support at one end and supported by a linear helical flexible spring at another location. Sinusoidal excitation spanning the first three natural frequencies was applied in the horizontal plane. The orientation of the excitation and the test structure in the horizontal plane minimizes the effect of gravity on the behavior of the test structure. The excitation was applied using a linear sine sweep technique. The span of the test structure, the mass of the impact damper, the distance of travel, and the location of the impact damper along the span of the test structure were varied. The damping ratio are estimated for sixty test configurations. The results show that the impact damper significantly increases the damping ratio of the test structure. Statistical analysis of the results using the method of multiple linear regression indicates that a reasonable fit has been accomplished. It is concluded that additional experimental analysis of flexible structures in microgravity environment is needed in order to achieve a better understanding of the behavior of impact damper under conditions of microgravity. Numerical solution of the behavior of flexible structures equipped with impact dampers is also needed to predict stresses and deformations under operating conditions of microgravity in space applications.
Akl, Fred A.↗
Application of a data-mining method based on Bayesian networks to lesion-deficit analysis
Although lesion-deficit analysis (LDA) has provided extensive information about structure-function associations in the human brain, LDA has suffered from the difficulties inherent to the analysis of spatial data, i.e., there are many more variables than subjects, and data may be difficult to model using standard distributions, such as the normal distribution. We herein describe a Bayesian method for LDA; this method is based on data-mining techniques that employ Bayesian networks to represent structure-function associations. These methods are computationally tractable, and can represent complex, nonlinear structure-function associations. When applied to the evaluation of data obtained from a study of the psychiatric sequelae of traumatic brain injury in children, this method generates a Bayesian network that demonstrates complex, nonlinear associations among lesions in the left caudate, right globus pallidus, right side of the corpus callosum, right caudate, and left thalamus, and subsequent development of attention-deficit hyperactivity disorder, confirming and extending our previous statistical analysis of these data. Furthermore, analysis of simulated data indicates that methods based on Bayesian networks may be more sensitive and specific for detecting associations among categorical variables than methods based on chi-square and Fisher exact statistics.
NASA Discipline Neuroscience↗
A study of various methods for calculating locations of lightning events
This article reports on the results of numerical experiments on finding the location of lightning events using different numerical methods. The methods include linear least squares, nonlinear least squares, statistical estimations, cluster analysis and angular filters and combinations of such techniques. The experiments involved investigations of methods for excluding fake solutions which are solutions that appear to be reasonable but are in fact several kilometers distant from the actual location. Some of the conclusions derived from the study are that bad data produces fakes, that no fool-proof method of excluding fakes was found, that a short base-line interferometer under development at Kennedy Space Center to measure the direction cosines of an event shows promise as a filter for excluding fakes. The experiments generated a number of open questions, some of which are discussed at the end of the report.
Cannon, John R.↗
Design and analysis of numerical experiments
Methods for the design and analysis of numerical experiments that are especially useful and efficient in multidimensional parameter spaces are presented. The analysis method, which is similar to kriging in the spatial analysis literature, fits a statistical model to the output of the numerical model. The method is applied to a fully nonlinear, global, equivalent-barotropic dynamical model. The statistical model also provides estimates for the uncertainty of predicted numerical model output, which can provide guidance on where in the parameter space to conduct further experiments, if necessary. The method can provide significant improvements in the efficiency with which numerical sensitivity experiments are conducted.
Bowman, Kenneth P.↗
VAPEPS Management Center
A VibroAcoustic Payload Environment Prediction System (VAPEPS) Management Center is established and being maintained at JPL. VAPEPS is a computer program that utilizes statistical energy analysis (SEA) theory and SEA extrapolation methods to predict the vibroacoustic environments of complex systems. The program is commonly utilized to establish random vibration and acoustic test requirements for aerospace components exposed to launch environments. It can also be used in the payload or launch vehicle design process for control or mitigation of the launch or on-orbit vibration and acoustic environments, as well as to calculate acoustically induced stresses in structures such as solar panels and reflectors.
VAPEPS↗
Models of space averaged energetics of plates
The analysis of high frequency vibrations in plates is of particular interest in the study of structure borne noise in aircrafts. The current methods of analysis are either too expensive (finite element method) or may have a confidence band wider than desirable (Statistical Energy Analysis). An alternative technique to model the space and time averaged response of structural acoustics problems with enough detail to include all significant mechanisms of energy generation, transmission, and absorption is highly desirable. The focus of this paper is the development of a set of equations which govern the space and time averaged energy density in plates. To solve this equation, a new type of boundary value problem must be treated in terms of energy density variables using energy and intensity boundary conditions. A computer simulation verification study of the energy governing equation is performed. A finite element formulation of the new equations is also implemented and several test cases are analyzed and compared to analytical solutions.
Bouthier, O. M.↗