SEARCH · Engineering Papers

Results for “probability and statistical 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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12

All sources NASA NTRS DOE OSTI

NASA NTRS1989

Frame synchronization methods based on channel symbol measurements

The current DSN frame synchronization procedure is based on monitoring the decoded bit stream for the appearance of a sync marker sequence that is transmitted once every data frame. The possibility of obtaining frame synchronization by processing the raw received channel symbols rather than the decoded bits is explored. Performance results are derived for three channel symbol sync methods, and these are compared with results for decoded bit sync methods reported elsewhere. It is shown that each class of methods has advantages or disadvantages under different assumptions on the frame length, the global acquisition strategy, and the desired measure of acquisition timeliness. It is shown that the sync statistics based on decoded bits are superior to the statistics based on channel symbols, if the desired operating region utilizes a probability of miss many orders of magnitude higher than the probability of false alarm. This operating point is applicable for very large frame lengths and minimal frame-to-frame verification strategy. On the other hand, the statistics based on channel symbols are superior if the desired operating point has a miss probability only a few orders of magnitude greater than the false alarm probability. This happens for small frames or when frame-to-frame verifications are required.

Dolinar, S.↗

NASA NTRS1993

Statistical computation of tolerance limits

Based on a new theory, two computer codes were developed specifically to calculate the exact statistical tolerance limits for normal distributions within unknown means and variances for the one-sided and two-sided cases for the tolerance factor, k. The quantity k is defined equivalently in terms of the noncentral t-distribution by the probability equation. Two of the four mathematical methods employ the theory developed for the numerical simulation. Several algorithms for numerically integrating and iteratively root-solving the working equations are written to augment the program simulation. The program codes generate some tables of k's associated with the varying values of the proportion and sample size for each given probability to show accuracy obtained for small sample sizes.

Wheeler, J. T.↗

NASA NTRS1994

Data Analysis with Graphical Models: Software Tools

Probabilistic graphical models (directed and undirected Markov fields, and combined in chain graphs) are used widely in expert systems, image processing and other areas as a framework for representing and reasoning with probabilities. They come with corresponding algorithms for performing probabilistic inference. This paper discusses an extension to these models by Spiegelhalter and Gilks, plates, used to graphically model the notion of a sample. This offers a graphical specification language for representing data analysis problems. When combined with general methods for statistical inference, this also offers a unifying framework for prototyping and/or generating data analysis algorithms from graphical specifications. This paper outlines the framework and then presents some basic tools for the task: a graphical version of the Pitman-Koopman Theorem for the exponential family, problem decomposition, and the calculation of exact Bayes factors. Other tools already developed, such as automatic differentiation, Gibbs sampling, and use of the EM algorithm, make this a broad basis for the generation of data analysis software.

Buntine, Wray L.↗

NASA NTRS1998

Role of metabolic gases in bubble formation during hypobaric exposures

Our hypothesis is that metabolic gases play a role in the initial explosive growth phase of bubble formation during hypobaric exposures. Models that account for optimal internal tensions of dissolved gases to predict the probability of occurrence of venous gas emboli were statistically fitted to 426 hypobaric exposures from National Aeronautics and Space Administration tests. The presence of venous gas emboli in the pulmonary artery was detected with an ultrasound Doppler detector. The model fit and parameter estimation were done by using the statistical method of maximum likelihood. The analysis results were as follows. 1) For the model without an input of noninert dissolved gas tissue tension, the log likelihood (in absolute value) was 255.01. 2) When an additional parameter was added to the model to account for the dissolved noninert gas tissue tension, the log likelihood was 251.70. The significance of the additional parameter was established based on the likelihood ratio test (P < 0.012). 3) The parameter estimate for the dissolved noninert gas tissue tension participating in bubble formation was 19. 1 kPa (143 mmHg). 4) The additional gas tissue tension, supposedly due to noninert gases, did not show an exponential decay as a function of time during denitrogenation, but it remained constant. 5) The positive sign for this parameter term in the model is characteristic of an outward radial pressure of gases in the bubble. This analysis suggests that dissolved gases other than N2 in tissues may facilitate the initial explosive bubble-growth phase.

NASA Center JSC↗

NASA NTRS2005

Surveillance system and method having an adaptive sequential probability fault detection test

System and method providing surveillance of an asset such as a process and/or apparatus by providing training and surveillance procedures that numerically fit a probability density function to an observed residual error signal distribution that is correlative to normal asset operation and then utilizes the fitted probability density function in a dynamic statistical hypothesis test for providing improved asset surveillance.

Herzog, James P.↗

NASA NTRS2006

Surveillance system and method having an adaptive sequential probability fault detection test

Bickford, Randall L.↗

NASA NTRS2008

Surveillance System and Method having an Adaptive Sequential Probability Fault Detection Test

Bickford, Randall L.↗

NASA NTRS2003

Automated Monitoring with a BSP Fault-Detection Test

The figure schematically illustrates a method and procedure for automated monitoring of an asset, as well as a hardware- and-software system that implements the method and procedure. As used here, asset could signify an industrial process, power plant, medical instrument, aircraft, or any of a variety of other systems that generate electronic signals (e.g., sensor outputs). In automated monitoring, the signals are digitized and then processed in order to detect faults and otherwise monitor operational status and integrity of the monitored asset. The major distinguishing feature of the present method is that the fault-detection function is implemented by use of a Bayesian sequential probability (BSP) technique. This technique is superior to other techniques for automated monitoring because it affords sensitivity, not only to disturbances in the mean values, but also to very subtle changes in the statistical characteristics (variance, skewness, and bias) of the monitored signals.

Bickford, Randall L.↗

NASA NTRSDate not supplied

Use of Design of Experiments and Rule-Based Inference in Determining Neural Network Architectures for Loss of Control Detection

In this work, we describe methods for selecting the neural network architectures and input spaces to implement belief state inference on generic commercial transport aircraft. First, we highlight a case study on the planning, execution, and analysis of a set of experiments to determine the configurations of a conditional variational autoencoder (CVAE). We present a structured method that can be used in a number of aerospace applications, to optimize the structure and training parameters of the CVAE for belief state inference, using Design of Experiments (DOE) statistical methodologies. The motivation for this specific DOE was to identify the appropriate hyperparameters for measuring the CVAE reconstruction probability and latent space, such that the measurements can be used to infer qualitative state changes for the aircraft. We demonstrate that this process yields information about a trained neural network’s utility for this specific application, along with a quantifiable range of certainty. We execute 84 experiments using loss-of-control flight maneuver data from a NASA T-2 aircraft, demonstrating that this empirical process allows us to construct cheap and simple models with specific attributes amenable to belief state inference in aerospace applications. While theoretically, we could create a single CVAE with an input space the size of all measurable flight variables and environmental dynamics, it becomes intractable to use such a neural network in an in-situ intelligent multi-agent system. Using the recommendations from our case study, we introduce a technical approach for feasibly describing the belief space by (1) identifying significant statistical relationships among flight variables using rule induction, (2) using a set of rules that cover all features to define the input space of multiple CVAEs, and (3) forming a belief space based on the joint probability density of their collective latent spaces. This results in a series of relatively small matrix multiplications that can be performed in real time, as opposed to large matrix computations in a single CVAE. We demonstrate the application of this approach on the T-2 flight loss-of control experiments, using the architecture and hyperparameter recommendations from the case study. We compare the utilities of an individual CVAE trained on all flight variables and multiple CVAEs defined on subsets of flight variables for detecting qualitative changes in flight. We demonstrate that the use of multiple CVAEs with smaller input spaces permits the CVAE to capture more granular relationships in the latent space, permitting better state space characterization and loss-of-control detection.

Design of experiments↗

NASA NTRS2019

Discovery of Activities via Statistical Clustering of Fixation Patterns

Human behavior often consists of a series of distinct activities, each characterized by a unique pattern of interaction with the visual environment. This is true even in a restricted domain, such as a pilot flying an airplane; in this case, activities with distinct visual signatures might be things like communicating, navigating, monitoring, etc. We propose a novel analysis method for gaze-tracking data, to perform blind discovery of these hypothetical activities. We compare, not individual fixations, but groups of fixations aggregated over a fixed time interval (Tau). We assume that the environment has been divided into a finite set of discrete areas-of-interest (AOIs). For a given time interval, we compute the proportion of time spent fixating each AOI, resulting in an N-dimensional vector, where N is the number of AOIs. These proportions can be converted to integer counts by multiplying by Tau divided by the average fixation duration, a parameter that we fix at 283 milliseconds. We compare different intervals by computing the chi-squared statistic. The p-value associated with the statistic is the likelihood of observing the data under the hypothesis that the data in the two intervals were generated by a single process with a single set of probabilities governing the fixation of each AOI. We cluster the intervals, first by merging adjacent intervals that are sufficiently similar, optionally shifting the boundary between non-merged intervals to maximize the difference. Then we compare and cluster non-adjacent intervals. The method is evaluated using synthetic data generated by a hand-crafted set of activities. While the method generally finds more activities than put into the simulation, we have obtained agreement as high as 80 percent between the inferred activity labels and ground truth.

Eye Movements↗

NASA NTRS1977

Scintillation statistics caused by atmospheric turbulence and speckle in satellite laser ranging

We study the statistics of scintillation at the ground-based receiver for the earth-space-earth retroreflector configuration of satellite laser ranging. These statistics are governed by the joint effects of atmospheric turbulence and speckle produced by the retroreflector array. An expression for the probability density function of scintillation is obtained and evaluated numerically. Comparison of the normalized variance of scintillation calculated by using this function shows good agreement with results obtained by other methods.

Bufton, J. L.↗

NASA NTRS1979

Higher-order skewness and excess coefficients of some probability distributions applicable to optical propagation phenomena

Expressions are derived for higher-order skewness and excess coefficients using central moments and cumulants up to 8th order. These coefficients are then calculated for three probability distributions: (1) Log-normal, (2) Rice-Nakagami, and (3) Gamma distributions. Curves are given to shown the variation of skewness with excess coefficients for these distributions. These curves are independent of the particular distribution parameters. This method is useful for studying fluctuating phenomena, which obey non-Gaussian statistics.

Majumdar, A. K.↗

NASA NTRS1990

Statistical mechanics models for motion and force planning

The models of statistical mechanics provide an alternative to the methods of classical mechanics more traditionally used in robotics. They have a potential to: improve analysis of object collisions; handle kinematic and dynamic contact interactions within the same frmework; and reduce the need for perfect deterministic world model information. The statistical mechanics models characterize the state of the system as a probability density function (p.d.f.) whose time evolution is governed by a partial differential equation subject to boundary and initial conditions. The boundary conditions when rigid objects collide reflect the conservation of momentum. The models are being developed to embedd in remote semi-autonomous systems with a need to reason and interact with a multiobject environment.

Rodriguez, G.↗

NASA NTRS1995

A Bayesian approach to microwave precipitation profile retrieval

A multichannel passive microwave precipitation retrieval algorithm is developed. Bayes theorem is used to combine statistical information from numerical cloud models with forward radiative transfer modeling. A multivariate lognormal prior probability distribution contains the covariance information about hydrometeor distribution that resolves the nonuniqueness inherent in the inversion process. Hydrometeor profiles are retrieved by maximizing the posterior probability density for each vector of observations. The hydrometeor profile retrieval method is tested with data from the Advanced Microwave Precipitation Radiometer (10, 19, 37, and 85 GHz) of convection over ocean and land in Florida. The CP-2 multiparameter radar data are used to verify the retrieved profiles. The results show that the method can retrieve approximate hydrometeor profiles, with larger errors over land than water. There is considerably greater accuracy in the retrieval of integrated hydrometeor contents than of profiles. Many of the retrieval errors are traced to problems with the cloud model microphysical information, and future improvements to the algorithm are suggested.

Evans, K. Franklin↗

NASA NTRS1983

Information retrieval from wide-band meteorological data - An example

The methods proposed by Smith and Adelfang (1981) and Smith et al. (1982) are used to calculate probabilities over rectangles and sectors of the gust magnitude-gust length plane; probabilities over the same regions are also calculated from the observed distributions and a comparison is also presented to demonstrate the accuracy of the statistical model. These and other statistical results are calculated from samples of Jimsphere wind profiles at Cape Canaveral. The results are presented for a variety of wavelength bands, altitudes, and seasons. It is shown that wind perturbations observed in Jimsphere wind profiles in various wavelength bands can be analyzed by using digital filters. The relationship between gust magnitude and gust length is modeled with the bivariate gamma distribution. It is pointed out that application of the model to calculate probabilities over specific areas of the gust magnitude-gust length plane can be useful in aerospace design.

Adelfang, S. I.↗

NASA NTRS1990

Modeling of solar oscillation power spectra

To produce accurate estimates of the line-profile parameters of a model used to represent the spectral features in a solar oscillation power spectrum, it is necessary to (1) select the appropriate probability density function when deriving the maximum-likelihood function to be employed for the parameter estimation and (2) allow for the redistribution of spectral power caused by gaps in the data string. This paper describes a maximum-likelihood method for estimating the model parameters (based on the observed power spectrum statistics) that accounts for redistribution of spectral power caused by gaps in the data string, by convolving the model with the power spectrum of the observed window function. The accuracy and reliability of the method were tested using both artificial and authentic solar oscillation power spectrum data. A comparison of this method with various least-squares techniques is also presented.

Anderson, Edwin R.↗

NASA NTRS2005

A Comparative Study of Probability Collectives Based Multi-agent Systems and Genetic Algorithms

We compare Genetic Algorithms (GA's) with Probability Collectives (PC), a new framework for distributed optimization and control. In contrast to GA's, PC-based methods do not update populations of solutions. Instead they update an explicitly parameterized probability distribution p over the space of solutions. That updating of p arises as the optimization of a functional of p. The functional is chosen so that any p that optimizes it should be p peaked about good solutions. The PC approach works in both continuous and discrete problems. It does not suffer from the resolution limitation of the finite bit length encoding of parameters into GA alleles. It also has deep connections with both game theory and statistical physics. We review the PC approach using its motivation as the information theoretic formulation of bounded rationality for multi-agent systems. It is then compared with GA's on a diverse set of problems. To handle high dimensional surfaces, in the PC method investigated here p is restricted to a product distribution. Each distribution in that product is controlled by a separate agent. The test functions were selected for their difficulty using either traditional gradient descent or genetic algorithms. On those functions the PC-based approach significantly outperforms traditional GA's in both rate of descent, trapping in false minima, and long term optimization.

Huang, Chien-Feng↗

NASA NTRSDate not supplied

Probability Bounds Analysis Applied to Multi-Purpose Crew Vehicle Nonlinearity

The Multi-Purpose Crew Vehicle (MPCV) Program Orion vehicle finite element model (FEM) was updated based on a modal test performed by Lockheed Martin. Due to nonlinearity observed in the test results, linear low force level (LL) and high force level (HL) FEMs were developed for use during various Space Launch System (SLS) flight regimes depending on expected forcing levels. Uncertainty models were derived for the combined MPCV and MPCV Stage Adaptor LL and HL Hurty/Craig-Bampton (HCB) components based on the MPCV structural test article Configuration 4 modal test-analysis correlation results. Subsequently, system-level uncertainty quantification analyses were performed using both models for various SLS flight configurations to determine the impact of the nonlinearity on important system metrics. The system metrics included both transfer functions associated with attitude control and dynamic loads associated with aerodynamic buffeting during ascent. In each case, an independent Monte Carlo (MC) analysis was performed, and no attempt was made to combine the results. The Hybrid Parametric Variation (HPV) method was used to develop the LL and HL MPCV HCB uncertainty models. The HPV method provides both parametric and non-parametric components of uncertainty. The non-parametric uncertainty accounts for the difference in model-form between the linearized analytical model and the corresponding linearized component test results in the form of mode shapes and frequencies at that force level. This linear model-form uncertainty is implemented in the HPV method using random matrix theory. However, the HPV uncertainty models developed for the linear LL and HL MPCV components do not account for the nonlinearity in the MPCV. With respect to the linearized models, this nonlinearity is also an uncertainty in model form, but in this case, it must be treated independently as an epistemic uncertainty. It represents a lack of knowledge, in contrast to an aleatory uncertainty due to the randomness of a variable. In the case of an epistemic variable, the true value is unknown, only the interval within which it lies is known. Epistemic uncertainty can be reduced with increased knowledge, while in general, aleatory uncertainty cannot. This work combines the epistemic uncertainty due to the MPCV nonlinearity with the parametric and non-parametric uncertainty within the HPV method using a second order propagation approach. The LL and HL test data is augmented with surrogate test data derived from a nonlinear MPCV representation. The impact of the MPCV nonlinearity on system response statistics is determined using a series of cumulative distribution functions in the form of a horsetail plot, or p-box. This results in an interval of probabilities for a specific response value, or an interval of response values at a specific probability.

Daniel C Kammer↗