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NASA NTRS2004

Use of Probability Distribution Functions for Discriminating Between Cloud and Aerosol in Lidar Backscatter Data

In this paper we describe the algorithm hat will be used during the upcoming Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) mission for discriminating between clouds and aerosols detected in two wavelength backscatter lidar profiles. We first analyze single-test and multiple-test classification approaches based on one-dimensional and multiple-dimensional probability density functions (PDFs) in the context of a two-class feature identification scheme. From these studies we derive an operational algorithm based on a set of 3-dimensional probability distribution functions characteristic of clouds and aerosols. A dataset acquired by the Cloud Physics Lidar (CPL) is used to test the algorithm. Comparisons are conducted between the CALIPSO algorithm results and the CPL data product. The results obtained show generally good agreement between the two methods. However, of a total of 228,264 layers analyzed, approximately 5.7% are classified as different types by the CALIPSO and CPL algorithm. This disparity is shown to be due largely to the misclassification of clouds as aerosols by the CPL algorithm. The use of 3-dimensional PDFs in the CALIPSO algorithm is found to significantly reduce this type of error. Dust presents a special case. Because the intrinsic scattering properties of dust layers can be very similar to those of clouds, additional algorithm testing was performed using an optically dense layer of Saharan dust measured during the Lidar In-space Technology Experiment (LITE). In general, the method is shown to distinguish reliably between dust layers and clouds. The relatively few erroneous classifications occurred most often in the LITE data, in those regions of the Saharan dust layer where the optical thickness was the highest.

Liu, Zhaoyan↗

NASA NTRS2004

Probability Distribution Estimated From the Minimum, Maximum, and Most Likely Values: Applied to Turbine Inlet Temperature Uncertainty

Modern engineering design practices are tending more toward the treatment of design parameters as random variables as opposed to fixed, or deterministic, values. The probabilistic design approach attempts to account for the uncertainty in design parameters by representing them as a distribution of values rather than as a single value. The motivations for this effort include preventing excessive overdesign as well as assessing and assuring reliability, both of which are important for aerospace applications. However, the determination of the probability distribution is a fundamental problem in reliability analysis. A random variable is often defined by the parameters of the theoretical distribution function that gives the best fit to experimental data. In many cases the distribution must be assumed from very limited information or data. Often the types of information that are available or reasonably estimated are the minimum, maximum, and most likely values of the design parameter. For these situations the beta distribution model is very convenient because the parameters that define the distribution can be easily determined from these three pieces of information. Widely used in the field of operations research, the beta model is very flexible and is also useful for estimating the mean and standard deviation of a random variable given only the aforementioned three values. However, an assumption is required to determine the four parameters of the beta distribution from only these three pieces of information (some of the more common distributions, like the normal, lognormal, gamma, and Weibull distributions, have two or three parameters). The conventional method assumes that the standard deviation is a certain fraction of the range. The beta parameters are then determined by solving a set of equations simultaneously. A new method developed in-house at the NASA Glenn Research Center assumes a value for one of the beta shape parameters based on an analogy with the normal distribution (ref.1). This new approach allows for a very simple and direct algebraic solution without restricting the standard deviation. The beta parameters obtained by the new method are comparable to the conventional method (and identical when the distribution is symmetrical). However, the proposed method generally produces a less peaked distribution with a slightly larger standard deviation (up to 7 percent) than the conventional method in cases where the distribution is asymmetric or skewed. The beta distribution model has now been implemented into the Fast Probability Integration (FPI) module used in the NESSUS computer code for probabilistic analyses of structures (ref. 2).

Holland, Frederic A., Jr.↗

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 NTRS1993

The Probable Ages of Asteroid Families

There has been considerable debate recently over the ages of the Hirayama families, and in particular if some of the families are very oung(u) It is a straightforward task to estimate the characteristic time of a collision between a body of a given diameter, d_o, by another body of diameter greater of equal to d_1. What is less straightforward is to estimate the critical diameter ratio, d_1/d_o, above which catastrophic disruption occurs, from which one could infer probable ages of the Hirayama families, by knowing the diameter of the parent body, d_o. One can gain some insight into the probable value of d_1/d_o, and of the likely ages of existing families, from the plot below. I have computed the characteristic time between collisions in the asteroid belt of a size ratio greater of equal to d_1/d_o, for 4 sizes of target asteroids, d_o. The solid curves to the lower right are the characteristic times for a single object...

Harris, A. W.↗

NASA NTRS1996

Simulations of Probabilities for Quantum Computing

It has been demonstrated that classical probabilities, and in particular, probabilistic Turing machine, can be simulated by combining chaos and non-LIpschitz dynamics, without utilization of any man-made devices (such as random number generators). Self-organizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed.

Turing machines↗

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

Probability of Detection Study on Impact Damage to Honeycomb Composite Structure using Thermographic Inspection

A probability of detection study was performed for the detection of impact damage using flash heating infrared thermography on a full scale honeycomb composite structure. The honeycomb structure was an intertank structure from a previous NASA technology demonstration program. The intertank was fabricated from IM7/8552 carbon fiber/epoxy facesheets and aluminum honeycomb core. The intertank was impacted in multiple locations with a range of impact energies utilizing a spherical indenter. In a single blind study, the intertank was inspected with thermography before and after impact damage was incurred. Following thermographic inspection several impact sites were sectioned from the intertank and cross-sectioned for microscopic comparisons of NDE detection and actual damage incurred. The study concluded that thermographic inspection was a good method of detecting delamination damage incurred by impact. The 90/95 confidence level on the probability of detection was close to the impact energy that delaminations were first observed through cross-sectional analysis.

Hodge, Andrew J.↗

NASA NTRS2008

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

Bickford, Randall L.↗

NASA NTRS2009

Processing and Probability Analysis of Pulsed Terahertz NDE of Corrosion under Shuttle Tile Data

This paper examines data processing and probability analysis of pulsed terahertz NDE scans of corrosion defects under a Shuttle tile. Pulsed terahertz data collected from an aluminum plate with fabricated corrosion defects and covered with a Shuttle tile is presented. The corrosion defects imaged were fabricated by electrochemically etching areas of various diameter and depth in the plate. In this work, the aluminum plate echo signal is located in the terahertz time-of-flight data and a threshold is applied to produce a binary image of sample features. Feature location and area are examined and identified as corrosion through comparison with the known defect layout. The results are tabulated with hit, miss, or false call information for a probability of detection analysis that is used to identify an optimal processing threshold.

Anastasi, Robert F.↗

NASA NTRS2009

Recent Advances in Model-Assisted Probability of Detection

The increased role played by probability of detection (POD) in structural integrity programs, combined with the significant time and cost associated with the purely empirical determination of POD, provides motivation for alternate means to estimate this important metric of NDE techniques. One approach to make the process of POD estimation more efficient is to complement limited empirical experiments with information from physics-based models of the inspection process or controlled laboratory experiments. The Model-Assisted Probability of Detection (MAPOD) Working Group was formed by the Air Force Research Laboratory, the FAA Technical Center, and NASA to explore these possibilities. Since the 2004 inception of the MAPOD Working Group, 11 meetings have been held in conjunction with major NDE conferences. This paper will review the accomplishments of this group, which includes over 90 members from around the world. Included will be a discussion of strategies developed to combine physics-based and empirical understanding, draft protocols that have been developed to guide application of the strategies, and demonstrations that have been or are being carried out in a number of countries. The talk will conclude with a discussion of future directions, which will include documentation of benefits via case studies, development of formal protocols for engineering practice, as well as a number of specific technical issues.

Thompson, R. Bruce↗

NASA NTRS2008

Directed Design of Experiments for Validating Probability of Detection Capability of NDE Systems (DOEPOD)

The capability of an inspection system is established by applications of various methodologies to determine the probability of detection (POD). One accepted metric of an adequate inspection system is that there is 95% confidence that the POD is greater than 90% (90/95 POD). Directed design of experiments for probability of detection (DOEPOD) has been developed to provide an efficient and accurate methodology that yields observed POD and confidence bounds for both Hit- Miss or signal amplitude testing. Specifically, DOEPOD demands utilization of observance of occurrences. Directed DOEPOD does not assume prescribed POD logarithmic or similar functions with assumed adequacy over a wide range of flaw sizes and inspection system technologies, so that multi-parameter curve fitting or model optimization approaches to generate a POD curve are not required.

Generazio, Edward R.↗

NASA NTRS2010

Sequential Probability Ratio Test for Collision Avoidance Maneuver Decisions

When facing a conjunction between space objects, decision makers must chose whether to maneuver for collision avoidance or not. We apply a well-known decision procedure, the sequential probability ratio test, to this problem. We propose two approaches to the problem solution, one based on a frequentist method, and the other on a Bayesian method. The frequentist method does not require any prior knowledge concerning the conjunction, while the Bayesian method assumes knowledge of prior probability densities. Our results show that both methods achieve desired missed detection rates, but the frequentist method's false alarm performance is inferior to the Bayesian method's

Carpenter, J. Russell↗

NASA NTRS2010

Initialization and Restart in Stochastic Local Search: Computing a Most Probable Explanation in Bayesian Networks

For hard computational problems, stochastic local search has proven to be a competitive approach to finding optimal or approximately optimal problem solutions. Two key research questions for stochastic local search algorithms are: Which algorithms are effective for initialization? When should the search process be restarted? In the present work we investigate these research questions in the context of approximate computation of most probable explanations (MPEs) in Bayesian networks (BNs). We introduce a novel approach, based on the Viterbi algorithm, to explanation initialization in BNs. While the Viterbi algorithm works on sequences and trees, our approach works on BNs with arbitrary topologies. We also give a novel formalization of stochastic local search, with focus on initialization and restart, using probability theory and mixture models. Experimentally, we apply our methods to the problem of MPE computation, using a stochastic local search algorithm known as Stochastic Greedy Search. By carefully optimizing both initialization and restart, we reduce the MPE search time for application BNs by several orders of magnitude compared to using uniform at random initialization without restart. On several BNs from applications, the performance of Stochastic Greedy Search is competitive with clique tree clustering, a state-of-the-art exact algorithm used for MPE computation in BNs.

Mengshoel, Ole J.↗

NASA NTRS2010

Modifications to the Objective Lightning Probability Forecast Tool at Kennedy Space Center/Cape Canaveral Air Force Station, Florida

The 45th Weather Squadron (45 WS) at Cape Canaveral Air Force Station (CCAFS) includes the probability of lightning occurrence in their 24-Hour and Weekly Planning Forecasts, briefed at 0700 EDT for daily operations planning on Kennedy Space Center (KSC) and CCAFS. This forecast is based on subjective analyses of model and observational data and output from an objective tool developed by the Applied Meteorology Unit (AMU). This tool was developed over two phases (Lambert and Wheeler 2005, Lambert 2007). It consists of five equations, one for each warm season month (May-Sep), that calculate the probability of lightning occurrence for the day and a graphical user interface (GUI) to display the output. The Phase I and II equations outperformed previous operational tools by a total of 56%. Based on this success, the 45 WS tasked the AMU with Phase III to improve the tool further.

Crawford, Winifred↗

NASA NTRS2008

Terahertz Imaging and Backscatter Radiography Probability of Detection Study for Space Shuttle Foam Inspections

This slide presentation reviews the use of terahertz imaging and Backscatter Radiography in a probability of detection study of the foam on the external tank (ET) shedding and damaging the shuttle orbiter. Non-destructive Examination (NDE) is performed as one method of preventing critical foam debris during the launch. Conventional NDE methods for inspection of the foam are assessed and the deficiencies are reviewed. Two methods for NDE inspection are reviewed: Backscatter Radiography (BSX) and Terahertz (THZ) Imaging. The purpose of the Probability of Detection (POD) study was to assess performance and reliability of the use of BSX and or THZ as an appropriate NDE method. The study used a test article with inserted defects, and a sample of blanks included to test for false positives. The results of the POD study are reported.

Ussery, Warren↗

NASA NTRS2011

Mesh-Based Entry Vehicle and Explosive Debris Re-Contact Probability Modeling

The risk to a crewed vehicle arising from potential re-contact with fragments from an explosive breakup of any jettisoned spacecraft segments during entry has long sought to be quantified. However, great difficulty lies in efficiently capturing the potential locations of each fragment and their collective threat to the vehicle. The method presented in this paper addresses this problem by using a stochastic approach that discretizes simulated debris pieces into volumetric cells, and then assesses strike probabilities accordingly. Combining spatial debris density and relative velocity between the debris and the entry vehicle, the strike probability can be calculated from the integral of the debris flux inside each cell over time. Using this technique it is possible to assess the risk to an entry vehicle along an entire trajectory as it separates from the jettisoned segment. By decoupling the fragment trajectories from that of the entry vehicle, multiple potential separation maneuvers can then be evaluated rapidly to provide an assessment of the best strategy to mitigate the re-contact risk.

McPherson, Mark A.↗

NASA NTRS2011

Method for Identifying Probable Archaeological Sites from Remotely Sensed Data

Archaeological sites are being compromised or destroyed at a catastrophic rate in most regions of the world. The best solution to this problem is for archaeologists to find and study these sites before they are compromised or destroyed. One way to facilitate the necessary rapid, wide area surveys needed to find these archaeological sites is through the generation of maps of probable archaeological sites from remotely sensed data. We describe an approach for identifying probable locations of archaeological sites over a wide area based on detecting subtle anomalies in vegetative cover through a statistically based analysis of remotely sensed data from multiple sources. We further developed this approach under a recent NASA ROSES Space Archaeology Program project. Under this project we refined and elaborated this statistical analysis to compensate for potential slight miss-registrations between the remote sensing data sources and the archaeological site location data. We also explored data quantization approaches (required by the statistical analysis approach), and we identified a superior data quantization approached based on a unique image segmentation approach. In our presentation we will summarize our refined approach and demonstrate the effectiveness of the overall approach with test data from Santa Catalina Island off the southern California coast. Finally, we discuss our future plans for further improving our approach.

Tilton, James C.↗