Bayesian probabilistic propagation of imprecise probabilities with large epistemic uncertainty
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Wei, Pengfei↗
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Imprecise global sensitivity analysis using bayesian multimodel inference and importance sampling
Global Sensitivity Analysis (GSA) aims to understand the relative importance of uncertain input variables to model response. Conventional GSA involves calculating sensitivity (Sobol’) indices for a model with known model parameter distributions. However, model parameters are affected by aleatory and epistemic uncertainty, with the latter often caused by lack of data. In this paper, we propose a new framework to quantify uncertainty in probability model-form and model parameters resulting from small datasets and integrate these uncertainties into Sobol’ index estimates. First, the process establishes, through Bayesian multimodel inference, a set of candidate probability models and their associated probabilities. Imprecise Sobol’ indices are calculated from these probability models using an importance sampling reweighting approach. This results in probabilistic Sobol’ indices, whose distribution characterizes uncertainty in the sensitivity resulting from small dataset size. The imprecise Sobol’ indices thus provide a measure of confidence in the sensitivity estimate and, moreover, can be used to inform data collection efforts targeted to minimize the impact of uncertainties. Through an example studying the parameters of a Timoshenko beam, we show that these probabilistic Sobol’ indices converge to the true/deterministic Sobol’ indices as the dataset size increases and hence, distribution-form uncertainty reduces. The approach is then applied to assess the sensitivity of the out-of-plane properties of an E-glass fiber composite material to its constituent properties. This second example illustrates the approach for an important class of materials with wide-ranging applications when data may be lacking for some input parameters.
42 ENGINEERING↗
Topics in inference and decision-making with partial knowledge
Two essential elements needed in the process of inference and decision-making are prior probabilities and likelihood functions. When both of these components are known accurately and precisely, the Bayesian approach provides a consistent and coherent solution to the problems of inference and decision-making. In many situations, however, either one or both of the above components may not be known, or at least may not be known precisely. This problem of partial knowledge about prior probabilities and likelihood functions is addressed. There are at least two ways to cope with this lack of precise knowledge: robust methods, and interval-valued methods. First, ways of modeling imprecision and indeterminacies in prior probabilities and likelihood functions are examined; then how imprecision in the above components carries over to the posterior probabilities is examined. Finally, the problem of decision making with imprecise posterior probabilities and the consequences of such actions are addressed. Application areas where the above problems may occur are in statistical pattern recognition problems, for example, the problem of classification of high-dimensional multispectral remote sensing image data.
Safavian, S. Rasoul↗
Dynamic remapping decisions in multi-phase parallel computations
The effectiveness of any given mapping of workload to processors in a parallel system is dependent on the stochastic behavior of the workload. Program behavior is often characterized by a sequence of phases, with phase changes occurring unpredictably. During a phase, the behavior is fairly stable, but may become quite different during the next phase. Thus a workload assignment generated for one phase may hinder performance during the next phase. We consider the problem of deciding whether to remap a paralled computation in the face of uncertainty in remapping's utility. Fundamentally, it is necessary to balance the expected remapping performance gain against the delay cost of remapping. This paper treats this problem formally by constructing a probabilistic model of a computation with at most two phases. We use stochastic dynamic programming to show that the remapping decision policy which minimizes the expected running time of the computation has an extremely simple structure: the optimal decision at any step is followed by comparing the probability of remapping gain against a threshold. This theoretical result stresses the importance of detecting a phase change, and assessing the possibility of gain from remapping. We also empirically study the sensitivity of optimal performance to imprecise decision threshold. Under a wide range of model parameter values, we find nearly optimal performance if remapping is chosen simply when the gain probability is high. These results strongly suggest that except in extreme cases, the remapping decision problem is essentially that of dynamically determining whether gain can be achieved by remapping after a phase change; precise quantification of the decision model parameters is not necessary.
Nicol, D. M.↗
Laboratory Astrophysics Under the Ultraviolet, Visible, and Gravitational Astrophysics Research Program
Space-borne facilities, such as the Hubble Space Telescope, the recent ORFEUS-SPAS II Shuttle mission, and the soon-to-be launched Far Ultraviolet Spectroscopic Explorer, are providing data at ultraviolet wavelengths of unprecedented quality for spectroscopic studies of many astronomical environments. The first step in the analysis of these data involves the derivation of abundances. Obtaining accurate abundances is possible only when the correspondence between line strength and abundance is well known. The conversion of line strength to abundance relies on knowledge of transition probabilities and oscillator strengths, often obtained from mean lives branching fractions. For many ultraviolet transitions, the necessary atomic and molecular data are either relatively imprecise or not available. Our program addresses this need for accurate oscillator strengths; our focus is on transitions that probe the nature and composition of the interstellar medium.
Federman, Steven R.↗
Robustness-Based Design Optimization Under Data Uncertainty
This paper proposes formulations and algorithms for design optimization under both aleatory (i.e., natural or physical variability) and epistemic uncertainty (i.e., imprecise probabilistic information), from the perspective of system robustness. The proposed formulations deal with epistemic uncertainty arising from both sparse and interval data without any assumption about the probability distributions of the random variables. A decoupled approach is proposed in this paper to un-nest the robustness-based design from the analysis of non-design epistemic variables to achieve computational efficiency. The proposed methods are illustrated for the upper stage design problem of a two-stage-to-orbit (TSTO) vehicle, where the information on the random design inputs are only available as sparse point and/or interval data. As collecting more data reduces uncertainty but increases cost, the effect of sample size on the optimality and robustness of the solution is also studied. A method is developed to determine the optimal sample size for sparse point data that leads to the solutions of the design problem that are least sensitive to variations in the input random variables.
Zaman, Kais↗
Spatial Acquisition in the Presence of Satellite Vibrations for Free Space Optical Communication Link
Laser communication systems offer distinct advantages over radio frequency based systems for near earth and particularly for deep space communicaiton links. Some of the advantages are smaller size, lower power requirements and higher data rates. However, laser beam widths are very narrow and require more precise pointing, acquisition and tracking (PAT) compared to RF communication sytems. In addition to imprecise knowledge of relative position and complex relative motion between the spacecrafts, the problem of pointing and acquisition is complicated by vibrations present in the spacecraft. This paper analyzes the impact of satellite vibration on acquisition time and acquisition probability for a charge coupled device (CCD) based acquisition scheme.
laser↗
System Would Detect Foreign-Object Damage in Turbofan Engine
A proposed data-fusion system, to be implemented mostly in software, would further process the digitized and preprocessed outputs of sensors in a turbofan engine to detect foreign-object damage (FOD) [more precisely, damage caused by impingement of such foreign objects as birds, pieces of ice, and runway debris]. The proposed system could help a flight crew to decide what, if any, response is necessary to complete a flight safely, and could aid mechanics in deciding what post-flight maintenance action might be needed. The sensory information to be utilized by the proposed system would consist of (1) the output of an accelerometer in an engine-vibration-monitoring subsystem and (2) features extracted from a gas path analysis. ["Gas path analysis" (GPA) is a term of art that denotes comprehensive analysis of engine performance derived from readings of fuel-flow meters, shaft-speed sensors, temperature sensors, and the like.] The acceleration signal would first be processed by a wavelet-transform-based algorithm, using a wavelet created for the specific purpose of finding abrupt FOD-induced changes in noisy accelerometer signals. Two additional features extracted would be the amplitude of vibration (determined via a single- frequency Fourier transform calculated at the rotational speed of the engine), and the rate of change in amplitude due to an FOD-induced rotor imbalance. This system would utilize two GPA features: the fan efficiency and the rate of change of fan efficiency with time. The selected GPA and vibrational features would be assessed by two fuzzy-logic inference engines, denoted the "Gas Path Expert" and the "Vibration Expert," respectively (see Figure 1). Each of these inference engines would generate a "possibility" distribution for occurrence of an FOD event: Each inference engine would assign, to its input information, degrees of membership, which would subsequently be transformed into basic probability assignments for the gas path and vibration components. The outputs of the inference engines would be fused by use of Dempster s combination algorithm (more precisely, an algorithm, based on the Dempster-Shafer-Yager theory of evidence, for fusing uncertain or imprecise information) to provide a reduced body of information to a human or computer decision maker. Figure 2 depicts some outputs generated in response to simulated accelerometer and GPA signals
Torso, James A.↗
The Uncertain Nature of Cometary Motions
The number of active short- and long-periodic comets crossing the Earth's orbit each year is less than 10 percent of the corresponding number of asteroids crossing the Earth's orbit. However, the higher relative velocities of comets with respect to the Earth and the uncertainties associated with accurately computing their future trajectories can cause considerable problems when assessing the risks of Earth-crossing objects. Unlike asteroids, the motions of active comets are often affected by so-called nongravitational (outgassing) forces that are imperfectly modeled. In addition, the astrometric optical observations that are used to refine a comet's orbit are often imprecise because a comet's center of mass can be hidden by atmospheric gas and dust. For long-period comets, there is the additional problem of having to base orbital solutions on relatively short observational data intervals. Long-term numerical integrations extending two centuries into the future have been carried out to investigate upcoming Earth-close approaches by known periodic comets. Error analyses and impact probabilities have been computed for those comets that will pass closest to the Earth. Although there are no known comets that will make dangerously close Earth approaches in the next two centuries, there are a few objects that warrant future monitoring.
Yeomans, Donald K.↗
Development of Fuzzy Logic and Soft Computing Methodologies
Our earlier research on computing with words (CW) has led to a new direction in fuzzy logic which points to a major enlargement of the role of natural languages in information processing, decision analysis and control. This direction is based on the methodology of computing with words and embodies a new theory which is referred to as the computational theory of perceptions (CTP). An important feature of this theory is that it can be added to any existing theory - especially to probability theory, decision analysis, and control - and enhance the ability of the theory to deal with real-world problems in which the decision-relevant information is a mixture of measurements and perceptions. The new direction is centered on an old concept - the concept of a perception - a concept which plays a central role in human cognition. The ability to reason with perceptions perceptions of time, distance, force, direction, shape, intent, likelihood, truth and other attributes of physical and mental objects - underlies the remarkable human capability to perform a wide variety of physical and mental tasks without any measurements and any computations. Everyday examples of such tasks are parking a car, driving in city traffic, cooking a meal, playing golf and summarizing a story. Perceptions are intrinsically imprecise. Imprecision of perceptions reflects the finite ability of sensory organs and ultimately, the brain, to resolve detail and store information. More concretely, perceptions are both fuzzy and granular, or, for short, f-granular. Perceptions are f-granular in the sense that: (a) the boundaries of perceived classes are not sharply defined; and (b) the elements of classes are grouped into granules, with a granule being a clump of elements drawn together by indistinguishability, similarity. proximity or functionality. F-granularity of perceptions may be viewed as a human way of achieving data compression. In large measure, scientific progress has been, and continues to be, driven by a quest to progress from perceptions to measurements. Pursuit of this aim has led to brilliant successes. But alongside the successes stand problems whose solutions are not in sight. Representative of such problems is the problem of automation of driving in city traffic. In this case, as in many others, what can be done with ease by humans - without any measurements and a computations - is an intractable task for machines.
Zadeh, L. A.↗
A Foreign Object Damage Event Detector Data Fusion System for Turbofan Engines
A Data Fusion System designed to provide a reliable assessment of the occurrence of Foreign Object Damage (FOD) in a turbofan engine is presented. The FOD-event feature level fusion scheme combines knowledge of shifts in engine gas path performance obtained using a Kalman filter, with bearing accelerometer signal features extracted via wavelet analysis, to positively identify a FOD event. A fuzzy inference system provides basic probability assignments (bpa) based on features extracted from the gas path analysis and bearing accelerometers to a fusion algorithm based on the Dempster-Shafer-Yager Theory of Evidence. Details are provided on the wavelet transforms used to extract the foreign object strike features from the noisy data and on the Kalman filter-based gas path analysis. The system is demonstrated using a turbofan engine combined-effects model (CEM), providing both gas path and rotor dynamic structural response, and is suitable for rapid-prototyping of control and diagnostic systems. The fusion of the disparate data can provide significantly more reliable detection of a FOD event than the use of either method alone. The use of fuzzy inference techniques combined with Dempster-Shafer-Yager Theory of Evidence provides a theoretical justification for drawing conclusions based on imprecise or incomplete data.
Turso, James A.↗
Machine Learning to Increase the Quality and Repeatability of 3D Printing - Workflow
The imprecise nature of three-dimensional (3D) printing limits the technology’s use beyond prototyping. For production of end-use parts, such as those for aerospace applications, improvements are needed to enhance quality and repeatability. Much of the difficulty in obtaining high quality printed parts lies in finding optimum printing parameters. Currently, this requires trial and error performed by an expert. Finding the optimum printing parameters is also obfuscated by the variation in optimum parameters throughout the part due to part geometry and printer effects. To allow for locally optimized printing parameters, one can envision a machine learning algorithm that could take in an object, predict the best printing parameters, and communicate these parameters to a printer. With this scenario in mind, we developed a tool that can predict and implement locally optimized printing parameters in 3D printing. This tool consists of elements designed to detect errors in a printed part, predict the probability of local flaws occurring at each point in the part, and select the optimal local parameters for the highest quality part given hardware limitations. The results of this work were highlighted in Advanced Materials Technologies. In this paper, we will discuss in greater depth the workflow and algorithms involved with this tool that were not detailed in the journal publication.
additive manufacturing↗
Predicting Real-Time Safety of the National Airspace System
To gain the situational awareness necessary for informed decision making regarding avoidance of airspace hazards, each operator must consolidate operations-relevant information from disparate sources and apply extensive domain knowledge to correctly interpret not just the current state of the NAS but forecast its (combined) evolution over the duration of the operation. This time- and workload-intensive process is periodically repeated throughout the operation so that changes can be managed in a timely manner.The imprecision, inaccuracies, inconsistency, and incompleteness of the incoming data further challenges the process. To facilitate informed decision making, this paper presents a model-based framework for the textitautomated real-time monitoring and prediction of possible effects of airspace hazards on the safety of the National Airspace System (NAS). First, hazards to flight are identified and transformed into sms, that is, quantities of interest that could be evaluated based on available data and are predictive of an unsafe event. The sms and associated thresholds that specify when an event transitions from emphsafe to emphunsafe are combined with models of airspace operations and aircraft dynamics. The framework can include any hazard to flight that can be modeled quantitatively. Models can be detailed and complex, or they can be considerably simplifed, as appropriate to the application. Real-time NAS safety monitoring and prediction begins with an estimate of the state of the NAS using the dynamic models. Given the state estimate and a probability distribution of future inputs to the NAS, we can then predict the evolution of the NAS - the future state - and the occurrence of hazards and unsafe events. The entire probability distribution of airspace sms is computed, not just point estimates, without significant assumptions regarding the distribution type andor parameters. We demonstrate our overall approach through a simulated scenario in which we predict the occurrence of some unsafe events and show how these predictions evolve in time as flight operations progress. Predictions accounting for common sources of uncertainty are included and it is shown how the predictions improve in time, become more confident, and change dynamically as new information is made available to the prediction algorithm.
safety↗
Summary and Annotated Bibliography of Measurement Error Corrections with Potential Application in Future Quesst Mission Community Noise Studies
This document is motivated by likely needs of the Quesst mission community response tests, which will culminate in data collection and estimation of dose-response regression relationships for consideration by domestic and international aviation regulators. Furthermore, basic research questions evaluating interactions between rates of community annoyance, dose levels, and indicators of the presence of rattle, vibration, and startle hinge on hypothesis testing in the context of regression models. For a variety of reasons, noise doses may be known only imprecisely and may not reflect the actual level experienced by responding subjects. These differences between true dose and estimated dose, be they systematic or random, constitute covariate measurement error. Available statistics literature speaks to the impacts of measurement error on regression models, both in terms of bias in estimated coefficients and predicted values, and in terms of the loss of statistical power for hypothesis testing. Given the particulars of a categorical annoyance response variable and a continuous noise dose predictor variable subject to measurement error during testing, the emphasis of this report is on findings and methods pertinent to generalized linear (and mixed) models likely to be employed during the Quesst mission community tests. We reach the following conclusions: 1. Of four reviewed methods, structural Bayesian measurement error models and simulation extrapolation (SIMEX) may be the most readily applicable to Quesst mission community noise study objectives. 2. If warranted, a linear measurement model can help model systematic sources of measurement error that the classical measurement error does not. 3. For its ready implementation and small additional input requirements, simulation extrapolation may be ideally suited for addressing secondary research questions involving interactions between annoyance, noise dose, and other factors through hypothesis testing. 4. For their flexibility and ability to propagate uncertainty, structural Bayesian hierarchical models have great appeal for mission purposes; some care may be needed in developing appropriate probability models describing actual noise exposure during testing. An annotated bibliography logs additional papers and resources that may be of value to analysts in other projects and disciplines.
Dose-Response Model↗