Uncertainty Reduction using Bayesian Inference and Sensitivity Analysis: A Sequential Approach to the NASA Langley Uncertainty Quantification Challenge

This paper presents a computational framework for uncertainty characterization and propagation, and sensitivity analysis under the presence of aleatory and epistemic un- certainty, and develops a rigorous methodology for efficient refinement of epistemic un- certainty by identifying important epistemic variables that significantly affect the overall performance of an engineering system. The proposed methodology is illustrated using the NASA Langley Uncertainty Quantification Challenge (NASA-LUQC) problem that deals with uncertainty analysis of a generic transport model (GTM). First, Bayesian inference is used to infer subsystem-level epistemic quantities using the subsystem-level model and corresponding data. Second, tools of variance-based global sensitivity analysis are used to identify four important epistemic variables (this limitation specified in the NASA-LUQC is reflective of practical engineering situations where not all epistemic variables can be refined due to time/budget constraints) that significantly affect system-level performance. The most significant contribution of this paper is the development of the sequential refine- ment methodology, where epistemic variables for refinement are not identified all-at-once. Instead, only one variable is first identified, and then, Bayesian inference and global sensi- tivity calculations are repeated to identify the next important variable. This procedure is continued until all 4 variables are identified and the refinement in the system-level perfor- mance is computed. The advantages of the proposed sequential refinement methodology over the all-at-once uncertainty refinement approach are explained, and then applied to the NASA Langley Uncertainty Quantification Challenge problem

Uncertainty Quantification in Remaining Useful Life of Aerospace Components using State Space Models and Inverse FORM

This paper investigates the use of the inverse first-order reliability method (inverse- FORM) to quantify the uncertainty in the remaining useful life (RUL) of aerospace components. The prediction of remaining useful life is an integral part of system health prognosis, and directly helps in online health monitoring and decision-making. However, the prediction of remaining useful life is affected by several sources of uncertainty, and therefore it is necessary to quantify the uncertainty in the remaining useful life prediction. While system parameter uncertainty and physical variability can be easily included in inverse-FORM, this paper extends the methodology to include: (1) future loading uncertainty, (2) process noise; and (3) uncertainty in the state estimate. The inverse-FORM method has been used in this paper to (1) quickly obtain probability bounds on the remaining useful life prediction; and (2) calculate the entire probability distribution of remaining useful life prediction, and the results are verified against Monte Carlo sampling. The proposed methodology is illustrated using a numerical example

Prospective Architectures for Onboard vs Cloud-Based Decision Making for Unmanned Aerial Systems

This paper investigates propsective architectures for decision-making in unmanned aerial systems. When these unmanned vehicles operate in urban environments, there are several sources of uncertainty that affect their behavior, and decision-making algorithms need to be robust to account for these different sources of uncertainty. It is important to account for several risk-factors that affect the flight of these unmanned systems, and facilitate decision-making by taking into consideration these various risk-factors. In addition, there are several technical challenges related to autonomous flight of unmanned aerial systems; these challenges include sensing, obstacle detection, path planning and navigation, trajectory generation and selection, etc. Many of these activities require significant computational power and in many situations, all of these activities need to be performed in real-time. In order to efficiently integrate these activities, it is important to develop a systematic architecture that can facilitate real-time decision-making. Four prospective architectures are discussed in this paper; on one end of the spectrum, the first architecture considers all activities/computations being performed onboard the vehicle whereas on the other end of the spectrum, the fourth and final architecture considers all activities/computations being performed in the cloud, using a new service known as Prognostics as a Service that is being developed at NASA Ames Research Center. The four different architectures are compared, their advantages and disadvantages are explained and conclusions are presented

An Uncertainty Quantification Framework for Prognostics and Condition-Based Monitoring

This paper presents a computational framework for uncertainty quantification in prognostics in the context of condition-based monitoring of aerospace systems. The different sources of uncertainty and the various uncertainty quantification activities in condition-based prognostics are outlined in detail, and it is demonstrated that the Bayesian subjective approach is suitable for interpreting uncertainty in online monitoring. A state-space model-based framework for prognostics, that can rigorously account for the various sources of uncertainty, is presented. Prognostics consists of two important steps. First, the state of the system is estimated using Bayesian tracking, and then, the future states of the system are predicted until failure, thereby computing the remaining useful life of the system. The proposed framework is illustrated using the power system of a planetary rover test-bed, which is being developed and studied at NASA Ames Research Center

Towards Characterizing the Variability in the Loading Demands of an Unmanned Aerial Vehicle

This paper presents a computational methodology to characterize and quantify the variability in the power demands during the take-off of an unmanned aerial vehicle (UAV). A lithium-ion battery-based power system is used to power the unmanned aerial vehicle, and the capabilities of the unmanned aerial vehicle are driven by the amount of charge in this battery. In order to design the power system, it is necessary to analyze the power and charge requirements of the UAV. This paper focuses on the take-off segment, and aims to quantify the amount of charge that is required for this particular segment. Sparse data is available through different flight tests and this data is used to analyze the flight profile and the charge requirement during take-off. The amount of charge required for take-off depends on several factors that are not only variable but cannot be controlled in reality, and hence, the entire flight profile and the corresponding charge requirement are variable in nature. The information available through flight tests is converted into multi-dimensional sparse data and a new method is developed in this paper for variability characterization using multi-dimensional sparse data. This analysis is useful for prognostics and health management where it is necessary to anticipate future charge requirements in order to compute the end-of-discharge of the battery, and hence, the remaining useful life of the power system

Remaining Useful Life Estimation in Prognosis: An Uncertainty Propagation Problem

The estimation of remaining useful life is significant in the context of prognostics and health monitoring, and the prediction of remaining useful life is essential for online operations and decision-making. However, it is challenging to accurately predict the remaining useful life in practical aerospace applications due to the presence of various uncertainties that affect prognostic calculations, and in turn, render the remaining useful life prediction uncertain. It is challenging to identify and characterize the various sources of uncertainty in prognosis, understand how each of these sources of uncertainty affect the uncertainty in the remaining useful life prediction, and thereby compute the overall uncertainty in the remaining useful life prediction. In order to achieve these goals, this paper proposes that the task of estimating the remaining useful life must be approached as an uncertainty propagation problem. In this context, uncertainty propagation methods which are available in the literature are reviewed, and their applicability to prognostics and health monitoring are discussed

Advanced Methods for Determining Prediction Uncertainty in Model-Based Prognostics with Application to Planetary Rovers

Prognostics is centered on predicting the time of and time until adverse events in components, subsystems, and systems. It typically involves both a state estimation phase, in which the current health state of a system is identified, and a prediction phase, in which the state is projected forward in time. Since prognostics is mainly a prediction problem, prognostic approaches cannot avoid uncertainty, which arises due to several sources. Prognostics algorithms must both characterize this uncertainty and incorporate it into the predictions so that informed decisions can be made about the system. In this paper, we describe three methods to solve these problems, including Monte Carlo-, unscented transform-, and first-order reliability-based methods. Using a planetary rover as a case study, we demonstrate and compare the different methods in simulation for battery end-of-discharge prediction

[Random Variable Read Me File]

Readme for the Random Variable Toolbox usable manner. is a Web-based Git version control repository hosting service. It is mostly used for computer code. It offers all of the distributed version control and source code management (SCM) functionality of Git as well as adding its own features. It provides access control and several collaboration features such as bug tracking, feature requests, task management, and wikis for every project.[3] GitHub offers both plans for private and free repositories on the same account[4] which are commonly used to host open-source software projects.[5] As of April 2017, GitHub reports having almost 20 million users and 57 million repositories,[6] making it the largest host of source code in the world.[7] GitHub has a mascot called Octocat, a cat with five tentacles and a human-like fac

Effects of Aircraft Health on Airspace Safety

This manuscript investigates the effects of aircraft health on the surrounding airspace, and proposes a methodology to understand how different aircraft-level faults (system faults, communication faults, etc.) can adversely affect the safety of the airspace, and qualitatively assess the impact of such faults on airspace safety metrics (such as congestion, controller/pilot workload, etc.). The topic of systems health management deals with continuously monitoring the performance of an engineering system, identifying and detecting the presence of faults, predicting the growth/progression of faults, computing the remaining useful life, and aiding online decision-making for the robust, continued operation of such engineering systems. The topic of real-time airspace modeling and safety analysis deals with defining and computing safety metrics for airspace operations in order to support risk-informed decision-making activities for various airspace entities including pilots, air traffic controllers, airlines, etc. This report presents recent research efforts that focus on combining multiple aspects of the aforementioned topics, and investigates the impact of aircraft-level faults on the airspace safet