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In-Time Safety Assessment & Risk Prediction for Unmanned Aerial Systems

One of the critical challenges in emerging autonomous systems is timely mitigation of hazards encountered during operation which may not be known or accounted for at the time of design. Efficient execution of unmanned systems therefore demands a paradigm shift from scheduled periodic maintenance to predictive risk analysis that includes condition-based-monitoring, real-time reliability assessment and hazard mitigation. Particularly, the state-of-health parameters needs to be computed at the component level, unit level as well as the integrated system level. While in the former two levels, the physics of health propagation may be based on underlying electro-mechanical properties, system level prognostics often relies on data-driven models. Further, uncertainty from model, measurements and input sources should be accurately quantified to generate meaningful prediction results that can be fed into reliable decision making processes. Finally, the expected risk and time to failure has to be computed based on the current state-of-health of the overall system. This talk presents a conceptual design of such an in-time safety assurance approach for unmanned aerial vehicles (UAV) operating at low altitudes near and over populated areas. Typical in-flight hazard incidents include unplanned detour, proximity to obstacles, mid-flight component faults, limited battery life and poor quality of GPS measurements. Safety assessment therefore comprises trajectory generation and re-plan, battery RUL computation, distributed fault diagnostics and uncertainty management of predicted trajectory based on GPS measurement noise. The entire monitoring framework will be demonstrated on simulated as well as real UAV flight experiments conducted at the NASA Langley Research Center. This tutorial will therefore guide the audience through a step-by-step tracking of an autonomous system with focus on in-time risk prediction in the presence of unforeseen hazards and uncertain environment.

diagnostics↗
NASA NTRS2021

Astrophysics Milestones for Pulsar Timing Array Gravitational-wave Detection

The NANOGrav Collaboration reported strong Bayesian evidence for a common-spectrum stochastic process in its12.5 yr pulsar timing array data set, with median characteristic strain amplitude at periods of a year of A(yr) = 1.92(+0.75,-0.55) x 10^(-15). However, evidence for the quadrupolar Hellings & Downs interpulsar correlations, which are characteristic of gravitational-wave signals, was not yet significant. We emulate and extend the NANOGrav data set, injecting a wide range of stochastic gravitational-wave background(GWB)signals that encompass a variety of amplitudes and spectral shapes, and quantify three key milestones.(I)Given the amplitude measured in the 12.5 yr analysis and assuming this signal is a GWB, we expect to accumulate robust evidence of an interpulsar-correlated GWB signal with 15–17 yr of data, i.e., an additional 2–5 yr from the 12.5 yr data set.(II)At the initial detection, we expect a fractional uncertainty of 40% on the power-law strain spectrum slope, which is sufficient to distinguish a GWB of supermassive black hole binary origin from some models predicting more exotic origins.(III)Similarly, the measured GWB amplitude will have an uncertainty of 44% upon initial detection, allowing us to arbitrate between some population models of supermassive black hole binaries. In addition, power-law models are distinguishable from those having low-frequency spectral turnovers once 20 yr of data are reached. Even though our study is based on the NANOGrav data, we also derive relations that allow for a generalization to other pulsar timing array data sets. Most notably, by combining the data of individual arrays into the International Pulsar Timing Array, all of these milestones can be reached significantly earlier.

Nihan S. Pol↗
NASA NTRS2012

Analysis of Fine-Mode Aerosol Retrieval Capabilities by Different Passive Remote Sensing Instrument Designs

Remote sensing of aerosol optical properties is difficult, but multi-angle, multi-spectral, polarimetric instruments have the potential to retrieve sufficient information about aerosols that they can be used to improve global climate models. However, the complexity of these instruments means that it is difficult to intuitively understand the relationship between instrument design and retrieval success. We apply a Bayesian statistical technique that relates instrument characteristics to the information contained in an observation. Using realistic simulations of fine size mode dominated spherical aerosols, we investigate three instrument designs. Two of these represent instruments currently in orbit: the Multiangle Imaging SpectroRadiometer (MISR) and the POLarization and Directionality of the Earths Reflectances (POLDER). The third is the Aerosol Polarimetry Sensor (APS), which failed to reach orbit during recent launch, but represents a viable design for future instruments. The results show fundamental differences between the three, and offer suggestions for future instrument design and the optimal retrieval strategy for current instruments. Generally, our results agree with previous validation efforts of POLDER and airborne prototypes of APS, but show that the MISR aerosol optical thickness uncertainty characterization is possibly underestimated.

Knobelspiesse, Kirk↗
NASA NTRS2014

Reconstructing the Sky Location of Gravitational-Wave Detected Compact Binary Systems: Methodology for Testing and Comparison

The problem of reconstructing the sky position of compact binary coalescences detected via gravitational waves is a central one for future observations with the ground-based network of gravitational-wave laser interferometers, such as Advanced LIGO and Advanced Virgo. Different techniques for sky localization have been independently developed. They can be divided in two broad categories: fully coherent Bayesian techniques, which are high latency and aimed at in-depth studies of all the parameters of a source, including sky position, and "triangulation-based" techniques, which exploit the data products from the search stage of the analysis to provide an almost real-time approximation of the posterior probability density function of the sky location of a detection candidate. These techniques have previously been applied to data collected during the last science runs of gravitational-wave detectors operating in the so-called initial configuration. Here, we develop and analyze methods for assessing the self consistency of parameter estimation methods and carrying out fair comparisons between different algorithms, addressing issues of efficiency and optimality. These methods are general, and can be applied to parameter estimation problems other than sky localization. We apply these methods to two existing sky localization techniques representing the two above-mentioned categories, using a set of simulated inspiralonly signals from compact binary systems with a total mass of equal to or less than 20M solar mass and nonspinning components. We compare the relative advantages and costs of the two techniques and show that sky location uncertainties are on average a factor approx. equals 20 smaller for fully coherent techniques than for the specific variant of the triangulation-based technique used during the last science runs, at the expense of a factor approx. equals 1000 longer processing time.

technique used↗
NASA NTRS2021

A NICER View of the Massive Pulsar PSR J0740+6620 Informed by Radio Timing and XMM-Newton Spectroscopy

We report on Bayesian estimation of the radius, mass, and hot surface regions of the massive millisecond pulsar PSR J0740+6620, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer X-ray Timing Instrument event data. We condition on informative pulsar mass, distance, and orbital inclination priors derived from the joint North American Nanohertz Observatory for Gravitational Waves and Canadian Hydrogen Intensity Mapping Experiment/Pulsar wideband radio timing measurements of Fonseca et al. We use XMM-Newton European Photon Imaging Camera spectroscopic event data to inform our X-ray likelihood function. The prior support of the pulsar radius is truncated at 16 km to ensure coverage of current dense matter models. We assume conservative priors on instrument calibration uncertainty. We constrain the equatorial radius and mass of PSR J0740+6620 to be-+12.390.981.30km and-+2.0720.0660.067Me respectively, each reported as the posterior credible interval bounded by the 16% and 84% quantiles, conditional on surface hot regions that are non-overlapping spherical caps of fully ionized hydrogen atmosphere with uniform effective temperature; a posteriori, the temperature is=-+TlogK5.99100.060.05([])for each hot region. All software for the X-ray modeling framework is open-source and all data, model, and sample information is publicly available, including analysis notebooks and model modules in the Python language. Our marginal likelihood function of mass and equatorial radius is proportional to the marginal joint posterior density of those parameters(within the prior support)and can thus be computed from the posterior samples.

Millisecond pulsars↗
NASA NTRS2004

Automatic Generation of Algorithms for the Statistical Analysis of Planetary Nebulae Images

Analyzing data sets collected in experiments or by observations is a Core scientific activity. Typically, experimentd and observational data are &aught with uncertainty, and the analysis is based on a statistical model of the conjectured underlying processes, The large data volumes collected by modern instruments make computer support indispensible for this. Consequently, scientists spend significant amounts of their time with the development and refinement of the data analysis programs. AutoBayes [GF+02, FS03] is a fully automatic synthesis system for generating statistical data analysis programs. Externally, it looks like a compiler: it takes an abstract problem specification and translates it into executable code. Its input is a concise description of a data analysis problem in the form of a statistical model as shown in Figure 1; its output is optimized and fully documented C/C++ code which can be linked dynamically into the Matlab and Octave environments. Internally, however, it is quite different: AutoBayes derives a customized algorithm implementing the given model using a schema-based process, and then further refines and optimizes the algorithm into code. A schema is a parameterized code template with associated semantic constraints which define and restrict the template s applicability. The schema parameters are instantiated in a problem-specific way during synthesis as AutoBayes checks the constraints against the original model or, recursively, against emerging sub-problems. AutoBayes schema library contains problem decomposition operators (which are justified by theorems in a formal logic in the domain of Bayesian networks) as well as machine learning algorithms (e.g., EM, k-Means) and nu- meric optimization methods (e.g., Nelder-Mead simplex, conjugate gradient). AutoBayes augments this schema-based approach by symbolic computation to derive closed-form solutions whenever possible. This is a major advantage over other statistical data analysis systems which use numerical approximations even in cases where closed-form solutions exist. AutoBayes is implemented in Prolog and comprises approximately 75.000 lines of code. In this paper, we take one typical scientific data analysis problem-analyzing planetary nebulae images taken by the Hubble Space Telescope-and show how AutoBayes can be used to automate the implementation of the necessary anal- ysis programs. We initially follow the analysis described by Knuth and Hajian [KHO2] and use AutoBayes to derive code for the published models. We show the details of the code derivation process, including the symbolic computations and automatic integration of library procedures, and compare the results of the automatically generated and manually implemented code. We then go beyond the original analysis and use AutoBayes to derive code for a simple image segmentation procedure based on a mixture model which can be used to automate a manual preproceesing step. Finally, we combine the original approach with the simple segmentation which yields a more detailed analysis. This also demonstrates that AutoBayes makes it easy to combine different aspects of data analysis.

Fischer, Bernd↗
NASA NTRS2012

Safety Risk Knowledge Elicitation in Support of Aeronautical R and D Portfolio Management: A Case Study

Aviation is a problem domain characterized by a high level of system complexity and uncertainty. Safety risk analysis in such a domain is especially challenging given the multitude of operations and diverse stakeholders. The Federal Aviation Administration (FAA) projects that by 2025 air traffic will increase by more than 50 percent with 1.1 billion passengers a year and more than 85,000 flights every 24 hours contributing to further delays and congestion in the sky (Circelli, 2011). This increased system complexity necessitates the application of structured safety risk analysis methods to understand and eliminate where possible, reduce, and/or mitigate risk factors. The use of expert judgments for probabilistic safety analysis in such a complex domain is necessary especially when evaluating the projected impact of future technologies, capabilities, and procedures for which current operational data may be scarce. Management of an R&D product portfolio in such a dynamic domain needs a systematic process to elicit these expert judgments, process modeling results, perform sensitivity analyses, and efficiently communicate the modeling results to decision makers. In this paper a case study focusing on the application of an R&D portfolio of aeronautical products intended to mitigate aircraft Loss of Control (LOC) accidents is presented. In particular, the knowledge elicitation process with three subject matter experts who contributed to the safety risk model is emphasized. The application and refinement of a verbal-numerical scale for conditional probability elicitation in a Bayesian Belief Network (BBN) is discussed. The preliminary findings from this initial step of a three-part elicitation are important to project management practitioners as they illustrate the vital contribution of systematic knowledge elicitation in complex domains.

Shih, Ann T.↗
NASA NTRS2021

Analysis of simultaneous aerosol and ocean glint retrieval using multi-angle observations

Since early 2000, NASA's Multi-angle Imaging SpectroRadiometer (MISR) instrument has been performing remote sensing retrievals of aerosol optical properties from the polar-orbiting Terra spacecraft. A noteworthy aspect of MISR observations over the ocean is that, for much of the Earth, some of the multi-angle views have contributions from solar reflection by the ocean surface (glint, or glitter), while others do not. Aerosol retrieval algorithms often discard these glint-influenced observations because they can overwhelm the signal and are difficult to predict without knowledge of the (wind-speed-driven) ocean surface roughness. However, theoretical studies have shown that multi-angle observations of a location at geometries with and without reflected sun glint can be a rich source of information, sufficient to support simultaneous retrieval of both the aerosol state and the wind speed at the ocean surface. We are in the early stages of creating such an algorithm. In this paper, we describe our assessment of the appropriate level of parameterization for simultaneous aerosol and ocean surface property retrievals using sun glint. For this purpose, we use generalized nonlinear retrieval analysis (GENRA), an information content assessment (ICA) technique employing Bayesian inference, and simulations from the Ahmad–Fraser iterative radiative transfer code. We find that four parameters are suitable: aerosol optical depth (τ), particle size distribution (expressed as the fine mode fraction f of small particles in a bimodal size distribution), surface wind speed (w), and relative humidity (r, to define the aerosol water content and complex refractive index). None of these parameters define ocean optical properties, as we found that the aerosol state could be retrieved with the nine MISR near-infrared views alone, where the ocean body is strongly absorbing in the open ocean. We also found that retrieval capability varies with observation geometry and that as τ increases so does the ability to determine aerosol intensive optical properties (r and f, while it decreases for w). Increases in w decrease the ability to determine the true value of that parameter but have minimal impact on retrieval of aerosol properties. We explored the benefit of excluding the two most extreme MISR view angles for which radiative transfer with the plane-parallel approximation is less certain, but we found no advantage in doing so. Finally, the impact of treating wind speed as a scalar parameter, rather than as a two-parameter directional wind, was tested. While the simpler scalar model does contribute to overall aerosol uncertainty, it is not sufficiently large to justify the addition of another dimension to parameter space. An algorithm designed upon these principles is in development. It will be used to perform an atmospheric correction with MISR for coincident ocean color (OC) observations by the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument, also on the NASA Terra spacecraft. Unlike MISR, MODIS is a single-view-angle instrument, but it has a more complete set of spectral channels ideal for determination of optical ocean properties. The atmospheric correction of MODIS OC data can therefore benefit from MISR aerosol retrievals. Furthermore, higher-spatial-resolution data from coincident MISR observations may also improve glint screening.

Kirk Knobelspiesse↗
NASA NTRS2015

Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating each component weight during the nonlinear propagation stage an approximation of the true pdf can be successfully reconstructed. Particle filtering (PF) methods have gained popularity recently for solving nonlinear estimation problems due to their straightforward approach and the processing capabilities mentioned above. The basic concept behind PF is to represent any pdf as a set of random samples. As the number of samples increases, they will theoretically converge to the exact, equivalent representation of the desired pdf. When the estimated qth moment is needed, the samples are used for its construction allowing further analysis of the pdf characteristics. However, filter performance deteriorates as the dimension of the state vector increases. To overcome this problem Ref. [5] applies a marginalization technique for PF methods, decreasing complexity of the system to one linear and another nonlinear state estimation problem. The marginalization theory was originally developed by Rao and Blackwell independently. According to Ref. [6] it improves any given estimator under every convex loss function. The improvement comes from calculating a conditional expected value, often involving integrating out a supportive statistic. In other words, Rao-Blackwellization allows for smaller but separate computations to be carried out while reaching the main objective of the estimator. In the case of improving an estimator's variance, any supporting statistic can be removed and its variance determined. Next, any other information that dependents on the supporting statistic is found along with its respective variance. A new approach is developed here by utilizing the strengths of the adaptive Gaussian sum propagation in Ref. [2] and a marginalization approach used for PF methods found in Ref. [7]. In the following sections a modified filtering approach is presented based on a special state-space model within nonlinear systems to reduce the dimensionality of the optimization problem in Ref. [2]. First, the adaptive Gaussian sum propagation is explained and then the new marginalized adaptive Gaussian sum propagation is derived. Finally, an example simulation is presented.

state estimation↗