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NASA NTRS2008

Approximation of Failure Probability Using Conditional Sampling

In analyzing systems which depend on uncertain parameters, one technique is to partition the uncertain parameter domain into a failure set and its complement, and judge the quality of the system by estimating the probability of failure. If this is done by a sampling technique such as Monte Carlo and the probability of failure is small, accurate approximation can require so many sample points that the computational expense is prohibitive. Previous work of the authors has shown how to bound the failure event by sets of such simple geometry that their probabilities can be calculated analytically. In this paper, it is shown how to make use of these failure bounding sets and conditional sampling within them to substantially reduce the computational burden of approximating failure probability. It is also shown how the use of these sampling techniques improves the confidence intervals for the failure probability estimate for a given number of sample points and how they reduce the number of sample point analyses needed to achieve a given level of confidence.

Giesy. Daniel P.↗
NASA NTRS2008

Optimal Planning and Problem-Solving

CTAEMS MDP Optimal Planner is a problem-solving software designed to command a single spacecraft/rover, or a team of spacecraft/rovers, to perform the best action possible at all times according to an abstract model of the spacecraft/rover and its environment. It also may be useful in solving logistical problems encountered in commercial applications such as shipping and manufacturing. The planner reasons around uncertainty according to specified probabilities of outcomes using a plan hierarchy to avoid exploring certain kinds of suboptimal actions. Also, planned actions are calculated as the state-action space is expanded, rather than afterward, to reduce by an order of magnitude the processing time and memory used. The software solves planning problems with actions that can execute concurrently, that have uncertain duration and quality, and that have functional dependencies on others that affect quality. These problems are modeled in a hierarchical planning language called C_TAEMS, a derivative of the TAEMS language for specifying domains for the DARPA Coordinators program. In realistic environments, actions often have uncertain outcomes and can have complex relationships with other tasks. The planner approaches problems by considering all possible actions that may be taken from any state reachable from a given, initial state, and from within the constraints of a given task hierarchy that specifies what tasks may be performed by which team member.

Clemet, Bradley↗
NASA NTRS2008

Controller for Driving a Piezoelectric Actuator at Resonance

A digital control system based partly on an extremum-seeking control algorithm tracks the changing resonance frequency of a piezoelectric actuator or an electrically similar electromechanical device that is driven by a sinusoidal excitation signal and is required to be maintained at or near resonance in the presence of uncertain, changing external loads and disturbances. Somewhat more specifically, on the basis of measurements of the performance of the actuator, this system repeatedly estimates the resonance frequency and alters the excitation frequency as needed to keep it at or near the resonance frequency. In the original application for which this controller was developed, the piezoelectric actuator is part of an ultrasonic/sonic drill/corer. Going beyond this application, the underlying principles of design and operation are generally applicable to tracking changing resonance frequencies of heavily perturbed harmonic oscillators. Resonance-frequency-tracking analog electronic circuits are commercially available, but are not adequate for the present purpose for several reasons: The input/output characteristics of analog circuits tend to drift, often necessitating recalibration, especially whenever the same controller is used in driving a different resonator. In the case of an actuator in a system that has multiple modes characterized by different resonance frequencies, an analog controller can tune erroneously to one of the higher-frequency modes. The lack of programmability of analog controllers is problematic when faults occur, and is especially problematic for preventing tuning to a higher-frequency mode. In contrast, a digital controller can be programmed to restrict itself to a specified frequency range and to maintain stability even when the affected resonator is driven at high power and subjected to uncertain disturbances and variable loads. The present digital control system (see figure) is implemented by means of an algorithm that comprises three main subalgorithms: a hill-climbing control algorithm, an estimation-based extremum-seeking control (ESC) algorithm, and a supervisory algorithm. The hill-climbing algorithm is useful for coarse tracking to find and remain within the vicinity of the resonance. The ESC algorithm is not capable of coarse resonance tracking, but is capable of fine resonance tracking once the estimates of parameters generated by the hill-climbing algorithm have converged sufficiently. On the basis of the parameter-estimation errors, the supervisory algorithm switches operation to whichever of the other two algorithms performs best at a given time.

Aldrich, Jack↗
NASA NTRS2010

A Computational Framework to Control Verification and Robustness Analysis

This paper presents a methodology for evaluating the robustness of a controller based on its ability to satisfy the design requirements. The framework proposed is generic since it allows for high-fidelity models, arbitrary control structures and arbitrary functional dependencies between the requirements and the uncertain parameters. The cornerstone of this contribution is the ability to bound the region of the uncertain parameter space where the degradation in closed-loop performance remains acceptable. The size of this bounding set, whose geometry can be prescribed according to deterministic or probabilistic uncertainty models, is a measure of robustness. The robustness metrics proposed herein are the parametric safety margin, the reliability index, the failure probability and upper bounds to this probability. The performance observed at the control verification setting, where the assumptions and approximations used for control design may no longer hold, will fully determine the proposed control assessment.

Crespo, Luis G.↗
NASA NTRS2009

Stability and Performance Metrics for Adaptive Flight Control

This paper addresses the problem of verifying adaptive control techniques for enabling safe flight in the presence of adverse conditions. Since the adaptive systems are non-linear by design, the existing control verification metrics are not applicable to adaptive controllers. Moreover, these systems are in general highly uncertain. Hence, the system's characteristics cannot be evaluated by relying on the available dynamical models. This necessitates the development of control verification metrics based on the system's input-output information. For this point of view, a set of metrics is introduced that compares the uncertain aircraft's input-output behavior under the action of an adaptive controller to that of a closed-loop linear reference model to be followed by the aircraft. This reference model is constructed for each specific maneuver using the exact aerodynamic and mass properties of the aircraft to meet the stability and performance requirements commonly accepted in flight control. The proposed metrics are unified in the sense that they are model independent and not restricted to any specific adaptive control methods. As an example, we present simulation results for a wing damaged generic transport aircraft with several existing adaptive controllers.

Stepanyan, Vahram↗
NASA NTRS2010

Adapting ASPEN for Orbital Express

By studying the Orbital Express mission, modeling the spacecraft and scenarios, and testing the system, a technique has been developed that uses recursive decomposition to represent procedural actions declaratively, schema-level uncertainty reasoning to make uncertainty reasoning tractable, and lightweight, natural language processing to automatically parse procedures to produce declarative models. Schema-level uncertainty reasoning has, at its core, the basic assumption that certain variables are uncertain, but not independent. Once any are known, then the others become known. This is important where a variable is uncertain for an action and many actions of the same type exist in the plan. For example, if the number of retries to purge pump lines was unknown (but bounded), and each attempt required a sub-plan, then, once the correct number of attempts required for a purge was known, it would likely be the same for all subsequent purges. This greatly reduces the space of plans that needs to be searched to ensure that all executions are feasible. To accommodate changing scenario procedures, each is ingested into a tabular format in temporal order, and a simple natural-language parser is used to read each step and to derive the impact of that step on memory, power, and communications. Then an ASPEN (Activity Scheduling and Planning Environment) model is produced based on this analysis. The model is tested and further changed by hand, if necessary, to reflect the actual procedure. This results in a great savings of time used for modeling procedures. Many processes that need to be modeled in ASPEN (a declarative system) are, in fact, procedural. ASPEN includes the ability to model activities in a hierarchical fashion, but this representation breaks down if there is a practically unbounded number of sub-activities and decomposition topologies. However, if recursive decomposition is allowed, HTN-like encodings are enabled to represent most procedural phenomena. For example, if a switch requires a variable (but known at the time of the attempt) number of attempts to switch on, one can recurse on the number of remaining switch attempts and decompose into either the same switching activity with one less required attempt, or not decompose at all (or decompose into a dummy task), resulting in the end of the decomposition. In fact, any bounded procedural behavior can be modeled using recursive decompositions assuming that the variables impinging the disjunctive decomposition decision are computable at the time that the decision is made. This enables one to represent tasks that are controlled outside of the scheduler, but that the scheduler must accommodate, without requiring one to give a declarative model of the procedural behavior.

Chouinard, Caroline↗
NASA NTRS2005

Generalized Maximum Entropy

A long standing mystery in using Maximum Entropy (MaxEnt) is how to deal with constraints whose values are uncertain. This situation arises when constraint values are estimated from data, because of finite sample sizes. One approach to this problem, advocated by E.T. Jaynes [1], is to ignore this uncertainty, and treat the empirically observed values as exact. We refer to this as the classic MaxEnt approach. Classic MaxEnt gives point probabilities (subject to the given constraints), rather than probability densities. We develop an alternative approach that assumes that the uncertain constraint values are represented by a probability density {e.g: a Gaussian), and this uncertainty yields a MaxEnt posterior probability density. That is, the classic MaxEnt point probabilities are regarded as a multidimensional function of the given constraint values, and uncertainty on these values is transmitted through the MaxEnt function to give uncertainty over the MaXEnt probabilities. We illustrate this approach by explicitly calculating the generalized MaxEnt density for a simple but common case, then show how this can be extended numerically to the general case. This paper expands the generalized MaxEnt concept introduced in a previous paper [3].

Cheeseman, Peter↗
NASA NTRS2012

Interactions in Massive Colliding Wind Binaries

The most massive stars (M> 60 Solar Mass) play crucial roles in altering the chemical and thermodynamic properties of their host galaxies. Stellar mass is the fundamental stellar parameter that determines their ancillary properties and which ultimately determines the fate of these stars and their influence on their galactic environs. Unfortunately, stellar mass becomes observationally and theoretically less well constrained as it increases. Theory becomes uncertain mostly because very massive stars are prone to strong, variable mass loss which is difficult to model. Observational constraints are uncertain too. Massive stars are rare, and massive binary stars (needed for dynamical determination of mass) are rarer still: and of these systems only a fraction have suitably high orbital inclinations for direct photometric and spectroscopic radial-velocity analysis. Even in the small number of cases in which a high-inclination binary near the upper mass limit can be identified, rotational broadening and contamination of spectral line features from thick circumstellar material (either natal clouds or produced by strong stellar wind driven mass loss from one or both of he stellar components) biases the analysis. In the wilds of the upper HR diagram, we're often left with indirect and circumstantial means of determining mass, a rather unsatisfactory state of affairs.

Corcoran, M.↗
NASA NTRS2012

Uncertainty Quantification for Polynomial Systems via Bernstein Expansions

This paper presents a unifying framework to uncertainty quantification for systems having polynomial response metrics that depend on both aleatory and epistemic uncertainties. The approach proposed, which is based on the Bernstein expansions of polynomials, enables bounding the range of moments and failure probabilities of response metrics as well as finding supersets of the extreme epistemic realizations where the limits of such ranges occur. These bounds and supersets, whose analytical structure renders them free of approximation error, can be made arbitrarily tight with additional computational effort. Furthermore, this framework enables determining the importance of particular uncertain parameters according to the extent to which they affect the first two moments of response metrics and failure probabilities. This analysis enables determining the parameters that should be considered uncertain as well as those that can be assumed to be constants without incurring significant error. The analytical nature of the approach eliminates the numerical error that characterizes the sampling-based techniques commonly used to propagate aleatory uncertainties as well as the possibility of under predicting the range of the statistic of interest that may result from searching for the best- and worstcase epistemic values via nonlinear optimization or sampling.

Crespo, Luis G.↗
NASA NTRS2011

Combined Retrievals of Boreal Forest Fire Aerosol Properties with a Polarimeter and Lidar

Absorbing aerosols play an important, but uncertain, role in the global climate. Much of this uncertainty is due to a lack of adequate aerosol measurements. While great strides have been made in observational capability in the previous years and decades, it has become increasingly apparent that this development must continue. Scanning polarimeters have been designed to help resolve this issue by making accurate, multi-spectral, multi-angle polarized observations. This work involves the use of the Research Scanning Polarimeter (RSP). The RSP was designed as the airborne prototype for the Aerosol Polarimetery Sensor (APS), which was due to be launched as part of the (ultimately failed) NASA Glory mission. Field observations with the RSP, however, have established that simultaneous retrievals of aerosol absorption and vertical distribution over bright land surfaces are quite uncertain. We test a merger of RSP and High Spectral Resolution Lidar (HSRL) data with observations of boreal forest fire smoke, collected during the Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS). During ARCTAS, the RSP and HSRL instruments were mounted on the same aircraft, and validation data were provided by instruments on an aircraft flying a coordinated flight pattern. We found that the lidar data did indeed improve aerosol retrievals using an optimal estimation method, although not primarily because of the constraints imposed on the aerosol vertical distribution. The more useful piece of information from the HSRL was the total column aerosol optical depth, which was used to select the initial value (optimization starting point) of the aerosol number concentration. When ground based sun photometer network climatologies of number concentration were used as an initial value, we found that roughly half of the retrievals had unrealistic sizes and imaginary indices, even though the retrieved spectral optical depths agreed within uncertainties to independent observations. The convergence to an unrealistic local minimum by the optimal estimator is related to the relatively low sensitivity to particles smaller than 0.1 ( m) at large optical thicknesses. Thus, optimization algorithms used for operational aerosol retrievals of the fine mode size distribution, when the total optical depth is large, will require initial values generated from table look-ups that exclude unrealistic size/complex index mixtures. External constraints from lidar on initial values used in the optimal estimation methods will also be valuable in reducing the likelihood of obtaining spurious retrievals.

Knobelspiesse, K.↗
NASA NTRS2012

Using Markov Models of Fault Growth Physics and Environmental Stresses to Optimize Control Actions

A generalized Markov chain representation of fault dynamics is presented for the case that available modeling of fault growth physics and future environmental stresses can be represented by two independent stochastic process models. A contrived but representatively challenging example will be presented and analyzed, in which uncertainty in the modeling of fault growth physics is represented by a uniformly distributed dice throwing process, and a discrete random walk is used to represent uncertain modeling of future exogenous loading demands to be placed on the system. A finite horizon dynamic programming algorithm is used to solve for an optimal control policy over a finite time window for the case that stochastic models representing physics of failure and future environmental stresses are known, and the states of both stochastic processes are observable by implemented control routines. The fundamental limitations of optimization performed in the presence of uncertain modeling information are examined by comparing the outcomes obtained from simulations of an optimizing control policy with the outcomes that would be achievable if all modeling uncertainties were removed from the system.

Bole, Brian↗
NASA NTRS2013

An Extremely Luminous and Variable Ultraluminous X-ray Source in the Outskirts of Circinus Observed with Nustar

Following a serendipitous detection with the Nuclear Spectroscopic Telescope Array (NuSTAR), we present a multiepoch spectral and temporal analysis of an extreme ultraluminous X-ray source (ULX) located in the outskirts of the Circinus galaxy, hereafter Circinus ULX5, including coordinated XMM-Newton+NuSTAR follow-up observations. The NuSTAR data presented here represent one of the first instances of a ULX reliably detected at hard (E greater than 10 keV) X-rays. CircinusULX5is variable on long time scales by at least a factor of approx. 5 in flux, and was caught in a historically bright state during our 2013 observations (0.3-30.0 keV luminosity of 1.6 × 10(exp 40) erg s(exp−1)). During this epoch, the source displayed a curved 3-10 keV spectrum, broadly similar to other bright ULXs. Although pure thermal models result in a high energy excess in the NuSTAR data, this excess is too weak to be modeled with the disk reflection interpretation previously proposed to explain the 3-10 keV curvature in other ULXs. In addition to flux variability, clear spectral variability is also observed. While in many cases the interpretation of spectral components in ULXs is uncertain, the spectral and temporal properties of all the high quality data sets currently available strongly support a simple disk-corona model reminiscent of that invoked for Galactic binaries, with the accretion disk becoming more prominent as the luminosity increases. However, although the disk temperature and luminosity are well correlated across all time scales currently probed, the observed luminosity follows L alpha T (exp 1.70+/-0.17), flatter than expected for simple blackbody radiation. The spectral variability displayed here is highly reminiscent of that observed from known Galactic black hole binaries (BHBs) at high luminosities. This comparison implies a black hole mass of approx. 90M for Circinus ULX5. However, given the diverse behavior observed from Galactic BHB accretion disks, this mass estimate is still uncertain. Finally, the limits placed on any undetected iron absorption features with the 2013 data set imply that we are not viewing the central regions of Circinus ULX5 through any extreme super-Eddington outflow.

black hole physics↗
NASA NTRS2014

Combined Uncertainty and A-Posteriori Error Bound Estimates for CFD Calculations: Theory and Implementation

Simulation codes often utilize finite-dimensional approximation resulting in numerical error. Some examples include, numerical methods utilizing grids and finite-dimensional basis functions, particle methods using a finite number of particles. These same simulation codes also often contain sources of uncertainty, for example, uncertain parameters and fields associated with the imposition of initial and boundary data,uncertain physical model parameters such as chemical reaction rates, mixture model parameters, material property parameters, etc.

CFD↗
NASA NTRS2015

Uncertainty Quantification of Turbulence Model Closure Coefficients for Transonic Wall-Bounded Flows

The goal of this work was to quantify the uncertainty and sensitivity of commonly used turbulence models in Reynolds-Averaged Navier-Stokes codes due to uncertainty in the values of closure coefficients for transonic, wall-bounded flows and to rank the contribution of each coefficient to uncertainty in various output flow quantities of interest. Specifically, uncertainty quantification of turbulence model closure coefficients was performed for transonic flow over an axisymmetric bump at zero degrees angle of attack and the RAE 2822 transonic airfoil at a lift coefficient of 0.744. Three turbulence models were considered: the Spalart-Allmaras Model, Wilcox (2006) k-w Model, and the Menter Shear-Stress Trans- port Model. The FUN3D code developed by NASA Langley Research Center was used as the flow solver. The uncertainty quantification analysis employed stochastic expansions based on non-intrusive polynomial chaos as an efficient means of uncertainty propagation. Several integrated and point-quantities are considered as uncertain outputs for both CFD problems. All closure coefficients were treated as epistemic uncertain variables represented with intervals. Sobol indices were used to rank the relative contributions of each closure coefficient to the total uncertainty in the output quantities of interest. This study identified a number of closure coefficients for each turbulence model for which more information will reduce the amount of uncertainty in the output significantly for transonic, wall-bounded flows.

Schaefer, John↗
NASA NTRS2016

Lightning NOx and Impacts on Air Quality

Lightning generates relatively large but uncertain quantities of nitrogen oxides, critical precursors for ozone and hydroxyl radical (OH), the primary tropospheric oxidants. Lightning nitrogen oxide strongly influences background ozone and OH due to high ozone production efficiencies in the free troposphere, effecting small but non-negligible contributions to surface pollutant concentrations. Lightning globally contributes 3-4 ppbv of simulated annual-mean policy-relevant background (PRB) surface ozone, comprised of local, regional, and hemispheric components, and up to 18 ppbv during individual events. Feedbacks via methane may counter some of these effects on decadal time scales. Lightning contributes approximately 1 percent to annual-mean surface particulate matter, as a direct precursor and by promoting faster oxidation of other precursors. Lightning also ignites wildfires and contributes to nitrogen deposition. Urban pollution influences lightning itself, with implications for regional lightning-nitrogen oxide production and feedbacks on downwind surface pollution. How lightning emissions will change in a warming world remains uncertain.

Reactive nitrogen oxides↗
NASA NTRS2016

Uncertainty and Sensitivity Analysis of Afterbody Radiative Heating Predictions for Earth Entry

The objective of this work was to perform sensitivity analysis and uncertainty quantification for afterbody radiative heating predictions of Stardust capsule during Earth entry at peak afterbody radiation conditions. The radiation environment in the afterbody region poses significant challenges for accurate uncertainty quantification and sensitivity analysis due to the complexity of the flow physics, computational cost, and large number of un-certain variables. In this study, first a sparse collocation non-intrusive polynomial chaos approach along with global non-linear sensitivity analysis was used to identify the most significant uncertain variables and reduce the dimensions of the stochastic problem. Then, a total order stochastic expansion was constructed over only the important parameters for an efficient and accurate estimate of the uncertainty in radiation. Based on previous work, 388 uncertain parameters were considered in the radiation model, which came from the thermodynamics, flow field chemistry, and radiation modeling. The sensitivity analysis showed that only four of these variables contributed significantly to afterbody radiation uncertainty, accounting for almost 95% of the uncertainty. These included the electronic- impact excitation rate for N between level 2 and level 5 and rates of three chemical reactions in uencing N, N(+), O, and O(+) number densities in the flow field.

West, Thomas K., IV↗
NASA NTRS2015

Ammonia and Methane Dairy Emission Plumes in the San Joaquin Valley of California from Individual Feedlot to Regional Scales

Agricultural ammonia (NH3) emissions are highly uncertain, with high spatiotemporal variability and a lack of widespread in situ measurements. Regional NH3 emission estimates using mass balance or emission ratio approaches are uncertain due to variable NH3 sources and sinks as well as unknown plume correlations with other dairy source tracers. We characterize the spatial distributions of NH3 and methane (CH4) dairy plumes using in situ surface and airborne measurements in the Tulare dairy feedlot region of the San Joaquin Valley, California, during the NASA Deriving Information on Surface conditions from Column and Vertically Resolved Observations Relevant to Air Quality 2013 field campaign. Surface NH3 and CH4 mixing ratios exhibit large variability with maxima localized downwind of individual dairy feedlots. The geometric mean NH3:CH4 enhancement ratio derived from surface measurements is 0.15 +/- 0.03 ppmv ppmv−1. Individual dairy feedlots with spatially distinct NH3 and CH4 source pathways led to statistically significant correlations between NH3 and CH4 in 68% of the 69 downwind plumes sampled. At longer sampling distances, the NH3:CH4 enhancement ratio decreases 20-30%, suggesting the potential for NH3 deposition as a loss term for plumes within a few kilometers downwind of feedlots. Aircraft boundary layer transect measurements directly above surface mobile measurements in the dairy region show comparable gradients and geometric mean enhancement ratios within measurement uncertainties, even when including NH3 partitioning to submicron particles. Individual NH3 and CH4 plumes sampled at close proximity where losses are minimal are not necessarily correlated due to lack of mixing and distinct source pathways. Our analyses have important implications for constraining NH3 sink and plume variability influences on regional NH3 emission estimates and for improving NH3 emission inventory spatial allocations.

Miller, David J.↗
NASA NTRS2017

A Probabilistic Asteroid Impact Risk Model

Asteroid threat assessment requires the quantification of both the impact likelihood and resulting consequence across the range of possible events. This paper presents a probabilistic asteroid impact risk (PAIR) assessment model developed for this purpose. The model incorporates published impact frequency rates with state-of-the-art consequence assessment tools, applied within a Monte Carlo framework that generates sets of impact scenarios from uncertain parameter distributions. Explicit treatment of atmospheric entry is included to produce energy deposition rates that account for the effects of thermal ablation and object fragmentation. These energy deposition rates are used to model the resulting ground damage, and affected populations are computed for the sampled impact locations. The results for each scenario are aggregated into a distribution of potential outcomes that reflect the range of uncertain impact parameters, population densities, and strike probabilities. As an illustration of the utility of the PAIR model, the results are used to address the question of what minimum size asteroid constitutes a threat to the population. To answer this question, complete distributions of results are combined with a hypothetical risk tolerance posture to provide the minimum size, given sets of initial assumptions. Model outputs demonstrate how such questions can be answered and provide a means for interpreting the effect that input assumptions and uncertainty can have on final risk-based decisions. Model results can be used to prioritize investments to gain knowledge in critical areas or, conversely, to identify areas where additional data has little effect on the metrics of interest.

Asteroid↗