The effects of tracking station location uncertainty and measurement bias errors during phases of the Apollo mission
Effects of measurement noise, measurement bias, and station location uncertainties on Apollo mission phases
NAVIGATION SYSTEM↗
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Stochastic multiscale modeling for quantifying statistical and model errors with application to composite materials
This paper provides a coherent and efficient computational framework for stochastic multiscale analysis of material systems in the presence of parametric uncertainties and modeling errors. Uncertainty in those model parameters that are not deduced as upscaled quantities is attributed to an uncertainty “germ”. While such parameters can appear at any scale, they are predominant at the finest analysis scale. Additional uncertainties stemming from statistical estimation, attributed to lack of data and model error, are associated with each submodel contributing to the multiscale system. Here, a robust and efficient framework based on a generalized extended polynomial chaos expansion (gEPCE) is proposed to simultaneously propagate all these uncertainties in order to provide a probabilistic representation of specific quantities of interest (QoI). We characterize the full probability distribution of the QoI and the uncertainty in the failure probability pertaining to its tails. By combining gEPCE with kernel density estimation (KDE) and directional derivatives, we construct sensitivity measures that connect these statistical metrics of QoI to the various sources of uncertainty to assess their individual and combined impacts. An illustrative problem featuring three-point bending of a composite beam is investigated to demonstrate the presented approach.
36 MATERIALS SCIENCE↗
Role of Forcing Uncertainty and Background Model Error Characterization in Snow Data Assimilation
Accurate specification of the model error covariances in data assimilation systems is a challenging issue. Ensemble land data assimilation methods rely on stochastic perturbations of input forcing and model prognostic fields for developing representations of input model error covariances. This article examines the limitations of using a single forcing dataset for specifying forcing uncertainty inputs for assimilating snow depth retrievals. Using an idealized data assimilation experiment, the article demonstrates that the use of hybrid forcing input strategies (either through the use of an ensemble of forcing products or through the added use of the forcing climatology) provide a better characterization of the background model error, which leads to improved data assimilation results, especially during the snow accumulation and melt-time periods. The use of hybrid forcing ensembles is then employed for assimilating snow depth retrievals from the AMSR2 (Advanced Microwave Scanning Radiometer 2) instrument over two domains in the continental USA with different snow evolution characteristics. Over a region near the Great Lakes, where the snow evolution tends to be ephemeral, the use of hybrid forcing ensembles provides significant improvements relative to the use of a single forcing dataset. Over the Colorado headwaters characterized by large snow accumulation, the impact of using the forcing ensemble is less prominent and is largely limited to the snow transition time periods. The results of the article demonstrate that improving the background model error through the use of a forcing ensemble enables the assimilation system to better incorporate the observational information.
assimilation↗
The Effects of Thrust Uncertainty and Attitude Knowledge Errors on the MMS Formation Maintenance Maneuver
The Magnetospheric Multiscale (MMS) Mission will use a formation of four spinning spacecraft to study the Earth s magnetosphere. The science objectives of MMS require a near-regular tetrahedron formation to be maintained with side lengths ranging from ten kilometers to several thousand kilometers at orbit apogee. To reduce spacecraft complexity and cost, the current mission concept assumes MMS can achieve its formation goals through open-loop orbit control from the ground, rather than in-flight, closed-loop formation control that has been the subject of recent study. Significant analysis has been performed to provide optimal reference orbit and relative orbit designs. However, the feasibility of achieving these orbits, and maintaining them for an extended period of time in the presence of real world errors and perturbations has not been investigated. In particular, attitude knowledge and control errors, which may have a negligible effect on orbit control for conventional missions with spinning spacecraft, can contribute significant errors to the MMS orbits. In this work, a 6 degree-of-freedom (DOF) simulation is developed and used to analyze the effects of realistic errors on formation maintenance maneuver accuracy. Several realistic considerations including a finite-burn model, attitude perturbations, and thrust uncertainty are studied. The primary objective is to quantify the effects of realistic attitude and orbit control, knowledge, and actuator errors on the formation geometry by observing representative maneuver errors of a single spacecraft.
Tsai, Dean C.↗
The Relationship Between Two Methods for Estimating Uncertainties in Data Assimilation
This note examines the relationship between two apparently unrelated methods for estimating error statistics or uncertainties of relevance to data assimilation. The first method is due to (Desroziers et al., 2005, Q. J. R. Meteorol. Soc., 131, 3385–3396; referred to as DBCP hereafter) and relies on residual statistics readily available from data assimilation applications. The second method, the three- cornered hat (3CH) developed by Gray and Allan (1974, IEEE 28th Annual Symp. Freq. Control, 243–246), only recently applied to atmospheric sciences, uses three data sets and can derive estimates of relevant error uncertainties as well. The usefulness of both methods lies in them not requiring knowledge of the true value of the quantities at play. DBCP derives its results by relying explicitly on the constraints as- sociated with the data assimilation minimization problem; 3CH is general and its estimates hold as long as errors in the three data sets of choice are uncorrelated. Establishing the relationship between the methods requires applying the 3CH approach to the same observation, background, and analysis data sets used by DBCP. In this case, the same assumptions of DBCP on residual errors allow for cancellation of error cross–covariance terms in 3CH such that two of its corners derive identical estimates for observation and background error covariances as those of DBCP. The error cross–covariance terms associated with the third corner are shown to add up to twice the analysis error covariance so that the 3CH estimate for the third corner recovers the negative of the analysis error covariance. Illustrations of these findings are provided by deriving uncertainties for radio occultation bending angles.
Ricardo Todling↗
Combined Uncertainty and A-Posteriori Error Bound Estimates for General CFD Calculations: Theory and Software Implementation
This workshop presentation discusses the design and implementation of numerical methods for the quantification of statistical uncertainty, including a-posteriori error bounds, for output quantities computed using CFD methods. Hydrodynamic realizations often contain numerical error arising from finite-dimensional approximation (e.g. numerical methods using grids, basis functions, particles) and statistical uncertainty arising from incomplete information and/or statistical characterization of model parameters and random fields. The first task at hand is to derive formal error bounds for statistics given realizations containing finite-dimensional numerical error [1]. The error in computed output statistics contains contributions from both realization error and the error resulting from the calculation of statistics integrals using a numerical method. A second task is to devise computable a-posteriori error bounds by numerically approximating all terms arising in the error bound estimates. For the same reason that CFD calculations including error bounds but omitting uncertainty modeling are only of limited value, CFD calculations including uncertainty modeling but omitting error bounds are only of limited value. To gain maximum value from CFD calculations, a general software package for uncertainty quantification with quantified error bounds has been developed at NASA. The package provides implementations for a suite of numerical methods used in uncertainty quantification: Dense tensorization basis methods [3] and a subscale recovery variant [1] for non-smooth data, Sparse tensorization methods[2] utilizing node-nested hierarchies, Sampling methods[4] for high-dimensional random variable spaces.
CFD↗
Uncertainties in predicting solar panel power output
The problem of calculating solar panel power output at launch and during a space mission is considered. The major sources of uncertainty and error in predicting the post launch electrical performance of the panel are considered. A general discussion of error analysis is given. Examples of uncertainty calculations are included. A general method of calculating the effect on the panel of various degrading environments is presented, with references supplied for specific methods. A technique for sizing a solar panel for a required mission power profile is developed.
Anspaugh, B.↗
Identifying Bearing Rotordynamic Coefficients using an Extended Kalman Filter
An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor-dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter s performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor-bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.
Miller, Bard A.↗
Identifying Bearing Rotordynamic Coefficients using an Extended Kalman Filter
An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor-dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter s performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor-bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.
Miller, Brad A.↗
Identifying Bearing Rotodynamic Coefficients Using an Extended Kalman Filter
An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter's performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.
Miller, Brad A.↗
Uncertainties in climate data sets
Climate diagnostics are constructed from either analyzed fields or from observational data sets. Those that have been commonly used are normally considered ground truth. However, in most of these collections, errors and uncertainties exist which are generally ignored due to the consistency of usage over time. Examples of uncertainties and errors are described in NMC and ECMWF analyses and in satellite observational sets-OLR, TOVS, and SMMR. It is suggested that these errors can be large, systematic, and not negligible in climate analysis.
Mcguirk, James P.↗
Uncertainty-Aware and Explainable Human Error Detection in the Operation of Nuclear Power Plants
The timely and accurate identification of incidents, such as human factor error, is important to restore nuclear power plants (NPPs) to a stable state. However, the identification of abnormal operating conditions is difficult because of the existence of multiple scenarios. In addition, to implement mitigation actions rapidly after an incident occurs, operators must accurately identify an incident by monitoring the trends of many variables. The mental burden posed by this can increase human error and cause failure in identifying incidents. Failure to identify incidents directly results in erroneous mitigation measures, which are detrimental to NPPs. In this study, we leverage uncertainty-aware models to identify such errors and thereby increase the chances of mitigating them. We use the data collected from a physical test bed. The goal is to identify both certain and accurate models. For this, the two main aspects of focus in this study are explainable artificial intelligence (XAI) and uncertainty quantification (UQ). While XAI elucidates the decision pathway, UQ evaluates decision reliability. Their integration paints a comprehensive picture, signifying that understanding decisions and their confidence should be interlinked. Thus, in this study we leverage UQ measures (e.g. entropy and mutual information) along with Shapley additive explanations to gain insights into the features contributing to both accuracy and uncertainty in error identification. Furthermore, our results show that uncertainty-aware models combined with XAI tools can explain the artificial intelligence–prescribed decisions, with the potential of better explaining errors for the operators.
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
A Best Practices System to Enhance CFD Use in Stability and Control Applications
Successful use of CFD to provide aerodynamics for stability and control (S&C) applications will require that the traditional time and costs associated with CFD be reduced and that the errors and uncertainties currently associated with CFD be better understood. CFD will be required to work under a wide range of flow conditions and provide fast and reliable aerodynamics if it is to contribute to this next generation of S&C analyses. CFD solutions have errors and uncertainties due to poorly converged solutions, solution anomalies caused by grids, turbulence models, and parameter selection, and other manifold reasons. In addition to the above problems, there will be a requirement for communications between the CFD expert and the S&C expert and possibly experts from other related disciplines. The CFD expert may not understand the technical problems associated with S&C, and it is almost certain the converse is true.
Morrison, Joseph H.↗
Curating AI-Ready Datasets for Equity and Environmental Justice: A Data-Centric AI Case Study
An equitable and environmentally just community is essentialin order to avoid disproportionate burden borne by vulnerablecommunities. This need becomes pressing in the aftermathof an extreme event such as disaster or hazard when it is diffi-cult for the governing bodies to implement resource allocationas per the need. Artificial Intelligence (AI) algorithms canhelp surface Equity and Environmental Justice (EEJ) issueswhen trained on EEJ datasets. However, curating AI-readyEEJ training datasets is challenging due to differences in fac-tors such as heterogeneity, resolution, modality, and level ofexpertise in labeling. Additionally, EEJ issues involve sensi-tive information where uncertainties and errors could degradethe performance of AI algorithms. For eg. Error in seasonalcrop yield information can highly affect the prediction of an-nual crop yield. To address these challenges, Data-centricAI (DCAI) methods are employed, which enhance AI algo-rithm performance even with limited training samples. DCAIprioritizes data quality, thereby reducing the adverse effectsof uncertainties and errors during the model training process.This research proposes a novel dataset and benchmark for an-alyzing the effect of the Maui Wildfire of 2023 for Equityand Environmental Justice (EEJ) issues. The proposed datasetaligns with the concepts of DCAI such as annotation quality,data preprocessing, privacy, feature engineering, governanceand provenance. We firmly believe that the proposed datasetwould lay a foundation to implement robust and reliable mod-ern AI algorithms for addressing EEJ issues.
Paridhi Parajuli↗
Real-time Identification and Control of Satellite Signal Impairments Solution and Application of the Stratonovich Equation Part 1. Theoretical Development
As satellite communications systems become both more complex and reliant with respect to their operating environment, it has become imperative to be able to identify, during real-time operation, the onset of one or more impairments to the quality of overall communications system integrity. One of the most important aspects to monitor of a satellite link operating within the Earth's atmosphere is the signal fading due to the occurrence of rain and/or phase scintillations. This, of course, must be done in the presence of the associated measurement uncertainty or potentially faulty measurement equipment such as in the Advanced Communication Technology Satellite (ACTS) experiment. In the present work, an approach originally suggested in 1991, and apparently still considered iconoclastic, will be significantly developed and applied to the satellite communications link on which the deleterious composite signal fade is the result of one or many component fade mechanisms. Through the measurement (with the attendant uncertainty or 'error' in the measurement) of such a composite fading satellite signal, it is desired to extract the level of each of the individual fading mechanisms so they can be appropriately mitigated before they impact the overall performance of the communications network. Rather than employing simple-minded deterministic filtering to the real-time fading, the present approach is built around all the models and/or descriptions used to describe the individual fade components, including their dynamic evolution. The latter is usually given by a first-order Langevin equation. This circumstance allows the description of the associated temporal transition probability densities of each of the component processes. By using this description, along with the real-time measurements of the composite fade (along with the measurement errors), one can obtain statistical estimates of the levels of each of the component fading mechanisms as well as their predicted values into the future. This is all accomplished by the use of the well-known Stratonovich integro-differential equation that results from the model of the measured signal fade that is also tailored to adaptively adjust the values of the parameters used in the statistical models of the individual fade mechanisms. Three examples of increasing complexity are addressed and solved for the iterative determination of fade component levels from the measured composite signal fade in the presence of measurement error and, in the last case, with uncertainty in the model parameters.
Countermeasure↗
A general model for attitude determination error analysis
An overview is given of a comprehensive approach to filter and dynamics modeling for attitude determination error analysis. The models presented include both batch least-squares and sequential attitude estimation processes for both spin-stabilized and three-axis stabilized spacecraft. The discussion includes a brief description of a dynamics model of strapdown gyros, but it does not cover other sensor models. Model parameters can be chosen to be solve-for parameters, which are assumed to be estimated as part of the determination process, or consider parameters, which are assumed to have errors but not to be estimated. The only restriction on this choice is that the time evolution of the consider parameters must not depend on any of the solve-for parameters. The result of an error analysis is an indication of the contributions of the various error sources to the uncertainties in the determination of the spacecraft solve-for parameters. The model presented gives the uncertainty due to errors in the a priori estimates of the solve-for parameters, the uncertainty due to measurement noise, the uncertainty due to dynamic noise (also known as process noise or measurement noise), the uncertainty due to the consider parameters, and the overall uncertainty due to all these sources of error.
Markley, F. Landis↗
Orbit Determination for the 2007 Mars Phoenix Lander
The Phoenix mission is designed to study the arctic region of Mars. To achieve this goal, the spacecraft must be delivered to a narrow corridor at the top of the Martian atmosphere, which is approximately 20 km wide. This paper will discuss the details of the Phoenix orbit determination process and the effort to reduce errors below the level necessary to achieve successful atmospheric entry at Mars. Emphasis will be placed on properly modeling forces that perturb the spacecraft trajectory and the errors and uncertainties associated with those forces. Orbit determination covariance analysis strongly influenced mission operations scenarios, which were chosen to minimize errors and associated uncertainties.
Ryne, Mark S.↗
Nonperturbatively renormalized nucleon gluon momentum fraction in the continuum limit of N f = 2 + 1 + 1 lattice QCD
We present the nonperturbatively renormalized nucleon gluon momentum fraction using ensembles with 2+1+1 flavors of highly improved staggered quarks (HISQ), generated by the MILC Collaboration. The calculation is done using clover fermions for the valence action with three pion masses, 220, 310, and 690 MeV, and three lattice spacings, 0.09, 0.12, and 0.15 fm. The renormalization is done using RI/MOM nonperturbative renormalization and using cluster-decomposition error reduction (CDER) to enhance the signal-to-noise ratio of the renormalization constant. We find the CDER technique is particularly important to improve the signal at the finer lattice ensembles where the lattice volume is larger. We extrapolate the gluon momentum fraction to the continuum-physical limit and obtain $\langle{x}\rangle$ g = 0.502(53) stat+NPR (50) mixing in the $\overline{MS}$ scheme at 2 GeV, where first error includes the statistical error and uncertainties in nonperturbative renormalization, while the latter systematic error accounts for ignoring quark mixing. Our gluon momentum fraction is consistent with other recent lattice-QCD results at physical pion mass.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗