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NASA NTRS1989

Robustness analysis for real parametric uncertainty

Some key results in the literature in the area of robustness analysis for linear feedback systems with structured model uncertainty are reviewed. Some new results are given. Model uncertainty is described as a combination of real uncertain parameters and norm bounded unmodeled dynamics. Here the focus is on the case of parametric uncertainty. An elementary and unified derivation of the celebrated theorem of Kharitonov and the Edge Theorem is presented. Next, an algorithmic approach for robustness analysis in the cases of multilinear and polynomic parametric uncertainty (i.e., the closed loop characteristic polynomial depends multilinearly and polynomially respectively on the parameters) is given. The latter cases are most important from practical considerations. Some novel modifications in this algorithm which result in a procedure of polynomial time behavior in the number of uncertain parameters is outlined. Finally, it is shown how the more general problem of robustness analysis for combined parametric and dynamic (i.e., unmodeled dynamics) uncertainty can be reduced to the case of polynomic parametric uncertainty, and thus be solved by means of the algorithm.

Sideris, Athanasios↗

NASA NTRS2004

Development of an Expert Judgement Elicitation and Calibration Methodology for Risk Analysis in Conceptual Vehicle Design

A comprehensive expert-judgment elicitation methodology to quantify input parameter uncertainty and analysis tool uncertainty in a conceptual launch vehicle design analysis has been developed. The ten-phase methodology seeks to obtain expert judgment opinion for quantifying uncertainties as a probability distribution so that multidisciplinary risk analysis studies can be performed. The calibration and aggregation techniques presented as part of the methodology are aimed at improving individual expert estimates, and provide an approach to aggregate multiple expert judgments into a single probability distribution. The purpose of this report is to document the methodology development and its validation through application to a reference aerospace vehicle. A detailed summary of the application exercise, including calibration and aggregation results is presented. A discussion of possible future steps in this research area is given.

Unal, Resit↗

NASA NTRS2007

Numerical Uncertainty Quantification for Radiation Analysis Tools

Recently a new emphasis has been placed on engineering applications of space radiation analyses and thus a systematic effort of Verification, Validation and Uncertainty Quantification (VV&UQ) of the tools commonly used for radiation analysis for vehicle design and mission planning has begun. There are two sources of uncertainty in geometric discretization addressed in this paper that need to be quantified in order to understand the total uncertainty in estimating space radiation exposures. One source of uncertainty is in ray tracing, as the number of rays increase the associated uncertainty decreases, but the computational expense increases. Thus, a cost benefit analysis optimizing computational time versus uncertainty is needed and is addressed in this paper. The second source of uncertainty results from the interpolation over the dose vs. depth curves that is needed to determine the radiation exposure. The question, then, is what is the number of thicknesses that is needed to get an accurate result. So convergence testing is performed to quantify the uncertainty associated with interpolating over different shield thickness spatial grids.

Anderson, Brooke↗

NASA NTRS1996

Concurrent Probabilistic Simulation of High Temperature Composite Structural Response

A computational structural/material analysis and design tool which would meet industry's future demand for expedience and reduced cost is presented. This unique software 'GENOA' is dedicated to parallel and high speed analysis to perform probabilistic evaluation of high temperature composite response of aerospace systems. The development is based on detailed integration and modification of diverse fields of specialized analysis techniques and mathematical models to combine their latest innovative capabilities into a commercially viable software package. The technique is specifically designed to exploit the availability of processors to perform computationally intense probabilistic analysis assessing uncertainties in structural reliability analysis and composite micromechanics. The primary objectives which were achieved in performing the development were: (1) Utilization of the power of parallel processing and static/dynamic load balancing optimization to make the complex simulation of structure, material and processing of high temperature composite affordable; (2) Computational integration and synchronization of probabilistic mathematics, structural/material mechanics and parallel computing; (3) Implementation of an innovative multi-level domain decomposition technique to identify the inherent parallelism, and increasing convergence rates through high- and low-level processor assignment; (4) Creating the framework for Portable Paralleled architecture for the machine independent Multi Instruction Multi Data, (MIMD), Single Instruction Multi Data (SIMD), hybrid and distributed workstation type of computers; and (5) Market evaluation. The results of Phase-2 effort provides a good basis for continuation and warrants Phase-3 government, and industry partnership.

Abdi, Frank↗

NASA NTRS1991

Study of geopotential error models used in orbit determination error analysis

The uncertainty in the geopotential model is currently one of the major error sources in the orbit determination of low-altitude Earth-orbiting spacecraft. The results of an investigation of different geopotential error models and modeling approaches currently used for operational orbit error analysis support at the Goddard Space Flight Center (GSFC) are presented, with emphasis placed on sequential orbit error analysis using a Kalman filtering algorithm. Several geopotential models, known as the Goddard Earth Models (GEMs), were developed and used at GSFC for orbit determination. The errors in the geopotential models arise from the truncation errors that result from the omission of higher order terms (omission errors) and the errors in the spherical harmonic coefficients themselves (commission errors). At GSFC, two error modeling approaches were operationally used to analyze the effects of geopotential uncertainties on the accuracy of spacecraft orbit determination - the lumped error modeling and uncorrelated error modeling. The lumped error modeling approach computes the orbit determination errors on the basis of either the calibrated standard deviations of a geopotential model's coefficients or the weighted difference between two independently derived geopotential models. The uncorrelated error modeling approach treats the errors in the individual spherical harmonic components as uncorrelated error sources and computes the aggregate effect using a combination of individual coefficient effects. This study assesses the reasonableness of the two error modeling approaches in terms of global error distribution characteristics and orbit error analysis results. Specifically, this study presents the global distribution of geopotential acceleration errors for several gravity error models and assesses the orbit determination errors resulting from these error models for three types of spacecraft - the Gamma Ray Observatory, the Ocean Topography Experiment, and the Cosmic Background Explorer.

Yee, C.↗

NASA NTRSDate not supplied

Accounting for Point Estimate Uncertainty in Space Systems Reliability and Risk Analysis

Understanding and accounting for uncertainty in risk analysis is a critical step in the management and communication of risk in engineered systems. The component and system-level analysis to determine the probability of a negative outcome and its consequence is often quantified by a point estimate. Many Program and Enterprise decisions involving technical concerns and issues rely on reliability engineering activities to produce quantified risk analysis to inform the decision making process. At NASA, it is common to use a Probabilistic Risk Analysis (PRA) to inform the overall risk to Loss of Mission or Loss of Crew that involves integration across all spacecraft subsystem fault trees to produce an overall probability of mission failure. The point estimate is an estimate of this overall probability and is an immediate result of a fault tree model. It is the result of a model where the probability of each event is taken to be equal to its mean. The value provides an approximation of the overall mean without running any uncertainty calculations (e.g., no sampling). Using only the point estimate can lead to a false sense of precision and the point estimate may not match the resulting mean when uncertainty is taken into consideration. This paper will explore five conditions that can cause the PRA model mean to diverge from the point estimate and will provide engineers and managers insight into the importance of understanding uncertainty in the elements of PRA models.

Paul J Collier↗

NASA NTRS2010

Reduced Uncertainties in the Flutter Analysis of the Aerostructures Test Wing

Tuning the finite element model using measured data to minimize the model uncertainties is a challenging task in the area of structural dynamics. A test validated finite element model can provide a reliable flutter analysis to define the flutter placard speed to which the aircraft can be flown prior to flight flutter testing. Minimizing the difference between numerical and experimental results is a type of optimization problem. Through the use of the National Aeronautics and Space Administration Dryden Flight Research Center s (Edwards, California, USA) multidisciplinary design, analysis, and optimization tool to optimize the objective function and constraints; the mass properties, the natural frequencies, and the mode shapes are matched to the target data and the mass matrix orthogonality is retained. The approach in this study has been applied to minimize the model uncertainties for the structural dynamic model of the aerostructures test wing, which was designed, built, and tested at the National Aeronautics and Space Administration Dryden Flight Research Center. A 25-percent change in flutter speed has been shown after reducing the uncertainties

Pak, Chan-gi↗

NASA NTRS2011

Reduced Uncertainties in the Flutter Analysis of the Aerostructures Test Wing

Tuning the finite element model using measured data to minimize the model uncertainties is a challenging task in the area of structural dynamics. A test validated finite element model can provide a reliable flutter analysis to define the flutter placard speed to which the aircraft can be flown prior to flight flutter testing. Minimizing the difference between numerical and experimental results is a type of optimization problem. Through the use of the National Aeronautics and Space Administration Dryden Flight Research Center's (Edwards, California) multidisciplinary design, analysis, and optimization tool to optimize the objective function and constraints; the mass properties, the natural frequencies, and the mode shapes are matched to the target data, and the mass matrix orthogonality is retained. The approach in this study has been applied to minimize the model uncertainties for the structural dynamic model of the aerostructures test wing, which was designed, built, and tested at the National Aeronautics and Space Administration Dryden Flight Research Center. A 25 percent change in flutter speed has been shown after reducing the uncertainties.

Pak, Chan-Gi↗

NASA NTRSDate not supplied

Uncertainty Quantification and Sensitivity Analysis in Process-Structure-Property Simulations for Laser Powder Bed Fusion Additive Manufacturing

Process variations and process-induced defects like porosity cause significant uncertainty in the microstructure and mechanical behavior of additively manufactured metals. Establishing process-structure-property (PSP) relationships and quantifying uncertainty using experiments alone is costly, especially for structural applications where mechanical allowables must be established for qualification and certification. This work presents a PSP simulation framework for laser powder bed fusion with a focus on uncertainty quantification through probabilistic calibration and multi-fidelity uncertainty propagation. Motivated by phenomenological input parameters related to grain nucleation and growth that are difficult to characterize, a global sensitivity analysis (GSA) is completed. Through GSA, the most important input parameters are identified based on their influence on the statistical distributions of microstructural metrics that influence mechanical behavior, including grain size, morphology, and crystallographic texture. The results provide insight on what experiments are necessary to quantify and control PSP uncertainties, particularly those associated with the more challenging input parameters.

additive manufacturing↗

NASA NTRS1993

Several examples where turbulence models fail in inlet flow field analysis

Computational uncertainties in turbulence modeling for three dimensional inlet flow fields include flows approaching separation, strength of secondary flow field, three dimensional flow predictions of vortex liftoff, and influence of vortex-boundary layer interactions; computational uncertainties in vortex generator modeling include representation of generator vorticity field and the relationship between generator and vorticity field. The objectives of the inlet flow field studies presented in this document are to advance the understanding, prediction, and control of intake distortion and to study the basic interactions that influence this design problem.

Anderson, Bernhard H.↗

NASA NTRS1996

Uncertainty Modeling for Structural Control Analysis and Synthesis

The development of an accurate model of uncertainties for the control of structures that undergo a change in operational environment, based solely on modeling and experimentation in the original environment is studied. The application used throughout this work is the development of an on-orbit uncertainty model based on ground modeling and experimentation. A ground based uncertainty model consisting of mean errors and bounds on critical structural parameters is developed. The uncertainty model is created using multiple data sets to observe all relevant uncertainties in the system. The Discrete Extended Kalman Filter is used as an identification/parameter estimation method for each data set, in addition to providing a covariance matrix which aids in the development of the uncertainty model. Once ground based modal uncertainties have been developed, they are localized to specific degrees of freedom in the form of mass and stiffness uncertainties. Two techniques are presented: a matrix method which develops the mass and stiffness uncertainties in a mathematical manner; and a sensitivity method which assumes a form for the mass and stiffness uncertainties in macroelements and scaling factors. This form allows the derivation of mass and stiffness uncertainties in a more physical manner. The mass and stiffness uncertainties of the ground based system are then mapped onto the on-orbit system, and projected to create an analogous on-orbit uncertainty model in the form of mean errors and bounds on critical parameters. The Middeck Active Control Experiment is introduced as experimental verification for the localization and projection methods developed. In addition, closed loop results from on-orbit operations of the experiment verify the use of the uncertainty model for control analysis and synthesis in space.

Campbell, Mark E.↗

NASA NTRS1990

Attitude determination error analysis - General model and specific application

This paper presents a comprehensive approach to filter and dynamics modeling for attitude determination error analysis. The discussion includes models for both batch least-squares and sequential estimators, a specific dynamic model for attitude determination error analysis of a three-axis stabilized spacecraft equipped with strapdown gyros, and the incorporation of general attitude sensor observations. An analyst using this approach to perform an error analysis chooses a subset of the spacecraft parameters to be 'solve-for' parameters, which are to be estimated, and another subset to be 'consider' parameters, which are assumed to have errors but not to be estimated. The result of the error analysis is an indication of overall uncertainties in the 'solve-for' parameters, as well as the contributions of the various error sources to these uncertainties, including those of errors in the a priori 'solve-for' estimates, of measurement noise, of dynamic noise (also known as process noise or plant noise), and of 'consider' parameter uncertainties. The analysis of attitude, star tracker alignment, and gyro bias uncertainties for the Gamma Ray Observatory spacecraft provide a specific example of the use of a general-purpose software package incorporating these models.

Markley, F. Landis↗

NASA NTRS2019

A Double Bootstrap Approach to Superposed Epoch Analysis to Evaluate Response Uncertainty

The association between climate variability and episodic events, such as the antecedent moisture conditions prior to wildfire or the cooling following volcanic eruptions, is commonly assessed using Superposed Epoch Analysis (SEA). In SEA the epochal response is typically calculated as the average climate conditions prior to and following all event years or their deviation from climatology. However, the magnitude and significance of the inferred climate association may be sensitive to the selection or omission of individual key years, potentially resulting in a biased assessment of the relationship between these events and climate. Here we describe and test a modified double-bootstrap SEA that generates multiple unique draws of the key years and evaluates the sign, magnitude, and significance of event-climate relationships within a probabilistic framework. This multiple resampling helps quantify multiple uncertainties inherent in conventional applications of SEA within dendrochronology and paleoclimatology. We demonstrate our modified SEA by evaluating the volcanic cooling signal in a Northern Hemisphere tree-ring temperature reconstruction and the link between drought and wildfire events in the western United States. Finally, we make our Matlab and R code available to be adapted for future SEA applications.

Dendroclimatology↗

NASA NTRS2017

Aeroelastic Uncertainty Quantification Studies Using the S4T Wind Tunnel Model

This paper originates from the joint efforts of an aeroelastic study team in the Applied Vehicle Technology Panel from NATO Science and Technology Organization, with the Task Group number AVT-191, titled "Application of Sensitivity Analysis and Uncertainty Quantification to Military Vehicle Design." We present aeroelastic uncertainty quantification studies using the SemiSpan Supersonic Transport wind tunnel model at the NASA Langley Research Center. The aeroelastic study team decided treat both structural and aerodynamic input parameters as uncertain and represent them as samples drawn from statistical distributions, propagating them through aeroelastic analysis frameworks. Uncertainty quantification processes require many function evaluations to asses the impact of variations in numerous parameters on the vehicle characteristics, rapidly increasing the computational time requirement relative to that required to assess a system deterministically. The increased computational time is particularly prohibitive if high-fidelity analyses are employed. As a remedy, the Istanbul Technical University team employed an Euler solver in an aeroelastic analysis framework, and implemented reduced order modeling with Polynomial Chaos Expansion and Proper Orthogonal Decomposition to perform the uncertainty propagation. The NASA team chose to reduce the prohibitive computational time by employing linear solution processes. The NASA team also focused on determining input sample distributions.

Nikbay, Melike↗

NASA NTRS2019

Improvements in the Uncertainty Model in the Goddard Institute for Space Studies Surface Temperature (GISTEMP) Analysis

We outline a new and improved uncertainty analysis for the Goddard Institute of Space Studies (GISS) Surface Temperature product version 4 (GISTEMP v4). Historical spatial variations in surface temperature anomalies are derived from historical weather station data and ocean data from ships, buoys and other sensors. Uncertainties arise from measurement uncertainty, changes in spatial coverage of the station record, and systematic biases due to technology shifts and land cover changes. Previously published uncertainty estimates for GISTEMP included only the effect of incomplete station coverage. Here, we update this term using currently available spatial distributions of source data, state‐of‐the‐art reanalyses and incorporate independently derived estimates for ocean data processing, station homogenization and other structural biases. The resulting 95% uncertainties are near 0.05° C in the global annual mean for the last 50 years, and increase going back further in time reaching 0.15° C in 1880. In addition, we quantify the benefits and inherent uncertainty due to the GISTEMP interpolation and averaging method. We use the total uncertainties to estimate the probability for each record year in the GISTEMP to actually be the true record year (to that date), and conclude with 86% likelihood that 2016 was indeed the hottest year of the instrumental period (so far).

Nathan J L Lenssen↗

NASA NTRS2011

Assessment of MODIS Thermal Emissive Band On-Orbit Calibration

Sixteen Moderate Resolution Imaging Spectroradiometer thermal emissive bands (TEBs) cover the wavelength from 3.75 to 14.24 m. TEB calibration uses data collected from the detector responses to the onboard blackbody (BB) and space view. The BB was designed to operate either at a constant temperature for detector linear gain calibration or at temperatures varying from ambient ( 270 K) to 315 K for on-orbit characterization of nonlinear coefficients. In this paper, we assess TEB on-orbit calibration performance in two aspects: One is to review the calibration trending on the orbital, daily, and multiyear timescales, and the other is to analyze the on-orbit calibration radiance uncertainty and its impact on the calibration. The calibration trending confirms the detector response dependence on the instrument temperature. The temperature trending and prelaunch characterization provide the basis for determining the calibration radiance source temperature range and uncertainties. An analytical approach was used to assess the impacts of onboard radiance uncertainties. The BB emission uncertainty, resulting from the temperature measurement error and emissivity uncertainty, causes a calibration uncertainty up to 0.3%, a value decreasing with the band wavelength. The BB nonblackness effect is analyzed and found to be insignificant. For the band with the lowest BB emissivity, the nonblackness affects the calibration radiance by less than 0.08%. The cavity emission uncertainty and the scan-mirror emission uncertainty both cause a less than 0.1% calibration uncertainty. The analysis of the nonlinear calibration coefficient uncertainty shows that its effect on the low Earth-view brightness-temperature range varies by band and is generally insignificant.

Chang, Tiejun↗

NASA NTRS1991

mu analysis with real parametric uncertainty

The authors give a broad overview, from a LFT (linear fractional transformation)/mu perspective, of some of the theoretical and practical issues associated with robustness in the presence of real parametric uncertainty, with a focus on computation. Recent results on the properties of mu in the mixed case are reviewed, including issues of NP completeness, continuity, computation of bounds, the equivalence of mu and its bounds, and some direct comparisons with Kharitonov-type analysis methods. In addition, some advances in the computational aspects of the problem, including a novel branch and bound algorithm, are briefly presented together with numerical results. The results suggest that while the mixed mu problem may have inherently combinatoric worst-case behavior, practical algorithms with modest computational requirements can be developed for problems of medium size (less than 100 parameters) that are of engineering interest.

Young, Peter M.↗

NASA NTRSDate not supplied

Uncertainty Quantification Methodology for Sonic Boom Loudness of a Low-Boom Supersonic Concept

This paper presents a comprehensive analysis of uncertainty quantification for sonic boom loudness metrics associated with the X-59 aircraft during its acoustic validation phase. The study focuses on employing advanced methodologies to characterize uncertainties in key sonic boom parameters predicted from a database derived from a computational fluid dynamics (CFD) solver. These methodologies include creating a polynomial chaos expansion (PCE) surrogate model, which is then used to run a Monte Carlo analysis to obtain 95% uncertainty intervals for sonic boom loudness parameters across the full carpet. Atmospheric uncertainties are rigorously considered, leveraging weather models based on historical data near Edwards Air Force Base to simulate potential flight conditions. The findings include preliminary uncertainty results for the full carpet during the validation phase of the Quesst mission. Additionally, a sensitivity study reveals that the primary sources of uncertainty are humidity and cruise weight.

Laura M. White↗