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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Uncertainty Analysis of Inertial Model Attitude Sensor Calibration and Application with a Recommended New Calibration Method

Statistical tools, previously developed for nonlinear least-squares estimation of multivariate sensor calibration parameters and the associated calibration uncertainty analysis, have been applied to single- and multiple-axis inertial model attitude sensors used in wind tunnel testing to measure angle of attack and roll angle. The analysis provides confidence and prediction intervals of calibrated sensor measurement uncertainty as functions of applied input pitch and roll angles. A comparative performance study of various experimental designs for inertial sensor calibration is presented along with corroborating experimental data. The importance of replicated calibrations over extended time periods has been emphasized; replication provides independent estimates of calibration precision and bias uncertainties, statistical tests for calibration or modeling bias uncertainty, and statistical tests for sensor parameter drift over time. A set of recommendations for a new standardized model attitude sensor calibration method and usage procedures is included. The statistical information provided by these procedures is necessary for the uncertainty analysis of aerospace test results now required by users of industrial wind tunnel test facilities.

Tripp, John S.↗
NASA NTRS1984

Utilization of SAGE aerosol profiles in the analysis of Mauna Loa stratospheric lidar data

A systematic approach to analyzing lidar data collected at NOAA's Mauna Loa Observatory (MLO) was developed which relies on parameters derived from SAGE satellite extinction profile measurements to verify boundary conditions applied to analysis. The approach also provides a means of assessing the uncertainties associated with the various inputs, so that the accuracy of the analysis of the MLO lidar data is available. The stratosphere during the 1980 to 1981 period was only mildly perturbed and could be easily represented by the SAMII/SAGE background aerosol model. The MLO lidar observations collected during this period provided stratospheric optical depths with uncertainties ranging between 15% and 25%. Uncertainties in the aerosol optical model contribute errors of 3% to 4% in the computed optical depths. Most of the optical depth uncertainty is associated with the calibration assumption in which no marked improvement can be expected.

Fernald, F. G.↗
NASA NTRS2006

Realistic Covariance Prediction For the Earth Science Constellations

Routine satellite operations for the Earth Science Constellations (ESC) include collision risk assessment between members of the constellations and other orbiting space objects. One component of the risk assessment process is computing the collision probability between two space objects. The collision probability is computed via Monte Carlo techniques as well as numerically integrating relative probability density functions. Each algorithm takes as inputs state vector and state vector uncertainty information for both objects. The state vector uncertainty information is expressed in terms of a covariance matrix. The collision probability computation is only as good as the inputs. Therefore, to obtain a collision calculation that is a useful decision-making metric, realistic covariance matrices must be used as inputs to the calculation. This paper describes the process used by NASA Goddard's Earth Science Mission Operations Project to generate realistic covariance predictions for three of the ESC satellites: Aqua, Aura, and Terra

Duncan, Matthew↗
NASA NTRS2006

Realistic Covariance Prediction for the Earth Science Constellation

Routine satellite operations for the Earth Science Constellation (ESC) include collision risk assessment between members of the constellation and other orbiting space objects. One component of the risk assessment process is computing the collision probability between two space objects. The collision probability is computed using Monte Carlo techniques as well as by numerically integrating relative state probability density functions. Each algorithm takes as inputs state vector and state vector uncertainty information for both objects. The state vector uncertainty information is expressed in terms of a covariance matrix. The collision probability computation is only as good as the inputs. Therefore, to obtain a collision calculation that is a useful decision-making metric, realistic covariance matrices must be used as inputs to the calculation. This paper describes the process used by the NASA/Goddard Space Flight Center's Earth Science Mission Operations Project to generate realistic covariance predictions for three of the Earth Science Constellation satellites: Aqua, Aura and Terra.

Duncan, Matthew↗
NASA NTRSDate not supplied

Estimation of Permanent Magnet Synchronous Motor Parameters using a Linear Unknown Input Interval Observer

This paper develops and evaluate a technique to estimate the speed and unknown load torque of a permanent magnet synchronous motor (PMSM). An interval unknown input observer (UIO) for linear time-invariant (LTI) systems is designed and utilized to estimate the PMSM parameters. Interval UIOs are advantageous as they allow for the estimation of both states and unknown inputs, while accounting for varying uncertainty sources, such as model and measurement uncertainties inherent in dynamic systems and processes. First, the nonlinear PMSM model is linearized to transform it to a suitable form for application of the linear interval UIO. Then, the interval UIO is applied to jointly estimate the motor speed and the unknown load torque disturbance. Assuming that the measurement noise and disturbances are bounded, lower and upper bounds are first computed for the unmeasured state (motor speed) and then for the unknown input (load torque). The proposed approach and its limitations are demonstrated for the nonlinear PMSM model derived from its equivalent electrical circuit.

Elinirina I Robinson↗
NASA NTRS2016

Estimating Model Prediction Error: Should You Treat Predictions as Fixed or Random?

Crop models are important tools for impact assessment of climate change, as well as for exploring management options under current climate. It is essential to evaluate the uncertainty associated with predictions of these models. We compare two criteria of prediction error; MSEP fixed, which evaluates mean squared error of prediction for a model with fixed structure, parameters and inputs, and MSEP uncertain( X), which evaluates mean squared error averaged over the distributions of model structure, inputs and parameters. Comparison of model outputs with data can be used to estimate the former. The latter has a squared bias term, which can be estimated using hindcasts, and a model variance term, which can be estimated from a simulation experiment. The separate contributions to MSEP uncertain (X) can be estimated using a random effects ANOVA. It is argued that MSEP uncertain (X) is the more informative uncertainty criterion, because it is specific to each prediction situation.

model structure uncertainty↗
NASA NTRSDate not supplied

An Inverse Chance-constrained Approach to the Calibration of Robust Models

This paper proposes a strategy to calibrate computational models according to uncertain input-output data. To this end, uncertainty in the data is first quantified by creating adversarial data sets. Samples drawn from such sets are then mapped from the input-output space to the parameter space using an inverse mapping. This mapping minimizes the collective output spread of an ensemble of point predictions while satisfying a set of individual data-matching requirements. The distribution of the resulting parameter points, which often exhibits strong parameter dependencies, is then modeled using sliced-normals. The chance-constrained formulation used to learn this distribution enables the analyst to trade-off a greater likelihood for most of the data against a lower likelihood for some of the data thereby relaxing the conservatism of the calibrated model. This formulation not only neglects the worst-performing quantiles of each adversarial distribution but also eliminates the potentially serious effects that outliers might have on the resulting model. This calibration approach not only has a considerably lower computational cost than the standard forward approach but it also allows for the identification of suitable distribution classes, which in turn yield better calibrated models.

Calibration↗
NASA NTRS2012

The Pursuit of K: Reflections on the Current State-of-the-Art in Stress Intensity Factor Solutions for Practical Aerospace Applications

The elastic stress intensity factor (SIF, commonly denoted as K) is the foundation of practical fracture mechanics (FM) analysis for aircraft structures. This single parameter describes the first-order effects of stress magnitude and distribution as well as the geometry of both structure/component and crack. Hence, the calculation of K is often the most significant step in fatigue analysis based on FM. This presentation will provide several reflections on the current state-of-the-art in SIF solution methods used for practical aerospace applications, including a brief historical perspective, descriptions of some recent and ongoing advances, and comments on some remaining challenges. Newman and Raju made significant early contributions to practical structural analysis by developing closed-form SIF equations for surface and corner cracks in simplified geometries, often based on empirical fits of finite element (FE) solutions. Those solutions (and others like them) were sometimes revised as new analyses were conducted or limitations discovered. The foundational solutions have exhibited striking longevity, despite the relatively "coarse" FE models employed many decades ago. However, in recent years, the accumulation of different generations of solutions for the same nominal geometry has led to some confusion (which solution is correct?), and steady increases in computational capabilities have facilitated the discovery of inaccuracies in some (not all!) of the legacy solutions. Some examples of problems and solutions are presented and discussed, including the challenge of maintaining consistency with legacy design applications. As computational power has increased, the prospect of calculating large numbers of SIF solutions for specific complex geometries with advanced numerical methods has grown more attractive. Fawaz and Andersson, for example, have been generating literally millions of new SIF solutions for different combinations of multiple cracks under simplified loading schemes using p-version FE methods. These data are invaluable, but questions remain about their practical use, because the tabular databases of key results needed to support practical life analysis can occupy gigabytes of storage for only a few classes of geometries. The prospect of using such advanced numerical methods to calculate in real time only those K solutions actually needed to support a specific crack growth analysis is also tempting, but the stark reality is that the computational cost is still so high that the approach is not practical except for specific, critical application problems. Some thoughts are offered about alternative paradigms. Compounding approaches are some of the earliest building blocks of SIF development for more complex geometries. These approaches are especially attractive because of their very low computational cost and their conceptual robustness; they are, in some ways, an intriguing contrast and complement to the brute-force numerical methods. In recent years, researchers at NRC-Canada have published remarkable results showing how compounding approaches can be used to generate accurate solutions for very difficult problems. Examples are provided of some successes--and some limitations--using this approach. These closed-form, tabulated numerical, and compounding approaches have typically been used for simple remote loading with simple load paths to the crack. However, many significant cracks occur in complex stress gradient fields. This is a job for weight function (WF) methods, where the arbitrary stress distribution on the crack plane in the corresponding uncracked body (typically determined using FE methods) is used to determine K. Several significant recent advances in WF methods and solutions are highlighted here. Fueled by advanced 3D numerical methods, many new solutions have been generated for classic geometries such as surface and corner cracks with wide ranges of geometrical validity. A new WF formulation has also be developed for part-through cracks considering the arbitrary stress gradients in all directions in the crack plane (so-called bivariant solutions). Basic WF methods have recently been combined with analytical expressions for crack plane stresses to develop a large family of accurate SIF solutions for corner, surface, and through cracks at internal or external notches with very wide ranges of shapes, sizes, acuities, and offsets. Finally, WF solutions are much faster than FE or boundary element solutions, but can still be much slower than simple closed-form solutions, especially for bivariant solutions that can require 2D numerical integration. Novel pre-integration and dynamic tabular methods have been developed that substantially increase the speed of these advanced WF solutions. The practical utility of advanced SIF methods, including both WF and direct numerical methods, is greatly enhanced if the FM life analysis can be directly and efficiently linked with digital models of the actual structure or component (e.g., FE models for stress analysis). Two recent advances of this type will be described. One approach directly interfaces the FM life analysis with the FE model of the uncracked component (including stress results). Through a powerful graphical user interface, simplified FM life models can be constructed (and visualized) directly on the component model, with the computer collecting the geometry and stress gradient information needed for the life calculation. An even more powerful paradigm uses expert logic to automatically build an optimum simple fracture model at any and every desired location in the component model, perform the life calculation, and even generate fatigue crack growth life contour maps, all with minimal user intervention. This paradigm has also been extended to the automatic calculation of fracture risk, considering uncertainty or variability in key input parameters such as initial crack size or location. Another new integrated approach links the engineering life analysis, the component model, and a 3D numerical fracture analysis built with the same component model to generate a table of SIF values at a specific location that can then be employed efficiently to perform the life calculation. Some attention must be given to verification and validation (V&V) issues and challenges: how good are these SIF solutions, how good is good enough, and does anyone believe the life answer? It is important to think critically about the different sources of error or uncertainty and to perform V&V in a hierarchal, building-block manner. Some accuracy issues for SIF solutions, for example, may actually involve independent material behavior issues, such as constraint loss effects for crack fronts near component surfaces, and can be a source of confusion. Recommendations are proposed for improved V&V approaches. This presentation will briefly but critically survey the range of issues and advances mentioned above, with a particular view towards assembling an integrated approach that combines different methods to create practical tools for real-world design and analysis problems. Examples will be selectively drawn from the recent literature, from recent enhancements in the NASGRO and DARWIN computer codes, and from previously unpublished research

CraigMcClung, R.↗
NASA NTRS2011

On Time Delay Margin Estimation for Adaptive Control and Optimal Control Modification

This paper presents methods for estimating time delay margin for adaptive control of input delay systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent an adaptive law by a locally bounded linear approximation within a small time window. The time delay margin of this input delay system represents a local stability measure and is computed analytically by three methods: Pade approximation, Lyapunov-Krasovskii method, and the matrix measure method. These methods are applied to the standard model-reference adaptive control, s-modification adaptive law, and optimal control modification adaptive law. The windowing analysis results in non-unique estimates of the time delay margin since it is dependent on the length of a time window and parameters which vary from one time window to the next. The optimal control modification adaptive law overcomes this limitation in that, as the adaptive gain tends to infinity and if the matched uncertainty is linear, then the closed-loop input delay system tends to a LTI system. A lower bound of the time delay margin of this system can then be estimated uniquely without the need for the windowing analysis. Simulation results demonstrates the feasibility of the bounded linear stability method for time delay margin estimation.

Nguyen, Nhan T.↗
NASA NTRSDate not supplied

Uncertainty Quantification of CFD Model Assumptions Against Sonic Boom Noise Prediction of a Commercial Supersonic Transport

This paper presents the results of uncertainty modeling of sonic boom noise generation from commercial supersonic transport considering the Spalart-Allmaras (SA) turbulence modeling parameters as well as Mach number, angle of attack and altitude. Sample generation and analysis for this uncertainty model was performed by UQPCE, which is a software package developed at the NASA Langley Research Center. To build the uncertainty model, 42 cases of sonic boom noise calculation were performed. Computation of the ground noise can be briefly summarized in two steps. First, the near field pressure waveforms are sampled from CFD calculation using the NASA Langley’s FUN3D solver. Second, this information is passed to an atmospheric propagation code, sBOOM, which solves an augmented Burger’s equation and simulates how the near field waveforms will change while passing through the atmosphere. The ground signature is further processed to obtain the perceived loudness, PLdB. Having a high spatial resolution near the shockwave in the CFD calculation is critical in sonic boom noise prediction. Because the variation in the input parameters for the current uncertainty quantification (UQ) study is likely to lead to change in shock location, angle and strength, the grid adaptation for shock capturing is independently applied for each condition. The final mesh used in the CFD calculation consists of approximately 420 million cells. The pressure signatures are sampled at three, four and five body lengths away from the aircraft to make sure the three dimensional effects around the aircraft are resolved. The results of the UQ analysis shows that within the three aleatory variables, the angle of attack had the most impact against ground noise, followed by the altitude and the Mach number. Between the two SA model parameters, the Kármán constant (𝜅) was significantly more important than the turbulent Prandtl number (𝜎), but these two parameters were only marginally significant in the overall prediction variance in ground noise. The UQ procedure explained in this paper can be widely applied to other model parameters.

Uncertainty Quantification↗
NASA NTRSDate not supplied

Uncertainty Quantification of CFD Model Assumptions Against Sonic Boom Noise Prediction of a Commercial Supersonic Transport

This paper presents the results of uncertainty modeling of sonic boom noise generation from commercial supersonic transport considering the Spalart-Allmaras (SA) turbulence modeling parameters as well as Mach number, angle of attack and altitude. Sample generation and analysis for this uncertainty model was performed by UQPCE, which is a software package developed at the NASA Langley Research Center. To build the uncertainty model, 42 cases of sonic boom noise calculation were performed. Computation of the ground noise can be briefly summarized in two steps. First, the near field pressure waveforms are sampled from CFD calculation using the NASA Langley’s FUN3D solver. Second, this information is passed to an atmospheric propagation code, sBOOM, which solves an augmented Burger’s equation and simulates how the near field waveforms will change while passing through the atmosphere. The ground signature is further processed to obtain the perceived loudness, PLdB. Having a high spatial resolution near the shock wave in the CFD calculation is critical in sonic boom noise prediction. Because the variation in the input parameters for the current uncertainty quantification (UQ) study is likely to lead to change in shock location, angle and strength, the grid adaptation for shock capturing is independently applied for each condition. The final mesh used in the CFD calculation consists of approximately 420 million cells. The pressure signatures are sampled at three, four and five body lengths away from the aircraft to make sure the three dimensional effects around the aircraft are resolved. The results of the UQ analysis shows that within the three aleatory variables, the angle of attack had the most impact against ground noise, followed by the altitude and the Mach number. Between the two SA model parameters, the Kármán constant (𝜅) was significantly more important than the turbulent Prandtl number (𝜎), but these two parameters were only marginally significant in the overall prediction variance in ground noise. The UQ procedure explained in this paper can be widely applied to other model parameters.

Uncertainty Quantifications↗
NASA NTRSDate not supplied

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 NTRS2004

Employing Sensitivity Derivatives for Robust Optimization under Uncertainty in CFD

A robust optimization is demonstrated on a two-dimensional inviscid airfoil problem in subsonic flow. Given uncertainties in statistically independent, random, normally distributed flow parameters (input variables), an approximate first-order statistical moment method is employed to represent the Computational Fluid Dynamics (CFD) code outputs as expected values with variances. These output quantities are used to form the objective function and constraints. The constraints are cast in probabilistic terms; that is, the probability that a constraint is satisfied is greater than or equal to some desired target probability. Gradient-based robust optimization of this stochastic problem is accomplished through use of both first and second-order sensitivity derivatives. For each robust optimization, the effect of increasing both input standard deviations and target probability of constraint satisfaction are demonstrated. This method provides a means for incorporating uncertainty when considering small deviations from input mean values.

Newman, Perry A.↗
NASA NTRSDate not supplied

TPSAS-NF1676L-12725-DND

Uncertainty analysis and robust design - increase confidence and consistency in aerospace vehicle safety predictions by developing improved methods for quantifying and managing uncertainty. Quantifying: uncertainty modeling (model uncertainty based on experimental data, simulations and/or expert opinion) and uncertainty propagation (given uncertainty models of a system’s inputs, how to propagate them through system models, to efficiently evaluate the corresponding system’s outputs?). Managing: robust design (generate designs that robustly accommodate uncertainty) and uncertainty decomposition (identify uncertainties that contribute the most to performance degradation and determine the parameters that should (not) be modeled as uncertain).

Sean P Kenny↗
NASA NTRSDate not supplied

Variational Coupled Loads Analysis using the Hybrid Parametric Variation Method

Time-domain coupled loads analysis (CLA)is used to determine the response of a launch vehicle and payload system to transient forces, such as liftoff, engine ignitions and shutdowns, jettison events, and atmospheric flight loads, such as buffet. CLA, using Hurty/Craig-Bampton (HCB)component models, is the accepted method for the establishment of design-level loads for launch systems. However, uncertainty in the component models flows into uncertainty in predicted system results. Uncertainty in the structural responses during launch is a significant concern because small variations in launch vehicle and payload mode shapes and their interactions can result in significant variations in system loads. Uncertainty quantification (UQ)is used to determine statistical bounds on prediction accuracy based on model uncertainty. In this paper uncertainty is treated at the HCB component-model level. In an effort to account for model uncertainties and statistically bound their effect on CLA predictions, this work combines CLA with UQ in a process termed variational coupled loads analysis (VCLA). The modeling of uncertainty using a parametric approach, in which input parameters are represented by random variables, is common, but its major drawback is the resulting uncertainty is limited to the form of the nominal model. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. Model-form uncertainty can be represented using a nonparametric approach based on random matrix theory (RMT). In this work, UQ is performed using the hybrid parametric variation (HPV)method, which combines parametric with nonparametric uncertainty at the HCB component model level. The HPV method requires the selection of dispersion values for the HCB fixed-interface (FI)eigenvalues, and the HCB mass and stiffness matrices. The dispersions are based upon component test-analysis modal correlation results. During VCLA, random component models are assembled into an ensemble of random systems using a Monte Carlo (MC)approach. CLA is applied to each of the ensemble members to produce an ensemble of system-level responses for statistical analysis. The proposed methodology is demonstrated through its application to a buffet loads analysis of NASA’s Space Launch System (SLS)during the transonic regime fifty seconds after liftoff. Core stage (CS)section shears and moments are recovered, and statistics are computed.

Uncertainty Quantification↗
NASA NTRS1993

Analysis of open-loop conical scan pointing error and variance estimators

General pointing error and variance estimators for an open-loop conical scan (conscan) system are derived and analyzed. The conscan algorithm is modeled as a weighted least-squares estimator whose inputs are samples of receiver carrier power and its associated measurement uncertainty. When the assumptions of constant measurement noise and zero pointing error estimation are applied, the variance equation is then strictly a function of the carrier power to uncertainty ratio and the operator selectable radius and period input to the algorithm. The performance equation is applied to a 34-m mirror-based beam-waveguide conscan system interfaced with the Block V Receiver Subsystem tracking a Ka-band (32-GHz) downlink. It is shown that for a carrier-to-noise power ratio greater than or equal to 30 dB-Hz, the conscan period for Ka-band operation may be chosen well below the current DSN minimum of 32 sec. The analysis presented forms the basis of future conscan work in both research and development as well as for the upcoming DSN antenna controller upgrade for the new DSS-24 34-m beam-waveguide antenna.

Alvarez, L. S.↗
NASA NTRS1976

Technique for atmospheric rate chemistry calculations

The possibility that predictions of atmospheric photochemistry/transport models are sensitive to uncertainties in reaction rates and other inputs stresses the need for rapid numerical integration schemes in rate photochemistry problems. Reducing the computational burden has a major merit in facilitating sensitivity studies to assess the effect of uncertainties on predicted ozone diminutions from NOx (NO + NO2) in the exhaust plume of SST engines. The paper discusses the validity of an algorithmic approach to integration of rate chemistry problems in combustion, developed by Rubel and Baronti for an approximate calculation of the production rate of the i-th chemical species involved. An analysis of two projected SST engines confirms the validity of the proposed algorithm. Because of the relative arithmetical simplicity, it may be easier to treat diffusion rate chemistry calculations using the Rubel and Baronti approximation than would be possible by other approaches.

Matloff, G. L.↗
NASA NTRS1984

Estimation of spectral reflectance signatures from spectral radiance profiles

This paper presents a technique for converting spectral radiance to the more fundamental quantity of interest, spectral reflectance. A full implementation of the technique requires the availability of radiative transfer software. However, a set of tables (which allows an approximate derivation of reflectance) is included herein, and covers a representative range of environmental parameter values. An error analysis is performed which gives, for an uncertainty in each of the input parameters (solar zenith angle, visibility, sensor altitude, off-nadir viewing angle, background reflectance and surface elevation), the resulting error in derived reflectance. As a demonstration of the technique, several sets of spectral radiance data from the Imperial Valley, California, are presented as spectral reflectances.

Bowker, D. E.↗