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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Quantification of model error via an interval model with nonparametric error bound

The quantification of model uncertainty is becoming increasingly important as robust control is an important tool for control system design and analysis. This paper presents an algorithm that effectively characterizes the model uncertainty in terms of parametric and nonparametric uncertainties. The algorithm utilizes the frequency domain model error which is estimated from the spectra of output error and input data. The parametric uncertainty is represented as an interval transfer function while the nonparametric uncertainty is bounded by a designed error bound transfer function. Both discrete and continuous systems are discussed in this paper. The algorithm is applied to the Mini-Mast example, and the detail analysis is given.

Lew, Jiann-Shiun↗
NASA NTRS1985

Analysis and quantification of errors in the geometric correction of satellite images

The quantitative use of remote sensing satellite images in many applications requires that the geometric distortion inherent in these images be corrected, or rectified, to a desired map projection. The most widely used technique relies on ground control points to empirically determine a mathematical coordinate transformation to correct the geometry. In this paper, using the method of least squares, expressions for the accuracy of the geometric transformation and of the rectification of the satellite image to a map projection are derived. Explicit relations between the global accuracy of the transformation and the number, location, and local accuracy of the ground control points are obtained. The results are applied to the correction of a Landsat MSS image.

Ford, G. E.↗
NASA NTRS1990

A quantification of errors in surface albedo due to common assumptions

A study comparing the performance of three approaches to estimating the spectral albedo of a typical land surface is presented. The most accurate albedo estimates under all atmospheric situations are those for which the scattering properties of the atmosphere can be used. Simply utilizing the direct-to-total ratio as a weight between direct and Lambertian albedos reduced the errors in broadband albedo to less than one percent for almost all simulated atmospheric conditions.

Arduini, Robert F.↗
NASA NTRS2018

Quantification of Error Associated with Using Misaligned Meshes in Continuum Damage Mechanics Material Models for Matrix Crack Growth Predictions in Composites

The ability of a material model to capture in-plane matrix mode I and mode II crack growth is an essential component for modeling ply level damage evolution in composite structures. Previous studies using a continuum damage mechanics (CDM) approach have shown success in satisfying benchmark solutions for mode I and II crack growth. However, success was shown using a fiber-aligned meshing strategy, which encourages matrix cracks to propagate in a single band of elements, along the fiber direction. Generating a fiber-aligned mesh becomes a highly involved process for laminates including off-axis (non 0° or 90°) plies. The objective of this study is to quantify the effect of non-fiber aligned mesh discretization on predictions of in-plane matrix crack propagation. The approach taken incrementally varies the mesh orientation angle relative to the fiber orientation; more specifically, misaligned meshes are used to quantify the effect of element angle orientation relative to the initial crack orientation on the energy released during matrix crack propagation simulations using a CDM method. CDM solutions obtained with the misaligned meshes are evaluated against known benchmarks for mode I and II matrix crack growth. The CDM solutions reveal a near-polynomial trend of increased predicted failure stress with increased mesh misalignment angle; hence implying a potential relationship between element orientation angle and apparent fracture toughness.

Justusson, Brian↗
NASA NTRS2011

A Generalized Framework for Constrained Design Optimization of General Supersonic Configurations Using Adjoint Based Sensitivity Derivatives

The Aeronautics Research Mission Directorate (ARMD) sent out an NASA Research Announcement (NRA) for proposals soliciting research and technical development. The proposed research program was aimed at addressing the desired milestones and outcomes of ROA (ROA-2006) Subtopic A.4.1.1 Advanced Computational Methods. The second milestone, SUP.1.06.02 Robust, validated mesh adaptation and error quantification for near field Computational Fluid Dynamics (CFD), was addressed by the proposed research. Additional research utilizing the direct links to geometry through a CAD interface enabled by this work will allow for geometric constraints to be applied and address the final milestone, SUP2.07.06 Constrained low-drag supersonic aerodynamic design capability. The original product of the proposed research program was an integrated system of tools that can be used for the mesh mechanics required for rapid high fidelity analysis and for design of supersonic cruise vehicles. These Euler and Navier-Stokes volume grid manipulation tools were proposed to efficiently use parallel processing. The mesh adaptation provides a systematic approach for achieving demonstrated levels of accuracy in the solutions. NASA chose to fund only the mesh generation/adaptation portion of the proposal. So this report describes the completion of the proposed tasks for mesh creation, manipulation and adaptation as it pertains to sonic boom prediction of supersonic configurations.

Karman, Steve L., Jr.↗
NASA NTRS2010

Error and Uncertainty Quantification in the Numerical Simulation of Complex Fluid Flows

The failure of numerical simulation to predict physical reality is often a direct consequence of the compounding effects of numerical error arising from finite-dimensional approximation and physical model uncertainty resulting from inexact knowledge and/or statistical representation. In this topical lecture, we briefly review systematic theories for quantifying numerical errors and restricted forms of model uncertainty occurring in simulations of fluid flow. A goal of this lecture is to elucidate both positive and negative aspects of applying these theories to practical fluid flow problems. Finite-element and finite-volume calculations of subsonic and hypersonic fluid flow are presented to contrast the differing roles of numerical error and model uncertainty. for these problems.

Barth, Timothy J.↗
NASA NTRS2016

Performance Metrics, Error Modeling, and Uncertainty Quantification

A common set of statistical metrics has been used to summarize the performance of models or measurements-­ the most widely used ones being bias, mean square error, and linear correlation coefficient. They assume linear, additive, Gaussian errors, and they are interdependent, incomplete, and incapable of directly quantifying un­certainty. The authors demonstrate that these metrics can be directly derived from the parameters of the simple linear error model. Since a correct error model captures the full error information, it is argued that the specification of a parametric error model should be an alternative to the metrics-based approach. The error-modeling meth­odology is applicable to both linear and nonlinear errors, while the metrics are only meaningful for linear errors. In addition, the error model expresses the error structure more naturally, and directly quantifies uncertainty. This argument is further explained by highlighting the intrinsic connections between the performance metrics, the error model, and the joint distribution between the data and the reference.

Quantification↗
NASA NTRS2018

Combined Error and Uncertainty Estimates for CFD Problems

Given input sources of uncertainty, non-intrusive uncertainty propagation methods quantify the uncertainty in output quantities of interest (QoI) by performing a nite number of CFD (Computational Fluid Dynamics) instance realizations needed in the calculation of output statistics. It is well known that this introduces multiple sources of error. CFD codes often utilize finite-dimensional approximation (grids, basis functions, etc.) thus incurring CFD numerical errors often approximately reinterpreted as a statistical bias. Uncertainty propagation methods calculate uncertainty statistics for output quantities of interest using a numerical method (e.g. deterministic quadrature, sampling, etc.) thus incurring UQ (Uncertainty Quantification) numerical errors. Importance of quantifying these errors in large scale scientific computing: How accurate is an output statistic?; How should additional computational resources be invested to further reduce the error in a statistic?

Posteriori↗
NASA NTRS2000

New imaging technology: measurement of myocardial perfusion by contrast echocardiography

Myocardial perfusion imaging has long been a goal for the non-invasive echocardiographic assessment of the heart. However, many factors at play in perfusion imaging have made this goal elusive. Harmonic imaging and triggered imaging with newer contrast agents have made myocardial perfusion imaging potentially practical in the very near future. The application of indicator dilution theory to the coronary circulation and bubble contrast agents is fraught with complexities and sources of error. Therefore, quantification of myocardial perfusion by non-invasive echocardiographic imaging requires further investigation in order to make this technique clinically viable.

NASA Program Biomedical Research and Countermeasur↗
NASA NTRS2007

A Review of Hypersonics Aerodynamics, Aerothermodynamics and Plasmadynamics Activities within NASA's Fundamental Aeronautics Program

The research program of the aerodynamics, aerothermodynamics and plasmadynamics discipline of NASA's Hypersonic Project is reviewed. Details are provided for each of its three components: 1) development of physics-based models of non-equilibrium chemistry, surface catalytic effects, turbulence, transition and radiation; 2) development of advanced simulation tools to enable increased spatial and time accuracy, increased geometrical complexity, grid adaptation, increased physical-processes complexity, uncertainty quantification and error control; and 3) establishment of experimental databases from ground and flight experiments to develop better understanding of high-speed flows and to provide data to validate and guide the development of simulation tools.

Salas, Manuel D.↗
NASA NTRS2007

Determination of Fiber Volume in Carbon/Cyanate Ester Composites Using Thermogravimetric Analysis (TGA)

The resin content, and by extension the fiber volume, of carbon fiber/cyanate ester composite laminates are measured using thermogravimetric analysis (TGA). Conventional measurement involves acid digestion of the laminate to determine resin content. The mean difference between techniques is 0.03%. In addition to eliminating the hazards and environmental impact of standard acid digestion, the TGA technique allows quantification of errors associated with fiber volume measurements, e.g. incomplete resin removal or fiber degradation. An additional benefit of the TGA technique is a reduction in sample size requirements, allowing the examination of fiber volume changes in complex shapes.

Sovinski, Marjorie F.↗
NASA NTRS2016

Piloted Well Clear Performance Evaluation of Detect and Avoid Systems with Suggestive Guidance

Regulations to establish operational and performance requirements for unmanned aircraft systems (UAS) are being developed by a consortium of government, industry and academic institutions (RTCA, 2013). Those requirements will apply to the new detect-and-avoid (DAA) systems and other equipment necessary to integrate UAS with the United States (U.S) National Airspace System (NAS) and will be determined according to their contribution to the overall safety case. That safety case requires demonstration that DAA-equipped UAS collectively operating in the NAS meet an airspace safety threshold (AST). Several key gaps must be closed in order to link equipment requirements to an airspace safety case. Foremost among these is calculation of the systems risk ratio, the degree to which a particular system mitigates violation of an aircraft separation standard (FAA, 2013). The risk ratio of a DAA system, in combination with risk ratios of other collision mitigation mechanisms, will determine the overall safety of the airspace measured in terms of the number of collisions per flight hour. It is not known what the effectiveness is of a pilot-in-the-loop DAA system or even what parameters of the DAA system most improve the pilots ability to maintain separation. The relationship between the DAA system design and the overall effectiveness of the DAA system that includes the pilot, expressed as a risk ratio, must be determined before DAA operational and performance requirements can be finalized. Much research has been devoted to integrating UAS into non-segregated airspace (Dalamagkidis, 2009, Ostwald, 2007, Gillian, 2012, Hesselink, 2011, Santiago, 2015, Rorie 2015 and 2016). Several traffic displays intended for use as part of a DAA system have gone through human-in-the-loop simulation and flight-testing. Most of these evaluations were part of development programs to produce a deployable system, so it is unclear how to generalize particular aspects of those designs to general requirements for future traffic displays (Calhoun, 2014). Other displays have undergone testing to collect data that may generalize to new displays, but have not been evaluated in the context of the development of an overall safety case for UAS equipped with DAA systems in the NAS (Bell, 2012). Other research efforts focus on DAA surveillance performance and separation standards. Together with this work, they are expected to facilitate validation of the airspace safety case (Park, 2014 and Johnson, 2015). The contribution of the present work is to quantify the effectiveness of the pilot-automation system to remain well clear as a function of display features and surveillance sensor error. This quantification will help enable selection of a minimum set of DAA design features that meets the AST, a set that may not be unique for all UAS platforms. A second objective is to collect and analyze pilot performance parameters that will improve the modeling of overall DAA system performance in non-human-in-the-loop simulations. Simulating the DAA-equipped UAS in such batch experiments will allow investigation of a much larger number of encounters than is possible in human simulations. This capability is necessary to demonstrate that a particular set of DAA requirements meets the AST under all foreseeable operational conditions.

detect and avoid↗
NASA NTRS2019

Health Management and Prognostics for Electric Aircraft Powertrain

W and c Any air borne vehicle needs incorporating safety as key parameter of measure, and inclusion of autonomy raises the critical need for safety under autonomous operations. Management of faults and component degradation is key as complexity in autonomous operations grow over the period of time. Therefore, in addition to basic operational requirements, an autonomous electric vehicle should be able to make accurate estimates of its current system health and take the correct decisions to complete its mission successfully. Real-time safety and state-awareness tools are therefore essential for the vehicle to be able to reach its destination in a safe and successful manner. The need for safety assurance and health management capabilities is particularly relevant for aircraft electric propulsion systems, which are relatively new and with limited historical to learn. They are critical systems requiring high power density along with reliability, resilience, efficient management of weight, and operational costs. A model- based fault diagnosis and prognostics approach of complex critical systems can successfully accomplish the safety and state awareness goal for such electric propulsion systems, enabling autonomous decision making capability for safe and efficient operation. To identify critical components in the system a Qualitative Bayesian approach using FMECA is implemented. This requires the assessment of some quantities representing the state of the electric unmanned aerial systems (e-UAS), as well as look-ahead forecasts of such states during the entire flight, presented in form of safety metrics (SM). In-service data and performance data gathered from degraded components sup- ports diagnostic and prognostic methods for these systems, but this data can be difficult to obtain as weight and packaging restrictions reduce redundancy and instrumentation on-board the vehicle. Therefore, an model-based framework should be capable or operating with limited data. In addition to data scarcity, the variability of such complex critical systems re- quires the model-based framework to reason in the presence of uncertainty, such as sensor noise, and modeling imperfections. Quantification of errors and uncertainties in the measured states and quantities is therefore a fundamental step for a precise estimation of such SMs; un-modeled uncertainty may result in erroneous state assessment and un- reliable predictions of future states of e-UAVs. Typical, centralized model-based schemes suffer from inherent disadvantages such as computational complexity, single point of failure, and scalability issues, and therefore may fail in such a complex scenario. This paper presents a methodology for developing a system level diagnostics and prognostics approach using a Qualitative Bayesian FMECA approach along with a formal uncertainty management framework for an e-UAS. In this work we demonstrate the efficacy of the framework to predict effects of sub-system level degradation on vehicle operation incorporating uncertainty management to predict future behavior under different operating conditions.

Kulkarni, Chetan↗
NASA NTRS2010

Multiple Velocity Profile Measurements in Hypersonic Flows Using Sequentially-Imaged Fluorescence Tagging

Nitric-oxide planar laser-induced fluorescence (NO PLIF) was used to perform velocity measurements in hypersonic flows by generating multiple tagged lines which fluoresce as they convect downstream. For each laser pulse, a single interline, progressive scan intensified CCD (charge-coupled device) camera was used to obtain two sequential images of the NO molecules that had been tagged by the laser. The CCD configuration allowed for sub-microsecond acquisition of both images, resulting in sub-microsecond temporal resolution as well as sub-mm spatial resolution (0.5-mm horizontal, 0.7-mm vertical). Determination of axial velocity was made by application of a cross-correlation analysis of the horizontal shift of individual tagged lines. A numerical study of measured velocity error due to a uniform and linearly-varying collisional rate distribution was performed. Quantification of systematic errors, the contribution of gating/exposure duration errors, and the influence of collision rate on temporal uncertainty were made. Quantification of the spatial uncertainty depended upon the signal-to-noise ratio of the acquired profiles. This velocity measurement technique has been demonstrated for two hypersonic flow experiments: (1) a reaction control system (RCS) jet on an Orion Crew Exploration Vehicle (CEV) wind tunnel model and (2) a 10-degree half-angle wedge containing a 2-mm tall, 4-mm wide cylindrical boundary layer trip. The experiments were performed at the NASA Langley Research Center's 31-Inch Mach 10 Air Tunnel.

Bathel, Brett F.↗
NASA NTRS2010

Multiple Velocity Profile Measurements in Hypersonic Flows using Sequentially-Imaged Fluorescence Tagging

Nitric-oxide planar laser-induced fluorescence (NO PLIF) was used to perform velocity measurements in hypersonic flows by generating multiple tagged lines which fluoresce as they convect downstream. For each laser pulse, a single interline, progressive scan intensified CCD camera was used to obtain separate images of the initial undelayed and delayed NO molecules that had been tagged by the laser. The CCD configuration allowed for sub-microsecond acquisition of both images, resulting in sub-microsecond temporal resolution as well as sub-mm spatial resolution (0.5-mm x 0.7-mm). Determination of axial velocity was made by application of a cross-correlation analysis of the horizontal shift of individual tagged lines. Quantification of systematic errors, the contribution of gating/exposure duration errors, and influence of collision rate on fluorescence to temporal uncertainty were made. Quantification of the spatial uncertainty depended upon the analysis technique and signal-to-noise of the acquired profiles. This investigation focused on two hypersonic flow experiments: (1) a reaction control system (RCS) jet on an Orion Crew Exploration Vehicle (CEV) wind tunnel model and (2) a 10-degree half-angle wedge containing a 2-mm tall, 4-mm wide cylindrical boundary layer trip. The experiments were performed at the NASA Langley Research Center's 31-inch Mach 10 wind tunnel.

Bathel, Brett F.↗
NASA NTRS2005

Application of Parallel Adjoint-Based Error Estimation and Anisotropic Grid Adaptation for Three-Dimensional Aerospace Configurations

This paper demonstrates the extension of error estimation and adaptation methods to parallel computations enabling larger, more realistic aerospace applications and the quantification of discretization errors for complex 3-D solutions. Results were shown for an inviscid sonic-boom prediction about a double-cone configuration and a wing/body segmented leading edge (SLE) configuration where the output function of the adjoint was pressure integrated over a part of the cylinder in the near field. After multiple cycles of error estimation and surface/field adaptation, a significant improvement in the inviscid solution for the sonic boom signature of the double cone was observed. Although the double-cone adaptation was initiated from a very coarse mesh, the near-field pressure signature from the final adapted mesh compared very well with the wind-tunnel data which illustrates that the adjoint-based error estimation and adaptation process requires no a priori refinement of the mesh. Similarly, the near-field pressure signature for the SLE wing/body sonic boom configuration showed a significant improvement from the initial coarse mesh to the final adapted mesh in comparison with the wind tunnel results. Error estimation and field adaptation results were also presented for the viscous transonic drag prediction of the DLR-F6 wing/body configuration, and results were compared to a series of globally refined meshes. Two of these globally refined meshes were used as a starting point for the error estimation and field-adaptation process where the output function for the adjoint was the total drag. The field-adapted results showed an improvement in the prediction of the drag in comparison with the finest globally refined mesh and a reduction in the estimate of the remaining drag error. The adjoint-based adaptation parameter showed a need for increased resolution in the surface of the wing/body as well as a need for wake resolution downstream of the fuselage and wing trailing edge in order to achieve the requested drag tolerance. Although further adaptation was required to meet the requested tolerance, no further cycles were computed in order to avoid large discrepancies between the surface mesh spacing and the refined field spacing.

Lee-Rausch, E. M.↗
NASA NTRS1987

A measurement-based model of software reliability in a production environment

In this paper, a semi-Markov model is built to describe the software error and recovery process in a large mainframe system. The model is based on low-level error data from the MVS operating system running on an IBM 3081 machine. The semi-Markov model developed provides a quantification of system error characteristics and the interaction between different types of errors. As an example, a detailed model is provided, and an analysis is made of multiple errors, which constitute approximately an 17 percent of all software errors and result in considerable recovery overhead.

Hsueh, M. C.↗