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NASA NTRS2000

Uncertainties in Remote Sensing of Aerosol Radiative Forcing

The role of aerosol forcing remains one of the largest uncertainties in estimating man's impact on the global climate system. One school of thought suggests that remote sensing by satellite sensors will provide the data necessary to narrow these uncertainties. Much effort has gone into the development of new satellite sensors specifically designed to retrieve aerosol loading and some information about the sizes of the aerosols. These next generation remote sensing instruments (EOS-MODIS, EOS-MISR, POLDER, ATSR) will provide unprecedented accuracy in the retrieval of aerosol loading. Although the new generation of sensors has excellent accuracy compared to the heritage instruments of the past, they still have measurement limitations. In clean, pristine regions the absolute magnitude of the uncertainty in the aerosol retrieval becomes comparable in magnitude to the signal itself. If much of the aerosol forcing is occurring at very low magnitudes of aerosol concentrations, satellite remote sensing will miss it. This study attempts to quantify remote sensing limitations due to the accuracy limits of the retrieval algorithms. We use a combination of numerical aerosol transport models, ground-based AERONET data and ISCCP cloud climatology to determine how much of the forcing occurs in regions too clean to determine from satellite retrievals. This study is not an intercomparison of global transport models. It is not an estimation of global aerosol forcing. This study is an exercise to determine whether satellite remote sensing can live up to our high expectations.

Remer, L.↗
NASA NTRS1999

Exploration of Uncertainty in Glacier Modelling

There are procedures and methods for verification of coding algebra and for validations of models and calculations that are in use in the aerospace computational fluid dynamics (CFD) community. These methods would be efficacious if used by the glacier dynamics modelling community. This paper is a presentation of some of those methods, and how they might be applied to uncertainty management supporting code verification and model validation for glacier dynamics. The similarities and differences between their use in CFD analysis and the proposed application of these methods to glacier modelling are discussed. After establishing sources of uncertainty and methods for code verification, the paper looks at a representative sampling of verification and validation efforts that are underway in the glacier modelling community, and establishes a context for these within overall solution quality assessment. Finally, an information architecture and interactive interface is introduced and advocated. This Integrated Cryospheric Exploration (ICE) Environment is proposed for exploring and managing sources of uncertainty in glacier modelling codes and methods, and for supporting scientific numerical exploration and verification. The details and functionality of this Environment are described based on modifications of a system already developed for CFD modelling and analysis.

Thompson, David E.↗
NASA NTRS2000

Uncertainty Analysis of Decomposing Polyurethane Foam

Sensitivity/uncertainty analyses are necessary to determine where to allocate resources for improved predictions in support of our nation's nuclear safety mission. Yet, sensitivity/uncertainty analyses are not commonly performed on complex combustion models because the calculations are time consuming, CPU intensive, nontrivial exercises that can lead to deceptive results. To illustrate these ideas, a variety of sensitivity/uncertainty analyses were used to determine the uncertainty associated with thermal decomposition of polyurethane foam exposed to high radiative flux boundary conditions. The polyurethane used in this study is a rigid closed-cell foam used as an encapsulant. Related polyurethane binders such as Estane are used in many energetic materials of interest to the JANNAF community. The complex, finite element foam decomposition model used in this study has 25 input parameters that include chemistry, polymer structure, and thermophysical properties. The response variable was selected as the steady-state decomposition front velocity calculated as the derivative of the decomposition front location versus time. An analytical mean value sensitivity/uncertainty (MV) analysis was used to determine the standard deviation by taking numerical derivatives of the response variable with respect to each of the 25 input parameters. Since the response variable is also a derivative, the standard deviation was essentially determined from a second derivative that was extremely sensitive to numerical noise. To minimize the numerical noise, 50-micrometer element dimensions and approximately 1-msec time steps were required to obtain stable uncertainty results. As an alternative method to determine the uncertainty and sensitivity in the decomposition front velocity, surrogate response surfaces were generated for use with a constrained Latin Hypercube Sampling (LHS) technique. Two surrogate response surfaces were investigated: 1) a linear surrogate response surface (LIN) and 2) a quadratic response surface (QUAD). The LHS techniques do not require derivatives of the response variable and are subsequently relatively insensitive to numerical noise. To compare the LIN and QUAD methods to the MV method, a direct LHS analysis (DLHS) was performed using the full grid and timestep resolved finite element model. The surrogate response models (LIN and QUAD) are shown to give acceptable values of the mean and standard deviation when compared to the fully converged DLHS model.

Hobbs, Michael L.↗
NASA NTRS2001

Developing Uncertainty Models for Robust Flutter Analysis Using Ground Vibration Test Data

A ground vibration test can be used to obtain information about structural dynamics that is important for flutter analysis. Traditionally, this information#such as natural frequencies of modes#is used to update analytical models used to predict flutter speeds. The ground vibration test can also be used to obtain uncertainty models, such as natural frequencies and their associated variations, that can update analytical models for the purpose of predicting robust flutter speeds. Analyzing test data using the -norm, rather than the traditional 2-norm, is shown to lead to a minimum-size uncertainty description and, consequently, a least-conservative robust flutter speed. This approach is demonstrated using ground vibration test data for the Aerostructures Test Wing. Different norms are used to formulate uncertainty models and their associated robust flutter speeds to evaluate which norm is least conservative.

Potter, Starr↗
NASA NTRS2002

Space Radiation Cancer Risk Projections for Exploration Missions: Uncertainty Reduction and Mitigation

In this paper we discuss expected lifetime excess cancer risks for astronauts returning from exploration class missions. For the first time we make a quantitative assessment of uncertainties in cancer risk projections for space radiation exposures. Late effects from the high charge and energy (HZE) ions present in the galactic cosmic rays including cancer and the poorly understood risks to the central nervous system constitute the major risks. Methods used to project risk in low Earth orbit are seen as highly uncertain for projecting risks on exploration missions because of the limited radiobiology data available for estimating HZE ion risks. Cancer risk projections are described as a product of many biological and physical factors, each of which has a differential range of uncertainty due to lack of data and knowledge. Monte-Carlo sampling from subjective error distributions represents the lack of knowledge in each factor to quantify risk projection overall uncertainty. Cancer risk analysis is applied to several exploration mission scenarios. At solar minimum, the number of days in space where career risk of less than the limiting 3% excess cancer mortality can be assured at a 95% confidence level is found to be only of the order of 100 days.

Cucinotta, Francis↗
NASA NTRS2002

Global Surface Temperature Change and Uncertainties Since 1861

The objective of this talk is to analyze the warming trend and its uncertainties of the global and hemi-spheric surface temperatures. By the method of statistical optimal averaging scheme, the land surface air temperature and sea surface temperature observational data are used to compute the spatial average annual mean surface air temperature. The optimal averaging method is derived from the minimization of the mean square error between the true and estimated averages and uses the empirical orthogonal functions. The method can accurately estimate the errors of the spatial average due to observational gaps and random measurement errors. In addition, quantified are three independent uncertainty factors: urbanization, change of the in situ observational practices and sea surface temperature data corrections. Based on these uncertainties, the best linear fit to annual global surface temperature gives an increase of 0.61 +/- 0.16 C between 1861 and 2000. This lecture will also touch the topics on the impact of global change on nature and environment. as well as the latest assessment methods for the attributions of global change.

Shen, Samuel S. P.↗
NASA NTRS2002

Optimization of Systems with Uncertainty: Initial Developments for Performance, Robustness and Reliability Based Designs

This paper presents a study on the optimization of systems with structured uncertainties, whose inputs and outputs can be exhaustively described in the probabilistic sense. By propagating the uncertainty from the input to the output in the space of the probability density functions and the moments, optimization problems that pursue performance, robustness and reliability based designs are studied. Be specifying the desired outputs in terms of desired probability density functions and then in terms of meaningful probabilistic indices, we settle a computationally viable framework for solving practical optimization problems. Applications to static optimization and stability control are used to illustrate the relevance of incorporating uncertainty in the early stages of the design. Several examples that admit a full probabilistic description of the output in terms of the design variables and the uncertain inputs are used to elucidate the main features of the generic problem and its solution. Extensions to problems that do not admit closed form solutions are also evaluated. Concrete evidence of the importance of using a consistent probabilistic formulation of the optimization problem and a meaningful probabilistic description of its solution is provided in the examples. In the stability control problem the analysis shows that standard deterministic approaches lead to designs with high probability of running into instability. The implementation of such designs can indeed have catastrophic consequences.

Crespo, Luis G.↗
NASA NTRS1999

Uncertainty Modeling Via Frequency Domain Model Validation

Abstract The majority of literature on robust control assumes that a design model is available and that the uncertainty model bounds the actual variations about the nominal model. However, methods for generating accurate design models have not received as much attention in the literature. The influence of the level of accuracy of the uncertainty model on closed loop performance has received even less attention. The research reported herein is an initial step in applying and extending the concept of model validation to the problem of obtaining practical uncertainty models for robust control analysis and design applications. An extension of model validation called 'sequential validation' is presented and applied to a simple spring-mass-damper system to establish the feasibility of the approach and demonstrate the benefits of the new developments.

Waszak, Martin R.↗
NASA NTRS2005

Uncertainty Modeling for Robustness Analysis of Control Upset Prevention and Recovery Systems

Formal robustness analysis of aircraft control upset prevention and recovery systems could play an important role in their validation and ultimate certification. Such systems (developed for failure detection, identification, and reconfiguration, as well as upset recovery) need to be evaluated over broad regions of the flight envelope and under extreme flight conditions, and should include various sources of uncertainty. However, formulation of linear fractional transformation (LFT) models for representing system uncertainty can be very difficult for complex parameter-dependent systems. This paper describes a preliminary LFT modeling software tool which uses a matrix-based computational approach that can be directly applied to parametric uncertainty problems involving multivariate matrix polynomial dependencies. Several examples are presented (including an F-16 at an extreme flight condition, a missile model, and a generic example with numerous crossproduct terms), and comparisons are given with other LFT modeling tools that are currently available. The LFT modeling method and preliminary software tool presented in this paper are shown to compare favorably with these methods.

Belcastro, Christine M.↗
NASA NTRS2008

An Uncertainty Structure Matrix for Models and Simulations

Software that is used for aerospace flight control and to display information to pilots and crew is expected to be correct and credible at all times. This type of software is typically developed under strict management processes, which are intended to reduce defects in the software product. However, modeling and simulation (M&S) software may exhibit varying degrees of correctness and credibility, depending on a large and complex set of factors. These factors include its intended use, the known physics and numerical approximations within the M&S, and the referent data set against which the M&S correctness is compared. The correctness and credibility of an M&S effort is closely correlated to the uncertainty management (UM) practices that are applied to the M&S effort. This paper describes an uncertainty structure matrix for M&S, which provides a set of objective descriptions for the possible states of UM practices within a given M&S effort. The columns in the uncertainty structure matrix contain UM elements or practices that are common across most M&S efforts, and the rows describe the potential levels of achievement in each of the elements. A practitioner can quickly look at the matrix to determine where an M&S effort falls based on a common set of UM practices that are described in absolute terms that can be applied to virtually any M&S effort. The matrix can also be used to plan those steps and resources that would be needed to improve the UM practices for a given M&S effort.

Green, Lawrence L.↗
NASA NTRS2007

Managing Uncertainty Due to a Fundamental Error Source Arising from Scatterer Distribution Complexity in Radar Remote Sensing of Precipitation

The assumption that cloud and rain drops are spatially distributed according to a Poisson distribution within a scattering volume probed by a radar being used to estimate precipitation has represented bedrock theory in establishing 'rules of the game' for pulse averaging--the process needed to beat down noise to an acceptable level in the measurement of radar reflectivity factor. Based on relatively recent observations of 'realistic' spatial distributions of hydrometeor scatterers in a cloudy atmosphere motivates a renewed examination of the consequences of using a too simplified assumption underlying volume scattering--particularly in regards to the standard pulse averaging rule. Our investigation addresses two extremes, simple to complex, insofar as allowed for complexities in an underlying scatterer distribution. It is demonstrated that as the spatial distribution ranges from Poisson (a narrow distribution) to multi-fractal (much broader distribution), uncertainty in a measurement increases if the rule for pulse averaging goes unchanged from its Poisson distribution reference county. [A bounded cascade is used for the multi-fractal distribution, a regularly observed distribution vis-a-vis cloud liquid water content.] The resultant measurement uncertainty leads to a fundamental source of error in the estimation of rain rate from radar measurements, one that has been disregarded since the early 1950s when radar sets first began to be used for rainfall measuring. It is shown how this source of error can be 'managed'--under the assumption that number of data analysis experiments would be carried out, experiments involving pulse-by-pulse measurements obtained from a radar set modified to output individual pulses of reflectivity factor. For practical applications, a new parameter called normalized k-sample intensity invariance is developed to enable defining the required pulse average count according to a preferred degree of uncertainty.

Smith, Eric A.↗
NASA NTRS2008

Sensitivity of Polar Stratospheric Ozone Loss to Uncertainties in Chemical Reaction Kinetics

Several recent observational and laboratory studies of processes involved in polar stratospheric ozone loss have prompted a reexamination of aspect of out understanding for this key indicator of global change. To a large extent, our confidence in understanding and projecting changes in polar and global ozone is based on our ability to to simulate these process in numerical models of chemistry and transport. These models depend on laboratory-measured kinetic reaction rates and photlysis cross section to simulate molecular interactions. In this study we use a simple box-model scenario for Antarctic ozone to estimate the uncertainty in loss attributable to known reaction kinetic uncertainties. Following the method of earlier work, rates and uncertainties from the latest laboratory evaluation are applied in random combinations. We determine the key reaction and rates contributing the largest potential errors and compare the results to observations to evaluate which combinations are consistent with atmospheric data. Implications for our theoretical and practical understanding of polar ozone loss will be assessed.

Kawa, S. Randolph↗
NASA NTRS2009

Uncertainty Management in Remote Sensing of Climate Data. Summary of A Workshop

Great advances have been made in our understanding of the climate system over the past few decades, and remotely sensed data have played a key role in supporting many of these advances. Improvements in satellites and in computational and data-handling techniques have yielded high quality, readily accessible data. However, rapid increases in data volume have also led to large and complex datasets that pose significant challenges in data analysis (NRC, 2007). Uncertainty characterization is needed for every satellite mission and scientists continue to be challenged by the need to reduce the uncertainty in remotely sensed climate records and projections. The approaches currently used to quantify the uncertainty in remotely sensed data, including statistical methods used to calibrate and validate satellite instruments, lack an overall mathematically based framework.

Remote sensing↗
NASA NTRS2007

Accounting for Uncertainties in Strengths of SiC MEMS Parts

A methodology has been devised for accounting for uncertainties in the strengths of silicon carbide structural components of microelectromechanical systems (MEMS). The methodology enables prediction of the probabilistic strengths of complexly shaped MEMS parts using data from tests of simple specimens. This methodology is intended to serve as a part of a rational basis for designing SiC MEMS, supplementing methodologies that have been borrowed from the art of designing macroscopic brittle material structures. The need for this or a similar methodology arises as a consequence of the fundamental nature of MEMS and the brittle silicon-based materials of which they are typically fabricated. When tested to fracture, MEMS and structural components thereof show wide part-to-part scatter in strength. The methodology involves the use of the Ceramics Analysis and Reliability Evaluation of Structures Life (CARES/Life) software in conjunction with the ANSYS Probabilistic Design System (PDS) software to simulate or predict the strength responses of brittle material components while simultaneously accounting for the effects of variability of geometrical features on the strength responses. As such, the methodology involves the use of an extended version of the ANSYS/CARES/PDS software system described in Probabilistic Prediction of Lifetimes of Ceramic Parts (LEW-17682-1/4-1), Software Tech Briefs supplement to NASA Tech Briefs, Vol. 30, No. 9 (September 2006), page 10. The ANSYS PDS software enables the ANSYS finite-element-analysis program to account for uncertainty in the design-and analysis process. The ANSYS PDS software accounts for uncertainty in material properties, dimensions, and loading by assigning probabilistic distributions to user-specified model parameters and performing simulations using various sampling techniques.

Nemeth, Noel↗
NASA NTRS2010

Impact of Damping Uncertainty on SEA Model Response Variance

Statistical Energy Analysis (SEA) is commonly used to predict high-frequency vibroacoustic levels. This statistical approach provides the mean response over an ensemble of random subsystems that share the same gross system properties such as density, size, and damping. Recently, techniques have been developed to predict the ensemble variance as well as the mean response. However these techniques do not account for uncertainties in the system properties. In the present paper uncertainty in the damping loss factor is propagated through SEA to obtain more realistic prediction bounds that account for both ensemble and damping variance. The analysis is performed on a floor-equipped cylindrical test article that resembles an aircraft fuselage. Realistic bounds on the damping loss factor are determined from measurements acquired on the sidewall of the test article. The analysis demonstrates that uncertainties in damping have the potential to significantly impact the mean and variance of the predicted response.

Schiller, Noah↗
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 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 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↗