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NASA NTRS1996

An Inversion of Gravity and Topography for Mantle and Crustal Structure on Mars

Analysis of the gravity and topography of Mars presently provides our primary quantitative constraints on the internal structure of Mars. We present an inversion of the long-wavelength (harmonic degree less than or equal to 10) gravity and topography of Mars for lateral variations of mantle temperature and crustal thickness. Our formulation incorporates both viscous mantle flow (which most prior studies have neglected) and isostatically compensated density anomalies in the crust and lithosphere. Our nominal model has a 150-km-thick high-viscosity surface layer over an isoviscous mantle, with a core radius of 1840 km. It predicts lateral temperature variations of up to a few hundred degrees Kelvin relative to the mean mantle temperature, with high temperature under Tharsis and to a lesser extent under Elysium and cool temperatures elsewhere. Surprisingly, the model predicts crustal thinning beneath Tharsis. If correct, this implies that thinning of the crust by mantle shear stresses dominates over thickening of the crust by volcanism. The major impact basins (Hellas, Argyre, Isidis, Chryse, and Utopia) are regions of crustal thinning, as expected. Utopia is also predicted to be a region of hot mantle, which is hard to reconcile with the surface geology. An alternative model for Utopia treats it as a mascon basin. The Utopia gravity anomaly is consistent with the presence of a 1.2 to 1.6 km thick layer of uncompensated basalt, in good agreement with geologic arguments about the amount of volcanic fill in this area. The mantle thermal structure is the dominant contributor to the observed geoid in our inversion. The mantle also dominates the topography at the longest wavelengths, but shorter wavelengths (harmonic degrees greater than or equal to 4) are dominated by the crustal structure. Because of the uncertainty about the appropriate numerical values for some of the model's input parameters, we have examined the sensitivity of the model results to the planetary structural model (core radius and core and mantle densities), the mantle's viscosity stratification, and the mean crustal thickness. The model results are insensitive to the specific thickness or viscosity contrast of the high-viscosity surface layer and to the mean crustal thickness in the range 25 to 100 km. Models with a large core radius or with an upper mantle low-viscosity zone require implausibly large lateral variations in mantle temperature.

Kiefer, Walter S.↗

NASA NTRS1994

An optimization-based approach for integrated controls-structures design of flexible spacecraft

The control of flexible spacecraft is a difficult problem because of large number of elastic modes; low value, closely-spaced frequencies; very small damping; and uncertainties in math models. The traditional design approach is to design the structure first and then to design the control system. This view-graph presentation develops a methodology for spacecraft design which addresses control/structure interaction issues, produces technology for simultaneous control/structure design, and translates into algorithms and computational tools for practical integrated computer-aided design.

Maghami, P. G.↗

NASA NTRS1997

Worst-Case Flutter Margins from F/A-18 Aircraft Aeroelastic Data

An approach for computing worst-case flutter margins has been formulated in a robust stability framework. Uncertainty operators are included with a linear model to describe modeling errors and flight variations. The structured singular value, micron, computes a stability margin which directly accounts for these uncertainties. This approach introduces a new method of computing flutter margins and an associated new parameter for describing these margins. The micron margins are robust margins which indicate worst-case stability estimates with respect to the defined uncertainty. Worst-case flutter margins are computed for the F/A-18 SRA using uncertainty sets generated by flight data analysis. The robust margins demonstrate flight conditions for flutter may lie closer to the flight envelope than previously estimated by p-k analysis.

Lind, Rick↗

NASA NTRS1998

Robust Flutter Margin Analysis that Incorporates Flight Data

An approach for computing worst-case flutter margins has been formulated in a robust stability framework. Uncertainty operators are included with a linear model to describe modeling errors and flight variations. The structured singular value, mu, computes a stability margin that directly accounts for these uncertainties. This approach introduces a new method of computing flutter margins and an associated new parameter for describing these margins. The mu margins are robust margins that indicate worst-case stability estimates with respect to the defined uncertainty. Worst-case flutter margins are computed for the F/A-18 Systems Research Aircraft using uncertainty sets generated by flight data analysis. The robust margins demonstrate flight conditions for flutter may lie closer to the flight envelope than previously estimated by p-k analysis.

Lind, Rick↗

NASA NTRSDate not supplied

High Temperature Material Property Data and Challenges to Thermal Process Model Predictions and In-Situ/Ex-Situ Measurements for Metallic Additive Manufacturing

Understanding and predicting performance properties of parts produced by metallic additive manufacturing has improved significantly over the past decade; however, difficult to measure material properties and process outcomes continue to be challenges. The qualification or certification of aerospace parts require extensive measures to quantify variable part properties in order to buy down the risk of component failure. The variability, inherent to the additive manufacturing, process adds unwanted uncertainty in the production of load critical structural components. Process modeling has proven valuable in providing predictions and context for understanding outcomes of the additive manufacturing process; however, these physically informed process models require material properties at temperatures that are difficult to measure and rarely available. Further, calibrating or validating such models is difficult because the process itself is challenging to measure. This talk will explore some of the challenges resulting from difficult to acquire input data by relating thermal process model predictions to in-situ and ex-situ optical microscopy measurements.

Process Model↗

NASA NTRS2018

Improving Carbon Estimation of Large Tropical Trees by Linking Airborne Lidar Crown Size to Field Inventory

Quantifying tropical aboveground biomass (agb) is an outstanding challenge that requires knowledge on the 3D structure of forests. Recent studies suggest that the uncertainty in estimating agb of large trees is significantly reduced if tree height and crown size are accounted for in addition to the traditional trunk diameter and wood density. Due to the fact that field inventory techniques are not adapted to characterize the 3D forest structure, crown size metrics (e.g. height and radius) are commonly estimated as a function of trunk diameter using allometric models with limitations in explaining crown variability. Airborne lidar techniques have the potential for characterizing tree height and crown size but are not adapted to estimate trunk diameter, which is a strong predictor of agb. Here, we investigate the synergy of field inventory and airborne lidar techniques to characterize the forest structure by assessing the uncertainty introduced by the field-based allometric models in the estimation of agb at the tree-level. We focus in 1454 large individual trees (trunk diameter > 60 cm) located within the La Selva Biological Station for which we dispose of field observations (trunk diameter and wood density) and lidar derived metrics (tree height and crown radius). We show that the field-based allometric models overestimate tree height and underestimate crown radius. As a result, the allometric approach overestimates the tree-level agb in 0.8 Mg when considering the 1454 individuals and the errors can reach more than 50% of the agb of individual trees. These errors on the large trees agb highly impact on the plot-level results and then propagate to the estimation of carbon stocks at the regional and national-levels.

Clark, David↗

NASA NTRS1986

Feedback system design with an uncertain plant

A method is developed to design a fixed-parameter compensator for a linear, time-invariant, SISO (single-input single-output) plant model characterized by significant structured, as well as unstructured, uncertainty. The controller minimizes the H(infinity) norm of the worst-case sensitivity function over the operating band and the resulting feedback system exhibits robust stability and robust performance. It is conjectured that such a robust nonadaptive control design technique can be used on-line in an adaptive control system.

Milich, D.↗

NASA NTRS1986

Feedback system design with an uncertain plant

A method is developed to design a fixed-parameter compensator for a linear, time-invariant, SISO (single-output single-output) plant model characterized by significant structured, as well as unstructured, uncertainty. The controller minimizes the H(infinity) norm of the worst-case sensitivity function over the operating band and the resulting feedback system exhibits robust stability and robust performance. It is conjectured that such a robust nonadaptive control design technique can be used on-line in an adaptive control system.

Milich, D.↗

NASA NTRS1988

Parameter identification of material constants in a composite shell structure

One of the basic requirements in engineering analysis is the development of a mathematical model describing the system. Frequently comparisons with test data are used as a measurement of the adequacy of the model. An attempt is typically made to update or improve the model to provide a test verified analysis tool. System identification provides a systematic procedure for accomplishing this task. The terms system identification, parameter estimation, and model correlation all refer to techniques that use test information to update or verify mathematical models. The goal of system identification is to improve the correlation of model predictions with measured test data, and produce accurate, predictive models. For nonmetallic structures the modeling task is often difficult due to uncertainties in the elastic constants. A finite element model of the shell was created, which included uncertain orthotropic elastic constants. A modal survey test was then performed on the shell. The resulting modal data, along with the finite element model of the shell, were used in a Bayes estimation algorithm. This permitted the use of covariance matrices to weight the confidence in the initial parameter values as well as confidence in the measured test data. The estimation procedure also employed the concept of successive linearization to obtain an approximate solution to the original nonlinear estimation problem.

Martinez, David R.↗

NASA NTRS1998

A Worst-Case Approach for On-Line Flutter Prediction

Worst-case flutter margins may be computed for a linear model with respect to a set of uncertainty operators using the structured singular value. This paper considers an on-line implementation to compute these robust margins in a flight test program. Uncertainty descriptions are updated at test points to account for unmodeled time-varying dynamics of the airplane by ensuring the robust model is not invalidated by measured flight data. Robust margins computed with respect to this uncertainty remain conservative to the changing dynamics throughout the flight. A simulation clearly demonstrates this method can improve the efficiency of flight testing by accurately predicting the flutter margin to improve safety while reducing the necessary flight time.

Lind, Rick C.↗

NASA NTRSDate not supplied

Probability Bounds Analysis Applied to Multi-Purpose Crew Vehicle Nonlinearity

The Multi-Purpose Crew Vehicle (MPCV) Program Orion vehicle finite element model (FEM) was updated based on a modal test performed by Lockheed Martin. Due to nonlinearity observed in the test results, linear low force level (LL) and high force level (HL) FEMs were developed for use during various Space Launch System (SLS) flight regimes depending on expected forcing levels. Uncertainty models were derived for the combined MPCV and MPCV Stage Adaptor LL and HL Hurty/Craig-Bampton (HCB) components based on the MPCV structural test article Configuration 4 modal test-analysis correlation results. Subsequently, system-level uncertainty quantification analyses were performed using both models for various SLS flight configurations to determine the impact of the nonlinearity on important system metrics. The system metrics included both transfer functions associated with attitude control and dynamic loads associated with aerodynamic buffeting during ascent. In each case, an independent Monte Carlo (MC) analysis was performed, and no attempt was made to combine the results. The Hybrid Parametric Variation (HPV) method was used to develop the LL and HL MPCV HCB uncertainty models. The HPV method provides both parametric and non-parametric components of uncertainty. The non-parametric uncertainty accounts for the difference in model-form between the linearized analytical model and the corresponding linearized component test results in the form of mode shapes and frequencies at that force level. This linear model-form uncertainty is implemented in the HPV method using random matrix theory. However, the HPV uncertainty models developed for the linear LL and HL MPCV components do not account for the nonlinearity in the MPCV. With respect to the linearized models, this nonlinearity is also an uncertainty in model form, but in this case, it must be treated independently as an epistemic uncertainty. It represents a lack of knowledge, in contrast to an aleatory uncertainty due to the randomness of a variable. In the case of an epistemic variable, the true value is unknown, only the interval within which it lies is known. Epistemic uncertainty can be reduced with increased knowledge, while in general, aleatory uncertainty cannot. This work combines the epistemic uncertainty due to the MPCV nonlinearity with the parametric and non-parametric uncertainty within the HPV method using a second order propagation approach. The LL and HL test data is augmented with surrogate test data derived from a nonlinear MPCV representation. The impact of the MPCV nonlinearity on system response statistics is determined using a series of cumulative distribution functions in the form of a horsetail plot, or p-box. This results in an interval of probabilities for a specific response value, or an interval of response values at a specific probability.

Daniel C Kammer↗

NASA NTRS1992

Desensitizing structural-control design

A new method for targeted robustness optimization is presented. This method allows the analyst to 'target' the most critical performance parameter (or family of design requirements with almost the same criticality) for enhanced protection from uncertainties in the model. To create this protection, this method uses knowledge about the uncertainties in some of the parameters of the model - this information is usually available to the structural analyst. The power of the targeted robustness method is demonstrated numerically using an active damping example. The results show that the most critical damping ratio is protected - its sensitivity to the uncertainties is far below those of non-critical damping ratios.

Ponslet, E.↗

NASA NTRSDate not supplied

Characterizing Spatiotemporal Uncertainty in Interpolated Meteorological Data

Interpolated meteorological data invariably contain errors. These errors have structure in time and space, particularly autocorrelation, which can cause the effects of errors to compound when model outputs are aggregated temporally or spatially. One way to account for this uncertainty is with a probabilistic model from which samples can be drawn that are coherent with respect to underlying spatial and temporal covariance structure. This work describes a probabilistic method for spatial interpolation of point-wise meteorological time series. Observational data from weather stations are generally sparse in space and dense in time (but sometimes missing). The method works by projecting time series onto orthogonal basis vectors and spatially interpolating each resulting component independently. Under suitable assumptions, and data transformations to better satisfy those assumptions, Gaussian process regression provides a complete description of the joint predictive distribution over a Gaussian random field. Spatiotemporally coherent realizations are generated as the sum of conditional (spatial) simulations of each orthogonal (temporal) component. Data-derived and generic orthogonal bases are considered. In addition to spatial interpolation, imputation of missing observational data is examined. The method is applied using near-surface air temperature over the Western United States and validated by comparing theoretical versus actual coverage of predictive distributions and analyzing the degree to which spatial and temporal covariance structure is reproduced. Computational considerations, relating to conditional simulation of random fields, are also addressed.

Conor T Doherty↗

NASA NTRS1999

Substructure Synthesis: A Controls Approach

Substructure synthesis from a controls perspective is considered. An efficient and computationally robust method for synthesis of substructures is developed. The method considers the interface forces/moments as control inputs and redefines the synthesis problem in terms of obtaining a constant gain compensator which would ensure the connectivity requirements of the combined structure. Orthogonal similarity transformations are used to provide simplified synthesized dynamics of the combined system. The simplicity of form in transformed coordinates are exploited to effectively deal with modeling parametric and non-parametric uncertainties at substructure level. Uncertainty models of reasonable size and complexity are derived for the combined structure from those in the substructure models.

Maghami, Peiman G.↗

NASA NTRS1999

MHD Streamer Structure, Slow Solar Wind, and the Streamer Brightness Boundary

Flow tubes adjacent to closed magnetic field lines on the boundaries of streamers can have extremely large geometric spreading factors. Numerical models in this thin layer are subject to grid definition uncertainties. Therefore, we compute flow tube geometry using the analytic model of streamer structure described by Pneuman. This model has been found to be more widely applicable than commonly believed as a consequence of observations made with SOHO/UVCS and YOKHOH/SXT. We use the model to compute the radial dependence of flow tube geometry (the "spreading factors") for several different streamer models. The results are used to analyze the hypothesis that extremely slow flows in these open flow tubes may cause high densities relative to adjacent coronal hole flow. Such high density could mean that the streamer brightness boundary is defined by the open flow tubes adjacent to streamers rather than closed field lines.

Suess, Steven T.↗

NASA NTRS2008

Ares I Flight Control System Overview

This paper describes the control challenges posed by the Ares I vehicle, the flight control system design and performance analyses used to test and verify the design. The major challenges in developing the control system are structural dynamics, dynamic effects from the powerful first stage booster, aerodynamics, first stage separation and large uncertainties in the dynamic models for all these. Classical control techniques were employed using innovative methods for structural mode filter design and an anti-drift feature to compensate for translational and rotational disturbances. This design was coded into an integrated vehicle flight simulation and tested by Monte Carlo methods. The product of this effort is a linear, robust controller design that is easy to implement, verify and test.

Hall, Charles↗

NASA NTRS1977

Study of synthesis techniques for insensitive aircraft control systems

Insensitive flight control system design criteria was defined in terms of maximizing performance (handling qualities, RMS gust response, transient response, stability margins) over a defined parameter range. Wing load alleviation for the C-5A was chosen as a design problem. The C-5A model was a 79-state, two-control structure with uncertainties assumed to exist in dynamic pressure, structural damping and frequency, and the stability derivative, M sub w. Five new techniques (mismatch estimation, uncertainty weighting, finite dimensional inverse, maximum difficulty, dual Lyapunov) were developed. Six existing techniques (additive noise, minimax, multiplant, sensitivity vector augmentation, state dependent noise, residualization) and the mismatch estimation and uncertainty weighting techniques were synthesized and evaluated on the design example. Evaluation and comparison of these six techniques indicated that the minimax and the uncertainty weighting techniques were superior to the other six, and of these two, uncertainty weighting has lower computational requirements. Techniques based on the three remaining new concepts appear promising and are recommended for further research.

Harvey, C. A.↗

NASA NTRS2016

Model Based Mission Assurance: Emerging Opportunities for Robotic Systems

The emergence of Model Based Systems Engineering (MBSE) in a Model Based Engineering framework has created new opportunities to improve effectiveness and efficiencies across the assurance functions. The MBSE environment supports not only system architecture development, but provides for support of Systems Safety, Reliability and Risk Analysis concurrently in the same framework. Linking to detailed design will further improve assurance capabilities to support failures avoidance and mitigation in flight systems. This also is leading new assurance functions including model assurance and management of uncertainty in the modeling environment. Further, the assurance cases, a structured hierarchal argument or model, are emerging as a basis for supporting a comprehensive viewpoint in which to support Model Based Mission Assurance (MBMA).

Mission Assurance↗