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At least 343 records · Page 19

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NASA NTRS2019

Polarimetric Retrievals of Cloud Droplet Number Concentrations

Cloud droplet number concentration (Nd) is an important parameter of liquid clouds and is crucial to understanding aerosol-cloud interactions. It couples boundary layer aerosol composition, size and concentration with cloud reflectivity. It affects cloud evolution, precipitation, radiative forcing, global climate and, through observation, can be used to partially monitor the first indirect effect. With its unique combination of multi-wavelength, multi-angle, total and polarized reflectance measurements, the Research Scanning Polarimeter (RSP) retrieves Nd with relatively few assumptions. The approach involves measuring cloud optical thickness, mean droplet extinction cross-section and cloud physical thickness. Polarimetric observations are capable of measuring the effective variance, or width, of the droplet size distribution. Estimating cloud geometrical thickness is also an important component of the polarimetric Nd retrieval, which is accomplished using polarimetric measurements in a water vapor absorption band to retrieve the amount of in-cloud water vapor and relating this to physical thickness. We highlight the unique abilities and quantify uncertainties of the polarimetric approach. We validate the approach using observational data from the North Atlantic and Marine Ecosystems Study (NAAMES). NAAMES targets specific phases in the seasonal phytoplankton lifecycle and ocean-atmosphere linkages. This study provides an excellent opportunity for the RSP to evaluate its approach of sensing Nd over a range of concentrations and cloud types with in situ measurements from a Cloud Droplet Probe (CDP). The RSP and CDP, along with an array of other instruments, are flown on the NASA C-130 aircraft, which flies in situ and remote sensing legs in sequence. Cloud base heights retrieved by the RSP compare well with those derived in situ (R=0.83) and by a ceilometer aboard the R.V. Atlantis (R=0.79). Comparing geometric mean values from 12 science flights throughout the NAAMES-1 and NAAMES-2 campaigns, we find a strong correlation between Nd retrieved by the RSP and CDP (R=0.96). A linear least squares fit has a slope of 0.92 and an intercept of 0.3 cm−3. Uncertainty in this comparison can be attributed to cloud 3D effects, nonlinear liquid water profiles, multilayered clouds, measurement uncertainty, variation in spatial and temporal sampling, and assumptions used within the method. Radiometric uncertainties of the RSP measurements lead to biases on derived optical thickness and cloud physical thickness, but these biases largely cancel out when deriving Nd for most conditions and geometries. We find that a polarimetric approach to sensing Nd is viable and the RSP is capable of accurately retrieving Nd for a variety of cloud types and meteorological conditions.

Droplet concentration↗

NASA NTRS1999

Practical Aspects of Stabilized FEM Discretizations of Nonlinear Conservation Law Systems with Convex Extension

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the Galerkin least-squares (GLS) and the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the POE system. Central to the development of the simplified GLS and DG methods is the Degenerative Scaling Theorem which characterizes right symmetrizes of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobean matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler, Navier-Stokes, and magnetohydrodynamic (MHD) equations. Linear and nonlinear energy stability is proven for the simplified GLS and DG methods. Spatial convergence properties of the simplified GLS and DO methods are numerical evaluated via the computation of Ringleb flow on a sequence of successively refined triangulations. Finally, we consider a posteriori error estimates for the GLS and DG demoralization assuming error functionals related to the integrated lift and drag of a body. Sample calculations in 20 are shown to validate the theory and implementation.

Barth, Timothy↗

NASA NTRS2018

Fuzzy Modeling and Parallel Distributed Compensation for Aircraft Flight Control from Simulated Flight Data

A method is described that combines fuzzy system identification techniques with Parallel Distributed Compensation (PDC) to develop nonlinear control methods for aircraft using minimal a priori knowledge, as part of NASA’s Learn-to-Fly initiative. A fuzzy model was generated with simulated flight data, and consisted of a weighted average of multiple linear time invariant state-space cells having parameters estimated using the equation-error approach and a least-squares estimator. A compensator was designed for each subsystem using Linear Matrix Inequalities (LMI) to guarantee closed-loop stability and performance requirements. This approach is demonstrated using simulated flight data to automatically develop a fuzzy model and design control laws for a simplified longitudinal approximation of the F-16 nonlinear flight dynamics simulation. Results include a comparison of flight data with the estimated fuzzy models and simulations that illustrate the feasibility and utility of the combined fuzzy modeling and control approach.

Weinstein, Rose↗

DOE OSTI2022

Extended real-time voltage instability identification method based on synchronized phasor measurements

This paper presents an extended adaptive approach designed to accurately estimate the Thévenin equivalent parameters using phasor measurements at a given bus for measurements lying in any of four quadrants of the PQ-plane. The improvement is achieved by using a new condition to properly update the estimated parameters after an initial guess. Based on an adaptive philosophy, the proposed approach can correctly account for the intrinsic nonlinearities of a power system, can provide a real-time estimation of Thévenin parameters, and does not require network topology knowledge. The method is validated using the Kundur 2-area system, showing estimation improvements compared to the current adaptive approach and the classical recursive least-squares method. The proposed approach is able to estimate both sides of the system with respect to the measurement bus. In addition, a data-driven voltage stability index is developed. To illustrate the performance of the proposed approach in a larger power system, a voltage stability assessment is carried out on the IEEE 39-bus system, considering the action of overexcitation limiters of generators and nonlinear loads. The proposed approach is suitable for applications that require an accurate Thévenin equivalent estimation in real-time, such as for voltage stability assessment. The new approach provides a reliable tool for the system operators to make proper and timely decisions.

42 ENGINEERING↗

NASA NTRS1990

Error analysis for reducing noisy wide-gap concentric cylinder rheometric data for nonlinear fluids - Theory and applications

This work discusses the propagation of errors for the recovery of the shear rate from wide-gap concentric cylinder viscometric measurements of non-Newtonian fluids. A least-square regression of stress on angular velocity data to a system of arbitrary functions is used to propagate the errors for the series solution to the viscometric flow developed by Krieger and Elrod (1953) and Pawlowski (1953) ('power-law' approximation) and for the first term of the series developed by Krieger (1968). A numerical experiment shows that, for measurements affected by significant errors, the first term of the Krieger-Elrod-Pawlowski series ('infinite radius' approximation) and the power-law approximation may recover the shear rate with equal accuracy as the full Krieger-Elrod-Pawlowski solution. An experiment on a clay slurry indicates that the clay has a larger yield stress at rest than during shearing, and that, for the range of shear rates investigated, a four-parameter constitutive equation approximates reasonably well its rheology. The error analysis presented is useful for studying the rheology of fluids such as particle suspensions, slurries, foams, and magma.

Borgia, Andrea↗

NASA NTRS1980

Atmospheric particulate analysis using angular light scattering

Using the light scattering matrix elements measured by a polar nephelometer, a procedure for estimating the characteristics of atmospheric particulates was developed. A theoretical library data set of scattering matrices derived from Mie theory was tabulated for a range of values of the size parameter and refractive index typical of atmospheric particles. Integration over the size parameter yielded the scattering matrix elements for a variety of hypothesized particulate size distributions. A least squares curve fitting technique was used to find a best fit from the library data for the experimental measurements. This was used as a first guess for a nonlinear iterative inversion of the size distributions. A real index of 1.50 and an imaginary index of -0.005 are representative of the smoothed inversion results for the near ground level atmospheric aerosol in Tucson.

Hansen, M. Z.↗

NASA NTRS1995

Aerodynamic parameter estimation via Fourier modulating function techniques

Parameter estimation algorithms are developed in the frequency domain for systems modeled by input/output ordinary differential equations. The approach is based on Shinbrot's method of moment functionals utilizing Fourier based modulating functions. Assuming white measurement noises for linear multivariable system models, an adaptive weighted least squares algorithm is developed which approximates a maximum likelihood estimate and cannot be biased by unknown initial or boundary conditions in the data owing to a special property attending Shinbrot-type modulating functions. Application is made to perturbation equation modeling of the longitudinal and lateral dynamics of a high performance aircraft using flight-test data. Comparative studies are included which demonstrate potential advantages of the algorithm relative to some well established techniques for parameter identification. Deterministic least squares extensions of the approach are made to the frequency transfer function identification problem for linear systems and to the parameter identification problem for a class of nonlinear-time-varying differential system models.

Pearson, A. E.↗

NASA NTRS2020

Global Aerodynamic Modeling Using Automated Local Model Networks in Real Time

A novel method is presented for automated real-time global aerodynamic modeling using local model networks, known as Smoothed Partitioning with Localized Trees in Real Time (SPLITR), as part of NASA’s Learn-to-Fly technology development initiative. The global nonlinear aerodynamics are partitioned into several local regions known as cells, with the dimension, location, and timing of each partition automatically selected based on a residual characterization procedure, under the constraints of real-time operation. Regression trees represent the successive partitioning of the global flight envelope and describe the evolution of the cell structure. Recursive equation-error least-squares parameter estimation in the time domain is used to estimate a model that represents the local aerodynamics in each region, so that it can be updated independently with non-contiguous data in the range of each cell over time. A weighted superposition of these piecewise local models across the flight envelope forms a global nonlinear model that also accurately captures the local aerodynamics. The SPLITR approach is demonstrated using both simulation and flight data, and the results are analyzed in terms of model predictive capabilities as well as interpretability. The results show that SPLITR can be used to automatically partition complex nonlinear aerodynamic behavior, produce an accurate model, and provide valuable physical insight into the local and global aerodynamics.

Weinstein, Rose↗

DOE OSTI2020

Nonlinear Photovoltaic Degradation Rates: Modeling and Comparison Against Conventional Methods

Although common practice for estimating photovoltaic (PV) degradation rate (RD) assumes a linear behavior, field data have shown that degradation rates are frequently nonlinear. This article presents a new methodology to detect and calculate nonlinear RD based on PV performance time-series from nine different systems over an eight-year period. Prior to performing the analysis and in order to adjust model parameters to reflect actual PV operation, synthetic datasets were utilized for calibration purposes. A change-point analysis is then applied to detect changes in the slopes of PV trends, which are extracted from constructed performance ratio (PR) time-series. Once the number and location of change points is found, the ordinary least squares method is applied to the different segments to compute the corresponding rates. The obtained results verified that the extracted trends from the PR time-series may not always be linear and therefore, “nonconventional” models need to be applied. All thin-film technologies demonstrated nonlinear behavior whereas nonlinearity detected in the crystalline silicon systems is thought to be due to a maintenance event. A comparative analysis between the new methodology and other conventional methods demonstrated levelized cost of energy differences of up to 6.14%, highlighting the importance of considering nonlinear degradation behavior

14 SOLAR ENERGY↗

NASA NTRS1994

A linear method for analyzing lightning field changes

A constrained, least-squares method for analyzing multiple-station measurements of lightning field changes (delta Es) is introduced. Previous methods have attempted to fit the spatial pattern of lightning delta Es using nonlinear models, such as a point charge (Q) or a point dipole (P) model. With the linear method, the delta Es are described not by models but by a general volume charge distribution that is deposited on a large (40 x 40 x 20 cu km) Cartesian grid above the measuring network. A linear system of equations is used to relate the measured delta Es to the charges that are deposited at each grid point. With this approach, the information content of the measurements can be quantified by an eigenanalysis of the covariance matrix of the linear system. Constraints can be used to reduce the infinity of possible solutions to the linear system and also to reduce systematic biases that can be introduced by the method of solution. It is shown that a Landweber iterative method, derived from the general method of steepest descent, can be used to solve the linear system and that the resulting volume charge distributions are generally consistent with computer-simulated charge sources, when these sources are over the measuring network. The Landweber iteration has also provided solutions for natural lightning events that are consistent with Q- and P-model results.

Koshak, William J.↗

DOE OSTI2020

Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems

In this work, we present Lift & Learn, a physics-informed method for learning low-dimensional models for large-scale dynamical systems. The method exploits knowledge of a system’s governing equations to identify a coordinate transformation in which the system dynamics have quadratic structure. This transformation is called a lifting map because it often adds auxiliary variables to the system state. The lifting map is applied to data obtained by evaluating a model for the original nonlinear system. This lifted data is projected onto its leading principal components, and low-dimensional linear and quadratic matrix operators are fit to the lifted reduced data using a least-squares operator inference procedure. Analysis of our method shows that the Lift & Learn models are able to capture the system physics in the lifted coordinates at least as accurately as traditional intrusive model reduction approaches. This preservation of system physics makes the Lift & Learn models robust to changes in inputs. Numerical experiments on the FitzHugh–Nagumo neuron activation model and the compressible Euler equations demonstrate the generalizability of our model.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1994

Multi-application controls: Robust nonlinear multivariable aerospace controls applications

This viewgraph presentation describes the general methodology used to apply Honywell's Multi-Application Control (MACH) and the specific application to the F-18 High Angle-of-Attack Research Vehicle (HARV) including piloted simulation handling qualities evaluation. The general steps include insertion of modeling data for geometry and mass properties, aerodynamics, propulsion data and assumptions, requirements and specifications, e.g. definition of control variables, handling qualities, stability margins and statements for bandwidth, control power, priorities, position and rate limits. The specific steps include choice of independent variables for least squares fits to aerodynamic and propulsion data, modifications to the management of the controls with regard to integrator windup and actuation limiting and priorities, e.g. pitch priority over roll, and command limiting to prevent departures and/or undesirable inertial coupling or inability to recover to a stable trim condition. The HARV control problem is characterized by significant nonlinearities and multivariable interactions in the low speed, high angle-of-attack, high angular rate flight regime. Systematic approaches to the control of vehicle motions modeled with coupled nonlinear equations of motion have been developed. This paper will discuss the dynamic inversion approach which explicity accounts for nonlinearities in the control design. Multiple control effectors (including aerodynamic control surfaces and thrust vectoring control) and sensors are used to control the motions of the vehicles in several degrees-of-freedom. Several maneuvers will be used to illustrate performance of MACH in the high angle-of-attack flight regime. Analytical methods for assessing the robust performance of the multivariable control system in the presence of math modeling uncertainty, disturbances, and commands have reached a high level of maturity. The structured singular value (mu) frequency response methodology is presented as a method for analyzing robust performance and the mu-synthesis method will be presented as a method for synthesizing a robust control system. The paper concludes with the author's expectations regarding future applications of robust nonlinear multivariable controls.

Enns, Dale F.↗

DOE OSTI2024

Leveraging design of experiments to build chemometric models for the quantification of uranium (VI) and HNO3 by Raman spectroscopy

Partial least squares regression (PLSR) and support vector regression (SVR) models were optimized for the quantification of U(VI) (10–320 g L −1 ) and HNO 3 (0.6–6 M) by Raman spectroscopy with optimized calibration sets chosen by optimal design of experiments. The designed approach effectively minimized the number of samples in the calibration set for PLSR and SVR by selecting sample concentrations with a quadratic process model, despite complex confounding and covarying spectral features in the spectra. The top PLS2 model resulted in percent root mean square errors of prediction for U(VI), HNO 3 , and NO 3 − of 3.7%, 3.6%, and 2.9%, respectively. PLS1 models performed similarly despite modeling an analyte with a majority linear response (i.e., uranyl symmetric stretch) and another with more covarying vibrational modes (i.e., HNO 3 ). Partial least squares (PLS) model loadings and regression coefficients were evaluated to better understand the relationship between weaker Raman bands and covarying spectral features. Support vector machine models outperformed PLS1 models, resulting in percent root mean square error of prediction values for U(VI) and HNO 3 of 1.5% and 3.1%, respectively. The optimal nonlinear SVR model was trained using a similar number of samples (11) compared with the PLSR model, even though PLS is a linear modeling approach. The generic D-optimal design presented in this work provides a robust statistical framework for selecting training set samples in disparate two-factor systems. This approach reinforces Raman spectroscopy for the quantification of species relevant to the nuclear fuel cycle and provides a robust chemometric modeling approach to bolster online monitoring in challenging process environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Multiscale modeling high-order methods and data-driven modeling

Projection-based reduced-order models (ROMs) comprise a promising set of data-driven approaches for accelerating the simulation of high-fidelity numerical simulations. Standard projection-based ROM approaches, however, suffer from several drawbacks when applied to the complex nonlinear dynamical systems commonly encountered in science and engineering. These limitations include a lack of stability, accuracy, and sharp a posteriori error estimators. This work addresses these limitations by leveraging multiscale modeling, least-squares principles, and machine learning to develop novel reduced-order modeling approaches, along with data-driven a posteriori error estimators, for dynamical systems. Theoretical and numerical results demonstrate that the two ROM approaches developed in this work - namely the windowed least-squares method and the Adjoint Petrov - Galerkin method - yield substantial improvements over state-of-the-art approaches. Additionally, numerical results demonstrate the capability of the a posteriori error models developed in this work.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1988

A flight-test methodology for identification of an aerodynamic model for a V/STOL aircraft

Described is a flight test methodology for developing a data base to be used to identify an aerodynamic model of a vertical and short takeoff and landing (V/STOL) fighter aircraft. The aircraft serves as a test bed at Ames for ongoing research in advanced V/STOL control and display concepts. The flight envelope to be modeled includes hover, transition to conventional flight, and back to hover, STOL operation, and normaL cruise. Although the aerodynamic model is highly nonlinear, it has been formulated to be linear in the parameters to be identified. Motivation for the flight test methodology advocated in this paper is based on the choice of a linear least-squares method for model identification. The paper covers elements of the methodology from maneuver design to the completed data base. Major emphasis is placed on the use of state estimation with tracking data to ensure consistency among maneuver variables prior to their entry into the data base. The design and processing of a typical maneuver is illustrated.

Bach, Ralph E., Jr.↗

NASA NTRS1989

A flight-test methodology for identification of an aerodynamic model for a V/STOL aircraft

This paper describes a flight-test methodology for developing a data base to be used to identify an aerodynamic model of a V/STOL fighter aircraft. The aircraft serves as a test bed at NASA Ames for ongoing research in advanced V/STOL control and display concepts. The flight envelope to be modeled includes hover, transition to conventional flight and back to hover, STOL operation, and normal cruise. Although the aerodynamic model is highly nonlinear, it has been formulated to be linear in the parameters to be identified. Motivation for the flight-test methodology advocated in this paper is based on the choice of a linear least-squares method for model identification. The paper covers elements of the methodology from maneuver design to the completed data base. Major emphasis is placed on the use of state estimation with tracking data to ensure consistency among maneuver variables prior to their entry into the data base. The design and processing of a typical maneuver are illustrated.

Bach, R. E., Jr.↗

DOE OSTI2026

Efficient data-driven regression for reduced-order modeling of spatial pattern formation

We present an efficient data-driven regression approach for constructing reduced-order models (ROMs) of reaction-diffusion systems exhibiting pattern formation. The ROMs are learned non-intrusively from available training data of physically accurate numerical simulations. The method can be applied to general nonlinear systems through the use of polynomial model form, while not requiring knowledge of the underlying physical model, governing equations, or numerical solvers. The process of learning ROMs is posed as a low-cost least-squares problem in a reduced-order subspace identified via Proper Orthogonal Decomposition (POD). Numerical experiments on classical pattern-forming systems–including the Schnakenberg and Mimura–Tsujikawa models–demonstrate that higher-order surrogate models significantly improve prediction accuracy while maintaining low computational cost. The proposed method provides a flexible, non-intrusive model reduction framework, well suited for the analysis of complex spatio-temporal pattern formation phenomena.

Data-driven modeling↗

NASA NTRS1986

Parameter estimation and error analysis in environmental modeling and computation

A method for the estimation of parameters and error analysis in the development of nonlinear modeling for environmental impact assessment studies is presented. The modular computer program can interactively fit different nonlinear models to the same set of data, dynamically changing the error structure associated with observed values. Parameter estimation techniques and sequential estimation algorithms employed in parameter identification and model selection are first discussed. Then, least-square parameter estimation procedures are formulated, utilizing differential or integrated equations, and are used to define a model for association of error with experimentally observed data.

Kalmaz, E. E.↗