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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 OSTI2023

Polarimetric Geometric Modeling for mm-VLBI Observations of Black Holes

The Event Horizon Telescope (EHT) is a millimeter very long baseline interferometry (VLBI) array that has imaged the apparent shadows of the supermassive black holes M87* and Sagittarius A*. Polarimetric data from these observations contain a wealth of information on the black hole and accretion flow properties. In this work, we develop polarimetric geometric modeling methods for mm-VLBI data, focusing on approaches that fit data products with differing degrees of invariance to broad classes of calibration errors. We establish a fitting procedure using a polarimetric “m-ring” model to approximate the image structure near a black hole. By fitting this model to synthetic EHT data from general relativistic magnetohydrodynamic models, we show that the linear and circular polarization structure can be successfully approximated with relatively few model parameters. We then fit this model to EHT observations of M87* taken in 2017. In total intensity and linear polarization, the m-ring fits are consistent with previous results from imaging methods. In circular polarization, the m-ring fits indicate the presence of event-horizon-scale circular polarization structure, with a persistent dipolar asymmetry and orientation across several days. The same structure was recovered independently of observing band, used data products, and model assumptions. Despite this broad agreement, imaging methods do not produce similarly consistent results. Our circular polarization results, which imposed additional assumptions on the source structure, should thus be interpreted with some caution. Polarimetric geometric modeling provides a useful and powerful method to constrain the properties of horizon-scale polarized emission, particularly for sparse arrays like the EHT.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1980

Stabilization of aerodynamically excited turbomachinery with hydrodynamic journal bearings and supports

A method of analyzing the first mode stability and unbalance response of multimass flexible rotors is presented whereby the multimass system is modeled as an equivalent single mass modal model including the effects of rotor flexibility, general linearized hydrodynamic journal bearings, squeeze film bearing supports and rotor aerodynamic cross coupling. Expressions for optimum bearing and support damping are presented for both stability and unbalance response. The method is intended to be used as a preliminary design tool to quickly ascertain the effects of bearing and support changes on rotor-bearing system performance.

Barrett, L. E.↗

NASA NTRS1989

Numerical simulation of controlled large space structures

Large Space Structures do not have much damping, which necessitates the installation of a controller onto the structure. If the controller is improperly designed, the structure may become unstable and be destroyed. Since Large Space Structures are extremely expensive pieces of hardware, new controllers must not be tested first on the structure. They must first be tested in computer simulations. Until now, the usual procedure for simulating controlled Large Space Structures is to compute a reduced order modal representation of the structure and then apply the controller. However, this procedure entails modal truncation error. A new software package which is free from this error is currently under development within the Center for Space Construction. The more accurate finite element representation of the structure is used in the simulation, instead of the less accurate reduced order modal representation. This software also features an efficient matrix storage scheme, which effectively deals with the asymmetric system matrices which occur when control is added to the structure. Also, an integration algorithm was chosen so that the simulation is a reliable indicator of system stability or instability. The software package is fairly general in nature. Linearity of the finite element model and of the controller is the only assumption made. Actuator dynamics, sensor dynamics, noise, and disturbances can be handled by the package. In addition, output feedback of displacement, velocity, and/or acceleration signals can be simulated. Kalman state estimation was also implemented. This software was tested on a finite element model of a real Large Space Structure: The Mini-Mast Truss. Mini-Mast is a testbed at NASA-Langley which is currently under development. A 714 degree of freedom finite element model was computed, and a 19 state controller was designed for it. Torque wheel dynamics were added to the model, and the entire closed loop system was simulated with the software package.

Quan, Ralph↗

NASA NTRS1988

Direct assessment of two-dimensional wind-tunnel interference from measurements on two interfaces

A direct assessment of two-dimensional wind-tunnel wall interference using upwash component measured on two interfaces has been formulated by the Prandtl-Glauert equation of the flow field and solved by the Fourier transform technique. The analytic formulae obtained for the interference of upwash and pressure on the model are presented. The formulae have been applied successfully to the analytic models for lifting and blockage interferences induced by the general linear slotted and perforated tunnel wall boundary conditions. The formulae have been derived in terms of Fourier coefficients of the measured upwash and illustrated its merits applying to a wavy-wall model case.

Lo, Ching F.↗

DOE OSTI2023

Generalized Bayesian Framework for Evaluation of Integral Benchmark Experiments

A recently published generalized Bayesian optimization framework has provided a way to retract any or all of the three common assumptions underlying the conventional Generalized Linear Least Squares (GLLS) optimization method based on the concepts introduced in Ref. [2]. These assumptions are: 1. Perfection: The model used for data evaluation and the prior probability distribution function (PDF) of generalized data are perfect. 2. Normality: The prior and posterior PDF are normal. 3. Linearity: The model is linear. In this work we outline how the framework in [1] could be directly adopted for improved evaluation of nuclear criticality integral benchmark experiments (IBEs) by: 1. Removing the first assumption alone by utilizing the concept of imperfections introduced in [1] to enable evaluation in the presence of discrepancies between the data and model or of missing covariance information by a GLLS method that will be seen as a generalization of the conventional GLLS method employed by the TSURFER code, and by 2. Removing the remaining two assumptions by implementing a Markov Chain Monte Carlo method for computation of the posterior PDF in the SAMPLER code, where TSURFER and SAMPLER are the uncertainty quantification (UQ) codes for IBEs in the SCALE code system based on the GLLS and the stochastic method, respectively. The graphic in Figure 1 categorizes the methods discussed in terms of the assumptions that they employ to determine posterior PDFs.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Disjunctive optimization model and algorithm for long-term capacity expansion planning of reliable power generation systems

This paper proposes a new optimization model and algorithm for long-term capacity expansion planning of reliable power generation systems. The model optimizes both investment decisions (e.g., size, location, and time to install, retire and decommission facilities) and operation decisions (e.g., on/off status, operating capacity, and expected power output). It is also able to optimize reserve systems (or backup systems), as well as the main systems, to improve power systems reliability. An impact of operational strategies of generators (i.e., participating in electricity production vs. remaining as idle units during operation) on power systems reliability is considered. Probability of equipment failures and capacity failure states are used to rigorously estimate the power systems reliability depending on design and operation strategies. The optimization model is formulated with Generalized Disjunctive Programming (GDP), which is reformulated as a mixed-integer linear programming (MILP) model using the Hull relaxation. Two reliability-related penalties, such as downtime penalty and unmet demand penalty, are included in the objective function to maximize reliability while minimizing the total net present cost. Furthermore, a bilevel decomposition with tailored cuts is developed to reduce computational times of the multi-scale optimization model. The effectiveness of the proposed model is shown by comparing the results with the results obtained from the expansion planning models that do not explicitly consider reliability. In conclusion, we also show that the proposed bilevel decomposition is computationally efficient for solving large scale problems through 5-years and 10-years planning case studies.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

NASA NTRS1974

A decision and control multi-axis pilot model based on an urgency for action concept

An all digital multiple axis, multiple input, multiple output pilot model flies five different tasks in aircraft of different classes while encountering turbulence represented by the Dryden spectral model. Six degree of freedom linearized aircraft equations of motion are used together with a generalized stability augmentation system. The pilot model consists of two parts: (1) a decision maker, and (2) a control action implementer. This decision maker selects the critical variable and predicts the error at action implementation. The control action implementer decides the magnitude of control to be applied and applies it. This system has been successfully compared with hybrid/analog man in the loop simulations of the F-5, A-7, T-33, and 707 aircraft, thus validating the all digital simulation and the decision and control pilot model.

Pollard, J. J.↗

NASA NTRS2004

Progressive Aerodynamic Model Identification From Dynamic Water Tunnel Test of the F-16XL Aircraft

Development of a general aerodynamic model that is adequate for predicting the forces and moments in the nonlinear and unsteady portions of the flight envelope has not been accomplished to a satisfactory degree. Predicting aerodynamic response during arbitrary motion of an aircraft over the complete flight envelope requires further development of the mathematical model and the associated methods for ground-based testing in order to allow identification of the model. In this study, a general nonlinear unsteady aerodynamic model is presented, followed by a summary of a linear modeling methodology that includes test and identification methods, and then a progressive series of steps suggesting a roadmap to develop a general nonlinear methodology that defines modeling, testing, and identification methods. Initial steps of the general methodology were applied to static and oscillatory test data to identify rolling-moment coefficient. Static measurements uncovered complicated dependencies of the aerodynamic coefficient on angle of attack and sideslip in the stall region making it difficult to find a simple analytical expression for the measurement data. In order to assess the effect of sideslip on the damping and unsteady terms, oscillatory tests in roll were conducted at different values of an initial offset in sideslip. Candidate runs for analyses were selected where higher order harmonics were required for the model and where in-phase and out-of-phase components varied with frequency. From these results it was found that only data in the angle-of-attack range of 35 degrees to 37.5 degrees met these requirements. From the limited results it was observed that the identified models fit the data well and both the damping-in-roll and the unsteady term gain are decreasing with increasing sideslip and motion amplitude. Limited similarity between parameter values in the nonlinear model and the linear model suggest that identifiability of parameters in both terms may be a problem. However, the proposed methodology can still be used with careful experiment design and carefully selected values of angle of attack, sideslip, amplitude, and frequency of the oscillatory data.

Murphy, Patrick C.↗

DOE OSTI2021

ACCRUE—An Integral Index for Measuring Experimental Relevance in Support of Neutronic Model Validation

A key challenge for the introduction of any design changes, e.g., advanced fuel concepts, first-of-a-kind nuclear reactor designs, etc., is the cost of the associated experiments, which are required by law to validate the use of computer models for the various stages, starting from conceptual design, to deployment, licensing, operation, and safety. To achieve that, a criterion is needed to decide on whether a given experiment, past or planned, is relevant to the application of interest. This allows the analyst to select the best experiments for the given application leading to the highest measures of confidence for the computer model predictions. The state-of-the-art methods rely on the concept of similarity or representativity, which is a linear Gaussian-based inner-product metric measuring the angle—as weighted by a prior model parameters covariance matrix—between two gradients, one representing the application and the other a single validation experiment. This manuscript emphasizes the concept of experimental relevance which extends the basic similarity index to account for the value accrued from past experiments and the associated experimental uncertainties, both currently missing from the extant similarity methods. Accounting for multiple experiments is key to the overall experimental cost reduction by prescreening for redundant information from multiple equally-relevant experiments as measured by the basic similarity index. Accounting for experimental uncertainties is also important as it allows one to select between two different experimental setups, thus providing for a quantitative basis for sensor selection and optimization. The proposed metric is denoted by ACCRUE, short for Accumulative Correlation Coefficient for Relevance of Uncertainties in Experimental validation. Using a number of criticality experiments for highly enriched fast metal systems and low enriched thermal compound systems with accident tolerant fuel concept, the manuscript will compare the performance of the ACCRUE and basic similarity indices for prioritizing the relevance of a group of experiments to the given application.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2003

Modeling Aircraft Wing Loads from Flight Data Using Neural Networks

Neural networks were used to model wing bending-moment loads, torsion loads, and control surface hinge-moments of the Active Aeroelastic Wing (AAW) aircraft. Accurate loads models are required for the development of control laws designed to increase roll performance through wing twist while not exceeding load limits. Inputs to the model include aircraft rates, accelerations, and control surface positions. Neural networks were chosen to model aircraft loads because they can account for uncharacterized nonlinear effects while retaining the capability to generalize. The accuracy of the neural network models was improved by first developing linear loads models to use as starting points for network training. Neural networks were then trained with flight data for rolls, loaded reversals, wind-up-turns, and individual control surface doublets for load excitation. Generalization was improved by using gain weighting and early stopping. Results are presented for neural network loads models of four wing loads and four control surface hinge moments at Mach 0.90 and an altitude of 15,000 ft. An average model prediction error reduction of 18.6 percent was calculated for the neural network models when compared to the linear models. This paper documents the input data conditioning, input parameter selection, structure, training, and validation of the neural network models.

Allen, Michael J.↗

DOE OSTI2024

First Sagittarius A* Event Horizon Telescope Results. VIII. Physical Interpretation of the Polarized Ring

Abstract In a companion paper, we present the first spatially resolved polarized image of Sagittarius A* on event horizon scales, captured using the Event Horizon Telescope, a global very long baseline interferometric array operating at a wavelength of 1.3 mm. Here we interpret this image using both simple analytic models and numerical general relativistic magnetohydrodynamic (GRMHD) simulations. The large spatially resolved linear polarization fraction (24%–28%, peaking at ∼40%) is the most stringent constraint on parameter space, disfavoring models that are too Faraday depolarized. Similar to our studies of M87*, polarimetric constraints reinforce a preference for GRMHD models with dynamically important magnetic fields. Although the spiral morphology of the polarization pattern is known to constrain the spin and inclination angle, the time-variable rotation measure (RM) of Sgr A* (equivalent to ≈46° ± 12° rotation at 228 GHz) limits its present utility as a constraint. If we attribute the RM to internal Faraday rotation, then the motion of accreting material is inferred to be counterclockwise, contrary to inferences based on historical polarized flares, and no model satisfies all polarimetric and total intensity constraints. On the other hand, if we attribute the mean RM to an external Faraday screen, then the motion of accreting material is inferred to be clockwise, and one model passes all applied total intensity and polarimetric constraints: a model with strong magnetic fields, a spin parameter of 0.94, and an inclination of 150°. We discuss how future 345 GHz and dynamical imaging will mitigate our present uncertainties and provide additional constraints on the black hole and its accretion flow.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1997

Closed Form Solution for Minimum Norm Model-Validating Uncertainty

A methodology in which structured uncertainty models are directly constructed from measurement data for use in robust control design of multivariable systems is proposed. The formulation allows a general linear fractional transformation uncertainty structure connections with respect to a given nominal model. Existence conditions are given, and under mild assumptions, a closed-form expression for the smallest norm structured uncertainty that validates the model is given. The uncertainty bound computation is simple and is formulated for both open and closed loop systems.

Lim, Kyong Been↗

NASA NTRS1982

Feedback stabilization and control of linear neutral systems

The first problem treated here is the realization and stabilization of linear neutral systems with discrete delays. It is shown that any autonomous linear neutral system with discrete delays is zero-state equivalent to an abstract linear system over a local ring of operators. Using the abstract model, the basic existence question for neutral realization is then settled. For general infinite dimensional linear systems, there is no precise analog of the finite dimensional state space isomorphism theorem. Because of this, the notion of spectral minimality must be introduced. For the case of single input-single output systems, realizations are obtained that are both minimal and spectrally minimal. Using the Cruz-Hale theory of stable D-operators, conditions are given that ensure that any poles introduced into the realization are strictly contained in the left half plane and indeed are characterized as characteristic values of the D-operator. The problem of the feedback stabilization of neutral systems is then considered using the abstract model. It is shown that, for neutral systems with commensurable delays and a stable D-operator in the sense of Cruz and Hale, Morses theorem (1976) on pole assignment over a PID implies stabilizability in the reachable case.

Tarn, T. J.↗

NASA NTRS2002

Evaluation of the DAO Retrospective Data Assimilation System

We have developed and implemented a retrospective data assimilation system (RDAS) as an upgrade to the operational DAO/Terra data assimilation system. This formulation aims at improving analysis over filter analysis by the dynamically consistent incorporation of observation information past a given analysis time. The current implementation of the RDAS uses the adjoint of the tangent linear model of a simplified version of the Terra general circulation model and extensions to the physical-space statistical analysis system to propagate observation information back in time. The RDAS adopts the same assumptions of the regular data assimilation system, particularly, no explicit propagation of error covariances are involved therefore rendering a procedure that is computationally affordable. In this study, we show results of experiments conducted to investigate the performance of the 6-hour (lag-1) RDAS. Statistical results obtained over one month during a winter season indicate that the RDAS represents considerable improvement over the regular assimilation. Plans for implementation of the RDAS capability in our new finite-volume data assimilation system will also be presented at the time of the conference.

Zhu, Yanqiu↗

NASA NTRS2005

Statistical Calibration and Validation of a Homogeneous Ventilated Wall-Interference Correction Method for the National Transonic Facility

Wind tunnel experiments will continue to be a primary source of validation data for many types of mathematical and computational models in the aerospace industry. The increased emphasis on accuracy of data acquired from these facilities requires understanding of the uncertainty of not only the measurement data but also any correction applied to the data. One of the largest and most critical corrections made to these data is due to wall interference. In an effort to understand the accuracy and suitability of these corrections, a statistical validation process for wall interference correction methods has been developed. This process is based on the use of independent cases which, after correction, are expected to produce the same result. Comparison of these independent cases with respect to the uncertainty in the correction process establishes a domain of applicability based on the capability of the method to provide reasonable corrections with respect to customer accuracy requirements. The statistical validation method was applied to the version of the Transonic Wall Interference Correction System (TWICS) recently implemented in the National Transonic Facility at NASA Langley Research Center. The TWICS code generates corrections for solid and slotted wall interference in the model pitch plane based on boundary pressure measurements. Before validation could be performed on this method, it was necessary to calibrate the ventilated wall boundary condition parameters. Discrimination comparisons are used to determine the most representative of three linear boundary condition models which have historically been used to represent longitudinally slotted test section walls. Of the three linear boundary condition models implemented for ventilated walls, the general slotted wall model was the most representative of the data. The TWICS code using the calibrated general slotted wall model was found to be valid to within the process uncertainty for test section Mach numbers less than or equal to 0.60. The scatter among the mean corrected results of the bodies of revolution validation cases was within one count of drag on a typical transport aircraft configuration for Mach numbers at or below 0.80 and two counts of drag for Mach numbers at or below 0.90.

Walker, Eric Lee↗

NASA NTRS2005

Statistical Calibration and Validation of a Homogeneous Ventilated Wall-Interference Correction Method for the National Transonic Facility

Walker, Eric L.↗

NASA NTRS2000

Theory of the lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability

The generalized hydrodynamics (the wave vector dependence of the transport coefficients) of a generalized lattice Boltzmann equation (LBE) is studied in detail. The generalized lattice Boltzmann equation is constructed in moment space rather than in discrete velocity space. The generalized hydrodynamics of the model is obtained by solving the dispersion equation of the linearized LBE either analytically by using perturbation technique or numerically. The proposed LBE model has a maximum number of adjustable parameters for the given set of discrete velocities. Generalized hydrodynamics characterizes dispersion, dissipation (hyper-viscosities), anisotropy, and lack of Galilean invariance of the model, and can be applied to select the values of the adjustable parameters which optimize the properties of the model. The proposed generalized hydrodynamic analysis also provides some insights into stability and proper initial conditions for LBE simulations. The stability properties of some 2D LBE models are analyzed and compared with each other in the parameter space of the mean streaming velocity and the viscous relaxation time. The procedure described in this work can be applied to analyze other LBE models. As examples, LBE models with various interpolation schemes are analyzed. Numerical results on shear flow with an initially discontinuous velocity profile (shock) with or without a constant streaming velocity are shown to demonstrate the dispersion effects in the LBE model; the results compare favorably with our theoretical analysis. We also show that whereas linear analysis of the LBE evolution operator is equivalent to Chapman-Enskog analysis in the long wave-length limit (wave vector k = 0), it can also provide results for large values of k. Such results are important for the stability and other hydrodynamic properties of the LBE method and cannot be obtained through Chapman-Enskog analysis.

Lallemand, Pierre↗