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DOE OSTI2024

Minimum entropy filtering for a single output non-Gaussian stochastic system using state transformation

This paper presents a novel filter design for the single-output stochastic non-linear systems subjected to non-Gaussian noises and the proposed assumptions. Based on a state transformation, the unmeasurable states of the systems can be estimated where non-linear terms in the systems have been eliminated. It has been shown that the estimation error is linearly dynamical regarding to the presented vector-valued filter gain which can be optimised by minimising the entropy-based performance criterion. In addition, the convergence of the presented algorithm is analysed in mean-square sense and a numerical example is given to verify the effectiveness of the presented filtering algorithm. Meanwhile, the extended Kalman filter, unscented particle filter and minimum entropy filter are given for the comparisons of the filtering performance. Following the presented framework, some extensions of the presented filtering algorithm are discussed to indicate the flexibility of the filter design. The contribution of this paper can be summarised as establishing a novel minimum entropy filtering framework which consists of model transformation, entropy optimisation and convergence analysis.

42 ENGINEERING↗

DOE OSTI2023

Triple interference, non-linear Talbot effect and gravitization of the quantum

Recently we have discussed a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini–Study metric in the Hilbert space of states, become dynamical and so implement the idea of gravitizing the quantum. Here, in this paper we elaborate on a specific test of this new approach to quantum gravity using triple interference in a varying gravitational field. Our discussion is driven by a profound analogy with recent triple-path interference experiments performed in the context of non-linear optics. We emphasize that the triple interference experiment in a varying gravitational field would deeply influence the present understanding of the kinematics of quantum gravity and quantum gravity phenomenology. We also discuss the non-linear Talbot effect as another striking phenomenological probe of gravitization of the geometry of quantum theory.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2011

Characterizing Observed Limit Cycles in the Cassini Main Engine Guidance Control System

The Cassini spacecraft dynamics-related telemetry during long Main Engine (ME) burns has indicated the presence of stable limit cycles between 0.03-0.04 Hz frequencies. These stable limit cycles cause the spacecraft to possess non-zero oscillating rates for extended periods of time. This indicates that the linear ME guidance control system does not model the complete dynamics of the spacecraft. In this study, we propose that the observed limit cycles in the spacecraft dynamics telemetry appear from a stable interaction between the unmodeled nonlinear elements in the ME guidance control system. Many nonlinearities in the control system emerge from translating the linear engine gimbal actuator (EGA) motion into a spacecraft rotation. One such nonlinearity comes from the gear backlash in the EGA system, which is the focus of this paper. The limit cycle characteristics and behavior can be predicted by modeling this gear backlash nonlinear element via a describing function and studying the interaction of this describing function with the overall dynamics of the spacecraft. The linear ME guidance controller and gear backlash nonlinearity are modeled analytically. The frequency, magnitude, and nature of the limit cycle are obtained from the frequency response of the ME guidance controller and nonlinear element. In addition, the ME guidance controller along with the nonlinearity is simulated. The simulation response contains a limit cycle with similar characterstics as predicted analytically: 0.03-0.04 Hz frequency and stable, sustained oscillations. The analytical and simulated limit cycle responses are compared to the flight telemetry for long burns such as the Saturn Orbit Insertion and Main Engine Orbit Trim Maneuvers. The analytical and simulated limit cycle characteristics compare well with the actual observed limit cycles in the flight telemetry. Both have frequencies between 0.03-0.04 Hz and stable oscillations. This work shows that the stable limit cycles occur due to the interaction between the unmodeled nonlinear elements and linear ME guidance controller.

stable limit cycle↗

NASA NTRS1996

Numerical Study of Steady and Unsteady Canard-Wing-Body Aerodynamics

The use of canards in advanced aircraft for control and improved aerodynamic performance is a topic of continued interest and research. In addition to providing maneuver control and trim, the influence of canards on wing aerodynamics can often result in increased maximum lift and decreased trim drag. In many canard-configured aircraft, the main benefits of canards are realized during maneuver or other dynamic conditions. Therefore, the detailed study and understanding of canards requires the accurate prediction of the non-linear unsteady aerodynamics of such configurations. For close-coupled canards, the unsteady aerodynamic performance associated with the canard-wing interaction is of particular interest. The presence of a canard in close proximity to the wing results in a highly coupled canard-wing aerodynamic flowfield which can include downwash/upwash effects, vortex-vortex interactions and vortex-surface interactions. For unsteady conditions, these complexities of the canard-wing flowfield are further increased. The development and integration of advanced computational technologies provide for the time-accurate Navier-Stokes simulations of the steady and unsteady canard-wing-body flox,fields. Simulation, are performed for non-linear flight regimes at transonic Mach numbers and for a wide range of angles of attack. For the static configurations, the effects of canard positioning and fixed deflection angles on aerodynamic performance and canard-wing vortex interaction are considered. For non-static configurations, the analyses of the canard-wing body flowfield includes the unsteady aerodynamics associated with pitch-up ramp and pitch oscillatory motions of the entire geometry. The unsteady flowfield associated with moving canards which are typically used as primary control surfaces are considered as well. The steady and unsteady effects of the canard on surface pressure integrated forces and moments, and canard-wing vortex interaction are presented in detail including the effects of the canard on the static and dynamic stability characteristics. The current study provides an understanding of the steady and unsteady canard-wing-body flowfield. Emphasis is placed on the effects of the canard on aerodynamic performance as well as the detailed flow physics of the canard-wing flowfield interactions. The computational tools developed to accurately predict the time-accurate flowfield of moving canards provides for the capability of coupled fluids-controls simulations desired in the detailed design and analysis of advanced aircraft.

Eugene, L. Tu↗

DOE OSTI2021

INTEGRATE - Inverse Network Transformations for Efficient Generation of Robust Airfoil and Turbine Enhancements

The INTEGRATE (Inverse Network Transformations for Efficient Generation of Robust Airfoil and Turbine Enhancements) project is developing a new inverse-design capability for the aerodynamic design of wind turbine rotors using invertible neural networks. This AI-based design technology can capture complex non-linear aerodynamic effects while being 100 times faster than design approaches based on computational fluid dynamics. This project enables innovation in wind turbine design by accelerating time to market through higher-accuracy early design iterations to reduce the levelized cost of energy. INVERTIBLE NEURAL NETWORKS Researchers are leveraging a specialized invertible neural network (INN) architecture along with the novel dimension-reduction methods and airfoil/blade shape representations developed by collaborators at the National Institute of Standards and Technology (NIST) learns complex relationships between airfoil or blade shapes and their associated aerodynamic and structural properties. This INN architecture will accelerate designs by providing a cost-effective alternative to current industrial aerodynamic design processes, including: - Blade element momentum (BEM) theory models: limited effectiveness for design of offshore rotors with large, flexible blades where nonlinear aerodynamic effects dominate - Direct design using computational fluid dynamics (CFD): cost-prohibitive - Inverse-design models based on deep neural networks (DNNs): attractive alternative to CFD for 2D design problems, but quickly overwhelmed by the increased number of design variables in 3D problems AUTOMATED COMPUTATIONAL FLUID DYNAMICS FOR TRAINING DATA GENERATION - MERCURY FRAMEWORK The INN is trained on data obtained using the University of Marylands (UMD) Mercury Framework, which has with robust automated mesh generation capabilities and advanced turbulence and transition models validated for wind energy applications. Mercury is a multi-mesh paradigm, heterogeneous CPU-GPU framework. The framework incorporates three flow solvers at UMD, 1) OverTURNS, a structured solver on CPUs, 2) HAMSTR, a line based unstructured solver on CPUs, and 3) GARFIELD, a structured solver on GPUs. The framework is based on Python, that is often used to wrap C or Fortran codes for interoperability with other solvers. Communication between multiple solvers is accomplished with a Topology Independent Overset Grid Assembler (TIOGA). NOVEL AIRFOIL SHAPE REPRESENTATIONS USING GRASSMAN SPACES We developed a novel representation of shapes which decouples affine-style deformations from a rich set of data-driven deformations over a submanifold of the Grassmannian. The Grassmannian representation as an analytic generative model, informed by a database of physically relevant airfoils, offers (i) a rich set of novel 2D airfoil deformations not previously captured in the data , (ii) improved low-dimensional parameter domain for inferential statistics informing design/manufacturing, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal shapes. TECHNOLOGY TRANSFER DEMONSTRATION - COUPLING WITH NREL WISDEM Researchers have integrated the inverse-design tool for 2D airfoils (INN-Airfoil) into WISDEM (Wind Plant Integrated Systems Design and Engineering Model), a multidisciplinary design and optimization framework for assessing the cost of energy, as part of tech-transfer demonstration. The integration of INN-Airfoil into WISDEM allows for the design of airfoils along with the blades that meet the dynamic design constraints on cost of energy, annual energy production, and the capital costs. Through preliminary studies, researchers have shown that the coupled INN-Airfoil + WISDEM approach reduces the cost of energy by around 1% compared to the conventional design approach. This page will serve as a place to easily access all the publications from this work and the repositories for the software developed and released through this pr...

aerodynamics↗

NASA NTRS1984

A substructure coupling procedure applicable to general linear time-invariant dynamic systems

A substructure synthesis procedure applicable to structural systems containing general nonconservative terms is presented. In their final form, the non-self-adjoint substructure equations of motion are cast in state vector form through the use of a variational principle. A reduced-order model for each substructure is implemented by representing the substructure as a combination of a small number of Ritz vectors. For the method presented, the substructure Ritz vectors are identified as a truncated set of substructure eigenmodes, which are typically complex, along with a set of generalized real attachment modes. The formation of the generalized attachment modes does not require any knowledge of the substructure flexible modes; hence, only the eigenmodes used explicitly as Ritz vectors need to be extracted from the substructure eigenproblem. An example problem is presented to illustrate the method.

Howsman, T. G.↗

NASA NTRS1991

Theoretical and computational dynamics of a compressible flow

An introduction to the theoretical and computational fluid dynamics of a compressible fluid is presented. The general topics addressed include: thermodynamics and physical properties of compressible fluids; 1D flow of an inviscid compressible fluid; shock waves; fundamental equations of the dynamics of a compressible inviscid non-heat-conducting and radiating fluid, method of small perturbations, linearized theory; 2D subsonic steady potential flow; hodograph and rheograph methods, exact solutions of 2D insentropic steady flow equations, 2D steady transonic and hypersonic flows, method of characteristics, linearized theory of 3D potential flow, nonlinear theory of 3D compressibe flow, anisentropic (rotational) flow of inviscid compressible fluid, electromagnetogasdynamics, multiphase flows, flows of a compressible fluid with transport phenomena.

Pai, Shih-I↗

NASA NTRS1992

A study of the physical mechanisms for filament eruption and coronal mass ejection via numerical simulation

During this period of performance (1 Jan. 1992 - 31 Dec. 1992), the investigation of the following tasks was accomplished: (1) application of the Non-linear Force-free Field (NLFF) Model to study the active region evolution; (2) coronal dynamical responses due to emerging flux including the transition region; (3) loss of MHD equilibrium due to footpoint motions; and (4) two-dimensional MHD global coronal model: steady-state streamers. The detailed description of these studies are included.

Wu, S. T.↗

NASA NTRS2011

Filtering Methods for Error Reduction in Spacecraft Attitude Estimation Using Quaternion Star Trackers

Precision attitude determination for recent and planned space missions typically includes quaternion star trackers (ST) and a three-axis inertial reference unit (IRU). Sensor selection is based on estimates of knowledge accuracy attainable from a Kalman filter (KF), which provides the optimal solution for the case of linear dynamics with measurement and process errors characterized by random Gaussian noise with white spectrum. Non-Gaussian systematic errors in quaternion STs are often quite large and have an unpredictable time-varying nature, particularly when used in non-inertial pointing applications. Two filtering methods are proposed to reduce the attitude estimation error resulting from ST systematic errors, 1) extended Kalman filter (EKF) augmented with Markov states, 2) Unscented Kalman filter (UKF) with a periodic measurement model. Realistic assessments of the attitude estimation performance gains are demonstrated with both simulation and flight telemetry data from the Lunar Reconnaissance Orbiter.

Calhoun, Philip C.↗

NASA NTRSDate not supplied

Method for Extracting Aerodynamic Coefficients and Winds On-the-Fly Using Real-Time GPS Data

The landing accuracy of an autonomous guided parafoil is influenced by its ability to predict the trajectory, which is shaped by the parafoil’s aerodynamic characteristics and atmospheric winds. The parafoil is subjective to imperfections from manufacturing, damage during deployment, lateral asymmetry, and so forth, leading to discrepancies between the actual aerodynamic properties and the onboard aerodynamic model. Thus, by acquiring an accurate knowledge of the aerodynamic properties and real-time winds, the onboard simulation can reduce the undertainties in the dynamics modeling for trajectory propagation to improve the landing accuracy. For that purpose, a non-linear least-squares method is developed to calculate differential corrections for optimizing and extracting the parafoil aerodynamic coefficients and winds on-the-fly using real-time data from the Global Positioning System (GPS). Post-flight analyses from two test flights have shown that the method provides improved simulations that closely match the GPS trajectories.

Lisa Ling↗

NASA NTRS1989

Simulation of shuttle flight control system structural interaction with RMS deployed payloads

A simulation of the system made up of the Orbiter, Remote Manipulator System (RMS), and payload grappled by the RMS was completed. The simulation was used to study the stability of this overall system when its attitude is under control of the Orbiter's on-orbit Flight Control System (FCS). The simulation was also used to study the dynamics of the system when the RMS and its associated command software are in active control of the relative Orbiter to payload position and orientation. The simulation models all of the following elements: RMS boom bending (represented by two cubic bending models); RMS boom torsion; RMS joint gearbox compliance (represented by a non-linear wind-up model); flexibility at the RMS to Orbiter interface; flexibility at the RMS to payload interface; joint motor dynamics; joint servo-loop dynamics; RMS on-board computer command logic; data transfer delays between the RMS sensor and the RMS on-board computer and between the RMS on-board computer and RMS joint servos; on-orbit flight control nonlinear control logic; and the Reaction Control System (both Primary and Vernier) jet forces and moments.

Turnball, Joe↗

NASA NTRS1979

Filtering of non-linear instabilities

For Courant numbers larger than one and cell Reynolds numbers larger than two, oscillations and in some cases instabilities are typically found with implicit numerical solutions of the fluid dynamics equations. This behavior has sometimes been associated with the loss of diagonal dominance of the coefficient matrix. It is shown here that these problems can in fact be related to the choice of the spatial differences, with the resulting instability related to aliasing or nonlinear interaction. Appropriate 'filtering' can reduce the intensity of these oscillations and in some cases possibly eliminate the instability. These filtering procedures are equivalent to a weighted average of conservation and non-conservation differencing. The entire spectrum of filtered equations retains a three-point character as well as second-order spatial accuracy. Burgers equation has been considered as a model. Several filters are examined in detail, and smooth solutions have been obtained for extremely large cell Reynolds numbers.

Khosla, P. K.↗

DOE OSTI2025

Numerical simulation of compressible fluid-dynamics in the chamber of inertial fusion energy systems

Here, this paper aims to establish new and innovative modeling capabilities for analyzing chambers in Inertial Fusion Energy (IFE) systems. IFE is emerging as a promising method to achieve fusion power production, but several challenges must be overcome to develop an IFE pilot plant or deploy commercial IFE systems. These challenges are both theoretical and technical, encompassing a deeper understanding of the underlying physical phenomena and the development of new technologies and materials. One of the needs is to develop mathematical models to describe IFE systems and numerical tools to simulate them. This paper contributes to this endeavor by presenting a new OpenFOAM solver for IFE systems, focusing on gas dynamics in their chambers. The analysis and development of chamber designs will play a significant role in the transition from single-shot experiments to high-repetition rates, as there is a need to protect the chamber walls from the intense radiation fields produced by fusion reactions. A promising design option, normally referred to as thick wall chamber design, consists in using lithium or molten salt jet arrays within the chamber. A critical phenomenon is the venting of high-pressure gases from the center to the external part of the chamber, passing through the blanket array. This process involves the propagation and attenuation of strong pressure waves, requiring suitable modeling approaches for compressible fluid-dynamics. The solver proposed in this work implements a multi-material hydrodynamics model tailored to accurately describe the non-linear propagation of pressure waves while avoiding numerical oscillation issues typical of high-velocity compressible simulation. This solver is verified against numerical test cases, validated against experimental data, and applied to the analysis of the High-Yield Lithium-Injection Fusion-Energy (HYLIFE-I) concept. The relevance of this paper is threefold. Firstly, it contributes to developing and testing modeling approaches for compressible fluid-dynamics phenomena, with specific focus on the new and unexplored topic of IFE thick-liquid-wall blanket modeling. Secondly, it marks one of the first applications of the OpenFOAM library in the research field of IFE systems. Finally, the investigated problem is of practical interest for IFE developers, as it provides useful indications about relevant phenomena in pressure wave propagation in the chamber of these systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2017

Comparison of EKF and UKF for Robotic Missions to Mars

The batched Kalman lter works well for a wide variety of orbit determination scenarios but requires linearized approximations to the underlying dynamical system. Furthermore, implementation depends on the computation of partial derivatives for all measurements and parameters used in the lter, a non-trivial task even when analytical derivations are possible. To address these limitations, many extensions and modi - cations to the linear Kalman lter have been proposed over the years since Kalman's initial publication. Our investigation examines two popular variants of the Kalman lter, namely the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF), within the context of spacecraft missions to Mars. The EKF relies on the same mathematical basis as the classic version of the lter, however it sequentially updates the linearization as the ltering process is conducted. In contrast, the UKF is built upon the unscented transform which samples the nearby solution space and numerically propagates perturbed trajectories as part of the update / estimation process. We assess the performance of the ltering algorithms under a variety of mission scenarios with the goal of establishing decision criteria for which implementation to use under di ering circumstances.

Ely, Todd↗

NASA NTRS2000

Modeling the Dynamics of the Middle Atmosphere and Lower Thermosphere Under the Influence of Gravity Waves

Our Numerical Spectral Model (NSM), which extends from the ground up into the thermosphere, is non-linear, time-dependent and has been employed for 2D and 3D applications. The standard version of the NSM incorporates Hines' Doppler Spread Parameterization for small scale gravity waves (GW), but planetary waves generated in the troposphere have also been incorporated. The NSM has been applied to describe: (1) the anomalous seasonal variations of the zonal circulation and temperature in the upper mesosphere, (2) the equatorial oscillations (quasi-biennial and semi-annual oscillations (QBO and SAO)) extending from the stratosphere into the upper mesosphere, (3) the diurnal and semi-diurnal tides, and (4) the planetary waves that are excited in the mesosphere. With the emphasis to provide understanding, we present here results from numerical experiments with the NSM that shed light on the GW processes that are of central importance in the mesosphere and lower thermosphere. These are our conclusions: (1) The large semiannual variations in the diurnal tide (DT), with peak amplitudes observed around equinox, are produced primarily by GW interactions that involve, in part, planetary waves. The DT, like planetary waves, tends to be amplified by GW momentum deposition, which reduces also the vertical wavelength, but variations in eddy viscosity associated with GW interactions are also important. (2) The semidiurnal tide (SDT) and its phase in particular, is strongly influenced by the mean zonal circulation. The SDT, individually, is also amplified by GW. But the DT filters out GW such that the GW interaction effectively reduces the amplitude of the SDT, producing a strong nonlinear interaction between the DT and SDT. (3) Without external time dependent energy or momentum sources, planetary waves (PW) are generated in the model for zonal wavenumbers 1 to 4, which have amplitudes in the mesosphere above 50 km as large as 40 m/s and periods between 50 and 2 days. The waves are generated primarily during solstice conditions, which indicates that the baroclinic instability (associated with the GW induced reversal in the latitudinal temperature gradient) is playing an important role. Numerical experiment show that GW, directly, also greatly amplify the PW. A common feature of the PW generated in summer and winter is that their vertical wavelengths throughout the mesosphere are large, which indicates that the waves are not propagating freely but are generated throughout the region. Another common feature is that the PW propagate preferentially westward in summer and eastward in winter, being launched from the westward and eastward zonal winds that prevail respectively in summer and winter at altitudes below 80 km. (4) Planetary waves generated internally by baroclinic instability and GW interaction produce large amplitude modulations of the DT and SDT. In summary we conclude that GW play major roles in generating and amplifying the dynamical components in the MLT region and, acting principally through wave filtering, produce important non-linear interactions between the components.

Mayr, H. G.↗

DOE OSTI2024

On the Interplay Between Distributed Bulk Plasticity and Local Fault Slip in Evolving Fault Zone Complexity

Abstract We numerically investigate the role of plastic strain accumulation on the mechanical response of a planar strike‐slip fault. Our models show that fault‐zone strength significantly impacts the ensuing sequence of earthquakes. Weaker fault zones accumulating more plastic strain promote more complexity in the seismicity pattern through aperiodic earthquake occurrences and intermittent episodes of rupture and arrest. However, if the fault zone strength is high enough, the overall earthquake sequence is characterized by periodic fault‐spanning events. We find that both the fault normal stress and the fault geometric profile evolve throughout the earthquake sequence, suggesting a self‐roughening mechanism. Despite the significant impact of plasticity on the fault response, the width of the plastically deforming region in the fault zone is small compared to the fault length. Our results suggest a rich behavior in dynamically evolving fault zones and support the need for further high‐resolution studies of the highly non‐linear near‐fault region.

Geology↗

DOE OSTI2024

Enabling "Fuel" Switching through On-Demand Wind Control

This work demonstrates that classical shear-flow stability theory can be successfully applied to modify wind turbine wakes and also explains the success of several emerging, empirically-arrived control methods (i.e., dynamic induction and helix control). Linear stability theory predictions are extended to include the effects of non-axisymmetric inflow profiles, such as wind shear, which is shown to not strongly affect the primary forcing frequency. The predictions, as well as idealized large-eddy simulations using actuator-line representation of the turbine blades, agree that the n = 0 and ±1 modes have faster initial growth rates than higher-order modes, suggesting the lower-order modes are more appropriate for wake control. Exciting the lower-order modes with periodic pitching of the blades produces higher entrainment into the wake and consequently faster wake recovery.

17 WIND ENERGY↗

NASA NTRS1982

Blade loss transient dynamic analysis of turbomachinery

This paper reports on work completed to develop an analytical method for predicting the transient non-linear response of a complete aircraft engine system due to the loss of a fan blade, and to validate the analysis by comparing the results against actual blade loss test data. The solution, which is based on the component element method, accounts for rotor-to-casing rubs, high damping and rapid deceleration rates associated with the blade loss event. A comparison of test results and predicted response show good agreement except for an initial overshoot spike not observed in test. The method is effective for analysis of large systems.

Stallone, M. J.↗