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Results for “Linear and nonlinear operators”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Bilinear modeling and state estimation of slew-induced deformations of a flexible multibody system

A model of the nonlinear dynamics of a deformable maneuvering multibody system is described, whereby elastic deformations are modeled by restoring forces and dissipative forces at point mass appendages. This model is brought into bilinear form. Estimation of deformations occasioned by rapid slewing maneuvers is carried out by a filter based on a globally equivalent linear model of the bilinear dynamics, and is shown to be an improvement over the extended Kalman filter. To further alleviate the computational burden, the estimated deformation state is propagated between observations by a low dimensional operator spline interpolator of bilinear system Volterra series, which is easily implemented.

Dwyer, Thomas A. W., III↗
DOE OSTI2026

Ultrasound Characterization of Plastic Bonded Explosives With Varied Binder Content and Density

Advanced explosive formulations and methods of production require rapid characterization for both processes and materials. Here, we present results for ultrasound characterization of a plastic bonded explosive (PBX) formulation as a function of binder weight percent and pressing density using through-transmission sound speed measurements. The explosive in this study was composed of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) combined with the fluoropolymer binder Kynar Ultraflex B. Binder content ranged from 2.6 wt.% to 11.5 wt.% with associated explosive formulation densities from 1.69 g/cc to 1.89 g/cc. We find linear and nonlinear changes in longitudinal and shear sound speeds, peak frequencies, and measured elastic properties for the different PBX formulations. These measured changes can differentiate the tested formulations, highlighting the potential for ultrasound as a nondestructive characterization method for newly-formulated PBXs. We also demonstrate through-transmission measurements using different coupling media and present results from an ultrasound technique called resonant ultrasound spectroscopy (RUS). Both transmission and RUS approaches may allow for rapid and even automated characterization of PBX components suitable for high-throughput manufacturing operations.

Engineering↗
DOE OSTI2023

Anticipating gelation and vitrification with medium amplitude parallel superposition (MAPS) rheology and artificial neural networks

Abstract Anticipating qualitative changes in the rheological response of complex fluids (e.g., a gelation or vitrification transition) is an important capability for processing operations that utilize such materials in real-world environments. One class of complex fluids that exhibits distinct rheological states are soft glassy materials such as colloidal gels and clay dispersions, which can be well characterized by the soft glassy rheology (SGR) model. We first solve the model equations for the time-dependent, weakly nonlinear response of the SGR model. With this analytical solution, we show that the weak nonlinearities measured via medium amplitude parallel superposition (MAPS) rheology can be used to anticipate the rheological aging transitions in the linear response of soft glassy materials. This is a rheological version of a technique called structural health monitoring used widely in civil and aerospace engineering. We design and train artificial neural networks (ANNs) that are capable of quickly inferring the parameters of the SGR model from the results of sequential MAPS experiments. The combination of these data-rich experiments and machine learning tools to provide a surrogate for computationally expensive viscoelastic constitutive equations allows for rapid experimental characterization of the rheological state of soft glassy materials. We apply this technique to an aging dispersion of Laponite ® clay particles approaching the gel point and demonstrate that a trained ANN can provide real-time detection of transitions in the nonlinear response well in advance of incipient changes in the linear viscoelastic response of the system.

Lennon, Kyle R. (ORCID:0000000212515461)↗
NASA NTRSDate not supplied

Aeroservoelastic Control Law Development for the Integrated Adaptive Wing Technology Maturation Wind-Tunnel Test

The NASA Advanced Air Transport Technology (AATT) Project seeks to “explore and develop technologies and concepts for improved energy efficiency and environmental compatibility for fixed wing subsonic transports” [1]. The IAWTM project is a subproject within AATT and is a joint Boeing/NASA effort to, in part, demonstrate the active control systems necessary to employ high-aspect ratio wings for improved aerodynamic efficiency. The aircraft configuration under study for the IAWTM project is a generic jet transport based on the NASA Common Research Model (CRM) whose wing aspect ratio has been increased to 13.5 (as opposed to nominal CRM aspect ratio of 9) and whose development is given in Ref. [2]. A semi-span model of the high-aspect-ratio CRM with 10 trailing edge control surfaces is currently being fabricated and will be delivered to the NASA Langley Transonic Dynamics Tunnel (TDT). There, several tests will be conducted to demonstrate maneuver load alleviation (MLA), gust load alleviation (GLA), active flutter suppression (AFS), and drag reduction, all at transonic conditions. A layout of the wind tunnel model is shown in Fig. 1. The wind-tunnel model is a spar/pod wing design with a relatively rigid fuselage attached to a mounting structure (seen in Fig. 1), which in turn is attached to a load balance behind the tunnel wall. Shims exist that can be attached to force the load to go through the fuselage rather than through the balance so as not to damage the balance in the event of flutter. The spar/pod design is similar to that used in the Boeing truss-braced wing aeroelastic model tested in the TDT in 2013 [3]. There is a central spar running the span of the wing to which the pods are attached that form the aerodynamic shape of the wing. The pods are constructed of ribs for attachment to the spar and skins to create the outer mold line. There are ten active control surfaces that will be used for the test objectives discussed above. Three of these (two outboard ailerons and one inboard aileron) are high-speed electrohydraulic actuators, and the remaining seven are low-speed mini-plane flaps, which have slower servo motors that will be used primarily for drag and maneuver load reductions. Control laws must be developed for each test (MLA, GLA, AFS, and drag reduction) and must be able to work in tandem when two or more control strategies are being tested simultaneously (e.g., when control laws to mitigate maneuver loads and gust loads operate simultaneously). The development of these control laws requires accurate mathematical representations of the aerodynamics, structural dynamics, and control surface dynamics of the system. Taken together, this mathematical representation—which is often in state-space form— is the ASE model. Three low-order ASE models of differing fidelities were developed for the IAWTM test and will be presented here. The differences in fidelity appeared in the aerodynamic modeling—one model assumed purely linear aerodynamics, while the other two models used different techniques to linearize the aerodynamics about a nonlinear mean. Furthermore, simple observer-based full-state feedback controllers for each test (MLA, GLA, AFS, and drag reduction) were designed from these low-order ASE models and implemented in a higher-order, nonlinear computational ASE simulation to assess the effectiveness of each controller. Observers were designed from each of the three lower-order ASE models, and each (linear) observer was then used as an estimate of the nonlinear dynamics of the system. Using the estimated states and the full-state feedback controller, control surface commands were fed back to the higher-order, nonlinear ASE system. The insight gained during this development will be applied to control law development for the physical IAWTM wind-tunnel test.

Josiah M Waite↗
NASA NTRS1989

A space-time discretization procedure for wave propagation problems

Higher order compact algorithms are developed for the numerical simulation of wave propagation by using the concept of a discrete dispersion relation. The dispersion relation is the imprint of any linear operator in space-time. The discrete dispersion relation is derived from the continuous dispersion relation by examining the process by which locally plane waves propagate through a chosen grid. The exponential structure of the discrete dispersion relation suggests an efficient splitting of convective and diffusive terms for dissipative waves. Fourth- and eighth-order convection schemes are examined that involve only three or five spatial grid points. These algorithms are subject to the same restrictions that govern the use of dispersion relations in the constructions of asymptotic expansions to nonlinear evolution equations. A new eighth-order scheme is developed that is exact for Courant numbers of 1, 2, 3, and 4. Examples are given of a pulse and step wave with a small amount of physical diffusion.

Davis, Sanford↗
DOE OSTI2020

Conservative discontinuous Galerkin schemes for nonlinear Dougherty–Fokker–Planck collision operators

Here, we present a novel discontinuous Galerkin algorithm for the solution of a class of Fokker–Planck collision operators. These operators arise in many fields of physics, and our particular application is for kinetic plasma simulations. In particular, we focus on an operator often known as the ‘Lenard–Bernstein’ or ‘Dougherty’ operator. Several novel algorithmic innovations, based on the concept of weak equality, are reported. These weak equalities are used to define weak operators that compute primitive moments, and are also used to determine a reconstruction procedure that allows an efficient and accurate discretization of the diffusion term. We show that when two integrations by parts are used to construct the discrete weak form, and finite velocity-space extents are accounted for, a scheme that conserves density, momentum and energy exactly is obtained. One novel feature is that the requirements of momentum and energy conservation lead to unique formulas to compute primitive moments. Careful definition of discretized moments also ensure that energy is conserved in the piecewise linear case, even though the kinetic-energy term, $v^2$ is not included in the basis set used in the discretization. A series of benchmark problems is presented and shows that the scheme conserves momentum and energy to machine precision. Empirical evidence also indicates that entropy is a non-decreasing function. The collision terms are combined with the Vlasov equation to study collisional Landau damping and plasma heating via magnetic pumping.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Joint Estimation of Topology and Injection Statistics in Distribution Grids with Missing Nodes

Optimal operation of distribution grid resources relies on accurate estimation of its state and topology. Practical estimation of such quantities is complicated by the limited presence of real-time meters. This article discusses a theoretical framework to jointly estimate the operational topology and statistics of injections in radial distribution grids under limited availability of nodal voltage measurements. In particular, we show that our proposed algorithms are able to provably learn the exact grid topology and injection statistics at all unobserved nodes as long as they are not adjacent. The algorithm design is based on novel ordered trends in voltage magnitude fluctuations at node groups, that are independently of interest for radial physical flow networks. The complexity of the designed algorithms is theoretically analyzed and their performance is validated using both linearized and nonlinear ac power flow samples in test distribution grids.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1971

A multifilter phase-lock loop.

The phase model for the generalized multifilter phase-lock loop (M PLL) is considered and state equations for this model are derived. A linear analysis is presented to aid in the preliminary design of an M PLL and to indicate the noise improvement over a conventional phase-lock loop (PLL). Performance characteristics are examined for an M PLL with low-pass and bandpass characteristics used in a specific FM communication system. Both single and double sinusoidal FM are used and a region of proper operation of the M PLL is determined in terms of modulation index and modulati ng frequency. These results are obtained from both analog and digital computer simulation of the nonlinear system.

Carden, F.↗
NASA NTRS1993

The middeck 0-gravity dynamics experiment

The Middeck 0-Gravity Dynamics Experiment (MODE), flown onboard the Shuttle STS-48 Mission, consists of three major elements: the Experiment Support Module, a dynamics test bed providing computer experiment control, analog signal conditioning, power conditioning, an operator interface consisting of a keypad and display, experiment electrical and thermal control, and archival data storage: the Fluid Test Article assembly, used to investigate the dynamics of fluid-structure interaction in 0-gravity; and the Structural Test Article for investigating the open-loop dynamics of structures in 0-gravity. Deployable, erectable, and rotary modules were assembled to form three one- and two-dimensional structures, in which variations in bracing wire and rotary joint preload could be introduced. Change in linear modal parameters as well as the change in nonlinear nature of the response is examined. Trends in modal parameters are presented as a function of force amplitude, joint preload, and ambient gravity. An experimental study of the lateral slosh behavior of contained fluids is also presented. A comparison of the measured earth and space results identifies and highlights the effects of gravity on the linear and nonlinear slosh behavior of these fluids.

Crawley, Edward F.↗
DOE OSTI2026

Integral Kernel Methods for Nonlinear Parabolic-Elliptic Systems

Nonlinear parabolic-elliptic systems arise in many physical, biological, and chemical phenomena such as chemotaxis, ion transport, self-gravitating particles, and Brownian vortices. Existing methods struggle with the strong coupling and high nonlinearity and nonlocality of some of these systems, especially the ill-conditioned, convection-dominated problems. To overcome numerical difficulties, current approaches rely on initial guesses, preconditioning, or iterative techniques with no convergence guarantees. They might suffer from poor scalability, large memory usage, and difficulty to parallelize. Inspired by the connection of parabolic-elliptic systems to stochastic processes, we introduce a novel meshless, monolithic, and fully explicit method that naturally encapsulates the elliptic and parabolic operators into a single step which updates each node deterministically with global information. By being fully quadrature-based, it avoids solving systems of discretized equations and does not utilize initial guesses or preconditioning, while requiring little memory and being easy to parallelize. We first derive the method in an integral kernel formulation with quadratic complexity in the number of integration nodes and then leverage kernel-independent fast multipole methods (FMM) to present a scalable algorithm with linear complexity. We provide numerical examples for the Poisson-Nernst-Planck equations in one, two, and three dimensions, together with the derivation of the integral kernel for each case. Furthermore, the examples demonstrate the fast convergence and scalability of the FMM-accelerated algorithm, as well as its suitability for convection-dominated problems, making it competitive against traditional PDE solvers.

PDE systems↗
DOE OSTI2022

Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference

Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction). Here, this work focuses on the large class of physical systems that can be well described by models with quadratic and cubic nonlinear terms and proposes a regularizer for operator inference that induces a stability bias onto learned models. The proposed regularizer is physics informed in the sense that it penalizes higher-order terms with large norms and so explicitly leverages the polynomial model form that is given by the underlying physics. This means that the proposed approach judiciously learns from data and physical insights combined, rather than from either data or physics alone. Additionally, a formulation of operator inference is proposed that enforces model constraints for preserving structure such as symmetry and definiteness in linear terms. Numerical results demonstrate that models learned with operator inference and the proposed regularizer and structure preservation are accurate and stable even in cases where using no regularization and Tikhonov regularization leads to models that are unstable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A review of active probing-based system identification techniques with applications in power systems

System identification is becoming a relevant research area for numerous applications in power grids due to the increasing complexity of the system. A paradigm shift in power system infrastructure driven by renewable energy resources, controllable loads, and new power electronics technologies have given rise to new challenges in power systems operation and control. This increased complexity of power systems and unavailability of physics-based models of most inverter-based resources requires that traditional modeling of power systems approaches be complemented by system identification-based black or grey box modeling techniques. In light of the importance of system identification and little attention paid to the applications of these techniques in transforming power systems, this paper provides a comprehensive review of active probing-based system identification methods in the context of power system applications. It reviews applications of both linear and nonlinear system identification with discussion on their potential and key takeaways. To motivate a further practical use in power systems, the paper provides an example of system identification, to develop a state space model of an unknown plant with step-by-step details. The paper highlights the advantages of using modern power electronics-based sources in the identification process and discusses the emerging research directions for future.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS2018

Multi-Parameter Nonlinear Gain Correction of X-Ray Transition Edge Sensors for the X-Ray Integral Field Unit

With its array of 3840 Transition Edge Sensors (TESs), the Athena X-ray Integral Field Unit (X-IFU) will provide spatially resolved high-resolution spectroscopy (2.5 eV up to 7 keV) from 0.2 to 12 keV, with an absolute energy scale accuracy of 0.4 eV. Slight changes in the TES operating environment can cause significant variations in its energy response function, which may result in systematic errors in the absolute energy scale. We plan to monitor such changes at pixel level via onboard X-ray calibration sources and correct the energy scale accordingly using a linear or quadratic interpolation of gain curves obtained during ground calibration. However, this may not be sufficient to meet the 0.4 eV accuracy required for the XIFU. In this contribution, we introduce a newtwo-parameter gain correction technique, based on both the pulse-height estimate of a fiducial line and the baseline value of the pixels. Using gain functions that simulate ground calibration data, we show that this technique can accurately correct deviations in detector gain due to changes in TES operating conditions such as heat sink temperature, bias voltage, thermal radiation loading and linear amplifier gain. We also address potential optimisations of the onboard calibration source and compare the performance of this new technique with those previously used.

Cucchetti, E.↗
DOE OSTI2021

A new and alternative look at nonlinear Alfvénic states

The formulation for studying nonlinear Alfvenic states, sustainable in Hall Magnetohydrodynamics (HMHD), becomes considerably simpler and more tractable when circularly polarized Beltrami vectors (the eigenstates of linear HMHD) are used as the basis functions. Nonlinear HMHD is, then, reduced to a rather simple looking set of scalar equations from which a model problem of three interacting Beltrami modes is formulated and analytically solved. The triplet interactions span a variety of familiar nonlinear processes leading to a redistribution as well as periodic exchange of energy. The energy exchange processes (whose strength is measured by an energy exchange/depletion time) will, perhaps, play a dominant role in determining the spectral content of an eventual Alfvenic state. All nonlinearities (sensitive functions of the interacting wave vectors) operate at par, and none is dominant over any substantial region of k-space; their intricate interplay prevents a “universal” picture from emerging; few generalizations on the processes that may, for instance, lead to a turbulent state, are possible. However, the theory can definitely claim: (1) the energy tends to flow from lower to higher k and (2) the higher k z (in the direction of the ambient magnetic field) components of a mode with a given k are depleted/oscillate faster—in some cases much faster. It is noteworthy that the mode coupling is the strongest (with the shortest depletion time) when the participating wave vectors are nearly perpendicular; perhaps, an expected consequence of the curl (cross product) nonlinearities. Numerical simulations will be necessary to help create a fully reliable picture.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Turbulence simulations of drift-Alfvén wave effects on edge-localized modes and divertor target heat flux width

A series of BOUT++ turbulence simulations are performed for two Pre-Fusion Power Operation (PFPO-1,2) phases of the ITER Research plan proclaimed in 2019. Linear simulation results show that PFPO-1 is unstable to Peeling-ballooning modes (PB), while the PFPO-2 is unstable to the coupling of PB and Drift-Alfvén wave (DAW) instabilities. The linear results are qualitatively consistent with the dispersion relation of DAW. To study the influence of the DAW on the edge-localized mode (ELM) crash, the PFPO-2 is adopted in this section. Different from the grassy ELM in [Li et al 2022 Nucl. Fusion 62, 096030], nonlinear simulations show that the ELM size of PFPO-2 is almost one-third of the grassy ELM, representing a distinct small ELM. However, simulations then show that if the PB instability is removed, the fluctuation amplitude drops by an order of magnitude and the ELM crash disappears, which is in accord with the theory in [Xu et al 2010 Physical Review Letters, Vol. 105, 175005] and the results in [Li et al 2022 Nucl. Fusion 62, 096030], confirming that the PB instability is a necessary condition for an ELM crash. Furthermore, removing the DAW drive also suppresses ELM crashes, implying that PB instability is necessary but insufficient for PFPO-2 ELM and that DAW could amplify PB-driven turbulence. In addition, by integrating results of both PFPO phases by BOUT++ turbulence analysis with heat flux width (λ q ) and electron thermal diffusivity (χ e ), these simulations establish a predictive framework for heat flux width and its dominant mechanisms, thereby providing a comprehensive scheme for the prediction of the heat flux width. Moreover, simulations indicate that DAW driving can increase the transport coefficient by enhancing the turbulent transport, leading to a broadened heat flux width once the transport coefficient exceeds

Drift-Alfvén wave↗
NASA NTRS1991

A linear control design structure to maintain loop properties during limit operation in a multi-nozzle turbofan engine

The implementation of multi-variable control systems on turbofan engines requires the use of limit protection to maintain safe engine operation. Since a turbofan engine typically encounters limits during transient operation, the use of a limit protection scheme that modifies the feedback loop may void the desired 'guarantees' associated with linear multi-variable control design methods, necessitating considerable simulation to validate the control with limited protection. An alternative control design structure is proposed that maintains the desired linear feedback properties when certain safety limits are encountered by moving the limit protection scheme outside the feedback loop. This proposed structure is compared to a structure with a limit protection scheme that modifies the feedback loop properties. The two design structures are compared using both linear and nonlinear simulations. The evaluation emphasizes responses where the fan surge margin limit is encountered.

Mattern, Duane↗
NASA NTRS1992

Nonlinear, nonbinary cyclic group codes

New cyclic group codes of length 2(exp m) - 1 over (m - j)-bit symbols are introduced. These codes can be systematically encoded and decoded algebraically. The code rates are very close to Reed-Solomon (RS) codes and are much better than Bose-Chaudhuri-Hocquenghem (BCH) codes (a former alternative). The binary (m - j)-tuples are identified with a subgroup of the binary m-tuples which represents the field GF(2 exp m). Encoding is systematic and involves a two-stage procedure consisting of the usual linear feedback register (using the division or check polynomial) and a small table lookup. For low rates, a second shift-register encoding operation may be invoked. Decoding uses the RS error-correcting procedures for the m-tuple codes for m = 4, 5, and 6.

Solomon, G.↗
DOE OSTI2023

Machine-learning-based spectral methods for partial differential equations

Spectral methods are an important part of scientific computing’s arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the solution of a PDE. The last decade has seen the emergence of deep learning as a strong contender in providing efficient representations of complex functions. In the current work, we present an approach for combining deep neural networks with spectral methods to solve PDEs. In particular, we use a deep learning technique known as the Deep Operator Network (DeepONet) to identify candidate functions on which to expand the solution of PDEs. We have devised an approach that uses the candidate functions provided by the DeepONet as a starting point to construct a set of functions that have the following properties: (1) they constitute a basis, (2) they are orthonormal, and (3) they are hierarchical, i.e., akin to Fourier series or orthogonal polynomials. We have exploited the favorable properties of our custom-made basis functions to both study their approximation capability and use them to expand the solution of linear and nonlinear time-dependent PDEs. The proposed approach advances the state of the art and versatility of spectral methods and, more generally, promotes the synergy between traditional scientific computing and machine learning.

97 MATHEMATICS AND COMPUTING↗