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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 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Exponential integration algorithms applied to viscoplasticity

Four, linear, exponential, integration algorithms (two implicit, one explicit, and one predictor/corrector) are applied to a viscoplastic model to assess their capabilities. Viscoplasticity comprises a system of coupled, nonlinear, stiff, first order, ordinary differential equations which are a challenge to integrate by any means. Two of the algorithms (the predictor/corrector and one of the implicits) give outstanding results, even for very large time steps.

Freed, Alan D.↗
NASA NTRS1990

A computational algorithm for spacecraft control and momentum management

Developments in the area of nonlinear control theory have shown how coordinate changes in the state and input spaces of a dynamical system can be used to transform certain nonlinear differential equations into equivalent linear equations. These techniques are applied to the control of a spacecraft equipped with momentum exchange devices. An optimal control problem is formulated that incorporates a nonlinear spacecraft model. An algorithm is developed for solving the optimization problem using feedback linearization to transform to an equivalent problem involving a linear dynamical constraint and a functional approximation technique to solve for the linear dynamics in terms of the control. The original problem is transformed into an unconstrained nonlinear quadratic program that yields an approximate solution to the original problem. Two examples are presented to illustrate the results.

Dzielski, John↗
NASA NTRS1991

Coupled rotor-flexible fuselage vibration reduction using open loop higher harmonic control

A fundamental study of vibration prediction and vibration reduction in helicopters using active controls was performed. The nonlinear equations of motion for a coupled rotor/flexible fuselage system have been derived using computer algebra on a special purpose symbolic computer facility. The trim state and vibratory response of the helicopter are obtained in a single pass by applying the harmonic balance technique and simultaneously satisfying the trim and the vibratory response of the helicopter for all rotor and fuselage degrees of freedom. The influence of the fuselage flexibility on the vibratory response is studied. It is shown that the conventional single frequency higher harmonic control is capable of reducing either the hub loads or only the fuselage vibrations but not both simultaneously. It is demonstrated that for simultaneous reduction of hub shears and fuselae vibrations a new scheme called multiple higher harmonic control is required.

Papavassiliou, I.↗
NASA NTRS1990

A study of coupled rotor-fuselage vibration with higher harmonic control using a symbolic computing facility

A fundamental study of vibration prediction and vibration reduction in helicopters using active controls was performed. The nonlinear equations of motion for a coupled rotor/flexible fuselage system have been derived using computer algebra on a special purpose symbolic computing facility. The details of the derivation using the MACSYMA program are described. The trim state and vibratory response of the helicopter are obtained in a single pass by applying the harmonic balance technique and simultaneously satisfying the trim and the vibratory response of the helicopter for all rotor and fuselage degrees of freedom. The influence of the fuselage flexibility on the vibratory response is studied. It is shown that the conventional single frequency higher harmonic control (HHC) capable of reducing either the hub loads or only the fuselage vibrations but not both simultaneously. It is demonstrated that for simultaneous reduction of hub shears and fuselage vibrations a new scheme called multiple higher harmonic control (MHHC) is required. The fundamental aspects of this scheme and its uniqueness are described in detail, providing new insight on vibration reduction in helicopters using HHC.

Papavassiliou, I.↗
NASA NTRS1994

Wavelets, period-doubling, and time-frequency localization with application to organization of convection over the tropical western Pacific

In this paper, preliminary results in using orthogonal and continuous wavelet transform (WT) to identify period doubling and time-frequency localization in both synthetic and real data are presented. First, the Haar WT is applied to synthetic time series derived from a simple nonlinear dynamical system- a first-order quadratic difference equation. Second, the complex Morlet WT is used to study the time-frequency localization of tropical convection based on a high-resolution Japanese Geostationary Meteorological Satellite infrared (IR) radiance dataset. The Haar WT of the synthetic time series indicates the presence and distinct separation of multiple frequencies in a period-doubling sequence. The period-doubling process generates a multiplicity of intermediate frequencies, which are manifested in the nonuniformity in time with respect to the phase of oscillations in the lower frequencies. Wavelet transform also enables the detection of extremely weak signals in high-order subharmonics resulting from the period-doubling bifurcations. These signals are either undetected or considered statistically insignificant by traditional Fourier analysis. The Morlet WT of the IR radiance dataset indicates the presence of multiple timescales, which are localized in both frequency and time. There are two regimes in the variation of IR radiance, corresponding to the wet and dry periods. Multiple timescales, ranging from semidiurnal, diurnal, synoptic, to intraseasonal with embedding structures, are active in the wet regime. In particular, synoptic variability is more prominent during the wet phase of an intensive intraseasonal cycle. These are not only consistent with, but also show more details than, previous findings by using other techniques. The phase-locking relationships among the oscillations with different time-scales suggest that both synoptic and intraseasonal variations may be mixed oscillations due to the interaction of self-excited oscillations in the tropical atmosphere and external forcings such as annual and diurnal solar radiation variations. Both examples show that WT is a powerful tool for analysis of phenomena involving multiscale interactions that exhibit localization in both frequency and time. A discussion on the caveats in the use of WT in geophysical data analysis is also presented.

Weng, Hengyi↗
DOE OSTI2020

thornado-transport: Anderson- and GPU-accelerated nonlinear solvers for neutrino-matter coupling

Algorithms for neutrino-matter coupling in core-collapse supernovae (CCSNe) are investigated in the context of a spectral two-moment model, which is discretized in space with the discontinuous Galerkin method, integrated in time with implicit-explicit (IMEX) methods, and implemented in the toolkit for high-order neutrino-radiation hydrodynamics (thornado). The model considers electron neutrinos and antineutrinos and tabulated opacities from Bruenn (1985), which includes neutrino-electron scattering and pair processes. The nonlinear system arising from implicit time discretization of the equations governing neutrino-matter coupling is iterated to convergence using Anderson-accelerated fixed-point methods, which avoid formation of Jacobians and inversion of dense linear systems. Numerical experiments show that, for a given tolerance, a nested iteration scheme which aims to reduce opacity evaluations can lower the computational cost. Our initial port to GPUs, using both OpenMP and OpenACC, shows an overall speedup of up to ~ 100× when compared to results using a single CPU core. These results indicate that the algorithms implemented in thornado are well-suited to GPU acceleration.

Laiu, Paul↗
NASA NTRS1972

Procedure for estimating stability and control parameters from flight test data by using maximum likelihood methods employing a real-time digital system

A maximum likelihood parameter estimation procedure and program were developed for the extraction of the stability and control derivatives of aircraft from flight test data. Nonlinear six-degree-of-freedom equations describing aircraft dynamics were used to derive sensitivity equations for quasilinearization. The maximum likelihood function with quasilinearization was used to derive the parameter change equations, the covariance matrices for the parameters and measurement noise, and the performance index function. The maximum likelihood estimator was mechanized into an iterative estimation procedure utilizing a real time digital computer and graphic display system. This program was developed for 8 measured state variables and 40 parameters. Test cases were conducted with simulated data for validation of the estimation procedure and program. The program was applied to a V/STOL tilt wing aircraft, a military fighter airplane, and a light single engine airplane. The particular nonlinear equations of motion, derivation of the sensitivity equations, addition of accelerations into the algorithm, operational features of the real time digital system, and test cases are described.

Grove, R. D.↗
NASA NTRS1995

Preliminary control system design and analysis for the Space Station Furnace Facility thermal control system

This report presents the Space Station Furnace Facility (SSFF) thermal control system (TCS) preliminary control system design and analysis. The SSFF provides the necessary core systems to operate various materials processing furnaces. The TCS is defined as one of the core systems, and its function is to collect excess heat from furnaces and to provide precise cold temperature control of components and of certain furnace zones. Physical interconnection of parallel thermal control subsystems through a common pump implies the description of the TCS by coupled nonlinear differential equations in pressure and flow. This report formulates the system equations and develops the controllers that cause the interconnected subsystems to satisfy flow rate tracking requirements. Extensive digital simulation results are presented to show the flow rate tracking performance.

Jackson, M. E.↗
NASA NTRS1987

Response of joint dominated space structures

An efficient linearization method is presented for calculating the transient response of nonlinear systems due to initial disturbances. The method is an extension of the describing function approach in which the steady state response of the system is calculated by representing the nonlinear element, typically joints in the case of space structures, by impedances which are functions of the amplitude of response. Thus, the problem of solving the differential equation for the steady state response becomes one of solving a set of nonlinear algebraic equations involving the steady state amplitudes and phases of the system. It is shown that for the transient case the steady state impedances can be averaged over the range of responses in order to provide equivalent values of stiffness and damping that, for a given set of initial displacements, may be treated as being constant for purposes of calculating system response. Single degree of freedom system are used to demonstrate the method and to develop an approach for optimizing the joint's characteristics so as to minimize transient response times. The use of this method for response estimation and optimization in multiple degree of freedom systems is investigated.

Source record↗
NASA NTRS1990

Application of adjoint operators to neural learning

A technique for the efficient analytical computation of such parameters of the neural architecture as synaptic weights and neural gain is presented as a single solution of a set of adjoint equations. The learning model discussed concentrates on the adiabatic approximation only. A problem of interest is represented by a system of N coupled equations, and then adjoint operators are introduced. A neural network is formalized as an adaptive dynamical system whose temporal evolution is governed by a set of coupled nonlinear differential equations. An approach based on the minimization of a constrained neuromorphic energylike function is applied, and the complete learning dynamics are obtained as a result of the calculations.

Barhen, J.↗
NASA NTRS1995

Design of a real-time wind turbine simulator using a custom parallel architecture

The design of a new parallel-processing digital simulator is described. The new simulator has been developed specifically for analysis of wind energy systems in real time. The new processor has been named: the Wind Energy System Time-domain simulator, version 3 (WEST-3). Like previous WEST versions, WEST-3 performs many computations in parallel. The modules in WEST-3 are pure digital processors, however. These digital processors can be programmed individually and operated in concert to achieve real-time simulation of wind turbine systems. Because of this programmability, WEST-3 is very much more flexible and general than its two predecessors. The design features of WEST-3 are described to show how the system produces high-speed solutions of nonlinear time-domain equations. WEST-3 has two very fast Computational Units (CU's) that use minicomputer technology plus special architectural features that make them many times faster than a microcomputer. These CU's are needed to perform the complex computations associated with the wind turbine rotor system in real time. The parallel architecture of the CU causes several tasks to be done in each cycle, including an IO operation and the combination of a multiply, add, and store. The WEST-3 simulator can be expanded at any time for additional computational power. This is possible because the CU's interfaced to each other and to other portions of the simulation using special serial buses. These buses can be 'patched' together in essentially any configuration (in a manner very similar to the programming methods used in analog computation) to balance the input/ output requirements. CU's can be added in any number to share a given computational load. This flexible bus feature is very different from many other parallel processors which usually have a throughput limit because of rigid bus architecture.

Hoffman, John A.↗
DOE OSTI2021

Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms

The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic computational plasma physics. This motivates exploring whether a future error-corrected quantum computer could perform these simulations more efficiently than any classical computer. In this work, we describe a method for mapping any finite nonlinear dynamical system to an infinite linear dynamical system (embedding) and detail three specific cases of this method that correspond to previously studied mappings. Then we explore an approach for approximating the resulting infinite linear system with finite linear systems (truncation). Using a number of qubits only logarithmic in the number of variables of the nonlinear system, a quantum computer could simulate truncated systems to approximate output quantities if the nonlinearity is sufficiently weak. Other aspects of the computational efficiency of the three detailed embedding strategies are also discussed.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

A theory of post-stall transients in axial compression systems. I - Development of equations

An approximate theory is presented for post-stall transients in multistage axial compression systems. The theory leads to a set of three simultaneous nonlinear third-order partial differential equations for pressure rise, and average and disturbed values of flow coefficient, as functions of time and angle around the compressor. By a Galerkin procedure, angular dependence is averaged, and the equations become first order in time. These final equations are capable of describing the growth and possible decay of a rotating-stall cell during a compressor mass-flow transient. It is shown how rotating-stall-like and surgelike motions are coupled through these equations, and also how the instantaneous compressor pumping characteristic changes during the transient stall process.

Moore, F. K.↗
NASA NTRS1983

Linear approximations of nonlinear systems

A method for designing an automatic flight controller for short and vertical takeoff aircraft is presently being developed at NASA Ames Research Center. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system, called the modified tangent model, was recently introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this an approximation of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x(0) yields the same modified tangent model.

Hunt, L. R.↗
DOE OSTI2022

Development of a Control Co-Design Modeling Tool for Marine Hydrokinetic Turbines: Preprint

This report describes the ongoing and planned development of the software package CT-Opt (Current/Tidal Optimization), a control co-design modeling tool for marine hydrokinetic turbines. The commercialization of these turbines has faced significant challenges due to the complex, multidisciplinary nature of their design and the extreme environmental conditions of their operation. This project aims to create a modeling tool that will enable the efficient design of robust, cost-competitive hydrokinetic turbine systems. Rather than using traditional optimization methods, CT-Opt combines multiple models across a range of fidelities to enable coupled optimization of the system design and system controller via a control co-design approach. With this method, the parameters that affect system performance are considered more comprehensively at every stage of the design process. The lowest-fidelity, frequency-domain model called by CT-Opt is RAFT (Response Amplitudes of Floating Turbines), which was originally developed by the National Renewable Energy Laboratory (NREL) to model response amplitudes of floating offshore wind turbines. The highest-fidelity, time-domain model is OpenFAST, which was developed by NREL for land-based and offshore wind turbines. As part of the CT-Opt project, new functionalities will be added to RAFT and OpenFAST to enable the accurate simulation of fixed and floating marine hydrokinetic turbines. In addition to expanding the capabilities of RAFT and OpenFAST, new midfidelity models will be developed. These models will be based on RAFT and OpenFAST and will consist of linearized, state-space models derived from the fully coupled, nonlinear OpenFAST equations and derivative function surrogate models that approximate the nonlinear system behavior. Each model will be coupled with controllers to allow control co-design methods to be applied both within models and across fidelity levels, enabling efficient system optimization.

control co-design↗
NASA NTRS1983

Linear approximations of nonlinear systems

The development of a method for designing an automatic flight controller for short and vertical take off aircraft is discussed. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system called the modified tangent model was introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this the linear part (about a state space point x sub 0) of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x sub 0 yields the same modified tangent model.

Hunt, L. R.↗
NASA NTRS1995

Dynamics of Vapour Bubbles in Nucleate Boiling: Basic Equations of Bubble Evolution - 1

We consider the behaviour of a vapour bubble formed at a nucleation site on a heated horizontal wall. There is no forced convection of an ambient liquid, and the bubble is presumably separated from the wall by a thin liquid microlayer. The energy conservation law results in a variational equation for the mechanical energy of the whole system consisting of the bubble and liquid. It leads to a set of two strongly nonlinear equations which govern bubble expansion and motion of its centre of mass. A supplementary equation to find out the vapour temperature follows from consideration of heat transfer to the bubble, both from the bulk of surrounding liquid and through the microlayer. The average thickness of the microlayer is shown to increase monotonously with time as the bubble meniscus spreads along the wall. Bubble expansion is driven by the pressure head between vapour inside and liquid far away from the bubble, with due allowance for surface tension and gravity effects. It is resisted by inertia of liquid being placed into motion as the bubble grows. The inertia originates also a force that presses the bubble to the wall. This force is counteracted by the buoyancy and an effective surface tension force that tends to transform the bubble into a sphere. The analysis brings about quite a new formulation of the familiar problem of bubble growth and detachment under conditions of nucleate pool boiling.

Buyevich, Yu A.↗