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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 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Criteria for analysis-test correlation of structural dynamic systems

A rational criterion for structural dynamic analysis-test correlation has been established by using a matrix perturbation technique. This criterion can be used for the verification of an analytical model by the test results. Also, the same technique can be applied to update the analytical results by using the test results without repeating the entire analytical procedure. A sample problem has been used to demonstrate this technique. Very satisfactory results are obtained with only the first-order perturbation solution included for transient loading. For periodic loading, higher-order perturbation solutions are needed to achieve the same accuracy.

Chen, J. C.↗
DOE OSTI2020

Space–time reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems

A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing much accuracy, which results in a considerably more speed-up than the spatial reduction only. Recently, a novel space–time reduced order model for dynamical problems has been developed [17], where the space–time reduced order model shows an order of a hundred speed-up with a relative error of 10 –4 for small academic problems. However, in order for the method to be applicable to a large-scale problem, an efficient space–time reduced basis construction algorithm needs to be developed. Here we present the incremental space–time reduced basis construction algorithm. The incremental algorithm is fully parallel and scalable. Additionally, the block structure in the space–time reduced basis is exploited, which enables the avoidance of constructing the reduced space–time basis. These novel techniques are applied to a large-scale particle transport simulation with million and billion degrees of freedom. The numerical example shows that the algorithm is scalable and practical. Also, it achieves a tremendous speed-up, maintaining a good accuracy. Finally, error bounds for space-only and space–time reduced order models are derived.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRSDate not supplied

Towards Formalization of Advanced Linear Algebra with Applications to Dynamical Systems using PVS

Linear Algebra is essential for numerous aerospace problems of interest. Formal reasoning about hybrid systems that contain variables modeled by differential equations rely on concepts from Linear Algebra such as eigenvalues, matrix decompositions, and matrix valued functions. For example, the long-term dynamics of a system of differential equations depend on the stability/instability of its equilibrium points, which often reduces to an eigenvalue problem. This talk will embark on a quest to formalize theorems and results about eigenvalues and eigenvectors using PVS. We shall start our journey with 2 x 2 complex matrices, where we will apply our PVS code to a simple example of a dynamical system. Since it can be difficult or impossible to give simple expressions of eigenvalues for larger matrices (i.e. 5 x 5 or higher), we then move towards specifying the power method for verified computation of eigenvalue approximations in PVS. This effort requires development of multivariate complex arithmetic. At the end of the day, having such additions to the PVS NASA libraries will help move towards the use of formal methods to verify concepts of control theory and system level verification.

Linear Algebra↗
NASA NTRS1982

Constrained multibody system dynamics: An automated approach

The governing equations for constrained multibody systems are formulated in a manner suitable for their automated, numerical development and solution. The closed loop problem of multibody chain systems is addressed. The governing equations are developed by modifying dynamical equations obtained from Lagrange's form of d'Alembert's principle. The modifications is based upon a solution of the constraint equations obtained through a zero eigenvalues theorem, is a contraction of the dynamical equations. For a system with n-generalized coordinates and m-constraint equations, the coefficients in the constraint equations may be viewed as constraint vectors in n-dimensional space. In this setting the system itself is free to move in the n-m directions which are orthogonal to the constraint vectors.

Kamman, J. W.↗
DOE OSTI2020

Application of Detectability Analysis for Power System Dynamic State Estimation

To guide the measurement placement and selection for dynamic state estimation in power systems, it is important to determine the existence of an observer that can estimate the dynamic states. Past studies have been focused on observability analysis, which determines whether the initial states can be uniquely determined. In this paper, detectability analysis is proposed to determine whether the current states can be estimated as time involving. Through the proposed detectability analysis, the states of an unobservable system can be categorized into the detectable states and undetectable states. It is shown that if the eigenvalues corresponding to the unobservable states are stable, the states are detectable and their estimates will converge to the true ones asymptotically. The study can be used to guide measurement placement and selection.

Detectability, dynamic state estimation↗
NASA NTRS1977

The effects of participatory mode and task workload on the detection of dynamic system failures

The ability of operators to detect step changes in the dynamics of control systems is investigated as a joint function of, (1) participatory mode: whether subjects are actively controlling those dynamics or are monitoring an autopilot controlling them, and (2) concurrent task workload. A theoretical analysis of detection in the two modes identifies factors that will favor detection in either mode. Three subjects detected system failures in either an autopilot or manual controlling mode, under single-task conditions and concurrently with a subcritical tracking task. Latency and accuracy of detection were assessed and related through a speed accuracy tradeoff representation. It was concluded that failure detection performance was better during manual control than during autopilot control, and that the extent of this superiority was enhanced as dual-task load increased. Ensemble averaging and multiple regression techniques were then employed to investigate the cues utilized by the subjects in making their detection decisions.

Wickens, C. D.↗
DOE OSTI2014

Characterizing system dynamics with a weighted and directed network constructed from time series data

In this work, we propose a novel method to transform a time series into a weighted and directed network. For a given time series, we first generate a set of segments via a sliding window, and then use a doubly symbolic scheme to characterize every windowed segment by combining absolute amplitude information with an ordinal pattern characterization. Based on this construction, a network can be directly constructed from the given time series: segments corresponding to different symbol-pairs are mapped to network nodes and the temporal succession between nodes is represented by directed links. With this conversion, dynamics underlying the time series has been encoded into the network structure. We illustrate the potential of our networks with a well-studied dynamical model as a benchmark example. Results show that network measures for characterizing global properties can detect the dynamical transitions in the underlying system. Moreover, we employ a random walk algorithm to sample loops in our networks, and find that time series with different dynamics exhibits distinct cycle structure. That is, the relative prevalence of loops with different lengths can be used to identify the underlying dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Quantum system dynamics with a weakly nonlinear Josephson junction bath

Here, we investigate the influence of a weakly nonlinear Josephson bath consisting of a chain of Josephson junctions on the dynamics of a small quantum system (LC oscillator). Focusing on the regime where the charging energy is the largest energy scale, we perturbatively calculate the correlation function of the Josephson bath to the leading order in the Josephson energy divided by the charging energy while keeping the cosine potential exactly. When the variation of the charging energy along the chain ensures fast decay of the bath correlation function, the dynamics of the LC oscillator that is weakly and capacitively coupled to the Josephson bath can be solved through the Markovian master equation. We establish a duality relation for the Josephson bath between the regimes of large charging and Josephson energies, respectively. The results can be applied to cases where the charging energy either is nonuniformly engineered or disordered in the chain. Furthermore, we find that the Josephson bath may become non-Markovian when the temperature is increased beyond the zero-temperature limit in that the bath correlation function gets shifted by a constant and does not decay with time.

1-dimensional systems↗
DOE OSTI2025

Understanding latent timescales in neural ordinary differential equation models of advection-dominated dynamical systems

The neural ordinary differential equation (ODE) framework has shown considerable promise in recent years in developing highly accelerated surrogate models for complex physical systems characterized by partial differential equations (PDEs). For PDE-based systems, state-of-the-art neural ODE strategies leverage a two-step procedure to achieve this acceleration: a nonlinear dimensionality reduction step provided by an autoencoder, and a time integration step provided by a neural-network based model for the resultant latent space dynamics (the neural ODE). This work explores the applicability of such autoencoder-based neural ODE strategies for PDEs in which advection terms play a critical role. More specifically, alongside predictive demonstrations, physical insight into the sources of model acceleration (i.e., how the neural ODE achieves its acceleration) is the scope of the current study. Such investigations are performed by quantifying the effects of both autoencoder and neural ODE components on latent system time-scales using eigenvalue analysis of dynamical system Jacobians. To this end, the sensitivity of various critical training parameters – de-coupled versus end-to-end training, latent space dimensionality, and the role of training trajectory length, for example – to both model accuracy and the discovered latent system timescales is quantified. Furthermore, this work specifically uncovers the key role played by the training trajectory length (the number of rollout steps in the loss function during training) on the latent system timescales: larger trajectory lengths correlate with an increase in limiting neural ODE time-scales, and optimal neural ODEs are found to recover the largest time-scales of the full-order (ground-truth) system. Demonstrations are performed across fundamentally different unsteady fluid dynamics configurations influenced by advection: (1) the Kuramoto–Sivashinsky equations (2) Hydrogen-Air channel detonations (the compressible reacting Navier–Stokes equations with detailed chemistry), and (3) 2D Atmospheric flow.

Advection-dominated dynamical systems↗
NASA NTRS1992

Sub-domain decomposition methods and computational controls for multibody dynamical systems

This paper presents a concurrent methodology to simulate the dynamics of flexible multibody systems with a large number of degrees of freedom. A general class of open-loop structures is treated and a redundant coordinate formulation is adopted. A range space method is used in which the constraint forces are calculated using a preconditioned conjugate gradient method. By using a preconditioner motivated by the regular ordering of the directed graph of the structures, it is shown that the method is order N in the total number of coordinates of the system. The overall formulation has the advantage that it permits fine parallelization and does not rely on system topology to induce concurrency. It can be efficiently implemented on the present generation of parallel computers with a large number of processors. Validation of the method is presented via numerical simulations of space structures incorporating large number of flexible degrees of freedom.

Menon, R. G.↗
NASA NTRS1989

A decoupled recursive approach for constrained flexible multibody system dynamics

A variational-vector calculus approach is employed to derive a recursive formulation for dynamic analysis of flexible multibody systems. Kinematic relationships for adjacent flexible bodies are derived in a companion paper, using a state vector notation that represents translational and rotational components simultaneously. Cartesian generalized coordinates are assigned for all body and joint reference frames, to explicitly formulate deformation kinematics under small deformation kinematics and an efficient flexible dynamics recursive algorithm is developed. Dynamic analysis of a closed loop robot is performed to illustrate efficiency of the algorithm.

Lai, Hao-Jan↗
NASA NTRS1991

Modal interaction in linear dynamic systems near degenerate modes

In various problems in structural dynamics, the eigenvalues of a linear system depend on a characteristic parameter of the system. Under certain conditions, two eigenvalues of the system approach each other as the characteristic parameter is varied, leading to modal interaction. In a system with conservative coupling, the two eigenvalues eventually repel each other, leading to the curve veering effect. In a system with nonconservative coupling, the eigenvalues continue to attract each other, eventually colliding, leading to eigenvalue degeneracy. Modal interaction is studied in linear systems with conservative and nonconservative coupling using singularity theory, sometimes known as catastrophe theory. The main result is this: eigenvalue degeneracy is a cause of instability; in systems with conservative coupling, it induces only geometric instability, whereas in systems with nonconservative coupling, eigenvalue degeneracy induces both geometric and elastic instability. Illustrative examples of mechanical systems are given.

Afolabi, D.↗
NASA NTRS1995

Analysis of solar receiver flux distributions for US/Russian solar dynamic system demonstration on the MIR Space Station

The United States and Russia have agreed to jointly develop a solar dynamic (SD) system for flight demonstration on the Russian MIR space station starting in late 1997. Two important components of this SD system are the solar concentrator and heat receiver provided by Russia and the U.S., respectively. This paper describes optical analysis of the concentrator and solar flux predictions on target receiver surfaces. The optical analysis is performed using the code CIRCE2. These analyses account for finite sun size with limb darkening, concentrator surface slope and position errors, concentrator petal thermal deformation, gaps between petals, and the shading effect of the receiver support struts. The receiver spatial flux distributions are then combined with concentrator shadowing predictions. Geometric shadowing patterns are traced from the concentrator to the target receiver surfaces. These patterns vary with time depending on the chosen MIR flight attitude and orbital mechanics of the MIR spacecraft. The resulting predictions provide spatial and temporal receiver flux distributions for any specified mission profile. The impact these flux distributions have on receiver design and control of the Brayton engine are discussed.

Kerslake, Thomas W.↗
NASA NTRS1991

Spatial operator approach to flexible multibody system dynamics and control

The inverse and forward dynamics problems for flexible multibody systems were solved using the techniques of spatially recursive Kalman filtering and smoothing. These algorithms are easily developed using a set of identities associated with mass matrix factorization and inversion. These identities are easily derived using the spatial operator algebra developed by the author. Current work is aimed at computational experiments with the described algorithms and at modelling for control design of limber manipulator systems. It is also aimed at handling and manipulation of flexible objects.

Rodriguez, G.↗