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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

On Information Transfer in Dynamical Systems with applications in Control of Non-equilibrium Dynamics

In this paper we develop the concept of information transfer between the Borel-measurable sets for a dynamical system described by a measurable space and a non-singular transformation. The concept is based on how Shannon entropy is transferred between the measurable sets, as the dynamical system evolves. We show that the proposed definition of information transfer satisfies the usual notions of information transfer and causality, namely, zero transfer and transfer asymmetry. Furthermore, we show how the information transfer measure can be used to characterize ergodicity and mixing in dynamical systems. We also develop the computational methods for information transfer computation and apply the framework for optimal placements of actuators and sensors for control of non-equilibrium dynamics.

Sinha, Subhrajit↗
DOE OSTI2023

Projective embedding of dynamical systems: Uniform mean field equations

Herein we study embeddings of continuous dynamical systems in larger dimensions via projector operators. We call this technique PEDS, projective embedding of dynamical systems, as the stable fixed point of the original system dynamics are recovered via projection from the higher dimensional space. In this paper we provide a general definition and prove that for a particular type of rank-1 projector operator, the uniform mean field projector, the equations of motion become a mean field approximation of the dynamical system. While in general the embedding depends on a specified variable ordering, the same is not true for the uniform mean field projector. We prove a variety of results on the relationship between the spectrum of the Jacobian for fixed points in the original and in the embedded system. Direct applications of PEDS can be non-convex optimization and machine learning.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems

The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous, sequential, or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2004

Application of the GRC Stirling Convertor System Dynamic Model

The GRC Stirling Convertor System Dynamic Model (SDM) has been developed to simulate dynamic performance of power systems incorporating free-piston Stirling convertors. This paper discusses its use in evaluating system dynamics and other systems concerns. Detailed examples are provided showing the use of the model in evaluation of off-nominal operating conditions. The many degrees of freedom in both the mechanical and electrical domains inherent in the Stirling convertor and the nonlinear dynamics make simulation an attractive analysis tool in conjunction with classical analysis. Application of SDM in studying the relationship of the size of the resonant circuit quality factor (commonly referred to as Q) in the various resonant mechanical and electrical sub-systems is discussed.

Regan, Timothy F.↗
DOE OSTI2017

Measurement-based Power System Dynamic Model Reductions

Interconnected power systems have experienced a significant increase in its size and complexity, due to continuous topology and operating condition changes. It is computationally burdensome to represent entire system models in detail to conduct power system analysis. In the large-scale power system dynamic simulations, the models in the study area need to be retained in detail while the external area can be reduced without compromising accuracy, which can preserve the full system dynamic properties. This paper develops measurement-based continuous-time dynamic equivalents for power systems in order to both improve the model accuracy of the reduced system and increase the speed of dynamic simulation. Our method is based on a set of measurements at the boundary nodes between the study area and external area. Case studies demonstrate that the measurement-based model can capture the full system behavior sufficiently, and improve computational efficiency.Interconnected power systems experienced a significant increase in size and complexity. It is computationally burdensome to represent the entire system in detail to conduct power system analysis. Therefore, the model of the study system must be retained in detail while the external system can be reduced using system reduction techniques. This paper proposes a measurement-based dynamic equivalent in order to increase both model accuracy and simulation speed. The proposed method uses a set of measurements at the boundary nodes between the study area and external area for model parameter identification. Case studies demonstrate that the measurement-based technique can capture the main system behaviors accurately and improve computational efficiency.

Xue, Yaosuo↗
NASA NTRS1992

Control and stabilization of nonholonomic dynamic systems

The paper establishes a theoretical framework for the control of nonholonomic dynamic systems, i.e., dynamic systems with nonintegrable constraints, with emphasis on control properties for nonholonomic systems that have no counterpart in holonomic systems. A model for nonholonomic dynamic systems is presented in terms of differential-algebraic equations defined on a phase space. A reduction procedure is carried out to obtain reduced-order state equations. Conditions for smooth asymptotic stabilization to an m-dimensional equilibrium manifold are presented. It is also demonstrated that a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback. An approach using geometric phases is developed as a basis for the control of Caplygin systems.

Bloch, Anthony M.↗
NASA NTRS1992

Non-scalar uncertainty: Uncertainty in dynamic systems

The following point is stated throughout the paper: dynamic systems are usually subject to uncertainty, be it the unavoidable quantic uncertainty when working with sufficiently small scales or when working in large scales uncertainty can be allowed by the researcher in order to simplify the problem, or it can be introduced by nonlinear interactions. Even though non-quantic uncertainty can generally be dealt with by using the ordinary probability formalisms, it can also be studied with the proposed non-scalar formalism. Thus, non-scalar uncertainty is a more general theoretical framework giving insight into the nature of uncertainty and providing a practical tool in those cases in which scalar uncertainty is not enough, such as when studying highly nonlinear dynamic systems. This paper's specific contribution is the general concept of non-scalar uncertainty and a first proposal for a methodology. Applications should be based upon this methodology. The advantage of this approach is to provide simpler mathematical models for prediction of the system states. Present conventional tools for dealing with uncertainty prove insufficient for an effective description of some dynamic systems. The main limitations are overcome abandoning ordinary scalar algebra in the real interval (0, 1) in favor of a tensor field with a much richer structure and generality. This approach gives insight into the interpretation of Quantum Mechanics and will have its most profound consequences in the fields of elementary particle physics and nonlinear dynamic systems. Concepts like 'interfering alternatives' and 'discrete states' have an elegant explanation in this framework in terms of properties of dynamic systems such as strange attractors and chaos. The tensor formalism proves especially useful to describe the mechanics of representing dynamic systems with models that are closer to reality and have relatively much simpler solutions. It was found to be wise to get an approximate solution to an accurate model than to get a precise solution to a model constrained by simplifying assumptions. Precision has a very heavy cost in present physical models, but this formalism allows the trade between uncertainty and simplicity. It was found that modeling reality sometimes requires that state transition probabilities should be manipulated as nonscalar quantities, finding at the end that there is always a transformation to get back to scalar probability.

Martinez, Salvador Gutierrez↗
NASA NTRS2004

Overview of the GRC Stirling Convertor System Dynamic Model

A Stirling Convertor System Dynamic Model has been developed at the Glenn Research Center for controls, dynamics, and systems development of free-piston convertor power systems. It models the Stirling cycle thermodynamics, heat flow, gas, mechanical, and mounting dynamics, the linear alternator, and the controller. The model's scope extends from the thermal energy input to thermal, mechanical dynamics, and electrical energy out, allowing one to study complex system interactions among subsystems. The model is a non-linear time-domain model containing sub-cycle dynamics, allowing it to simulate transient and dynamic phenomena that other models cannot. The model details and capability are discussed.

Lewandowski, Edward J.↗
DOE OSTI2023

Structural inference of networked dynamical systems with universal differential equations

Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical) units to exhibit a wide range of nontrivial behaviors, such as the emergence of coherent structures (e.g., waves and patterns) or otherwise notable dynamics (e.g., synchrony and chaos). Here, we seek to infer (i) the intrinsic physics of a base unit of a population, (ii) the underlying graphical structure shared between units, and (iii) the coupling physics of a given networked dynamical system given observations of nodal states. These tasks are formulated around the notion of the Universal Differential Equation, whereby unknown dynamical systems can be approximated with neural networks, mathematical terms known a priori (albeit with unknown parameterizations), or combinations of the two. We demonstrate the value of these inference tasks by investigating not only future state predictions but also the inference of system behavior on varied network topologies. The effectiveness and utility of these methods are shown with their application to canonical networked nonlinear coupled oscillators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

On dynamical systems approaches and methods in f ( R ) cosmology

We discuss dynamical systems approaches and methods applied to flat Robertson-Walker models in f ( R )-gravity. We argue that a complete description of the solution space of a model requires a global state space analysis that motivates globally covering state space adapted variables. This is shown explicitly by an illustrative example, f ( R ) = R + α R {sup 2}, α > 0, for which we introduce new regular dynamical systems on global compactly extended state spaces for the Jordan and Einstein frames. This example also allows us to illustrate several local and global dynamical systems techniques involving, e.g., blow ups of nilpotent fixed points, center manifold analysis, averaging, and use of monotone functions. As a result of applying dynamical systems methods to globally state space adapted dynamical systems formulations, we obtain pictures of the entire solution spaces in both the Jordan and the Einstein frames. This shows, e.g., that due to the domain of the conformal transformation between the Jordan and Einstein frames, not all the solutions in the Jordan frame are completely contained in the Einstein frame. We also make comparisons with previous dynamical systems approaches to f ( R ) cosmology and discuss their advantages and disadvantages.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2008

Similarity Metrics for Closed Loop Dynamic Systems

To what extent and in what ways can two closed-loop dynamic systems be said to be "similar?" This question arises in a wide range of dynamic systems modeling and control system design applications. For example, bounds on error models are fundamental to the controller optimization with modern control design methods. Metrics such as the structured singular value are direct measures of the degree to which properties such as stability or performance are maintained in the presence of specified uncertainties or variations in the plant model. Similarly, controls-related areas such as system identification, model reduction, and experimental model validation employ measures of similarity between multiple realizations of a dynamic system. Each area has its tools and approaches, with each tool more or less suited for one application or the other. Similarity in the context of closed-loop model validation via flight test is subtly different from error measures in the typical controls oriented application. Whereas similarity in a robust control context relates to plant variation and the attendant affect on stability and performance, in this context similarity metrics are sought that assess the relevance of a dynamic system test for the purpose of validating the stability and performance of a "similar" dynamic system. Similarity in the context of system identification is much more relevant than are robust control analogies in that errors between one dynamic system (the test article) and another (the nominal "design" model) are sought for the purpose of bounding the validity of a model for control design and analysis. Yet system identification typically involves open-loop plant models which are independent of the control system (with the exception of limited developments in closed-loop system identification which is nonetheless focused on obtaining open-loop plant models from closed-loop data). Moreover the objectives of system identification are not the same as a flight test and hence system identification error metrics are not directly relevant. In applications such as launch vehicles where the open loop plant is unstable it is similarity of the closed-loop system dynamics of a flight test that are relevant.

Whorton, Mark S.↗
DOE OSTI2024

Semi-supervised Learning of Dynamical Systems with Neural Ordinary Differential Equations: A Teacher-Student Model Approach

Modeling dynamical systems is crucial for a wide range of tasks, but it remains challenging due to complex nonlinear dynamics, limited observations, or lack of prior knowledge. Recently, data-driven approaches such as Neural Ordinary Differential Equations (NODE) have shown promising results by leveraging the expressive power of neural networks to model unknown dynamics. However, these approaches often suffer from limited labeled training data, leading to poor generalization and suboptimal predictions. On the other hand, semi-supervised algorithms can utilize abundant unlabeled data and have demonstrated good performance in classification and regression tasks. We propose TS-NODE, the first semi-supervised approach to modeling dynamical systems with NODE. TS-NODE explores cheaply generated synthetic pseudo rollouts to broaden exploration in the state space and to tackle the challenges brought by lack of ground-truth system data under a teacher-student model. TS-NODE employs an unified optimization framework that corrects the teacher model based on the student's feedback while mitigating the potential false system dynamics present in pseudo rollouts. TS-NODE demonstrates significant performance improvements over a baseline Neural ODE model on multiple dynamical system modeling tasks.

Wang, Yu↗
DOE OSTI2018

Generative Adversarial Network based Autoencoder: Application to fault detection problem for closed loop dynamical systems

Fault detection problem for closed loop uncertain dynamical systems, is investigated in this paper, using different deep learning based methods. Traditional classifier based method does not perform well, because of the inherent difficulty of detecting system level faults for closed loop dynamical system. Specifically, acting controller in any closed loop dynamical system, works to reduce the effect of system level faults. A novel Generative Adversarial based deep Autoencoder is designed to classify datasets under normal and faulty operating conditions. This proposed network performs significantly well when compared to any available classifier based methods, and moreover, does not require labeled fault incorporated datasets for training purpose. Finally, this aforementioned network's performance is tested on a high complexity building energy system dataset.

deep learning, Active fault detection↗
DOE OSTI2018

Minimax Program Terminal Control in Two-Level Hierarchic Nonlinear Discrete Dynamical System

We consider a discrete dynamical system consisting of a number of controllable objects whose dynamics is governed by vector nonlinear discrete recurrent relations with control parameters and perturbations (noises). In such system, two levels of making management decisions are distinguished: the dominating (first) level and the subordinate (second) level, which have different criteria of functioning. These levels are integrated by certain information and control relations. We consider the problem of two-level minimax program terminal control in a discrete dynamical system and propose its mathematical statement and a general scheme of its solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Online data-driven changepoint detection for high-dimensional dynamical systems

In this study, the detection of anomalies or transitions in complex dynamical systems is of critical importance to various applications. In this study, we propose the use of machine learning to detect changepoints for high-dimensional dynamical systems. Here, changepoints indicate instances in time when the underlying dynamical system has a fundamentally different characteristic—which may be due to a change in the model parameters or due to intermittent phenomena arising from the same model. We propose two complementary approaches to achieve this, with the first devised using arguments from probabilistic unsupervised learning and the latter devised using supervised deep learning. To accelerate the deployment of transition detection algorithms in high-dimensional dynamical systems, we introduce dimensionality reduction techniques. Our experiments demonstrate that transitions can be detected efficiently, in real-time, for the two-dimensional forced Kolmogorov flow and the Rössler dynamical system, which are characterized by anomalous regimes in phase space where dynamics are perturbed off the attractor at potentially uneven intervals. Finally, we also demonstrate how variations in the frequency of detected changepoints may be utilized to detect a significant modification to the underlying model parameters by utilizing the Lorenz-63 dynamical system.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

Solar dynamic systems

The development of the solar dynamic system is discussed. The benefits of the solar dynamic system over pv systems are enumerated. The history of the solar dynamic development is recounted. The purpose and approach of the advanced development are outlined. Critical concentrator technology and critical heat recover technology are examined.

Dustin, M. O.↗
NASA NTRS1989

DYSCO: A software system for modeling general dynamic systems

The DYSCO program has been under development since 1979. It has been funded by Army and Air Force laboratories and by the Kaman Aerospace Corporation. It is presently available at a number of government and nongovernment installations. It has been used to analyze a very broad range of dynamics problems. A principle feature of the software design of DYSCO is the separation of the executive from the technology. The executive, which controls all the operations, is intelligent in the sense that it knows that its function is to assemble differential equations and to prepare them for solution. The technology library contains FORTRAN routines which perform standard functions, such as, computing the equation coefficients of an element (or component) given the local state at any time. The technology library also contains algorithms and procedures for solving the coupled system equations. The system was designed to allow easy additional of technology to the library. Any linear or nonlinear structural entity, control system, or set of ordinary differential equations may be simply coded and added to the library, as well as algorithms for time or frequency domain solution. The program is described with emphasis on its usefulness in easily modeling unusual concepts and configurations, performing analysis of damage, evaluating new algorithms, and simulating dynamic tests.

Berman, Alex↗