New Horizons of Systems Science: Systems Dynamics Relationship to Systems Engineering Principles, Complex Systems, Category Theory
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Systems Engineering Principles↗
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A predictability study of Lorenz's 28-variable model as a dynamical system
The dynamics of error growth in a two-layer nonlinear quasi-geostrophic model has been studied to gain an understanding of the mathematical theory of atmospheric predictability. The growth of random errors of varying initial magnitudes has been studied, and the relation between this classical approach and the concepts of the nonlinear dynamical systems theory has been explored. The local and global growths of random errors have been expressed partly in terms of the properties of an error ellipsoid and the Liapunov exponents determined by linear error dynamics. The local growth of small errors is initially governed by several modes of the evolving error ellipsoid but soon becomes dominated by the longest axis. The average global growth of small errors is exponential with a growth rate consistent with the largest Liapunov exponent. The duration of the exponential growth phase depends on the initial magnitude of the errors. The subsequent large errors undergo a nonlinear growth with a steadily decreasing growth rate and attain saturation that defines the limit of predictability. The degree of chaos and the largest Liapunov exponent show considerable variation with change in the forcing, which implies that the time variation in the external forcing can introduce variable character to the predictability.
Krishnamurthy, V.↗
Data Systems Dynamic Simulation - A total system for data system design assessments and trade studies
Data Systems Dynamic Simulation is a simulation system designed to reduce cost and time and increase the confidence and comprehensiveness of Data Systems Simulation. It is designed to simulate large data processing and communications systems from end-to-end or by subsystem. Those features relevant to system timing, control, sizing, personnel support activities, cost and external influences are modeled. Emphasis is placed on ease of use, comprehensive system performance measures, and extensive post simulation analysis capability. The system has been used to support trade studies of the NASA data system needs in the 1985 to 1990 time frame.
Hooper, J. W.↗
A survey of intelligent tutoring systems: Implications for complex dynamic systems
An overview of the research in the field of intelligent tutorial systems (ITS) is provided. The various approaches in the design and implementation of ITS are examined and discussed in the context of problem solving in an environment of a complex dynamic system (CDS). Issues pertaining to a CDS and the nature of human problem solving especially in light of a CDS are considered. An overview of the architecture of an ITS is provided as the basis for the in-depth examination of various systems. Finally, the implications for the design and evaluation of an ITS are discussed.
Chu, Rose W.↗
Criticality of Inverter Controller Order in Power System Dynamic Studies – Case Study: Maui Island
Not Available
Kenyon, Rick Wallace↗
Towards a circular economy for PET bottle resin using a system dynamics inspired material flow model
Not Available
Ghosh, Tapajyoti (ORCID:0000000205220235)↗
Application of dynamical systems theory to nonlinear aircraft dynamics
Dynamical systems theory has been used to study nonlinear aircraft dynamics. A six degree of freedom model that neglects gravity has been analyzed. The aerodynamic model, supplied by NASA, is for a generic swept wing fighter and includes nonlinearities as functions of the angle of attack. A continuation method was used to calculate the steady states of the aircraft, and bifurcations of these steady states, as functions of the control deflections. Bifurcations were used to predict jump phenomena and the onset of periodic motion for roll coupling instabilities and high angle of attack maneuvers. The predictions were verified with numerical simulations.
Culick, Fred E. C.↗
Effects of Ambient High Temperature Exposure on Alumina-Titania High Emittance Surfaces for Solar Dynamic Systems
Solar dynamic (SD) space power systems require durable, high emittance surfaces on a number of critical components, such as heat receiver interior surfaces and parasitic load radiator (PLR) elements. To enhance surface characteristics, an alumina-titania coating has been applied to 500 heat receiver thermal energy containment canisters and the PLR of NASA Lewis Research Center's (LeRC) 2 kW SD ground test demonstrator (GTD). The alumina-titania coating was chosen because it had been found to maintain its high emittance under vacuum (less than or equal to 10(exp -6) torr) at high temperatures (1457 F (827 C)) for an extended period (approximately 2,700 hours). However, preflight verification of SD systems components, such as the PLR require operation at ambient pressure and high temperatures. Therefore, the purpose of this research was to evaluate the durability of the alumina-titania coating at high temperature in air. Fifteen of sixteen alumina-titania coated Incoloy samples were exposed to high temperatures (600 F (316 C) to l500 F (816 C)) for various durations (2 to 32 hours). Samples, were characterized prior to and after heat treatment for reflectance, solar absorptance, room temperature emittance and emittance at 1,200 F (649 C). Samples were also examined to detect physical defects and to determine surface chemistry using optical microscopy, scanning electron microscopy operated with an energy dispersive spectroscopy (EDS) system, and x ray photoelectron spectroscopy (XPS). Visual examination of the heat-treated samples showed a whitening of samples exposed to temperatures of 1,000 F (538 C) and above. Correspondingly, the optical properties of these samples had degraded. A sample exposed to 1,500 F (816 C) for 24 hours had whitened and the thermal emittance at 1,200 F (649 C) had decreased from the non-heat treated value of 0.94 to 0.62. The coating on this sample had become embrittled with spalling off the substrate noticeable at several locations. Based on this research it is recommended that preflight testing of SD components with alumina-titania coatings be restricted to temperatures no greater than 600 F (316 C) in air to avoid optical degradation. Moreover, components with the alumina-titania coating are likely to experience optical property degradation with direct atomic oxygen exposure in space.
deGroh, Kim K.↗
Parameterizing Coefficients of a POD-Based Dynamical System
A method of parameterizing the coefficients of a dynamical system based of a proper orthogonal decomposition (POD) representing the flow dynamics of a viscous fluid has been introduced. (A brief description of POD is presented in the immediately preceding article.) The present parameterization method is intended to enable construction of the dynamical system to accurately represent the temporal evolution of the flow dynamics over a range of Reynolds numbers. The need for this or a similar method arises as follows: A procedure that includes direct numerical simulation followed by POD, followed by Galerkin projection to a dynamical system has been proven to enable representation of flow dynamics by a low-dimensional model at the Reynolds number of the simulation. However, a more difficult task is to obtain models that are valid over a range of Reynolds numbers. Extrapolation of low-dimensional models by use of straightforward Reynolds-number-based parameter continuation has proven to be inadequate for successful prediction of flows. A key part of the problem of constructing a dynamical system to accurately represent the temporal evolution of the flow dynamics over a range of Reynolds numbers is the problem of understanding and providing for the variation of the coefficients of the dynamical system with the Reynolds number. Prior methods do not enable capture of temporal dynamics over ranges of Reynolds numbers in low-dimensional models, and are not even satisfactory when large numbers of modes are used. The basic idea of the present method is to solve the problem through a suitable parameterization of the coefficients of the dynamical system. The parameterization computations involve utilization of the transfer of kinetic energy between modes as a function of Reynolds number. The thus-parameterized dynamical system accurately predicts the flow dynamics and is applicable to a range of flow problems in the dynamical regime around the Hopf bifurcation. Parameter-continuation software can be used on the parameterized dynamical system to derive a bifurcation diagram that accurately predicts the temporal flow behavior.
Kalb, Virginia L.↗
Method and system for detecting a failure or performance degradation in a dynamic system such as a flight vehicle
A method and system for detecting a failure or performance degradation in a dynamic system having sensors for measuring state variables and providing corresponding output signals in response to one or more system input signals are provided. The method includes calculating estimated gains of a filter and selecting an appropriate linear model for processing the output signals based on the input signals. The step of calculating utilizes one or more models of the dynamic system to obtain estimated signals. The method further includes calculating output error residuals based on the output signals and the estimated signals. The method also includes detecting one or more hypothesized failures or performance degradations of a component or subsystem of the dynamic system based on the error residuals. The step of calculating the estimated values is performed optimally with respect to one or more of: noise, uncertainty of parameters of the models and un-modeled dynamics of the dynamic system which may be a flight vehicle or financial market or modeled financial system.
Miller, Robert H.↗
Attractors in dynamical systems
Attractors in dynamic systems - Liapunov and plain stability of compact invariant set
SET THEORY↗
Generalized recurrence in dynamical systems.
Generalized recurrence in dynamical systems with aid of continuous real valued function on phase space
PHASE-SPACE INTEGRAL↗
Predictability of weather and climate in a coupled ocean-atmosphere model: A dynamical systems approach
A dynamical systems approach is used to quantify the instantaneous and time-averaged predictability of a low-order moist general circulation model. Specifically, the effects on predictability of incorporating an active ocean circulation, implementing annual solar forcing, and asynchronously coupling the ocean and atmosphere are evaluated. The predictability and structure of the model attractors is compared using the Lyapunov exponents, the local divergence rates, and the correlation, fractal, and Lyapunov dimensions. The Lyapunov exponents measure the average rate of growth of small perturbations on an attractor, while the local divergence rates quantify phase-spatial variations of predictability. These local rates are exploited to efficiently identify and distinguish subtle differences in predictability among attractors. In addition, the predictability of monthly averaged and yearly averaged states is investigated by using attractor reconstruction techniques.
Nese, Jon M.↗
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↗
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.↗
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.↗
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↗