On the Hermite-Fujiwara theorem in stability theory.
Proof of Hermite-Fujiwara theorem of dynamic system stability based on Liapunov-type methods
DYNAMIC STABILITY↗
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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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Structural Mechanics and Dynamics Branch
The 2002 annual report of the Structural Mechanics and Dynamics Branch reflects the majority of the work performed by the branch staff during the 2002 calendar year. Its purpose is to give a brief review of the branch s technical accomplishments. The Structural Mechanics and Dynamics Branch develops innovative computational tools, benchmark experimental data, and solutions to long-term barrier problems in the areas of propulsion aeroelasticity, active and passive damping, engine vibration control, rotor dynamics, magnetic suspension, structural mechanics, probabilistics, smart structures, engine system dynamics, and engine containment. Furthermore, the branch is developing a compact, nonpolluting, bearingless electric machine with electric power supplied by fuel cells for future "more electric" aircraft. An ultra-high-power-density machine that can generate projected power densities of 50 hp/lb or more, in comparison to conventional electric machines, which generate usually 0.2 hp/lb, is under development for application to electric drives for propulsive fans or propellers. In the future, propulsion and power systems will need to be lighter, to operate at higher temperatures, and to be more reliable in order to achieve higher performance and economic viability. The Structural Mechanics and Dynamics Branch is working to achieve these complex, challenging goals.
Stefko, George↗
Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism
The Mori-Zwanzig formalism for coarse-graining a complex dynamical system typically introduces memory effects. The Markovian assumption of delta-correlated fluctuating forces is often employed to simplify the formulation of coarse-grained (CG) models and numerical implementations. However, when the time scales of a system are not clearly separated, the memory effects become strong and the Markovian assumption becomes inaccurate. To this end, we incorporate memory effects into CG modeling by preserving non-Markovian interactions between CG variables, and the memory kernel is evaluated directly from microscopic dynamics. For a specific example, molecular dynamics (MD) simulations of star polymer melts are performed while the corresponding CG system is defined by grouping many bonded atoms into single clusters. Then, the effective interactions between CG clusters as well as the memory kernel are obtained from the MD simulations. The constructed CG force field with a memory kernel leads to a non-Markovian dissipative particle dynamics (NM-DPD). Quantitative comparisons between the CG models with Markovian and non-Markovian approximations indicate that including the memory effects using NM-DPD yields similar results as the Markovian-based DPD if the system has clear time scale separation. However, for systems with small separation of time scales, NM-DPD can reproduce correct short-time properties that are related to how the system responds to high-frequency disturbances, which cannot be captured by the Markovian-based DPD model.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Bifurcation analysis and dimension reduction of a predator-prey model for the L-H transition
The L-H transition denotes a shift to an improved confinement state of a toroidal plasma in a fusion reactor. A model of the L-H transition is required to simulate the time dependence of tokamak discharges that include the L-H transition. A 3-ODE predator-prey type model of the L-H transition is investigated with bifurcation theory of dynamical systems. The analysis shows that the model contains three types of transitions: an oscillating transition, a sharp transition with hysteresis, and a smooth transition. The model is recognized as a slow-fast system. A reduced 2-ODE model consisting of the full model restricted to the flow on the critical manifold is found to contain all the same dynamics as the full model. This means that all the dynamics in the system is essentially 2-dimensional, and a minimal model of the L-H transition could be a 2-ODE model.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Instrumental variables algorithm for modal parameter identification in flutter testing
The paper is concerned with the task of estimating modal parameters from system response measurement in aircraft flutter testing. A frequency-domain derivation of an instrumental-variables algorithm is presented for a linear time-invariant dynamic system of order n. Basically, this algorithm fits a set of poles and zeros to the measured transfer function. An illustrative example is provided regarding the application of the algorithm to aeroelasticity testing. It is shown that the algorithm can be implemented for on-line data reduction with a microcomputer-based analysis system. By using instrumental variables the sensitivity of the modal parameter estimates to noise in the system-response measurements is reduced greatly. The algorithm is expected to be a powerful and valuable tool for on-line estimation of modal parameters in flutter testing and should be useful in control system and structural dynamics tests.
Johnson, W.↗
Indirect Identification of Linear Stochastic Systems with Known Feedback Dynamics
An algorithm is presented for identifying a state-space model of linear stochastic systems operating under known feedback controller. In this algorithm, only the reference input and output of closed-loop data are required. No feedback signal needs to be recorded. The overall closed-loop system dynamics is first identified. Then a recursive formulation is derived to compute the open-loop plant dynamics from the identified closed-loop system dynamics and known feedback controller dynamics. The controller can be a dynamic or constant-gain full-state feedback controller. Numerical simulations and test data of a highly unstable large-gap magnetic suspension system are presented to demonstrate the feasibility of this indirect identification method.
Huang, Jen-Kuang↗
Dynamic testing of docking system hardware
Extensive dynamic testing was conducted to verify the flight readiness of the Apollo docking hardware. Testing was performed on a unique six degree-of-freedom motion simulator controlled by a computer that calculated the associated spacecraft motions. The test system and the results obtained by subjecting flight-type docking hardware to actual impact loads and resultant spacecraft dynamics are described.
Dorland, W. D.↗
Sizing Considerations for EV Dynamic Wireless Charging Systems with Integrated Energy Storage
Roadways with dynamic wireless charging systems (DWCS) enable charge-sustaining in-motion EV charging, which can reduce charging idle time while increasing range capabilities. Spatially distributed transmitter coils are controlled in response to traffic load that varies significantly minute to minute with high power levels, very short charging time, and low system utilization like wind turbine power. Traffic load estimation and localized analysis may guide effective sizing and topology adoption for feasible and scalable DWCS deployment. DWCS traffic load approximation is reviewed with measured Automated Traffic Recorder (ATR) data and statistical distributions being used to create a synthetic load analyzed using proposed metrics quantifying system utilization over time. Lumped coil section segmentation is compared between second-based distance and spatial density analysis methods, offering 17-27% greater system utilization. A peak load shifting method is proposed for traffic redirection across two tracks with optional BESS integration increasing system utilization by 50-60% depending on time-based and power reserve-based sizing and control.
Lewis, Donovin D.↗
Crustal Dynamics Data Information System (CDDIS) Contributions to GGOS
The Crustal Dynamics Data Information System (CDDIS) provides essential support for the Global Geodetic Observing System (GGOS) by operating a data and product archive for the main geodetic techniques. As GGOS matures and grows, the CDDIS adopts the latest data practices to strengthen its support for the community and ensure quality products are available in a timely manner. To this end, the CDDIS is continually refining its software backend, performing developments such as the 2023 implementation of a middleware processing system, which is successfully being used in operation to provide GNSS-based Upper Atmospheric Realtime Disaster Information and Alert Network (GUARDIAN) and Global Differential GPS System (GDGPS) products. In addition, the CDDIS has 1) released new data and products, 2) performed updates to facilitate navigation of the archive, and 3) made it easier to cite the data and products being added. This poster explores the breadth of work done at the CDDIS and provides highlights of the latest developments.
Justine Woo↗
Dynamic data filtering system and method
A computer-implemented dynamic data filtering system and method for selectively choosing operating data of a monitored asset that modifies or expands a learned scope of an empirical model of normal operation of the monitored asset while simultaneously rejecting operating data of the monitored asset that is indicative of excessive degradation or impending failure of the monitored asset, and utilizing the selectively chosen data for adaptively recalibrating the empirical model to more accurately monitor asset aging changes or operating condition changes of the monitored asset.
97 MATHEMATICS AND COMPUTING↗
Dynamic Radioisotope Power Systems Development Status and Path to Flight
Dynamic power conversion offers the potential to produce Radioisotope Power Systems (RPS) that generate higher power outputs and utilize the Pu-238 radioisotope more efficiently. Additionally, dynamic power conversion offers the potential of producing generators with minimal degradation resulting in more power at the end of the mission, when the power is needed. Dynamic power conversion technologies being developed for space applications include the Stirling and Brayton thermodynamic cycle machines. Machines can be built based on these cycles while eliminating wear mechanisms of the moving components, enabling long design life necessary for space missions. The Dynamic Radioisotope Power Systems (DRPS) project at NASA Glenn Research Center (Glenn Research Center) is pursuing the realization of this type of power source on a flight mission. The project currently has three convertor development contracts that will deliver prototype hardware in 2020. This hardware will undergo a gamut of experimental performance verification efforts at NASA GRC. In parallel, the project has also initiated generator design efforts based on these underlying convertor options, and is also on track to build an in-house version of a generator for laboratory system-level testing. The project is also funding control electronics technology, which are necessary to convert alternating current from the dynamic devices to direct current for use by a spacecraft. A lunar mission is being targeted as the first use of this new technology, as DRPS enables a wide range of high-return scientific missions on the moon, while the mission being short in duration (2 years rather than 10 years for an outer planets mission).
Salvatore M Oriti↗
Dynamic Event Tree Analysis Through RAVEN
Conventional Event-Tree (ET) based methodologies are extensively used as tools to perform reliability and safety assessment of complex and critical engineering systems. One of the disadvantages of these methods is that timing/sequencing of events and system dynamics is not explicitly accounted for in the analysis. In order to overcome these limitations several techniques, also know as Dynamic Probabilistic Risk Assessment (D-PRA), have been developed. Monte-Carlo (MC) and Dynamic Event Tree (DET) are two of the most widely used D-PRA methodologies to perform safety assessment of Nuclear Power Plants (NPP). In the past two years, the Idaho National Laboratory (INL) has developed its own tool to perform Dynamic PRA: RAVEN (Reactor Analysis and Virtual control ENvironment). RAVEN has been designed in a high modular and pluggable way in order to enable easy integration of different programming languages (i.e., C++, Python) and coupling with other application including the ones based on the MOOSE framework, developed by INL as well. RAVEN performs two main tasks: 1) control logic driver for the new Thermo-Hydraulic code RELAP-7 and 2) post-processing tool. In the first task, RAVEN acts as a deterministic controller in which the set of control logic laws (user defined) monitors the RELAP-7 simulation and controls the activation of specific systems. Moreover, RAVEN also models stochastic events, such as components failures, and performs uncertainty quantification. Such stochastic modeling is employed by using both MC and DET algorithms. In the second task, RAVEN processes the large amount of data generated by RELAP-7 using data-mining based algorithms. This paper focuses on the first task and shows how it is possible to perform the analysis of dynamic stochastic systems using the newly developed RAVEN DET capability. As an example, the Dynamic PRA analysis, using Dynamic Event Tree, of a simplified pressurized water reactor for a Station Black-Out scenario is presented.
42 ENGINEERING↗
Learning Koopman Operators for Systems with Isolated Critical Points
The Koopman operator provides a way to transform a (potentially) nonlinear finite-dimensional dynamical system into an infinite-dimensional linear system by lifting the nonlinear state dynamics into a functional space of observables, where the dynamics are linear. Previous literature has claimed that it is not possible to represent nonlinear dynamics with multiple isolated critical points if the set of observables is finite and contains the state; more precisely, such a set cannot be invariant under the Koopman operator. In this paper, we investigate this claim in more detail and provide an analytical counterexample to disprove it. We also consider the convergence of discretetime Koopman approximation error to the continuous-time error: we show both how this convergence occurs in general and how it can fail for systems with multiple isolated critical points. In particular, discontinuities in Koopman observables at the boundaries of basins of attraction may cause the continuous-time error to diverge; the discretetime error also suffers from this as the sampling time step goes to zero.
Bakker, Craig KR↗
Development and Use of Engineering Standards for Computational Fluid Dynamics for Complex Aerospace Systems
Computational fluid dynamics (CFD) and other advanced modeling and simulation (M&S) methods are increasingly relied on for predictive performance, reliability and safety of engineering systems. Analysts, designers, decision makers, and project managers, who must depend on simulation, need practical techniques and methods for assessing simulation credibility. The AIAA Guide for Verification and Validation of Computational Fluid Dynamics Simulations (AIAA G-077-1998 (2002)), originally published in 1998, was the first engineering standards document available to the engineering community for verification and validation (V&V) of simulations. Much progress has been made in these areas since 1998. The AIAA Committee on Standards for CFD is currently updating this Guide to incorporate in it the important developments that have taken place in V&V concepts, methods, and practices, particularly with regard to the broader context of predictive capability and uncertainty quantification (UQ) methods and approaches. This paper will provide an overview of the changes and extensions currently underway to update the AIAA Guide. Specifically, a framework for predictive capability will be described for incorporating a wide range of error and uncertainty sources identified during the modeling, verification, and validation processes, with the goal of estimating the total prediction uncertainty of the simulation. The Guide's goal is to provide a foundation for understanding and addressing major issues and concepts in predictive CFD. However, this Guide will not recommend specific approaches in these areas as the field is rapidly evolving. It is hoped that the guidelines provided in this paper, and explained in more detail in the Guide, will aid in the research, development, and use of CFD in engineering decision-making.
Lee, Hyung B.↗
Nearly Periodic Maps and Geometric Integration of Noncanonical Hamiltonian Systems
Abstract M. Kruskal showed that each continuous-time nearly periodic dynamical system admits a formal U (1)-symmetry, generated by the so-called roto-rate. When the nearly periodic system is also Hamiltonian, Noether’s theorem implies the existence of a corresponding adiabatic invariant. We develop a discrete-time analog of Kruskal’s theory. Nearly periodic maps are defined as parameter-dependent diffeomorphisms that limit to rotations along a U (1)-action. When the limiting rotation is non-resonant, these maps admit formal U (1)-symmetries to all orders in perturbation theory. For Hamiltonian nearly periodic maps on exact presymplectic manifolds, we prove that the formal U (1)-symmetry gives rise to a discrete-time adiabatic invariant using a discrete-time extension of Noether’s theorem. When the unperturbed U (1)-orbits are contractible, we also find a discrete-time adiabatic invariant for mappings that are merely presymplectic, rather than Hamiltonian. As an application of the theory, we use it to develop a novel technique for geometric integration of non-canonical Hamiltonian systems on exact symplectic manifolds.
97 MATHEMATICS AND COMPUTING↗
A microfluidic flow-cell for the study of the ultrafast dynamics of biological systems
The study of biochemical dynamics by ultrafast spectroscopic methods is often restricted by the limited amount of liquid sample available, while the high repetition rate of light sources can induce photodamage. In order to overcome these limitations, we designed a high flux, sub-ml, capillary flow-cell. While the 0.1 mm thin window of the 0.5 mm cross-section capillary ensures an optimal temporal resolution and a steady beam deviation, the cell-pump generates flows up to ~0.35 ml/s that are suitable to pump laser repetition rates up to ~14 kHz, assuming a focal spot-diameter of 100 μm. In addition, a decantation chamber efficiently removes bubbles and allows, via septum, for the addition of chemicals while preserving the closed atmosphere. The minimal useable amount of sample is ~250 μl.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Data-Driven Learning of Non-Autonomous Systems
We present a numerical framework for recovering unknown non-autonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the non-autonomous nature of the system, our method transforms the solution state into piecewise integration of the system over a discrete set of time instances. The time-dependent inputs are then locally parameterized by using a proper model, for example, polynomial regression, in the pieces determined by the time instances. This transforms the original system into a piecewise parametric system that is locally time invariant. We then design a deep neural network structure to learn the local models. Once the network model is constructed, it can be iteratively used over time to conduct global system prediction. We provide theoretical analysis of our algorithm and present a number of numerical examples to demonstrate the effectiveness of the method.
97 MATHEMATICS AND COMPUTING↗
Physics of the Solar System, Proceedings of the Conference on Physics of the Solar System and Reentry Dynamics
Physics of the solar system
SOLAR SYSTEM↗