A solution of nonlinear plane strain problems in dynamic soil mechanics
Nonlinear plane strain problems in dynamic soil mechanics and solutions for spacecraft landing loads
Cox, W. R.↗
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Spacecraft nonlinear control
The feedback linearization technique is applied to the problem of spacecraft attitude control and momentum management with control moment gyros (CMGs). The feedback linearization consists of a coordinate transformation, which transforms the system to a companion form, and a nonlinear feedback control law to cancel the nonlinear dynamics resulting in a linear equivalent model. Pole placement techniques are then used to place the closed-loop poles. The coordinate transformation proposed here evolves from three output functions of relative degree four, three, and two, respectively. The nonlinear feedback control law is presented. Stability in a neighborhood of a controllable torque equilibrium attitude (TEA) is guaranteed and this fact is demonstrated by the simulation results. An investigation of the nonlinear control law shows that singularities exist in the state space outside the neighborhood of the controllable TEA. The nonlinear control law is simplified by a standard linearization technique and it is shown that the linearized nonlinear controller provides a natural way to select control gains for the multiple-input, multiple-output system. Simulation results using the linearized nonlinear controller show good performance relative to the nonlinear controller in the neighborhood of the TEA.
Sheen, Jyh-Jong↗
THE DYNAMICAL GENERATION OF CURRENT SHEETS IN ASTROPHYSICAL PLASMA TURBULENCE
Turbulence profoundly affects particle transport and plasma heating in many astrophysical plasma environments, from galaxy clusters to the solar corona and solar wind to Earth's magnetosphere. Both fluid and kinetic simulations of plasma turbulence ubiquitously generate coherent structures, in the form of current sheets, at small scales, and the locations of these current sheets appear to be associated with enhanced rates of dissipation of the turbulent energy. Therefore, illuminating the origin and nature of these current sheets is critical to identifying the dominant physical mechanisms of dissipation, a primary aim at the forefront of plasma turbulence research. Here, we present evidence from nonlinear gyrokinetic simulations that strong nonlinear interactions between counterpropagating Alfvén waves, or strong Alfvén wave collisions, are a natural mechanism for the generation of current sheets in plasma turbulence. Furthermore, we conceptually explain this current sheet development in terms of the nonlinear dynamics of Alfvén wave collisions, showing that these current sheets arise through constructive interference among the initial Alfvén waves and nonlinearly generated modes. The properties of current sheets generated by strong Alfvén wave collisions are compared to published observations of current sheets in the Earth's magnetosheath and the solar wind, and the nature of these current sheets leads to the expectation that Landau damping of the constituent Alfvén waves plays a dominant role in the damping of turbulently generated current sheets.
79 ASTRONOMY AND ASTROPHYSICS↗
Dynamic characterization and performance evaluation of a 10-kW power take-off with mechanical motion rectifier for wave energy conversion
The power take-off (PTO) is a key component for wave energy converters. In this paper, a compact PTO with mechanical motion rectification rated at 10 kW is designed and prototyped, and characterized. A piecewise nonlinear dynamic model is established to describe its unique dynamic property. A linear hydraulic actuator is adopted in lab testing to drive the prototype and the unknown parameters of the dynamic model are identified. Further verification shows that the model can predict the dynamic performance of the PTO well. The test results show that the mechanical motion rectifier-based PTO can achieve overall energy transfer efficiency as high as 65% in regular waves even when the generator is working below the rated electric load and speed. In the irregular wave test, the PTO achieved the overall energy transfer efficiency of 54%, and the peak-to-average ratio acquired during the test is 12.5.
16 TIDAL AND WAVE POWER↗
The joy of transient chaos
We intend to show that transient chaos is a very appealing, but still not widely appreciated, subfield of nonlinear dynamics. Besides flashing its basic properties and giving a brief overview of the many applications, a few recent transient-chaos-related subjects are introduced in some detail. These include the dynamics of decision making, dispersion, and sedimentation of volcanic ash, doubly transient chaos of undriven autonomous mechanical systems, and a dynamical systems approach to energy absorption or explosion.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Functional expansion representations of artificial neural networks
In the past few years, significant interest has developed in using artificial neural networks to model and control nonlinear dynamical systems. While there exists many proposed schemes for accomplishing this and a wealth of supporting empirical results, most approaches to date tend to be ad hoc in nature and rely mainly on heuristic justifications. The purpose of this project was to further develop some analytical tools for representing nonlinear discrete-time input-output systems, which when applied to neural networks would give insight on architecture selection, pruning strategies, and learning algorithms. A long term goal is to determine in what sense, if any, a neural network can be used as a universal approximator for nonliner input-output maps with memory (i.e., realized by a dynamical system). This property is well known for the case of static or memoryless input-output maps. The general architecture under consideration in this project was a single-input, single-output recurrent feedforward network.
Gray, W. Steven↗
Aeroservoelastic Control Law Development for the Integrated Adaptive Wing Technology Maturation Wind-Tunnel Test
The NASA Advanced Air Transport Technology (AATT) Project seeks to “explore and develop technologies and concepts for improved energy efficiency and environmental compatibility for fixed wing subsonic transports” [1]. The IAWTM project is a subproject within AATT and is a joint Boeing/NASA effort to, in part, demonstrate the active control systems necessary to employ high-aspect ratio wings for improved aerodynamic efficiency. The aircraft configuration under study for the IAWTM project is a generic jet transport based on the NASA Common Research Model (CRM) whose wing aspect ratio has been increased to 13.5 (as opposed to nominal CRM aspect ratio of 9) and whose development is given in Ref. [2]. A semi-span model of the high-aspect-ratio CRM with 10 trailing edge control surfaces is currently being fabricated and will be delivered to the NASA Langley Transonic Dynamics Tunnel (TDT). There, several tests will be conducted to demonstrate maneuver load alleviation (MLA), gust load alleviation (GLA), active flutter suppression (AFS), and drag reduction, all at transonic conditions. A layout of the wind tunnel model is shown in Fig. 1. The wind-tunnel model is a spar/pod wing design with a relatively rigid fuselage attached to a mounting structure (seen in Fig. 1), which in turn is attached to a load balance behind the tunnel wall. Shims exist that can be attached to force the load to go through the fuselage rather than through the balance so as not to damage the balance in the event of flutter. The spar/pod design is similar to that used in the Boeing truss-braced wing aeroelastic model tested in the TDT in 2013 [3]. There is a central spar running the span of the wing to which the pods are attached that form the aerodynamic shape of the wing. The pods are constructed of ribs for attachment to the spar and skins to create the outer mold line. There are ten active control surfaces that will be used for the test objectives discussed above. Three of these (two outboard ailerons and one inboard aileron) are high-speed electrohydraulic actuators, and the remaining seven are low-speed mini-plane flaps, which have slower servo motors that will be used primarily for drag and maneuver load reductions. Control laws must be developed for each test (MLA, GLA, AFS, and drag reduction) and must be able to work in tandem when two or more control strategies are being tested simultaneously (e.g., when control laws to mitigate maneuver loads and gust loads operate simultaneously). The development of these control laws requires accurate mathematical representations of the aerodynamics, structural dynamics, and control surface dynamics of the system. Taken together, this mathematical representation—which is often in state-space form— is the ASE model. Three low-order ASE models of differing fidelities were developed for the IAWTM test and will be presented here. The differences in fidelity appeared in the aerodynamic modeling—one model assumed purely linear aerodynamics, while the other two models used different techniques to linearize the aerodynamics about a nonlinear mean. Furthermore, simple observer-based full-state feedback controllers for each test (MLA, GLA, AFS, and drag reduction) were designed from these low-order ASE models and implemented in a higher-order, nonlinear computational ASE simulation to assess the effectiveness of each controller. Observers were designed from each of the three lower-order ASE models, and each (linear) observer was then used as an estimate of the nonlinear dynamics of the system. Using the estimated states and the full-state feedback controller, control surface commands were fed back to the higher-order, nonlinear ASE system. The insight gained during this development will be applied to control law development for the physical IAWTM wind-tunnel test.
Josiah M Waite↗
Subharmonic Route to Boundary-Layer Transition - Critical Layer Nonlinearity
The linear and nonlinear dynamics of a triad of initially linear stability waves comprising a single plane wave at fundamental frequency and two symmetric oblique waves with half the frequency and streamwise wave number of the plane wave are presented. Analysis is performed for the initial nonlinear development of the waves where the order of the oblique waves' amplitude is equal to or less than that of the plane wave. Results show that the fundamental basically follows the linear theory, while the subharmonic follows an exponential-of-an-exponential growth.
Mankbadi, Reda R.↗
Cardiovascular dynamics during space sickness and deconditioning
We are currently funded by NASA for the project, 'Cardiovascular Dynamics During Space Sickness and Deconditioning.' NASA has given priority to the investigation of two problems encountered in the long-term space flights currently being planned: (1) space motion sickness; and (2) cardiovascular deconditioning. We have proposed to use spectral and nonlinear dynamical analysis of heart rate data to quantify the presence of these problems and to evaluate countermeasures against them.
Goldberger, Ary L.↗
Nonlinear evolution of a large-amplitude circularly polarized Alfven wave: High beta
The nonlinear dynamics following saturation of the parametric instabilities of a monochromatic field-aligned large-amplitude circularly polarized Alfven wave is investigated via direct numerical simulation in the case of high plasma beta and no wave dispersion. The magnetohydrodynamic (MHD) code permits nonlinear couplings in the parallel direction to the ambient magnetic field and one perpendicular direction. Compressibility is included in the form of a polytropic equation of state. Turbulent cascades develop after saturation of two coupled oblique three-wave parametric instabilities; one of which is an oblique filamentationlike instability reported earlier. Remnants of the parametric processes, as well as of the original Alfven pump wave, persist during late nonlinear times. Nearly incompressible MHD features such as spectral anisotropies appear as well.
Ghosh, S.↗
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.↗
Application of finite-element methods to dynamic analysis of flexible spatial and co-planar linkage systems, part 2
An approach is described to modeling the flexibility effects in spatial mechanisms and manipulator systems. The method is based on finite element representations of the individual links in the system. However, it should be noted that conventional finite element methods and software packages will not handle the highly nonlinear dynamic behavior of these systems which results form their changing geometry. In order to design high-performance lightweight systems and their control systems, good models of their dynamic behavior which include the effects of flexibility are required.
Dubowsky, Steven↗
Comprehensive comparison of two tracking codes for single-particle dynamics evaluation of a next-generation storage ring light source
Next-generation light sources based on the multibend achromat concept place great reliance on the accuracy of beam dynamics modeling. To ensure the success of such light sources, confirmation of design performance with at least two independent codes is prudent. The APS Upgrade (APS-U) lattice has been designed using the code ELEGANT, which has existing and new features that are needed by the design. Corresponding, independent improvements have recently been made to the accelerator toolbox (AT), in order to permit an independent check of nonlinear dynamics predictions. The new developments include the modeling of combined-function bending magnets with straight geometry and improved fringe field effects of quadrupole magnets. Calculations of linear and nonlinear lattice parameters and particle tracking results were compared, showing remarkable agreement was found between the two independently developed codes. This provides significant confirmation of the feasibility of the APS-U design.
storage ring↗
Simulation of filamentation instability of a current-carrying plasma by particle in cell method
The nonlinear dynamics of filamentation instability in a weakly ionized current-carrying plasma in the diffusion frequency region is studied using particle in cell simulation. The effects of electron thermal motion and ion-neutral collision on the evolution of this instability in the nonlinear stage of the filaments coalescence are discussed. It is found that the coalescence of the current filaments is enhanced by increasing the temperature and is delayed by increasing the collision frequency.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Virtual to Physical: Reinforcement Learning to Optimize SNS Particle Accelerator Controls
Complex accelerators must have control systems that can handle dynamic nonlinear environments. This makes traditional control methods unsuitable as they can struggle to adapt to these uncertainties. This provides an ideal environment for reinforcement learning algorithms as they are adaptable and generalizable. We present a reinforcement learning pipeline that can effectively handle the dynamics of a complex accelerator. We test and prove our pipelines capabilities on multiple environments including the Spallation Neutron Source (SNS) and the Beam Test Facility (BTF) at Oakridge National Lab (ORNL). Due to the limited time available to train an online algorithm like reinforcement learning on a real accelerator, we utilize a virtual twin accelerator (VIRAC) developed by ORNL to pretrain the policy and show its ability to converge in the virtual environment. We then test the adaptability of the pretrained RL model by applying it on the real accelerator and comparing the results. Utilizing our Scientific Optimization and Controls Toolkit (SOCT) and open-source standards such as Gymnasium we create and solve for a MEBT orbit correction problem in the SNS and an emittance maximization problem in the BTF. We show how Twin Delayed Deep Deterministic Policy Gradient (TD3) can solve this optimization environment in the virtual accelerator and transfer this policy onto the real accelerator for inference and model retraining. We show how reinforcement learning can be utilized as a control system for complex accelerators and provide a model pipeline for how an implementation performs and can be adapted to new accelerator control problems.
Kasparian, Armen [Thomas Jefferson National Accele↗
A chaotic attractor in timing noise from the Vela pulsar?
Fourteen years of timing residual data from the Vela pulsar have been analyzed in order to determine if a chaotic dynamical process is the origin of timing noise. Using the correlation sum technique, a dimension of about 1.5 is obtained. This low dimension indicates underlying structure in the phase residuals which may be evidence for a chaotic attractor. It is therefore possible that nonlinear dynamics intrinsic to the spin-down may be the cause of the timing noise in the Vela pulsar. However, it has been found that the stimulated random walks in frequency and frequency derivative often used to model pulsar timing noise also have low fractal dimension, using the same analysis technique. Recent work suggesting that random processes with steep power spectra can mimic strange attractors seems to be confirmed in the case of these random walks. It appears that the correlation sum estimator for dimension is unable to distinguish between chaotic and random processes.
Harding, Alice K.↗
Simulating Effects of High Angle of Attack on Turbofan Engine Performance
A method of investigating the effects of high angle of attack (AOA) flight on turbofan engine performance is presented. The methodology involves combining a suite of diverse simulation tools. Three-dimensional, steady-state computational fluid dynamics (CFD) software is used to model the change in performance of a commercial aircraft-type inlet and fan geometry due to various levels of AOA. Parallel compressor theory is then applied to assimilate the CFD data with a zero-dimensional, nonlinear, dynamic turbofan engine model. The combined model shows that high AOA operation degrades fan performance and, thus, negatively impacts compressor stability margins and engine thrust. In addition, the engine response to high AOA conditions is shown to be highly dependent upon the type of control system employed.
Liu, Yuan↗
Some remarks to application of bifurcation analysis in BWR stability analysis
Currently, BWR stability analysis is most often performed by application of system codes which provide the time evolution of the neutron flux or thermal power at a defined operational point (OP) after imposing a system parameter perturbation. However, in general, it is impossible to understand the real stability state of the BWR at a specific OP by application of system code analysis alone. Hence, we are searching for methods developed in the nonlinear dynamics field in order to reveal the nature of the BWR stability states when power oscillations are observed. A powerful method is bifurcation analysis. In this paper, we will demonstrate an example of a possible BWR instability phenomenon, which can be understood only in nonlinear terms. (authors)
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗