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DOE OSTI2023

Design and Characterization of a Lens-Coupled System for Dynamic X-Ray Diffraction

X-ray diffraction (XRD) is a necessary technique for understanding states of materials under static and dynamic loading conditions. The higher-pressure Equation of State (EOS) of many materials can only be explored via shock or ramp compression at temperatures and pressures of interest. While static XRD work has yielded EOS measurements in the 100 - 200 GPa regime, dynamic X-ray diffraction (DXRD) can explore EOS phases in the TPa regime, which closely resembles inner-core planetary conditions. DXRD hinges on the ability to measure the exact phase or phase change of a material while under dynamic loading conditions. Macroscopic diagnostic systems (e.g. velocimetry and pyrometry) can infer a phase change but not identify the specific phase entered by a material. While microscopic (atomic-level) diagnostic systems (e.g. DXRD) have been designed and implemented in Department of Energy’s (DOE) National Laboratories complex, the unique nature of Sandia National Laboratories’ Pulsed Power Facility (Z Machine) prohibits the use of such devices. The destructive nature of Z experiments presents a challenge to data capture and retrieval. Furthermore there are electromagnetic interference, X-ray background, and mechanical constraints to consider. Thus, a multi-part X-ray diagnostic for use on the Z Machine and Z-Beamlet Laser system has been designed and analyzed. Portions of this new DYnamic SCintillator Optic (DYSCO) have been built, tested and fielded. A data analysis software has been written. Finally, the radiance profile of the DYSCO’s scintillator has been characterized through experiments performed at the University of Arizona.

36 MATERIALS SCIENCE↗

NASA NTRS2017

Risk Management for Dynamic Radioisotope Power Systems

The implementation of dynamic power conversion technology in Radioisotope Power Systems (RPS) for spaceflight has potential for improved specific power and efficiency, compared with existing Radioisotope Thermoelectric Generators (RTGs). This proposed expansion of current RPS technology necessitates a full exploration of the requirements, goals, and concerns related to risks in developing and deploying such systems. The nature of dynamic systems also presents a new set of challenges related to the presence of moving machinery not intrinsic to traditional RTG units. A general RPS risk management methodology is outlined, which is used to identify and assess the variables and operational scenarios introducing risk throughout the design, fabrication, and system integration processes. This paper will demonstrate how mission requirements for Dynamic RPS concepts (DRPS) drive decisions throughout the development process. This work will define the standard practices for decision making within the scope of the risks associated with DRPS hardware development and deployment in sensitive spacecraft near sensitive payloads. Examples of potential risk areas are analyzed for the proposed dynamic systems, and compared to those associated with traditional RTG technologies. This analysis shows the promise for DRPS systems to elevate and extend the capabilities for power systems used in future NASA missions.

Matthes, Christopher S. R.↗

DOE OSTI2019

Online Optimization as a Feedback Controller: Stability and Tracking

This paper develops and analyzes feedback-based online optimization methods to regulate the output of a linear time-invariant (LTI) dynamical system to the optimal solution of a time-varying convex optimization problem. The design of the algorithm is based on continuous-time primal-dual dynamics, properly modified to incorporate feedback from the LTI dynamical system, applied to a proximal augmented Lagrangian function. The resultant closed-loop algorithm tracks the solution of the time-varying optimization problem without requiring knowledge of (time-varying) disturbances in the dynamical system. The analysis leverages integral quadratic constraints to provide linear matrix inequality (LMI) conditions that guarantee global exponential stability and bounded tracking error. Analytical results show that, under a sufficient time-scale separation between the dynamics of the LTI dynamical system and the algorithm, the LMI conditions can be always satisfied. The paper further proposes a modified algorithm that can track an approximate solution trajectory of the constrained optimization problem under less restrictive assumptions. As an illustrative example, the proposed algorithms are showcased for power transmission systems, to compress the time scales between secondary and tertiary control, and allow to simultaneously power re-balancing and tracking of DC optimal power flow points.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Thermal Modeling and Simulation of the Packed-bed Thermal Energy Storage Combined with INL Thermal Energy Distribution System

Dynamic Energy Transport and Integration Lab (DETAIL) at Idaho National Laboratory is to support experimental demonstration and validation research on Nuclear-Renewable Hybrid Energy System [1]. The Thermal Energy Distribution System (TEDS) is a thermal-hydraulic flow loop in DETAIL with its own dedicated control system to support the integration of co-located multiple experimental systems, where a packed-bed thermal energy storage (TES) is installed as a thermal buffer and storage unit. Among various TES options, the packed-bed TES is adopted in TEDS because it offers a low-cost single-tank thermal storage option compared to the traditional two-tank TES. However, since the TES tank is filled with granular fillers having different thermophysical properties from those of TES tank wall, there is a potential thermo-mechanical issue to be carefully addressed like thermal ratcheting which may pose a significant design concern for the packed-bed TES tank. Thermal ratcheting is a thermomechanical process caused by the repeated rearrangement of granular filler inside a TES tank during continuous thermal cycling operation of the packed-bed TES system. If the thermally induced stress exceeds the yield strength of a TES tank wall, catastrophic consequences may happen like rupture of the TES tank. Thus, it is important to understand the phenomenon to ensure the robust operation of the packed-bed TES tank. Given that thermal ratcheting is caused by complex interaction of thermal transport in the porous bed and solid mechanics, the accurate prediction of transient thermal behavior of the packed-bed TES tank, which is the focus of this paper, is critical to the reliable thermal ratcheting analysis. This paper discusses the numerical modeling, simulation, and validation studies that are ongoing at INL to investigate the transient thermal behavior of the packed-bed TES. Of particular concern is the transient thermal process occurring in the packed-bed TES unit that is operated in conjunction with the INL TEDS. The main goal of this research is three-fold: (i) provide preliminary insights into the transient thermal behavior of the TEDS TES tank, (ii) support the thermal measurement and validation plan for TEDS experiment, and (iii) provide transient thermal boundary conditions to support the reliable thermal ratcheting analysis of the TEDS TES tank. For the transient thermal modeling and analysis, a CFD model was developed, and the validity of the modeling approach was examined via comparing the numerical simulation results with the experimental data obtained from various design characteristics of packed-bed TES tanks. Then, the present modeling method was applied for the transient thermal analysis of the TEDS TES tank, and the results are discussed along with the potential improvement of data acquisition strategy for the future TEDS experiments for more precise validation study.

25 ENERGY STORAGE↗

NASA NTRS1993

Dimensional analysis of acoustically propagated signals

Traditionally, long term measurements of atmospherically propagated sound signals have consisted of time series of multiminute averages. Only recently have continuous measurements with temporal resolution corresponding to turbulent time scales been available. With modern digital data acquisition systems we now have the capability to simultaneously record both acoustical and meteorological parameters with sufficient temporal resolution to allow us to examine in detail relationships between fluctuating sound and the meteorological variables, particularly wind and temperature, which locally determine the acoustic refractive index. The atmospheric acoustic propagation medium can be treated as a nonlinear dynamical system, a kind of signal processor whose innards depend on thermodynamic and turbulent processes in the atmosphere. The atmosphere is an inherently nonlinear dynamical system. In fact one simple model of atmospheric convection, the Lorenz system, may well be the most widely studied of all dynamical systems. In this paper we report some results of our having applied methods used to characterize nonlinear dynamical systems to study the characteristics of acoustical signals propagated through the atmosphere. For example, we investigate whether or not it is possible to parameterize signal fluctuations in terms of fractal dimensions. For time series one such parameter is the limit capacity dimension. Nicolis and Nicolis were among the first to use the kind of methods we have to study the properties of low dimension global attractors.

Hansen, Scott D.↗

NASA NTRS1993

Optimization for efficient structure-control systems

The efficiency of a structure-control system is a nondimensional parameter which indicates the fraction of the total control power expended usefully in controlling a finite-dimensional system. The balance of control power is wasted on the truncated dynamics serving no useful purpose towards the control objectives. Recently, it has been demonstrated that the concept of efficiency can be used to address a number of control issues encountered in the control of dynamic systems such as the spillover effects, selection of a good input configuration and obtaining reduced order control models. Reference (1) introduced the concept and presented analyses of several Linear Quadratic Regulator designs on the basis of their efficiencies. Encouraged by the results of Ref. (1), Ref. (2) introduces an efficiency modal analysis of a structure-control system which gives an internal characterization of the controller design and establishes the link between the control design and the initial disturbances to affect efficient structure-control system designs. The efficiency modal analysis leads to identification of principal controller directions (or controller modes) distinct from the structural natural modes. Thus ultimately, many issues of the structure-control system revolve around the idea of insuring compatibility of the structural modes and the controller modes with each other, the better the match the higher the efficiency. A key feature in controlling a reduced order model of a high dimensional (or infinity-dimensional distributed parameter system) structural dynamic system must be to achieve high efficiency of the control system while satisfying the control objectives and/or constraints. Formally, this can be achieved by designing the control system and structural parameters simultaneously within an optimization framework. The subject of this paper is to present such a design procedure.

Oz, Hayrani↗

DOE OSTI2020

Enforcing constraints for time series prediction in supervised, unsupervised and reinforcement learning

We assume that we are given a time series of data from a dynamical system and our task is to learn the flow map of the dynamical system. We present a collection of results on how to enforce constraints coming from the dynamical system in order to accelerate the training of deep neural networks to represent the flow map of the system as well as increase their predictive ability. In particular, we provide ways to enforce constraints during training for all three major modes of learning, namely supervised, unsupervised and reinforcement learning. In general, the dynamic constraints need to include terms which are analogous to memory terms in model reduction formalisms. Such memory terms act as a restoring force which corrects the errors committed by the learned flow map during prediction. For supervised learning, the constraints are added to the objective function. For the case of unsupervised learning, in particular generative adversarial networks, the constraints are introduced by augmenting the input of the discriminator. Finally, for the case of reinforcement learning and in particular actor-critic methods, the constraints are added to the reward function. In addition, for the reinforcement learning case, we present a novel approach based on homotopy of the action-value function in order to stabilize and accelerate training. We use numerical results for the Lorenz system to illustrate the various constructions.

Stinis, Panagiotis↗

NASA NTRS1992

Phase change energy storage for solar dynamic power systems

This paper presents the results of a transient computer simulation that was developed to study phase change energy storage techniques for Space Station Freedom (SSF) solar dynamic (SD) power systems. Such SD systems may be used in future growth SSF configurations. Two solar dynamic options are considered in this paper: Brayton and Rankine. Model elements consist of a single node receiver and concentrator, and takes into account overall heat engine efficiency and power distribution characteristics. The simulation not only computes the energy stored in the receiver phase change material (PCM), but also the amount of the PCM required for various combinations of load demands and power system mission constraints. For a solar dynamic power system in low earth orbit, the amount of stored PCM energy is calculated by balancing the solar energy input and the energy consumed by the loads corrected by an overall system efficiency. The model assumes an average 75 kW SD power system load profile which is connected to user loads via dedicated power distribution channels. The model then calculates the stored energy in the receiver and subsequently estimates the quantity of PCM necessary to meet peaking and contingency requirements. The model can also be used to conduct trade studies on the performance of SD power systems using different storage materials.

Chiaramonte, F. P.↗

DOE OSTI2024

Learning Constrained Parametric Differentiable Predictive Control Policies With Guarantees

We present differentiable predictive control (DPC), a method for offline learning of constrained neural control policies for nonlinear dynamical systems with performance guarantees. We show that the sensitivities of the parametric optimal control problem can be used to obtain direct policy gradients. Specifically, we employ automatic differentiation (AD) to efficiently compute the sensitivities of the model predictive control (MPC) objective function and constraints penalties. To guarantee safety upon deployment, we derive probabilistic guarantees on closed-loop stability and constraint satisfaction based on indicator functions and Hoeffding’s inequality. We empirically demonstrate that the proposed method can learn neural control policies for various parametric optimal control tasks. In particular, we show that the proposed DPC method can stabilize systems with unstable dynamics, track time-varying references, and satisfy nonlinear state and input constraints. Our DPC method has practical time savings compared to alternative approaches for fast and memory-efficient controller design. Specifically, DPC does not depend on a supervisory controller as opposed to approximate MPC based on imitation learning. We demonstrate that, without losing performance, DPC is scalable with greatly reduced demands on memory and computation compared to implicit and explicit MPC while being more sample efficient than model-free reinforcement learning (RL) algorithms.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1990

Integrated system identification and modal state estimation for control of flexible space structures

A novel approach of integrated system identification and modal state estimation is proposed for control of linear dynamical systems including flexible space structures. There are four steps involved in this approach. First, the relation between a stochastic state space model of a dynamical system and the coefficients of its autoregressive model with exogenous input is derived. Second, an adaptive least-squares transversal predictor is used to estimate the coefficients of the model. Third, a state space model and a steady state Kalman filter gain of the dynamical system are then identified from the coefficients of the model by using the eigensystem realization algorithm. Fourth, a modal state estimator is constructed using the modal parameters of the identified model. On-line implementation of this algorithm can continually improve the modal parameters and the filter gain. It can also gradually update the system model when the system characteristics are slowly changing. A numerical example is used to illustrate the feasibility of the new approach.

Chen, Chung-Wen↗

DOE OSTI2019

Generalized logarithmic equation of state in classical and loop quantum cosmology dark energy–dark matter coupled systems

In this paper we shall study the phase space of a coupled dark energy–dark matter fluids system, in which the dark energy has a generalized logarithmic corrected equation of state. Particularly, the equation of state for the dark energy will contain a logarithmic function of the dark energy density ρ{sub d} and will also have quadratic and Chaplygin gas-like terms, expressed in terms of ρ{sub d}. We shall use the dynamical system approach in order to study the cosmological dynamics, and by appropriately choosing the dynamical system variables, we shall construct an autonomous dynamical system. The study will be performed in the context of classical and loop quantum cosmology, and the focus is on finding stable de Sitter attractors. As we demonstrate, in both the classical and loop quantum cosmology cases, there exist stable de Sitter attractors in the phase space, with the loop quantum cosmology case though having a wider range of the free parameter values for which the stable de Sitter attractors may occur. It is emphasized that the use of a generalized dark energy equation of state makes possible the existence of de Sitter attractors, which were absent in the case that a simple logarithmic term constitutes the dark energy equation of state.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

On Computation of Koopman Operator from Sparse Data

In this paper, we propose a novel approach to compute the Koopman operator from sparse time series data. In recent years there has a considerable interest in operator theoretic methods for data-driven analysis of dynamical systems and existing techniques for the approximation of the Koopman operator require rich enough data-sets. However, in many applications, the data set may not be rich enough to approximate the operators to acceptable limits. In this paper, using ideas from robust optimization, we propose an algorithm to compute the Koopman operator from sparse data. In particular, we enrich the sparse data set with artificial data points and use robust optimization techniques to obtain the transfer operator. We illustrate the efficiency of our proposed approach in three different dynamical systems, namely, a linear system, a nonlinear system and a dynamical system governed by a partial differential equation.

Sinha, Subhrajit↗

DOE OSTI2026

Experimental considerations and applications for time-resolved impedance on silicon-anode battery systems

Dynamic electrochemical impedance spectroscopy (dEIS) utilizes a superimposed multi-sinusoidal waveform and enables temporally resolved investigations on various electrochemical processes; however, the signal-to-noise ratio must be maximized while retaining linearity and stationarity within the system. In the present work, we probe the impact of the waveform’s total amplitude as well as the waveform and phase profiles. The equal amplitude multi-sinusoidal waveform with 35 mV total amplitude (<1 mV per frequency) and random phase profile exhibits the lowest impedance noise. This input signal is sufficient in avoiding the high frequency signal attenuation from the potentiostat’s low-pass filter. Additionally, we demonstrate the optimized dEIS waveform’s utility in investigating surface passivation within thin-film and composite silicon (Si) anodes. Within a two-electrode Si-lithium metal coin cell, the charge transfer resistance (RCT) associated with alloying kinetics dominates the overall impedance. RCT increases with state of charge indicating a kinetic bottleneck at higher lithiation states. To explore this further, we utilize a three-electrode Si-LiNi0.8Mn0.1Co0.1O2 pouch cell to deconvolute the Si impedance contributions. The evolution of the solid electrolyte interphase (SEI) and charge transfer resistances correlate to specific Li–Si alloy phases. We attribute this to the influence of Si particle volume expansion on SEI instabilities and a kinetic bottleneck at higher lithiation states.

Lam, Steven [ORNL]↗

NASA NTRS1990

Neural networks for self-learning control systems

It is shown how a neural network can learn of its own accord to control a nonlinear dynamic system. An emulator, a multilayered neural network, learns to identify the system's dynamic characteristics. The controller, another multilayered neural network, next learns to control the emulator. The self-trained controller is then used to control the actual dynamic system. The learning process continues as the emulator and controller improve and track the physical process. An example is given to illustrate these ideas. The 'truck backer-upper,' a neural network controller that steers a trailer truck while the truck is backing up to a loading dock, is demonstrated. The controller is able to guide the truck to the dock from almost any initial position. The technique explored should be applicable to a wide variety of nonlinear control problems.

Nguyen, Derrick H.↗

DOE OSTI2017

Lyapunov exponent as a metric for assessing the dynamic content and predictability of large-eddy simulations

Metrics used to assess the quality of large-eddy simulations commonly rely on a statistical assessment of the solution. While these metrics are valuable, a dynamic measure is desirable to further characterize the ability of a numerical simulation for capturing dynamic processes inherent in turbulent flows. To address this issue, a dynamic metric based on the Lyapunov exponent is proposed which assesses the growth rate of the solution separation. Specifically, this metric is applied to two turbulent flow configurations: forced homogeneous isotropic turbulence and a turbulent jet diffusion flame. First, it is shown that, despite the direct numerical simulation (DNS) and large-eddy simulation (LES) being high-dimensional dynamical systems with O(107) degrees of freedom, the separation growth rate qualitatively behaves like a lower-dimensional dynamical system, in which the dimension of the Lyapunov system is substantially smaller than the discretized dynamical system. Second, a grid refinement analysis of each configuration demonstrates that as the LES filter width approaches the smallest scales of the system the Lyapunov exponent asymptotically approaches a plateau. Third, a small perturbation is superimposed onto the initial conditions of each configuration, and the Lyapunov exponent is used to estimate the time required for divergence, thereby providing a direct assessment of the predictability time of simulations. By comparing inert and reacting flows, it is shown that combustion increases the predictability of the turbulent simulation as a result of the dilatation and increased viscosity by heat release. The predictability time is found to scale with the integral time scale in both the reacting and inert jet flows. Fourth, an analysis of the local Lyapunov exponent is performed to demonstrate that this metric can also determine flow-dependent properties, such as regions that are sensitive to small perturbations or conditions of large turbulence within the flow field. Finally, it is demonstrated that the global Lyapunov exponent can be utilized as a metric to determine if the computational domain is large enough to adequately encompass the dynamic nature of the flow.

42 ENGINEERING↗

DOE OSTI2018

Contact manifolds and dissipation, classical and quantum

Motivated by a geometric decomposition of the vector field associated with the Gorini–Kossakowski–Lindblad–Sudarshan (GKLS) equation for finite-level open quantum systems, we propose a generalization of the recently introduced contact Hamiltonian systems for the description of dissipative-like dynamical systems in the context of (non-necessarily exact) contact manifolds. In particular, we show how this class of dynamical systems naturally emerges in the context of Lagrangian Mechanics and in the case of nonlinear evolutions on the space of pure states of a finite-level quantum system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Heavy flavor dynamics across system size at the LHC

One of the fundamental signatures of the Quark Gluon Plasma has been the suppression of heavy flavor (specifically D mesons), which has been measured via the nuclear modification factor, R AA and azimuthal anisotropies, v n , in large systems. However, multiple competing models can reproduce the same data for R AA to v n . In this talk we break down the competing effects that conspire together to successfully reproduce R AA and v n in experimental data using Trento+v-USPhydro+DAB-MOD. Then using our best fit model we make predictions for R AA and v n across system size for 208 PbPb, 129 XeXe, 40 ArAr, and 16 OO collisions. We find that 0–10% centrality has a non-trivial interplay between the system size and eccentricities such that system size effects are masked in v 2 whereas in 30–50% centrality the eccentricities are approximately constant across system size and, therefore, is a better centrality class to study D meson dynamics across system size.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Memory-efficient nonsmooth dynamic optimization using adaptive randomized compression

Dynamic optimization problems arise in many applications including flow control, full waveform inversion, and medical imaging. These problems are plagued by significant computational challenges. One such challenge — and the focus of this work — is the memory limitation induced by the size of the underlying dynamical system. In particular, the entire dynamic trajectory is required for derivative computation and therefore must be stored or recomputed using, e.g., checkpointing. Although recent work demonstrated the use of adaptive randomized sketching to overcome the memory challenge, that work only applies to smooth unconstrained problems, prohibiting its use for nonsmooth regularized and constrained problems. The inclusion of nonsmooth regularizers and constraints is critical as they often arise in an attempt to preserve certain physical properties or to promote sparsity. To solve these problems, we introduce a trust-region algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function that leverages randomized sketching to compress the dynamical system trajectories and adaptively adjust the sketch rank to satisfy a gradient inexactness condition. We prove convergence of this algorithm and demonstrate that it achieves substantial memory reduction on three discretized PDE-constrained optimization applications.

97 MATHEMATICS AND COMPUTING↗