Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Nonlinear models”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,117 records · Page 62

Implications of a two-fluid heat diffusion model for RF condensation effects in magnetic islands

Theoretical calculations have predicted an “RF condensation” effect through which the temperature perturbation and current drive may be nonlinearly enhanced in electron cyclotron (EC) heated magnetic islands. Previously, two-fluid effects had been neglected in the OCCAMI code used to model RF condensation. For realistic experimental conditions, we show that two-fluid effects in an EC heated plasma may have a major impact on RF condensation. Less collisional plasmas, where electron and ion temperatures are decoupled, exhibit an enhanced linear temperature perturbation in the island, and an even stronger nonlinear enhancement of the perturbed temperature. This can occur even when nonlinear effects are small in the single-fluid limit. We also calculate corresponding hysteresis effects. Finally, we demonstrate that other physical effects, including the rotation of the magnetic island and the Gaussian spread of the beam from a gyrotron, can significantly decrease the predicted observable RF condensation effect.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Viscous effects on plasmoid formation from nonlinear resistive tearing growth in a Harris sheet

Abstract In this work, the evolution of a highly unstable m = 1 resistive tearing mode, leading to plasmoid formation in a Harris sheet, is studied in the framework of full MHD model using the Non-Ideal Magnetohydrodynamics with Rotation, Open Discussion simulation. Following the initial nonlinear growth of the primary m = 1 island, the X-point develops into a secondary elongated current sheet that eventually breaks into plasmoids. Two distinctive viscous regimes are found for the plasmoid formation and saturation. In the low viscosity regime (i.e. P r ≲ 1), the plasmoid width increases sharply with viscosity, whereas in the viscosity dominant regime (i.e. P r ≳ 1), the plasmoid size gradually decreases with viscosity. Such a finding quantifies the role of viscosity in modulating the plasmoid formation process through its effects on the plasma flow and the reconnection itself.

Physics↗

Algebraic Multigrid with Filtering: An Efficient Preconditioner for Interior Point Methods in Large-Scale Contact Mechanics Optimization

Large-scale contact mechanics simulations are crucial in many engineering fields such as structural design and manufacturing. In the frictionless case, contact can be modeled by minimizing an energy functional; however, these problems are often nonlinear, nonconvex, and increasingly difficult to solve as mesh resolution increases. In this work, we employ a Newton-based interior-point (IP) filter line-search method, an effective approach for large-scale constrained optimization. While this method converges rapidly, each iteration requires solving a large saddle-point linear system that becomes ill-conditioned as the optimization process converges, largely due to IP treatment of the contact constraints. Such ill-conditioning can hinder solver scalability and increase iteration counts with mesh refinement. Here, to address this, we introduce a novel preconditioner, algebraic multigrid with filtering (AMGF), tailored to the Schur complement of the saddle-point system. Building on the classical AMG solver, commonly used for elasticity, we augment it with a specialized subspace correction that filters near null space components introduced by contact interface constraints. Through theoretical analysis and numerical experiments on a range of linear and nonlinear contact problems, we demonstrate that the proposed solver achieves mesh independent convergence and maintains robustness against the ill-conditioning that notoriously plagues IP methods. These results indicate that AMGF makes contact mechanics simulations more tractable and broadens the applicability of Newton-based IP methods in challenging engineering scenarios. More broadly, AMGF is well suited for problems, optimization or otherwise, where solver performance is limited by a low-dimensional subspace, such as those arising from localized constraints, interface conditions, or model heterogeneities. This makes the method widely applicable beyond contact mechanics and constrained optimization.

Mathematics and Computing↗

Utilizing CellBox to Describe Varied Dynamical Systems

CellBox is a hybrid modeling framework that integrates machine-learning approaches with explicit mathematical modeling to determine the behavior of dynamical systems, intended for determining the complex interactions of molecule and phenotype within a cellular environment using perturbation/response-based data. The original work utilized analysis of a melanoma cell line, SK-Mel-133, which we sought to expand to and evaluate effectiveness in describing other nonlinear systems both within and outside of biology. We evaluated with two models. One model is based upon the free-fall of an object under a velocity-dependent drag force; this produced inherent perturbation/response data. The other model is based upon a form of mass-action molecular kinetics; for this, we ran the simulation to steady state in each species for each perturbation and select the steady state as input for CellBox. We determined that CellBox, outside of its original use case, can still strongly predict even non-biological dynamical systems in the small-perturbation regime, with r = 0.99977 to 0.85123, p < 0.05 for freefall. However, CellBox cannot accurately predict behavior within large-perturbation regimes, p >> 0.05 for freefall. In addition, we performed a naïve comparison of CellBox network structure to known network structure in the mass-action model to assess accuracy.

97 MATHEMATICS AND COMPUTING↗

Two-fluid model of rf current condensation in magnetic islands

The stabilization of tearing modes with rf waves is subject to a nonlinear effect, termed rf current condensation, that has the potential to greatly enhance and localize current driven within magnetic islands. Here we extend previous investigations of this effect with a two fluid model that captures the balance of diffusive and thermal equilibration processes within the island. We show that the effective power and resulting strength of the condensation effect can be greatly enhanced by avoiding collisional heat loss to the ions. The relative impact of collisions on the overall power balance within the island depends on the ratio of the characteristic diffusion timescale and the electron–ion equilibration time, rather than the latter alone. Although relative heat loss to ions increases with island size, the heating efficiency does as well. In particular, we show that the latter safely dominates for large deposition profiles, as is typically the case for lower hybrid current drive. This supports the possibility of passive stabilization of neoclassical tearing modes without the precise aiming of the rf waves required for electron cyclotron current drive stabilization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov n-width. However, for physical phenomena not of this type, e.g., any advection-dominated flow phenomena such as in traffic flow, atmospheric flows, and air flow over vehicles, a low-dimensional linear subspace poorly approximates the solution. To address cases such as these, we have developed a fast and accurate physics-informed neural network ROM, namely nonlinear manifold ROM (NM-ROM), which can better approximate high-fidelity model solutions with a smaller latent space dimension than the LS-ROMs. Our method takes advantage of the existing numerical methods that are used to solve the corresponding full order models. The efficiency is achieved by developing a hyper-reduction technique in the context of the NM-ROM. Numerical results show that neural networks can learn a more efficient latent space representation on advection-dominated data from 1D and 2D Burgers' equations. A speedup of up to 2.6 for 1D Burgers' and a speedup of 11.7 for 2D Burgers' equations are achieved with an appropriate treatment of the nonlinear terms through a hyper-reduction technique. Lastly, a posteriori error bounds for the NM-ROMs are derived that take account of the hyper-reduced operators.

97 MATHEMATICS AND COMPUTING↗

Extraordinary frequency stabilization by resonant nonlinear mode coupling

Here, we show that a self-sustained oscillator with a frequency-selective element operating with two nonlinearly coupled modes can achieve a level of frequency stability well beyond that available using single-mode operation. The system of interest consists of a self-sustained oscillator based on a nonlinear primary mode that is coupled via an internal resonance to a passive secondary mode. Analysis of a generic model for this resonance with both additive and multiplicative noises reveals that the stability improvements accrue from two sources: (i) nonlinear frequency veering in the primary mode, a classical analogue to quantum-level repulsion, that eliminates amplitude-to-frequency noise conversion; and (ii) phase cleaning of the oscillator through an intrinsic phase constraint arising from synchronization of the modes. This latter effect can significantly reduce the effects of intrinsic frequency fluctuations of the primary mode, which are not accessible by any known strategy using single-mode operation. The theoretical predictions are supported by experimental measurements of a microelectromechanical systems-based oscillator that demonstrate a reduction in oscillator line width of several orders of magnitude. This approach offers a means of optimizing frequency stability in self-sustained oscillators, which has direct implications for applications in timekeeping and sensing.

36 MATERIALS SCIENCE↗

Multiscale model predictive control of battery systems for frequency regulation markets using physics-based models

In this work, we propose a multiscale model predictive control (MPC) framework for stationary battery systems that exploits high-fidelity models to trade-off short-term economic incentives provided by energy and frequency regulation (FR) markets and long-term degradation effects. We find that the MPC framework can drastically reduce long-term degradation while properly responding to FR and energy market signals (compared to MPC formulations that use low-fidelity models). Our results also provide evidence that sophisticated battery models can be embedded within closed-loop MPC simulations by using modern nonlinear programming solvers (we provide an efficient and easy-to-use implementation in Julia). We use insights obtained with our simulations to design a low-complexity MPC formulation that matches the behavior obtained with high-fidelity models. This is done by designing a suitable terminal penalty term that implicitly captures long-term degradation. The results suggest that complex degradation behavior can be accounted for in low-complexity MPC formulations by properly designing the cost function. We believe that our proof-of-concept results can be of industrial relevance, as battery vendors are seeking to participate in fast-changing electricity markets while maintaining asset integrity.

42 ENGINEERING↗

An analytic theory for the degree of Arctic Amplification

Arctic Amplification (AA), the amplified surface warming in the Arctic relative to the global mean, is a robust and impactful feature of climate change. While the basic physical picture of AA has been depicted, a clear understanding of how the degree of AA is determined has not been established. Here, by deciphering the intricate role of atmospheric heat transport (AHT), we build a two-box energy-balance model of AA and derive that the degree of AA is a simple nonlinear function of the Arctic and global feedbacks, the meridional heterogeneity in radiative forcing, and the partial sensitivities of AHT to global mean warming and meridional warming gradient. The formula captures the varying degree of AA in individual climate models and attributes the variation to specific physical factors. It further conveys a concise picture of how essential physics mutually determine the degree of AA and limit the range within 1.5~3.5. Our results articulate AHT as both forcing and feedback to AA, highlighting its partial sensitivities instead of total change as the key parameters for understanding AA. We also find that the effect of lapse rate feedback, a widely-recognized major contributor to AA, is fully offset by the effect of water vapor feedback.

54 ENVIRONMENTAL SCIENCES↗

Toward fusion plasma scenario planning for NSTX-U using machine-learning-accelerated models

One of the most promising devices for realizing power production through nuclear fusion is the tokamak. To maximize performance, it is preferable that tokamak reactors achieve advanced operating scenarios characterized by good plasma confinement, improved magnetohydrodynamic (MHD) stability, and a largely non-inductively driven plasma current. Such scenarios could enable steady-state reactor operation with high \emph{fusion gain} --- the ratio of produced fusion power to the external power provided through the plasma boundary. Precise and robust control of the evolution of the plasma boundary shape as well as the spatial distribution of the plasma current, density, temperature, and rotation will be essential to achieving and maintaining such scenarios. The complexity of the evolution of tokamak plasmas, arising due to nonlinearities and coupling between various parameters, motivates the use of model-based control algorithms that can account for the system dynamics. In this work, a learning-based accelerated model trained on data from the National Spherical Torus Experiment Upgrade (NSTX-U) is employed to develop planning and control strategies for regulating the density and temperature profile evolution around desired trajectories. The proposed model combines empirical scaling laws developed across multiple devices with neural networks trained on empirical data from NSTX-U and a database of first-principles-based computationally intensive simulations. The reduced execution time of the accelerated model will enable practical application of optimization algorithms and reinforcement learning approaches for scenario planning and control development. An initial demonstration of applying optimization approaches to the learning-based model is presented, including a strategy for mitigating the effect of leaving the finite validity range of the accelerated model. The approach shows promise for actuator planning between experiments and in real-time.

machine learning↗

Simultaneous reproduction of experimental profiles, fluxes, transport coefficients, and turbulence characteristics via nonlinear gyrokinetic profile predictions in a DIII-D ITER similar shape plasma

Experimental conditions obtained on the DIII-D tokamak in the ITER Similar Shape (ISS) have been compared extensively with nonlinear gyrokinetic simulation using the CGYRO code [Candy et al., J. Comput. Phys. 324, 73–93 (2016)] with comparisons spanning ion and electron heat fluxes, electron and impurity particle transport, and turbulent fluctuation levels and characteristics. Bayesian optimization techniques [Rodriguez-Fernandez et al., Nucl. Fusion 62(7), 076036 (2022)], combined with nonlinear gyrokinetics, have been used to obtain simultaneously Qi, Qe, and Γe flux-matched profiles that are found to be in good agreement with experimental profile measurements. Synthetic diagnostics were used to compare measured beam emission spectroscopy and correlation electron cyclotron emission turbulent fluctuations with nonlinear simulation. Although some disagreements exist, nonlinear simulations are found to be in generally good agreement with measured fluctuation levels, spectral shapes, and measured radial trends in low-k δne/ne and δTe/Te. Low (Li and C) and mid-Z (Ca) impurity transport was also compared with these flux-matched simulations. Fully stripped, low-Z impurities are well reproduced by the gyrokinetic modeling while clear disagreement exists in comparisons with mid-Z impurities. Nonlinear gyrokinetic investigation into the Z dependence of impurity transport in the ISS conditions is also performed, demonstrating clear trends of impurity diffusion with impurity Z (both D∝Z and D∝1/Z) that vary with the radial location studied. These trends are shown to result from the local dominance of ion temperature gradient or ∇n driven trapped electron mode turbulence and may contribute to the disagreement between simulation and experiment in mid-Z impurity transport. The results of this work represent one of the most complete validation studies of the gyrokinetic model performed to date and provide an example of new capabilities for predicting performance in future fusion devices.

Physics↗

Improving the performance of cryogenic calorimeters with nonlinear multivariate noise cancellation algorithms

Abstract State-of-the-art physics experiments require high-resolution, low-noise, and low-threshold detectors to achieve competitive scientific results. However, experimental environments invariably introduce sources of noise, such as electrical interference or microphonics. The sources of this environmental noise can often be monitored by adding specially designed “auxiliary devices” (e.g. microphones, accelerometers, seismometers, magnetometers, and antennae). A model can then be constructed to predict the detector noise based on the auxiliary device information, which can then be subtracted from the true detector signal. Here, we present a multivariate noise cancellation algorithm which can be used in a variety of settings to improve the performance of detectors using multiple auxiliary devices. To validate this approach, we apply it to simulated data to remove noise due to electromagnetic interference and microphonic vibrations. We then employ the algorithm to a cryogenic light detector in the laboratory and show an improvement in the detector performance. Finally, we motivate the use of nonlinear terms to better model vibrational contributions to the noise in thermal detectors. We show a further improvement in the performance of a particular channel of the CUORE detector when using the nonlinear algorithm in combination with optimal filtering techniques.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Experimental validation of a Kalman observer using linearized OpenFAST and a fully instrumented 1:70 model

Abstract To enable real‐time monitoring and control strategies for floating offshore wind turbines, accurate information about the state of the system is needed. This paper details the application of a Kalman filter to the UMaine VolturnUS‐S floating wind platform to provide accurate state estimates in real time using minimal system measurements. The midfidelity nonlinear simulation tool OpenFAST was used to generate the underlying linear state‐space model for the Kalman filter. This linear model and its limitations are demonstrated through comparison with experimental data collected on a 1:70 froude‐scaled model of the floating platform and tower. Using a selection of five measurements from the real system, a Kalman filter was developed to provide estimates for the remaining system states and measurements. These estimates were then validated against the experimental values collected from testing of the scale model. Validation of the Kalman filter produced accurate estimates of surge, heave, and tower base bending moment, measurements of which were not available to the Kalman filter. Performance of the Kalman filter was tested and validated over a range of sea conditions from rated wind speed to storm events and demonstrated robustness in the Kalman filter to maintain accuracy across all operating conditions despite significant error in the underlying linear model for extreme conditions.

17 WIND ENERGY↗

Denoising diffusion probabilistic models for generative alloy design

Inverse material design is an extremely challenging optimization task made difficult by, in part, the highly nonlinear relationship linking performance with composition. Quantitative approaches have improved significantly owing to advances in high throughput experimentation and computational thermodynamics. However, existing physics-based tools are mostly forward models; input a chemistry and obtain a prediction. More recently the materials community has leveraged advances in the machine learning community to establish novel inverse design frameworks. Very recently denoising diffusion probabilistic models have been shown to be extremely powerful generators producing synthetic data of various modalities e.g. images, text, audio, tables, etc.. In this work a novel framework for alloy design and optimization is proposed leveraging these class of models. Five key generative tasks are demonstrated (1) unconditional generation (2) composition conditioned generation (3) property conditioned generation (4) multi-feedstock conditioned generation and (5) generative optimization. These methods were tested on three case studies: high entropy alloy design, superalloy binder jet additive manufacturing, and in-situ dual-feedstock wire-arc additive manufacturing. Results indicate that the established models are extremely flexible, expressive, and robust. The architecture’s flexibility and training procedure empower the model to learn complex intra-compositional and composition-property relationships. Furthermore, the probabilistic nature of these models makes them well suited for addressing solution non-uniqueness and tackling uncertainty quantification tasks. While the fidelity and quantity of the underlying training data is paramount, we envision that future alloy design frameworks will make extensive use of these kinds of machine learning models as “search” tools bolstering the utility of experimental and computational approaches.

36 MATERIALS SCIENCE↗

GDSA PFLOTRAN Development (FY2021)

The Spent Fuel & Waste Science and Technology (SFWST) Campaign of the U.S. Department of Energy (DOE) Office of Nuclear Energy (NE), Office of Spent Fuel & Waste Disposition (SFWD) is conducting research and development (R&D) on geologic disposal of spent nuclear fuel (SNF) and high-level nuclear waste (HLW). A high priority for SFWST disposal R&D is to develop a disposal system modeling and analysis capability for evaluating disposal system performance for nuclear waste in geologic media. This report describes fiscal year (FY) 2021 advances of the PFLOTRAN Development group of the SFWST Campaign. The mission of this group is to develop a geologic disposal system modeling capability for nuclear waste that can be used to probabilistically assess the performance of generic disposal concepts. In FY 2021, development proceeded along three main thrusts: software infrastructure, code performance, and process model advancement. Software infrastructure improvements included implementing an Agile software development framework and making improvements to the QA Test Suite. Code performance improvements included development of advanced linear and nonlinear solvers as well as design of flexible smoothing algorithms for capillary pressure functions. Process modeling advancements included the addition of flexible thermal conductivity function definitions and refinement of multi-continuum reactive transport to support Sandia’s participation in DECOVALEX

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

PFLOTRAN Development FY2021

The Spent Fuel & Waste Science and Technology (SFWST) Campaign of the U.S. Department of Energy (DOE) Office of Nuclear Energy (NE), Office of Spent Fuel & Waste Disposition (SFWD) is conducting research and development (R&D) on geologic disposal of spent nuclear fuel (SNF) and high-level nuclear waste (HLW). A high priority for SFWST disposal R&D is to develop a disposal system modeling and analysis capability for valuating disposal system performance for nuclear waste in geologic media. This report describes fiscal year (FY) 2021 advances of the PFLOTRAN Development group of the SFWST Campaign. The mission of this group is to develop a geologic disposal system modeling capability for nuclear waste that can be used to probabilistically assess the performance of generic disposal concepts. In FY 2021, development proceeded along three main thrusts: software infrastructure, code performance, and process model advancement. Software infrastructure improvements included implementing an Agile software development framework and making improvements to the QA Test Suite. Code performance improvements included development of advanced linear and nonlinear solvers as well as design of flexible smoothing algorithms for capillary pressure functions. Process modeling advancements included the addition of flexible thermal conductivity function definitions and refinement of multi-continuum reactive transport to support Sandia’s participation in DECOVALEX. This report fulfills the GDSA PFLOTRAN Development Work Package Level 3 Milestone – PFLOTRAN Development, FY2021, M3SF-21SN010304072.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

A 1D coupled transport/cold plasma wave model for parallel ponderomotive density modification near RF actuators

The plasma density profile close to RF actuators plays a vital role in the efficiency of power coupling from the antenna to the core plasma of fusion devices. Nonlinear interactions can be significant when considering the interaction of applied RF power and the tenuous SOL plasma, and the inclusion of this region in computational analysis is essential to providing robust predictive simulations of plasma response to RF application. Of particular interest is the observed density modification during RF operation. Here we present a self consistent description of the nonlinear ponderomotive force in the antenna near field region, via coupling a 1D field aligned transport model with a 1D cold plasma wave model. Results are presented, which show a parallel electric field of 300 Vm -1 drove a density reduction of ~ 20% over 25 RF periods.

Barnett, Rhea↗

Inference of neutrino flavor evolution through data assimilation and neural differential equations

The evolution of neutrino flavor in dense environments such as core-collapse supernovae and binary compact object mergers constitutes an important and unsolved problem. Its solution has potential implications for the dynamics and heavy-element nucleosynthesis in these environments. In this paper, we build upon recent work to explore inference-based techniques for the estimation of model parameters and neutrino flavor evolution histories. Here, we combine data assimilation, ordinary differential equation solvers, and neural networks to craft an inference approach tailored for nonlinear dynamical systems. Using this architecture, and a simple two-neutrino-beam, two-flavor model, we compare the performances of nine different optimization algorithms and expand upon previous assessments of the efficacy of inference for tackling problems in flavor evolution. We find that employing this new architecture, together with evolutionary optimization algorithms, accurately captures flavor histories in the small-scale model and allows us to quickly explore both model parameters and initial flavor content. In future work we plan to extend these inference techniques to large numbers of neutrinos.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗