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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Nonlinear two-fluid modeling of plasma response to RMPs for the ELM control in the ITER baseline

Numerical modeling, combining the toroidal ideal MHD code GPEC and the nonlinear two-fluid MHD code TM1, was used for comprehensive studies of the plasma response to resonant magnetic perturbations (RMPs) with toroidal mode number n = 1–5 for controlling edge-localized modes (ELMs) in ITER for the standard operation scenario (15 MA Q = 10). Several issues related to RMP ELM control are investigated, including the optimization of the RMP coils configuration, the evaluation of the magnitude of density pump-out and the q95 windows of ELM suppression. GPEC calculates the magnetic response, which consistently includes the very important edge kink/peeling response to static magnetic perturbations. Furthermore, GPEC two-dimensional scans of the relative coil current phasing among the three rows of internal coils, at fixed coil current amplitude, reveal the optimal phasing for the RMP coil configuration with n = 1–5, respectively. The poloidal half wavelength of resonant mode at the edge of plasma calculated by GPEC indicates that the midplane row coils have the best resonant coupling with the plasma for n = 2, while the upper and lower row coils have the best resonant coupling with the plasma for n = 3. Based on the plasma kinetic equilibrium and the GPEC calculations of the magnetic response, TM1 was used to simulate the conditions for RMP field penetration in the ITER pedestal. TM1 shows magnetic island formation at the foot of ITER pedestal with RMP coil current threshold ranging from 4 kAt to 8 kAt with n = 2 to 4. These magnetic islands at the pedestal-foot lead to density pump-out, the magnitude of which scales as ${I}_{\text{RMP}}^{0.5}$ and ranges from 5% to 20% at the pedestal-top when scanning the coil current from 4 to 60 kAt. The density pump-out is found to be weaker for higher n RMP. The nonlinear TM1 simulations also show field penetration at the pedestal-top, where the threshold of RMP coil current depends on the q 95 . The alignment of the magnetic island and the location of the pedestal-top decreases the height and width of the pedestal to suppress ELMs. Simulations by two-dimensional scans of RMP coil current and q 95 reveal the accessible q 95 windows of ELM suppression for both n = 3 and 4 RMPs. The predicted q 95 windows of ELM suppression are very similar to the ones in currently operating tokamaks and the required RMP coil current for ELM suppression is less than 40–50 kAt, which is well within the designed capability for ITER. In addition, the simulations indicate that wide q 95 windows of ELM suppression may be accessible in ITER by operating with dominant n = 4 (or n = 5) RMPs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Modeling the Yaw Behavior of Tail Fins for Small Wind Turbines: November 22, 2021 - May 21, 2024

This report describes the aerodynamic modelling of the yaw behavior of tail fins for small wind turbines (SWTs). The analysis is based on unsteady slender body theory (USBT) and is formulated to be used with the proposed tail fin module to be added to OpenFAST. Linearized USBT, which has been applied in the past to SWT tail fins, is developed in three main ways. First, USBT is extended to high yaw angles and aspect ratios by modelling the associated nonlinear vortex dynamics and the chordwise load distribution respectively. Second, we consider the effect of time-varying wind speed. The extended theory is compared to recent unpublished measurements at the University of Perugia, Italy, for the yaw behavior of delta, elliptical, and rectangular tail fins without a rotor and nacelle. The fins were released from initial yaw angles of -40 degrees and -80 degrees ; the latter is of sufficient magnitude to show the importance of the nonlinear yaw dynamics. Further, the friction in the model tail fin bearings was measured and modelled. The constants in the aerodynamic models were taken from the literature but significant improvement in accuracy is achieved by using system identification techniques to optimize the values. This leads to the third main finding: extended USBT is accurate for all generic tail fin shapes that we considered and is, therefore, very suitable for inclusion in aeroelastic codes for SWTs. The final development is of a general nonlinear equation for yaw response that is simpler than the extended USBT and is also suitable for inclusion in OpenFAST. The two nonlinear models are used to highlight the geometric requirements for good tail fin design.

distributed wind↗
DOE OSTI2025

Nonlinear Ensemble Filtering with Diffusion Models: Application to the Surface Quasigeostrophic Dynamics

The intersection between classical data assimilation methods and novel machine learning techniques has attracted significant interest in recent years. Here, we explore another promising solution in which diffusion models are used to formulate a robust nonlinear ensemble filter for sequential data assimilation. Unlike standard machine learning methods, the proposed ensemble score filter (EnSF) is completely training free and can efficiently generate a set of analysis ensemble members. Here, in this study, we apply the EnSF to a surface quasigeostrophic model and compare its performance against the popular local ensemble transform Kalman filter (LETKF), which makes Gaussian assumptions in the analysis step. Numerical tests demonstrate that EnSF maintains stable performance in the absence of localization and for a variety of experimental settings. We find that while LETKF maintains optimal performance in the case of linear observations of the entire state and a perfect model, EnSF shows improvements over LETKF when nonlinear observations are assimilated and the system is subject to unexpected model errors. A spectral decomposition of the analysis results in this nonlinear observation regime shows that the largest improvements over LETKF occur at large scales (small wavenumbers), where LETKF lacks sufficient ensemble spread. Overall, this initial application of EnSF to a geophysical model of intermediate complexity motivates further development of the algorithm for more realistic problems.

Artificial intelligence↗
DOE OSTI2020

Nonlinear Photovoltaic Degradation Rates: Modeling and Comparison Against Conventional Methods

Although common practice for estimating photovoltaic (PV) degradation rate (RD) assumes a linear behavior, field data have shown that degradation rates are frequently nonlinear. This article presents a new methodology to detect and calculate nonlinear RD based on PV performance time-series from nine different systems over an eight-year period. Prior to performing the analysis and in order to adjust model parameters to reflect actual PV operation, synthetic datasets were utilized for calibration purposes. A change-point analysis is then applied to detect changes in the slopes of PV trends, which are extracted from constructed performance ratio (PR) time-series. Once the number and location of change points is found, the ordinary least squares method is applied to the different segments to compute the corresponding rates. The obtained results verified that the extracted trends from the PR time-series may not always be linear and therefore, “nonconventional” models need to be applied. All thin-film technologies demonstrated nonlinear behavior whereas nonlinearity detected in the crystalline silicon systems is thought to be due to a maintenance event. A comparative analysis between the new methodology and other conventional methods demonstrated levelized cost of energy differences of up to 6.14%, highlighting the importance of considering nonlinear degradation behavior

14 SOLAR ENERGY↗
DOE OSTI2024

Modeling information flow in a computer processor with a multi-stage queuing model

In this paper, we introduce a nonlinear stochastic model to describe the propagation of information inside a computer processor. In this model, a computational task is divided into stages, and information can flow from one stage to another. The model is formulated as a spatially-extended, continuous-time Markov chain where space represents different stages. This model is equivalent to a spatially-extended version of the M/M/s queue. The main modeling feature is the throttling function which describes the processor slowdown when the amount of information falls below a certain threshold. We derive the stationary distribution for this stochastic model and develop a closure for a deterministic ODE system that approximates the evolution of the mean and variance of the stochastic model. In conclusion, we demonstrate the validity of the closure with numerical simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Time-dependent SOLPS-ITER simulations of the tokamak plasma boundary for model predictive control using SINDy *

Abstract Time-dependent SOLPS-ITER simulations have been used to identify reduced models with the sparse identification of nonlinear dynamics (SINDy) method and develop model-predictive control of the boundary plasma state using main ion gas puff actuation. A series of gas actuation sequences are input into SOLPS-ITER to produce a dynamic response in upstream and divertor plasma quantities. The SINDy method is applied to identify reduced linear and nonlinear models for the electron density at the outboard midplane n e , s e p O M P and the electron temperature at the outer divertor T e , s e p d i v . Note that T e , s e p d i v is not necessarily the peak value of T e along the divertor. The identified reduced models are interpretable by construction (i.e. not black box), and have the form of coupled ordinary differential equations. Despite significant noise in T e , s e p d i v , the reduced models can be used to predict the response over a range of actuation levels to a maximum deviation of 0.5% in n e , s e p O M P and 5%–10% in T e , s e p d i v for the cases considered. Model retraining using time history data triggered by a preset error threshold is also demonstrated. A model predictive control strategy for nonlinear models is developed and used to perform feedback control of a SOLPS-ITER simulation to produce a setpoint trajectory in n e , s e p O M P using the integrated plasma simulator framework. The developed techniques are general and can be applied to time-dependent data from other boundary simulations or experimental data. Ongoing work is extending the approach to model identification and control for divertor detachment, which will present transient nonlinear behavior from impurity seeding, including realistic latency and synthetic diagnostic signals derived from the full SOLPS-ITER output.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Nonlinear Logistic Regression Mixture Experiment Modeling for Binary Data Using Dimensionally Reduced Components

This article presents and illustrates an approach using nonlinear logistic regression for modeling binary response data from a mixture experiment when the components can be partitioned into groups used to form dimensionally-reduced pseudocomponents (DRPs). A DRP is a linear combination of the components in a group, where the linear combinations over all groups are normalized so that the DRP proportions sum to unity. Nonlinear logistic regression is required because, after normalization of the linear combinations, the model expressed in terms of the DRPs is nonlinear in the parameters that specify the linear combinations. A method for obtaining nonparametric tolerance limits on the probability of a “success” for the binary response variable using a bootstrap approach is also presented. Having three DRPs enables viewing data and modeling results on a ternary plot even though there may be many more than three mixture components. A real database, involving whether or not nepheline crystals form in simulated nuclear waste glass after cooling, is used to illustrate the nonlinear logistic regression modeling and nonparametric tolerance limit approaches when there are three DRPs.

Waste glass, Nepheline, Mixture experiment, Logist↗
DOE OSTI2021

Shaker-structure interaction modeling and analysis for nonlinear force appropriation testing

Nonlinear force appropriation is an extension of its linear counterpart where sinusoidal excitation is applied to a structure with a modal shaker and phase quadrature is achieved between the excitation and response. While a standard practice in modal testing, modal shaker excitation has the potential to alter the dynamics of the structure under test. Previous studies have been conducted to address several concerns, but this work specifically focuses on a shaker-structure interaction phenomenon which arises during the force appropriation testing of a nonlinear structure. Under pure-tone sinusoidal forcing, a nonlinear structure may respond not only at the fundamental harmonic but also potentially at sub- or superharmonics, or it can even produce aperiodic and chaotic motion in certain cases. Shaker-structure interaction occurs when the response physically pushes back against the shaker attachment, producing non-fundamental harmonic content in the force measured by the load cell, even for pure tone voltage input to the shaker. This work develops a model to replicate these physics and investigates their influence on the response of a nonlinear normal mode of the structure. Experimental evidence is first provided that demonstrates the generation of harmonic content in the measured load cell force during a force appropriation test. This interaction is replicated by developing an electromechanical model of a modal shaker attached to a nonlinear, three-mass dynamical system. Several simulated experiments are conducted both with and without the shaker model in order to identify which effects are specifically due to the presence of the shaker. Finally, the results of these simulations are then compared to the undamped nonlinear normal modes of the structure under test to evaluate the influence of shaker-structure interaction on the identified system’s dynamics.

42 ENGINEERING↗
DOE OSTI2021

Non-intrusive data-driven model reduction for differential–algebraic equations derived from lifting transformations

In this paper we present a non-intrusive data-driven approach for model reduction of nonlinear systems. The approach considers the particular case of nonlinear partial differential equations (PDEs) that form systems of partial differential–algebraic equations (PDAEs) when lifted to polynomial form. Such systems arise, for example, when the governing equations include Arrhenius reaction terms (e.g., in reacting flow models) and thermodynamic terms (e.g., the Helmholtz free energy terms in a phase-field solidification model). Using the known structured form of the lifted algebraic equations, the approach computes the reduced operators for the algebraic equations explicitly, using straightforward linear algebra operations on the basis matrices. The reduced operators for the differential equations are inferred from lifted snapshot data using operator inference, which solves a linear least squares regression problem. The approach is illustrated for the nonlinear model of solidification of a pure material. The lifting transformations reformulate the solidification PDEs as a system of PDAEs that have cubic structure. The operators of the lifted system for this solidification example have affine dependence on key process parameters, permitting us to learn a parametric reduced model with operator inference. Numerical experiments show the effectiveness of the resulting reduced models in capturing key aspects of the solidification dynamics.

42 ENGINEERING↗
DOE OSTI2026

Tree-ring evidence marks year 2022 as the driest spring season in nearly four centuries in the Western Himalayas

The Hindukush-Karakoram-Himalayan region is a crucial freshwater source for billions across South Asia, yet its climate remains poorly understood due to limited long-term records. Winter and spring precipitation govern snow accumulation and downstream water availability in dry months particularly across the Western Himalayas (WH), but recent decades show intensifying droughts with unclear long-term context. Here, we have reconstructed a nearly four-century-long spring i.e. February to May (FMAM) precipitation for the Lahaul region of the (WH), an area dominated by the Western Disturbances. This record was developed using moisture-sensitive Cedrus deodara (Deodar) tree-rings from three high-elevation sites. A regional composite tree-ring-width chronology, developed through a Nested Principal Component Analysis and modeled with a nonlinear Generalized Additive Model (GAM) that explains 71 % of the variance during the calibration period. We identified the last two decades as the most precipitation deficit phase and the year 2022 showing the driest FMAM on record. The observed rise in the FMAM dry episodes post 1999 CE in our reconstruction, corresponds to the meteorological records. This recent drying is linked to a northward shift of the subtropical westerly jet and reduced moisture transport, both associated with unusual sea surface temperature patterns in the tropical Indian Ocean and the Western Pacific Ocean. Our results provide compelling evidence of long-term hydroclimatic instability in the WH and emphasize the value of tree-ring records in extending precipitation histories beyond the instrumental observations. Such reconstructions can be benchmarks to validate high-resolution climate models and formulate adaptation policies to mitigate future risks.

Cedrus deodara↗
DOE OSTI2023

Automated Symbolic Upscaling: 2. Model Generation for Extended Applicability Regimes

Abstract In this second part of the two paper series, we detail an algorithmic procedure for systematically implementing the generalized closure form strategy presented in Part 1. This strategy extends the applicability of homogenized models with respect to classical homogenization theory, as demonstrated in Part 1 where upscaled models are rigorously derived in moderately reactive physical regimes. After encoding the algorithm into Symbolica, an automated upscaling framework, we upscale two reactive mass transport problems and numerically validate the resulting nonlinear homogenized models by showing the absolute error estimates predicted by homogenization theory are satisfied. In both problems, nontrivial closure forms and closure problems are automatically formulated using the encoded strategy with no human interaction, nor prior knowledge regarding the closure required for the systems. We hope these demonstrations spark further interest in automated analytical frameworks for multiscale modeling, as such capabilities are invaluable for generating rigorous multiscale models of complex phenomena in porous media.

Pietrzyk, Kyle↗
DOE OSTI2021

Approach to nonlinear magnetohydrodynamic simulations in stellarator geometry

The capability to model the nonlinear magnetohydrodynamic (MHD) evolution of stellarator plasmas is developed by extending the M3D-C 1 code to allow non-axisymmetric domain geometry. We introduce a set of logical coordinates, in which the computational domain is axisymmetric, to utilize the existing finite-element framework of M3D-C 1 . A C 1 coordinate mapping connects the logical domain to the non-axisymmetric physical domain, where we use the M3D-C 1 extended MHD models essentially without modifications. We present several numerical verifications on the implementation of this approach, including simulations of the heating, destabilization, and equilibration of a stellarator plasma with strongly anisotropic thermal conductivity, and of the relaxation of stellarator equilibria to integrable and non-integrable magnetic field configurations in realistic geometries.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Nonlinear manifold reduced order model

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 lowdimensional 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 software 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.

Choi, Youngsoo↗
DOE OSTI2023

Gallium-doped zinc oxide: nonlinear reflection and transmission measurements and modeling in the ENZ region

Abstract Strong nonlinear materials have been sought after for decades for applications in telecommunications, sensing, and quantum optics. Gallium-doped zinc oxide is a II–VI transparent conducting oxide that shows promising nonlinearities similar to indium tin oxide and aluminum-doped zinc oxide for the telecommunications band. Here we explore its nonlinearities in the epsilon near zero (ENZ) region and show n 2,eff values on the order of 4.5 × 10 −3 cm 2 GW −1 for IR pumping on 200–300 nm thin films. Measuring nonlinear changes in transmission and reflection with a white light source probe in the near-IR while exciting in the near-IR provides data in both time and wavelength. Three films varying in thickness, optical loss, and ENZ crossover wavelength are numerically modeled and compared to experimental data showing agreement for both dispersion and temporal relaxation. In addition, we discuss optimal excitation and probing wavelengths occur around ENZ for thick films but are red-shifted for thin films where our model provides an additional degree of freedom to explore. Obtaining accurate nonlinear measurements is a difficult and time-consuming task where our method in this paper provides experimental and modeled data to the community for an ENZ material of interest.

Ball, Adam (ORCID:0000000318167813)↗
DOE OSTI2024

Divertor-safe nonlinear burn control based on a SOLPS parameterized core-edge model for ITER

Abstract For ITER operations, the range of desirable burning-plasma regimes with high fusion power output will be restricted by various operational constraints. These constraints include the saturation of ITER’s various heating and fueling actuators such as the neutral beam injectors, the ion and electron cyclotron heating systems, the gas puffing system, and the deuterium–tritium pellet injectors. In addition to these actuator constraints, the H-mode power threshold, divertor detachment, and the heat load on the divertor targets may apply limitations to ITER’s operational space. In this work, Plasma Operation Contour (POPCON) plots that map the aforementioned constraints to the temperature-density space are used to investigate which constraints are most limiting towards accessing regimes with high fusion power output. The presented POPCON plots are based on a control-oriented core-edge model that couples the nonlinear density and energy response models for the core-plasma region with SOLPS4.3 parameterizations for conditions in the edge-plasma regions (scrape-off-layer and divertor). Using this control-oriented core-edge model, a nonlinear burn controller, which aims to regulate the plasma temperature and density in the core-plasma region, is constructed in this work. This controller is augmented with an online optimization scheme that governs the control references such that the plasma can be guided towards regimes with high fusion powers while protecting the divertor targets from dangerously high heat loads. A closed-loop simulation study illustrates the capability of this burn control scheme.

Physics↗
DOE OSTI2020

SNS: A Solution-Based Nonlinear Subspace Method for Time-Dependent Model Order Reduction

Several reduced order models have been successfully developed for nonlinear dynamical systems. To achieve a considerable speed-up, a hyper-reduction step is needed to reduce the computational complexity due to nonlinear terms. Many hyper-reduction techniques require the construction of nonlinear term basis, which introduces a computationally expensive offline phase. A novel way of constructing nonlinear term basis within the hyper-reduction process is introduced. In contrast to the traditional hyper-reduction techniques where the collection of nonlinear term snapshots is required, the SNS method avoids collecting the nonlinear term snapshots. Instead, it uses the solution snapshots that are used for building a solution basis, which enables avoiding an extra data compression of nonlinear term snapshots. As a result, the SNS method provides a more efficient offline strategy than the traditional model order reduction techniques, such as the DEIM, GNAT, and ST-GNAT methods. The SNS method is theoretically justified by the conforming subspace condition and the subspace inclusion relation. It is useful for model order reduction of large-scale nonlinear dynamical problems to reduce the offline cost. It is especially useful for ST-GNAT that has shown promising results, such as a good accuracy with a considerable online speed-up for hyperbolic problems in a recent paper by Choi and Carlberg [SIAM J. Sci. Comput., 41 (2019), pp. A26--A58], because ST-GNAT involves an expensive offline cost related to collecting nonlinear term snapshots. Error analysis for the SNS method is presented. Numerical results support that the accuracy of the solution from the SNS method is comparable to the traditional methods and a considerable speed-up (i.e., a factor of two to a hundred) is achieved in the offline phase.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A parametric study of slow dynamic nonlinear elasticity with comparisons to models

Several phenomenological models that aspire to quantitative description of anomalous nonlinear mesoscopic elasticity are reviewed and compared with laboratory measurements. This class of nonlinearity, best known perhaps for slow dynamics and aging, is seen widely in imperfectly consolidated granular solids but is not well understood. Typical slow dynamic tests show that a modest conditioning oscillatory "pump" strain depresses material stiffness, which then recovers like the logarithm of time after conditioning ceases. Several phenomenological models based on physical arguments have been proposed that predict the material stiffness response to arbitrary pump strain histories during conditioning and recovery. Approximate closed form and numerical solutions to the models are presented that predict the quantitative influence of three key pump parameters: the pump's strain amplitude, the pump's strain rate, and the pump’s duration. Laboratory measurements on Berea sandstone, concrete and a confined single aluminum bead find that slow dynamic responses are linear in pump strain and independent of pump frequency. Measurements also show that, after pump-off, stiffness recovers over times far longer than the pump duration. These observations and others are compared to model predictions. One of the considered models, based on a picture of fast brittle damage and slow healing, successfully matches all these behaviors.

36 MATERIALS SCIENCE↗
DOE OSTI2022

IC Report for project “Developing nonlinear laser-plasma instability models for high-fidelity, multi-physics simulation capability for ICF/HED” [Slides]

We’ve achieved our technical goals: (1) Perform large-scale kinetic simulations of SRS and CBET a range of plasma and laser conditions; (2) Develop a new $\delta f$-Gaussian-mixture algorithm to represent non-Maxwellian distribution functions from particle trapping and time-dependent plasma response; (3) Develop physics-based preliminary nonlinear LPI models for coupling to LRT/ Mazinisin and AMP; and (4) Begin implementation of LPI sub-grid models into Mazinisin.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗