Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “nonlinear systems”

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 973 records · Page 54
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Nonlinear Model Predictive Control Based on Real-Time Iteration Scheme for Wave Energy Converters Using WEC-Sim: Preprint

One of several challenges that wave energy technologies face is their inability to generate electricity cost-competitively with other grid-scale energy generation sources. Several studies have identified two approaches to lower the levelised cost of electricity: reduce the cost over the device's lifetime or increase its overall electrical energy production. Several advanced control strategies have been developed to address the latter. However, only a few take into account the overall efficiency of the power take-off (PTO) system, and none of them solve the optimisation problem that arises at each sampling time on real-time. In this paper, a detailed Nonlinear model predictive control (NMPC) approach based on the real-time iteration (RTI) scheme is presented, and the controller performance is evaluated using a time-domain hydrodynamics model (WEC-Sim). The proposed control law incorporates the PTO system's efficiency in a control law to maximise the energy extracted. The study also revealed that RTI-NMPC clearly outperforms a simple resistive controller.

model predictive control↗
DOE OSTI2022

Trust-Region Approximation of Extreme Trajectories in Power System Dynamics

In this work we present a novel technique, based on a trust-region optimization algorithm and second-order trajectory sensitivities, to compute the extreme trajectories of power system dynamic simulations given a bounded set that represents parametric uncertainty. Furthermore, we show how this method, while remaining computationally efficient compared with sampling-based techniques, overcomes the limitations of previous sensitivity-based techniques to approximate the bounds of the trajectories when the local approximation loses validity because of the nonlinearity. We present several numerical experiments that showcase the accuracy and scalability of the technique, including a demonstration on the IEEE New England test system.

42 ENGINEERING↗
DOE OSTI2023

Maximum respiration rates in hyporheic zone sediments are primarily constrained by organic carbon concentration and secondarily by organic matter chemistry

Abstract. River corridors are fundamental components of the Earth system, and their biogeochemistry can be heavily influenced by processes in subsurface zones immediately below the riverbed, referred to as the hyporheic zone. Within the hyporheic zone, organic matter (OM) fuels microbial respiration, and OM chemistry heavily influences aerobic and anaerobic biogeochemical processes. The link between OM chemistry and respiration has been hypothesized to be mediated by OM molecular diversity, whereby respiration is predicted to decrease with increasing diversity. Here we test the specific prediction that aerobic respiration rates will decrease with increases in the number of unique organic molecules (i.e., OM molecular richness, as a measure of diversity). We use publicly available data across the United States from crowdsourced samples taken by the Worldwide Hydrobiogeochemical Observation Network for Dynamic River Systems (WHONDRS) consortium. Our continental-scale analyses rejected the hypothesis of a direct limitation of respiration by OM molecular richness. In turn, we found that organic carbon (OC) concentration imposes a primary constraint over hyporheic zone respiration, with additional potential influences of OM richness. We specifically observed respiration rates to decrease nonlinearly with the ratio of OM richness to OC concentration. This relationship took the form of a constraint space with respiration rates in most systems falling below the constraint boundary. A similar, but slightly weaker, constraint boundary was observed when relating respiration rate to the inverse of OC concentration. These results indicate that maximum respiration rates may be governed primarily by OC concentration, with secondary influences from OM richness. Our results also show that other variables often suppress respiration rates below the maximum associated with the richness-to-concentration ratio. An important focus of future research will identify physical (e.g., sediment grain size), chemical (e.g., nutrient concentrations), and/or biological (e.g., microbial biomass) factors that suppress hyporheic zone respiration below the constraint boundaries observed here.

58 GEOSCIENCES↗
DOE OSTI2025

Leveraging FPGA Advantages for Quicker Data Processing for LBNF

The Long Baseline Neutrino Facility (LBNF) will deliver a 2.4 MW muon neutrino beam from Fermilab to the Deep Underground Neutrino Experiment (DUNE), requiring unprecedented precision in beamline alignment to achieve DUNE's neutrino oscillation measurement goals. Vertical misalignments of beamline components as small as 0.5 mm can contribute 6-7\% uncertainty in predicted neutrino flux, necessitating sub-0.1 mm alignment monitoring capabilities. The Horn Location Sensor (HLS) system employs frequency sweep interferometry (FSI) in a distributed hydrostatic leveling network to achieve the required precision under harsh radiation conditions up to 5000 kRad/year. Traditional FSI implementations suffer from laser sweep nonlinearities that degrade resolution and require computationally intensive post-processing corrections using gas reference cells. This work presents a real-time FPGA-based implementation of the HLS data acquisition and processing system using a sweep tracker interferometer for dynamic sweep linearization. The system utilizes a PYNQ-Z2 FPGA with programmable logic implementing parallel 16k-point FFT processing across four channels, synchronized by the sweep tracker signal to eliminate post-processing requirements. Spectral performance testing demonstrates significant improvements in peak sharpness compared to traditional fixed-frequency digitization. The FPGA implementation enables real-time displacement monitoring with processing speeds orders of magnitude faster than software-based approaches, essential for the operational requirements of LBNF's eventual distributed sensor network. This advancement in real-time FSI processing directly supports DUNE's precision neutrino physics program by providing the rapid feedback necessary for maintaining stringent beamline alignment tolerances during high-power beam operations.

Rossel, Jacob↗
DOE OSTI2025

Real-Time FPGA Implementation For Frequency Sweep Interferometry In The LBNF Complex

The Long Baseline Neutrino Facility (LBNF) will deliver a 2.4 MW muon neutrino beam from Fermilab to the Deep Underground Neutrino Experiment (DUNE), requiring unprecedented precision in beamline alignment to achieve DUNE's neutrino oscillation measurement goals. Vertical misalignments of beamline components as small as 0.5 mm can contribute 6-7\% uncertainty in predicted neutrino flux, necessitating sub-0.1 mm alignment monitoring capabilities. The Horn Location Sensor (HLS) system employs frequency sweep interferometry (FSI) in a distributed hydrostatic leveling network to achieve the required precision under harsh radiation conditions up to 5000 kRad/year. Traditional FSI implementations suffer from laser sweep nonlinearities that degrade resolution and require computationally intensive post-processing corrections using gas reference cells. This work presents a real-time FPGA-based implementation of the HLS data acquisition and processing system using a sweep tracker interferometer for dynamic sweep linearization. The system utilizes a PYNQ-Z2 FPGA with programmable logic implementing parallel 16k-point FFT processing across four channels, synchronized by the sweep tracker signal to eliminate post-processing requirements. Spectral performance testing demonstrates significant improvements in peak sharpness compared to traditional fixed-frequency digitization. The FPGA implementation enables real-time displacement monitoring with processing speeds orders of magnitude faster than software-based approaches, essential for the operational requirements of LBNF's eventual distributed sensor network. This advancement in real-time FSI processing directly supports DUNE's precision neutrino physics program by providing the rapid feedback necessary for maintaining stringent beamline alignment tolerances during high-power beam operations.

Rossel, A. Jacob [Fermilab; Unlisted]↗
DOE OSTI2024

Single-shot Quantum Signal Processing Interferometry

Quantum systems of infinite dimension, such as bosonic oscillators, provide vast resources for quantum sensing. Yet, a general theory on how to manipulate such bosonic modes for sensing beyond parameter estimation is unknown. We present a general algorithmic framework, quantum signal processing interferometry (QSPI), for quantum sensing at the fundamental limits of quantum mechanics by generalizing Ramsey-type interferometry. Our QSPI sensing protocol relies on performing nonlinear polynomial transformations on the oscillator's quadrature operators by generalizing quantum signal processing (QSP) from qubits to hybrid qubit-oscillator systems. We use our QSPI sensing framework to make efficient binary decisions on a displacement channel in the single-shot limit. Theoretical analysis suggests the sensing accuracy, given a single-shot qubit measurement, scales inversely with the sensing time or circuit depth of the algorithm. We further concatenate a series of such binary decisions to perform parameter estimation in a bit-by-bit fashion. Numerical simulations are performed to support these statements. Our QSPI protocol offers a unified framework for quantum sensing using continuous-variable bosonic systems beyond parameter estimation and establishes a promising avenue toward efficient and scalable quantum control and quantum sensing schemes beyond the NISQ era.

Physics↗
DOE OSTI2025

An Adaptive Newton-Based Free-Boundary Grad–Shafranov Solver

Equilibria in magnetic confinement devices result from force balancing between the Lorentz force and the plasma pressure gradient. In an axisymmetric configuration like a tokamak, such an equilibrium is described by an elliptic equation for the poloidal magnetic flux, commonly known as the Grad–Shafranov equation. It is challenging to develop a scalable and accurate free-boundary Grad–Shafranov solver, since it is a fully nonlinear optimization problem that simultaneously solves for the magnetic field coil current outside the plasma to control the plasma shape. In this work, we develop a Newton-based free-boundary Grad–Shafranov solver using adaptive finite elements and preconditioning strategies. The free-boundary interaction leads to the evaluation of a domain-dependent nonlinear form of which its contribution to the Jacobian matrix is achieved through shape calculus. The optimization problem aims to minimize the distance between the plasma boundary and specified control points while satisfying two nontrivial constraints, which correspond to the nonlinear finite element discretization of the Grad–Shafranov equation and a constraint on the total plasma current involving a nonlocal coupling term. The linear system is solved by a block factorization, and AMG is called for subblock elliptic operators. The unique contributions of this work include the treatment of a global constraint, preconditioning strategies, nonlocal reformulation, and the implementation of adaptive finite elements. Furthermore, it is found that the resulting Newton solver is robust, successfully reducing the nonlinear residual to 1e-6 and lower in a small handful of iterations while addressing the challenging case to find a Taylor state equilibrium where conventional Picard-based solvers fail to converge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Understanding latent timescales in neural ordinary differential equation models of advection-dominated dynamical systems

The neural ordinary differential equation (ODE) framework has shown considerable promise in recent years in developing highly accelerated surrogate models for complex physical systems characterized by partial differential equations (PDEs). For PDE-based systems, state-of-the-art neural ODE strategies leverage a two-step procedure to achieve this acceleration: a nonlinear dimensionality reduction step provided by an autoencoder, and a time integration step provided by a neural-network based model for the resultant latent space dynamics (the neural ODE). This work explores the applicability of such autoencoder-based neural ODE strategies for PDEs in which advection terms play a critical role. More specifically, alongside predictive demonstrations, physical insight into the sources of model acceleration (i.e., how the neural ODE achieves its acceleration) is the scope of the current study. Such investigations are performed by quantifying the effects of both autoencoder and neural ODE components on latent system time-scales using eigenvalue analysis of dynamical system Jacobians. To this end, the sensitivity of various critical training parameters – de-coupled versus end-to-end training, latent space dimensionality, and the role of training trajectory length, for example – to both model accuracy and the discovered latent system timescales is quantified. Furthermore, this work specifically uncovers the key role played by the training trajectory length (the number of rollout steps in the loss function during training) on the latent system timescales: larger trajectory lengths correlate with an increase in limiting neural ODE time-scales, and optimal neural ODEs are found to recover the largest time-scales of the full-order (ground-truth) system. Demonstrations are performed across fundamentally different unsteady fluid dynamics configurations influenced by advection: (1) the Kuramoto–Sivashinsky equations (2) Hydrogen-Air channel detonations (the compressible reacting Navier–Stokes equations with detailed chemistry), and (3) 2D Atmospheric flow.

Advection-dominated dynamical systems↗
DOE OSTI2026

Multiresolution Quantum Chemistry: Nonlinear Response Properties at the Basis Set Limit

We benchmark the accuracy of Dunning correlation-consistent Gaussian basis sets for computing frequencydependent second-order hyperpolarizabilities relevant to second-harmonic generation (SHG), using multiresolution analysis (MRA) as a reference. Basis set errors are analyzed using a unit-sphere representation of the effective hyperpolarizability vector, enabling direct assessment of directional error structure. We introduce a relative RMS total error metric that integrates directional deviations over the unit sphere and complement it with signed projection errors that distinguish over- and underestimation. Unsupervised clustering based on these signed directional metrics reveals four distinct convergence behaviors across a set of 68 molecules. Unitsphere visualizations of representative systems show that basis set errors are often highly anisotropic and localized along specific bond directions, even when global error measures appear small. Doubly augmented basis sets consistently outperform singly augmented ones, and core-polarization functions are required for uniform convergence in second-row systems. Overall, this work demonstrates that directional analysis combined with clustering provides a robust framework for understanding basis set convergence in nonlinear optical response properties.

Basis sets↗
DOE OSTI2024

Frequency Support From Electric Vehicles for Advancing Renewable Energy Integration

The integration of renewable energy resources (RERs) in the modern power grid is increasing rapidly because of aggressive decarbonization goals, lower costs, and increased government investment. However, higher penetrations of inverter-based generation can lead to frequency stability issues because of reduced system inertia. This paper develops a framework for quantifying the contribution of electric vehicles (EVs) toward providing frequency support to the grid and thus increasing the penetration limit of renewable energy resources (RERs). EVs are considered to provide both inertial response and primary frequency response support to the grid. A stochastic approach incorporating the uncertainties associated with the behavior of EVs is developed to derive the discharge limit of EV aggregators. A multi-machine system frequency response (MM-SFR) model is developed, which incorporates the dynamic virtual inertia and droop coefficients of EV aggregators derived from the EV control modules. Frequency security constraints are developed from this MM-SFR model, which, along with the converter voltage security and low voltage ride-through constraints, are integrated within a nonlinear optimization framework to determine the RER integration limit. Here, the efficacy of the proposed approach is validated using the RTS-GMLC test system.

25 ENERGY STORAGE↗
DOE OSTI2025

Comprehensive assessment of deep reinforcement learning approaches for economic dispatch in nuclear-driven microgrids

As the electrical grid integrates more variable renewable energy sources such as wind and solar, the demand for distributed and flexible systems to address this increased variability becomes critical. Nuclear-driven microgrids provide a promising solution by offering stable generation to complement intermittent renewables, ensuring grid reliability and operating efficiency. This paper proposes a recurrent deep reinforcement learning framework for optimal economic dispatch in a nuclear-powered microgrid integrating renewable energy sources, small modular reactors, battery storage systems, and balance-of-plant dynamics. A three-agent control architecture is developed, where demand and renewable energy agents act as forecasters, and a reinforcement learning-based dispatch agent performs real-time energy allocation. A nonlinear programming formulation is first used to generate an optimal baseline for benchmarking. The proposed dispatch controller, based on Proximal Policy Optimization enhanced with Long Short-Term Memory networks, exploits temporal correlations in system dynamics by taking advantage of the time series used as inputs to improve policy robustness under uncertainty. Comparative analysis against established deep reinforcement learning methods, including Proximal Policy Optimization with a feedforward architecture, Soft Actor-Critic, and Twin Delayed Deep Deterministic Policy Gradient, demonstrates superior performance. Numerical results indicate that the proposed controller achieves a 0.39% cost reduction relative to the nonlinear programming benchmark and outperforms other learning-based methods by generating additional revenue of up to 0.35%. All reinforcement learning controllers compute dispatch actions in less than 0.3 s, resulting in a computational speedup of more than three orders of magnitude over the nonlinear programming baseline. The findings of this paper highlight their applicability for real-time operation and control in nuclear-integrated microgrids under volatile operating conditions.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Optimization under uncertainty of a hybrid waste tire and natural gas feedstock flexible polygeneration system using a decomposition algorithm

Market uncertainties motivate the development of flexible polygeneration systems that are able to adjust operating conditions to favor production of the most profitable product portfolio. However, this operational flexibility comes at the cost of higher capital expenditure. A scenario-based two-stage stochastic nonconvex Mixed-Integer Nonlinear Programming (MINLP) approach lends itself naturally to optimizing these trade-offs. This work studies the optimal design and operation under uncertainty of a hybrid feedstock flexible polygeneration system producing electricity, methanol, dimethyl ether, olefins or liquefied (synthetic) natural gas. A recently developed C++ based software framework (named GOSSIP) is used for modeling the optimization problem as well as its efficient solution using the Nonconvex Generalized Benders Decomposition (NGBD) algorithm. Two different cases are studied: The first uses estimates of the means and variances of the uncertain parameters from historical data, whereas the second assesses the impact of increased uncertain parameter volatility. The value of implementing flexible designs characterized by the value of the stochastic solution (VSS) is in the range of 260–405 M$ for a scale of approximately 893 MW of thermal input. Increased price volatility around the same mean results in higher expected net present value and VSS as operational flexibility allows for asymmetric exploitation of price peaks.

42 ENGINEERING↗
DOE OSTI2026

Relaxations of the steady optimal gas flow problem for a non-Ideal gas

Natural gas ranks second in U.S. primary energy consumption. Because most production sites are remote, gas must be transported through pipeline networks equipped with compressors, valves, and other components. For both economic efficiency and system reliability, it is desirable to operate these networks optimally. The governing physics across pipeline components entails nonlinear, non-convex equality and inequality constraints, and the most general steady-flow operations problem is a Mixed-Integer Nonlinear Program (MINLP).This work focuses on one such steady-flow problem-the Optimal Gas Flow (OGF) for a natural gas pipeline network-which minimizes production cost subject to the steady-flow physics. For day-to-day operations, the ability to quickly compute a globally optimal solution and a strong lower bound for varying demand profiles is crucial. A promising strategy is to build tight relaxations of the OGF’s nonlinear constraints. However, many nonlinearities arising from non-ideal equations of state either lack relaxations or have relaxations that do not scale to realistic network sizes. We address this gap by combining recent advances in polyhedral relaxations for univariate functions to construct tight, computationally efficient relaxations of the OGF with a non-ideal equation of state. These relaxations solve within seconds on a standard laptop. In conclusion, we demonstrate their quality through extensive numerical experiments on very large-scale test networks from the literature and find that the proposed approach proves optimality in 92% of tested instances.

03 NATURAL GAS↗
DOE OSTI2020

Multiphysics for nuclear energy applications using a cohesive computational framework

With the recent development of advanced numerical algorithms, software design, and low-cost high-performance computer hardware, reliance on coupled multiphysics to predict the behavior of complex physical systems is beginning to become standard practice. This is especially true in nuclear energy applications where strong nonlinear interdependencies exist between reactor physics, radiation transport, multi-scale nuclear fuels performance, thermal fluids, etc. Resolving these nonlinear dependencies requires choices in multiphysics software approaches. Two main multiphysics modeling and simulation approaches have emerged. The first is based upon "code coupling" where disparate physics codes of different software design, code languages, and spatial and temporal integration schemes are coupled together with relatively complex data passing interfaces. The second multiphysics software approach is to employ a "cohesive" framework where all physics applications are developed with a common software design, i.e., data structures, syntax, input format, integrated spatial and temporal discretization schemes, etc. In this paper we present the Multiphysics Object-Oriented Simulation Environment (MOOSE) development and runtime framework and describe the framework's cohesive modeling and simulation multiphysics approach. Then, a "cohesive-like" extension of the MOOSE framework is presented where MOOSE-based physics software applications are efficiently coupled to non-MOOSE (external) physics codes to form multiphysics applications using MOOSE's unique interface capabilities. Finally, several examples of MOOSE's cohesive and cohesive-like multiphysics applications will be demonstrated. These multiphysics demonstrations will incorporate both MOOSE-based applications and external codes, including Nek5000, RELAP-7, TRACE, BISON, and Pronghorn.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Permutationally Invariant Networks for Enhanced Sampling (PINES): Discovery of Multimolecular and Solvent-Inclusive Collective Variables

The typically rugged nature of molecular free energy landscapes can frustrate efficient sampling of the thermodynamically relevant phase space due to the presence of high free energy barriers. Enhanced sampling techniques can improve phase space exploration by accelerating sampling along particular collective variables (CVs). A number of techniques exist for data-driven discovery of CVs parameterizing the important large scale motions of the system. A challenge to CV discovery is learning CVs invariant to symmetries of the molecular system, frequently rigid translation, rigid rotation, and permutational relabeling of identical particles. Of these, permutational invariance has proved a persistent challenge in frustrating the data-driven discovery of multi-molecular CVs in systems of self-assembling particles and solvent-inclusive CVs for solvated systems. In this work, we integrate Permutation Invariant Vector (PIV) featurizations with autoencoding neural networks to learn nonlinear CVs invariant to translation, rotation, and permutation, and perform interleaved rounds of CV discovery and enhanced sampling to iteratively expand sampling of configurational phase space and obtain converged CVs and free energy landscapes. Here, we demonstrate the Permutationally Invariant Network for Enhanced Sampling (PINES) approach in applications to the self-assembly of a 13-atom Argon cluster, association/dissociation of a NaCl ion pair in water, and hydrophobic collapse of a C 45 H 92 n-pentatetracontane polymer chain. We make the approach freely available as a new module within the PLUMED2 enhanced sampling libraries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Transverse photoresistivity from photothermal current deflection in metal films

Quantum geometry in centrosymmetric systems has motivated the search for photocurrent responses beyond second order. In particular, electric field-induced nonlinear responses may also enable intrinsic polarization-sensitive optical detectors. Despite numerous efforts, clear methods are still needed to remove experimental artifacts, separating intrinsic from extrinsic effects, and disentangling linear responses from their higher-order counterparts. Here, we provide a systematic study of fabrication and measurement techniques to remove external artifacts in photoelectronic responses. This reveals a previously hidden photothermoelectric response in the transverse photoresistivity of symmetric thin films of simple metals. We identify its origin in thermal gradients producing current deflection and determine the device design and measurement parameters to minimize extrinsic effects that arise in photoinduced electronic responses.

Bolometric effect↗
DOE OSTI2025

Soft x-ray high-harmonic generation in an anti-resonant hollow core fiber driven by a 3 μ m ultrafast laser

High-harmonic upconversion driven by a mid-infrared femtosecond laser can generate coherent soft x-ray beams in a tabletop-scale setup. Here, we report on a compact ytterbium-pumped optical parametric chirped pulse amplifier (OPCPA) laser system seeded by an all-fiber front-end and employing periodically poled lithium niobate (PPLN) nonlinear media operated near the pulse fluence limits of current commercially available PPLN crystals. The OPCPA delivers 3 µm wavelength pulses with 775 µJ energy at 1 kHz repetition rate, with transform-limited 120 fs pulse duration, diffraction-limited beam quality, and ultrahigh 0.33% rms energy stability over >18 h. Using this laser, we generate soft x-ray high harmonics (HHG) in argon gas by focusing into a low-loss, high-pressure gas-filled anti-resonant hollow core fiber (ARHCF), generating coherent light at photon energies up to the argon L-edge (250 eV) and carbon K-edge (284 eV), with high beam quality and ∼1% rms energy stability. This work demonstrates soft x-ray HHG in a high-efficiency guided-wave phase matched geometry, overcoming the high losses inherent to mid-IR propagation in unstructured waveguides, or the short interaction lengths of gas cells or jets. The ARHCF can operate in the long term without damage and with the repetition rate, stability, and robustness required for demanding applications in spectromicroscopy and imaging. Finally, we discuss routes for further optimizing the soft x-ray HHG flux by driving He at higher laser intensities using either the signal (1.5 μm) or idler wavelengths (3 μm).

Femtosecond lasers↗