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DOE OSTI2022

OC6 Phase Ia Definition Document: Validation of Nonlinear Hydrodynamic Loading on the DeepCwind Semisubmersible

The objective of OC6 Phase I is to investigate the persistent under-prediction (about 20% on average) of the structural loads in the OC5-DeepCwind floating semisubmersible wind system, as observed within the previous OC5 Phase II project. The OC5 results indicate that much of this under-prediction originates from the low-frequency response of the system at the surge/pitch natural frequencies, resulting from nonlinear hydrodynamic loading and/or overprediction of hydrodynamic damping. This work package therefore focuses on better understanding this low-frequency response behavior, the applicability of computational-fluid-dynamics (CFD) models and engineering-level hydrodynamic models for predicting the nonlinear hydrodynamic loading, and the level of uncertainty in the measured response characteristics. To address these objectives, two experimental campaigns were developed and performed in 2017 and 2018 by a sub-group of the OC5 project: Floating test campaign: A simplified OC5-DeepCwind semisubmersible model (no turbine, rigid tower) was moored to three taut-spring lines and subjected to motion decay and wave tests (regular and irregular waves), during which motion amplitudes of the model were measured (see Figure 1a). The purpose of this test campaign was to examine the repeatability of the low-frequency response of the system to wave excitation and determine the level of uncertainty in the response behavior.Constrained test campaign: The same model, but without the tower present, was fixed to a carriage and subjected to towing, forced oscillation and wave tests (regular and irregular waves), during which forces exerted upon the model were measured (see Figure 1b). The purpose of this test campaign was to examine the hydrodynamic loading contributions by separating the wave excitation and radiation forces. Both model test campaigns were performed in the concept basin of the Maritime Research Institute Netherlands (MARIN) in Wageningen, the Netherlands and the first test was within the framework of the MARINET2 project. Both experimental campaigns were examined within Phase Ia of the OC6 project. The purpose of this report is to supply the needed information to participants of the OC6 project to build and simulate the experimental campaigns.

17 WIND ENERGY↗
DOE OSTI2025

Finite Element Analysis of the TRUST Nonlinear Dynamics Testbed

This paper builds on prior work conducted within the Los Alamos National Laboratory (LANL) Testbeds to Reduce Uncertainty in Simulations and Tests (TRUST) program. Specifically, it builds on finite element (FE) modeling efforts for the TRUST program’s Nonlinear Dynamics (ND) testbed. Historically, the FE model for the ND testbed has exclusively utilized a Lanczos eigensolver that linearly extracts the system’s natural frequencies. This paper investigates the Abaqus 2024’s explicit dynamic solver, which implements a central difference explicit solver. The central difference method used in Abaqus can capture nonlinear material responses in structural dynamic simulations making it suitable for the ND FE model.

42 ENGINEERING↗
DOE OSTI2022

Stabilization of the Polar Structure and Giant Second-Order Nonlinear Response of Single Crystal γ-NaAs 0.95 Sb 0.05 Se 2

The dearth of suitable materials significantly restricts the practical development of infrared (IR) laser systems with highly efficient and broadband tuning. Recently, γ-NaAsSe 2 is reported, and it exhibits a large nonlinear second-harmonic generation (SHG) coefficient of 590 pm V —1 at 2 µm. However, the crystal growth of γ-NaAsSe 2 is challenging because it undergoes a phase transition to centrosymmetric δ-NaAsSe 2 . Herein, the stabilization of non-centrosymmetric γ-NaAsSe 2 by doping the As site with Sb, which results in γ-NaAs 0.95 Sb 0.05 Se 2 is reported. The congruent melting behavior is confirmed by differential thermal analysis with a melting temperature of 450 °C and crystallization temperature of 415 °C. Single crystals with dimensions of 3 mm × 2 mm are successfully obtained via zone refining and the Bridgman method. The purification of the material plays a significant role in crystal growth and results in a bandgap of 1.78 eV and thermal conductivity of 0.79 Wm —1 K —1 . The single-crystal SHG coefficient of γ-NaAs 0.95 Sb 0.05 Se 2 exhibits an enormous value of |d 11 | = 648 ± 74 pm V —1 , which is comparable to that of γ-NaAsSe 2 and ≈20× larger than that of AgGaSe 2 . Importantly, the bandgap of γ-NaAs 0.95 Sb 0.05 Se 2 (1.78 eV) is similar to that of AgGaSe 2 , thus rendering it highly attractive as a high-performing nonlinear optical material.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A machine learning approach for clinker quality prediction and nonlinear model predictive control design for a rotary cement kiln

Abstract Cement manufacturing is energy‐intensive (5Gj/t) and comprises a significant portion of the energy footprint of concrete systems. Incorporating modern monitoring, simulation and control systems will allow lower energy use, lower environmental impact, and lower costs of this widely used construction material. One of the goals of the CESMII roadmap project on the Smart Manufacturing of Cement included developing an analytical process model for clinker quality that includes the chemistry of the kiln feed and accounts for critical process variables. This predictive model will be used in nonlinear model predictive control system designed to significantly reduce process energy use while maintaining or improving product quality. In the cement manufacturing plant used in this study, the kiln feed (meal) is tested every 12 h and used to estimate the mineral composition of the cement kiln output (clinker) using the stoichiometry‐based Bogue's model and the expertise of the plant operators. During kiln operation, kiln output (clinker) is sampled and tested every 2 h to measure its chemical and mineral composition. The predicted and measured values of the clinker composition are used by the plant operators to adjust the kiln input stream and the production process characteristics to maintain stable operation and uniform product quality. However, the time delay between prediction and testing, along with inaccuracies inherent in the Bogue's model have made any process changes designed to minimize energy use problematic, especially in‐light of potential clinker quality issues that process changes often pose. A new analytical model that integrates quality information and process operation information has been developed from data collected from 2 years of production from an operating cement facility. To make the model fuel‐type‐independent, consumed heat energy was computed in the model instead of fuel type and amount. A Feedforward Network was trained and tailored from collected data. Many data‐based simulations were conducted to quantitatively evaluate the proposed model and the 5‐fold cross‐validation procedure was used to test the models. The resulting predictive model was shown to have a low root mean square error (MSE) with respect to the estimated clinker mineral composition compared to that using the industry standard “Bogue’ model”. The end goal of this work was to develop a single machine learning tool that allows the use of quality control data and process control variables to improve energy efficiency of the process in a continuous fashion. The proposed nonlinear model predictive control system (NMPC) can generate predicted kiln production characteristics based on manipulated variables in manner that accurately follows the target product quality values. Simulation results also show that the proposed model produced accurate predictions of kiln outputs that fell within the required constraints, while manipulating control variables within typical operational ranges.

Ali, Asem M.↗
DOE OSTI2022

Tuning Phonon Energies in Lanthanide‐doped Potassium Lead Halide Nanocrystals for Enhanced Nonlinearity and Upconversion

Abstract Optical applications of lanthanide‐doped nanoparticles require materials with low phonon energies to minimize nonradiative relaxation and promote nonlinear processes like upconversion. Heavy halide hosts offer low phonon energies but are challenging to synthesize as nanocrystals. Here, we demonstrate the size‐controlled synthesis of low‐phonon‐energy KPb 2 X 5 (X=Cl, Br) nanoparticles and the ability to tune nanocrystal phonon energies as low as 128 cm −1 . KPb 2 Cl 5 nanoparticles are moisture resistant and can be efficiently doped with lighter lanthanides. The low phonon energies of KPb 2 X 5 nanoparticles promote upconversion luminescence from higher lanthanide excited states and enable highly nonlinear, avalanche‐like emission from KPb 2 Cl 5 : Nd 3+ nanoparticles. The realization of nanoparticles with tunable, ultra‐low phonon energies facilitates the discovery of nanomaterials with phonon‐dependent properties, precisely engineered for applications in nanoscale imaging, sensing, luminescence thermometry and energy conversion.

Zhang, Zhuolei↗
DOE OSTI2022

Tuning Phonon Energies in Lanthanide-doped Potassium Lead Halide Nanocrystals for Enhanced Nonlinearity and Upconversion

Optical applications of lanthanide-doped nanoparticles require materials with low phonon energies to minimize nonradiative relaxation and promote nonlinear processes like upconversion. Heavy halide hosts offer low phonon energies but are challenging to synthesize as nanocrystals. Here, we demonstrate the size-controlled synthesis of low-phonon-energy KPb 2 X 5 (X=Cl, Br) nanoparticles and the ability to tune nanocrystal phonon energies as low as 128 cm -1 . KPb 2 Cl 5 nanoparticles are moisture resistant and can be efficiently doped with lighter lanthanides. Further, the low phonon energies of KPb 2 X 5 nanoparticles promote upconversion luminescence from higher lanthanide excited states and enable highly nonlinear, avalanche-like emission from KPb 2 Cl 5 : Nd 3+ nanoparticles. The realization of nanoparticles with tunable, ultra-low phonon energies facilitates the discovery of nanomaterials with phonon-dependent properties, precisely engineered for applications in nanoscale imaging, sensing, luminescence thermometry and energy conversion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Aspects of nonlinear effect on black hole superradiance

Under some conditions, light boson fields grow exponentially around a rotating black hole, called the superradiance instability. We discuss effects of nonlinear interactions of the boson on the instability. In particular, we focus on the effect of the particle production and show that the growth of the boson cloud may be saturated much before the black hole spin is extracted by the boson cloud, while the nonlinear interactions also induce the boson emission. For application, we revisit the superradiant instability of the standard model photon, axion and hidden photon.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

An Empirical Quantile Estimation Approach for Chance-Constrained Nonlinear Optimization Problems

We investigate an empirical quantile estimation approach to solve chance-constrained nonlinear optimization problems. Our approach is based on the reformulation of the chance constraint as an equivalent quantile constraint to provide stronger signals on the gradient. In this approach, the value of the quantile function is estimated empirically from samples drawn from the random parameters, and the gradient of the quantile function is estimated via a finite-difference approximation on top of the quantile-function-value estimation. We establish a convergence theory of this approach within the framework of an augmented Lagrangian method for solving general nonlinear constrained optimization problems. The foundation of the convergence analysis is a concentration property of the empirical quantile process, and the analysis is divided based on whether or not the quantile function is differentiable. In contrast to the sampling-and-smoothing approach used in the literature, the method developed in this paper does not involve any smoothing function and hence the quantile-function gradient approximation is easier to implement and there are less accuracy-control parameters to tune. Furthermore, we demonstrate the effectiveness of this approach and compare it with a smoothing method for the quantile-gradient estimation. Numerical investigation shows that the two approaches are competitive for certain problem instances.

Applied Probability↗
DOE OSTI2021

Sequence of polyhedral relaxations for nonlinear univariate functions

Here, given a nonlinear, univariate, bounded, and differentiable function f(x), this article develops a sequence of Mixed Integer Linear Programming (MILP) and Linear Programming (LP) relaxations that converge to the graph of f(x) and its convex hull, respectively. Theoretical convergence of the sequence of relaxations to the graph of the function and its convex hull is established. For nonlinear non-convex optimization problems, the relaxations presented in this article can be used to construct tight MILP and LP relaxations. These MILP and the LP relaxations can also be used with MILP-based and spatial branch-and-bound based global optimization algorithms, respectively.

42 ENGINEERING↗
DOE OSTI2022

A phase transition for finding needles in nonlinear haystacks with LASSO artificial neural networks

To fit sparse linear associations, a LASSO sparsity inducing penalty with a single hyperparameter provably allows to recover the important features (needles) with high probability in certain regimes even if the sample size is smaller than the dimension of the input vector (haystack). More recently learners known as artificial neural networks (ANN) have shown great successes in many machine learning tasks, in particular fitting nonlinear associations. Small learning rate, stochastic gradient descent algorithm and large training set help to cope with the explosion in the number of parameters present in deep neural networks. Yet few ANN learners have been developed and studied to find needles in nonlinear haystacks. Driven by a single hyperparameter, our ANN learner, like for sparse linear associations, exhibits a phase transition in the probability of retrieving the needles, which we do not observe with other ANN learners. To select our penalty parameter, we generalize the universal threshold of Donoho and Johnstone (Biometrika 81(3):425–455, 1994) which is a better rule than the conservative (too many false detections) and expensive cross-validation. In the spirit of simulated annealing, we propose a warm-start sparsity inducing algorithm to solve the high-dimensional, non-convex and non-differentiable optimization problem. We perform simulated and real data Monte Carlo experiments to quantify the effectiveness of our approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Direct Estimation of Parameters in ODE Models Using WENDy: Weak-Form Estimation of Nonlinear Dynamics

Abstract We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs. Without relying on any numerical differential equation solvers, WENDy computes accurate estimates and is robust to large (biologically relevant) levels of measurement noise. For low dimensional systems with modest amounts of data, WENDy is competitive with conventional forward solver-based nonlinear least squares methods in terms of speed and accuracy. For both higher dimensional systems and stiff systems, WENDy is typically both faster (often by orders of magnitude) and more accurate than forward solver-based approaches. The core mathematical idea involves an efficient conversion of the strong form representation of a model to its weak form, and then solving a regression problem to perform parameter inference. The core statistical idea rests on the Errors-In-Variables framework, which necessitates the use of the iteratively reweighted least squares algorithm. Further improvements are obtained by using orthonormal test functions, created from a set of $$C^{\infty }$$ C ∞ bump functions of varying support sizes.We demonstrate the high robustness and computational efficiency by applying WENDy to estimate parameters in some common models from population biology, neuroscience, and biochemistry, including logistic growth, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, and a Protein Transduction Benchmark model. Software and code for reproducing the examples is available at https://github.com/MathBioCU/WENDy .

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

An Integrated Computational Materials Engineering (ICME) Approach to Design Nonlinear Transition Zones Between Dissimilar Metals

Current approaches to designing graded transition joints (GTJs) between dissimilar metals often rely on linear changes in both composition profiles and thickness of each sublayer. This increases fabrication cost and may not be optimal with respect to residual stress or the formation of undesirable phases. Here, in this study, GTJs between P91 ferritic/martensitic steel and 347H austenitic stainless steel were designed using Integrated Computational Materials Engineering (ICME) principles with nonlinear composition and length profiles. Guided by inputs from classical mechanics and CALPHAD predictions of carbon chemical potential, a novel transition zone consisting of five discrete compositions was proposed, with the thickness of each sublayer varying according to a brachistochrone-inspired distribution. In addition to carbon potential gradients, CALPHAD was used to predict coefficients of thermal expansion, which were incorporated into finite element models to evaluate stress evolution. The proposed nonlinear design resulted in a smoother carbon potential gradient, lower carbon depletion at the P91 interface, and a comparable residual stress under long-term thermal exposure, compared to a conventional linear design using ten sublayers with equal thickness. This work introduces a brachistochrone-inspired distribution for GTJ design, offering a general framework for optimizing graded interfaces between dissimilar metals.

Directed Energy Deposition↗
DOE OSTI2024

Generalization error guaranteed auto-encoder-based nonlinear model reduction for operator learning

Many physical processes in science and engineering are naturally represented by operators between infinite-dimensional function spaces. The problem of operator learning, in this context, seeks to extract these physical processes from empirical data, which is challenging due to the infinite or high dimensionality of data. An integral component in addressing this challenge is model reduction, which reduces both the data dimensionality and problem size. In this paper, we utilize low-dimensional nonlinear structures in model reduction by investigating Auto-Encoder-based Neural Network (AENet). AENet first learns the latent variables of the input data and then learns the transformation from these latent variables to corresponding output data. Our numerical experiments validate the ability of AENet to accurately learn the solution operator of nonlinear partial differential equations. Furthermore, we establish a mathematical and statistical estimation theory that analyzes the generalization error of AENet. Finally, our theoretical framework shows that the sample complexity of training AENet is intricately tied to the intrinsic dimension of the modeled process, while also demonstrating the robustness of AENet to noise.

Auto-encoder↗
DOE OSTI2024

Lyapunov-based nonlinear control of nonautonomous systems with individual input constraints

A control algorithm that can locally stabilize a specific class of multi-input multi-output nonautonomous nonlinear dynamical systems while satisfying individual input constraints is developed. The proposed Lyapunov-based state-feedback control law inherently accounts for the actuator amplitude saturation limits without the need for computationally expensive real-time optimization techniques. In addition to the control law, a formal definition for the local “controllable region” within which the controller can asymptotically drive the system states to the origin and satisfy the input saturation limits is also presented. The nonautonomous nature of the system dynamics implies that the “controllable region” continuously evolves with time. Therefore, a sufficient condition to maintain the system states within the “controllable region” is proposed in this work to make practical implementation feasible. The effectiveness of the controller is tested for a specific control problem arising in tokamaks, which are toroidal devices that use strong magnetic fields to confine a plasma (hot ionized gas). Here, the primary emphasis of tokamak research is to regulate the plasma properties around predetermined values to achieve stable plasma confinement. Nonlinear simulations show that the proposed controller can achieve the desired plasma control objectives in a DIII-D tokamak scenario.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Probabilistic-learning-based stochastic surrogate model from small incomplete datasets for nonlinear dynamical systems

We consider a high-dimensional nonlinear computational model of a dynamical system, parameterized by a vector-valued control parameter, in the presence of uncertainties represented by an uncontrolled parameter modeled by a vector-valued random variable, and possibly with stochastic excitation. The objective is to construct a statistical surrogate model where the input is any deterministic value of the control parameter, and the output is a vector-valued observation of the computational model, which is a random vector whose probability measure is updated using a target dataset. To construct this statistical surrogate model, the stochastic response of the computational model must be built, which is a vector-valued time-discretized stochastic process in high dimension, depending on the control parameter. It is assumed that the computational cost of a single evaluation of the deterministic model is high. For the probabilistic updating, we consider a subset of the components of the observation of the computational model, defined as the “identification observation” of the computational model, for which a small target dataset is available. Therefore, the target dataset is associated with partial observability, corresponding to an incomplete data case. Given a prior probability model of the random control and uncontrolled parameters, a training dataset is constructed, consisting of realizations of the random triplet composed of the stochastic response, the random identification observation, and the random control parameter. Since the computational cost of a single evaluation of the deterministic model is assumed to be large, the training dataset is also of small size. The main challenges in this problem are the high dimensionality, partial observability leading to incomplete data in the target dataset for the identification observation of the computational model (which is not sufficient to identify the computational stochastic responses), and the availability of a small training dataset. To address these challenges, we propose a methodology based on statistical methods for constructing necessary reduced representations, direct probabilistic learning under constraints using probabilistic learning on manifolds (PLoM) constrained by the target dataset, and the use of a weak formulation of the Fourier transform of probability measures. Statistical conditioning is also employed to explore the learned dataset. The constructed predictive statistical surrogate model can be implemented in the context of online computation. Here, we apply this approach to a problem of nonlinear stochastic dynamics in high dimensions within the framework of deformable solids mechanics.

Engineering↗
DOE OSTI2023

A co-kurtosis PCA based dimensionality reduction with nonlinear reconstruction using neural networks

For turbulent reacting flow systems, identification of low-dimensional representations of the thermo-chemical state space is vitally important, primarily to significantly reduce the computational cost of device-scale simulations. Principal component analysis (PCA), and its variants, are a widely employed class of methods. Recently, an alternative technique that focuses on higher-order statistical interactions, co-kurtosis PCA (CoK-PCA), has been shown to effectively provide a low-dimensional representation by capturing the stiff chemical dynamics associated with spatiotemporally localized reaction zones. While its effectiveness has only been demonstrated based on a priori analyses with linear reconstruction, in this work, we employ nonlinear techniques to reconstruct the full thermo-chemical state and evaluate the efficacy of CoK-PCA compared to PCA. Specifically, we combine a CoK-PCA-/PCA-based dimensionality reduction (encoding) with an artificial neural network (ANN) based reconstruction (decoding) and examine, a priori, the reconstruction errors of the thermo-chemical state. In addition, we evaluate the errors in species production rates and heat release rates, which are nonlinear functions of the reconstructed state, as a measure of the overall accuracy of the dimensionality reduction technique. We employ four datasets to assess CoK-PCA/PCA coupled with ANN-based reconstruction: zero-dimensional (homogeneous) reactor for autoignition of an ethylene/air mixture that has conventional single-stage ignition kinetics, a dimethyl ether (DME)/air mixture which has two-stage (low and high temperature) ignition kinetics, a one-dimensional freely propagating premixed ethylene/air laminar flame, and a two-dimensional dataset representing turbulent autoignition of ethanol in a homogeneous charge compression ignition (HCCI) engine. Finally, results from the analyses demonstrate the robustness of the CoK-PCA based low-dimensional manifold with ANN reconstruction in accurately capturing the data, specifically from the reaction zones.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Stochastic nonlinear analysis of unidirectional fiber composites using image-based microstructural uncertainty quantification

Here, we present a data-driven nonlinear uncertainty quantification and propagation framework to study the microstructure-induced stochastic performance of unidirectional (UD) carbon fiber reinforced polymer (CFRP) composites. The proposed approach integrates (1) microscopic image characterization, (2) stochastic microstructure reconstruction, and (3) efficient multiscale finite element simulations enabled by self-consistent clustering (SCA) analysis. To model the complex microstructural variability, the proposed UQ methods take the non-Gaussian uncertainty sources into account through a distribution-free sampling approach leveraging nonparametric and asymptotic statistical tools. A hierarchical conditional sampling strategy enables the simultaneous sampling of multiple sources of uncertainties. Our approach provides insights into the impact of microstructural variabilities, which are shown to have an increasing impact on the nonlinear responses of UD CFRP parts under progressive compression loading and ultimately on the failure rate over time. We discover that before CFRP parts start to fail, a characteristic time period emerges with distinctive uncertainty distributions specific to the microstructure variability and the probability of failure. Identifying the failure time period is crucial to the reliability prediction, which is an essential component of CFRP design.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A higher-order finite-element implementation of the nonlinear Fokker–Planck collision operator for charged particle collisions in a low density plasma

Collisions between particles in a low density plasma are described by the Fokker–Planck collision operator. In applications, this nonlinear integro-differential operator is often approximated by linearised or ad-hoc model operators due to computational cost and complexity. In this work, we present an implementation of the nonlinear Fokker–Planck collision operator written in terms of Rosenbluth potentials in the Rosenbluth–MacDonald–Judd (RMJ) form. The Rosenbluth potentials may be obtained either by direct integration or by solving partial differential equations (PDEs) similar to Poisson's equation: we optimise for performance and scalability by using sparse matrices to solve the relevant PDEs. We represent the distribution function using a tensor-product continuous-Galerkin finite-element representation and we derive and describe the implementation of the weak form of the collision operator. We present tests demonstrating a successful implementation using an explicit time integrator and we comment on the speed and accuracy of the operator. Finally, we speculate on the potential for applications in the current and next generation of kinetic plasma models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗