Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “unknowns”

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 1,009 records · Page 56
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture

Meshfree discretizations of state-based peridynamic models are attractive due to their ability to naturally describe fracture of general materials. However, two factors conspire to prevent meshfree discretizations of state-based peridynamics from converging to corresponding local solutions as resolution is increased: quadrature error prevents an accurate prediction of bulk mechanics, and the lack of an explicit boundary representation presents challenges when applying traction loads. Herein, we develop a reformulation of the linear peridynamic solid (LPS) model to address these shortcomings, using improved meshfree quadrature, a reformulation of the nonlocal dilatation, and a consistent handling of the nonlocal traction condition to construct a model with rigorous accuracy guarantees. In particular, these improvements are designed to enforce discrete consistency in the presence of evolving fractures, whose a priori unknown location render consistent treatment difficult. In the absence of fracture, when a corresponding classical continuum mechanics model exists, our improvements provide asymptotically compatible convergence to corresponding local solutions, eliminating surface effects and issues with traction loading which have historically plagued peridynamic discretizations. When fracture occurs, our formulation automatically provides a sharp representation of the fracture surface by breaking bonds, avoiding the loss of mass. We provide rigorous error analysis and demonstrate convergence for a number of benchmarks, including manufactured solutions, free-surface, nonhomogeneous traction loading, and composite material problems. Finally, we validate simulations of brittle fracture against a recent experiment of dynamic crack branching in soda-lime glass, providing evidence that the scheme yields accurate predictions for practical engineering problems.

42 ENGINEERING↗
DOE OSTI2021

Bayesian learning of orthogonal embeddings for multi-fidelity Gaussian Processes

Uncertainty propagation in complex engineering systems often poses significant computational challenges related to modeling and quantifying probability distributions of model outputs, as those emerge as the result of various sources of uncertainty that are inherent in the system under investigation. Gaussian Processes regression (GPs) is a robust meta-modeling technique that allows for fast model prediction and exploration of response surfaces. Multi-fidelity variations of GPs further leverage information from cheap and low fidelity model simulations in order to improve their predictive performance on the high fidelity model. In order to cope with the high volume of data required to train GPs in high dimensional design spaces, a common practice is to introduce latent design variables that are typically projections of the original input space to a lower dimensional subspace, and therefore substitute the problem of learning the initial high dimensional mapping, with that of training a GP on a low dimensional space. Here in this paper, we present a Bayesian approach to identify optimal transformations that map the input points to low dimensional latent variables. The \projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to be inferred jointly with the GP parameters, conditioned on the available training data. The proposed Bayesian inference scheme relies on a two-step iterative algorithm that samples from the marginal posteriors of the GP parameters and the projection matrix respectively, both using Markov Chain Monte Carlo (MCMC) sampling. In order to take into account the orthogonality constraints imposed on the orthonormal projection matrix, a Geodesic Monte Carlo sampling algorithm is employed, that is suitable for exploiting probability measures on manifolds. We extend the proposed framework to multi-fidelity models using GPs including the scenarios of training multiple outputs together. We validate our framework on three synthetic problems with a known lower-dimensional subspace. The benefits of our proposed framework, are illustrated on the computationally challenging aerodynamic optimization of a last-stage blade for an industrial gas turbine, where we study the effect of an 85-dimensional shape parameterization of a three-dimensional airfoil on two output quantities of interest, specifically on the aerodynamic efficiency and the degree of reaction

42 ENGINEERING↗
DOE OSTI2022

A comparison of neural network architectures for data-driven reduced-order modeling

The popularity of deep convolutional autoencoders (CAEs) has engendered new and effective reduced-order models (ROMs) for the simulation of large-scale dynamical systems. Despite this, it is still unknown whether deep CAEs provide superior performance over established linear techniques or other network-based methods in all modeling scenarios. To elucidate this, the effect of autoencoder architecture on its associated ROM is studied through the comparison of deep CAEs against two alternatives: a simple fully connected autoencoder, and a novel graph convolutional autoencoder. Through benchmark experiments, it is shown that the superior autoencoder architecture for a given ROM application is highly dependent on the size of the latent space and the structure of the snapshot data, with the proposed architecture demonstrating benefits on data with irregular connectivity when the latent space is sufficiently large.

42 ENGINEERING↗
DOE OSTI2022

Enriched immersed boundary method (EIBM) for interface-coupled multi-physics and applications to convective conjugate heat transfer

It is challenging to develop numerical methods that simultaneously maintain accuracy of resolving boundary conditions and mesh flexibility to handle the interface in interface-coupled multi-physics problems involving large property discontinuity. On the one hand, boundary-fitted methods possess high accuracy in capturing the interfacial phenomenon but involve complicated volumetric mesh generation, mesh-motion, and even re-meshing procedures. On the other hand, immersed boundary methods (IBM) provide mesh flexibility but sometimes suffer from inferior interface representations, leading to poor enforcement of boundary conditions. This paper presents an enriched immersed boundary method (EIBM) to overcome this challenge and demonstrates its efficacy in conjugate heat transfer, a representative example in interface-coupled multi-physics systems that have implications for many industrial processes. Further, the core technique of the method is to enhance IBM’s accuracy of the fluid–solid interface by enriching the degrees of freedom of the cut elements to enforce temperature and flux compatibilities and resolve all the physical unknowns on the background mesh to simplify the volumetric mesh generation. We implement the EIBM under the framework of a variational multiscale formulation for coupled Navier–Stokes and thermodynamics equations. The enriched DoFs enable better enforcement of temperature and flux compatibilities with large conductivity ratios across the fluid–solid interface. At the same time, the immersed nature of the proposed method still attains mesh flexibility. The EIBM’s accuracy is thoroughly evaluated through a set of examples, ranging from benchmark problems with analytical solutions to real-world cooling processes of a moving metallic structure with complex geometry.

42 ENGINEERING↗
DOE OSTI2023

Peridynamic elastic waves in two-dimensional unbounded domains: Construction of nonlocal Dirichlet-type absorbing boundary conditions

The focus of this paper is on application of peridynamics (PD) to propagation of elastic waves in unbounded domains. We construct absorbing boundary conditions (ABCs) derived from a semi-analytical solution of the PD governing equation at the exterior region. This solution is made up of a finite series of plane waves, as fundamental solutions (modes), which satisfy the PD dispersion relations. The modes are adjusted to transmit the energy from the interior region (near field) to the exterior region (far field). The corresponding unknown coefficients of the series are found in terms of the displacement field at a layer of points adjacent to the absorbing boundary. This is accomplished through a collocation procedure at subregions (clouds) around each absorbing point. The proposed ABCs offer appealing advantages, which facilitate their application to PD. They are of Dirichlet-type, hence their implementation is relatively simple as no derivatives of the field variables are required. They are constructed in the time and space domains and thus application of Fourier and Laplace transforms, cumbersome for nonlocal models, is not required. At the discrete level, the modes satisfy the same numerical dispersion relations of the near field, which makes the far-field solution compatible with that of the near field. We scrutinize the performance of the proposed ABCs through several examples. So our investigation shows that the proposed ABCs perform stably in time with an appropriate level of accuracy even in problems characterized by highly-dispersive propagating waves, including crack propagation in semi-unbounded brittle solids.

42 ENGINEERING↗
DOE OSTI2023

Scalable Bayesian optimization with randomized prior networks

Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment. Bayesian Optimization (BO) techniques are known to be effective in tackling global optimization problems using a relatively small number objective function evaluations, but their performance suffers when dealing with high-dimensional outputs. To overcome the major challenge of dimensionality, here we propose a deep learning framework for BO and sequential decision making based on bootstrapped ensembles of neural architectures with randomized priors. Using appropriate architecture choices, we show that the proposed framework can approximate functional relationships between design variables and quantities of interest, even in cases where the latter take values in high-dimensional vector spaces or even infinite-dimensional function spaces. In the context of BO, we augmented the proposed probabilistic surrogates with re-parameterized Monte Carlo approximations of multiple-point (parallel) acquisition functions, as well as methodological extensions for accommodating black-box constraints and multi-fidelity information sources. We test the proposed framework against state-of-the-art methods for BO and demonstrate superior performance across several challenging tasks with high-dimensional outputs, including a constrained multi-fidelity optimization task involving shape optimization of rotor blades in turbo-machinery.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

11-th order of accuracy for numerical solution of 3-D Poisson equation with irregular interfaces on unfitted Cartesian meshes

For the first time the optimal local truncation error method (OLTEM) with 125-point stencils and unfitted Cartesian meshes has been developed in the general 3-D case for the Poisson equation for heterogeneous materials with smooth irregular interfaces. The 125-point stencils equations that are similar to those for quadratic finite elements are used for OLTEM. The interface conditions for OLTEM are imposed as constraints at a small number of interface points and do not require the introduction of additional unknowns, i.e., the sparse structure of global discrete equations of OLTEM is the same for homogeneous and heterogeneous materials. The stencils coefficients of OLTEM are calculated by the minimization of the local truncation error of the stencil equations. These derivations include the use of the Poisson equation for the relationship between the different spatial derivatives. Such a procedure provides the maximum possible accuracy of the discrete equations of OLTEM. In contrast to known numerical techniques with quadratic elements and third order of accuracy on conforming and unfitted meshes, OLTEM with the 125-point stencils provides 11-th order of accuracy, i.e., an extremely large increase in accuracy by 8 orders for similar stencils. The numerical results show that OLTEM yields much more accurate results than high-order finite elements with much wider stencils. The increased numerical accuracy of OLTEM leads to an extremely large increase in computational efficiency. Additionally, a new post-processing procedure with the 125-point stencil has been developed for the calculation of the spatial derivatives of the primary function. The post-processing procedure includes the minimization of the local truncation error and the use of the Poisson equation. It is demonstrated that the use of the partial differential equation (PDE) for the 125-point stencils improves the accuracy of the spatial derivatives by 6 orders compared to post-processing without the use of PDE as in existing numerical techniques. At an accuracy of 0.1% for the spatial derivatives, OLTEM reduces the number of degrees of freedom by 900 - 4∙10 6 times compared to quadratic finite elements. The developed post-processing procedure can be easily extended to unstructured meshes and can be independently used with existing post-processing techniques (e.g., with finite elements).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

The latent variable proximal point algorithm for variational problems with inequality constraints

The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a saddle point reformulation of the Bregman proximal point algorithm. At the continuous level, the two formulations are equivalent, but the saddle point formulation is more amenable to discretization because it introduces a structure-preserving transformation between a latent function space and the feasible set. Working in this latent space is much more convenient for enforcing inequality constraints than the feasible set, as discretizations can employ general linear combinations of suitable basis functions, and nonlinear solvers can involve general additive updates. LVPP yields numerical methods with observed mesh-independence for obstacle problems, contact, fracture, plasticity, and others besides; in many cases, for the first time. The framework also extends to more complex constraints, providing means to enforce convexity in the Monge–Ampère equation and handling quasi-variational inequalities, where the underlying constraint depends implicitly on the unknown solution. Here, in this paper, we describe the LVPP algorithm in a general form and apply it to ten problems from across mathematics.

Inequality constraints↗
DOE OSTI2025

Generative learning of densities on manifolds

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent) spaces in the high-dimensional data (ambient) space. Two approaches for sampling from the latent data density are described. The first is a score-based diffusion model, which is trained to map a standard normal distribution to the latent data distribution using a neural network. The second one involves solving an Itô stochastic differential equation in the latent space. Additional realizations of the data are generated by lifting the samples back to the ambient space using Double Diffusion Maps , a recently introduced technique typically employed in studying dynamical system reduction; here the focus lies in sampling densities rather than system dynamics. The proposed approaches enable sampling high dimensional data densities restricted to low-dimensional, a priori unknown manifolds. The efficacy of the proposed framework is demonstrated through a benchmark problem and a material with multiscale structure.

Double diffusion maps↗
DOE OSTI2024

Nonexistence of integrable nonlinear magnetic fields with invariants quadratic in momenta

Nonlinear, completely integrable Hamiltonian systems that serve as blueprints for novel particle accelerators at the intensity frontier are promising avenues for research, as Fermilab’s Integrable Optics Test Accelerator (IOTA) example clearly illustrates. Here, we show that only very limited generalizations are possible when no approximations in the underlying Hamiltonian or Maxwell equations are allowed, as was the case for IOTA. Specifically, no such systems exist with invariants quadratic in the momenta, precluding straightforward generalization of the Courant-Snyder theory of linear integrable systems in beam physics. We also conjecture that no such systems exist with invariants of higher degree in the momenta. This leaves solenoidal magnetic fields, including their nonlinear fringe fields, as the only completely integrable static magnetic fields, albeit with invariants that are linear in the momenta. The difficulties come from enforcing Maxwell equations; without constraints, we show that there are many solutions. In particular, we discover a previously unknown large family of integrable Hamiltonians.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Relating storm-snow avalanche instabilities to data collected from the Differential Emissivity Imaging Disdrometer (DEID)

Storm-snow avalanches are challenging to forecast due to complex alpine terrain and during rapidly changing weather conditions. They can result in loss of lives and significant economic impact. We describe how a new device that continuously measures with high-frequency snowflake mass, size, density, and type, the Differential Emissivity Imaging Disdrometer (DEID), and show how the DEID can be used to aid avalanche forecasting when coupled with a storm-snow stability model. DEID measurements of snow accumulation, snow water equivalent (SWE), and snow density obtained during seventeen storms taken at the mid-Collins Snow-Study Plot at Alta Ski Area in Utah's Central Wasatch mountain range during winter 2020–2021 show excellent agreement with infrequent manual measurements. Additionally, two new variables, the Shape Density Index (SDI) and Complexity, are proposed and used to classify snowflake habit and estimate storm-snow shear strength. We illustrate how these DEID-derived data can be used to identify layers of concern in the storm snow such as density inversions, in real-time without digging snow pits. Furthermore, the DEID-data are used to run four variations of the SNOw Slope Stability model (SNOSS) for the storms investigated. The results are evaluated with data collected from tilt-board tests, infrasound measurements, and visual observations of avalanches. For a total fourteen storms analyzed, the DEID-driven SNOSS-modeled minimum stability index predicts the general stability of the storm-snow as indicated by observed avalanches, both natural and of unknown cause. Finally, the results provide a promising approach for nowcasting instabilities within storm-snow layers with a single instrument.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Shock tube investigation of high-temperature, extremely-rich oxidation of several co-optima biofuels for spark-ignition engines

To reduce the reliance on fossil fuels in the transportation sector and increase combustion efficiency, the Co-Optima initiative from US Department of Energy identified the top 10 biofuels for downsized, boosted, spark-ignition engines. Most of these biofuels have detailed reaction mechanisms available in literature developed based on studies at temperatures lower than 1700 K and an equivalence ratio of less than five. As such, the performance of these detailed mechanisms at high temperature and extremely rich conditions are unknown. It is important to validate kinetic mechanisms at these conditions because they are conducive to soot formation. Prediction of soot by chemical kinetic models relies on the prediction of underlying benchmark species like carbon monoxide and ethylene. In this work, we conduct high temperature (1700–2050 K) and high equivalence ratio(Φ=8.6) oxidation of these biofuels, namely 2,4,4-trimethyl-1-pentene (α-diisobutylene), ethanol, cyclopentanone, methyl acetate, and 2-methylfuran, blended in ethylene behind reflected shock waves at 4–4.7 atm pressure. Carbon monoxide and ethylene time histories are measured simultaneously using a continuous feedback quantum cascade laser near 4.9 µm and a tunable CO 2 gas laser at 10.532 nm, respectively. Results show that ethanol blend forms more carbon monoxide than other biofuels and consumes ethylene faster than the biofuel blends in the temperature range considered. Overall, the performance of different mechanisms in literature are evaluated against the experimental results. The novel reaction mechanism ‘the Co-Optima model’, which includes the sub mechanisms for all the biofuels in this study, was found to be the best mechanism for the experimental conditions studied.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

In situ multi-tier auto-ignition detection applied to dual-fuel combustion simulations

Here we use an anomaly detection methodology that is centered on analyzing fourth-order joint moments (co-kurtosis), particularly focusing on its application in auto-ignition of combustion problems with large numbers of species. Unsupervised anomaly detection is challenging to generalize across problem types and domains. A recent technique, centered on analyzing information in the fourth-order joint moment co-kurtosis, has shown promise, especially for high-dimensional scientific data. In this work we present developments to the co-kurtosis based anomaly detection method needed to make it effective and scalable for large-scale distributed scientific data, such as those generated by massively parallel simulations. An in situ co-kurtosis algorithm is employed as the anomaly detection method for identifying ignition kernels in simulations of turbulent combustion. Here, we extend an existing methodology which identifies regions of the domain where anomalies are present, and add another tier of anomaly detection where the individual samples contributing to the anomaly are identified. We apply this algorithm on-the-fly to a variety of turbulent reacting flow problems and compare it to the widely used (but significantly more expensive) chemical explosive mode analysis (CEMA). We demonstrate the ability of the method to detect and identify the onset of low and high temperature ignition which can be used for computational steering, as chemical and combustion anomalies occur intermittently at spatio-temporal locations unknown a priori. Finally, we apply our lightweight in situ algorithm to an exascale high-fidelity simulation with a total of 2.4 Trillion degrees of freedom, performed using an adaptive mesh refinement solver. Furthermore, through a scalability analysis, we show that the relative computational cost of this in-situ anomaly detection algorithm compared to an iteration of the reacting flow solver is negligible.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Fabrication, oxidation, and combustion of nanoscale magnesium diboride and tetraboride

The difficult ignition and low combustion efficiency of boron particles decrease the performance of boron-loaded, fuel-rich propellants for solid fuel ramjets and ducted rockets. One approach to solving this problem involves the use of magnesium diboride (MgB 2 ), which ignites easier than boron. Magnesium tetraboride (MgB 4 ) offers greater energy density owing to its higher boron content. However, the effect of B/Mg ratio on the ignition and combustion is unknown. Additionally, while nanoscale MgB₂ particles and quasi-2D structures are promising energetic additives, the oxidation and combustion properties of nanoscale MgB₄ have not been explored. To address these knowledge gaps, the present work included synthesis and high-energy ball milling of MgB 2 and MgB 4 powders, thermogravimetric analysis (TGA) of their oxidation, and combustion experiments with thin layers of the obtained powders. Comparison of two synthesis routes (a solid-state reaction in a tube furnace and combustion synthesis) has shown that the former is the superior method for producing magnesium borides. TGA has revealed that oxidation of both MgB 2 and MgB 4 results in a high conversion into the oxides (88–91 %), far exceeding the low conversion of boron (62.5 %). MgB 4 begins to oxidize rapidly at a much lower temperature (∼900 °C) than MgB 2 (∼1200 °C). The burning rates of milled MgB 2 and MgB 4 are about eight and five times, respectively, faster than that of submicron boron. Magnesium borides exhibit a stable, sustained boron flame, needed for high combustion efficiency, whereas physical Mg/B mixtures undergo Mg-driven "flash" combustion.

Boron↗
DOE OSTI2022

First-principles study of Al/Al 3 Ni interfaces

Al-Ni alloys have shown promise for high-temperature applications due to the strengthening of Al 3 Ni fibers resistant to coarsening and spheroidization up to 400°C. While the interface between Al and Al 3 Ni phases affects the coarsening rate of Al 3 Ni at elevated temperatures, its characteristics are largely unknown to date. Here, we have constructed various supercells to model this interface and performed a first-principles study based on density functional theory (DFT). We have considered three groups of Al/Al 3 Ni interfaces: experimentally reported orientation relationships from the solidification studies, crystallographically similar Fe-Fe 3 C pearlite interfaces, and the family of low-index (100) termination planes. We have analyzed the correlation between the DFT Al/Al 3 Ni interfacial energies and characteristic features, e.g., excess free volume and the number of broken bonds. We outline the further experimental and computational analysis required to improve the interface modeling of Al/Al 3 Ni.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Perspectives on the integration between first-principles and data-driven modeling

Efficiently embedding and/or integrating mechanistic information with data-driven models is essential if it is desired to simultaneously take advantage of both engineering principles and data-science. Further the opportunity for hybridization occurs in many scenarios, such as the development of a faster model of an accurate high-fidelity computer model; the correction of a mechanistic model that does not fully-capture the physical phenomena of the system; or the integration of a data-driven component approximating an unknown correlation within a mechanistic model. At the same time, different techniques have been proposed and applied in different literatures to achieve this hybridization, such as hybrid modeling, physics-informed Machine Learning (ML) and model calibration. In this paper we review the methods, challenges, applications and algorithms of these three research areas and discuss them in the context of the different hybridization scenarios. Moreover, we provide a comprehensive comparison of the hybridization techniques with respect to their differences and similarities, as well as advantages and limitations and future perspectives. Finally, we apply and illustrate hybrid modeling, physics-informed ML and model calibration via a chemical reactor case study.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Development of algorithms for augmenting and replacing conventional process control using reinforcement learning

Here, this work seeks to allow for the online operation and training of model-free reinforcement learning (RL) agents but limit the risk to system equipment and personnel. The parallel implementation of RL alongside more conventional process control (CPC) allows for the RL algorithm to learn from CPC. The past performance of both methods are assessed on a continuous basis allowing for a transition from CPC to RL and, if needed, transitioning back to CPC from RL. This allows for the RL algorithm to slowly and safely assume control of the process without significant degradation in control performance. It is shown that the RL can derive a near optimal policy even when coupled with a suboptimal CPC. It is also demonstrated that the coupled RL-CPC algorithm learns at a faster rate than traditional RL methods of exploration while the algorithm’s performance does not deteriorate below CPC, even when exposed to an unknown operating condition.

30 DIRECT ENERGY CONVERSION↗