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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.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Multilevel Hierarchical Decomposition of Finite Element White Noise with Application to Multilevel Markov Chain Monte Carlo

In this work we develop a new hierarchical multilevel approach to generate Gaussian random field realizations in an algorithmically scalable manner that is well suited to incorporating into multilevel Markov chain Monte Carlo (MCMC) algorithms. This approach builds off of other partial differential equation (PDE) approaches for generating Gaussian random field realizations; in particular, a single field realization may be formed by solving a reaction-diffusion PDE with a spatial white noise source function as the right-hand side. While these approaches have been explored to accelerate forward uncertainty quantification tasks, e.g., multilevel Monte Carlo, the previous constructions are not directly applicable to multilevel MCMC frameworks which build fine-scale random fields in a hierarchical fashion from coarse-scale random fields. Our new hierarchical multilevel method relies on a hierarchical decomposition of the white noise source function in $L^2$ which allows us to form Gaussian random field realizations across multiple levels of discretization in a way that fits into multilevel MCMC algorithmic frameworks. After presenting our main theoretical results and numerical scaling results to showcase the utility of this new hierarchical PDE method for generating Gaussian random field realizations, this method is tested on a four-level MCMC algorithm to explore its feasibility.

algebraic multigrid↗
DOE OSTI2021

Modeling and Control of Cascaded Bridgeless Multilevel Rectifier Under Unbalanced Load Conditions

The goal of this project is to model and control a novel unidirectional cascaded multilevel bridgeless rectifier as an active front end in medium and high voltage applications. This topology has many advantages over a conventional cascaded H-bridge rectifier, such as lower implementation cost, higher reliability, and greater flexibility with similar power quality.The steady-state mathematical model is used to develop a method for the voltage balancing of dc cells. Power factor analysis is discussed to achieve unity power factor using fully controlled hbridge cells. Power loss, efficiency, and cost comparison studies between the traditional cascaded H-Bridge converter and the proposed bridgeless converter demonstrate the advantages. A novel control strategy is proposed to achieve dc voltage balancing, fast and robust grid synchronization and power factor correction under unbalanced load conditions. Simulation and experimental results validate the models and control method.

Cascaded Bridgeless Rectifier, Power factor analys↗
DOE OSTI2022

Internal Model-Based Active Damping Strategy for a Back-to-Back Modular Multilevel Converter System for Advanced Grid Support: Preprint

The proposed work focuses on the possibility of achieving the reduction in the size of the interfacing filter for the grid connection for a back-to-back modular multilevel converter system with the use of third order LCL filters. To achieve the same attenuation, it is possible to reduce the size of the interfacing filters by the usage of third order filters. However, this kind of filtering comes with the limitation of having sustained oscillations due to lack of damping especially during transient changes. Therefore, in this work, a methodology has been proposed based on the principle of internal model to cater for this unwanted oscillations. The third order system is modeled inside the microcontroller with the damping enabled. The error between the output from the model and the actual are compared and the error is utilized to accomplish the active damping strategy. The proposed architecture is verified via computer simulations based on MATLAB/Simulink domain and various case study results along with their discussion is presented in this paper.

dq control↗
DOE OSTI2024

Cyclable Variable Path Length Multilevel Structures for Lossless Ion Manipulations (SLIM) Platform for Enhanced Ion Mobility Separations

Ion mobility-mass spectrometry (IMS-MS) is increasingly used to analyze complex samples and provide structural information of unknown compounds. As the complexity of samples increases, there is a need to improve the resolution of IMS-MS instruments to increase the rate of molecular identification. In this work, we evaluated a cyclable and variable-pathlength multilevel Structures for Lossless Ion Manipulations (SLIM) platform to achieve a higher resolving power than previously possible. This new multilevel SLIM platform has eight separation levels connected by ion escalators and a path length of ~88 meters (~11 meters per level). Our new multilevel SLIM can also be operated in an ‘ion cycling’ mode where a set of return ion escalators transport ions from the eighth back to the first level, allowing even longer path lengths (and higher IMS resolution). The platform has been improved to enhance the ion transmission and IMS separation quality by reducing the spacing between SLIM boards as well as board thickness, reducing the ions’ escalator residence time. Compared to the previous generation, the new multilevel SLIM demonstrated a better transmission for a set of phosphazene ions, especially for the low-mobility ions. The new multilevel SLIM achieved better resolving powers than our previous 4-level SLIM. The collision cross-section-based resolving power of the SLIM platform was tested using a pair of singly-charged reverse sequence peptides (SDGRG 1+ , GRGDS 1+ ). We achieved 1100 resolving power using 88 meters of path length (i.e., 8 levels) and 1400 following an additional pass through the eight levels (i.e., 16 levels or 173.5 m). The multilevel SLIM was further evaluated to demonstrate the enhanced separation for a positively and negatively charged brain total lipid extract sample. Finally, the new multilevel SLIM enables much higher resolving powers for a wide range of ion mobilities, improved transmission for low-mobility ions, and the ability to perform even higher resolving power for ions of interest.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1990

Direct handling of equality constraints in multilevel optimization

In recent years there have been several hierarchic multilevel optimization algorithms proposed and implemented in design studies. Equality constraints are often imposed between levels in these multilevel optimizations to maintain system and subsystem variable continuity. Equality constraints of this nature will be referred to as coupling equality constraints. In many implementation studies these coupling equality constraints have been handled indirectly. This indirect handling has been accomplished using the coupling equality constraints' explicit functional relations to eliminate design variables (generally at the subsystem level), with the resulting optimization taking place in a reduced design space. In one multilevel optimization study where the coupling equality constraints were handled directly, the researchers encountered numerical difficulties which prevented their multilevel optimization from reaching the same minimum found in conventional single level solutions. The researchers did not explain the exact nature of the numerical difficulties other than to associate them with the direct handling of the coupling equality constraints. The coupling equality constraints are handled directly, by employing the Generalized Reduced Gradient (GRG) method as the optimizer within a multilevel linear decomposition scheme based on the Sobieski hierarchic algorithm. Two engineering design examples are solved using this approach. The results show that the direct handling of coupling equality constraints in a multilevel optimization does not introduce any problems when the GRG method is employed as the internal optimizer. The optimums achieved are comparable to those achieved in single level solutions and in multilevel studies where the equality constraints have been handled indirectly.

Renaud, John E.↗
NASA NTRS2019

Multilevel Monte Carlo Estimation of Unbiased Expectation via Sample Reuse and the Low Variance Estimation of Asymptotic Rates

A new variant of the multilevel Monte Carlo estimator [5, 3, 9, 12] is presented for the estimation of expectation statistics that utilizes sample reuse in specified levels, explicitly removes approximation error bias associated with numerically computed output quantities of interest that have an asymptotic limit behavior, and permits a low variance estimate of the asymptotic rate of convergence to that limit. In addition, it is shown that this new multilevel Monte Carlo variant can yield a computational cost savings. A review of Monte Carlo and multilevel Monte Carlo estimators is presented that includes analysis of expected value, expected mean squared error, and the calculation of optimized multilevel sample size parameters. The multilevel Monte Carlo estimator produces estimates of expectation for numerically approximated output quantities of interest that are biased by approximation error. When the quantity of interest can be modeled as the asymptotic limit of numerically approximated output quantities of interest, it is theoretically possible to remove this approximation error bias in the multilevel Monte Carlo estimator. In actual implementations, however, this procedure is unreliable due to statistical variability and inaccuracy in estimating the needed asymptotic limit. Analysis and numerical experiment show that the proposed variant of the multilevel Monte Carlo method greatly reduces (in some cases eliminates) the statistical variability in this limit estimation.

Barth, Timothy↗
DOE OSTI2025

Accelerating multilevel Markov Chain Monte Carlo using machine learning models

Here, this work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian inference often substitute computationally expensive high-fidelity models with machine learning models, thereby introducing approximation errors, our approach offers a computationally efficient alternative by augmenting high-fidelity models with low-fidelity ones within a hierarchical framework. The multilevel approach utilizes the low-fidelity machine learning model (MLM) for inexpensive evaluation of proposed samples thereby improving the acceptance of samples by the high-fidelity model. The hierarchy in our multilevel algorithm is derived from geometric multigrid hierarchy. We utilize an MLM to accelerate the coarse level sampling. Training machine learning model for the coarsest level significantly reduces the computational cost associated with generating training data and training the model. We present an MCMC algorithm to accelerate the coarsest level sampling using MLM and account for the approximation error introduced. We provide theoretical proofs of detailed balance and demonstrate that our multilevel approach constitutes a consistent MCMC algorithm. Additionally, we derive the expression for cost reduction due to machine learning model to facilitate cost analysis of the hierarchical sampling algorithm. Our technique is demonstrated on a standard benchmark inference problem in groundwater flow, where we estimate the probability density of a quantity of interest using a four-level MCMC algorithm. Our proposed algorithm accelerates multilevel sampling by a factor of two while achieving similar accuracy compared to sampling using the standard multilevel algorithm.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

New evidence favoring multilevel decomposition and optimization

The issue of the utility of multilevel decomposition and optimization remains controversial. To date, only the structural optimization community has actively developed and promoted multilevel optimization techniques. However, even this community acknowledges that multilevel optimization is ideally suited for a rather limited set of problems. It is warned that decomposition typically requires eliminating local variables by using global variables and that this in turn causes ill-conditioning of the multilevel optimization by adding equality constraints. The purpose is to suggest a new multilevel optimization technique. This technique uses behavior variables, in addition to design variables and constraints, to decompose the problem. The new technique removes the need for equality constraints, simplifies the decomposition of the design problem, simplifies the programming task, and improves the convergence speed of multilevel optimization compared to conventional optimization.

Padula, Sharon L.↗
NASA NTRS1986

An improved multilevel optimization approach for the design of complex engineering systems

Multilevel optimization methods are being considered for the design of complex systems on distributed networks of computers or even parallel processors. An obstacle to the use of multilevel methods is that they can be computationally expensive because of the cycling necessary to account for the coupling between the subproblems. This research effort aims at increasing the efficiency of multilevel optimization by adapting two techniques that are widely used in conventional one-level optimization: constraint approximation and temporary constraint deletion. These improvements are implemented and tested on three-, ten- and 52-bar planar truss designs. The results show that for larger problems (approximately 100 design variables and larger), the cost of analysis dominates the total cost so that multilevel optimization is no more expensive than one-level optimization. If parallel processing is used or the analysis process itself is decomposed, then multilevel optimization stands to become more economical than one-level optimization.

Barthelemy, J.-F. M.↗
NASA NTRS2008

High-Density, High-Bandwidth, Multilevel Holographic Memory

A proposed holographic memory system would be capable of storing data at unprecedentedly high density, and its data transfer performance in both reading and writing would be characterized by exceptionally high bandwidth. The capabilities of the proposed system would greatly exceed even those of a state-of-the art memory system, based on binary holograms (in which each pixel value represents 0 or 1), that can hold .1 terabyte of data and can support a reading or writing rate as high as 1 Gb/s. The storage capacity of the state-of-theart system cannot be increased without also increasing the volume and mass of the system. However, in principle, the storage capacity could be increased greatly, without significantly increasing the volume and mass, if multilevel holograms were used instead of binary holograms. For example, a 3-bit (8-level) hologram could store 8 terabytes, or an 8-bit (256-level) hologram could store 256 terabytes, in a system having little or no more size and mass than does the state-of-the-art 1-terabyte binary holographic memory. The proposed system would utilize multilevel holograms. The system would include lasers, imaging lenses and other beam-forming optics, a block photorefractive crystal wherein the holograms would be formed, and two multilevel spatial light modulators in the form of commercially available deformable-mirror-device spatial light modulators (DMDSLMs) made for use in high speed input conversion of data up to 12 bits. For readout, the system would also include two arrays of complementary metal oxide/semiconductor (CMOS) photodetectors matching the spatial light modulators. The system would further include a reference-beam sterring device (equivalent of a scanning mirror), containing no sliding parts, that could be either a liquid-crystal phased-array device or a microscopic mirror actuated by a high-speed microelectromechanical system. Time-multiplexing and the multilevel nature of the DMDSLM would be exploited to enable writing and reading of multilevel holograms. The DMDSLM would also enable transfer of data at a rate of 7.6 Gb/s or perhaps somewhat higher.

Chao, Tien-Hsin↗
DOE OSTI2023

Multilevel-in-width training for deep neural network regression

A common challenge in regression is that for many problems, the degrees of freedom required for a high-quality solution also allows for overfitting. Regularization is a class of strategies that seek to restrict the range of possible solutions so as to discourage overfitting while still enabling good solutions, and different regularization strategies impose different types of restrictions. In this paper, we present a multilevel regularization strategy that constructs and trains a hierarchy of neural networks, each of which has layers that are wider versions of the previous network's layers. Here, we draw intuition and techniques from the field of Algebraic Multigrid (AMG), traditionally used for solving linear and nonlinear systems of equations, and specifically adapt the Full Approximation Scheme (FAS) for nonlinear systems of equations to the problem of deep learning. Training through V-cycles then encourage the neural networks to build a hierarchical understanding of the problem. We refer to this approach as multilevel-in-width to distinguish from prior multilevel works which hierarchically alter the depth of neural networks. The resulting approach is a highly flexible framework that can be applied to a variety of layer types, which we demonstrate with both fully connected and convolutional layers. We experimentally show with PDE regression problems that our multilevel training approach is an effective regularizer, improving the generalize performance of the neural networks studied.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Fast shared-memory streaming multilevel graph partitioning

In this report we show that a fast parallel graph partitioner can benefit many applications by reducing data transfers. The online methods for partitioning graphs have to be fast and they often rely on simple one-pass streaming algorithms, while the offline methods for partitioning graphs contain more involved algorithms and the most successful methods in this category belong to the multilevel approaches. In this work, we assess the feasibility of using streaming graph partitioning algorithms within the multilevel framework. Our end goal is to come up with a fast parallel offline multilevel partitioner that can produce competitive cutsize quality. We rely on a simple but fast and flexible streaming algorithm throughout the entire multilevel framework. This streaming algorithm serves multiple purposes in the partitioning process: a clustering algorithm in the coarsening, an effective algorithm for the initial partitioning, and a fast refinement algorithm in the uncoarsening. Its simple nature also lends itself easily for parallelization. The experiments on various graphs show that our approach is on the average up to 5.1x faster than the multi-threaded MeTiS, which comes at the expense of only 2x worse cutsize.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Multilevel-in-Space-and-Energy CMFD in VERA

For full-core modeling in the Virtual Environment for Reactor Analysis (VERA), the three-dimensional multigroup eigenvalue neutron transport problem is solved by MPACT. To improve the efficiency of MPACT, advancements have been made in the transport accelerator. Multilevel-in-energy and multilevel-in-space coarse mesh finite difference (CMFD) solvers were developed to improve the efficiency of the CMFD accelerator. In this paper a new multilevel-in-space-and-energy CMFD solver is developed with coarsening in both space and energy on every level. Several different strategies are investigated for coarsening groups in energy. Modified V-cycle and multiple-cycle algorithms are evaluated for solving the multilevel equations. The performance of these solvers is compared for typical full-core reactor physics problems.

42 ENGINEERING↗
DOE OSTI2023

Biomechanical Analysis of Multilevel Posterior Cervical Spinal Fusion Constructs

Study Design: Controlled Laboratory Study Objective: To compare multilevel posterior cervical fusion (PCF) constructs stopping at C7, T1, and T2 under cyclic load to determine the range of motion (ROM) between the lowest instrumented level and lowest instrumented-adjacent level (LIV-1). Summary of Background Data: PCF is a mainstay of treatment for various cervical spine conditions. The transition between the flexible cervical spine and rigid thoracic spine can lead to construct failure at the cervicothoracic junction. There is little evidence to determine the most appropriate level at which to stop a multilevel PCF. Methods: Fifteen human cadaveric cervicothoracic spines were randomly assigned to 1 of 3 treatment groups: PCF stopping at C7, T1, or T2. Specimens were tested in their native state, following a simulated PCF, and after cyclic loading. Specimens were loaded in flexion-extension), lateral bending, and axial rotation. Three-dimensional kinematics were recorded to evaluate ROM. Results: The C7 group had greater flexion-extension motion than the T1 and T2 groups following instrumentation (10.17±0.83 degree vs. 2.77±1.66 degree and 1.06±0.55 degree, P <0.001), and after cyclic loading (10.42±2.30 degree vs. 2.47±0.64 degree and 1.99±1.23 degree, P <0.001). There was no significant difference between the T1 and T2 groups. The C7 group had greater lateral bending ROM than both thoracic groups after instrumentation (8.81±3.44 degree vs. 3.51±2.52 degree, P =0.013 and 1.99±1.99 degree, P =0.003) and after cyclic loading. The C7 group had greater axial rotation motion than the thoracic groups (4.46±2.27 degree vs. 1.26±0.69 degree, P =0.010; and 0.73±0.74 degree, P =0.003) following cyclic loading. Conclusion: Motion at the cervicothoracic junction is significantly greater when a multilevel PCF stops at C7 rather than T1 or T2. This is likely attributable to the transition from a flexible cervical spine to a rigid thoracic spine. Although this does not account for in vivo fusion, surgeons should consider extending multilevel PCF constructs to T1 when feasible. Level of Evidence: Not applicable.

Neurosciences & Neurology↗
NASA NTRS1986

Simulator for multilevel optimization research

A computer program designed to simulate and improve multilevel optimization techniques is described. By using simple analytic functions to represent complex engineering analyses, the simulator can generate and test a large variety of multilevel decomposition strategies in a relatively short time. This type of research is an essential step toward routine optimization of large aerospace systems. The paper discusses the types of optimization problems handled by the simulator and gives input and output listings and plots for a sample problem. It also describes multilevel implementation techniques which have value beyond the present computer program. Thus, this document serves as a user's manual for the simulator and as a guide for building future multilevel optimization applications.

Padula, S. L.↗
NASA NTRS1989

Integrated structure/control law design by multilevel optimization

A new approach to integrated structure/control law design based on multilevel optimization is presented. This new approach is applicable to aircraft and spacecraft and allows for the independent design of the structure and control law. Integration of the designs is achieved through use of an upper level coordination problem formulation within the multilevel optimization framework. The method requires the use of structure and control law design sensitivity information. A general multilevel structure/control law design problem formulation is given, and the use of Linear Quadratic Gaussian (LQG) control law design and design sensitivity methods within the formulation is illustrated. Results of three simple integrated structure/control law design examples are presented. These results show the capability of structure and control law design tradeoffs to improve controlled system performance within the multilevel approach.

Gilbert, Michael G.↗