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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

High manganese redox variability and manganate predominance in temperate soil profiles as determined by X-ray absorption spectroscopy

Manganese speciation is a key to understanding the fate of contaminants, nutrients, and organic matter in soils. To date, quantification of Mn species in bulk soils has been performed mainly by sequential extraction methods and rarely supported by spectroscopic analysis. In order to obtain quantitative information on the Mn species inventory of soils, we investigated 46 soil horizons (<2-mm fraction, 45.1–2,280 mg/kg Mn) of nine typical Central European soils (Cambisols, Chernozems, Luvisols, Podzol, Stagnosol) by chemical Mn analyses and Mn K-edge X-ray absorption spectroscopy, and related speciation results to major soil properties. Amounts of Mn 2+ , Mn 3+ , and Mn 4+ and the average oxidation state of Mn were evaluated by linear combination fitting (LCF) of X-ray absorption near edge structure (XANES) spectra. Additionally, we used extended X-ray absorption fine structure (EXAFS) spectroscopy to identify and quantify major Mn species. For this, EXAFS spectra of 20 organic and mineral soil samples from five soils (Cambisols, Chernozem, Luvisol) were analyzed by LCF and shell fitting. XANES analyses revealed a high Mn redox variability in organic surface layers, with Mn 2+ being most abundant (≤100%, $\overline{x}$ = 54%), followed by Mn 3+ (≤80%, $\overline{x}$ = 32%) and Mn 4+ (≤55%, $\overline{x}$ = 14%). Mineral soil horizons contained significantly less Mn 2+ (≤56%, $\overline{x}$ = 23%), about equal quantities of Mn 3+ (≤68%, $\overline{x}$ = 31%), and were enriched in Mn 4+ (≤89%, $\overline{x}$ = 46%). EXAFS analyses implied the presence of six major Mn species groups: manganates, organically complexed Mn, Mn(III) oxyhydroxides, silicate-bound Mn, Mn oxides without tunnel- or layer structure, and physisorbed Mn. In litter horizons, Mn was mainly present in organic complexes (58–91%, $\overline{x}$ = 78%) and as physisorbed Mn (≤15%), but individual horizons also comprised manganates, Mn(III) oxyhydroxides, and silicate-bound Mn. Manganates, likely mixtures of phyllomanganates with hexagonal layer symmetry and tectomanganates, dominated in all mineral soil horizons (37–94%, $\overline{x}$ = 67%). Correlation analysis showed that manganates dissolve completely during dithionite-citrate and acid ammonium oxalate extractions, and suggested that Mn 4+ -rich manganates preferentially form under less acidic soil conditions, partly by oxidation of organically complexed Mn(II), and that they are enriched in the soil clay fraction. Mineral soil horizons also contained minor quantities of organically complexed Mn (≤39%, $\overline{x}$ = 11%), silicate-bound Mn (≤30%, $\overline{x}$ = 8%), Mn(III) oxyhydroxides (≤37%, $\overline{x}$ = 7%), Mn oxides without tunnel- or layer structure (≤18%, $\overline{x}$ = 5%), and physisorbed Mn (≤14%, $\overline{x}$ <1%). The detection of Mn(III) oxyhydroxides such as feitknechtite (β-MnOOH) or groutite (α-MnOOH) as well as the spinel hausmannite (Mn 3 O 4 ) in acidic soils is remarkable, since their formation is normally linked to neutral or alkaline pH conditions. Minor contributions of silicate-bound Mn indicate the release of Mn from primary minerals already at early stages of soil formation, and low concentrations of physisorbed Mn suggest that exchangeable Mn is rapidly converted into manganates in oxic soils. In conclusion, the predominance of manganates in mineral soils has far-reaching implications for the functioning of soils and biogeochemical element cycles, as these minerals play an important role in metal binding, plant nutrition, and redox-related processes.

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

Competition between Solvation and Intramolecular Hydrogen-Bonding in Microsolvated Protonated Glycine and β-Alanine

Infrared predissociation (IRPD) spectroscopy is used to reveal and compare the microsolvation motifs of GlyH + (H 2 O) n and β-AlaH + (H 2 O) n . The chemical structure of these amino acids differ only in the length of the carbon chain connecting the amine and carboxyl terminals, which nonetheless leads to a significant difference in the strength of the intramolecular C=O···H-N hydrogen bond in the unsolvated ions. This difference makes them useful in our studies of the competition between solvation and internal hydrogen bonding interactions. Analysis of the IRPD results reveals that the sequential addition of water molecules leads to similar effects on the intramolecular interaction in both GlyH + (H 2 O) n and β-AlaH + (H 2 O) n . Solvation of the -NH 3 + group leads to a weakening of the C=O···H-N hydrogen bond, while solvation of the carboxyl -OH leads to a strengthening of this bond. Additionally, we have found that for β-AlaH + , the addition of a H 2 O to the second solvation shell can still influence the strength of the C=O···H-N hydrogen bonding interaction. Lastly because the C=O···H-N interaction in β-AlaH + is stronger than that in GlyH + , more solvent molecules are needed to sufficiently weaken the intramolecular hydrogen bond such that isomers without this bond begin to be energetically competitive; this occurs at n=5 for β-AlaH + and n=1 for GlyH + .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1991

Lanczos eigensolution method for high-performance computers

The theory, computational analysis, and applications are presented of a Lanczos algorithm on high performance computers. The computationally intensive steps of the algorithm are identified as: the matrix factorization, the forward/backward equation solution, and the matrix vector multiples. These computational steps are optimized to exploit the vector and parallel capabilities of high performance computers. The savings in computational time from applying optimization techniques such as: variable band and sparse data storage and access, loop unrolling, use of local memory, and compiler directives are presented. Two large scale structural analysis applications are described: the buckling of a composite blade stiffened panel with a cutout, and the vibration analysis of a high speed civil transport. The sequential computational time for the panel problem executed on a CONVEX computer of 181.6 seconds was decreased to 14.1 seconds with the optimized vector algorithm. The best computational time of 23 seconds for the transport problem with 17,000 degs of freedom was on the the Cray-YMP using an average of 3.63 processors.

Bostic, Susan W.↗
NASA NTRS2012

Linear Covariance Analysis and Epoch State Estimators

This paper extends in two directions the results of prior work on generalized linear covariance analysis of both batch least-squares and sequential estimators. The first is an improved treatment of process noise in the batch, or epoch state, estimator with an epoch time that may be later than some or all of the measurements in the batch. The second is to account for process noise in specifying the gains in the epoch state estimator. We establish the conditions under which the latter estimator is equivalent to the Kalman filter.

Markley, F. Landis↗
NASA NTRS2003

Effect of Variations in IRU Integration Time Interval On Accuracy of Aqua Attitude Estimation

During Aqua launch support, attitude analysts noticed several anomalies in Onboard Computer (OBC) rates and in rates computed by the ground Attitude Determination System (ADS). These included: 1) periodic jumps in the OBC pitch rate every 2 minutes; 2) spikes in ADS pitch rate every 4 minutes; 3) close agreement between pitch rates computed by ADS and those derived from telemetered OBC quaternions (in contrast to the step-wise pattern observed for telemetered OBC rates); 4) spikes of +/- 10 milliseconds in telemetered IRU integration time every 4 minutes (despite the fact that telemetered time tags of any two sequential IRU measurements were always 1 second apart from each other). An analysis presented in the paper explains this anomalous behavior by a small average offset of about 0.5 +/- 0.05 microsec in the time interval between two sequential accumulated angle measurements. It is shown that errors in the estimated pitch angle due to neglecting the aforementioned variations in the integration time interval by the OBC is within +/- 2 arcseconds. Ground attitude solutions are found to be accurate enough to see the effect of the variations on the accuracy of the estimated pitch angle.

Natanson, G. A.↗
DOE OSTI2021

Sequential Learning of Active Subspaces

This study shows that in recent years, active subspace methods (ASMs) have become a popular means of performing subspace sensitivity analysis on black-box functions. Naively applied, however, ASMs require gradient evaluations of the target function. In the event of noisy, expensive, or stochastic simulators, evaluating gradients via finite differencing may be infeasible. In such cases, often a surrogate model is employed, on which finite differencing is performed. When the surrogate model is a Gaussian process (GP), we show that the ASM estimator is available in closed form, rendering the finite-difference approximation unnecessary. We use our closed-form solution to develop acquisition functions focused on sequential learning tailored to sensitivity analysis on top of ASMs. We also show that the traditional ASM estimator may be viewed as a method of moments estimator for a certain class of GPs. We demonstrate how uncertainty on GP hyperparameters may be propagated to uncertainty on the sensitivity analysis, allowing model-based confidence intervals on the active subspace. Our methodological developments are illustrated on several examples.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2010

Automated Discovery and Modeling of Sequential Patterns Preceding Events of Interest

The integration of emerging data manipulation technologies has enabled a paradigm shift in practitioners' abilities to understand and anticipate events of interest in complex systems. Example events of interest include outbreaks of socio-political violence in nation-states. Rather than relying on human-centric modeling efforts that are limited by the availability of SMEs, automated data processing technologies has enabled the development of innovative automated complex system modeling and predictive analysis technologies. We introduce one such emerging modeling technology - the sequential pattern methodology. We have applied the sequential pattern methodology to automatically identify patterns of observed behavior that precede outbreaks of socio-political violence such as riots, rebellions and coups in nation-states. The sequential pattern methodology is a groundbreaking approach to automated complex system model discovery because it generates easily interpretable patterns based on direct observations of sampled factor data for a deeper understanding of societal behaviors that is tolerant of observation noise and missing data. The discovered patterns are simple to interpret and mimic human's identifications of observed trends in temporal data. Discovered patterns also provide an automated forecasting ability: we discuss an example of using discovered patterns coupled with a rich data environment to forecast various types of socio-political violence in nation-states.

Rohloff, Kurt↗
NASA NTRS2007

Development of the Functional Flow Block Diagram for the J-2X Rocket Engine System

The J-2X program calls for the upgrade of the Apollo-era Rocketdyne J-2 engine to higher power levels, using new materials and manufacturing techniques, and with more restrictive safety and reliability requirements than prior human-rated engines in NASA history. Such requirements demand a comprehensive systems engineering effort to ensure success. Pratt & Whitney Rocketdyne system engineers performed a functional analysis of the engine to establish the functional architecture. J-2X functions were captured in six major operational blocks. Each block was divided into sub-blocks or states. In each sub-block, functions necessary to perform each state were determined. A functional engine schematic consistent with the fidelity of the system model was defined for this analysis. The blocks, sub-blocks, and functions were sequentially numbered to differentiate the states in which the function were performed and to indicate the sequence of events. The Engine System was functionally partitioned, to provide separate and unique functional operators. Establishing unique functional operators as work output of the System Architecture process is novel in Liquid Propulsion Engine design. Each functional operator was described such that its unique functionality was identified. The decomposed functions were then allocated to the functional operators both of which were the inputs to the subsystem or component performance specifications. PWR also used a novel approach to identify and map the engine functional requirements to customer-specified functions. The final result was a comprehensive Functional Flow Block Diagram (FFBD) for the J-2X Engine System, decomposed to the component level and mapped to all functional requirements. This FFBD greatly facilitates component specification development, providing a well-defined trade space for functional trades at the subsystem and component level. It also provides a framework for function-based failure modes and effects analysis (FMEA), and a rigorous baseline for the functional architecture.

White, Thomas↗
NASA NTRS1999

Applications of Parallel Processing in Configuration Analyses

The paper presents the recent progress made towards developing an efficient and user-friendly parallel environment for routine analysis of large CFD problems. The coarse-grain parallel version of the CFL3D Euler/Navier-Stokes analysis code, CFL3Dhp, has been ported onto most available parallel platforms. The CFL3Dhp solution accuracy on these parallel platforms has been verified with the CFL3D sequential analyses. User-friendly pre- and post-processing tools that enable a seamless transfer from sequential to parallel processing have been written. Static load balancing tool for CFL3Dhp analysis has also been implemented for achieving good parallel efficiency. For large problems, load balancing efficiency as high as 95% can be achieved even when large number of processors are used. Linear scalability of the CFL3Dhp code with increasing number of processors has also been shown using a large installed transonic nozzle boattail analysis. To highlight the fast turn-around time of parallel processing, the TCA full configuration in sideslip Navier-Stokes drag polar at supersonic cruise has been obtained in a day. CFL3Dhp is currently being used as a production analysis tool.

Sundaram, Ppchuraman↗
DOE OSTI2025

Arabidopsis GALACTURONOSYLTRANSFERASE (GAUT) 1 synthesizes a homogalacturonan tightly bound to the cell wall and required for cell expansion

Arabidopsis GALACTURONOSYLTRANSFERASE1 (GAUT1) synthesizes homogalacturonan (HG), the most abundant pectin in growing plant cells. GAUT1 has the greatest in vitro enzyme activity of the six confirmed Arabidopsis HG biosynthetic GAUTs, but its biological activity remains elusive. Here we show that Arabidopsis GAUT1 homozygous mutants have a severe dwarfed seedling phenotype, survive several weeks as 2 to 3 mm seedlings, and have severely reduced shoot and root growth and hypocotyl epidermal, cortex and endodermal cell size. gaut1-1 pollen tubes are shorter than WT with increased bursting. Complementation of homozygous gaut1-1 with GAUT1 coding sequence driven by the GAUT1 promoter restored WT-like growth. The extreme dwarf phenotype of homozygous gaut1-1 seedlings precluded their use for detailed cell wall analysis, thus suspensions cultures were produced from callus generated from mutant and WT seedlings. Homozygous gaut1-1 suspension cells were smaller than WT with ∼30% reduced wall GalA content compared to WT. Sequential extraction of the walls with increasingly harsh solvents and sugar composition analysis revealed reduced GalA content in only the 4M KOH post-chlorite fraction, indicating that GAUT1-synthesized HG was held tightly in the wall by direct or indirect hydrogen bonding and/or oxidation-sensitive linkages. Treatment of wall fractions with endopolygalacturonase to hydrolyze HG and gel electrophoretic separation of hydrolysates exposed an HG-associated doublet band markedly downregulated in the homozygous gaut1-1 4M KOH post-chlorite fraction and to a lesser extent in 4M KOH and sodium chlorite fractions. NMR analysis identified the band as rhamnogalacturonan (RG)-II. Super resolution microscopy using anti-HG antibodies showed that, compared to WT, the homozygous gaut1-1 hypocotyl epidermal and callus cells had reduced content and length of HG nanofilaments, HG fibers associated with cell expansion in Arabidopsis. The results demonstrate that GAUT1-synthesized HG resides in a tightly-cell-wall-bound, RG-II-containing polymer required for HG nanofilament formation and seedling cell expansion.

Atmodjo↗
DOE OSTI2021

Microalgae Conversion to Biofuels and Biochemical via Sequential Hydrothermal Liquefaction (SEQHTL) and Bioprocessing: 2020 State of Technology

A preliminary techno-economic analysis (TEA) was developed for the fiscal year 2020 state of technology (SOT) assessment to evaluate the benefits and risks for a large-scale microalga hydrothermal liquefaction (HTL) system based on most recent testing results. The focus of the study is directed toward the conversion system, which consists of five processes: two-stage sequential HTL (SEQHTL), biocrude upgrading to final fuels, bioprocessing for co-product generation, hydrogen generation, and steam cycle. In this system, algae biomass with corn stover supplement during the lower algae productivity seasons (winter, fall, and spring) to match the maximum algae seasonal production rate in summer is employed to maintain a constant plant capacity in all the seasons. Algae only (summer season) or algae/corn stover blended feedstock (other seasons) are sent to a two-stage SEQHTL process. In stage I, the carbohydrates in the feedstock are extracted and separated from the residual solid. The residual solid from stage I is further converted to biocrude in the SEQHTL stage II step. The biocrude is upgraded to final fuel products in an upgrading process. The extract stream from HTL stage I is sent to the bioprocessing section for co-product generation via fermentation of carbohydrate. Lactic acid (LA) is assumed to be the co-product based on current bioprocessing testing results.

09 BIOMASS FUELS↗
DOE OSTI2022

Two- and three-body fragmentation of multiply charged tribromomethane by ultrafast laser pulses

We investigate the two- and three-body fragmentation of tribromomethane (bromoform, CHBr 3 ) resulting from multiple ionization by 28-femtosecond near-infrared laser pulses with a peak intensity of 6 × 10 14 W cm -2 . The analysis focuses on channels consisting exclusively of ionic fragments, which are measured by coincidence momentum imaging. The dominant two-body fragmentation channel is found to be Br + + CHBr 2 +. Weaker HBr + + CBr 2 +, CHBr + + Br 2 +, CHBr 2+ + Br 2 +, and Br + + CHBr 2 2+ channels, some of which require bond rearrangement prior to or during the fragmentation, are also observed. The dominant three-body fragmentation channel is found to be Br + + Br + + CHBr + . This channel includes both concerted and sequential fragmentation pathways, which we identify using the native frames analysis method. We compare the measured kinetic energy release and momentum correlations with the results of classical Coulomb explosion simulations and discuss the possible isomerization of CHBr 3 to BrCHBr–Br (iso-CHBr 3 ) prior to the fragmentation.

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

Microscale mechanical modeling of deformable geomaterials with dynamic contacts based on the numerical manifold method

Abstract Micromechanical modeling of geomaterials is challenging because of the complex geometry of discontinuities and potentially large number of deformable material bodies that contact each other dynamically. In this study, we have developed a numerical approach for micromechanical analysis of deformable geomaterials with dynamic contacts. In our approach, we detect contacts among multiple blocks with arbitrary shapes, enforce different contact constraints for three different contact states of separated, bonded, and sliding, and iterate within each time step to ensure convergence of contact states. With these features, we are able to simulate the dynamic contact evolution at the microscale for realistic geomaterials having arbitrary shapes of grains and interfaces. We demonstrate the capability with several examples, including a rough fracture with different geometric surface asperity characteristics, settling of clay aggregates, compaction of a loosely packed sand, and failure of an intact marble sample. With our model, we are able to accurately analyze (1) large displacements and/or deformation, (2) the process of high stress accumulated at contact areas, (3) the failure of a mineral cemented rock samples under high stress, and (4) post-failure fragmentation. The analysis highlights the importance of accurately capturing (1) the sequential evolution of geomaterials responding to stress as motion, deformation, and high stress; (2) large geometric features outside the norms (such as large asperities and sharp corners) as such features can dominate the micromechanical behavior; and (3) different mechanical behavior between loosely packed and tightly packed granular systems.

58 GEOSCIENCES↗
DOE OSTI2022

Metallic Technetium Sequestration in Nickel Core/Shell Microstructure during Fe(OH)2 Transformation with Ni doping

This study investigates the impacts of Ni doping on technetium-99 (Tc) sequestration in aqueous solutions through transformation of Fe(OH)2(s) to iron spinel (magnetite) under alkaline conditions. Extensive solid characterization was performed for the mineral phases produced, as well as the Tc/Ni speciation and distribution within these phases. X-ray diffraction results show that iron spinel was the dominant mineral product without detectable Ni incorporation. The doped Ni ions mainly precipitated as fine Fe/Ni oxide/hydroxide particles, including strongly reduced nanometer?sized spheroidal Ni-rich and metallic Ni phases. High-resolution analytical scanning transmission electron microscopy using energy dispersive X-ray spectroscopy and electron energy loss spectroscopy on the produced solid samples (focused ion beam-prepared specimens) revealed three Tc distribution domains dominated by nanocrystals and, especially, a Tc-rich metallic phase. Instances of metallic Tc were specifically found in spheroidal, Ni-rich and metallic nanoparticles exhibiting a core/shell microstructure that suggests strong reduction and sequential precipitation of Ni-Tc-Ni. Mass balance analysis showed nearly 100% Tc removal from the 4.8 × 10-4 M Tc solutions. The finding of the metallic Tc encapsulation indicates that Tc sequestration through Ni-doped Fe(OH)2(s)?to?iron spinel transformation process likely provides an alternative treatment pathway for Tc removal and could be combined into further waste treatment approaches.

Wang, Guohui↗
DOE OSTI2021

In situ synchrotron diffraction and modeling of non-equilibrium solidification of a MnFeCoNiCu alloy

The solidification mechanism and segregation behavior of laser-melted Mn 35 Fe 5 Co 20 Ni 20 Cu 20 was firstly investigated via in situ synchrotron x-ray diffraction at millisecond temporal resolution. The transient composition evolution of the random solid solution during sequential solidification of dendritic and interdendritic regions complicates the analysis of synchrotron diffraction data via any single conventional tool, such as Rietveld refinement. Therefore, a novel approach combining a hard-sphere approximation model, thermodynamic simulation, thermal expansion measurement and microstructural characterization was developed to assist in a fundamental understanding of the evolution of local composition, lattice parameter, and dendrite volume fraction corresponding to the diffraction data. This methodology yields self-consistent results across different methods. Via this approach, four distinct stages were identified, including: (I) FCC dendrite solidification, (II) solidification of FCC interdendritic region, (III) solid-state interdiffusion and (IV) final cooling with marginal diffusion. It was found out that in Stage I, Cu and Mn were rejected into liquid as Mn 35 Fe 5 Co 20 Ni 20 Cu 20 solidified dendritically. During Stage II, the lattice parameter disparity between dendrite and interdendritic region escalated as Cu and Mn continued segregating into the interdendritic region. After complete solidification, during Stage III, the lattice parameter disparity gradually decreases, demonstrating a degree of composition homogenization. The volume fraction of dendrites slightly grew from 58.3 to 65.5%, based on the evolving composition profile across a dendrite/interdendritic interface in diffusion calculations. Postmortem metallography further confirmed that dendrites have a volume fraction of 64.7 ± 5.3% in the final microstructure.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Unsupervised Segmentation and Clustering Workflow for Efficient Processing of 4D-STEM and 5D-STEM Data

Four-dimensional scanning transmission electron microscopy (4D-STEM) enables mapping of diffraction information with nanometer-scale spatial resolution, offering detailed insight into local structure, orientation, and strain. However, as data dimensionality and sampling density increase, particularly for in situ scanning diffraction experiments (5D-STEM), robust segmentation of structurally consistent behavior across sequential measurements becomes essential for efficient and physically meaningful analysis. Here, we introduce a clustering framework that identifies crystallographically distinct domains from 4D-STEM datasets. By using local diffraction-pattern similarity as a metric, the method extracts closed contours delineating spatially contiguous regions. This approach produces cluster-averaged diffraction patterns that improve signal quality while reducing data volume by orders of magnitude, enabling rapid and accurate orientation, phase, and strain mapping. We demonstrate the applicability of this approach to in situ liquid-cell 4D-STEM data of gold nanoparticle growth. Our method provides a scalable and generalizable route for spatially coherent segmentation, data compression, and quantitative structure–strain mapping across diverse 4D-STEM modalities. The full analysis code and example workflows are publicly available to support reproducibility and reuse.

4D-STEM↗
DOE OSTI2024

Custom Accessors: Enabling Scalable Data Ingestion, (Re-)Organization, and Analysis on Distributed Systems

The emerging class of high velocity and high volume data analytic workflows comprise interwoven data ingestion, organization, and processing stages, with ingestion and organization steps often contributing comparable or even higher computational costs than actual processing steps. Since complex workflows consist of a variety of phases that view and use data differently, being able to construct efficient, scalable, distributed data structures (arrays, vectors, sets, maps, and multi-maps) is essential and requires custom methods to extend and shrink containers, analyze and position data, and, maintain globallyconsistent meta-data. In this paper, we propose a novel datastructure access paradigm based on the concept of Accessors. At a high level, accessors are customizable callable objects that can modify the behavior of insert, read, update, and delete operations for distributed containers while preserving atomicity guarantees. Accessors provide a very clean and natural way to implement a variety of programming patterns, e.g., conditional insertion/deletion and cascading computations, which would be otherwise hard (or even impossible) to express in parallel and distributed settings without using locks. We demonstrate the practicality and usefulness of our approach with two representative use cases and study the performance of these applications on a distributed High-Performance Computing system. Our analysis highlights that our proposed abstraction allows for an effective overlapping and concurrent execution of different workflow steps (e.g., data ingestion and analysis), which in a conventional analytics pipeline would execute sequentially, contributing cumulatively to the overall latency.

Castellana, Vito G. [BATTELLE (PACIFIC NW LAB)] (O↗
DOE OSTI2022

On the Convergence of Overlapping Schwarz Decomposition for Nonlinear Optimal Control

Here, we study the convergence properties of an overlapping Schwarz decomposition algorithm for solving nonlinear optimal control problems (OCPs). The algorithm decomposes the time domain into a set of overlapping subdomains, and solves all subproblems defined over subdomains in parallel. The convergence is attained by updating primal-dual information at the boundaries of overlapping subdomains. We show that the algorithm exhibits local linear convergence, and that the convergence rate improves exponentially with the overlap size. We also establish global convergence results for a general quadratic programming, which enables the application of the Schwarz scheme inside second-order optimization algorithms (e.g., sequential quadratic programming). The theoretical foundation of our convergence analysis is a sensitivity result of nonlinear OCPs, which we call "exponential decay of sensitivity" (EDS). Intuitively, EDS states that the impact of perturbations at domain boundaries (i.e., initial and terminal time) on the solution decays exponentially as one moves into the domain. Here, we expand a previous analysis available in the literature by showing that EDS holds for both primal and dual solutions of nonlinear OCPs, under uniform second-order sufficient condition, controllability condition, and boundedness condition. We conduct experiments with a quadrotor motion planning problem and a partial differential equations (PDE) control problem to validate our theory, and show that the approach is significantly more efficient than alternating direction method of multipliers and as efficient as the centralized interior-point solver.

42 ENGINEERING↗