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At least 379 records · Page 21

PETSc/TAO Users Manual V.3.21

This manual describes the use of the Portable, Extensible Toolkit for Scientific Computation (PETSc) and the Toolkit for Advanced Optimization (TAO) for the numerical solution of partial differential equations (PDEs) and related problems on high-performance computers. PETSc/TAO is a suite of data structures and routines that provide the building blocks for implementing large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all distributed memory communication. PETSc/TAO includes a large suite of parallel linear solvers, nonlinear solvers, time integrators, and optimizers that may be used in application codes written in Fortran, C, C++, and Python (via petsc4py; see Getting Started ). The library is organized hierarchically, enabling users to employ the abstraction level most appropriate for a particular problem. By using techniques of object-oriented programming, PETSc provides enormous flexibility for users.

97 MATHEMATICS AND COMPUTING↗

A weak Hamiltonian finite element method for optimal guidance of an advanced launch vehicle

A temporal finite-element method based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables, which are expanded in terms of nodal values and simple shape functions. Time derivatives of the states and costates do not appear in the governing variational equation; the only quantities whose time derivatives appear therein are virtual states and virtual costates. Numerical results are presented for an elementary trajectory optimization problem; they show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The feasibility of this approach for real-time guidance applications is evaluated. A simplified model for an advanced launch vehicle application that is suitable for finite-element solution is presented.

Hodges, Dewey H.↗

A finite element based method for solution of optimal control problems

A temporal finite element based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables that are expanded in terms of elemental values and simple shape functions. Unlike other variational approaches to optimal control problems, however, time derivatives of the states and costates do not appear in the governing variational equation. Instead, the only quantities whose time derivatives appear therein are virtual states and virtual costates. Also noteworthy among characteristics of the finite element formulation is the fact that in the algebraic equations which contain costates, they appear linearly. Thus, the remaining equations can be solved iteratively without initial guesses for the costates; this reduces the size of the problem by about a factor of two. Numerical results are presented herein for an elementary trajectory optimization problem which show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The goal is to evaluate the feasibility of this approach for real-time guidance applications. To this end, a simplified two-stage, four-state model for an advanced launch vehicle application is presented which is suitable for finite element solution.

Bless, Robert R.↗

Vertical landing on an asteroid

This work is concerned with the final approach phase and vertical landing on an asteroid with a power-limited, electrically propelled spacecraft. With gravitational effects taken into account, a new solution to the fuel optimal vertical landing on an asteroid was obtained. In this solution, the spacecraft commanded acceleration is explicitly expressed as a function of vehicle velocity and time to go. Based on qualitative methods of analysis, the guidance strategy and the resulting trajectories were studied. It is shown that these fuel-optimal trajectories effectively assure a vertical soft landing on the asteroid. Results of numerical simulations for the vertical landing, starting from an elliptical orbit are presented.

Harel, D.↗

Structural Analysis and Optimization of a Composite Fan Blade for Future Aircraft Engine

This report addresses the structural analysis and optimization of a composite fan blade sized for a large aircraft engine. An existing baseline solid metallic fan blade was used as a starting point to develop a hybrid honeycomb sandwich construction with a polymer matrix composite face sheet and honeycomb aluminum core replacing the original baseline solid metallic fan model made of titanium. The focus of this work is to design the sandwich composite blade with the optimum number of plies for the face sheet that will withstand the combined pressure and centrifugal loads while the constraints are satisfied and the baseline aerodynamic and geometric parameters are maintained. To satisfy the requirements, a sandwich construction for the blade is proposed with composite face sheets and a weak core made of honeycomb aluminum material. For aerodynamic considerations, the thickness of the core is optimized whereas the overall blade thickness is held fixed so as to not alter the original airfoil geometry. Weight is taken as the objective function to be minimized by varying the core thickness of the blade within specified upper and lower bounds. Constraints are imposed on radial displacement limitations and ply failure strength. From the optimum design, the minimum number of plies, which will not fail, is back-calculated. The ply lay-up of the blade is adjusted from the calculated number of plies and final structural analysis is performed. Analyses were carried out by utilizing the OpenMDAO Framework, developed at NASA Glenn Research Center combining optimization with structural assessment.

Coroneos, Rula M.↗

Co-optimized Mixed-Mode Engine and Fuel Demonstrator for Improved Fuel Economy while Meeting Emissions Requirements

Progressively increasing regulatory demands on fuel economy and future global emission standards have led to a focus on advanced engine development to improve overall engine efficiency and fulfill emission requirements. Low temperature combustion (LTC) and gasoline compression ignition (GCI) are promising technologies to achieve these goals and have the advantage of using existing refinery infrastructure and subsequent economies of scale for a robust energy supply. By applying spark ignition (SI) for cold start, LTC for low load operations, and GCI for medium to high load operations, a multimode GCI engine concept was proposed and the fuel formation was co-optimized to maximize fuel economy improvement potential while maintaining ULEV 70 emissions standards. HATCI has successfully demonstrated the feasibility of this multimode GCI engine concept, and confirmed the fuel economy improvement over the baseline SI engine by simulating the FTP75 vehicle drive cycle. In this report, the technical approaches, multimode engine control, and engine test results of both steady state and transitions, CFD modeling, fuel testing, and FTP75 drive cycle simulation results are summarized, followed with technical challenges observed, and recommendations for possible follow-up studies.

02 PETROLEUM↗

Comparison of Two Multidisciplinary Optimization Strategies for Launch-Vehicle Design

The investigation focuses on development of a rapid multidisciplinary analysis and optimization capability for launch-vehicle design. Two multidisciplinary optimization strategies in which the analyses are integrated in different manners are implemented and evaluated for solution of a single-stage-to-orbit launch-vehicle design problem. Weights and sizing, propulsion, and trajectory issues are directly addressed in each optimization process. Additionally, the need to maintain a consistent vehicle model across the disciplines is discussed. Both solution strategies were shown to obtain similar solutions from two different starting points. These solutions suggests that a dual-fuel, single-stage-to-orbit vehicle with a dry weight of approximately 1.927 x 10(exp 5)lb, gross liftoff weight of 2.165 x 10(exp 6)lb, and length of 181 ft is attainable. A comparison of the two approaches demonstrates that treatment or disciplinary coupling has a direct effect on optimization convergence and the required computational effort. In comparison with the first solution strategy, which is of the general form typically used within the launch vehicle design community at present, the second optimization approach is shown to he 3-4 times more computationally efficient.

Braun, R. D.↗

Automatic Aircraft Structural Topology Generation for Multidisciplinary Optimization and Weight Estimation

An approach is proposed for the application of rapid generation of moderate-fidelity structural finite element models of air vehicle structures to allow more accurate weight estimation earlier in the vehicle design process. This should help to rapidly assess many structural layouts before the start of the preliminary design phase and eliminate weight penalties imposed when actual structure weights exceed those estimated during conceptual design. By defining the structural topology in a fully parametric manner, the structure can be mapped to arbitrary vehicle configurations being considered during conceptual design optimization. A demonstration of this process is shown for two sample aircraft wing designs.

Sensmeier, Mark D.↗

Rapid Assessment of Aircraft Structural Topologies for Multidisciplinary Optimization and Weight Estimation

Algorithms for rapid generation of moderate-fidelity structural finite element models of air vehicle structures to allow more accurate weight estimation earlier in the vehicle design process have been developed. Application of these algorithms should help to rapidly assess many structural layouts before the start of the preliminary design phase and eliminate weight penalties imposed when actual structure weights exceed those estimated during conceptual design. By defining the structural topology in a fully parametric manner, the structure can be mapped to arbitrary vehicle configurations being considered during conceptual design optimization. Recent enhancements to this approach include the porting of the algorithms to a platform-independent software language Python, and modifications to specifically consider morphing aircraft-type configurations. Two sample cases which illustrate these recent developments are presented.

Samareh, Jamshid A.↗

Multistage Stabilized Continuation for Indirect Optimal Control of Three-Dimensional Hypersonic Trajectories

This work presents the development of a multistaged stabilized continuation for the three-dimensional unpowered hypersonic trajectory planning problem using indirect optimal control methods. The stabilized continuation method is noniterative and guaranteed to terminate within a finite number of floating point operations, thereby making it well suited for onboard autonomous implementations. Here, we present a multistage formulation of the stabilized continuation scheme that involves starting with a “loose” integration tolerance during the first stage and ramping up toward a “strict” integration tolerance through subsequent stages. An important benefit of this approach is that even when the solution to the underlying optimal control problem is numerically unstable, such as with the hypersonic vehicle footprint generation problem, the stabilized continuation algorithm is shown to be successful in finding a solution while providing some additional insights into the underlying cause of the numerical instability.

33 ADVANCED PROPULSION SYSTEMS↗

Optimizing the lean hydrocarbon NO x trap: Sequential and dual-layer configurations

Vehicular emission control catalysts are ineffective in eliminating CO, hydrocarbons, and NO x during engine cold-start when exhaust temperatures are below 200 °C. In this study the performance of coupled low temperature NO x , n-C 12 H 26 (C 12 ), and C 3 H 6 trapping, release and conversion for a series of model Lean Hydrocarbon NO x Trap (LHCNT) catalysts are examined. Pd and Pt supported on small-pore (SSZ-13) and large-pore (BEA) zeolites are selected based on the performance during transient NO and C 12 uptake, release and conversion experiments. These catalysts are combined into sequential (Pt + Pd/BEA → Pd/SSZ-13; Pd/SSZ-13 → Pt + Pd/BEA) and dual-layer (Pt + Pd/BEA top, Pd/SSZ-13 bottom) configurations in an attempt to improve the trapping and conversion performance. While all three configurations trap between 75 and 100 μmolNO x /g-cat, the Pd/SSZ-13 → Pt + Pd/BEA sequential configuration is most effective in simultaneously trapping C 12 and NO in the presence of H 2 O, resulting in excellent NO and C 12 storage below 100 °C with release and/or conversion at or above 200 °C. For each configuration, C 12 oxidation lights-off below 300 °C and NO oxidation achieves ~35 % conversion in the absence of C 12 . Neither the presence of C 12 nor the order of the sequential configuration has a significant impact on NO uptake. C 12 significantly delays NO and NO 2 desorption to temperatures exceeding 300 °C. The more compact dual-layer catalyst is most effective in forming NO 2 as the release temperature lines up with the maximum NO conversion temperature but traps less C 12 than the sequential configurations. The addition of C 3 H 6 in the feed on the dual-layer catalyst leads to further delay in the NO x desorption as well as increased NO and C 12 conversion at high temperatures. Here, the overall findings provide guidance in the optimizing LHCNT configuration for realistic feeds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Machine Learning Framework for Error Compensation in Radiative Transfer Calculations

Radiative heat transfer influences the amount of heat flux transferred to the surface of the hypersonic vehicle, which is essential to evaluate the performance of thermal protection systems. The radiative heat flux is found to be computationally prohibitive while accounting for the variation in spatial, angular, and spectral domains. A new methodology has been recently developed to alleviate the cost of computation in the spectral domain by constructing flow-agnostic reduced-order models (ROMs). The developed spectral ROM databases provide grouping strategies that account for non-equilibrium absorption and emission as well as interaction between disparate species due to spectral overlap in associated radiative processes. However, the developed ROMs need to be optimized for a specific combination of interacting gas species and would need to re-calibrated in case individual species are added/omitted. In this work, we use various machine learning (ML) techniques to approximate the radiative intensities determined by a ROM optimized for a specific gas mixture. The ML model relies on the ROM databases developed for a single species which ignores any spectral overlap. Thus, radiation evaluation starts with a simple summation of radiative intensities predicted using these non-calibrated ROMs for the contributing species. The ML framework then provides a correction to account for the interplay in the frequency, i.e., emission of photons by one species and absorption by another, and yields mixture-specific radiation fields. Once trained on the individual ROM databases, the ML framework offers instantaneous corrections that serves as a time/cost effective alternative to the optimization of ROMs for a specific gas mixture. The ML framework is trained on both the high fidelity and ROM evaluated line of sight (LOS) data from Orion, Stardust, and FIRE II cases to obtain a general purpose correction model for earth re-entry scenarios when radiation contributions from both atomic nitrogen and atomic oxygen are considered. A geometric length scale parameter is used in the training process to account for errors introduced in the ROM databases as a consequence of high optical thickness. The efficacy of the ML framework is underscored through extensive analysis of train and test errors with respect to all the re-entry scenarios. The applicability of such an ML framework was further corroborated by embedding it in a state-of-the-art US3D - NERO system for determining the radiative heat flux transferred to the hypersonic vehicle surface.

Radiation↗

Inexact convex relaxations for AC optimal power flow: Towards AC feasibility

Convex relaxations of AC optimal power flow (AC-OPF) problems have attracted significant interest as in several instances they provably yield the global optimum to the original non-convex problem. If, however, the relaxation is inexact, the obtained solution is not AC-feasible. The quality of the obtained solution is essential for several practical applications of AC-OPF, but detailed analyses are lacking in existing literature. Here, this paper aims to cover this gap. We provide an in-depth investigation of the solution characteristics when convex relaxations are inexact, we assess the most promising AC feasibility recovery methods for large-scale systems, and we propose two new metrics that lead to a better understanding of the quality of the identified solutions. We perform a comprehensive assessment on 96 different test cases, ranging from 14 to 3120 buses, and we show the following: (i) Despite an optimality gap of less than 1%, several test cases still exhibit substantial distances to both AC feasibility and local optimality and the newly proposed metrics characterize these deviations. (ii) Penalization methods fail to recover an AC-feasible solution in 15 out of 45 test cases. (iii) The computational benefits of warm-starting non-convex solvers have significant variation, but a computational speedup exists in over 75% of cases.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Unsupervised learning-enabled pulsed infrared thermographic microscopy of subsurface defects in stainless steel

Metallic structures produced with laser powder bed fusion (LPBF) additive manufacturing method (AM) frequently contain microscopic porosity defects, with typical approximate size distribution from one to 100 microns. Presence of such defects could lead to premature failure of the structure. In principle, structural integrity assessment of LPBF metals can be accomplished with nondestructive evaluation (NDE). Pulsed infrared thermography (PIT) is a non-contact, one-sided NDE method that allows for imaging of internal defects in arbitrary size and shape metallic structures using heat transfer. PIT imaging is performed using compact instrumentation consisting of a flash lamp for deposition of a heat pulse, and a fast frame infrared (IR) camera for measuring surface temperature transients. However, limitations of imaging resolution with PIT include blurring due to heat diffusion, sensitivity limit of the IR camera. We demonstrate enhancement of PIT imaging capability with unsupervised learning (UL), which enables PIT microscopy of subsurface defects in high strength corrosion resistant stainless steel 316 alloy. PIT images were processed with UL spatial–temporal separation-based clustering segmentation (STSCS) algorithm, refined by morphology image processing methods to enhance visibility of defects. The STSCS algorithm starts with wavelet decomposition to spatially de-noise thermograms, followed by UL principal component analysis (PCA), fine-tuning optimization, and neural learning-based independent component analysis (ICA) algorithms to temporally compress de-noised thermograms. The compressed thermograms were further processed with UL-based graph thresholding K-means clustering algorithm for defects segmentation. The STSCS algorithm also includes online learning feature for efficient re-training of the model with new data. For this study, metallic specimens with calibrated microscopic flat bottom hole defects, with diameters in the range from 203 to 76 µm, were produced using electro discharge machining (EDM) drilling. While the raw thermograms do not show any material defects, using STSCS algorithm to process PIT images reveals defects as small as 101 µm in diameter. To the best of our knowledge, this is the smallest reported size of a sub-surface defect in a metal imaged with PIT, which demonstrates the PIT capability of detecting defects in the size range relevant to quality control requirements of LPBF-printed high-strength metals.

36 MATERIALS SCIENCE↗

Automated tabletop exfoliation and identification of monolayer graphene flakes

Over the past two decades, graphene has been intensively studied because of its remarkable mechanical, optical, and electronic properties. Initial studies were enabled by manual “Scotch Tape” exfoliation; nearly two decades later, this method is still widely used to obtain chemically pristine flakes of graphene and other 2D van der Waals materials. Unfortunately, the yield of large, pristine flakes with uniform thickness is inconsistent. Thus, significant time and effort are required to exfoliate and locate flakes suitable for fabricating multilayer van der Waals heterostructures. Here, we describe a relatively affordable tabletop device (the “eXfoliator”) that can reproducibly control key parameters and largely automate the exfoliation process. In a typical exfoliation run, the eXfoliator produces 3 or more large (≥ 400 μm 2 ) high-quality graphene monolayer flakes, allowing new users to produce such flakes at a rate comparable to manual exfoliation by an experienced user. Furthermore, we use an automated mapping system and a computer vision algorithm to locate candidate flakes. Our results provide a starting point for future research efforts to identify more precisely which parameters matter for the success of exfoliation and to optimize them.

47 OTHER INSTRUMENTATION↗

Visualizing Vehicle Acceleration and Braking Energy at Intersections along a Major Traffic Corridor

Automobiles approaching a controlled intersection need to brake and come to a full stop when the signal transitions from green to red, and the vehicle must later accelerate to normal speeds after the signal changes back to green. These stops and starts associated with normal signal changes lead to unnecessary energy consumption and vehicle emissions. Previous studies have revealed that the optimization of traffic intersections' signal controls and coordination facilitates smoother traffic flows with reduced stop-and-go driving, which can significantly reduce traffic congestion and unnecessary fuel waste. This paper presents an interactive visual analytics dashboard that allows transportation planners to explore and analyze energy consumption patterns resulting from temporally varying traffic signal phases at multiple intersections along a major transportation corridor using traffic simulation outputs. The visual dashboard is implemented as an accessible and responsive web application and employs a combination of visualization techniques to cover multiple aspects of vehicle acceleration and braking at multiple adjacent intersections along a corridor. The paper presents a case study of a simulated traffic scenario on the Shallowford Road traffic corridor located in Chattanooga, Tennessee to demonstrate the capability of the visual dashboard.

Xu, Haowen↗

Slicing Solutions for Wire Arc Additive Manufacturing

Both commercial and research applications of wire arc additive manufacturing (WAAM) have seen considerable growth in the additive manufacturing of metallic components. However, there remains a clear lack of a unified paradigm for toolpath generation when slicing parts for WAAM deposition. Existing toolpath generation options typically lack the appropriate features to account for all complexities of the WAAM process. This manuscript explores the key slicing challenges specific to toolpaths for WAAM geometry and pairs each consideration with multiple solutions to mitigate most negative effects on completed components. These challenges must be addressed to minimize voids, prevent bead collapse, and ensure deposited components accurately approximate the desired geometry. Slicing considerations are grouped into four general categories: geometric, process, thermal, and productivity. Geometric considerations are addressed with overhang compensation, corner-sharpening, and toolpath-smoothing features. Process considerations are addressed with start point configuration and controls for the bead lengths and end points. Thermal and productivity considerations are addressed with island optimization, multi-material printing, and connected insets. Finally, tools for the post-processing of generated G-code are explored. Overall, these solutions represent a critical set of slicing features used to improve generated toolpaths and the quality of the components deposited with those toolpaths.

36 MATERIALS SCIENCE↗

An explicit solution to the exoatmospheric powered flight guidance and trajectory optimization problem for rocket propelled vehicles

A derivation of an explicit solution to the two point boundary-value problem of exoatmospheric guidance and trajectory optimization is presented. Fixed initial conditions and continuous burn, multistage thrusting are assumed. Any number of end conditions from one to six (throttling is required in the case of six) can be satisfied in an explicit and practically optimal manner. The explicit equations converge for off nominal conditions such as engine failure, abort, target switch, etc. The self starting, predictor/corrector solution involves no Newton-Rhapson iterations, numerical integration, or first guess values, and converges rapidly if physically possible. A form of this algorithm has been chosen for onboard guidance, as well as real time and preflight ground targeting and trajectory shaping for the NASA Space Shuttle Program.

Jaggers, R. F.↗