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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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NASA NTRS1995

Integrated design and manufacturing for the high speed civil transport (a combined aerodynamics/propulsion optimization study)

This report documents the efforts of a Georgia Tech High Speed Civil Transport (HSCT) aerospace student design team in completing a design methodology demonstration under NASA's Advanced Design Program (ADP). Aerodynamic and propulsion analyses are integrated into the synthesis code FLOPS in order to improve its prediction accuracy. Executing the integrated product and process development (IPPD) methodology proposed at the Aerospace Systems Design Laboratory (ASDL), an improved sizing process is described followed by a combined aero-propulsion optimization, where the objective function, average yield per revenue passenger mile ($/RPM), is constrained by flight stability, noise, approach speed, and field length restrictions. Primary goals include successful demonstration of the application of the response surface methodolgy (RSM) to parameter design, introduction to higher fidelity disciplinary analysis than normally feasible at the conceptual and early preliminary level, and investigations of relationships between aerodynamic and propulsion design parameters and their effect on the objective function, $/RPM. A unique approach to aircraft synthesis is developed in which statistical methods, specifically design of experiments and the RSM, are used to more efficiently search the design space for optimum configurations. In particular, two uses of these techniques are demonstrated. First, response model equations are formed which represent complex analysis in the form of a regression polynomial. Next, a second regression equation is constructed, not for modeling purposes, but instead for the purpose of optimization at the system level. Such an optimization problem with the given tools normally would be difficult due to the need for hard connections between the various complex codes involved. The statistical methodology presents an alternative and is demonstrated via an example of aerodynamic modeling and planform optimization for a HSCT.

Baecher, Juergen↗
DOE OSTI2021

Utilizing ensemble learning for performance and power modeling and improvement of parallel cancer deep learning CANDLE benchmarks

Abstract Machine learning (ML) continues to grow in importance across nearly all domains in modeling to learn from data. Often a tradeoff exists between a model's ability to minimize bias and variance. In this article, we utilize ensemble learning to combine linear, nonlinear, and tree‐/rule‐based ML methods to cope with the bias‐variance tradeoff and result in more accurate models. We use the datasets collected for two parallel cancer deep learning CANDLE benchmarks, NT3 and P1B2, to build performance and power models based on hardware performance counters using single‐object and multiple‐objects ensemble learning to identify the most important counters for improvement on the Cray XC40 Theta at Argonne National Laboratory. Based on the insights from these models, we improve the performance and energy of P1B2 and NT3 by optimizing the deep learning environments TensorFlow, Keras, Horovod, and Python under the huge page size of 8 MB. Experimental results show that ensemble learning not only produces more accurate models but also provides more robust performance counter ranking. We achieve up to 61.15% performance improvement and up to 62.58% energy saving for P1B2 and up to 55.81% performance improvement and up to 52.60% energy saving for NT3 on up to 24,576 cores.

Wu, Xingfu↗
DOE OSTI2017

ELSI: A unified software interface for Kohn–Sham electronic structure solvers

Solving the electronic structure from a generalized or standard eigenproblem is often the bottleneck in large scale calculations based on Kohn-Sham density-functional theory. This problem must be addressed by essentially all current electronic structure codes, based on similar matrix expressions, and by high-performance computation. We here present a unified software interface, ELSI, to access different strategies that address the Kohn-Sham eigenvalue problem. Currently supported algorithms include the dense generalized eigensolver library ELPA, the orbital minimization method implemented in libOMM, and the pole expansion and selected inversion (PEXSI) approach with lower computational complexity for semilocal density functionals. The ELSI interface aims to simplify the implementation and optimal use of the different strategies, by offering (a) a unified software framework designed for the electronic structure solvers in Kohn-Sham density-functional theory; (b) reasonable default parameters for a chosen solver; (c) automatic conversion between input and internal working matrix formats, and in the future (d) recommendation of the optimal solver depending on the specific problem. As a result, comparative benchmarks are shown for system sizes up to 11,520 atoms (172,800 basis functions) on distributed memory supercomputing architectures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Synthesis and characterization of methyl esters from non-edible plant species yellow oleander oil, using magnesium oxide (MgO) nano-catalyst

Highlights: • Introduction of new non-edible oil source for bioenergy industry. • Nano-particles MgO used as a heterogeneous catalyst. • Maximum conversion yield at optimum level achieved 93.1%. • Fuel properties were matched and found similar to ASTM standards. - Abstract: Synthesis and characterization of methyl esters from non-edible oil sources provide a distinctive and sustainable approach towards sustainable energy and the cleaner environment, in general. This study aims the synthesis of methyl esters from non-edible plant species yellow oleander seeds oil. The transesterification process was carried for the synthesis of methyl esters, using heterogeneous nano-catalyst magnesium oxide (MgO). A well known co-precipitation method was used for the synthesis of MgO nano-catalyst. The application of MgO nano-catalyst showed the maximum conversion (93.1%) of triacylglycerols to methyl esters. Different parameters affecting the conversion percentage; alcohol to oil molar ratio, temperature and catalyst concentrations were checked and optimized, accordingly. The optimum conditions for the maximum conversion noted; 1:5 oil to methanol molar ratio at 90 °C, using 0.2% (w/w) MgO nano-catalyst. The various analytical techniques; XRD, SEM-EDX and TEM-EDS spectroscopes were used to check out the nano-particle morphology and crystalline size, accordingly while, the FTIR, GC–MS & NMR were used to quantify and determine the structural measurements of synthesized methyl esters. The fuel properties of oleander methyl esters papered sample were checked, compared and found within accordance to the ASTM standards.

09 BIOMASS FUELS↗
DOE OSTI2019

Hybridizing Classifiers and Collection Systems to Maximize Intelligence and Minimize Uncertainty in National Security Data Analytics Applications

There are numerous applications that combine data collected from sensors with machine-learning based classification models to predict the type of event or objects observed. Both the collection of the data itself and the classification models can be tuned for optimal performance, but we hypothesize that additional gains can be realized by jointly assessing both factors together. Through this research, we used a seismic event dataset and two neural network classification models that issued probabilistic predictions on each event to determine whether it was an earthquake or a quarry blast. Real world applications will have constraints on data collection, perhaps in terms of a budget for the number of sensors or on where, when, or how data can be collected. We mimicked such constraints by creating subnetworks of sensors with both size and locational constraints. We compare different methods of determining the set of sensors in each subnetwork in terms of their predictive accuracy and the number of events that they observe overall. Additionally, we take the classifiers into account, treating them both as black-box models and testing out various ways of combining predictions among models and among the set of sensors that observe any given event. We find that comparable overall performance can be seen with less than half the number of sensors in the full network. Additionally, a voting scheme that uses the average confidence across the sensors for a given event shows improved predictive accuracy across nearly all subnetworks. Lastly, locational constraints matter, but sometimes in unintuitive ways, as better-performing sensors may be chosen instead of the ones excluded based on location. This being a short-term research effort, we offer a lengthy discussion on interesting next-steps and ties to other ongoing research efforts that we did not have time to pursue. These include a detailed analysis of the subnetwork performance broken down by event type, specific location, and model confidence. This project also included a Campus Executive research partnership with Texas A&M University. Through this, we worked with a professor and student to study information gain for UAV routing. This was an alternative way of looking at the similar problem space that includes sensor operation for data collection and the resulting benefit to be gained from it. This work is described in an Appendix.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

High-throughput combinatorial approach expedites the synthesis of a lead-free relaxor ferroelectric system

Developing novel lead-free ferroelectric materials is crucial for next-generation microelectronic technologies that are energy efficient and environment friendly. However, materials discovery and property optimization are typically time-consuming due to the limited throughput of traditional synthesis methods. In this work, we use a high-throughput combinatorial synthesis approach to fabricate lead-free ferroelectric superlattices and solid solutions of (Ba 0.7 Ca 0.3 )TiO 3 (BCT) and Ba(Zr 0.2 Ti 0.8 )O 3 (BZT) phases with continuous variation of composition and layer thickness. High-resolution x-ray diffraction (XRD) and analytical scanning transmission electron microscopy (STEM) demonstrate high film quality and well-controlled compositional gradients. Ferroelectric and dielectric property measurements identify the “optimal property point” achieved at the composition of 48BZT–52BCT. Displacement vector maps reveal that ferroelectric domain sizes are tunable by varying {BCT–BZT} N superlattice geometry. This high-throughput synthesis approach can be applied to many other material systems to expedite new materials discovery and properties optimization, allowing for the exploration of a large area of phase space within a single growth.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Adaptive primal–dual control for distributed energy resource management

With the increased adoption of distributed energy resources (DERs) in distribution networks, their coordinated control with a DER management system (DERMS) that provides grid services (e.g., voltage regulation, virtual power plant) is becoming more necessary. One particular type of DERMS using primal–dual control has recently been found to be very effective at providing multiple grid services among an aggregation of DERs; however, the main parameter, the primal–dual step size, must be manually tuned for the DERMS to be effective, which can take a considerable amount of engineering time and labor. To this end, we design a simple method that self-tunes the step size(s) and adapts it to changing system conditions. Additionally, it gives the DER management operator the ability to prioritize among possibly competing grid services. Here we evaluate the automatic tuning method on a simulation model of a real-world feeder in Colorado with data obtained from an electric utility. Through a variety of scenarios, we demonstrate that the DERMS with automatically and adaptively tuned step sizes provides higher-quality grid services than a DERMS with a manually tuned step size.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Explicit physics-informed neural networks for nonlinear closure: The case of transport in tissues

In upscaling methods, closures for nonlinear problems present a well-known challenge. While a number of theoretical methods have been proposed for handling such closures, nonlinearities still remain a significant obstacle for many problems. In this work, we use a combination of formal upscaling and data-driven machine learning for explicitly closing a nonlinear transport and reaction process in multiscale tissues. The classical effectiveness factor model is used to formulate the macroscale reaction kinetics. We train a multilayer perceptron network using training data generated by direct numerical simulations over microscale examples. Once trained, the network is used in an algorithm for numerically solving the upscaled (coarse-grained) differential equation describing mass transport and reaction in two example tissues. The network is described as being explicit in the sense that the network is trained using macroscale concentrations and gradients of concentration as components of the feature space rather than incorporating them as part of a constraint in the optimization process. Network training and solutions to the macroscale transport equations were computed for two different tissues. The two tissue types (brain and liver) exhibit markedly different geometrical complexity and spatial scale (cell size and sample size). The upscaled solutions for the average concentration are compared with numerical solutions derived from the microscale concentration fields by a posteriori averaging. There are three outcomes of this work of particular note. 1) Our overall approach results in an upscaled nonlinear PDE. The PDE is closed using a neural network, and our approach results in the definition of the classical effectiveness factor for effecting closure. 2) We identify particular source terms for the closure problem that are important for representing the structure of the closure. These source terms involve macroscale concentrations and their gradients. We adopt these source terms to use as explicit features in the learning algorithm. We find the trained networks that include the macroscale source terms generate models that are able to predict the correction factor with increased fidelity over those that do not. 3) We find that the trained network exhibits good generalizability, and it is able to predict the effectiveness factor with high fidelity for realistically-structured tissues despite the significantly different scale and geometrical complexity of the two example tissue types. This latter result emphasizes our purposeful connection between conventional averaging methods with the use of machine learning for closure; this contrasts with some machine learning methods for upscaling where the exact form of the macroscale equation remains unknown.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Spatial resolution of different discretizations over long-time for the Dirac equation with small potentials

In this report we compare the long-time error bounds and spatial resolution of finite difference methods with different spatial discretizations for the Dirac equation with small electromagnetic potentials characterized by $\varepsilon \in (0, 1]$ a dimensionless parameter. We begin with the simple and widely used finite difference time domain (FDTD) methods, and establish rigorous error bounds of them, which are valid up to the time at $O(1/\varepsilon)$. In the error estimates, we pay particular attention to how the errors depend explicitly on the mesh size $h$ and time step $\tau$ as well as the small parameter $\varepsilon$. Based on the results, in order to obtain "correct" numerical solutions up to the time at $O(1/\varepsilon)$, the $\varepsilon$-scalability (or meshing strategy requirement) of the FDTD methods should be taken as $h = O(\varepsilon^{1/2})$ and $\tau = O(\varepsilon^{1/2})$. To improve the spatial resolution capacity, we apply the Fourier spectral method to discretize the Dirac equation in space. Error bounds of the resulting finite difference Fourier pseudospectral (FDFP) methods show that they exhibit uniform spatial errors in the long-time regime, which are optimal in space as suggested by the Shannon's sampling theorem. Extensive numerical results are reported to confirm the error bounds and demonstrate that they are sharp.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Drug discovery efforts at George Mason University

With over 39,000 students, and research expenditures in excess of $200 million, George Mason University (GMU) is the largest R1 (Carnegie Classification of very high research activity) university in Virginia. Mason scientists have been involved in the discovery and development of novel diagnostics and therapeutics in areas as diverse as infectious diseases and cancer. Below are highlights of the efforts being led by Mason researchers in the drug discovery arena. To enable targeted cellular delivery, and non-biomedical applications, Veneziano and colleagues have developed a synthesis strategy that enables the design of self-assembling DNA nanoparticles (DNA origami) with prescribed shape and size in the 10 to 100 nm range. The nanoparticles can be loaded with molecules of interest such as drugs, proteins and peptides, and are a promising new addition to the drug delivery platforms currently in use. The investigators also recently used the DNA origami nanoparticles to fine tune the spatial presentation of immunogens to study the impact on B cell activation. These studies are an important step towards the rational design of vaccines for a variety of infectious agents. To elucidate the parameters for optimizing the delivery efficiency of lipid nanoparticles (LNPs), Buschmann, Paige and colleagues have devised methods for predicting and experimentally validating the pKa of LNPs based on the structure of the ionizable lipids used to formulate the LNPs. These studies may pave the way for the development of new LNP delivery vehicles that have reduced systemic distribution and improved endosomal release of their cargo post administration. To better understand protein-protein interactions and identify potential drug targets that disrupt such interactions, Luchini and colleagues have developed a methodology that identifies contact points between proteins using small molecule dyes. The dye molecules noncovalently bind to the accessible surfaces of a protein complex with very high affinity, but are excluded from contact regions. When the complex is denatured and digested with trypsin, the exposed regions covered by the dye do not get cleaved by the enzyme, whereas the contact points are digested. The resulting fragments can then be identified using mass spectrometry. The data generated can serve as the basis for designing small molecules and peptides that can disrupt the formation of protein complexes involved in disease processes. For example, using peptides based on the interleukin 1 receptor accessory protein (IL-1RAcP), Luchini, Liotta, Paige and colleagues disrupted the formation of IL-1/IL-R/IL-1RAcP complex and demonstrated that the inhibition of complex formation reduced the inflammatory response to IL-1B. Working on the discovery of novel antimicrobial agents, Bishop, van Hoek and colleagues have discovered a number of antimicrobial peptides from reptiles and other species. DRGN-1, is a synthetic peptide based on a histone H1-derived peptide that they had identified from Komodo Dragon plasma. DRGN-1 was shown to disrupt bacterial biofilms and promote wound healing in an animal model. The peptide, along with others, is being developed and tested in preclinical studies. Other research by van Hoek and colleagues focuses on in silico antimicrobial peptide discovery, screening of small molecules for antibacterial properties, as well as assessment of diffusible signal factors (DFS) as future therapeutics. The above examples provide insight into the cutting-edge studies undertaken by GMU scientists to develop novel methodologies and platform technologies important to drug discovery.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Image processing tools for petabyte-scale light sheet microscopy data

Light sheet microscopy is a powerful technique for high-speed three-dimensional imaging of subcellular dynamics and large biological specimens. However, it often generates datasets ranging from hundreds of gigabytes to petabytes in size for a single experiment. Conventional computational tools process such images far slower than the time to acquire them and often fail outright due to memory limitations. To address these challenges, we present PetaKit5D, a scalable software solution for efficient petabyte-scale light sheet image processing. This software incorporates a suite of commonly used processing tools that are optimized for memory and performance. Notable advancements include rapid image readers and writers, fast and memory-efficient geometric transformations, high-performance Richardson–Lucy deconvolution and scalable Zarr-based stitching. These features outperform state-of-the-art methods by over one order of magnitude, enabling the processing of petabyte-scale image data at the full teravoxel rates of modern imaging cameras. The software opens new avenues for biological discoveries through large-scale imaging experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Simulation Evaluation of a Large-Scale Implementation of Virtual-Phase Link-Based Model Predictive Control

Traffic congestion is a serious problem in the US, and traffic signal control is one of the effective solutions to congestion. Previous research on model predictive control (MPC)-based traffic signal control showed substantial benefits over conventional methods. This study focused on implementing MPC over a large-scale network with complex intersections and the impact of cycle length, network size, and imperfect state estimation on performances. This study implemented a virtual phase link (VPL)-based model predictive control method which used the number of vehicles in each VPL as input state variables and was suitable for National Electrical Manufacturing Association (NEMA) ring-barrier control. To test the impact of network size, the performance of distributed MPC (36 intersections in the network are divided into five subnetworks) was compared with that of MPC over the full network for a set of cycle lengths. To test the impact of imperfect state estimation, we synthetically infused estimation error and developed two scenarios, MPC-error and MPC-error narrow, which had higher and lower estimation errors, respectively. The performance of these MPC methods was compared with that of the existing time-of-day (TOD) method and an offline method that used Webster's method for split and MULTIBAND for cycle length and offset optimization. Trajectory and linkwise signal performance measures were collected from the simulation to evaluate performance. The distributed MPC method with perfect state estimation had the lowest delay and highest energy efficiency of all the methods. The performance of MPC decreased as the prediction inaccuracy increased. MPC-error had 7% and 11% more delay than MPC-error narrow in the morning and evening peaks, respectively. Overall, simulation results suggest that even with imperfect state estimation, MPC methods will outperform offline methods significantly.

large-scale simulation↗
DOE OSTI2025

Strategic Placement and Sizing of Distributed Generation for Resilience Enhancement of Distribution Grids With Microgrid Formation

The rise in frequency and severity of extreme weather events highlights the need for resilient power distribution networks. Microgrids can help improve the resilience of distribution grids by providing continuous power supply using local distribution generation (DG) when the distribution grid fails. In this paper, we propose an approach for optimal placement and sizing of DG to form multiple microgrids throughout the distribution network by restoration actions such as switching operations in case of distribution grid outages caused by extreme weather events. Considering the randomness of damaged distribution lines, the DG placement and sizing problem is formulated as a two-stage stochastic mixed-integer program, with the first stage determining the placement and size of DG, and the second stage focusing on minimizing the amount of load shedding through network restoration and microgrid formations for each scenario. Due to the large number of scenarios, the sample average approximation (SAA) method is employed to solve the problem. The results of case studies on a modified IEEE 33 bus distribution grid demonstrate the effectiveness of the proposed DG placement and sizing strategy in improving the resilience of distribution grids by allowing the formation of multiple microgrids. In addition, the robustness and accuracy of the SAA method are validated through various case studies.

Distributed generation planning↗
DOE OSTI2025

Monitoring Sulfuric Acid and Temperature Using Raman Spectroscopy and Multivariate Chemometrics

Multivariate regression models were optimized for the quantification of sulfuric acid (H 2 SO 4 ) [0–8 M] and temperature (20 °C–80 °C) in the presence of ammonium sulfate ((NH 4 ) 2 SO 4 [0–0.6 M]) using Raman spectroscopy. Optical vibrational spectroscopy is a useful nondestructive technique for the in situ analysis of complex chemical systems notoriously difficult to monitor in situ and in real-time. Multivariate analysis, a chemometrics method, can be paired with these nondestructive optical methods for determining analyte concentration and speciation in complex solutions, such as dissociated species in polyprotic acids, e.g., H 2 SO 4 . The effect of temperature is often overlooked although it can have a major influence on speciation and the corresponding Raman spectra. Here, in this study, partial least squares regression models were optimized for the quantification of H 2 SO 4 and its two deprotonated forms as a function of temperature. Measuring bisulfate as a function of temperature is particularly challenging owing to changes in the second dissociation constant. A designed training set effectively minimized the sample set size and trained a robust predictive model with percent root mean square error of <3% for H 2 SO 4 . The practical strategy employed here was demonstrated to be effective for building chemometric models that directly account for dynamic temperatures with static samples and is shown to be amenable to flow cell analysis applications with a simple calibration transfer for process monitoring applications.

D-optimal design↗
NASA NTRS1989

A survey on the structured singular value

The structured singular value, U, is an important linear algebra tool to study a class of matrix perturbation problems. It is useful for analyzing the robustness of stability and performance of uncertain, (nominally) linear systems. Computation of (M) is difficult, and usually, upper and lower bounds are all that can be reliably computed. Upper bounds give conservative estimates of the sizes of allowable perturbations. The maximum singular value of a matrix M is an upper bound for (M). As an upper bound, it can be improved by finding a transformations to the data (i.e. M) which do not change the structured singular value, but do reduce the maximum singular value. Typically, upper bound algorithms involve searches over sets of transformations to yield the tightest bound. Lower bound algorithms are intelligent searches for minimum-norm solutions to multivariable polynomial equations, and are based on various optimality conditions that hold at the global (and, unfortunately, some local) minima. The current methods to compute both of these types of bounds are reviewed. Theoretical justification and extensive numerical experience with the various algorithms are covered.

Packard, Andy↗
NASA NTRS2011

Technique for Configuring an Actively Cooled Thermal Shield in a Flight System

Broad area cooling shields are a mass-efficient alternative to conductively cooled thermal radiation shielding. The shield would actively intercept a large portion of incident thermal radiation and transport the heat away using cryogenic helium gas. The design concept consists of a conductive and conformable surface that maximizes heat transfer and formability. Broad Area Cooled (BAC) shields could potentially provide considerable mass savings for spaceflight applications by eliminating the need for a rigid thermal radiation shield for cryogen tanks. The BAC consists of a network of capillary tubes that are thermally connected to a conductive shield material. Chilled helium gas is circulated through the network and transports unwanted heat away from the cryogen tanks. The cryogenic helium gas is pumped and chilled simultaneously using a specialized pulse-tube cryocooler, which further improves the mass efficiency of the system. By reducing the thermal environment temperature from 300 to 100 K, the radiative heat load on a cryogen tank could be reduced by an order of magnitude. For a cryogenic liquid propellant scenario of oxygen and hydrogen, the boiloff of hydrogen would be significantly reduced and completely eliminated for oxygen. A major challenge in implementing this technology on large tanks is that the BAC system must be easily scalable from lab demonstrations to full-scale missions. Also, the BAC shield must be conformable to complex shapes like spheres without losing the ability to maintain constant temperature throughout. The initial design maximizes thermal conductivity between the capillary tube and the conductive radiation shielding by using thin, corrugated aluminum foil with the tube running transverse to the folds. This configuration has the added benefit of enabling the foil to stretch and contract longitudinally. This allows the BAC to conform to the complex curvature of a cryogen tank, which is key to its success. To demonstrate a BAC shield system with minimal impact to current cryogen tank designs, the shielding must be applied after the final assembly of the tank and supporting structure. One method is to pre-fabricate the shield in long strips. A spool of corrugated aluminum foil with a thermally sunk aluminum capillary running through the center could then be simply wound around the cryogen tanks and encapsulated within the multi-layer insulation (MLI) blanket. Then, on orbit, the BAC would intercept thermal radiation coming in through the MLI and transport it away from the cryogen tanks. An optimization of the design could be done to take into account mass savings from thinner MLI blankets, eliminating solid thermal shields, and ultimately, a reduction in the required cryogen tank size.

Barkfknecht, Peter↗
NASA NTRS1989

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.↗
NASA NTRS1984

Structural optimization of large ocean-going structures

Ocean-going vehicles and platforms are among the largest structures in the world and are subjected to relatively harsh conditions of motions and loads. Some of them, such as semi-submersible platforms, are a relatively new type of structure and hence there is no formal, well evolved and established structural design code as there is for more traditional structures. More recently, efforts have also been made to develop a design method of this type for ships and other ocean structures. One of the many advantages of a rationally based design method is versatility; it can be used for structures that have widely differing purposes, measures of merit, shapes and sizes. The purpose is to describe a rationally based design method that has been developed within the field of ocean structures, in order that persons dealing with other types of structure can judge whether and to what extent its various features may be useful for those other types. Also, even though some features may not be applicable they might stimulate some useful ideas.

Hughes, O. F.↗