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NASA NTRS1975

A random search algorithm for laboratory computers

The small laboratory computer is ideal for experimental control and data acquisition. Postexperimental data processing is often performed on large computers because of the availability of sophisticated programs, but costs and data compatibility are negative factors. Parameter optimization can be accomplished on the small computer, offering ease of programming, data compatibility, and low cost. A previously proposed random-search algorithm ('random creep') was found to be very slow in convergence. A method is proposed (the 'random leap' algorithm) which starts in a global search mode and automatically adjusts step size to speed convergence. A FORTRAN executive program for the random-leap algorithm is presented which calls a user-supplied function subroutine. An example of a function subroutine is given which calculates maximum-likelihood estimates of receiver operating-characteristic parameters from binary response data. Other applications in parameter estimation, generalized least squares, and matrix inversion are discussed.

Curry, R. E.↗

NASA NTRS1999

New Approaches to HSCT Multidisciplinary Design and Optimization

New approaches to MDO have been developed and demonstrated during this project on a particularly challenging aeronautics problem- HSCT Aeroelastic Wing Design. To tackle this problem required the integration of resources and collaboration from three Georgia Tech laboratories: ASDL, SDL, and PPRL, along with close coordination and participation from industry. Its success can also be contributed to the close interaction and involvement of fellows from the NASA Multidisciplinary Analysis and Optimization (MAO) program, which was going on in parallel, and provided additional resources to work the very complex, multidisciplinary problem, along with the methods being developed. The development of the Integrated Design Engineering Simulator (IDES) and its initial demonstration is a necessary first step in transitioning the methods and tools developed to larger industrial sized problems of interest. It also provides a framework for the implementation and demonstration of the methodology. Attachment: Appendix A - List of publications. Appendix B - Year 1 report. Appendix C - Year 2 report. Appendix D - Year 3 report. Appendix E - accompanying CDROM.

Schrage, Daniel P.↗

NASA NTRS2000

Adjoint Techniques for Topology Optimization of Structures Under Damage Conditions

The objective of this cooperative agreement was to seek computationally efficient ways to optimize aerospace structures subject to damage tolerance criteria. Optimization was to involve sizing as well as topology optimization. The work was done in collaboration with Steve Scotti, Chauncey Wu and Joanne Walsh at the NASA Langley Research Center. Computation of constraint sensitivity is normally the most time-consuming step of an optimization procedure. The cooperative work first focused on this issue and implemented the adjoint method of sensitivity computation (Haftka and Gurdal, 1992) in an optimization code (runstream) written in Engineering Analysis Language (EAL). The method was implemented both for bar and plate elements including buckling sensitivity for the latter. Lumping of constraints was investigated as a means to reduce the computational cost. Adjoint sensitivity computation was developed and implemented for lumped stress and buckling constraints. Cost of the direct method and the adjoint method was compared for various structures with and without lumping. The results were reported in two papers (Akgun et al., 1998a and 1999). It is desirable to optimize topology of an aerospace structure subject to a large number of damage scenarios so that a damage tolerant structure is obtained. Including damage scenarios in the design procedure is critical in order to avoid large mass penalties at later stages (Haftka et al., 1983). A common method for topology optimization is that of compliance minimization (Bendsoe, 1995) which has not been used for damage tolerant design. In the present work, topology optimization is treated as a conventional problem aiming to minimize the weight subject to stress constraints. Multiple damage configurations (scenarios) are considered. Each configuration has its own structural stiffness matrix and, normally, requires factoring of the matrix and solution of the system of equations. Damage that is expected to be tolerated is local and represents a small change in the stiffness matrix compared to the baseline (undamaged) structure. The exact solution to a slightly modified set of equations can be obtained from the baseline solution economically without actually solving the modified system.. Shennan-Morrison-Woodbury (SMW) formulas are matrix update formulas that allow this (Akgun et al., 1998b). SMW formulas were therefore used here to compute adjoint displacements for sensitivity computation and structural displacements in damaged configurations.

Akgun, Mehmet A.↗

NASA NTRS1999

Optimization of Aerospace Structure Subject to Damage Tolerance Criteria

The objective of this cooperative agreement was to seek computationally efficient ways to optimize aerospace structures subject to damage tolerance criteria. Optimization was to involve sizing as well as topology optimization. The work was done in collaboration with Steve Scotti, Chauncey Wu and Joanne Walsh at the NASA Langley Research Center. Computation of constraint sensitivity is normally the most time-consuming step of an optimization procedure. The cooperative work first focused on this issue and implemented the adjoint method of sensitivity computation in an optimization code (runstream) written in Engineering Analysis Language (EAL). The method was implemented both for bar and plate elements including buckling sensitivity for the latter. Lumping of constraints was investigated as a means to reduce the computational cost. Adjoint sensitivity computation was developed and implemented for lumped stress and buckling constraints. Cost of the direct method and the adjoint method was compared for various structures with and without lumping. The results were reported in two papers. It is desirable to optimize topology of an aerospace structure subject to a large number of damage scenarios so that a damage tolerant structure is obtained. Including damage scenarios in the design procedure is critical in order to avoid large mass penalties at later stages. A common method for topology optimization is that of compliance minimization which has not been used for damage tolerant design. In the present work, topology optimization is treated as a conventional problem aiming to minimize the weight subject to stress constraints. Multiple damage configurations (scenarios) are considered. Each configuration has its own structural stiffness matrix and, normally, requires factoring of the matrix and solution of the system of equations. Damage that is expected to be tolerated is local and represents a small change in the stiffness matrix compared to the baseline (undamaged) structure. The exact solution to a slightly modified set of equations can be obtained from the baseline solution economically without actually solving the modified system. Sherrnan-Morrison-Woodbury (SMW) formulas are matrix update formulas that allow this. SMW formulas were therefore used here to compute adjoint displacements for sensitivity computation and structural displacements in damaged configurations.

Akgun, Mehmet A.↗

NASA NTRSDate not supplied

Computationally Guided Development of Components for High Energy Density Solid-State Lithium-Sulfur Batteries

All electric vertical take-off and landing vehicles (eVTOL) for urban air mobility (UAM) concepts face numerous challenging technical barriers before their introduction into the consumer marketplace. The most challenging of these technical barriers to overcome is developing an energy storage system capable of meeting the rigorous aerospace safety and performance criteria1. The performance metrics for eVTOL craft, such as specific energy, specific power, and safety, exceed those of electric automobiles by a factor of two to four. Current state-of-the-art (SOA) lithium-ion batteries are incapable of meeting the key performance criteria of energy and safety for eVTOL. Therefore, next generation advanced chemistries and designs must be developed to meet required performance metrics for electric aviation2. Beyond lithium-ion chemistries, such as lithium-sulfur, show promise in their high energy, while limitations exist in their power and cyclability due to low electrical conductivity and high intermediate solubility in organic liquid electrolytes. Several strategies to overcome the low electrical conductivity involve the use of selenium as a dopant in the active sulfur material, along with the incorporation of 2-dimensional electron-conducting holey-graphene to improve the composite cathodes electronic conductivity. Furthermore, combining this chemistry with a solid-electrolyte avoids the components’ dissolution issues3. However, the development of composite solid-state cathodes is non-trivial as several components must be intimately mixed so that the active component has sufficient access to both electrons and lithium ions to undergo full electrochemical conversion. Mathematical modeling of battery components can assist experimental design through a robust and rigorous combination of computational modeling techniques covering multiple length scales. The objective is to leverage modern computational materials methods combined with battery multiphysics tools to develop radically advanced compatible cathode and electrolyte materials, build and test solid state lithium-sulfur cells and packs. A NASA-based cross-organizational team of high-powered experts combined integrated computational predictive modeling, fundamental chemistry analysis, advanced material science, and battery cell development to tackle this very challenging, multidisciplinary problem. This presentation will show a multiscale computational modeling approach that has produced a novel particle dynamics method called Solid Electrolyte Sphere Approximation Model (SESAM). SESAM modeling targets the 1-10 µm scale structures and provides electromechanical and grain interactions for predictive design guidelines for the manufacturing of solid-state components. Parameters such as particle size and volume fraction of the constituent materials were modeled and experimentally fabricated to optimize electrochemical performance through improved microstructure design. Experimental feedback was provided through ionic and electronic conductivity assessment and structural analysis of developed materials and cell components.

battery↗

NASA NTRS2002

Very Large Scale Optimization

The purpose of this research under the NASA Small Business Innovative Research program was to develop algorithms and associated software to solve very large nonlinear, constrained optimization tasks. Key issues included efficiency, reliability, memory, and gradient calculation requirements. This report describes the general optimization problem, ten candidate methods, and detailed evaluations of four candidates. The algorithm chosen for final development is a modern recreation of a 1960s external penalty function method that uses very limited computer memory and computational time. Although of lower efficiency, the new method can solve problems orders of magnitude larger than current methods. The resulting BIGDOT software has been demonstrated on problems with 50,000 variables and about 50,000 active constraints. For unconstrained optimization, it has solved a problem in excess of 135,000 variables. The method includes a technique for solving discrete variable problems that finds a "good" design, although a theoretical optimum cannot be guaranteed. It is very scalable in that the number of function and gradient evaluations does not change significantly with increased problem size. Test cases are provided to demonstrate the efficiency and reliability of the methods and software.

Vanderplaats, Garrett↗

NASA NTRS1994

A parametric sensitivity study for single-stage-to-orbit hypersonic vehicles using trajectory optimization

The class of hypersonic vehicle configurations with single stage-to-orbit (SSTO) capability reflect highly integrated airframe and propulsion systems. These designs are also known to exhibit a large degree of interaction between the airframe and engine dynamics. Consequently, even simplified hypersonic models are characterized by tightly coupled nonlinear equations of motion. In addition, hypersonic SSTO vehicles present a major system design challenge; the vehicle's overall mission performance is a function of its subsystem efficiencies including structural, aerodynamic, propulsive, and operational. Further, all subsystem efficiencies are interrelated, hence, independent optimization of the subsystems is not likely to lead to an optimum design. Thus, it is desired to know the effect of various subsystem efficiencies on overall mission performance. For the purposes of this analysis, mission performance will be measured in terms of the payload weight inserted into orbit. In this report, a trajectory optimization problem is formulated for a generic hypersonic lifting body for a specified orbit-injection mission. A solution method is outlined, and results are detailed for the generic vehicle, referred to as the baseline model. After evaluating the performance of the baseline model, a sensitivity study is presented to determine the effect of various subsystem efficiencies on mission performance. This consists of performing a parametric analysis of the basic design parameters, generating a matrix of configurations, and determining the mission performance of each configuration. Also, the performance loss due to constraining the total head load experienced by the vehicle is evaluated. The key results from this analysis include the formulation of the sizing problem for this vehicle class using trajectory optimization, characteristics of the optimal trajectories, and the subsystem design sensitivities.

Lovell, T. Alan↗

NASA NTRS1984

A nonlinear programming method for system design with results that have been implemented

A general nonlinear programming algorithm (NICO) is discussed. An academic optimization example is given. The NICO multi-input, multi-output control system design is discussed. NICO applications relative to launch vehicle autopilot design, space shuttle static balance, transient response criteria in the design of a reentry vehicle control system, and waterjet propulsion and lift system components sized to a large surface effect ship are noted.

Hauser, F.↗

NASA NTRS1974

Optimal aeroelastic design of an oblique wing structure

A procedure is presented for determining the optimal cover panel thickness of a wing structure to meet specified strength and static aeroelastic divergence requirements for minimum weight. Efficient reanalysis techniques using discrete structural and aerodynamic methods are used in conjunction with redesign algorithms driven by optimality criteria. The optimality conditions for the divergence constraint are established, and expressions are obtained for derivatives of the dynamic pressure at divergence with respect to design variables. The procedure is applied to an oblique wing aircraft where strength and stiffness are critical design considerations for sizing the cover thickness of the wing structure.

Gwin, L. B.↗

NASA NTRS2015

Under-Track CFD-Based Shape Optimization for a Low-Boom Demonstrator Concept

The detailed outer mold line shaping of a Mach 1.6, demonstrator-sized low-boom concept is presented. Cruise trim is incorporated a priori as part of the shaping objective, using an equivalent-area-based approach. Design work is performed using a gradient-driven optimization framework that incorporates a three-dimensional, nonlinear flow solver, a parametric geometry modeler, and sensitivities derived using the adjoint method. The shaping effort is focused on reducing the under-track sonic boom level using an inverse design approach, while simultaneously satisfying the trim requirement. Conceptual-level geometric constraints are incorporated in the optimization process, including the internal layout of fuel tanks, landing gear, engine, and crew station. Details of the model parameterization and design process are documented for both flow-through and powered states, and the performance of these optimized vehicles presented in terms of inviscid L/D, trim state, pressures in the near-field and at the ground, and predicted sonic boom loudness.

Wintzer, Mathias↗

NASA NTRS2011

Estimated Accuracy of Three Common Trajectory Statistical Methods

Three well-known trajectory statistical methods (TSMs), namely concentration field (CF), concentration weighted trajectory (CWT), and potential source contribution function (PSCF) methods were tested using known sources and artificially generated data sets to determine the ability of TSMs to reproduce spatial distribution of the sources. In the works by other authors, the accuracy of the trajectory statistical methods was estimated for particular species and at specified receptor locations. We have obtained a more general statistical estimation of the accuracy of source reconstruction and have found optimum conditions to reconstruct source distributions of atmospheric trace substances. Only virtual pollutants of the primary type were considered. In real world experiments, TSMs are intended for application to a priori unknown sources. Therefore, the accuracy of TSMs has to be tested with all possible spatial distributions of sources. An ensemble of geographical distributions of virtual sources was generated. Spearman s rank order correlation coefficient between spatial distributions of the known virtual and the reconstructed sources was taken to be a quantitative measure of the accuracy. Statistical estimates of the mean correlation coefficient and a range of the most probable values of correlation coefficients were obtained. All the TSMs that were considered here showed similar close results. The maximum of the ratio of the mean correlation to the width of the correlation interval containing the most probable correlation values determines the optimum conditions for reconstruction. An optimal geographical domain roughly coincides with the area supplying most of the substance to the receptor. The optimal domain s size is dependent on the substance decay time. Under optimum reconstruction conditions, the mean correlation coefficients can reach 0.70 0.75. The boundaries of the interval with the most probable correlation values are 0.6 0.9 for the decay time of 240 h and 0.5 0.95 for the decay time of 12 h. The best results of source reconstruction can be expected for the trace substances with a decay time on the order of several days. Although the methods considered in this paper do not guarantee high accuracy they are computationally simple and fast. Using the TSMs in optimum conditions and taking into account the range of uncertainties, one can obtain a first hint on potential source areas.

Kabashnikov, Vitaliy P.↗

NASA NTRS1989

Grid sensitivity capability for large scale structures

The considerations and the resultant approach used to implement design sensitivity capability for grids into a large scale, general purpose finite element system (MSC/NASTRAN) are presented. The design variables are grid perturbations with a rather general linking capability. Moreover, shape and sizing variables may be linked together. The design is general enough to facilitate geometric modeling techniques for generating design variable linking schemes in an easy and straightforward manner. Test cases have been run and validated by comparison with the overall finite difference method. The linking of a design sensitivity capability for shape variables in MSC/NASTRAN with an optimizer would give designers a powerful, automated tool to carry out practical optimization design of real life, complicated structures.

Nagendra, Gopal K.↗

NASA NTRS1990

Optimum structural design of robotic manipulators with fiber reinforced composite materials

High-speed robotic arms with advanced structural characteristics can be fabricated from optimally tailored fiber reinforced composites. An integrated design methodology is presented for the optimal structural synthesis of composite robotic manipulators. Optimum configurations of ply angles and ply thicknesses are predicted for maximum structural end-effector stiffness and maximum end-effector load carrying capacity, without altering the geometric dimensions of the links. Multiple posture finite element-based static performance criteria are implemented. A new finite element has been developed for the modeling of tubular composite links. Unique features are the inclusion of shear effects and coupling between stretching and flexure. Numerical solutions are obtained via an efficient optimization algorithm. Applications to an existing SCARA-class manipulator illustrate the effectiveness of the method and demonstrate the dramatic influence of the multi-postural design criteria on the optimal design. For a filament wound structure using a high strength carbon fiber in a thermoplastic matrix, the resultant optimum ply configurations have increased the specific stiffness and specific load capacity by factors of 1.5 and 16, respectively, in comparison to identically sized aluminum links.

Saravanos, D. A.↗

NASA NTRS2000

Approximation Model Building for Reliability & Maintainability Characteristics of Reusable Launch Vehicles

This paper describes the development of parametric models for estimating operational reliability and maintainability (R&M) characteristics for reusable vehicle concepts, based on vehicle size and technology support level. A R&M analysis tool (RMAT) and response surface methods are utilized to build parametric approximation models for rapidly estimating operational R&M characteristics such as mission completion reliability. These models that approximate RMAT, can then be utilized for fast analysis of operational requirements, for lifecycle cost estimating and for multidisciplinary sign optimization.

Unal, Resit↗

NASA NTRS2018

An Overview of the Layered and Extensible Aircraft Performance System (LEAPS) Development

The Layered and Extensible Aircraft Performance System (LEAPS) is a new sizing and synthesis tool being developed within the Aeronautics Systems Analysis Branch (ASAB) at NASA Langley Research Center. It is a modular, multidisciplinary, multi- fidelity sizing and synthesis tool for modeling advanced aircraft concepts and architectures such as electric/hybrid-electric propulsion, unconventional propulsion airframe integration, and non-traditional mission trajectories. The development of LEAPS is motivated by the lack of existing tools that meet the needs of ASAB. The Flight Optimization System (FLOPS) has been the primary sizing and synthesis tool of ASAB for three decades. However, FLOPS has a number of limitations that make it dicult to use for unconventional aircraft designs. Three high-level goals have been adopted to guide the LEAPS development pro- cess. LEAPS is being developed in Python with an architecture built to enable a exible and extensible analysis capability using the concept of an aircraft object that combines data and analysis models. Five challenge problems for LEAPS have been identi ed to measure progress: analysis of a conventional tube-and-wing aircraft using legacy methods, coupled aeroelastic analysis for weight estimation of a conventional tube-and-wing aircraft, analysis of an advanced hybrid-electric concept, analysis of the X-57 Maxwell distributed electric propulsion aircraft, and optimization of the trajectory of a supersonic vehicle to minimize sonic boom. LEAPS will be a publicly available capability of exceptional quality with modularity and extensibility that makes it a robust tool for design and analysis of current and future unconventional aircraft concepts.

Welstead, Jason R.↗

NASA NTRS1974

Application of optimality criteria in structural synthesis

The rational use of optimality criteria was investigated for a class of structural synthesis problems where materials, configuration and applied load conditions are specified, and the minimum weight design is to be determined. The potential of hybrid methods of structural optimization for dealing with relatively large design problems involving practical complexity was explored. The reduced basis concept in design space was used to decrease the number of generalized design variables dealt with by the mathematical programming algorithm. Optimality criteria methods for obtaining design vectors associated with displacement, system buckling and natural frequency constraints are presented. A stress ratio method was used to generate a basis design vector representing the stress constraints. The finite element displacement method was used as the basic structural analysis tool. Results for several examples of truss systems subject to stress, displacement and minimum size constraints are presented. An assessment of these results indicates the effectiveness of the hybrid method developed.

Terai, K.↗

NASA NTRS2012

Development and Testing of Molecular Adsorber Coatings

The effect of on-orbit molecular contamination has the potential to degrade the performance of spaceflight hardware and diminish the lifetime of the spacecraft. For example, sensitive surfaces, such as optical surfaces, electronics, detectors, and thermal control surfaces, are vulnerable to the damaging effects of contamination from outgassed materials. The current solution to protect these surfaces is through the use of zeolite coated ceramic adsorber pucks. However, these pucks and its additional complex mounting hardware requirements result in several disadvantages, such as size, weight, and cost related concerns, that impact the spacecraft design and the integration and test schedule. As a result, a new innovative molecular adsorber coating was developed as a sprayable alternative to mitigate the risk of on-orbit molecular contamination. In this study, the formulation for molecular adsorber coatings was optimized using various binders, pigment treatment methods, binder to pigment ratios, thicknesses, and spray application techniques. The formulations that passed coating adhesion and vacuum thermal cycling tests were further tested for its adsorptive capacity. Accelerated molecular capacitance tests were performed in an innovatively designed multi-unit system containing idealized contaminant sources. This novel system significantly increased the productivity of the testing phase for the various formulations that were developed. Work performed during the development and testing phases has demonstrated successful application of molecular adsorber coatings onto metallic substrates, as well as, very promising results for the adhesion performance and the molecular capacitance of the coating. Continued testing will assist in the qualification of molecular adsorber coatings for use on future contamination sensitive spaceflight missions.

Abraham, Nithin↗

NASA NTRS2013

Small Launch Vehicle Trade Space Definition: Development of a Zero Level Mass Estimation Tool with Trajectory Validation

Recent high level interest in the capability of small launch vehicles has placed significant demand on determining the trade space these vehicles occupy. This has led to the development of a zero level analysis tool that can quickly determine the minimum expected vehicle gross liftoff weight (GLOW) in terms of vehicle stage specific impulse (Isp) and propellant mass fraction (pmf) for any given payload value. Utilizing an extensive background in Earth to orbit trajectory experience a total necessary delta v the vehicle must achieve can be estimated including relevant loss terms. This foresight into expected losses allows for more specific assumptions relating to the initial estimates of thrust to weight values for each stage. This tool was further validated against a trajectory model, in this case the Program to Optimize Simulated Trajectories (POST), to determine if the initial sizing delta v was adequate to meet payload expectations. Presented here is a description of how the tool is setup and the approach the analyst must take when using the tool. Also, expected outputs which are dependent on the type of small launch vehicle being sized will be displayed. The method of validation will be discussed as well as where the sizing tool fits into the vehicle design process.

Waters, Eric D.↗