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Numerical derivative techniques for trajectory optimization

The adoption of robust numerical optimization techniques in trajectory simulation programs has resulted in powerful design and analysis tools. These trajectory simulation/optimization programs are widely used, and a representative list includes the GTS system, the POST program, and newer collocation methods such as OTIS and FONPAC. All of these programs rely on optimization algorithms which require objective function and constraint gradient data during the iteration process. However, most trajectory optimization problems lack simple analytical expressions for these derivatives. In the general case a function evaluation involves integrating aerodynamic, propulsive, and gravity forces over multiple trajectory phases with complex control models. With the newer collocation methods, the integration is replaced by defect constraints and cubic approximations for the state. While analytic gradient expressions can sometimes be derived for trajectory optimization problems, the derivation is cumbersome, time consuming, and prone to mistakes. Fortunately, an alternate method exists for the gradient evaluation, namely finite difference approximations. In this paper some finite difference gradient techniques developed for use with the GTS system are presented. These techniques include methods for computing first and second partial derivatives of single and multiple sets of functions. A key feature of these methods is an error control mechanism which automatically adjusts the perturbation size to obtain accurate derivative values.

Hallman, Wayne P.↗

Process Cost Modeling for Multi-Disciplinary Design Optimization

For early design concepts, the conventional approach to cost is normally some kind of parametric weight-based cost model. There is now ample evidence that this approach can be misleading and inaccurate. By the nature of its development, a parametric cost model requires historical data and is valid only if the new design is analogous to those for which the model was derived. Advanced aerospace vehicles have no historical production data and are nowhere near the vehicles of the past. Using an existing weight-based cost model would only lead to errors and distortions of the true production cost. This report outlines the development of a process-based cost model in which the physical elements of the vehicle are costed according to a first-order dynamics model. This theoretical cost model, first advocated by early work at MIT, has been expanded to cover the basic structures of an advanced aerospace vehicle. Elemental costs based on the geometry of the design can be summed up to provide an overall estimation of the total production cost for a design configuration. This capability to directly link any design configuration to realistic cost estimation is a key requirement for high payoff MDO problems. Another important consideration in this report is the handling of part or product complexity. Here the concept of cost modulus is introduced to take into account variability due to different materials, sizes, shapes, precision of fabrication, and equipment requirements. The most important implication of the development of the proposed process-based cost model is that different design configurations can now be quickly related to their cost estimates in a seamless calculation process easily implemented on any spreadsheet tool. In successive sections, the report addresses the issues of cost modeling as follows. First, an introduction is presented to provide the background for the research work. Next, a quick review of cost estimation techniques is made with the intention to highlight their inappropriateness for what is really needed at the conceptual phase of the design process. The First-Order Process Velocity Cost Model (FOPV) is discussed at length in the next section. This is followed by an application of the FOPV cost model to a generic wing. For designs that have no precedence as far as acquisition costs are concerned, cost data derived from the FOPV cost model may not be accurate enough because of new requirements for shape complexity, material, equipment and precision/tolerance. The concept of Cost Modulus is introduced at this point to compensate for these new burdens on the basic processes. This is treated in section 5. The cost of a design must be conveniently linked to its CAD representation. The interfacing of CAD models and spreadsheets containing the cost equations is the subject of the next section, section 6. The last section of the report is a summary of the progress made so far, and the anticipated research work to be achieved in the future.

Bao, Han P.↗

Numerical analysis of flow through scramjet engine inlets

A set of computer programs was developed to analyze flow through supersonic combustion ramjet (scramjet) inlets. These programs solve either the two or three dimensional Euler/Navier-Stokes equations in full conservation form by MacCormack's explicit or explicit-implicit method. An algebraic two-layer eddy viscosity model is used for turbulent flow calculations. The programs are operational in Control Data CYBER-200 series vector-processing computer system and were optimized to take maximum advantage of the vector processing capability of the system. Since their development, the programs were extensively verified and used to analyze a number of very complex inlet configurations. Results are presented from two-dimensional, quasi-three-dimensional, and three-dimensional analyses of the inlet flow field to illustrate the use of the program.

Kumar, Ajay↗

Optimal thermionic energy conversion with established electrodes for high-temperature topping and process heating

Applied research-and-technology (ART) work reveals that optimal thermionic energy conversion (TEC) with approximately 1000 K to approximately 1100 K collectors is possible using well established tungsten electrodes. Such TEC with 1800 K emitters could approach 26.6% efficiency at 27.4 W/sq cm with approximately 1000 K collectors and 21.7% at 22.6 W/sq cm with approximately 1100 K collectors. These performances require 1.5 and 1.7 eV collector work functions (not the 1 eV ultimate) with nearly negligible interelectrode losses. Such collectors correspond to tungsten electrode systems in approximately 0.9 to approximately 6 torr cesium pressures with 1600 K to 1900 K emitters. Because higher heat-rejection temperatures for TEC allow greater collector work functions, interelectrode loss reduction becomes an increasingly important target for applications aimed at elevated temperatures. Studies of intragap modifications and new electrodes that will allow better electron emission and collection with lower cesium pressures are among the TEC-ART approaches to reduced interelectrode losses. These solutions will provide very effective TEC to serve directly in coal-combustion products for high-temperature topping and process heating. In turn this will help to use coal and to use it well.

Morris, J. F.↗

Computational Optimization of a Natural Laminar Flow Experimental Wing Glove

Computational optimization of a natural laminar flow experimental wing glove that is mounted on a business jet is presented and discussed. The process of designing a laminar flow wing glove starts with creating a two-dimensional optimized airfoil and then lofting it into a three-dimensional wing glove section. The airfoil design process does not consider the three dimensional flow effects such as cross flow due wing sweep as well as engine and body interference. Therefore, once an initial glove geometry is created from the airfoil, the three dimensional wing glove has to be optimized to ensure that the desired extent of laminar flow is maintained over the entire glove. TRANAIR, a non-linear full potential solver with a coupled boundary layer code was used as the main tool in the design and optimization process of the three-dimensional glove shape. The optimization process uses the Class-Shape-Transformation method to perturb the geometry with geometric constraints that allow for a 2-in clearance from the main wing. The three-dimensional glove shape was optimized with the objective of having a spanwise uniform pressure distribution that matches the optimized two-dimensional pressure distribution as closely as possible. Results show that with the appropriate inputs, the optimizer is able to match the two dimensional pressure distributions practically across the entire span of the wing glove. This allows for the experiment to have a much higher probability of having a large extent of natural laminar flow in flight.

Hartshom, Fletcher↗

Remote sensing of coal mine pollution in the upper Potomac River basin

A survey of remote sensing data pertinent to locating and monitoring sources of pollution resulting from surface and shaft mining operations was conducted in order to determine the various methods by which ERTS and aircraft remote sensing data can be used as a replacement for, or a supplement to traditional methods of monitoring coal mine pollution of the upper Potomac Basin. The gathering and analysis of representative samples of the raw and processed data obtained during the survey are described, along with plans to demonstrate and optimize the data collection processes.

Source record↗

Multidisciplinary Design Optimization (MDO) Methods: Their Synergy with Computer Technology in Design Process

The paper identifies speed, agility, human interface, generation of sensitivity information, task decomposition, and data transmission (including storage) as important attributes for a computer environment to have in order to support engineering design effectively. It is argued that when examined in terms of these attributes the presently available environment can be shown to be inadequate a radical improvement is needed, and it may be achieved by combining new methods that have recently emerged from multidisciplinary design optimization (MDO) with massively parallel processing computer technology. The caveat is that, for successful use of that technology in engineering computing, new paradigms for computing will have to be developed - specifically, innovative algorithms that are intrinsically parallel so that their performance scales up linearly with the number of processors. It may be speculated that the idea of simulating a complex behavior by interaction of a large number of very simple models may be an inspiration for the above algorithms, the cellular automata are an example. Because of the long lead time needed to develop and mature new paradigms, development should be now, even though the widespread availability of massively parallel processing is still a few years away.

Sobieszczanski-Sobieski, Jaroslaw↗

Enhanced Multiobjective Optimization Technique for Comprehensive Aerospace Design

A multidisciplinary design optimization procedure which couples formal multiobjectives based techniques and complex analysis procedures (such as computational fluid dynamics (CFD) codes) developed. The procedure has been demonstrated on a specific high speed flow application involving aerodynamics and acoustics (sonic boom minimization). In order to account for multiple design objectives arising from complex performance requirements, multiobjective formulation techniques are used to formulate the optimization problem. Techniques to enhance the existing Kreisselmeier-Steinhauser (K-S) function multiobjective formulation approach have been developed. The K-S function procedure used in the proposed work transforms a constrained multiple objective functions problem into an unconstrained problem which then is solved using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. Weight factors are introduced during the transformation process to each objective function. This enhanced procedure will provide the designer the capability to emphasize specific design objectives during the optimization process. The demonstration of the procedure utilizes a computational Fluid dynamics (CFD) code which solves the three-dimensional parabolized Navier-Stokes (PNS) equations for the flow field along with an appropriate sonic boom evaluation procedure thus introducing both aerodynamic performance as well as sonic boom as the design objectives to be optimized simultaneously. Sensitivity analysis is performed using a discrete differentiation approach. An approximation technique has been used within the optimizer to improve the overall computational efficiency of the procedure in order to make it suitable for design applications in an industrial setting.

Chattopadhyay, Aditi↗

On optimal nonlinear estimation. I - Continuous observation.

A generalization of Bucy's (1965) representation theorem is obtained under very weak hypotheses. The generalized theorem is shown to play the same role in the case of general optimal estimation for an arbitrary random process as does the Bucy theorem in the case of optimal filtering for a diffusion process. At least for the models considered, the possibility is pointed out to reduce all sequential estimation problems to the problem of filtering. Hence, filtering theory is seen to represent the core of estimation theory, and is believed to define the direction in which future research should be focused.

Lo, J. T.↗

FNAS materials processing and characterization

Research on melt-sintered high temperature superconducting materials is presented. The vibrating sample magnetometer has become a useful characterization tool for the study of high temperature superconductors. Important information regarding the superconducting properties of a sample can be obtained without actually making contact with the sample itself. A step toward microgravity processing of high temperature superconductors was taken. In the future, the samples need to be optimized prior to this processing of the sample before the specific effects of the microgravity environment can be isolated. A series of melt-sintered samples show that bulk processing of high temperature superconductors is getting better.

Golben, John P.↗

Assessment of impact damage of composite rocket motor cases

This contract reviewed the available literature on mechanisms of low velocity impact damage in filament wound rocket motor cases, MDE methods to quantify damage, critical coupon level test methods, manufacturing and material process variables and empirical and analytical modeling off impact damage. The critical design properties for rocket motor cases are biaxial hoop and axial tensile strength. Low velocity impact damage is insidious because it can create serious nonvisible damage at very low impact velocities. In thick rocket motor cases the prevalent low velocity impact damage is fiber fracture and matrix cracking adjacent to the front face. In contrast, low velocity loading of thin wall cylinders induces flexure, depending on span length and the flexure induces delamination and tensile cracking on the back face wall opposed to impact occurs due to flexural stresses imposed by impact loading. Important NDE methods for rocket motor cases are non-contacting methods that allow inspection from one side. Among these are vibrothermography, and pulse-echo methods based on acoustic-ultrasonic methods. High resolution techniques such as x-ray computed tomography appear to have merit for accurate geometrical characterization of local damage to support development of analytical models of micromechanics. The challenge of coupon level testing is to reproduce the biaxial stress state that the full scale article experiences, and to determine how to scale the composite structure to model full sized behavior. Biaxial tensile testing has been performed by uniaxially tensile loading internally pressurized cylinders. This is experimentally difficult due to gripping problems and pressure containment. Much prior work focused on uniaxial tensile testing of model filament wound cylinders. Interpretation of the results of some studies is complicated by the fact that the fabrication process did not duplicate full scale manufacturing. It is difficult to scale results from testing subscale cylinders since there are significant differences in out time of the resins relative to full scale cylinder fabrication, differences in hoop fiber tensioning and unsatisfactory coupon configurations. It appears that development of a new test method for subscale cylinders is merited. Damage tolerance may be improved by material optimization that uses fiber treatments and matrix modifications to control the fiber matrix interface bonding. It is difficult to develop process optimization in subscale cylinders without also modeling the longer out times resins experience in full scale testing. A major breakthrough in characterizing the effect of impact damage on residual strength, and understanding how to scale results of subscale evaluations, will be a sound micromechanical model that described progressive failure of the composite. Such models will utilize a three dimensional stress analysis due to the complex nature of low velocity impact stresses in thick composites. When these models are coupled with non-contact NDE methods that geometrically characterize the damage and acoustic methods that characterize the effective local elastic properties, accurate assessment of residual strength from impact damage may be possible. Directions for further development are suggested.

Paris, Henry G.↗

System Engineering & Integration (SE&I) In-Situ Resource Utilization (ISRU) Modeling and Analysis (SIMA) Tool for Subsystem Integration into Full-Scale Architectures

In situ resource utilization (ISRU) is the practice of producing mission consumables from local lunar/planetary resources, thereby minimizing system launch mass requirements, mainly through the production of propellant fuel components and life support resources. Modeling full ISRU technology architectures significantly impacts the design and optimization of individual unit processes and facilitates their introduction into service with the Science Technology Mission Directorate (STMD) logistical planning and operation space. The Mission Analysis and Integration Tool (MAIT) is a modeling framework that connects individual ISRU subsystem models for the purposes of technology down select, scaling & optimization, and end-to-end process planning. The development project team seeks to address specific STMD capability gaps by simulating ISRU systems in MAIT. The goal is to produce system architectures for the Moon and Mars that are linked to Key Performance Parameters (KPP) and environmental requirements. To that end, the framework is adaptive, flexible, and suitable for collaboration among government, private sector, and international entities. Our approach currently provides conventional outputs, such as mass, power, and volume, to analyze whole system trade spaces. However, the framework was designed to validate current breadboard subsystems, simulate future process design capacity, and allow flexibility to any external developer-driven subsystem model that is in a state of evolution.

SE&I↗

Glennan Microsystems Initiative

During the 2001-2002 award period, we performed research on Pt/Ti/bare 6H-SiC and bare 4H-SiC interfaces in order to identify their electronic properties as a function of surface preparation. The overall aim of this work is to optimize the electronic properties of metal contacts to SiC as well as the active SiC material itself as a function of surface preparation and subsequent processing. Initially, this work has involved identifying bare surface, subsurface, and metal induced gap states at the metal-SiC contact and correlating energies and densities of deep levels with Schottky barrier heights. We used low energy electron-excited nanoluminescence (LEEN) spectroscopy, X-ray photoemission spectroscopy (XPS), and Secondary Ion Mass Spectrometry (SIMS) in order to correlate electronic states and energy bands with chemical composition, bonding, and crystal structure. A major development has been the discovery of polytype transformations that occur in 4H-SiC under standard microelectronic process conditions used to fabricate SiC devices. Our results are consistent with the stacking fault generation, defect formation, and consequent degradation of SiC recently reported for state-of-the-art ABB commercial diodes under localized electrical stress. Our results highlight the importance of -optimizing process conditions and material properties - anneal times, temperatures and doping to control such structural changes within epitaxial SiC layers. Thus far, we have established threshold times and temperatures beyond which 4H-SiC exhibits 3C-SiC transformation bands for a subset of dopant concentrations and process conditions. On the basis of this temperature time behavior, we have been able to establish an activation energy of approximately 2.5 eV for polytype transformation and dislocation motion. Work continues to establish the fundamental mechanisms underlying the polytype changes and its dependence on material parameters.

Brillson, Leonard J.↗

High-Performance Computing Optimization for Aladyn – Adaptive Neural Network Molecular Dynamics Mini-Application

This report provides a description and performance evaluation of the optimization techniques for high performance computing (HPC) implementation of the open source Computational Materials mini-application Aladyn (https://github.com/nasa/aladyn). Aladyn is a basic molecular dynamics code written in FORTRAN 2003, which is designed to demonstrate the use of adaptive neural networks (ANNs) in atomistic simulations. The role of ANNs is to efficiently reproduce the very complex energy landscape resulting from the atomic interactions in materials with the accuracy of the more expensive quantum mechanics-based calculations. The ANN is trained on a large set of atomic structures calculated using the density functional theory (DFT) method. While achieving orders of magnitude faster computational performance than DFT, the ANN-based approach was still very computationally demanding compared to the conventional approach of using empirically fitted energy functions. After its initial development, Aladyn was evaluated and optimized by experts at the NASA Advanced Supercomputing (NAS) division to exploit modern supercomputer architectures. The code has been optimized for execution on multicore central processing units (CPUs), including Intel® Skylake microarchitecture, and on graphic accelerators, such as Nvidia® V100 graphic processing units (GPUs), using Open Multi-Processing (OpenMP) and Open Accelerators (OpenACC) programming interfaces. The optimization achieved a speedup of 4.7 times the baseline version on CPU performance and an additional 2.4 times on CPU+GPU performance. Atomistic computer simulations are a fundamental tool in materials research to model material properties form physics-based first principles. Atomic interaction, governed by Quantum Mechanics (QM) require sophisticated and highly computationally demanding mathematical models to calculate [1]. Classical methods use approximate functional forms, empirically fitted through a set of variable parameters to emulate atomic energies as direct functions of atomic coordinates [2]. While empirical potentials are computationally much simpler, allowing simulations of large-scale systems of up to a trillion (1012) atoms [3], they are substantially less accurate compared to quantum calculations and applicable only to very specific atomic configurations or predefined crystallographic phases. A recently suggested approach is to use heuristic machine learning methods [4], such as those based on Adaptive Neural Networks (ANNs) to predict atomic energies, after being trained on a sufficiently large database of QM-calculated structures [5,6]. This approach reduces significantly the computational complexity, allowing for simulations of orders of magnitude larger systems compared to QM-based methods without compromising accuracy. Still, compared to classical methods using empirical energy functions, ANN methods remain two- to three orders of magnitude more computationally demanding. Hence, the computational cost of simulations, together with the need for extensive training of ANNs, still makes the practical implementation of ANN-based methods quite challenging. The purpose of the Aladyn mini-application software [7], available as open source at https://github.com/nasa/aladyn, is to be a testbed for exploring possible optimization strategies to develop highly scalable parallel algorithms for ANN-based atomistic simulations. Aladyn is aimed at utilizing the architecture of the high-end modern highperformance computing (HPC) hardware based on multicore central processing units (CPUs) equipped with graphic processing unit (GPU) accelerators. Specifically, the goal is to optimize the performance on a single HPC compute node, before implementing scaling to multi-node parallelization using message passing interface (MPI). At the same time, the open source code of Aladyn can serve as a training model for students and professors in academia.

Yamakov, Vesselin I.↗

A stochastic constrained optimization technique and its application to detector array processing.

A stochastic projected gradient algorithm is proposed which can be used for finding a constrained optimum point for a concave or convex objective function subject to nonlinear constraints which form a connected region even when only a noisy estimate of the objective function is available. For a constraint described by a single linear equation, convergence to the constrained optimum value is proved, and the rate of convergence of the algorithm to the constrained optimum value is determined. The algorithm is applied to the nonlinear problem of obtaining automatically an array of detectors which forms a beam in a desired direction in space in the presence of interfering noise so as to maximize the SNR subject to a constraint on the super-gain ratio.

Winkler, L. P.↗

Sensitivity analysis of the optimal solution obtained from the structural damage indentification process

An identification procedure proposed by Shen and Taylor to determine the crack characteristics (location and size of the crack) from dynamic measurements is tested. This procedure was based on minimization of either the 'mean-square' measure of difference between measurement data (natural frequencies and mode shapes) and the corresponding predictions obtained from the computational model. The procedure is tested for simulated damage in the form of symmetric cracks in a simply-supported Bernoulli-Euler beam. The sensitivity of the solution of damage identification problems to the values of parameters that characterize damage is discussed. A sensitivity formula is derived.

Shen, Mo-How H.↗

Multiscale and Multiphysics Modeling of Additive Manufacturing of Advanced Materials

The objective of this proposed project is to research and develop a prediction tool for advanced additive manufacturing (AAM) processes for advanced materials and develop experimental methods to provide fundamental properties and establish validation data. Aircraft structures and engines demand materials that are stronger, useable at much higher temperatures, provide less acoustic transmission, and enable more aeroelastic tailoring than those currently used. Significant improvements in properties can only be achieved by processing the materials under nonequilibrium conditions, such as AAM processes. AAM processes encompass a class of processes that use a focused heat source to create a melt pool on a substrate. Examples include Electron Beam Freeform Fabrication and Direct Metal Deposition. These types of additive processes enable fabrication of parts directly from CAD drawings. To achieve the desired material properties and geometries of the final structure, assessing the impact of process parameters and predicting optimized conditions with numerical modeling as an effective prediction tool is necessary. The targets for the processing are multiple and at different spatial scales, and the physical phenomena associated occur in multiphysics and multiscale. In this project, the research work has been developed to model AAM processes in a multiscale and multiphysics approach. A macroscale model was developed to investigate the residual stresses and distortion in AAM processes. A sequentially coupled, thermomechanical, finite element model was developed and validated experimentally. The results showed the temperature distribution, residual stress, and deformation within the formed deposits and substrates. A mesoscale model was developed to include heat transfer, phase change with mushy zone, incompressible free surface flow, solute redistribution, and surface tension. Because of excessive computing time needed, a parallel computing approach was also tested. In addition, after investigating various methods, a Smoothed Particle Hydrodynamics Model (SPH Model) was developed to model wire feeding process. Its computational efficiency and simple architecture makes it more robust and flexible than other models. More research on material properties may be needed to realistically model the AAM processes. A microscale model was developed to investigate heterogeneous nucleation, dendritic grain growth, epitaxial growth of columnar grains, columnar-to-equiaxed transition, grain transport in melt, and other properties. The orientations of the columnar grains were almost perpendicular to the laser motion's direction. Compared to the similar studies in the literature, the multiple grain morphology modeling result is in the same order of magnitude as optical morphologies in the experiment. Experimental work was conducted to validate different models. An infrared camera was incorporated as a process monitoring and validating tool to identify the solidus and mushy zones during deposition. The images were successfully processed to identify these regions. This research project has investigated multiscale and multiphysics of the complex AAM processes thus leading to advanced understanding of these processes. The project has also developed several modeling tools and experimental validation tools that will be very critical in the future of AAM process qualification and certification.

Liou, Frank↗

Fracture Toughness of Carbon Fiber Composites Containing Various Fiber Sizings and a Puncture Self-Healing Thermoplastic Matrix

Ongoing efforts at NASA Langley Research Center (LaRC) have resulted in the identification of several commercially available thermoplastic resin systems which self-heal after ballistic impact and through penetration. One of these resins, polybutylene graft copolymer (PBg), was selected as a matrix for processing with unsized carbon fibers to fabricate reinforced composites for further evaluation. During process development, data from thermo-physical analyses was utilized to determine a processing cycle to fabricate laminate panels, which were analyzed by photo microscopy and acid digestion. The process cycle was further optimized based on these results to fabricate panels for mechanical property characterization. The results of the processing development effort of this composite material, as well as the results of the mechanical property characterization, indicated that bonding between the fiber and PBg was not adequate. Therefore, three sizings were investigated in this work to assess their potential to improve fiber/matrix bonding compared to previously tested unsized IM7 fiber. Unidirectional prepreg was made at NASA LaRC from three sized carbon fibers and utilized to fabricate test coupons that were tested in double cantilever beam configurations to determine GIc fracture toughness.

Cano, Roberto J.↗