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NASA NTRS1975

Sequential filtering applied to the determination of tracking station locations

The extended sequential filter has been applied to the problem of dynamically determining the geocentric coordinates of two laser satellite tracking stations. This filter provides significant advantages over the classical batch methods through (1) fewer iterations required for convergence, (2) wider radius of convergence, and (3) availability of the parameter estimate evolution. Processing the data sequentially readily identifies the data arcs required to minimize the effects of geopotential model errors. By means of the Smithsonian standard earth 2 and the Goddard earth model 1 geopotentials to reduce laser range observations of the Beacon Explorer-C satellite, it is demonstrated that a two-pass arc is optimal for estimating the height of one station and all coordinates of the second station while minimizing the effect of geopotential model error. These two-pass estimates are in good agreement with other determinations that utilize considerably more data as well as different satellites.

Schutz, B. E.↗

NASA NTRS1996

Finite Element Analysis of a NASA National Transonic Facility Wind Tunnel Balance

This paper presents the results of finite element analyses and correlation studies performed on a NASA National Transonic Facility (NTF) Wind Tunnel balance. In the past NASA has relied primarily on classical hand analyses, coupled with relatively large safety factors, for predicting maximum stresses in wind tunnel balances. Now, with the significant advancements in computer technology and sophistication of general purpose analysis codes, it is more reasonable to pursue finite element analyses of these balances. The correlation studies of the present analyses show very good agreement between the analyses and data measured with strain gages and therefore the studies give higher confidence for using finite element analyses to analyze and optimize balance designs in the future.

Lindell, Michael C.↗

NASA NTRS1999

Finite Element Analysis of a NASA National Transonic Facility Wide Tunnel Balance

Lindell, Michael C.↗

NASA NTRS1991

Blade design and analysis using a modified Euler solver

An iterative method for blade design based on Euler solver and described in an earlier paper is used to design compressor and turbine blades providing shock free transonic flows. The method shows a rapid convergence, and indicates how much the flow is sensitive to small modifications of the blade geometry, that the classical iterative use of analysis methods might not be able to define. The relationship between the required Mach number distribution and the resulting geometry is discussed. Examples show how geometrical constraints imposed upon the blade shape can be respected by using free geometrical parameters or by relaxing the required Mach number distribution. The same code is used both for the design of the required geometry and for the off-design calculations. Examples illustrate the difficulty of designing blade shapes with optimal performance also outside of the design point.

Leonard, O.↗

NASA NTRS1998

Combined Numerical/Analytical Perturbation Solutions of the Navier-Stokes Equations for Aerodynamic Ejector/Mixer Nozzle Flows

In spite of rapid advances in both scalar and parallel computational tools, the large number of variables involved in both design and inverse problems make the use of sophisticated fluid flow models impractical, With this restriction, it is concluded that an important family of methods for mathematical/computational development are reduced or approximate fluid flow models. In this study a combined perturbation/numerical modeling methodology is developed which provides a rigorously derived family of solutions. The mathematical model is computationally more efficient than classical boundary layer but provides important two-dimensional information not available using quasi-1-d approaches. An additional strength of the current methodology is its ability to locally predict static pressure fields in a manner analogous to more sophisticated parabolized Navier Stokes (PNS) formulations. To resolve singular behavior, the model utilizes classical analytical solution techniques. Hence, analytical methods have been combined with efficient numerical methods to yield an efficient hybrid fluid flow model. In particular, the main objective of this research has been to develop a system of analytical and numerical ejector/mixer nozzle models, which require minimal empirical input. A computer code, DREA Differential Reduced Ejector/mixer Analysis has been developed with the ability to run sufficiently fast so that it may be used either as a subroutine or called by an design optimization routine. Models are of direct use to the High Speed Civil Transport Program (a joint government/industry project seeking to develop an economically.viable U.S. commercial supersonic transport vehicle) and are currently being adopted by both NASA and industry. Experimental validation of these models is provided by comparison to results obtained from open literature and Limited Exclusive Right Distribution (LERD) sources, as well as dedicated experiments performed at Texas A&M. These experiments have been performed using a hydraulic/gas flow analog. Results of comparisons of DREA computations with experimental data, which include entrainment, thrust, and local profile information, are overall good. Computational time studies indicate that DREA provides considerably more information at a lower computational cost than contemporary ejector nozzle design models. Finally. physical limitations of the method, deviations from experimental data, potential improvements and alternative formulations are described. This report represents closure to the NASA Graduate Researchers Program. Versions of the DREA code and a user's guide may be obtained from the NASA Lewis Research Center.

DeChant, Lawrence Justin↗

NASA NTRS1990

H2, fixed architecture, control design for large scale systems

The H2, fixed architecture, control problem is a classic linear quadratic Gaussian (LQG) problem whose solution is constrained to be a linear time invariant compensator with a decentralized processing structure. The compensator can be made of p independent subcontrollers, each of which has a fixed order and connects selected sensors to selected actuators. The H2, fixed architecture, control problem allows the design of simplified feedback systems needed to control large scale systems. Its solution becomes more complicated, however, as more constraints are introduced. This work derives the necessary conditions for optimality for the problem and studies their properties. It is found that the filter and control problems couple when the architecture constraints are introduced, and that the different subcontrollers must be coordinated in order to achieve global system performance. The problem requires the simultaneous solution of highly coupled matrix equations. The use of homotopy is investigated as a numerical tool, and its convergence properties studied. It is found that the general constrained problem may have multiple stabilizing solutions, and that these solutions may be local minima or saddle points for the quadratic cost. The nature of the solution is not invariant when the parameters of the system are changed. Bifurcations occur, and a solution may continuously transform into a nonstabilizing compensator. Using a modified homotopy procedure, fixed architecture compensators are derived for models of large flexible structures to help understand the properties of the constrained solutions and compare them to the corresponding unconstrained ones.

Mercadal, Mathieu↗

NASA NTRS2020

Multi Model Monte Carlo with Python (MXMCPy)

Multi Model Monte Carlo with Python (\mxmc {}) is a software package developed as a general capability for computing the statistics of outputs from an expensive, high-fidelity model by leveraging faster, low-fidelity models for speedup. Motivated by uncertainty propagation problems where classical Monte Carlo (MC) simulation is computationally intractable, various multi-model MC approaches have recently emerged that yield unbiased estimators with significantly reduced variance relative to MC for the same cost. These existing methods include multi-level Monte Carlo (MLMC), multi-fidelity Monte Carlo (MFMC), and approximate control variates (ACV). Given a fixed computational budget and a collection of models with varying cost/accuracy, each method seeks a sample allocation strategy across the models that results in an estimator with optimal variance reduction. \mxmc {} is a versatile tool that enables convenient access to many existing multi-model MC approaches within one modular and extensible package. With \mxmc {}, users can easily compare existing methods to determine the best choice for their particular problem, while developers have a basis for implementing and sharing new variance reduction approaches. This report introduces the \mxmc {} software, providing a summary of the problem-solving workflow for users as well as a brief overview of the code layout for developers.

Geoffrey F Bomarito↗

NASA NTRSDate not supplied

Machine Learning Approaches for Rare-Earth Silicate Environmental Barrier Coating Thermochemical and Thermomechanical Property Predictions

Environmental barrier coatings (EBCs) are a necessary enabling technology for the transition from superalloys to silicon carbide (SiC) ceramic matrix composites (CMCs) in gas turbine engines for increased efficiency and decreased fuel costs. SiC-based CMCs are prone to oxidation-based degradation in the engine hot section, and rare-earth (RE) silicates are promising candidates for EBCs due to their close thermal expansion match to the composite substrate and oxidation resistance. However, the design of EBCs is hindered by the large chemical space of candidate materials and the difficulty in obtaining material properties for engineering optimization. This is especially difficult as research continues into mixed-cation or “high-entropy” RE silicates. First-principles computational methods such as density functional theory (DFT) are highly effective at calculating material properties to guide coating design but are limited by their computational cost. Atomistic simulations have the potential to both accelerate property calculations and expand the properties able to be calculated due to their lower computational compared to DFT. However, they require interatomic potentials (IAPs) specific to the material system of interest, and, to our knowledge, there are no suitable IAPs for RE silicates. Machine learning (ML) is a promising technique to accelerate material property predictions indirectly by generating IAPs for atomistic simulations or via direct prediction. In this work, we present two ML approaches to accelerate the calculation of RE silicate properties relevant to EBC design: 1) a ML-derived interatomic potential (IAP) for atomistic simulations of yttrium disilicate (Y2Si2O7) from DFT training data, and 2) a neural network (NN) model to directly predict thermochemical properties of RE silicates and oxides directly from easily obtainable unit cell parameters. Classical MD simulations using the IAP yield lattice properties and bond lengths in good agreement with both DFT and experimental results from x-ray diffraction. Thermodynamic properties calculated using the finite-displacement phonon method and quasi-harmonic approximation were orders of magnitude faster than DFT with good agreement to the DFT results. The IAP was also used to calculate properties such as coefficient of thermal expansion (CTE) that require large simulation supercells and are therefore difficult with DFT. The IAP correctly predicted the anisotropic nature of the CTE in three different phases of Y2Si2O7. The NN model predicts constant pressure heat capacity, Cp, orders of magnitude faster than DFT calculations, which can enable its use as a surrogate model for multiscale simulations. The two methods presented in this work demonstrate the utility of ML for accelerating the prediction of RE silicate properties, which can in turn accelerate EBC design and optimization.

machine learning↗

NASA NTRS1973

Optimal low thrust geocentric transfer

A computer code which will rapidly calculate time-optimal low thrust transfers is being developed as a mission analysis tool. The final program will apply to NEP or SEP missions and will include a variety of environmental effects. The current program assumes constant acceleration. The oblateness effect and shadowing may be included. Detailed state and costate equations are given for the thrust effect, oblateness effect, and shadowing. A simple but adequate model yields analytical formulas for power degradation due to the Van Allen radiation belts for SEP missions. The program avoids the classical singularities by the use of equinoctial orbital elements. Kryloff-Bogoliuboff averaging is used to facilitate rapid calculation. Results for selected cases using the current program are given.

Edelbaum, T. N.↗

NASA NTRS1975

System analysis of a piston steam engine employing the uniflow principle, a study in optimized performance

Results are reported which were obtained from a mathematical model of a generalized piston steam engine configuration employing the uniflow principal. The model accounted for the effects of clearance volume, compression work, and release volume. A simple solution is presented which characterizes optimum performance of the steam engine, based on miles per gallon. Development of the mathematical model is presented. The relationship between efficiency and miles per gallon is developed. An approach to steam car analysis and design is presented which has purpose rather than lucky hopefulness. A practical engine design is proposed which correlates to the definition of the type engine used. This engine integrates several system components into the engine structure. All conclusions relate to the classical Rankine Cycle.

Peoples, J. A.↗

NASA NTRS2011

Frame-Transfer Gating Raman Spectroscopy for Time-Resolved Multiscalar Combustion Diagnostics

Accurate experimental measurement of spatially and temporally resolved variations in chemical composition (species concentrations) and temperature in turbulent flames is vital for characterizing the complex phenomena occurring in most practical combustion systems. These diagnostic measurements are called multiscalar because they are capable of acquiring multiple scalar quantities simultaneously. Multiscalar diagnostics also play a critical role in the area of computational code validation. In order to improve the design of combustion devices, computational codes for modeling turbulent combustion are often used to speed up and optimize the development process. The experimental validation of these codes is a critical step in accepting their predictions for engine performance in the absence of cost-prohibitive testing. One of the most critical aspects of setting up a time-resolved stimulated Raman scattering (SRS) diagnostic system is the temporal optical gating scheme. A short optical gate is necessary in order for weak SRS signals to be detected with a good signal- to-noise ratio (SNR) in the presence of strong background optical emissions. This time-synchronized optical gating is a classical problem even to other spectroscopic techniques such as laser-induced fluorescence (LIF) or laser-induced breakdown spectroscopy (LIBS). Traditionally, experimenters have had basically two options for gating: (1) an electronic means of gating using an image intensifier before the charge-coupled-device (CCD), or (2) a mechanical optical shutter (a rotary chopper/mechanical shutter combination). A new diagnostic technology has been developed at the NASA Glenn Research Center that utilizes a frame-transfer CCD sensor, in conjunction with a pulsed laser and multiplex optical fiber collection, to realize time-resolved Raman spectroscopy of turbulent flames that is free from optical background noise (interference). The technology permits not only shorter temporal optical gating (down to <1 s, in principle), but also higher optical throughput, thus resulting in a substantial increase in measurement SNR.

Nguyen, Quang-Viet↗

NASA NTRS1975

A steepest descents method for reentry optimization

A steepest descents optimization program is applied to the problem of a lifting vehicle entering the earth's atmosphere. The program employs penalty functions representing terminal conditions and inflight inequality constraints. During each iteration, it reduces a single performance measure which is the sum of the performance index and the penalty functions. Therefore, only one set of adjoint equations must be integrated per iteration. Values of weight factors, multiplying the penalty functions, are automatically adjusted before each iteration in order that the penalty functions will approach acceptable values. This method is shown to be a form of the classical Lagrange multiplier methods.

Andrus, J. F.↗

NASA NTRS2014

Space Launch System Implementation of Adaptive Augmenting Control

Given the complex structural dynamics, challenging ascent performance requirements, and rigorous flight certification constraints owing to its manned capability, the NASA Space Launch System (SLS) launch vehicle requires a proven thrust vector control algorithm design with highly optimized parameters to provide stable and high-performance flight. On its development path to Preliminary Design Review (PDR), the SLS flight control system has been challenged by significant vehicle flexibility, aerodynamics, and sloshing propellant. While the design has been able to meet all robust stability criteria, it has done so with little excess margin. Through significant development work, an Adaptive Augmenting Control (AAC) algorithm has been shown to extend the envelope of failures and flight anomalies the SLS control system can accommodate while maintaining a direct link to flight control stability criteria such as classical gain and phase margin. In this paper, the work performed to mature the AAC algorithm as a baseline component of the SLS flight control system is presented. The progress to date has brought the algorithm design to the PDR level of maturity. The algorithm has been extended to augment the full SLS digital 3-axis autopilot, including existing load-relief elements, and the necessary steps for integration with the production flight software prototype have been implemented. Several updates which have been made to the adaptive algorithm to increase its performance, decrease its sensitivity to expected external commands, and safeguard against limitations in the digital implementation are discussed with illustrating results. Monte Carlo simulations and selected stressing case results are also shown to demonstrate the algorithm's ability to increase the robustness of the integrated SLS flight control system.

Wall, John H.↗

NASA NTRS2010

Searching for Cost-Optimized Interstellar Beacons

What would SETI beacon transmitters be like if built by civilizations that had a variety of motives but cared about cost? In a companion paper, we presented how, for fixed power density in the far field, a cost-optimum interstellar beacon system could be built. Here, we consider how we should search for a beacon if it were produced by a civilization similar to ours. High-power transmitters could be built for a wide variety of motives other than the need for two-way communication, this would include beacons built to be seen over thousands of light-years. Extraterrestrial beacon builders would likely have to contend with economic pressures just as their terrestrial counterparts do. Cost, spectral lines near 1GHz, and interstellar scintillation favor radiating frequencies substantially above the classic "water hole." Therefore, the transmission strategy for a distant, cost-conscious beacon would be a rapid scan of the galactic plane with the intent to cover the angular space. Such pulses would be infrequent events for the receiver. Such beacons built by distant, advanced, wealthy societies would have very different characteristics from what SETI researchers seek. Future searches should pay special attention to areas along the galactic disk where SETI searches have seen coherent signals that have not recurred on the limited listening time intervals we have used. We will need to wait for recurring events that may arrive in intermittent bursts. Several new SETI search strategies have emerged from these ideas. We propose a new test for beacons that is based on the Life Plane hypotheses.

Benford, Gregory↗

NASA NTRS1996

The Newton Modified Barrier Method for QP Problems

The Modified Barrier Functions (MBF) have elements of both Classical Lagrangians (CL) and Classical Barrier Functions (CBF). The MBF methods find an unconstrained minimizer of some smooth barrier function in primal space and then update the Lagrange multipliers, while the barrier parameter either remains fixed or can be updated at each step. The numerical realization of the MBF method leads to the Newton MBF method, where the primal minimizer is found by using Newton's method. This minimizer is then used to update the Lagrange multipliers. In this paper, we examine the Newton MBF method for the Quadratic Programming (QP) problem. It will be shown that under standard second-order optimality conditions, there is a ball around the primal solution and a cut cone in the dual space such that for a set of Lagrange multipliers in this cut cone, the method converges quadratically to the primal minimizer from any point in the aforementioned ball, and continues to do so after each Lagrange multiplier update. The Lagrange multipliers remain within the cut cone and converge linearly to their optimal values. Any point in this ball will be called a "hot start". Starting at such a "hot start", at most Omicron(1n 1n epsilon(exp -1)) Newton steps are sufficient to perform the primal minimization which is necessary for the Lagrange multiplier update. Here, epsilon > 0 is the desired accuracy. Because of the linear convergence of the Lagrange multipliers, this means that only Omicron(1n epsilon(exp -1))omicron(ln 1n epsilon(exp-1)) Newton steps are required to reach an epsilon-approximation to the solution from any "hot start". In order to reach the "hot start", one has to perform Omicron(square root(m) 1n C) Newton steps, where m characterizes the size of the problem and C > 0 is the condition number of the QP problem. This condition number will be characterized explicitly in terms of key parameters of the QP problem, which in turn depend on the input data and the size of the problem.

Melman, A.↗

NASA NTRS2017

Benchmarking the Collocation Stand-Alone Library and Toolkit (CSALT)

This paper describes the processes and results of Verification and Validation (V&V) efforts for the Collocation Stand Alone Library and Toolkit (CSALT). We describe the test program and environments, the tools used for independent test data, and comparison results. The V&V effort employs classical problems with known analytic solutions, solutions from other available software tools, and comparisons to benchmarking data available in the public literature. Presenting all test results are beyond the scope of a single paper. Here we present high-level test results for a broad range of problems, and detailed comparisons for selected problems.

optimal control↗

NASA NTRS1991

A look-ahead variant of the Lanczos algorithm and its application to the quasi-minimal residual method for non-Hermitian linear systems

The Lanczos algorithm can be used both for eigenvalue problems and to solve linear systems. However, when applied to non-Hermitian matrices, the classical Lanczos algorithm is susceptible to breakdowns and potential instabilities. In addition, the biconjugate gradient (BCG) algorithm, which is the natural generalization of the conjugate gradient algorithm to non-Hermitian linear systems, has a second source of breakdowns, independent of the Lanczos breakdowns. Here, we present two new results. We propose an implementation of a look-ahead variant of the Lanczos algorithm which overcomes the breakdowns by skipping over those steps where a breakdown or a near-breakdown would occur. The new algorithm can handle look-ahead steps of any length and requires the same number of matrix-vector products and inner products per step as the classical Lanczos algorithm without look-ahead. Based on the proposed look-ahead Lanczos algorithm, we then present a novel BCG-like approach, the quasi-minimal residual (QMR) method, which avoids the second source of breakdowns in the BCG algorithm. We present details of the new method and discuss some of its properties. In particular, we discuss the relationship between QMR and BCG, showing how one can recover the BCG iterates, when they exist, from the QMR iterates. We also present convergence results for QMR, showing the connection between QMR and the generalized minimal residual (GMRES) algorithm, the optimal method in this class of methods. Finally, we give some numerical examples, both for eigenvalue computations and for non-Hermitian linear systems.

Nachtigal, Noel M.↗

NASA NTRS2017

Benchmarking the Collocation Stand-Alone Library and Toolkit (CSALT)

This paper describes the processes and results of Verification and Validation (VV) efforts for the Collocation Stand Alone Library and Toolkit (CSALT). We describe the test program and environments, the tools used for independent test data, and comparison results. The VV effort employs classical problems with known analytic solutions, solutions from other available software tools, and comparisons to benchmarking data available in the public literature. Presenting all test results are beyond the scope of a single paper. Here we present high-level test results for a broad range of problems, and detailed comparisons for selected problems.

trajectory optimization↗