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NASA NTRS1991

Aerospace plane guidance using time-scale decomposition - A geometric approach

A method is proposed for developing the necessary guidance logic to steer single-stage vehicles into orbit. The minimum-fuel ascent problem is first considered to analyze the effects of dynamic pressure, acceleration, and heating constraints on guidance systems to thereby develop the guidance logic. The optimal solution consists of behavior with two time scales, and the control law is used to develop near-optimal guidance. The solution uses the slow manifold to delineate the control for minimum-fuel reduced-order trajectory and a separate control for tracking the optimal reduced-order trajectory. A family of fast manifolds is then employed to resolve the tracking problem via the feedback linearization methodology from nonlinear geometric control theory. The two-time-scale decomposition is found to produce a near-optimal ascent by tracking the applicable state-constraint boundary, as well as to simplify the control-design task.

Van Buren, Mark A.↗

NASA NTRS1991

Formal and heuristic system decomposition methods in multidisciplinary synthesis

The multidisciplinary interactions which exist in large scale engineering design problems provide a unique set of difficulties. These difficulties are associated primarily with unwieldy numbers of design variables and constraints, and with the interdependencies of the discipline analysis modules. Such obstacles require design techniques which account for the inherent disciplinary couplings in the analyses and optimizations. The objective of this work was to develop an efficient holistic design synthesis methodology that takes advantage of the synergistic nature of integrated design. A general decomposition approach for optimization of large engineering systems is presented. The method is particularly applicable for multidisciplinary design problems which are characterized by closely coupled interactions among discipline analyses. The advantage of subsystem modularity allows for implementation of specialized methods for analysis and optimization, computational efficiency, and the ability to incorporate human intervention and decision making in the form of an expert systems capability. The resulting approach is not a method applicable to only a specific situation, but rather, a methodology which can be used for a large class of engineering design problems in which the system is non-hierarchic in nature.

Bloebaum, Christina L.↗

NASA NTRS1991

Two alternative ways for solving the coordination problem in multilevel optimization

Two techniques for formulating the coupling between levels in multilevel optimization by linear decomposition, proposed as improvements over the original formulation, now several years old, that relied on explicit equality constraints which were shown by application experience as occasionally causing numerical difficulties. The two new techniques represent the coupling without using explicit equality constraints, thus avoiding the above diffuculties and also reducing computational cost of the procedure. The old and new formulations are presented in detail and illustrated by an example of a structural optimization. A generic version of the improved algorithm is also developed for applications to multidisciplinary systems not limited to structures.

Sobieszczanski-Sobieski, Jaroslaw↗

NASA NTRS2004

Automatic Generation of Algorithms for the Statistical Analysis of Planetary Nebulae Images

Analyzing data sets collected in experiments or by observations is a Core scientific activity. Typically, experimentd and observational data are &aught with uncertainty, and the analysis is based on a statistical model of the conjectured underlying processes, The large data volumes collected by modern instruments make computer support indispensible for this. Consequently, scientists spend significant amounts of their time with the development and refinement of the data analysis programs. AutoBayes [GF+02, FS03] is a fully automatic synthesis system for generating statistical data analysis programs. Externally, it looks like a compiler: it takes an abstract problem specification and translates it into executable code. Its input is a concise description of a data analysis problem in the form of a statistical model as shown in Figure 1; its output is optimized and fully documented C/C++ code which can be linked dynamically into the Matlab and Octave environments. Internally, however, it is quite different: AutoBayes derives a customized algorithm implementing the given model using a schema-based process, and then further refines and optimizes the algorithm into code. A schema is a parameterized code template with associated semantic constraints which define and restrict the template s applicability. The schema parameters are instantiated in a problem-specific way during synthesis as AutoBayes checks the constraints against the original model or, recursively, against emerging sub-problems. AutoBayes schema library contains problem decomposition operators (which are justified by theorems in a formal logic in the domain of Bayesian networks) as well as machine learning algorithms (e.g., EM, k-Means) and nu- meric optimization methods (e.g., Nelder-Mead simplex, conjugate gradient). AutoBayes augments this schema-based approach by symbolic computation to derive closed-form solutions whenever possible. This is a major advantage over other statistical data analysis systems which use numerical approximations even in cases where closed-form solutions exist. AutoBayes is implemented in Prolog and comprises approximately 75.000 lines of code. In this paper, we take one typical scientific data analysis problem-analyzing planetary nebulae images taken by the Hubble Space Telescope-and show how AutoBayes can be used to automate the implementation of the necessary anal- ysis programs. We initially follow the analysis described by Knuth and Hajian [KHO2] and use AutoBayes to derive code for the published models. We show the details of the code derivation process, including the symbolic computations and automatic integration of library procedures, and compare the results of the automatically generated and manually implemented code. We then go beyond the original analysis and use AutoBayes to derive code for a simple image segmentation procedure based on a mixture model which can be used to automate a manual preproceesing step. Finally, we combine the original approach with the simple segmentation which yields a more detailed analysis. This also demonstrates that AutoBayes makes it easy to combine different aspects of data analysis.

Fischer, Bernd↗

NASA NTRS1989

Constraint elimination in dynamical systems

Large space structures (LSSs) and other dynamical systems of current interest are often extremely complex assemblies of rigid and flexible bodies subjected to kinematical constraints. A formulation is presented for the governing equations of constrained multibody systems via the application of singular value decomposition (SVD). The resulting equations of motion are shown to be of minimum dimension.

Singh, R. P.↗

NASA NTRS2014

Diagnosability-Based Sensor Placement through Structural Model Decomposition

Systems health management, and in particular fault diagnosis, is important for ensuring safe, correct, and efficient operation of complex engineering systems. The performance of an online health monitoring system depends critically on the available sensors of the system. However, the set of selected sensors is subject to many constraints, such as cost and weight, and hence, these sensors must be selected judiciously. This paper presents an offline design-time sensor placement approach for complex systems. Our diagnosis method is built upon the analysis of model-based residuals, which are computed using structural model decomposition. Sensor placement in this framework manifests as a residual selection problem, and we aim to find the set of residuals that achieves single-fault diagnosability of the system, uses the minimum number of sensors, and corresponds to the best model decomposition for the best distribution of the diagnosis system. We present a set of algorithms for solving this problem and compare their performance in terms of computational complexity and optimality of solutions. We demonstrate the approach using a benchmark multi-tank system.

Daigle, Matthew↗

NASA NTRS2001

Rotation of EOFs by the Independent Component Analysis: Towards A Solution of the Mixing Problem in the Decomposition of Geophysical Time Series

The Independent Component Analysis is a recently developed technique for component extraction. This new method requires the statistical independence of the extracted components, a stronger constraint that uses higher-order statistics, instead of the classical decorrelation, a weaker constraint that uses only second-order statistics. This technique has been used recently for the analysis of geophysical time series with the goal of investigating the causes of variability in observed data (i.e. exploratory approach). We demonstrate with a data simulation experiment that, if initialized with a Principal Component Analysis, the Independent Component Analysis performs a rotation of the classical PCA (or EOF) solution. This rotation uses no localization criterion like other Rotation Techniques (RT), only the global generalization of decorrelation by statistical independence is used. This rotation of the PCA solution seems to be able to solve the tendency of PCA to mix several physical phenomena, even when the signal is just their linear sum.

Aires, Filipe↗

NASA NTRS2000

Rotation of EOFs by the Independent Component Analysis: Towards a Solution of the Mixing Problem in the Decomposition of Geophysical Time Series

Aires, Filipe↗

NASA NTRSDate not supplied

Fast Aircraft Separation Calculations for Gradient Based Optimization of Airspace Simulations

Simulations of airspace operational concepts can play a significant role in determining future paradigms that would allow for a safe increase in airspace density. In particular, airspace simulations which are capable of handling large numbers of aircraft act as an enabling capability for the testing of proposed airspace operational concepts. Simulations allowing for gradient based optimization methods are particularly attractive, since they would potentially allow for an efficient and empirical means to derive best operational practices. These could also allow for vehicle multidisciplinary design and optimization studies to include air traffic management considerations as a discipline. But any large scale simulation of airspace operations must include some methodology for addressing airspace separation requirements, which in the most direct sense would be tracked in a manner that computationally grows as a quadratic function of the number of simulated aircraft. Efficient indirect methods have been developed in certain contexts to address this limitation. However, any means of addressing separation requirements in a gradient based optimization context should be implemented by functions which provide analytic derivative information to maximize numerical precision and computational efficiency. In this paper, a fast and differentiable separation metric is described in application to gradient based optimization of airspace operations. Rather than computing the separation distance between every pair of aircraft in a simulation, this method effectively reduces the problem to a smaller relevant set using a geometric decomposition. This method guarantees that the smallest distance at all points in simulated time is determined exactly. When used in an optimization constraint context, this guarantees that a minimum separation is maintained between all pairs of aircraft. The presented metric has logarithmic computational growth with respect to the number of simulated aircraft, and is shown to perform well in a series of notional 2D airspace optimization problems when used to enforce specified airborne separation constraints. Results show that this is notably faster than a direct pairwise distance computing metric for optimizations involving both small and large numbers of aircraft, yet enforce separation requirements to the same tolerance. It is shown that this favorable scalability is an enabling capability for more sophisticated air traffic management conceptual studies.

Optimization↗

NASA NTRS1993

An integrated optimum design approach for high speed prop-rotors including acoustic constraints

The objective of this research is to develop optimization procedures to provide design trends in high speed prop-rotors. The necessary disciplinary couplings are all considered within a closed loop multilevel decomposition optimization process. The procedures involve the consideration of blade-aeroelastic aerodynamic performance, structural-dynamic design requirements, and acoustics. Further, since the design involves consideration of several different objective functions, multiobjective function formulation techniques are developed.

Chattopadhyay, Aditi↗

NASA NTRS2009

Regression Model Optimization for the Analysis of Experimental Data

A candidate math model search algorithm was developed at Ames Research Center that determines a recommended math model for the multivariate regression analysis of experimental data. The search algorithm is applicable to classical regression analysis problems as well as wind tunnel strain gage balance calibration analysis applications. The algorithm compares the predictive capability of different regression models using the standard deviation of the PRESS residuals of the responses as a search metric. This search metric is minimized during the search. Singular value decomposition is used during the search to reject math models that lead to a singular solution of the regression analysis problem. Two threshold dependent constraints are also applied. The first constraint rejects math models with insignificant terms. The second constraint rejects math models with near-linear dependencies between terms. The math term hierarchy rule may also be applied as an optional constraint during or after the candidate math model search. The final term selection of the recommended math model depends on the regressor and response values of the data set, the user s function class combination choice, the user s constraint selections, and the result of the search metric minimization. A frequently used regression analysis example from the literature is used to illustrate the application of the search algorithm to experimental data.

Ulbrich, N.↗

NASA NTRS2023

The First X-Ray Polarimetric Observation of the Black Hole Binary LMC X-1

We report on an X-ray polarimetric observation of the high-mass X-ray binary LMC X-1 in the high/soft state, obtained by the Imaging X-ray Polarimetry Explorer ( IXPE ) in 2022 October. The measured polarization is below the minimum detectable polarization of 1.1 per cent (at the 99 per cent confidence level). Simultaneously, the source was observed with the Neutron Star Interior Composition Explorer (NICER), Nuclear Spectroscopic Telescope Array ( NuSTAR ), and Spectrum-Rontgen-Gamma ( SRG )/Astronomical Roentgen Telescope – X-ray Concentrator (ART-XC) instruments, which enabled spectral decomposition into a dominant thermal component and a Comptonized one. The low 2–8 keV polarization of the source did not allow for strong constraints on the black hole spin and inclination of the accretion disc. However, if the orbital inclination of about 36◦ is assumed, then the upper limit is consistent with predictions for pure thermal emission from geometrically thin and optically thick discs. Assuming the polarization degree of the Comptonization component to be 0, 4, or 10 per cent, and oriented perpendicular to the polarization of the disc emission (in turn assumed to be perpendicular to the large-scale ionization cone orientation detected in the optical band), an upper limit to the polarization of the disc emission of 1.0, 0.9, or 0.9 per cent, respectively, is found (at the 99 per cent confidence level).

LMC X-1↗

NASA NTRS1994

Constraint-based integration of planning and scheduling for space-based observatory management

Progress toward the development of effective, practical solutions to space-based observatory scheduling problems within the HSTS scheduling framework is reported. HSTS was developed and originally applied in the context of the Hubble Space Telescope (HST) short-term observation scheduling problem. The work was motivated by the limitations of the current solution and, more generally, by the insufficiency of classical planning and scheduling approaches in this problem context. HSTS has subsequently been used to develop improved heuristic solution techniques in related scheduling domains and is currently being applied to develop a scheduling tool for the upcoming Submillimeter Wave Astronomy Satellite (SWAS) mission. The salient architectural characteristics of HSTS and their relationship to previous scheduling and AI planning research are summarized. Then, some key problem decomposition techniques underlying the integrated planning and scheduling approach to the HST problem are described; research results indicate that these techniques provide leverage in solving space-based observatory scheduling problems. Finally, more recently developed constraint-posting scheduling procedures and the current SWAS application focus are summarized.

Muscettola, Nicola↗

NASA NTRS1987

Evaluation of constraint stabilization procedures for multibody dynamical systems

Comparative numerical studies of four constraint treatment techniques for the simulation of general multibody dynamic systems are presented, and results are presented for the example of a classical crank mechanism and for a simplified version of the seven-link manipulator deployment problem. The staggered stabilization technique (Park, 1986) is found to yield improved accuracy and robustness over Baumgarte's (1972) technique, the singular decomposition technique (Walton and Steeves, 1969), and the penalty technique (Lotstedt, 1979). Furthermore, the staggered stabilization technique offers software modularity, and the only data each solution module needs to exchange with the other is a set of vectors plus a common module to generate the gradient matrix of the constraints, B.

Park, K. C.↗

NASA NTRS1993

Development of a large scale Chimera grid system for the Space Shuttle Launch Vehicle

The application of CFD techniques to large problems has dictated the need for large team efforts. This paper offers an opportunity to examine the motivations, goals, needs, problems, as well as the methods, tools, and constraints that defined NASA's development of a 111 grid/16 million point grid system model for the Space Shuttle Launch Vehicle. The Chimera approach used for domain decomposition encouraged separation of the complex geometry into several major components each of which was modeled by an autonomous team. ICEM-CFD, a CAD based grid generation package, simplified the geometry and grid topology definition by provoding mature CAD tools and patch independent meshing. The resulting grid system has, on average, a four inch resolution along the surface.

Pearce, Daniel G.↗

NASA NTRS2005

Predicting Flows of Rarefied Gases

DSMC Analysis Code (DAC) is a flexible, highly automated, easy-to-use computer program for predicting flows of rarefied gases -- especially flows of upper-atmospheric, propulsion, and vented gases impinging on spacecraft surfaces. DAC implements the direct simulation Monte Carlo (DSMC) method, which is widely recognized as standard for simulating flows at densities so low that the continuum-based equations of computational fluid dynamics are invalid. DAC enables users to model complex surface shapes and boundary conditions quickly and easily. The discretization of a flow field into computational grids is automated, thereby relieving the user of a traditionally time-consuming task while ensuring (1) appropriate refinement of grids throughout the computational domain, (2) determination of optimal settings for temporal discretization and other simulation parameters, and (3) satisfaction of the fundamental constraints of the method. In so doing, DAC ensures an accurate and efficient simulation. In addition, DAC can utilize parallel processing to reduce computation time. The domain decomposition needed for parallel processing is completely automated, and the software employs a dynamic load-balancing mechanism to ensure optimal parallel efficiency throughout the simulation.

LeBeau, Gerald J.↗

NASA NTRS2019

A Multi-Physics Study on High-Specific Power Li-O2 Batteries for Electric Aircraft

Commercialization of lithium-air batteries faces many challenges, such as electrolyte decomposition, short cycle life, low energy and power density, etc. However, commercialization of Li-O2 batteries for aeronautics is much more challenging due to additional safety constraints on cyclability and performance (high specific power and specific energy). For this presentation, we will discuss inter-related aspects of physics-based modeling of a pack: cell and battery model calibration. In addition, we will evaluate and present optimal battery designs for high discharge current density, high discharge time, and low battery mass using simulation-based optimization.The Finite Element Model (FEM) used to simulate a Li-O2 cell is based on the work of Bevara [1]. The different aspects of the model are based on: porous electrode theory and concentrated electrolyte theory; quantum tunneling model for the resistance of conformal layer of discharge product (Li2O2) [1]; Butler-Volmer kinetics for electrochemical reaction; Fick's diffusion for oxygen transport; and an oxygen dissolution model is applied at the air/electrolyte interface [2]. The electrolyte properties such as ion conductivity, ion diffusion, oxygen diffusion, and mass density of the electrolyte were taken from Molecular Dynamics (MD) simulations [3]; while the other model parameters, which includes mass of cell components, were calibrated to match experiments at high discharge current densities. The cell mass includes the anode, cathode, separator, electrolyte, and other components (such as current collector). This calibrated model is used to perform parametric studies on cathode thickness, porosity, tortuosity, carbon particle size, electrolyte transport and material properties, partial pressure of oxygen, discharge time, and discharge current density to study optimal designs for high specific power and energy. References:1. Bevara, V. & Andrei, P. (2014), J. Electrochem. Soc. 161 (14), A2068-A2079.2.Mehta, M. & Andrei, P. (2015), J. Power Sources. 286, 299-308.3.Liyana-Arachchi, T.; Haskins, J.; Burke, C.; Diederichsen, K.; McCloskey, B.; & Lawson, J. (2018), J. Phys. Chem. B. 122 (36), 8548 - 8559.4.Choi, W.; Kikumoto, H.; Choudhary, R. & Ooka, R. (2018), Applied Energy, 209, 306-321.

Mehta, Mohit↗

NASA NTRS1993

On the spectral stability of time integration algorithms for a class of constrained dynamics problems

Incomplete field formulations have recently been the subject of intense research because of their potential in coupled analysis of independently modeled substructures, adaptive refinement, domain decomposition, and parallel processing. This paper discusses the design and analysis of time-integration algorithms for these formulations and emphasizes the treatment of their inter-subdomain constraint equations. These constraints are shown to introduce a destabilizing effect in the dynamic system that can be analyzed by investigating the behavior of the time-integration algorithm at infinite and zero frequencies. Three different approaches for constructing penalty-free unconditionally stable second-order accurate solution procedures for this class of hybrid formulations are presented, discussed and illustrated with numerical examples. The theoretical results presented in this paper also apply to a large family of nonlinear multibody dynamics formulations. Some of the algorithms outlined herein are important alternatives to the popular technique consisting of transforming differential/algebraic equations into ordinary differential equations via the introduction of a stabilization term that depends on arbitrary constants and that influences the computed so1ution.

Farhat, Charbel↗