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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 595 records · Page 33

Using integrals of the state transition matrix for efficient transient-response computations

An iterative technique for the computation of lower-order state systems with poles at the origin (such as aircraft lateral dynamics) or with time-polynomial inputs is developed and demonstrated. The integrated input or output signals are computed using the integrals of the state transition matrix, thus reducing the system order and computation time. In an application to the lateral response of a DC-8 aircraft (Grunwald, 1981), this method required only 7824 multiplication or addition operations (at fourth order) to achieve the accuracy obtained in 15,012 operations by a conventional sixth-order computation.

Grunwald, A. J.↗

Robust control with structured perturbations

Two important problems in the area of control systems design and analysis are discussed. The first is the robust stability using characteristic polynomial, which is treated first in characteristic polynomial coefficient space with respect to perturbations in the coefficients of the characteristic polynomial, and then for a control system containing perturbed parameters in the transfer function description of the plant. In coefficient space, a simple expression is first given for the l(sup 2) stability margin for both monic and non-monic cases. Following this, a method is extended to reveal much larger stability region. This result has been extended to the parameter space so that one can determine the stability margin, in terms of ranges of parameter variations, of the closed loop system when the nominal stabilizing controller is given. The stability margin can be enlarged by a choice of better stabilizing controller. The second problem describes the lower order stabilization problem, the motivation of the problem is as follows. Even though the wide range of stabilizing controller design methodologies is available in both the state space and transfer function domains, all of these methods produce unnecessarily high order controllers. In practice, the stabilization is only one of many requirements to be satisfied. Therefore, if the order of a stabilizing controller is excessively high, one can normally expect to have a even higher order controller on the completion of design such as inclusion of dynamic response requirements, etc. Therefore, it is reasonable to have a lowest possible order stabilizing controller first and then adjust the controller to meet additional requirements. The algorithm for designing a lower order stabilizing controller is given. The algorithm does not necessarily produce the minimum order controller; however, the algorithm is theoretically logical and some simulation results show that the algorithm works in general.

Keel, Leehyun↗

A weak Hamiltonian finite element method for optimal control problems

A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

Hodges, Dewey H.↗

Computational analysis of a stability robustness margin for structured real-parameter perturbations

An efficient computational method is presented for stability robustness analysis with structured real-parameter perturbations. A generic model of a class of uncertain dynamical systems is used as an example. The parameter uncertainty is characterized by a real scalar, epsilon. Multilinearity of the closed-loop characteristic polynomial is exploited to permit application of the mapping theorem to calculate the stability robustness margin. It is found that sensitive geometry of the stability boundary in the epsilon, omega-plane renders problematic the calculation of the minimum epsilon as a function of omega. This difficulty is avoided by calculating the minimum distance to the image of the uncertainty domain over omega as a function of epsilon. It is also shown that a certain class of uncertain dynamical systems has the required multilinearity property and are thus amenable to the proposed technique.

Wedell, Evan↗

Modeling and synthesis of multicomputer interconnection networks

The type of interconnection network employed has a profound effect on the performance of a multicomputer and multiprocessor design. Adequate models are needed to aid in the design and development of interconnection networks. A novel modeling approach using statistical and optimization techniques is described. This method represents an attempt to compare diverse interconnection network designs in a way that allows not only the best of existing designs to be identified but to suggest other, perhaps hybrid, networks that may offer better performance. Stepwise linear regression is used to develop a polynomial surface representation of performance in a (k+1) space with a total of k quantitative and qualitative independent variables describing graph-theoretic characteristics such as size, average degree, diameter, radius, girth, node-connectivity, edge-connectivity, minimum dominating set size, and maximum number of prime node and edge cutsets. Dependent variables used to measure performance are average message delay and the ratio of message completion rate to network connection cost. Response Surface Methodology (RSM) optimizes a response variable from a polynomial function of several independent variables. Steepest ascent path may also be used to approach optimum points.

Standley, Hilda M.↗

Weak Hamiltonian finite element method for optimal control problems

A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

Hodges, Dewey H.↗

A weak Hamiltonian finite element method for optimal control problems

A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

Hodges, Dewey H.↗

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

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

Baecher, Juergen↗

Quadrature imposition of compatibility conditions in Chebyshev methods

This paper handles a problem encountered in the solution by way of Chebyshev spectral collocation discretization of the Poisson equation with homogeneous Neumann boundary conditions. When pseudospectral Chebyshev methodology is utilized to discretize the partial differential equation these integrals have to be approximated by an appropriate quadrature formula. The correct quadrature formula is developed for these problems, taking into account the degree of the polynomials involved. It is shown that this formula leads to a well-conditioned Chebyshev approximation to the differential equations and that the compatibility condition is automatically satisfied.

Gottlieb, D.↗

Analytic and approximate boundary-fitted coordinate systems for fluid flow simulation

A method for constructing a direct functional relation between the computational and physical domains such that boundaries in the computational domain map into boundaries in the physical domain is presented. This method which is called the 'two-boundary technique' is based on generating functions that represent two disconnected boundaries in the physical domain and an independent function which connects one boundary with another to generate grids. The suggested connecting functions are simple linear and cubic parametric polynomials with parameters based on position and derivatives at the disconnected boundaries. The boundaries can be defined by analytical, approximate, and tension spline functions; the grid density in specified regions is controlled by embedding contraction functions in either the boundary representation or the connecting function.

Smith, R. E.↗

Prediction and causal reasoning in planning

Nonlinear planners are often touted as having an efficiency advantage over linear planners. The reason usually given is that nonlinear planners, unlike their linear counterparts, are not forced to make arbitrary commitments to the order in which actions are to be performed. This ability to delay commitment enables nonlinear planners to solve certain problems with far less effort than would be required of linear planners. Here, it is argued that this advantage is bought with a significant reduction in the ability of a nonlinear planner to accurately predict the consequences of actions. Unfortunately, the general problem of predicting the consequences of a partially ordered set of actions is intractable. In gaining the predictive power of linear planners, nonlinear planners sacrifice their efficiency advantage. There are, however, other advantages to nonlinear planning (e.g., the ability to reason about partial orders and incomplete information) that make it well worth the effort needed to extend nonlinear methods. A framework is supplied for causal inference that supports reasoning about partially ordered events and actions whose effects depend upon the context in which they are executed. As an alternative to a complete but potentially exponential-time algorithm, researchers provide a provably sound polynomial-time algorithm for predicting the consequences of partially ordered events.

Dean, T.↗

A note on the accuracy of spectral method applied to nonlinear conservation laws

Fourier spectral method can achieve exponential accuracy both on the approximation level and for solving partial differential equations if the solutions are analytic. For a linear partial differential equation with a discontinuous solution, Fourier spectral method produces poor point-wise accuracy without post-processing, but still maintains exponential accuracy for all moments against analytic functions. In this note we assess the accuracy of Fourier spectral method applied to nonlinear conservation laws through a numerical case study. We find that the moments with respect to analytic functions are no longer very accurate. However the numerical solution does contain accurate information which can be extracted by a post-processing based on Gegenbauer polynomials.

Shu, Chi-Wang↗

Applying Simulated Annealing to Problems in Model-Based Diagnosis

Generating all diagnoses is computationally intractable. Therefore, many of the state-of-the-art approaches are incomplete. Quantum computers may however offer a solution. The first commercially available quantum computer is being used to minimize polynomials that are difficult for classical simulated annealing but easy for quantum annealing. All problems in Model-based Diagnosis (MBD) can be transformed into a polynomial minimization problem, allowing one to apply a quantum algorithm called quantum annealing to solve MBD problems. To better understand the need for this quantum approach, we designed two simulated annealingdiagnostic algorithms tailored to run on a polynomial representation of MBD. These algorithms differ on their policy for random neighborhood variable selection. In addition, enhanced metrics were devised to provide more diagnostic coverage. Finally, these two simulated annealing algorithms were analyzed and empirically evaluated and compared against state-of-the-art probabilistic methods for MBD such as SAFARI using ISCAS-85.

Simulated annealing↗

Exponential concentration in quantum kernel methods

Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model one is guaranteed to find the optimal model’s parameters due to the convexity of the training landscape. However, this is based on the assumption that the quantum kernel can be efficiently obtained from quantum hardware. In this work we study the performance of quantum kernel models from the perspective of the resources needed to accurately estimate kernel values. We show that, under certain conditions, values of quantum kernels over different input data can be exponentially concentrated (in the number of qubits) towards some fixed value. Thus on training with a polynomial number of measurements, one ends up with a trivial model where the predictions on unseen inputs are independent of the input data. We identify four sources that can lead to concentration including expressivity of data embedding, global measurements, entanglement and noise. For each source, an associated concentration bound of quantum kernels is analytically derived. Lastly, we show that when dealing with classical data, training a parametrized data embedding with a kernel alignment method is also susceptible to exponential concentration. Our results are verified through numerical simulations for several QML tasks. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation of quantum kernels and so the performance of quantum kernel methods.

97 MATHEMATICS AND COMPUTING↗

An improved method for precise automatic co-registration of moderate and high-resolution spacecraft imagery

Improvements to the automated co-registration and change detection software package, AFIDS (Automatic Fusion of Image Data System) has recently completed development for and validation by NGA/GIAT. The improvements involve the integration of the AFIDS ultra-fine gridding technique for horizontal displacement compensation with the recently evolved use of Rational Polynomial Functions/ Coefficients (RPFs/RPCs) for image raster pixel position to Latitude/Longitude indexing. Mapping and orthorectification (correction for elevation effects) of satellite imagery defies exact projective solutions because the data are not obtained from a single point (like a camera), but as a continuous process from the orbital path. Standard image processing techniques can apply approximate solutions, but advances in the state-of-the-art had to be made for precision change-detection and time-series applications where relief offsets become a controlling factor. The earlier AFIDS procedure required the availability of a camera model and knowledge of the satellite platform ephemeredes. The recent design advances connect the spacecraft sensor Rational Polynomial Function, a deductively developed model, with the AFIDS ultrafine grid, an inductively developed representation of the relationship raster pixel position to latitude /longitude. As a result, RPCs can be updated by AFIDS, a situation often necessary due to the accuracy limits of spacecraft navigation systems. An example of precision change detection will be presented from Quickbird.

co-registration↗

Finite elements based on consistently assumed stresses and displacements

Finite element stiffness matrices are derived using an extended Hellinger-Reissner principle in which internal displacements are added to serve as Lagrange multipliers to introduce the equilibrium constraint in each element. In a consistent formulation the assumed stresses are initially unconstrained and complete polynomials and the total displacements are also complete such that the corresponding strains are complete in the same order as the stresses. Several examples indicate that resulting properties for elements constructed by this consistent formulation are ideal and are less sensitive to distortions of element geometries. The method has been used to find the optimal stress terms for plane elements, 3-D solids, axisymmetric solids, and plate bending elements.

Pian, T. H. H.↗

Augmenting Parametric Optimal Ascent Trajectory Modeling with Graph Theory

It has been well documented that decisions made in the early stages of Conceptual and Pre-Conceptual design commit up to 80% of total Life-Cycle Cost (LCC) while engineers know the least about the product they are designing [1]. Once within Preliminary and Detailed design however, making changes to the design becomes far more difficult to enact in both cost and schedule. Primarily this has been due to a lack of detailed data usually uncovered later during the Preliminary and Detailed design phases. In our current budget-constrained environment, making decisions within Conceptual and Pre-Conceptual design which minimize LCC while meeting requirements is paramount to a program's success. Within the arena of launch vehicle design, optimizing the ascent trajectory is critical for minimizing the costs present within such concerns as propellant, aerodynamic, aeroheating, and acceleration loads while meeting requirements such as payload delivered to a desired orbit. In order to optimize the vehicle design its constraints and requirements must be known, however as the design cycle proceeds it is all but inevitable that the conditions will change. Upon that change, the previously optimized trajectory may no longer be optimal, or meet design requirements. The current paradigm for adjusting to these updates is generating point solutions for every change in the design's requirements [2]. This can be a tedious, time-consuming task as changes in virtually any piece of a launch vehicle's design can have a disproportionately large effect on the ascent trajectory, as the solution space of the trajectory optimization problem is both non-linear and multimodal [3]. In addition, an industry standard tool, Program to Optimize Simulated Trajectories (POST), requires an expert analyst to produce simulated trajectories that are feasible and optimal [4]. In a previous publication the authors presented a method for combatting these challenges [5]. In order to bring more detailed information into Conceptual and Pre-Conceptual design, knowledge of the effects originating from changes to the vehicle must be calculated. In order to do this, a model capable of quantitatively describing any vehicle within the entire design space under consideration must be constructed. This model must be based upon analysis of acceptable fidelity, which in this work comes from POST. Design space interrogation can be achieved with surrogate modeling, a parametric, polynomial equation representing a tool. A surrogate model must be informed by data from the tool with enough points to represent the solution space for the chosen number of variables with an acceptable level of error. Therefore, Design Of Experiments (DOE) is used to select points within the design space to maximize information gained on the design space while minimizing number of data points required. To represent a design space with a non-trivial number of variable parameters the number of points required still represent an amount of work which would take an inordinate amount of time via the current paradigm of manual analysis, and so an automated method was developed. The best practices of expert trajectory analysts working within NASA Marshall's Advanced Concepts Office (ACO) were implemented within a tool called multiPOST. These practices include how to use the output data from a previous run of POST to inform the next, determining whether a trajectory solution is feasible from a real-world perspective, and how to handle program execution errors. The tool was then augmented with multiprocessing capability to enable analysis on multiple trajectories simultaneously, allowing throughput to scale with available computational resources. In this update to the previous work the authors discuss issues with the method and solutions.

Patrick D Dees↗