SEARCH · Search NASA
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Sequential gradient restoration algorithm for optimal control requiring state, control and parameter to satisfy vector differential equation, initial and final conditions
Well-posed models and computational algorithms are developed and analyzed for control of a class of partial differential equations that describe the motions of thermo-viscoelastic structures. An abstract (state space) framework and a general well-posedness result are presented that can be applied to a large class of thermo-elastic and thermo-viscoelastic models. This state space framework is used in the development of a computational scheme to be used in the solution of a linear quadratic regulator (LQR) control problem. A detailed convergence proof is provided for the viscoelastic model and several numerical results are presented to illustrate the theory and to analyze problems for which the theory is incomplete.
Parameter-dependence properties are developed in the context of a linear abstract Cauchy problem governed by a parameter-dependent operator. Of particular interest are problems in which the parameter induces an unbounded perturbation of the evolution operator. Conditions are stated under which the derivative of the state with respect to the parameter possesses certain smoothness properties. These properties lead to local convergence results for a gradient-based estimation algorithm based on quasi-linearization. Numerical results concerning a delay-differential equation indicate the effect of a forcing function on parameter sensitivity.
An iterative algorithm suitable for the solution of a system of nonlinear hyperbolic partial differentiation equations in multiple dimensions is discussed. Current numerical methods for systems of nonlinear PDEs have limited parallelism due to strong coupling between the equations. This method decouples the PDEs by linearizing the convention coefficient for a space-time domain. This provides large grain parallelism. The linearization also allows the treatment of some terms in the equations as source terms, providing more freedom to choose from a wider variety of numerical methods. Smaller grain parallelism may be exploited within the solves for each equation. Thus, the method has potential for parallelism at several levels.
GEODYNII is a conventional batch least-squares differential corrector computer program with deterministic models of the physical environment. Conventional algorithms were used to process differenced phase and pseudorange data to determine eight-day Global Positioning system (GPS) orbits with several meter accuracy. However, random physical processes drive the errors whose magnitudes prevent improving the GPS orbit accuracy. To improve the orbit accuracy, these random processes should be modeled stochastically. The conventional batch least-squares algorithm cannot accommodate stochastic models, only a stochastic estimation algorithm is suitable, such as a sequential filter/smoother. Also, GEODYNII cannot currently model the correlation among data values. Differenced pseudorange, and especially differenced phase, are precise data types that can be used to improve the GPS orbit precision. To overcome these limitations and improve the accuracy of GPS orbits computed using GEODYNII, we proposed to develop a sequential stochastic filter/smoother processor by using GEODYNII as a type of trajectory preprocessor. Our proposed processor is now completed. It contains a correlated double difference range processing capability, first order Gauss Markov models for the solar radiation pressure scale coefficient and y-bias acceleration, and a random walk model for the tropospheric refraction correction. The development approach was to interface the standard GEODYNII output files (measurement partials and variationals) with software modules containing the stochastic estimator, the stochastic models, and a double differenced phase range processing routine. Thus, no modifications to the original GEODYNII software were required. A schematic of the development is shown. The observational data are edited in the preprocessor and the data are passed to GEODYNII as one of its standard data types. A reference orbit is determined using GEODYNII as a batch least-squares processor and the GEODYNII measurement partial (FTN90) and variational (FTN80, V-matrix) files are generated. These two files along with a control statement file and a satellite identification and mass file are passed to the filter/smoother to estimate time-varying parameter states at each epoch, improved satellite initial elements, and improved estimates of constant parameters.
This paper describes the derivation of a continuous matrix differential equation for the SIRF filter, and the development of a computer algorithm to implement this filter.
MueLu is intended for the research and development of multigrid algorithms used in the solution of sparse linear systems arising from systems of partial differential equations. The software provides multigrid source code, test programs, and short example programs to demonstrate the various interfaces for creating, accessing, and applying the solvers. MueLu currently provides an implementation of smoothed aggregation algebraic multigrid method and interfaces to many commonly used smoothers. However, the software is intended to be extensible, and new methods can be incorporated easily. MueLu also allows for advanced usage, such as combining multiple methods and segregated solves. The library supports point and block access to matrix data. All algorithms and methods in MueLu have been or will be published in the open scientific literature.
Power system dynamics are generally modeled by high dimensional nonlinear differential-algebraic equations due to a large number of generators, loads, and transmission lines. Thus, its computational complexity grows exponentially with the system size. This paper demonstrates the potential use of quantum computing algorithms to model the power system dynamics. Leveraging a symbolic programming framework, we equivalently convert the power system dynamics’ differential algebraic equations (DAEs) into ordinary differential equations (ODEs), where the data of the state vector can be encoded into quantum computers via amplitude encoding. The system's nonlinearity is captured by Taylor polynomial expansion, the quantum state tensor, and Hamiltonian simulation, whereas state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can simulate the dynamics of the power system with high accuracy, whereas its complexity is polynomial in the logarithm of the system dimension. Our work also illustrates the use of scientific machine learning tools for implementing scientific computing concepts, e.g., Taylor expansion, DAEs/ODEs transform, and quantum computing solver, in the field of power engineering.
A new algorithm based on a nonlinear programming technique to correct the geometrical distortions of one digital image with respect to another is discussed. This algorithm promises to be superior to existing ones in that it is capable of treating localized differential scaling, translational and rotational errors over the whole image plane. A series of piece-wise 'rubber-sheet' approximations are used, constrained in such a manner that a smooth approximation over the entire image can be obtained. The theoretical derivation is included. The result of using the algorithm to register four channel S065 Apollo IX digitized photography over Imperial Valley, California, is discussed in detail.
Atmospheric aerosol has uncertain impacts on the global climate system, as well as on atmospheric and bio-geo-chemical processes of regional and local scales. EOS-MODIS is one example of a satellite sensor designed to improve understanding of the aerosols' type, size and distribution at all temporal and spatial scales. Ocean scientists also plan to use data from EOS-MODIS to assess the temporal and spatial coverage of in-water chlorophyll. MODIS is the first sensor planned to observe the combined ocean-atmosphere system with a wide spectral range (from 410 to 2200 nm). Dust aerosol and salt aerosol have similar spectral signals for wavelengths longer than 550 nm, but because dust selectively absorbs blue light, they have divergent signals in the blue wavelength regions (412 to 490 nm). Chlorophyll also selectively absorbs blue radiation, so that varying chlorophyll concentrations produces a highly varying signal in the blue regions, but less variability in the green, and almost no signal in the red to mid-infrared regions. Thus, theoretically, it may be difficult to differentiate dust and salt in the presence of unknown chlorophyll in the ocean. This study attempts to address the cases in which aerosol and chlorophyll signals can and cannot be separated. For the aerosol spectra, we use the aerosol lookup table from the operational MODIS aerosol-over-ocean algorithm, and for chlorophyll spectra, we use the SeaBAM data set (created for SeaWiFS). We compare the signals using Principal Component Analysis and attempt to retrieve both chlorophyll and aerosol properties using a variant of the operational MODIS aerosol-over-ocean algorithm. Results show that for small optical depths, less than 0.5, it is not possible to differentiate between dust and salt and to determine the chlorophyll concentration at the same time. For larger aerosol optical depths, the chlorophyll signals are comparatively insignificant, and we can hope to distinguish between dust and salt.
Computational procedures for kinematic and dynamic analysis of three-dimensional multibody dynamic (MBD) systems are developed from the differential-algebraic equations (DAE's) viewpoint. Constraint violations during the time integration process are minimized and penalty constraint stabilization techniques and partitioning schemes are developed. The governing equations of motion, a two-stage staggered explicit-implicit numerical algorithm, are treated which takes advantage of a partitioned solution procedure. A robust and parallelizable integration algorithm is developed. This algorithm uses a two-stage staggered central difference algorithm to integrate the translational coordinates and the angular velocities. The angular orientations of bodies in MBD systems are then obtained by using an implicit algorithm via the kinematic relationship between Euler parameters and angular velocities. It is shown that the combination of the present solution procedures yields a computationally more accurate solution. To speed up the computational procedures, parallel implementation of the present constraint treatment techniques, the two-stage staggered explicit-implicit numerical algorithm was efficiently carried out. The DAE's and the constraint treatment techniques were transformed into arrowhead matrices to which Schur complement form was derived. By fully exploiting the sparse matrix structural analysis techniques, a parallel preconditioned conjugate gradient numerical algorithm is used to solve the systems equations written in Schur complement form. A software testbed was designed and implemented in both sequential and parallel computers. This testbed was used to demonstrate the robustness and efficiency of the constraint treatment techniques, the accuracy of the two-stage staggered explicit-implicit numerical algorithm, and the speed up of the Schur-complement-based parallel preconditioned conjugate gradient algorithm on a parallel computer.
This paper addresses the need for a fast batch chemistry solver to perform the kinetics part of a split operator formulation of turbulent reacting flows, with special attention focused on the solution of the ordinary differential equations governing a homogeneous gas-phase chemical reaction. For this purpose, a two-part predictor-corrector algorithm which incorporates an exponentially fitted trapezoidal method was developed. The algorithm performs filtering of ill-posed initial conditions, automatic step-size selection, and automatic selection of Jacobi-Newton or Newton-Raphson iteration for convergence to achieve maximum computational efficiency while observing a prescribed error tolerance. The new algorithm, termed CREK1D (combustion reaction kinetics, one-dimensional), compared favorably with the code LSODE when tested on two representative problems drawn from combustion kinetics, and is faster than LSODE.
MueMat is intended for the research and development of multigrid algorithms used in the solution of sparse linear systems arising from systems of partial differential equations. The software can generate example linear systems and provides short programs to demonstrate the various interfaces for creating, accessing, and applying the solvers. MueMat currently includes two types of algebraic multigrid methods and many commonly used smoothers. However, the software is intended to be extensible, and new methods can be incorporated easily. MueMat also allows for advanced usage, such as combining multiple methods and segregated solves. The library supports point and block access to matrix data. MueMat has been designed for use within the programming environment of the Mathworks program MATLAB®. All algorithms and methods in MueMat have been or will be published in the open scientific literature.
Purpose: This paper concerns the feasibility of x-ray differential phase contrast (DPC) tomosynthesis imaging using a grating-based DPC benchtop experimental system, which is equipped with a commercial digital flat-panel detector and a medical-grade rotating-anode x-ray tube. An extensive system characterization was performed to quantify its imaging performance. Methods: The major components of the benchtop system include a diagnostic x-ray tube with a 1.0 mm nominal focal spot size, a flat-panel detector with 96 μm pixel pitch, a sample stage that rotates within a limited angular span of ±30°, and a Talbot-Lau interferometer with three x-ray gratings. A total of 21 projection views acquired with 3° increments were used to reconstruct three sets of tomosynthetic image volumes, including the conventional absorption contrast tomosynthesis image volume (AC-tomo) reconstructed using the filtered-backprojection (FBP) algorithm with the ramp kernel, the phase contrast tomosynthesis image volume (PC-tomo) reconstructed using FBP with a Hilbert kernel, and the differential phase contrast tomosynthesis image volume (DPC-tomo) reconstructed using the shift-and-add algorithm. Three inhouse physical phantoms containing tissue-surrogate materials were used to characterize the signal linearity, the signal difference-to-noise ratio (SDNR), the three-dimensional noise power spectrum (3D NPS), and the through-plane artifact spread function (ASF). Results: While DPC-tomo highlights edges and interfaces in the image object, PC-tomo removes the differential nature of the DPC projection data and its pixel values are linearly related to the decrement of the real part of the x-ray refractive index. The SDNR values of polyoxymethylene in water and polystyrene in oil are 1.5 and 1.0, respectively, in AC-tomo, and the values were improved to 3.0 and 2.0, respectively, in PC-tomo. PC-tomo and AC-tomo demonstrate equivalent ASF, but their noise characteristics quantified by the 3D NPS were found to be different due to the difference in the tomosynthesis image reconstruction algorithms. Conclusions: It is feasible to simultaneously generate x-ray differential phase contrast, phase contrast, and absorption contrast tomosynthesis images using a grating-based data acquisition setup. The method shows promise in improving the visibility of several low-density materials and therefore merits further investigation.
Recent developments in machine learning have led to promising advances in accelerating the solution of constrained optimization problems. Increasing demand for real-time decision-making capabilities in applications such as artificial intelligence and optimal control has led to a variety of proposed strategies for learning to produce fast solutions to optimization problems. For example, recent works have shown that it is possible to accelerate the convergence of optimization algorithms by learning to select their parameters, such as gradient descent stepsizes. This work proposes a new approach, in which the underlying metric spaces of proximal operator splitting algorithms are learned to maximize convergence rate. While prior works in optimization theory have derived optimal metrics in simple cases, no such result exists for many practical problem forms including general Quadratic Programming (QP). This paper shows how differentiable optimization can enable the end-to-end learning of proximal metrics, enhancing the convergence of proximal algorithms for QP problems beyond what is possible based on known theory. Additionally, the results illustrate a strong connection between the learned proximal metrics and active constraints at the optima, leading to an interpretation in which the predicted proximal metrics can be viewed as a form of active set prediction.
A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the steady-state kinematics and thermodynamics of a variable viscosity, compressible multiple-species fluid. For an incompressible fluid, the motion may be transient as well. The primitive dependent variables are replaced by a vorticity-streamfunction description valid in domains spanned by rectangular, cylindrical and spherical coordinate systems. Use of derived variables provides a uniformly elliptic partial differential equation description for the Navier-Stokes system, and for which the finite element algorithm is established. Explicit non-linearity is accepted by the theory, since no psuedo-variational principles are employed, and there is no requirement for either computational mesh or solution domain closure regularity. Boundary condition constraints on the normal flux and tangential distribution of all computational variables, as well as velocity, are routinely piecewise enforceable on domain closure segments arbitrarily oriented with respect to a global reference frame.
There is considerable interest in developing a numerical scheme for solving the time dependent viscous compressible three dimensional flow to aid in the design of helicopter rotors. Numerical algorithms are examined to determine their overall suitability for the efficient and routine solution of an appropriate system of partial differential equations. It is concluded that a consistently split time linearized block implicit scheme using either quintic B spline collocation or the generalized operator compact implicit approach to generate a fourth order accurate algorithm is particularly well suited for use on the present problem. High cell Reynolds number behavior leads to favoring the generalized operator compact implicit approach over the quintic B spline collocation method.
A sequential filtering algorithm is presented for attitude and attitude-rate estimation from Global Positioning System (GPS) differential carrier phase measurements. A third-order, minimal-parameter method for solving the attitude matrix kinematic equation is used to parameterize the filter's state, which renders the resulting estimator computationally efficient. Borrowing from tracking theory concepts, the angular acceleration is modeled as an exponentially autocorrelated stochastic process, thus avoiding the use of the uncertain spacecraft dynamic model. The new formulation facilitates the use of aiding vector observations in a unified filtering algorithm, which can enhance the method's robustness and accuracy. Numerical examples are used to demonstrate the performance of the method.