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This paper presents the Fast Adaptive Composite Grid Method for Time Dependent Problems (TDFAC), a local grid refinement scheme for nonlinear, time dependent partial differential equations. The method is presented in a one dimensional setting to illustrate the basic features and components. Computational results which show the effectiveness of TDFAC as a computational tool are also included.
We present a novel adaptive machine-learning based approach for reconstructing three-dimensional (3D) crystals from coherent diffraction imaging. We represent the crystals using spherical harmonics (SH) and generate the corresponding synthetic diffraction patterns. We utilize 3D convolutional neural networks (CNNs) to learn a mapping between 3D diffraction volumes and the SH, which describe the boundary of the physical volumes from which they were generated. We use the 3D CNN-predicted SH coefficients as the initial guesses, which are then fine-tuned using adaptive model-independent feedback for improved accuracy. We also adaptively tune the locations, intensities, and decay rates of collections of radial basis functions in order to reproduce the non-uniform internal structure of 3D objects and demonstrate the method for a synthetic volume that has an internal void and a density ramp.
Active and adaptive systems and methods to prevent loss of control incidents by providing tactile feedback to a vehicle operator are disclosed. According to the present invention, an operator gives a control input to an inceptor. An inceptor sensor measures an inceptor input value of the control input. The inceptor input is used as an input to a Steady-State Inceptor Input/Effector Output Model that models the vehicle control system design. A desired effector output from the inceptor input is generated from the model. The desired effector output is compared to an actual effector output to get a distortion metric. A feedback force is generated as a function of the distortion metric. The feedback force is used as an input to a feedback force generator which generates a loss of control inhibitor system (LOCIS) force back to the inceptor. The LOCIS force is felt by the operator through the inceptor.
Active and adaptive systems and methods to prevent loss of control incidents by providing tactile feedback to a vehicle operator are disclosed. According to the present invention, an operator gives a control input to an inceptor. An inceptor sensor measures an inceptor input value of the control input. The inceptor input is used as an input to a Steady-State Inceptor Input/Effector Output Model that models the vehicle control system design. A desired effector output from the inceptor input is generated from the model. The desired effector output is compared to an actual effector output to get a distortion metric. A feedback force is generated as a function of the distortion metric. The feedback force is used as an input to a feedback force generator which generates a loss of control inhibitor system (LOCIS) force back to the inceptor. The LOCIS force is felt by the operator through the inceptor.
Simple method determines either inside or outside radius of cylindrical segment when full diametrical section of material is not accessible for caliper measurement or if size, condition, or maneuverability of cylinder is not amenable to use of template or comparator-type devices. Method employs standard micrometer or depth gage with ball-end rod and fixed-length baseplate. Method is more adaptable in variety of situations than are existing methods, and measurements can be obtained under conditions that may be difficult if not impossible using other methods.
Described are methods and apparatus, including computer program products, for reconfigurable environmentally adaptive computing technology. An environmental signal representative of an external environmental condition is received. A processing configuration is automatically selected, based on the environmental signal, from a plurality of processing configurations. A reconfigurable processing element is reconfigured to operate according to the selected processing configuration. In some examples, the environmental condition is detected and the environmental signal is generated based on the detected condition.
Multirate methods have been used for decades to temporally evolve initial-value problems in which different components evolve on distinct time scales, and thus use of different step sizes for these components can result in increased computational efficiency. Generally, such methods select these different step sizes based on experimentation or stability considerations. For problems that evolve on a single time scale, adaptivity approaches that strive to control local temporal error are widely used to achieve numerical results of a desired accuracy with minimal computational effort, while alleviating the need for manual experimentation with different time step sizes. However, there is a notable gap in the publication record on the development of adaptive time step controllers for multirate methods. In this paper, we extend the single-rate controller work of Gustafsson [ACM Trans. Math. Software, 20 (1994), pp. 496-517] to the multirate method setting. Specifically, we develop controllers based on polynomial approximations to the principal error functions for both the "fast" and "slow" time scales within multirate infinitesimal (MRI) methods. We additionally investigate a variety of approaches for estimating the errors arising from each time scale within MRI methods. We then numerically evaluate the proposed multirate controllers and error estimation strategies on a range of multirate test problems, comparing their performance against an estimated optimal performance. Through this work, we combine the most performant of these approaches to arrive at a set of multirate adaptive time step controllers that robustly achieve desired solution accuracy with minimal computational effort.
This study investigates the effects of grid topology and grid adaptation on numerical solutions of the Navier-Stokes equations. In the first part of this study, a general procedure is presented for computation of high-speed flow over complex three-dimensional configurations. The flow field is simulated on the surface of a Butler wing in a uniform stream. Results are presented for Mach number 3.5 and a Reynolds number of 2,000,000. The O-type and H-type grids have been used for this study, and the results are compared together and with other theoretical and experimental results. The results demonstrate that while the H-type grid is suitable for the leading and trailing edges, a more accurate solution can be obtained for the middle part of the wing with an O-type grid. In the second part of this study, methods of grid adaption are reviewed and a method is developed with the capability of adapting to several variables. This method is based on a variational approach and is an algebraic method. Also, the method has been formulated in such a way that there is no need for any matrix inversion. This method is used in conjunction with the calculation of hypersonic flow over a blunt-nose body. A movie has been produced which shows simultaneously the transient behavior of the solution and the grid adaption.
Importance of the role of human operator in control systems has led to the particular area of manual control theory. Human describing functions were developed to model human behavior for manual control studies to take advantage of the successful and safe human operations. A single variable approach is presented that can be extended for multi-variable tasks where a low order human response model is used together with its rules, to adapt the model on-line, being capable of responding to the changes in the controlled element dynamics. Basic control theory concepts are used to combine the model, constrained with the physical observations, particularly, for the case of aircraft control. Pilot experience is represented as the initial model parameters. An adaptive root-locus method is presented as the adaptation law of the model where the closed loop bandwidth of the system is to be preserved in a stable manner with the adjustments of the pilot handling qualities which relate the latter to the closed loop bandwidth and damping of the closed loop pilot aircraft combination. A Kalman filter parameter estimator is presented as the controlled element identifier of the adaptive model where any discrepancies of the open loop dynamics from the presented one, are sensed to be compensated.
The numerical solution of stiff initial value problems, which lead to the problem of solving large systems of mildly nonlinear equations are considered. For many problems derived from engineering and science, a solution is possible only with methods derived from iterative linear equation solvers. A common approach to solving the nonlinear equations is to employ an approximate solution obtained from an explicit method. The error is examined to determine how it is distributed among the stiff and non-stiff components, which bears on the choice of an iterative method. The conclusion is that error is (roughly) uniformly distributed, a fact that suggests the Chebyshev method (and the accompanying Manteuffel adaptive parameter algorithm). This method is described, also commenting on Richardson's method and its advantages for large problems. Richardson's method and the Chebyshev method with the Mantueffel algorithm are applied to the solution of the nonlinear equations by Newton's method.
Abstract Artificial intelligence methods show great promise in increasing the quality and speed of work with large astronomical datasets, but the high complexity of these methods leads to the extraction of dataset-specific, non-robust features. Therefore, such methods do not generalize well across multiple datasets. We present a universal domain adaptation method, DeepAstroUDA , as an approach to overcome this challenge. This algorithm performs semi-supervised domain adaptation (DA) and can be applied to datasets with different data distributions and class overlaps. Non-overlapping classes can be present in any of the two datasets (the labeled source domain, or the unlabeled target domain), and the method can even be used in the presence of unknown classes. We apply our method to three examples of galaxy morphology classification tasks of different complexities (three-class and ten-class problems), with anomaly detection: (1) datasets created after different numbers of observing years from a single survey (Legacy Survey of Space and Time mock data of one and ten years of observations); (2) data from different surveys (Sloan Digital Sky Survey (SDSS) and DECaLS); and (3) data from observing fields with different depths within one survey (wide field and Stripe 82 deep field of SDSS). For the first time, we demonstrate the successful use of DA between very discrepant observational datasets. DeepAstroUDA is capable of bridging the gap between two astronomical surveys, increasing classification accuracy in both domains (up to 40 % on the unlabeled data), and making model performance consistent across datasets. Furthermore, our method also performs well as an anomaly detection algorithm and successfully clusters unknown class samples even in the unlabeled target dataset.
The method of averaging is used to analyze discrete-time indirect adaptive control. The analysis focuses on various prediction-error-driven identification algorithms coupled with a general linear control law. The plant is not required to be in the model set of the identifier, which accounts for systems with unmodeled plant dynamics. Exogenous input signals including known command signals and unknown disturbances are also included. Both gradient and Newton-based algorithms are considered.
The present adaptive FEM technique for convection-dominated problems is based on a Petrov-Galerkin scheme for spatial approximation, whose typical time-step employs test functions chosen to yield an approximate solution coinciding with the exact solutions at the finite element grid nodes. The derivation of truly local a posteriori error estimates is made possible by this procedure, which is also shown to be a very effective solver by the numerical examples presented.
Most engineering materials contain second phase particles or fibers which serve to reinforce the matrix phase. The effect of reinforcements on material properties is usually analyzed in terms of the average volume fraction and spacing of reinforcements, quantities which are global microstructural characteristics. However, material properties can also depend on local microstructural characteristics; for example, on how uniformly the reinforcing phase is distributed in the material. The analysis method will then be applied to a materials processing problem to discover how processing parameters can be selected to maximize redistribution of the reinforcing phase during processing. Several mathematical analysis methods could be adapted to the problem of characterizing the distribution of particles in materials. A tessellation-based method was selected. In the first phase of the investigation, a software package was written to automate the analysis. Typical results are shown. The analysis technique allows the degree to which particles are clustered together, the size and spacing of particle clusters, and the particle density in clusters to be found. The analysis methods were applied to computer-generated distributions and to a few real particle-containing materials. Methods for analyzing a nonuniform particle distribution in a material can be applied to two broad classes of materials science problems: understanding how the resulting particle distribution affects properties. The analysis method described is applied to a materials processing problem: how to select extrusion conditions to maximize the redistribution of reinforcing particles that are initially nonuniformly distributed. In addition, the tessellation-based method to analyze star distributions in spiral galaxies was adapted, illustrating the diverse types of problems to which the analysis method can be applied.
The present work involves generation of hybrid prismatic/tetrahedral grids for complex 3-D geometries including multi-body domains. The prisms cover the region close to each body's surface, while tetrahedra are created elsewhere. Two developments are presented for hybrid grid generation around complex 3-D geometries. The first is a new octree/advancing front type of method for generation of the tetrahedra of the hybrid mesh. The main feature of the present advancing front tetrahedra generator that is different from previous such methods is that it does not require the creation of a background mesh by the user for the determination of the grid-spacing and stretching parameters. These are determined via an automatically generated octree. The second development is a method for treating the narrow gaps in between different bodies in a multiply-connected domain. This method is applied to a two-element wing case. A High Speed Civil Transport (HSCT) type of aircraft geometry is considered. The generated hybrid grid required only 170 K tetrahedra instead of an estimated two million had a tetrahedral mesh been used in the prisms region as well. A solution adaptive scheme for viscous computations on hybrid grids is also presented. A hybrid grid adaptation scheme that employs both h-refinement and redistribution strategies is developed to provide optimum meshes for viscous flow computations. Grid refinement is a dual adaptation scheme that couples 3-D, isotropic division of tetrahedra and 2-D, directional division of prisms.
In this paper, we will develop an adaptive modal identification method for identifying the frequencies and damping of a flutter mode based on model-reference adaptive control (MRAC) and least-squares methods. The least-squares parameter estimation will achieve parameter convergence in the presence of persistent excitation whereas the MRAC parameter estimation does not guarantee parameter convergence. Two adaptive flutter suppression control approaches are developed: one based on MRAC and the other based on the least-squares method. The MRAC flutter suppression control is designed as an integral part of the parameter estimation where the feedback signal is used to estimate the modal information. On the other hand, the separation principle of control and estimation is applied to the least-squares method. The least-squares modal identification is used to perform parameter estimation.
A recently developed numerical method based on the strip yield analysis approach was used to calculate the Crack Tip Opening Displacement (CTOD) and Crack Tip Opening Angle (CTOA) for a number of complex crack configurations of practical interest. This method is an adaptation of the dislocation-density based boundary element method. In this Boundary Element approach, crack-face opening displacements are obtained at any point on a crack using a series of definite integrals evaluated exactly in closed form for a variety of crack geometries, including infinite or finite extent, with arbitrarily applied loading conditions.
Autonomy of aerospace systems requires the ability for flight control systems to be able to adapt to complex uncertain dynamic environment. In spite of the five decades of research in adaptive control, the fact still remains that currently no adaptive control system has ever been deployed on any safety-critical or human-rated production systems such as passenger transport aircraft. The problem lies in the difficulty with the certification of adaptive control systems since existing certification methods cannot readily be used for nonlinear adaptive control systems. Research to address the notion of metrics for adaptive control began to appear in the recent years. These metrics, if accepted, could pave a path towards certification that would potentially lead to the adoption of adaptive control as a future control technology for safety-critical and human-rated production systems. Development of certifiable adaptive control systems represents a major challenge to overcome. Adaptive control systems with learning algorithms will never become part of the future unless it can be proven that they are highly safe and reliable. Rigorous methods for adaptive control software verification and validation must therefore be developed to ensure that adaptive control system software failures will not occur, to verify that the adaptive control system functions as required, to eliminate unintended functionality, and to demonstrate that certification requirements imposed by regulatory bodies such as the Federal Aviation Administration (FAA) can be satisfied. This presentation will discuss some of the technical issues with adaptive flight control and related V&V challenges.