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Presentation to be presented during the Site-Directed Research and Development (SDRD) program FY 2021 review meeting (Webex), September 22–23, 2021.
Two adaptive algorithms which make use of all the available samples to estimate the required gradient are proposed and studied. The first algorithm is referred to as the recursive LMS (least mean squares) and is applicable to a general array. The second algorithm is referred to as the improved LMS algorithm and exploits the Toeplitz structure of the ACM (array correlation matrix); it can be used only for an equispaced linear array.
The study of sea ice using airborne remote sensing platforms provides unique capabilities to measure a wide variety of sea ice properties. These measurements are useful for a variety of topics including model evaluation and improvement, assessment of satellite retrievals, and incorporation into climate data records for analysis of interannual variability and long-term trends in sea ice properties. In this paper we describe methods for the retrieval of sea ice thickness, freeboard, and snow depth using data from a multisensor suite of instruments on NASA's Operation IceBridge airborne campaign. We assess the consistency of the results through comparison with independent data sets that demonstrate that the IceBridge products are capable of providing a reliable record of snow depth and sea ice thickness. We explore the impact of inter-campaign instrument changes and associated algorithm adaptations as well as the applicability of the adapted algorithms to the ongoing IceBridge mission. The uncertainties associated with the retrieval methods are determined and placed in the context of their impact on the retrieved sea ice thickness. Lastly, we present results for the 2009 and 2010 IceBridge campaigns, which are currently available in product form via the National Snow and Ice Data Center
A solution-adaptive marching algorithm is developed and applied to a three-dimensional parabolized Navier-Stokes equation solver. The resulting algorithm obtains accurate solutions by using a spatial-marching/adaptive grid procedure. The adaptation step redistributes grid points line by line in both crossflow directions, with grid point motion controlled by forces analogous to tensional and torsional spring forces with the tensional force proportional to the error measure or weighting functions. The solution-adaptive marching procedure is applied to the hypersonic flow about two generic aircraft configurations. The first of these is an all-body-type geometry with elliptical cross sections and is studied at angles of attack of 0.5, and 15 deg. The second geometry is a generic blended-wing-body design. Results are presented that demonstrate the improvements in flowfield resolution obtainable with the solution-adaptive marching procedure over conventional fixed grid techniques. Computed pitot pressure profiles obtained using the solution-adaptive algorithm show improved agreement with experimental data compared to predictions obtained using a fixed grid.
An adaptive grid, finite-volume method has been applied to problems in planetary entry for computing complete flowfields. The adaption algorithm is implicit in nature and is keyed to resolve user specified gradients. The finite-volume algorithm is explicit, utilizing a maximum time step advancement at each grid point to accelerate convergence to the steady state. The present version of the code is for the laminar flow of a perfect gas. The role of the adaption algorithm in resolving various features of blunt body/wake flow for planetary entry conditions is emphasized.
A robust and computationally efficient object tracking algorithm is developed by incorporating various tracking techniques. Physical properties of the objects, such as brightness temperature or reflectivity, are not considered. Therefore, the algorithm is adaptable for tracking convection-like features in simulated data and remotely sensed two-dimensional images. In this algorithm, a first guess of the motion, estimated using the Fourier phase shift, is used to predict the candidates for matching. A disparity score is computed for each target–candidate pair. The disparity also incorporates overlapping criteria in the case of large objects. Then the Hungarian method is applied to identify the best pairs by minimizing the global disparity. The high-disparity pairs are unmatched, and their target and candidate are declared expired and newly initiated objects, respectively. They are tested for merger and split on the basis of their size and overlap with the other objects. The sensitivity of track duration is shown for different disparity and size thresholds. The report highlights the algorithm’s ability to study convective life cycles using radar and simulated data over Darwin, Australia. The algorithm skillfully tracks individual convective cells (a few pixels in size) and large convective systems. The duration of tracks and cell size are found to be lognormally distributed over Darwin. The evolution of size and precipitation types of isolated convective cells is presented in the Lagrangian perspective. This algorithm is part of a vision for a modular platform [viz., TINT is not TITAN (TINT) and Tracking and Object-Based Analysis of Clouds (tobac)] that will evolve into a sustainable choice to analyze atmospheric features.
A solution-adaptive grid algorithm has been developed for use in two and three dimensions. The algorithm uses a transformation from the cartesian coordinate system to a general coordinate space, which will be defined as a parallelepiped. A weighting function for adaption of the grid is developed that will allow adaption to the gradients of any combination of dependent variables in the flow. The adaption is carried out in the parametric space and a simple inverse mapping to return the new parametric space to the physical space is derived. The concept used to relocate the grid-points in the parametric space is based on the center of mass of distributed weights. Solution-adaptive results are presented for various laminar flows in two dimensions and for mathematical weighting functions in three dimensions.
A temporal adaptive algorithm for the time-integration of the two-dimensional Euler or Navier-Stokes equations is presented. The flow solver involves an upwind flux-split spatial discretization for the convective terms and central differencing for the shear-stress and heat flux terms on an unstructured mesh of triangles. The temporal adaptive algorithm is a time-accurate integration procedure which allows flows with high spatial and temporal gradients to be computed efficiently by advancing each grid cell near its maximum allowable time step. Results indicate that an appreciable computational savings can be achieved for both inviscid and viscous unsteady airfoil problems using unstructured meshes without degrading spatial or temporal accuracy.
A temporal adaptive algorithm for the time-integration of the two-dimensional Euler or Navier-Stokes equations is presented. The flow solver involves an upwind flux-split spatial discretization for the convective terms and central differencing for the shear-stress and heat flux terms on an unstructured mesh of triangles. The temporal adaptive algorithm is a time-accurate integration procedure which allows flows with high spatial and temporal gradients to be computed efficiently by advancing each grid cell near its maximum allowable time step. Results indicate that an appreciable computational savings can be achieved for both inviscid and viscous unsteady airfoil problems using unstructured meshes without degrading spatial or temporal accuracy.
Nonlinear adaptive recursive algorithm for estimating unknown probability density given sequence of independent samples, deriving adaptive estimators of population moments
We present a new adaptive parallel algorithm for the challenging problem of multi-dimensional numerical integration on massively parallel architectures. Adaptive algorithms have demonstrated the best performance, but efficient many-core utilization is difficult to achieve because the adaptive work-load can vary greatly across the integration space and is impossible to predict a priori. Existing parallel algorithms utilize sequential computations on independent processors, which results in bottlenecks due to the need for data redistribution and processor synchronization. Our algorithm employs a high-throughput approach in which all existing sub-regions are processed and sub-divided in parallel. Repeated sub-region classification and filtering improves upon a brute-force approach and allows the algorithm to make efficient use of computation and memory resources. A CUDA implementation shows orders of magnitude speedup over the fastest open-source CPU method and extends the achievable accuracy for difficult integrands. Our algorithm typically outperforms other existing deterministic parallel methods.
Abstract Adaptive protocols enable the construction of more efficient state preparation circuits in variational quantum algorithms (VQAs) by utilizing data obtained from the quantum processor during the execution of the algorithm. This idea originated with Adaptive Derivative-Assembled Problem-Tailored variational quantum eigensolver (ADAPT-VQE), an algorithm that iteratively grows the state preparation circuit operator by operator, with each new operator accompanied by a new variational parameter, and where all parameters acquired thus far are optimized in each iteration. In ADAPT-VQE and other adaptive VQAs that followed it, it has been shown that initializing parameters to their optimal values from the previous iteration speeds up convergence and avoids shallow local traps in the parameter landscape. However, no other data from the optimization performed at one iteration is carried over to the next. In this work, we propose an improved quasi-Newton optimization protocol specifically tailored to adaptive VQAs. The distinctive feature in our proposal is that approximate second derivatives of the cost function are recycled across iterations in addition to optimal parameter values. We implement a quasi-Newton optimizer where an approximation to the inverse Hessian matrix is continuously built and grown across the iterations of an adaptive VQA. The resulting algorithm has the flavor of a continuous optimization where the dimension of the search space is augmented when the gradient norm falls below a given threshold. We show that this inter-optimization exchange of second-order information leads the approximate Hessian in the state of the optimizer to be consistently closer to the exact Hessian. As a result, our method achieves a superlinear convergence rate even in situations where the typical implementation of a quasi-Newton optimizer converges only linearly. Our protocol decreases the measurement costs in implementing adaptive VQAs on quantum hardware as well as the runtime of their classical simulation.
Rain compensation algorithm using adaptive linear prediction is presented in viewgraph form. Topics covered include AMT scenario, summary of AMT-RCA, empirical basis for reducing attenuation extrapolation errors, and candidate adaptive 1-pole prediction filter for application to AMT-RCA (at the mobile terminal (MT)).
This paper reports the outcome of an exhaustive analytical and numerical investigation of stability and robustness properties of a wide class of adaptive control algorithms in the presence of unmodeled dynamics and output disturbances. The class of adaptive algorithms considered are those commonly referred to as model-reference adaptive control algorithms, self-tuning controllers, and dead-beat adaptive controllers; they have been developed for both continuous-time systems and discrete-time systems. The existing adaptive control algorithms have been proven to be globally asymptotically stable under certain assumptions, the key ones being (1) that the number of poles and zeroes of the unknown plant are known, and (2) that the primary performance criterion is related to good command following. These theoretical assumptions are too restrictive from an engineering point of view. Real plants always contain unmodeled high-frequency dynamics and small delays, and hence no upper bound on the number of the plant poles and zeroes exists. Also real plants are always subject to unmeasurable output additive disturbances, although these may be guide small. Hence, it is important to critically examine the stability robustness properties of the existing adaptive algorithms when some of the theoretical assumptions are removed; in particular, their stability and performance properties in the presence of unmodeled dynamics and output disturbances. Previously announced in STAR as N83-16061
Nonlinear adaptive and recursive algorithm to estimate unknown probability density from independent sample sequence
The dynamic solution adaptive grid algorithm, DSAGA3D, is extended to automatically adapt 2-D structured multi-block grids, including adaption of the block boundaries. The extension is general, requiring only input data concerning block structure, connectivity, and boundary conditions. Imbedded grid singular points are permitted, but must be prevented from moving in space. Solutions for workshop cases 1 and 2 are obtained on multi-block grids and illustrate both increased resolution of and alignment with the solution. A mesh quality assessment criteria is proposed to determine how well a given mesh resolves and aligns with the solution obtained upon it. The criteria is used to evaluate the grid quality for solutions of workshop case 6 obtained on both static and dynamically adapted grids. The results indicate that this criteria shows promise as a means of evaluating resolution.
While the performance of flight simulator motion system hardware has advanced substantially, the development of the motion cueing algorithm, the software that transforms simulated aircraft dynamics into realizable motion commands, has not kept pace. Prior research identified viable features from two algorithms: the nonlinear "adaptive algorithm", and the "optimal algorithm" that incorporates human vestibular models. A novel approach to motion cueing, the "nonlinear algorithm" is introduced that combines features from both approaches. This algorithm is formulated by optimal control, and incorporates a new integrated perception model that includes both visual and vestibular sensation and the interaction between the stimuli. Using a time-varying control law, the matrix Riccati equation is updated in real time by a neurocomputing approach. Preliminary pilot testing resulted in the optimal algorithm incorporating a new otolith model, producing improved motion cues. The nonlinear algorithm vertical mode produced a motion cue with a time-varying washout, sustaining small cues for longer durations and washing out large cues more quickly compared to the optimal algorithm. The inclusion of the integrated perception model improved the responses to longitudinal and lateral cues. False cues observed with the NASA adaptive algorithm were absent. The neurocomputing approach was crucial in that the number of presentations of an input vector could be reduced to meet the real time requirement without degrading the quality of the motion cues.
The basic goal of adaptive-mesh algorithms is to distribute computational resources wisely by increasing the resolution of 'important' regions of the flow and decreasing the resolution of regions that are less important. While this goal is one that is worthwhile, implementing schemes that have this degree of sophistication remains more of an art than a science. In this paper, the basic pieces of adaptive-mesh algorithms are described and some of the possible ways to implement them are discussed and compared. These basic pieces are the data structure to be used, the generation of an initial mesh, the criterion to be used to adapt the mesh to the solution, and the flow-solver algorithm on the resulting mesh. Each of these is discussed, with particular emphasis on methods suitable for the computation of compressible flows.