667 research outputs found
Stochastic collocation on unstructured multivariate meshes
Collocation has become a standard tool for approximation of parameterized
systems in the uncertainty quantification (UQ) community. Techniques for
least-squares regularization, compressive sampling recovery, and interpolatory
reconstruction are becoming standard tools used in a variety of applications.
Selection of a collocation mesh is frequently a challenge, but methods that
construct geometrically "unstructured" collocation meshes have shown great
potential due to attractive theoretical properties and direct, simple
generation and implementation. We investigate properties of these meshes,
presenting stability and accuracy results that can be used as guides for
generating stochastic collocation grids in multiple dimensions.Comment: 29 pages, 6 figure
A Review of Fault Diagnosing Methods in Power Transmission Systems
Transient stability is important in power systems. Disturbances like faults need to be segregated to restore transient stability. A comprehensive review of fault diagnosing methods in the power transmission system is presented in this paper. Typically, voltage and current samples are deployed for analysis. Three tasks/topics; fault detection, classification, and location are presented separately to convey a more logical and comprehensive understanding of the concepts. Feature extractions, transformations with dimensionality reduction methods are discussed. Fault classification and location techniques largely use artificial intelligence (AI) and signal processing methods. After the discussion of overall methods and concepts, advancements and future aspects are discussed. Generalized strengths and weaknesses of different AI and machine learning-based algorithms are assessed. A comparison of different fault detection, classification, and location methods is also presented considering features, inputs, complexity, system used and results. This paper may serve as a guideline for the researchers to understand different methods and techniques in this field
Orthogonal Polynomial Approximation in Higher Dimensions: Applications in Astrodynamics
We propose novel methods to utilize orthogonal polynomial approximation in higher dimension spaces, which enable us to modify classical differential equation solvers to perform high precision, long-term orbit propagation. These methods have immediate application to efficient propagation of catalogs of Resident Space Objects (RSOs) and improved accounting for the uncertainty in the ephemeris of these objects. More fundamentally, the methodology promises to be of broad utility in solving initial and two point boundary value problems from a wide class of mathematical representations of problems arising in engineering, optimal control, physical sciences and applied mathematics. We unify and extend classical results from function approximation theory and consider their utility in astrodynamics. Least square approximation, using the classical Chebyshev polynomials as basis functions, is reviewed for discrete samples of the to-be-approximated function. We extend the orthogonal approximation ideas to n-dimensions in a novel way, through the use of array algebra and Kronecker operations. Approximation of test functions illustrates the resulting algorithms and provides insight into the errors of approximation, as well as the associated errors arising when the approximations are differentiated or integrated. Two sets of applications are considered that are challenges in astrodynamics. The first application addresses local approximation of high degree and order geopotential models, replacing the global spherical harmonic series by a family of locally precise orthogonal polynomial approximations for efficient computation. A method is introduced which adapts the approximation degree radially, compatible with the truth that the highest degree approximations (to ensure maximum acceleration error < 10^−9ms^−2, globally) are required near the Earths surface, whereas lower degree approximations are required as radius increases. We show that a four order of magnitude speedup is feasible, with both speed and storage efficiency op- timized using radial adaptation. The second class of problems addressed includes orbit propagation and solution of associated boundary value problems. The successive Chebyshev-Picard path approximation method is shown well-suited to solving these problems with over an order of magnitude speedup relative to known methods. Furthermore, the approach is parallel-structured so that it is suited for parallel implementation and further speedups. Used in conjunction with orthogonal Finite Element Model (FEM) gravity approximations, the Chebyshev-Picard path approximation enables truly revolutionary speedups in orbit propagation without accuracy loss
A Compressed Sensing Approach to Uncertainty Propagation for Approximately Additive Functions
Computational models for numerically simulating physical systems are increasingly being used to support decision-making processes in engineering. Processes such as design decisions, policy level analyses, and experimental design settings are often guided by information gained from computational modeling capabilities. To ensure effective application of results obtained through numerical simulation of computational models, uncertainty in model inputs must be propagated to uncertainty in model outputs. For expensive computational models, the many thousands of model evaluations required for traditional Monte Carlo based techniques for uncertainty propagation can be prohibitive. This paper presents a novel methodology for constructing surrogate representations of computational models via compressed sensing. Our approach exploits the approximate additivity inherent in many engineering computational modeling capabilities. We demonstrate our methodology on some analytical functions, with comparison to the Gaussian process regression, and a cooled gas turbine blade application. We also provide some possible methods to build uncertainty information for our approach. The results of these applications reveal substantial computational savings over traditional Monte Carlo simulation with negligible loss of accuracy
Nonlinear Optimization of a New Polynomial Tyre Model.
Tyre behavior is strongly nonlinear. This article presents the validation of a new
polynomial tyre model with real test data, analyzing the convergence properties during the
optimization process to calculate the values of the parameters. A multivariate model with 13
parameters is shown, including normal load and camber angle. The article reviews the methods of
getting polynomial approximations of the magic formula tyre model used to develop the new
polynomial model, the numerical optimization methods who calculate the parameters of the model
from real test data and it explains how the terms of the Jacobian matrix are modified when we
impose constraints to the curve; this can be useful to improve the adjustment in some areas of the
curve. The convergence properties are shown both for the magic formula tyre model and for this
polynomial tyre model.
The proposed model presents a fast convergence both in one and in 3 variables. This is an additional
advantage to its excellent analytical properties, the model is very easy to compute and can be easily
derived and integrated. It is very well adapted for real time computing.pre-print534 K
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