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algorithmS FOR THE COMPUTATION OF WEIGHTS IN BOUNDED INFLUENCE REGRESSION

COMPUTATIONAL STATISTICS & DATA ANALYSIS 1988年第3期6卷 251-276页

作者： MARAZZI, A UNIV LAUSANNE INST MED SOCIALE & PREVENT DIV STAT & INFORMAT CH-1005 LAUSANNE SWITZERLAND

A preliminary step for the computation of bounded influence regression is the determination of weights for the points x i in the factor space. This can be achieved through the computation of a robust affinely invariant covariance matrix (with fixed location) and the computation of robust distances of the x i to the origin, in the metric defined by the covariance matrix. For a well known fixed point algorithm convergence has been proved. However, its speed is not very satisfactory in practice. Newton-like and conjugate gradient approaches have been suggested by P.J. Huber. This paper reviews the various proposals, discusses their implementations, some of their convergence properties and compares empirically their performances.

关键词： Robust regression Bounded influence regression Robust covariances Fixed point algorithm Newton algorithm conjugate gradient algorithm

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Direct determination of the rotation in the polar decomposition of the deformation gradient by maximizing a Rayleigh quotient

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ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK 2005年第3期85卷 155-162页

作者： Bouby, C Fortuné, D Pietraszkiewicz, W Vallée, C Polish Acad Sci Inst Fluid Flow Mach PL-80952 Gdansk Poland Univ Lille 1 LML F-59655 Villeneuve Dascq France LMS F-86962 Futuroscope France

We develop a new effective method of determining the rotation R and the stretches U and V in the polar decomposition F RU = VR of the deformation gradient. The method is based on a minimum property of R to have the smallest "distance" from F in the Euclidean norm. The proposed method does not require to perform any square root and/or inverse operations. With each F having nine independent components we associate a 4 x 4 symmetric traceless matrix Q. The rotation is described by quaternion parameters from which a quadrivector X is formed. It is shown that X corresponding to R maximizes X(T)QX over all X satisfying (XX)-X-T = 1. We prefer to equivalently maximize the Rayleigh quotient Y(T)QY/(YY)-Y-T over all non-vanishing Y and to deduce X by subsequent normalization X = Y/root(YY)-Y-T. The maximization of the Rayleigh quotient is performed by a conjugate gradient algorithm with all iterative steps carried out by explicit closed formulae. Efficiency and accuracy of the method is illustrated by a numerical example.

关键词： polar decomposition rotation quaternion Rayleigh quotient conjugate gradient algorithm continuum mechanics

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Time-domain hyperbolic Radon transform for separation of P-P and P-SV wavefields

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STUDIA GEOPHYSICA ET GEODAETICA 2016年第1期60卷 91-111页

作者： Jiang, Xiaoxue Zheng, Fan Jia, Haiqing Lin, Jun Yang, Hongyuan Jilin Univ Coll Instrumentat & Elect Engn Changchun 130026 Peoples R China

A time-domain hyperbolic Radon transform based method for separating multicomponent seismic data into P-P and P-SV wavefields is presented. This wavefield separation method isolates P-P and P-SV wavefields in the Radon panel due to their differences in slowness, and an inverse transform of only part of the data leads to separated wavefields. A problem of hyperbolic Radon transform is that it works in the time domain entailing the inversion of large operators which is prohibitively time-consuming. By applying the conjugate gradient algorithm during the inversion of hyperbolic Radon transform, the computational cost can be kept reasonably low for practical application. Synthetic data examples prove that P-P and P-SV wavefield separation by hyperbolic Radon transform produces more accurate separated wavefields compared with separation by high-resolution parabolic Radon transform, and the feasibility of the proposed separation scheme is also verified by a real field data example.

关键词： time-domain hyperbolic Radon transform multicomponent data wavefield separation conjugate gradient algorithm

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Intelligent Structural Rating System Based on Backpropagation Network

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JOURNAL OF AIRCRAFT 2013年第3期50卷 947-951页

作者： Chen, Xi Ren, He Liu, Jian RMIT Univ Sch Aerosp Mech & Mfg Engn Melbourne Vic 3083 Australia Shanghai Aircraft Customer Serv Co Ltd Dept Sci & Technol Shanghai 200241 Peoples R China

The existing structural rating system in the maintenance steering group-3 is facing difficulties with developing new aircraft. There is always a lack of available data to help make proper inspection intervals. By taking advantage of the powerful learning ability and data fusion capability of the backpropagation network, this paper aims to develop a new decision support system for the determination of scheduled maintenance inspection intervals for aircraft structures susceptible to accidental damage. As long as various data are available, regardless of engineering experience, experimental values, and in-service reliability data feedback, the backpropagation network has been proven able to make acceptable predictions after training, making accidental damage rating a dynamic and flexible procedure.

关键词： Data Fusion Aircraft Structures Decision Support System Feedforward Neural Network Material Properties Airbus conjugate gradient algorithm Control Optimization Aircraft Maintenance Composite Structures

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STATISTICAL-ANALYSIS OF STATIC SHAPE CONTROL IN SPACE STRUCTURES

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AIAA JOURNAL 1990年第8期28卷 1504-1508页

作者： BURDISSO, RA HAFTKA, RT Virginia Polytechnic Institute and State University Blacksburg Virginia

The article addresses the problem of efficient analysis of the statistics of initial and corrected shape distortions in space structures. Two approaches for improving efficiency are considered. One is an adjoint technique for calculating distortion shapes;the second is a modal expansion of distortion shapes in terms of pseudo-vibration modes. The two techniques are applied to the problem of optimizing actuator locations on a 55 m radiometer antenna. The adjoint analysis technique is used with a discrete-variable optimization method. The modal approximation technique is coupled with a standard conjugate-gradient continuous optimization method. The agreement between the two sets of results is good, validating both the approximate analysis and optimally of the results. © 1990 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Large Space Structures Statistical Analysis Actuators Antennas Shape Control Finite Element Analysis Trusses conjugate gradient algorithm Monte Carlo Simulation Structural Response

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UPDATING OF FINITE-ELEMENT MODELS USING VIBRATION TESTS

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AIAA JOURNAL 1994年第7期32卷 1485-1491页

作者： LADEVEZE, P NEDJAR, D REYNIER, M ENS de Cachan/CNES 94235 Cachan France

Today the adjustment of structural models is an essential step in the modeling of complex structures. In this paper, we are interested in the improvement of finite element models. Our approach is a parametric updating using modal test results, which supply eigenvalues and associated eigenvectors. It is based on the computation of the error measure on the constitutive relation and allows us to correct both the stiffness and the mass matrices. In particular, this paper shows how this tuning strategy can improve a given finite element model when the measures are noisy. Several simulation examples illustrate the behavior of this method.

关键词： Finite Element Modeling Cantilever Beam Trusses conjugate gradient algorithm Young's Modulus Free Vibrations Computing Numerical Simulation Lagrange Multipliers Structural Modeling

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A new method of coherent summation of laser beams by diffraction optical element

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OPTICS AND LASERS IN ENGINEERING 2004年第2期41卷 289-295页

作者： Lu, JY Shen, ZC Zhou, YZ Dong, YH Gao, HD Ma, ZG Habin Inst Technol Inst Optoelect Harbin 150001 Peoples R China Harbin Inst Technol Dept Automat Metrol & Control Harbin 150001 Peoples R China

A new method of coherent summation of laser beams is proposed. Two-dimension numerical simulation based on the conjugate gradient algorithm shows that the combination efficiency is about 94.8%, and an error less than 2.4% with a 16-level phase quantized diffraction optical element. Error analysis has also been performed. (C) 2003 Elsevier Science Ltd. All rights reserved.

关键词： diffractive optical element conjugate gradient algorithm coherent addition

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A variational approach to reconstruction of an initial tsunami source perturbation

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APPLIED NUMERICAL MATHEMATICS 2014年 83卷 22-37页

作者： Kabanikhin, Sergey Hasanov, Alemdar Marinin, Igor Krivorotko, Olga Khidasheli, David Novosibirsk State Univ Novosibirsk 630090 Russia Inst Computat Math & Math Geophys SB RAS Novosibirsk Russia Izmir Univ Dept Math & Comp Sci Izmir Turkey WAPMERR Geneva Switzerland

Tsunamis are gravitational, i.e. gravity-controlled waves generated by a given motion of the bottom. There are different natural phenomena, such as submarine slumps, slides, volcanic explosions, earthquakes, etc. that can lead to a tsunami. This paper deals with the case where the tsunami source is an earthquake. The mathematical model studied here is based on shallow water theory, which is used extensively in tsunami modeling. The inverse problem consists of determining an unknown initial tsunami source q(x, y) by using measurements f(m) (t) of the height of a passing tsunami wave at a finite number of given points (x(m), y(m)), m = 1,2,..., M, of the coastal area. The proposed approach is based on the weak solution theory for hyperbolic PDEs and adjoint problem method for minimization of the corresponding cost functional. The adjoint problem is defined to obtain an explicit gradient formula for the cost functional J(q) = parallel to Aq - F parallel to(2), F = (f(1),..., f(M)). Numerical algorithms are proposed for the direct as well as adjoint problems. conjugate gradient algorithm based on explicit gradient formula is used for numerical solution of the inverse problem. Results of computational experiments presented for the synthetic noise free and random noisy data in real scale illustrate bounds of applicability of the proposed approach, also its efficiency and accuracy. (C) 2014 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Reconstruction of initial tsunami source Shallow water equations Cost functional conjugate gradient algorithm Numerical calculations

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OPTIMIZATION OF EQUIVALENT PERIODIC TRUSS STRUCTURES

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AIAA JOURNAL 1987年第3期25卷 502-504页

作者： LAJCZOK, M Martin Marietta Denver Aerospace Denver Colorado

Through the use of equivalent modeling and simple hand calculations, an optimization of a truss structure was achieved. In addition, valuable insight was gained into the relative performance of a tubular and solid member truss structure. This approach could be extended to more complicated structures, resulting in inexpensive preliminary optimization. However, the analyst must be careful in selecting his equivalent models in order to avoid erroneous results.

关键词： Trusses Incompressible Flow Bernoulli Euler Beams Cantilever Space Structures Vorticity conjugate gradient algorithm Structural Vibration Structural Members Heat Conduction

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Riemannian Newton and trust-region algorithms for analytic rotation in exploratory factor analysis

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BRITISH JOURNAL OF MATHEMATICAL & STATISTICAL PSYCHOLOGY 2021年第1期74卷 139-163页

作者： Liu, Yang Univ Maryland Dept Human Dev & Quantitat Methodol 12308 Benjamin Bldg3942 Campus Dr College Pk MD 20742 USA

In exploratory factor analysis, latent factors and factor loadings are seldom interpretable until analytic rotation is performed. Typically, the rotation problem is solved by numerically searching for an element in the manifold of orthogonal or oblique rotation matrices such that the rotated factor loadings minimize a pre-specified complexity function. The widely used gradient projection (GP) algorithm, although simple to program and able to deal with both orthogonal and oblique rotation, is found to suffer from slow convergence when the number of manifest variables and/or the number of latent factors is large. The present work examines the effectiveness of two Riemannian second-order algorithms, which respectively generalize the well-established truncated Newton and trust-region strategies for unconstrained optimization in Euclidean spaces, in solving the rotation problem. When approaching a local minimum, the second-order algorithms usually converge superlinearly or even quadratically, better than first-order algorithms that only converge linearly. It is further observed in Monte Carlo studies that, compared to the GP algorithm, the Riemannian truncated Newton and trust-region algorithms require not only much fewer iterations but also much less processing time to meet the same convergence criterion, especially in the case of oblique rotation.

关键词： exploratory factor analysis analytic rotation Riemannian optimization matrix manifold truncated Newton algorithm trust-region algorithm conjugate gradient algorithm gradient projection algorithm gradient descent algorithm

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