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pattern search algorithms for nonlinear inversion of high-frequency Rayleigh-wave dispersion curves

COMPUTERS & GEOSCIENCES 2008年第6期34卷 611-624页

作者： Song, Xianhai Gu, Hanming Zhang, Xueqiang Liu, Hangping China Univ Geosci Inst Geophys & Geomat Wuhan 430074 Hubei Peoples R China

Inversion of Rayleigh wave dispersion curves is challenging for most local-search methods due to its high nonlinearity and to its multimodality. In this paper, we implemented and tested a Rayleigh wave dispersion curve inversion scheme based on GPS Positive Basis 2N, a commonly used pattern search algorithm. Incorporating complete poll and complete search strategies based on GPS Positive Basis 2N into the inverse procedure greatly enhances the performance of pattern search algorithms because the two steps can effectively locate the promising areas in the solution space containing the global minima and significantly reduce the computation cost, respectively. The proposed inverse procedure was applied to nonlinear inversion of fundamental-mode Rayleigh wave dispersion curves for a near-surface shear (S)-wave velocity profile. The calculation efficiency and stability of the inversion scheme are tested on three synthetic models and a real example from a roadbed survey in Henan, China. Effects of the number of data points, the reduction of the frequency range of the considered dispersion curve, errors in P-wave velocities and density, the initial S-wave velocity profile as well as the number of layers and their thicknesses on inversion results are also investigated in the present study to further evaluate the performance of the proposed approach. Results demonstrate that pattern search algorithms applied to nonlinear inversion of high-frequency surface wave data should be considered good not only in terms of accuracy but also in terms of the computation effort due to their global and deterministic search process. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： pattern search algorithms generalized pattern search surface waves Rayleigh waves dispersion curves

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Insights into performance of pattern search algorithms for high-frequency surface wave analysis

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COMPUTERS & GEOSCIENCES 2009年第8期35卷 1603-1619页

作者： Song, Xianhai Li, Duanyou Gu, Hanming Liao, Yonglong Ren, Dachun Changjiang River Sci Res Inst Wuhan 430010 Hubei Peoples R China China Univ Geosci Inst Geophys & Geomat Wuhan 430074 Hubei Peoples R China

Inversion of high-frequency surface wave dispersion curves is challenging for most local-search methods due to its high nonlinearity and to its multimodality. In this paper, we implemented an investigation to fully exploit and utilize the potentiality of pattern search algorithms and to further enhance their performance for surface wave analysis. We first investigate effects of different inversion strategies, initial mesh size and final mesh size, expansion factor, and contraction factor, as well as inclusion of noise in surface wave data on the performance of the approaches, by three synthetic earth models. Then, a comparative analysis with genetic algorithms is made to further highlight the advantages of the proposed inverse procedure. Finally, the insights issued from this analysis are verified by a real-world example from Henan, China. Results from both synthetic and field data demonstrate: (a) generalized pattern search (GPS) algorithm with the maximal positive basis set 2N vectors works better than GPS algorithm with the minimal positive basis set N+1 vectors;(b) if one gets a suitable initial mesh size by taking some experimentation, then setting expansion factor Lambda = 1 (i.e., not allow expansions) and contraction factor theta = 1/2 can greatly enhance the performance of pattern search algorithms. This is particularly true as the algorithm converges and final mesh size should go to zero;and (c) pattern search algorithms possess stronger immunity with respect to noise and should be considered good not only in terms of accuracy but also in terms of computation effort, especially when compared to the application of genetic algorithms to Rayleigh wave inversion. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： pattern search algorithms Generalized pattern search Rayleigh waves Dispersion curves

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Convergence results for generalized pattern search algorithms are tight

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OPTIMIZATION AND ENGINEERING 2004年第2期5卷 101-122页

作者： Audet, C Gerad Montreal PQ H3C 3A7 Canada Ecole Polytech Dept Math & Genie Ind Montreal PQ H3C 3A7 Canada

The convergence theory of generalized pattern search algorithms for unconstrained optimization guarantees under mild conditions that the method produces a limit point satisfying first order optimality conditions related to the local differentiability of the objective function. By exploiting the flexibility allowed by the algorithm, we derive six small dimensional examples showing that the convergence results are tight in the sense that they cannot be strengthened without additional assumptions, i.e., that certain requirement imposed on pattern search algorithms are not merely artifacts of the proofs. In particular, we first show the necessity of the requirement that some algorithmic parameters are rational. We then show that, even for continuously differentiable functions, the method may generate infinitely many limit points, some of which may have non-zero gradients. Finally, we consider functions that are not strictly differentiable. We show that even when a single limit point is generated, the gradient may be non-zero, and zero may be excluded from the generalized gradient, therefore, the method does not necessarily produce a Clarke stationary point.

关键词： pattern search algorithms convergence analysis unconstrained optimization non-smooth analysis Clarke derivatives

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pattern search ranking and selection algorithms for mixed variable simulation-based optimization

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EUROPEAN JOURNAL OF OPERATIONAL REsearch 2009年第3期198卷 878-890页

作者： Sriver, Todd A. Chrissis, James W. Abramson, Mark A. USAF Inst Technol Dept Operat Sci Wright Patterson AFB OH 45433 USA Headquarters US Air Forces Europe Anal Lessons Learned Div Ramstein Air Base APO AE 09094 USA Boeing Co Seattle WA 98124 USA

The class of generalized pattern search (GPS) algorithms for mixed variable optimization is extended to problems with stochastic objective functions. Because random noise in the objective function makes it more difficult to compare trial points and ascertain which points are truly better than others, replications are needed to generate sufficient statistical power to draw conclusions. Rather than comparing pairs of points, the approach taken here augments pattern search with a ranking and selection (R&S) procedure, which allows for comparing many function values simultaneously. Asymptotic convergence for the algorithm is established, numerical issues are discussed, and performance of the algorithm is studied on a set of test problems. Published by Elsevier B.V.

关键词： pattern search algorithms Mixed variable programming Nonlinear programming Simulation Ranking and selection

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Generalized pattern search and mesh adaptive direct search algorithms for protein structure prediction

Generalized pattern search and mesh adaptive direct search a...

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7th International Workshop on algorithms in Bioinformatics (WABI 2007)

作者： Nicosia, Giuseppe Stracquadanio, Giovanni Univ Catania Dept Math & Comp Sci Viale A Doria 6 I-95125 Catania Italy

ISBN: (纸本)9783540741251

Proteins are the most important molecular entities of a living organism and understanding their functions is an important task to treat diseases and synthesize new drugs. It is largely known that the function of a protein is strictly related to its spatial conformation: to tackle this problem, we have proposed a new approach based on a class of pattern search algorithms that is largely used in optimization of real world applications. The obtained results are interesting in terms of the quality of the structures (RMSD-C alpha) and energy values found.

关键词： protein folding pattern search algorithms non-linear optimization

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pattern search approach to ferromagnetic material modelling

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INTERNATIONAL JOURNAL OF NUMERICAL MODELLING-ELECTRONIC NETWORKS DEVICES AND FIELDS 2019年第4期32卷 e2271.1-e2271.6页

作者： Cardelli, E. Faba, A. Pompei, M. Antonio, S. Quondam Perugia Univ Dept Engn Perugia Italy

This paper deals with possible optimization-based techniques for the identification of the parameters of Preisach-inspired phenomenological model of vector hysteresis in ferromagnetic materials. After a summary of the key features of the phenomenological model mentioned above, the description of the identification technique proposed is given. The identification technique is based on a suitable pattern search algorithm and standard measurements. Results for the FeSi Non-Oriented Grains steel NOG are presented and discussed.

关键词： magnetic hysteresis pattern search algorithms phenomenological modelling

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An H-shaped low-field magnet for NMR spectroscopy designed using the finite element method

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INTERNATIONAL JOURNAL OF APPLIED ELECTROMAGNETICS AND MECHANICS 2019年第Sup1期60卷 S3-S14页

作者： Alnajjar, Belal M. K. Buchau, Andre Anders, Jens Bluemich, Bernhard Univ Stuttgart Inst Smart Sensors Pfaffenwaldring 47 D-70569 Stuttgart Germany Rhein Westfal TH Aachen Inst Tech & Makromol Chem Aachen Germany

An H-shaped low-field permanent magnet is presented. It has been designed, simulated and optimized using the finite element method. The magnet mainly consists of two poles, each of which consists of 37 hexagonal magnetic blocks that are magnetically connected by an iron yoke. To achieve the magnetic field homogeneity in the ppm range required for NMR applications, mechanical shimming by a vertical adjustment of the hexagonal magnetic blocks has been applied. Here, the displacement of each block from the initial equidistant symmetric design has been optimized by applying a pattern search method. In addition, two pole pieces made of iron have been added to the magnet to further improve the magnetic field homogeneity. The dimensions of these pole pieces have been optimized using a genetic algorithm. The magnetic field homogeneity of 15 ppm (parts per million) measured inside the manufactured prototype verifies the accuracy of the proposed simulation based design approach.

关键词： Finite element methods genetic algorithms mobile NMR NMR magnet permanent magnet design pattern search algorithms shimming

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An H-shaped low-field magnet for NMR spectroscopy designed using the finite element method

An H-shaped low-field magnet for NMR spectroscopy designed u...

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15th Biennial International Workshop on Optimization and Inverse Problems in Electromagnetism (OIPE)

关键词： Finite element methods genetic algorithms mobile NMR NMR magnet permanent magnet design pattern search algorithms shimming

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