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A global method of data reduction applied to seven-hole probes

EXPERIMENTS IN FLUIDS 2013年第6期54卷 1535-1535页

作者： Benay, R. Off Natl Etud & Rech Aerosp F-92190 Meudon France

A novel calibration method of multi-hole pressure probes is presented. The case of a particular in-house seven-hole probe is treated explicitly. The three components of the velocity vector are recovered by minimising the difference between the pressures measured at the ports and those interpolated in the calibration data set. A Levenberg algorithm is used for the minimisation procedure while interpolation is carried out by exponential splines. A local least square polynomial-fitting technique is also implemented as an auxiliary module. The method is efficient in determining the velocity vector in the largest part of the domain spanned by the Mach number and the orientation of the probe. An important point is that no zoning of the data is necessary. Uncertainties are found that are due to mechanical limitations of the experimental facility. An overall objective of the method is to reduce the size of the calibration data set needed for multi-hole pressure probe.

关键词： DATA reduction CALIBRATION PRESSURE interpolation algorithms MACH number POLYNOMIALS LEAST squares MODULES (Algebra)

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Research on Accurate Detection Algorithm for the Cross-Section of Shale Gas Casing Deformation Pipe String Based on Laser Ranging

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PROCESSES 2024年第7期12卷 1435页

作者： Yang, Shangyu Mou, Yisheng Cao, Jing Yan, Yan CNPC Tubular Goods Res Inst State Key Lab Performance & Struct Safety Petr Tub Xian 710077 Peoples R China

Under shear and non-uniform loads, the deformation of the section shape of a casing results in an irregular section, and the spatial continuity is poor. The change in the distance between the wall of the casing before and after stress is recorded to analyze the deformation of the casing, and the distance value is taken as the key characteristic of the casing. A large number of the key characteristic values of shale gas casing deformation can be obtained by using the circular traversal detection method. At the same time, this article focuses on the center deviation between the laser sensor axis and the pipe string axis, as well as on the disturbance problem during measurement. An eccentricity error correction algorithm is derived to correct the eccentricity error that occurs during the detection process, and then we use interpolation algorithms to draw cubic spline curves to improve detection accuracy. The test results show that the algorithm can effectively eliminate eccentricity errors in measurement and achieve the accurate measurement of deformation casing characteristic values, which can provide basic data for the study of a shale gas casing deformation mechanism.

关键词： casing deformation non-uniform loads interpolation algorithms laser ranging center deviation

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Nonlinear model reduction for dynamical systems using sparse sensor locations from learned libraries

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Physical Review E 2015年第3期92卷 033304-033304页

作者： Syuzanna Sargsyan Steven L. Brunton J. Nathan Kutz Department of Applied Mathematics University of Washington Seattle Washington 98195-3925 USA Department of Mechanical Engineering University of Washington Seattle Washington 98195 USA

We demonstrate the synthesis of sparse sampling and dimensionality reduction to characterize and model nonlinear dynamical systems over a range of bifurcation parameters. First, we construct modal libraries using the classical proper orthogonal decomposition in order to expose the dominant low-rank coherent structures. Here, libraries of the nonlinear terms are also constructed in order to take advantage of the discrete empirical interpolation method and projection that allows for the approximation of nonlinear terms from a sparse number of grid points. The selected grid points are shown to be effective sensing and measurement locations for characterizing the underlying dynamics, stability, and bifurcations of nonlinear dynamical systems. The use of empirical interpolation points and sparse representation facilitates a family of local reduced-order models for each physical regime, rather than a higher-order global model, which has the benefit of physical interpretability of energy transfer between coherent structures. The method advocated also allows for orders-of-magnitude improvement in computational speed and memory requirements. To illustrate the method, the discrete interpolation points and nonlinear modal libraries are used for sparse representation in order to classify and reconstruct the dynamic bifurcation regimes in the complex Ginzburg-Landau equation. It is also shown that point measurements of the nonlinearity are more effective than linear measurements when sensor noise is present.

关键词： Nonlinear dynamical systems Compressed sensing (Signal processing) Energy transfer Bifurcation theory interpolation algorithms Landau theory

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Řídicí systém pro 3D tiskárnu

Řídicí systém pro 3D tiskárnu

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作者： Vítek, Radim Brno University of Technology

Tato práce se zabývá způsoby řízení 3D tiskáren. Zejména krokovými motory spolu s jejich rozběhovými profily. Dále se pojednává o interpolačních algori... 详细信息

Tato práce se zabývá způsoby řízení 3D tiskáren. Zejména krokovými motory spolu s jejich rozběhovými profily. Dále se pojednává o interpolačních algoritmech. Pozornost je také věnována návrhu řídicí desky pro 3D tiskárnu, postavenou na kitu Nucleo F411. Poslední část rozebírá implementaci řídicího firmwaru.

关键词： CNC Nucleo F411 interpolační algoritmy rozběhové profily krokové motory 3D tiskárna S-křivka CNC Nucleo F411 interpolation algorithms motion profiles stepper motors 3D printer S-shaped curve Text

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Lattice Boltzmann method on quadtree grids

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Physical Review E 2011年第2期83卷 026707-026707页

作者： Yu Chen Qinjun Kang Qingdong Cai Dongxiao Zhang The State Key Laboratory for Turbulence and Complex Systems (LTCS) Center for Applied Physics and Technology (CAPT) and Department of Mechanics and Aerospace Engineering Peking University Beijing People’s Republic of China Sonny Astani Department of Civil and Environmental Engineering University of Southern California Los Angeles California 90089 USA Earth and Environmental Sciences Division Los Alamos National Laboratory Los Alamos New Mexico 87545 USA Department of Energy and Resources Engineering Peking University Beijing People’s Republic of China

A lattice Boltzmann method on nonuniform quadtree grids is proposed. Our method employs the interpolation-supplemented lattice Boltzmann model. The advantages of the quadtree grid are preserved by using linear interpolation instead of quadratic interpolation to complete the streaming step in the lattice Boltzmann method. The back-and-forth error compensation and correction (BFECC) method is used to improve the accuracy, so that the second-order accuracy of the conventional lattice Boltzmann method is maintained. Several numerical cases, including a BFECC streaming test, lid-driven cavity flow, and flow over an asymmetrically placed cylinder in a channel, are carried out to demonstrate the accuracy and efficiency of our method.

关键词： BOLTZMANN'S equation QUADTREES interpolation algorithms ERROR analysis (Mathematics) NUMERICAL analysis

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Random Variables and Stochastic Processes

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IFAC Proceedings Volumes 2000年第16期33卷 403-414页

作者： Vladimir I. Zubov St. Petersburg State University Bibliotechnaya sq. 2 St.Petersburg 198904 Russia

In this paper a solution is given for the problem of approximation of any given multivariate probability distribution function by a mixture of normal distributions or, in general case, a mixture of some other distributions suitable for the given particular case. The analogous problem is solved for distribution functions of stochastic processes, i.e. an interpolation time-dependent polynomial is constructed which approximates the distribution function in the uniform metric.

关键词： approximate analysis normal distribution probability distribution function random processes interpolation algorithms

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IMPROVING CNC MACHINE TOOLS ACCURACY USING MODELING AND COMPUTER SIMULATION TECHNIQUES

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IFAC Proceedings Volumes 2007年第18期40卷 881-886页

作者： Radu E. Breaz Octavian C. Bologa Gabriel S. Racz “Lucian Blaga” University of Sibiu Engineering Faculty radu.breaz@ulbsibiu.ro

The position was one of the first parameters that required the introduction of automatic control process. One of the most representative applications is represented by the feed drives of the computer numerically controlled (CNC) machine tools. Today, it is possible to use computer simulation techniques in analysing and synthesising position control systems. Thus, the behaviour of the CNC machine tools feed drives can be treated much more realistically. It is the purpose of this paper to show how simulation can be used to accurately represent, predict and improve the performance of a CNC machine tool feed servo drives.

关键词： interpolation algorithms machine tool position control simulation transfer functions

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DISTURBANCES REJECTION ON A ROBOT ARM USING AN EFFICIENT PREDICTIVE CONTROLLER

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IFAC Proceedings Volumes 2002年第1期35卷 49-54页

作者： S. Torres J.A. Méndez L. Acosta M. Sigut G.N. Marichal Automation and Control Group Department of Applied Physics University of La Laguna Tenerife SPAIN

This work proposes a predictive controller with interpolation in order to improve the behaviour of a typical MPC when the system presents constraints. Particularly, it is interesting to see how the interpolation, between the solution of the optimal unconstrained problem and other feasible solutions, assures the stability of the system in presence of disturbances. The system in which the controller is applied is a two-link robot manipulator arm. The predictive controller is inserted in an adaptive perturbation scheme to change adequately the nominal inputs, given by an inverse dynamics controller, in order to reject the disturbances produced. The efficiency of the proposed strategy is shown by simulation.

关键词： predictive control interpolation algorithms constraints robot arms optimal control robustness

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A Bayesian Approach to Terrain-Aided Navigation

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IFAC Proceedings Volumes 1997年第11期30卷 1457-1462页

作者： Niclas Bergman Dept. of Electrical Engineering Linköping University Sweden

The terrain-aided navigation problem is a highly nonlinear estimation problem with application to aircraft navigation and missile guidance. In this work the Bayesian approach is used to estimate the aircraft position. With a quantization of the state space an implementable algorithm is found. Problems with low excitation, rough terrain and parallel position hypothesis are handled in a reliable way. The algorithm is evaluated using simulations on real terrain databases.

关键词： Navigation systems estimation algorithms recursive estimation interpolation algorithms quantized states

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Easy and accurate state estimation for nonlinear systems

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IFAC Proceedings Volumes 1999年第2期32卷 5047-5052页

作者： Magnus Nørgaard Niels K. Poulsen Ole Ravn Department of Mathematical Modelling bld. 321 Technical University of Denmark 2800 Lyngby Denmark Department of Automation bld. 326 Technical University of Denmark 2800 Lyngby Denmark

Two new state estimation filters for nonlinear systems are derived in this paper. The filters are based on a multi-dimensional extension of Stirling's interpolation formula for approximation of the nonlinear transformations. The filters can be shown to perform better than filters based on Taylor approximations. Yet, they can be implemented more easily as no derivatives are required. Thus, it is believed that the new filters can replace well-known estimators, such as the extended Kalman filter (EKF) and its higher order relatives.

关键词： Nonlinear filters state estimation extended kalman filters interpolation algorithms parameter estimation

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