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error analysis of A New Higher Order Boundary Element Method for A Uniform Flow Passing Cylinders

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China Ocean Engineering 2023年第3期37卷 369-377页

作者： SUN Shi-yan CUI Jie BAO Chao-ming School of Naval Architecture and Ocean Engineering Jiangsu University of Science and TechnologyZhenjiang 212003China

A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity potential and its normal derivative.In present work,a new integral equation is derived for the tangential velocity.The boundary is discretized into higher order elements to ensure the continuity of slope at the element nodes.The velocity potential is also expanded with higher order shape functions,in which the unknown coefficients involve the tangential velocity.The expansion then ensures the continuities of the velocity and the slope of the boundary at element nodes.Through extensive comparison of the results for the analytical solution of cylinders,it is shown that the present HOBEM is much more accurate than the conventional BEM.

关键词： higher order boundary element method(HOBEM) error analysis integral equations for potential and velocity cylinders

Integral precession calibration method of PIGA on linear vibration table

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Chinese Journal of Aeronautics 2024年第3期37卷 219-236页

作者： Chuang SUN Shun-qing REN Jun-wei CAO Ru HUO Department of Automation Tsinghua UniversityBeijing 100084China School of Astronautics Harbin Institute of TechnologyHarbin 150001China Beijing National Research Center for Information Science and Technology Tsinghua UniversityBeijing 100084China Faculty of Information technology Beijing University of TechnologyBeijing 100124China

Linear vibration table can provide harmonic accelerations to excite the nonlinear error terms of Pendulous Integrating Gyro Accelerometer(PIGA).Integral precession calibration method is proposed to calibrate PIGA on a linear vibration table in this paper.Based on the precise expressions of PIGA’s inputs,the error calibration model of PIGA is established.Precession angular velocity errors of PIGA are suppressed by integer periodic precession and the errors caused by non-integer periods vibrating are compensated.The complete calibration process,including planning,preparation,PIGA testing,and coefficient identification,is designed to optimize the test operations and evaluate the calibration results.The effect of the main errors on calibration uncertainty is analyzed and the relative sensitivity function is proposed to further optimize the test positions.Experimental and simulation results verify that the proposed 10-position calibration method can improve calibration uncertainties after compensating for the related errors.The order of calibration uncertainties of the second-and third-order coefficients are decreased to 10^(-8)(rad.s^(-1))/g^(2)and 10^(-8)(rad.s^(-1))/g3,respectively.Compared with the other two classical calibration methods,the calibration uncertainties of PIGA’s nonlinear error coefficients can be effectively reduced and the proportional residual errors are decreased less than 3×10-6(rad.s^(-1))/g by using the proposed calibration method.

关键词： PIGA Linear vibration table Vibration measurement Calibration error analysis Uncertainty analysis

Attractive Multistep Reproducing Kernel Approach for Solving Stiffness Differential Systems of Ordinary Differential Equations and Some error analysis

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Computer Modeling in Engineering & Sciences 2022年第1期130卷 299-313页

作者： Radwan Abu-Gdairi Shatha Hasan Shrideh Al-Omari Mohammad Al-Smadi Shaher Momani Department of Mathematics Faculty of ScienceZarqa UniversityZarqa13132Jordan Department of Applied Science Ajloun CollegeAl-Balqa Applied UniversityAjloun26816Jordan Department of Physics and Basic Sciences Faculty of Engineering TechnologyAl-Balqa Applied UniversityAmman11134Jordan Nonlinear Dynamics Research Center(NDRC) Ajman UniversityAjman20550United Arab Emirates Department of Mathematics Faculty of ScienceThe University of JordanAmman11942Jordan

In this paper,an efficient multi-step scheme is presented based on reproducing kernel Hilbert space(RKHS)theory for solving ordinary stiff differential systems.The solution methodology depends on reproducing kernel functions to obtain analytic solutions in a uniform formfor a rapidly convergent series in the posed Sobolev space.Using the Gram-Schmidt orthogonality process,complete orthogonal essential functions are obtained in a compact field to encompass Fourier series expansion with the help of kernel properties reproduction.Consequently,by applying the standard RKHS method to each subinterval,approximate solutions that converge uniformly to the exact solutions are obtained.For this purpose,several numerical examples are tested to show proposed algorithm’s superiority,simplicity,and efficiency.The gained results indicate that themulti-step RKHSmethod is suitable for solving linear and nonlinear stiffness systems over an extensive duration and giving highly accurate outcomes.

关键词： Multi-step approach reproducing kernel Hilbert space method stiffness system error analysis numerical solution

Relationships between Terrain Features and Forecasting errors of Surface Wind Speeds in a Mesoscale Numerical Weather Prediction Model

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Advances in Atmospheric Sciences 2024年第6期41卷 1161-1170页

作者： Wenbo XUE Hui YU Shengming TANG Wei HUANG Chinese Academy of Meteorological Sciences Beijing 100081China University of Chinese Academy of Sciences Beijing 101408China Shanghai Typhoon Institute/CMA Shanghai 200030China Key Laboratory of Numerical Modeling for Tropical Cyclone/CMA Shanghai 200030China

Numerical weather prediction(NWP)models have always presented large forecasting errors of surface wind speeds over regions with complex terrain.In this study,surface wind forecasts from an operational NWP model,the SMS-WARR(Shanghai Meteorological Service-WRF ADAS Rapid Refresh System),are analyzed to quantitatively reveal the relationships between the forecasted surface wind speed errors and terrain features,with the intent of providing clues to better apply the NWP model to complex terrain regions.The terrain features are described by three parameters:the standard deviation of the model grid-scale orography,terrain height error of the model,and slope angle.The results show that the forecast bias has a unimodal distribution with a change in the standard deviation of orography.The minimum ME(the mean value of bias)is 1.2 m s^(-1) when the standard deviation is between 60 and 70 m.A positive correlation exists between bias and terrain height error,with the ME increasing by 10%−30%for every 200 m increase in terrain height error.The ME decreases by 65.6%when slope angle increases from(0.5°−1.5°)to larger than 3.5°for uphill winds but increases by 35.4%when the absolute value of slope angle increases from(0.5°−1.5°)to(2.5°−3.5°)for downhill winds.Several sensitivity experiments are carried out with a model output statistical(MOS)calibration model for surface wind speeds and ME(RMSE)has been reduced by 90%(30%)by introducing terrain parameters,demonstrating the value of this study.

关键词： surface wind speed terrain features error analysis MOS calibration model

error analysis of FLC Experimental Data at Warm/Hot Stamping Conditions

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Chinese Journal of Mechanical Engineering 2014年第4期27卷 730-737页

作者： ZHUANG Weimin ZHANG Mengxi CHEN Yanhong State Key Laboratory of Automotive Dynamic Simulation Jilin University Department of Aeronautics Imperial College

Forming limit curves（FLCs） are commonly used for evaluating the formability of sheet metals. However, it is difficult to obtain the FLCs with desirable accuracy by experiments due to that the friction effects are non-negligible under warm/hot stamping conditions. To investigate the experimental errors, experiments for obtaining the FLCs of the AA5754 are conducted at 250℃. Then, FE models are created and validated on the basis of experimental results. A number of FE simulations are carried out for FLC test-pieces and punches with different geometry configurations and varying friction coefficients between the test-piece and the punch. The errors for all the test conditions are predicted and analyzed. Particular attention of error analysis is paid to two special cases, namely, the biaxial FLC test and the uniaxial FLC test. The failure location and the variation of the error with respect to the friction coefficient are studied as well. The results obtained from the FLC tests and the above analyses show that, for the biaxial tension state, the friction coefficient should be controlled within 0.15 to avoid significant shifting of the necking location away from the center of the punch; for the uniaxial tension state, the friction coefficient should be controlled within 0.1 to guarantee the validity of the data collected from FLC tests. The conclusions summarized are beneficial for obtaining accurate FLCs under warm/hot stamping conditions.

关键词： forming limit curve（FLC） error analysis warm/hot stamping finite element analysis

In-situ strain measurement and error analysis of arc welding with 2D digital image correlation

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China Welding 2022年第3期31卷 17-23页

作者：黄宏浩胡明华徐爱杰宋育林陈华斌 School of Materials Science and Engineering Shanghai Jiao Tong UniversityShanghai200240China Shanghai Space Precision Machinery Research Institute Shanghai201600China

The deformation and residual stress generated by the welding process can seriously affect the use of components.As a result,it is very important to understand the evolution of stress and strain during the welding process.The strain measurement method based on digital image correlation(DIC)is an excellent method to detect welding strain and residual stress.The out-of-plane translation and out-of-plane rotation introduce errors to the two-dimensional DIC.In this paper,the causes of errors are analyzed theoretically,and the formulas of errors caused by the out-of-plane displacement and the out-of-plane rotation are derived.The out-of-plane translation experiment and the out-of-plane rotation experiment were carried out to verify the theory,and the experimental results are consistent with the theoretical analysis results.The error caused by the out-of-plane translation can be reduced by increasing the object distance;the error caused by the out-of-plane rotation is greatly affected by the rotation angle.

关键词： arc welding digital image correlation strain measurement error analysis

error analysis in Frequency Domain for Linear Multipass Algorithms

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Journal of Systems Engineering and Electronics 2001年第4期12卷 77-84页

作者：费景高 Beijing Institute of Computer Application and Technology 100854 P. R. China

error analysis methods in frequency domain are developed in this paper for determining the characteristic root and transfer function errors when the linear multipass algorithms are used to solve linear differential equations. The relation between the local truncation error in time domain and the error in frequency domain is established, which is the basis for developing the error estimation methods. The error estimation methods for the digital simulation model constructed by using the Runge-Kutta algorithms and the linear multistep predictor-corrector algorithms are also given.

关键词： Algorithms Computer simulation Differential equations error analysis Frequency domain analysis Runge Kutta methods

error analysis and Distribution of 6-SPS and 6-PSS Reconfigurable Parallel Manipulators

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Tsinghua Science and Technology 2010年第5期15卷 547-554页

作者：姚蕊唐晓强李铁民林春深 Department of Precision Instruments and Mechanology Tsinghua University

The purpose of this paper is to analyze an accuracy design method for reconfigurable parallel manipulators including a 6-SPS and a 6-PSS parallel manipulator.An error analysis method,based on the module error model,was used to express the relationship between the module error and the terminal error in the error transmission equation of the reconfigurable parallel manipulator.In addition,an error distribution method using a manufacturing and assembly difficulty coefficient was used to analyze each error module to determine a maximum terminal error.The error distribution result was then used to set up a reconfigurable parallel manipulator.error experiments with a reconfigurable parallel manipulator show that the error analysis and distribution method for reconfigurable parallel manipulators are effective and the maximum terminal errors of the reconfigurable parallel manipulators are less than 50 μm.

关键词： reconfigurable parallel manipulator error distributing error analysis

“Stop-and-go” error analysis of geosynchronous SAR

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Science China(Information Sciences) 2016年第6期59卷 177-188页

作者： Yurun TIAN Shenglong GUO Weidong YU Institute of Electronics Chinese Academy of Sciences University of Chinese Academy of Sciences

In this paper, the slant range error introduced by the "stop-and-go" assumption is analyzed in detail. Owing to the high orbit and long synthetic aperture time of geosynchronous SAR(Geo-SAR), the slant range error introduced by the "stop-and-go" assumption should be considered. In addition, an accurate signal propagation delay time equation of Geo-SAR based on circle orbit is presented, and the error of the "stop-andgo" assumption is demonstrated by simulation. An "equivalent position" model is proposed and validated by simulation. The error of various powers of "stop-and-go" slant range is analyzed using Legendre orthogonal series expansion. The limitation of the stop-and-so assumption is proved by point target simulation.

关键词： geosynchronous SAR stop-and-go assumption equivalent position model Legendre orthogonal series error analysis