Accurate Estimation of Phase Distribution on Reference Plane in Grating Projection Measurement

2005 ◽  
Vol 295-296 ◽  
pp. 221-226 ◽  
Author(s):  
M.R. Zhao ◽  
Yu Cheng Lin ◽  
X.B. Niu ◽  
D.M. Cheng
Keyword(s):  
Phase Distribution ◽  
Phase Error ◽  
Random Phase ◽  
Taylor Series Expansion ◽  
Least Square Method ◽  
Least Square ◽  
Measuring System ◽  
Reference Plane ◽  
Accurate Estimation ◽  
Rational Polynomial

A binary second order rational polynomial is adopted to simulate and extend the phase distribution on reference plane. In order to get the coefficients of the polynomial accurately, iterative least-square method based on the first order Taylor series expansion is used. The effect of the real reference plane profile error on measuring result is reduced by using extended unwrapped phase to substitute the original unwrapped phase. The effects of the random phase error and the system geometrical parameter error are decreased. The measuring accuracy of the system is improved. The principle of the 3D profile measuring system based on grating projection, the theoretic analysis for accurate estimate of phase distribution on reference plane, and the experimental results are presented.

scholarly journals Online Parameter Identification and State of Charge Estimation of Battery Based on Multitimescale Adaptive Double Kalman Filter Algorithm

2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Wenxian Duan ◽  
Chuanxue Song ◽  
Yuan Chen ◽  
Feng Xiao ◽  
Silun Peng ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Parameter Identification ◽  
Unscented Kalman Filter ◽  
Least Square Method ◽  
State Of Charge ◽  
Least Square ◽  
Accurate Estimation ◽  
Battery Life ◽  
Model Parameters ◽  
Simulation Results

An accurate state of charge (SOC) can provide effective judgment for the BMS, which is conducive for prolonging battery life and protecting the working state of the entire battery pack. In this study, the first-order RC battery model is used as the research object and two parameter identification methods based on the least square method (RLS) are analyzed and discussed in detail. The simulation results show that the model parameters identified under the Federal Urban Driving Schedule (HPPC) condition are not suitable for the Federal Urban Driving Schedule (FUDS) condition. The parameters of the model are not universal through the HPPC condition. A multitimescale prediction model is also proposed to estimate the SOC of the battery. That is, the extended Kalman filter (EKF) is adopted to update the model parameters and the adaptive unscented Kalman filter (AUKF) is used to predict the battery SOC. The experimental results at different temperatures show that the EKF-AUKF method is superior to other methods. The algorithm is simulated and verified under different initial SOC errors. In the whole FUDS operating condition, the RSME of the SOC is within 1%, and that of the voltage is within 0.01 V. It indicates that the proposed algorithm can obtain accurate estimation results and has strong robustness. Moreover, the simulation results after adding noise errors to the current and voltage values reveal that the algorithm can eliminate the sensor accuracy effect to a certain extent.

Subpixel Edge Detection Algorithm of the Glass Bottle Based on Zernike Moments

2011 ◽  
Vol 80-81 ◽  
pp. 1345-1349
Author(s):  
Hao Yang ◽  
Lei Pei
Keyword(s):  
Edge Detection ◽  
Fast Algorithm ◽  
Least Square Method ◽  
Threshold Value ◽  
Detection Algorithm ◽  
Zernike Moments ◽  
Least Square ◽  
Measuring System ◽  
Zernike Moment ◽  
Glass Bottle

The accuracy of edge detection determines the accuracy of actual dimension measurement，in order to improve the measuring accuracy, this paper proposes a fast algorithm of detecting the glass bottle dimension based on Zernike moments. Firstly, combines the traditional Zernike moment-based method with Otsu adaptive threshold algorithm and a new fast algorithm for edge detection is proposed. Then uses this fast algorithm to detect the edge of glass bottle with subpixel-level and uses the least square method to fit ellipses formed by the glass bottle mouth and bottom. Calibrated the system with standard gauge block and obtain the actual dimension at last. Experimental results show that the improved algorithm not only can make the edge detection reach the subpixel-level accuracy, but also can avoid the edge misidentification and inefficient causing by repeatedly manual adjustments to select the threshold value when detecting the edge. Making a rapid, accurate, non-contact measuring system becomes a reality.

The State of Charge Estimation of Lithium Battery in Electric Vehicle Based on Extended Kalman Filter

2014 ◽  
Vol 953-954 ◽  
pp. 796-799
Author(s):  
Huan Huan Sun ◽  
Jun Bi ◽  
Sai Shao
Keyword(s):  
Kalman Filter ◽  
Electric Vehicle ◽  
Extended Kalman Filter ◽  
Nonlinear Problems ◽  
Least Square Method ◽  
State Equation ◽  
State Of Charge ◽  
Least Square ◽  
Accurate Estimation ◽  
Battery State Of Charge

Accurate estimation of battery state of charge (SOC) is important to ensure operation of electric vehicle. Since a nonlinear feature exists in battery system and extended kalman filter algorithm performs well in solving nonlinear problems, the paper proposes an EKF-based method for estimating SOC. In order to obtain the accurate estimation of SOC, this paper is based on composite battery model that is a combination of three battery models. The parameters are identified using the least square method. Then a state equation and an output equation are identified. All experimental data are collected from operating EV in Beijing. The results of the experiment show  that the relative error of estimation of state of charge is reasonable, which proves this method has good estimation performance.

scholarly journals Structural Dynamic Modification Based on Combined Approximations Method

2021 ◽  
Vol 252 ◽  
pp. 03032
Author(s):  
Yuchen Jin ◽  
Xiaochen Yang ◽  
Rui Feng ◽  
Wenjie Zuo ◽  
Guikai Guo
Keyword(s):  
Sensitivity Analysis ◽  
Taylor Series Expansion ◽  
Least Square Method ◽  
Least Square ◽  
Structural Dynamic ◽  
Dynamic Design ◽  
Structural Dynamic Modification ◽  
Dynamic Modification ◽  
Combined Approximations Method ◽  
Combined Approximations

Structural dynamic modification plays an important role in structural dynamic design. This paper presents an algorithm for dynamic modification of the structure, which is based on the Combined Approximations (CA) approach, sensitivity analysis, Taylor series expansion and the least square method. The feasibility of the algorithm is verified by a numerical example and the results show that the algorithm is accurate enough and easy to be implemented.

An Algorithm and Design for RFID Velocity Measurement Based on Least Square Method

2011 ◽  
Vol 317-319 ◽  
pp. 1573-1576
Author(s):  
Lin Ying Jiang ◽  
Heng Zhang ◽  
Han Qing Tan
Keyword(s):  
Great Degree ◽  
Velocity Measurement ◽  
Least Square Method ◽  
Least Square ◽  
Measuring System ◽  
Rfid Technology ◽  
Velocity Measuring ◽  
The Cost

This paper comes up with an algorithm and application for velocity measurement based on RFID technology. This measurement can reduce the cost of velocity-measuring system to a great degree, and improve the accuracy of velocity measurement on the basis of the algorithm.

The Output Filter Identification of Three-Phase PWM Converter Using Weighted Least Square Method

2015 ◽  
Vol 734 ◽  
pp. 877-886
Author(s):  
Yi Long Zhang ◽  
Xue Guang Zhang
Keyword(s):  
Control Strategies ◽  
Least Square Method ◽  
Operating Conditions ◽  
Least Square ◽  
Accurate Estimation ◽  
Pwm Converter ◽  
Weighted Least Square ◽  
Three Phase ◽  
Mathematical Techniques ◽  
Output Filter

This paper proposed the Weighted Least Square method (WLS method) to identify the output filter of three-phase PWM converter, which incorporates the signal processing as well as mathematical techniques into conventional Least Square method. It sets different weights to different measurements according to the phase where it locates, based on the discovery of the correlation between accuracy and phase of current. The algorithm is tested in both simulation and experimental environment, and the results validate that proposed method gives accurate estimation in steady state, and can response within 10ms in when grid voltage drops. This method can work under both balanced and unbalanced operating conditions, therefore provides a powerful tool for various control strategies to better understand the operating conditions. Compared with the invasive method, which intentionally inject a series of white noise in the system, proposed WLS method does not bring any turbulence, while compared with conventional Least Square method, it possesses better stability as well as higher accuracy.

A Study on Velocity Decay of φ6mm Tungsten Ball Fragment

2014 ◽  
Vol 1042 ◽  
pp. 154-158
Author(s):  
Chun Lin Yi ◽  
De Ren Kong ◽  
Yi Zhao Li ◽  
Li Ping Li ◽  
Jin Qiu Zhang ◽  
...  
Keyword(s):  
High Speed ◽  
Least Square Method ◽  
Least Square ◽  
Experimental Results ◽  
Measuring System ◽  
Low Speed ◽  
Velocity Decay ◽  
Velocity Attenuation ◽  
Attenuation Models ◽  
Velocity Measuring

In order to explore the velocity attenuation law and model of φ6mm tungsten ball fragment, theory analysis combined with tests is employed to study its velocity experimental results. First of all, a fragment velocity measuring system including 12 groups of cutting device is established. Then the attenuation experiments of φ6mm tungsten ball fragment in high speed and low speed velocity are performed by the measuring system. Based on the least-square method, MATLAB software is adopted to analysis the experimental data and obtained the high speed and low speed velocity attenuation models. The results show that φ6mm tungsten ball fragment speed attenuation coefficient is consistent in high speed and low. Thus, the analysis on velocity experimental results verifies that the established model is reasonable.

Development of Measurement System for Accuracy Control in Subsection Manufacture

2008 ◽  
Vol 381-382 ◽  
pp. 79-82
Author(s):  
F. Zhang ◽  
Xing Hua Qu ◽  
J.F. Dai ◽  
S. Ye
Keyword(s):  
Least Square Method ◽  
Least Square ◽  
Measuring System ◽  
Large Radius ◽  
Accuracy Control ◽  
Data Processing Software ◽  
Geometrical Information ◽  
Cloud Points ◽  
Processing Software ◽  
Best Fit

The computer aided measuring system is established to evaluate geometrical information of the structure in subsection manufacture. The cloud points data of surface are collected by laser tracker so as to explore continuing data processing software and evaluate the error of dimension and shape, and then the real measuring model, matched by the corner information, is compared with CAD through the best-fit algorithm. The lack of fitting information which will cause the low measuring precision is solved by the least square method constrained by radius in structure with large radius and small central angle. As the research object, the tunnel structure is used in the quality control of manufacturers.

Design of Geometric Error Measuring System on a Miniaturized Machine Tool with Optics

2007 ◽  
Vol 364-366 ◽  
pp. 1215-1220 ◽  
Author(s):  
Wei Wang ◽  
Sung Hwan Kweon ◽  
Young Suk Kim ◽  
Seung Han Yang
Keyword(s):  
Machine Tool ◽  
Least Square Method ◽  
Geometric Error ◽  
Least Square ◽  
Measuring System ◽  
Geometric Errors ◽  
Motion Direction ◽  
Position Sensing ◽  
System Components ◽  
Configuration Simulation

Manufactured miniature parts conventional machine tools are substituted by mini-scale manufacturing system called miniaturized machine tool (mMT). However, calibration of mMT is extremely difficult due to its small dimensions. This paper presents a novel optical measuring system to measure integrated geometric errors namely a) three translation errors and b) three rotational errors. The squareness error between two moving axes was calculated by least-square method. These 7-DOF geometric errors were acquired simultaneously in one setup for each motion direction. The proposed measuring system consisted of two laser diodes, two beam splitters and three 2D position sensing detectors (PSDs). Configuration of this measuring system was proved by homogenous transformation matrix (HTM), and the relationship between PSD readings and geometric errors calculated by the algorithm were derived according to the configuration. Simulation were carried out to prove the validity of this algorithm. Sensitivity analysis based on mounting errors of system components is also presented in this paper. It is useful for further experiments in alignment of system components.

scholarly journals A new meshless method using Taylor series to solve elasticity problems

2012 ◽  
Author(s):  
Yendoubouam Tampango ◽  
Michel Potier-Ferry ◽  
Yao Koutsawa ◽  
Salim Belouettar
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Taylor Series ◽  
Meshless Method ◽  
Classical Method ◽  
Taylor Series Expansion ◽  
Least Square Method ◽  
Least Square ◽  
Radius Of Convergence ◽  
Elasticity Problems

A meshless method is presented and analysed. In this approach, one discretises only the boundary, the partial differential equation being solved in the domain by using Taylor series expansion. A least square method is used to apply boundary conditions. In this paper, the method is applied to Navier equations for linear elasticity. Various tests are presented to discuss the efficiency and robustness of the method. The convergence is exponential with respect to the degree but it depends on the radius of convergence of the series. That is why an algorithm has been associated with the Domb–Sykes plot that is a classical method to detect singularities and evaluate the radius of convergence.

Sign in / Sign up

Export Citation Format

Share Document