Minimum Zone Evaluation of Symmetry Error for Flatness to Flatness Based on the New Generation GPS

2013 ◽  
Vol 662 ◽  
pp. 887-891
Author(s):  
Qian Qian ◽  
Mei Fa Huang ◽  
Huan Yu Li
Keyword(s):  
Least Square Method ◽  
Mathematic Model ◽  
Least Square ◽  
Adaptive Genetic Algorithm ◽  
Machining Error ◽  
Minimum Zone ◽  
New Generation ◽  
Tolerance Method ◽  
The Mathematical Model ◽  
Better Than

Least square method (LSM) is the most popular method used to evaluate machining error nowadays. However, LSM is likely to overestimate the error value, therefore its solution is only approximate and rather than minimum. In order to obtain the minimum, we study the principle of the minimum zone tolerance method (MZT), analyze the characteristics of the new generation GPS, and give the minimum zone mathematic model of the symmetry error for flatness to flatness. For the purpose of optimizing the mathematical model, this paper describes the application of adaptive genetic algorithm to achieve the best estimation. Simultaneously, the process of optimization is realized by MALTAB. Finally, the experiment shows that the evaluation results of MZT is better than evaluation results of LSM.

Research on Generator Excitation Parameter Identification - PSS Low-Pass Link Parameter Identification

2013 ◽  
Vol 805-806 ◽  
pp. 716-720
Author(s):  
Tao Xu ◽  
Tian Long Shao ◽  
Dong Fang Zhang
Keyword(s):  
Mathematical Model ◽  
Parameter Identification ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
National Standards ◽  
Matlab Software ◽  
Low Pass ◽  
Newton Iterations ◽  
The Mathematical Model

Combined with the contents of the study-PSS low-pass link parameter identification. Least-squares method is selected. Using least-square method for PSS low-pass link mathematical model are also deduced. For the results, because of the mathematical model is solving nonlinear equations, cannot used by the Newton method directly. So we choose to use Newton iterations, with this feature, choose to use MATLAB software to solve the equation. Identification of the use of MATLAB software lags after the PSS parameters obtained recognition results compared with national standards, identifying and verifying the practicability.

The Mathematical Model of Welding Process Comparative Study of Identification Method

2012 ◽  
Vol 472-475 ◽  
pp. 2241-2244 ◽  
Author(s):  
Jun Feng Wu ◽  
Jing Huang
Keyword(s):  
Weld Pool ◽  
Academic Research ◽  
Welding Process ◽  
Least Square Method ◽  
Mathematic Model ◽  
Least Square ◽  
Complex Object ◽  
Strong Nonlinearity ◽  
Area Method ◽  
Pulsed Gtaw

The dynamic process of the weld pool is a high complex object with strong nonlinearity, mult-variable coupling and a mount of stochastic and uncertain factors. It is very difficult to obtain an analysis mathematic model of weld pool dynamics. Pulsed Gas Tungsten Arc Welding (GTAW) is an important metal’s welding technology, which has been widely applied in the aerospace and manufacturing areas. Therefore, the dynamic characteristic of the welding process has always been hot and difficult in the field of academic research and engineering applications. In order to solve the difficulties of modeling and controlling of nonlinear system, this paper investigates the dynamic characters of the pulsed GTAW from the classic control systems. It obtains the SISO transfer function model by the area method and least square method. The results of simulation experiment show that the area method is better between the two methods.

scholarly journals Intelligent Prediction of Sieving Efficiency in Vibrating Screens

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Bin Zhang ◽  
Jinke Gong ◽  
Wenhua Yuan ◽  
Jun Fu ◽  
Yi Huang
Keyword(s):  
Support Vector Machine ◽  
Cross Validation ◽  
Prediction Performance ◽  
Least Square ◽  
Support Vector ◽  
Adaptive Genetic Algorithm ◽  
Screen Length ◽  
Vibrating Screen ◽  
Working Parameters ◽  
Better Than

In order to effectively predict the sieving efficiency of a vibrating screen, experiments to investigate the sieving efficiency were carried out. Relation between sieving efficiency and other working parameters in a vibrating screen such as mesh aperture size, screen length, inclination angle, vibration amplitude, and vibration frequency was analyzed. Based on the experiments, least square support vector machine (LS-SVM) was established to predict the sieving efficiency, and adaptive genetic algorithm and cross-validation algorithm were used to optimize the parameters in LS-SVM. By the examination of testing points, the prediction performance of least square support vector machine is better than that of the existing formula and neural network, and its average relative error is only 4.2%.

scholarly journals Cylindricity Error Measuring and Evaluating for Engine Cylinder Bore in Manufacturing Procedure

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Qiang Chen ◽  
Xueheng Tao ◽  
Jinshi Lu ◽  
Xuejun Wang
Keyword(s):  
Least Square Method ◽  
Least Square ◽  
Zone Method ◽  
Method Error ◽  
Measuring Device ◽  
Engine Cylinder ◽  
Minimum Zone ◽  
Cylinder Method ◽  
Cylinder Bore ◽  
Cylindricity Error

On-line measuring device of cylindricity error is designed based on two-point method error separation technique (EST), which can separate spindle rotation error from measuring error. According to the principle of measuring device, the mathematical model of the minimum zone method for cylindricity error evaluating is established. Optimized parameters of objective function decrease to four from six by assuming thatcis equal to zero andhis equal to one. Initial values of optimized parameters are obtained from least square method and final values are acquired by the genetic algorithm. The ideal axis of cylinder is fitted in MATLAB. Compared to the error results of the least square method, the minimum circumscribed cylinder method, and the maximum inscribed cylinder method, the error result of the minimum zone method conforms to the theory of error evaluation. The results indicate that the method can meet the requirement of engine cylinder bore cylindricity error measuring and evaluating.

Error Model and Calibration Analysis of the Flexible Coordinate Measuring Machine

2011 ◽  
Vol 121-126 ◽  
pp. 3273-3277 ◽  
Author(s):  
Fang Li ◽  
Shu Gui Liu ◽  
Lei Zhao
Keyword(s):  
Mathematical Model ◽  
Coordinate Measuring Machine ◽  
Least Square Method ◽  
Coefficient Matrix ◽  
Error Model ◽  
Least Square ◽  
Parameter Calibration ◽  
Measuring Machine ◽  
Improving Accuracy ◽  
The Mathematical Model

A new 5-DOF flexible coordinate measuring machine (CMM) is introduced in this paper, which uses REVO system produced by Renishaw. According to the D-H method, the mathematical model is built, and then the error model of the flexible CMM is derived. The parameter calibration based on the nonlinear least square method is analyzed theoretically. Due to the disadvantages of Gauss-Newton method, LM method is researched, which improved the singularity of the coefficient matrix. The calibration analysis is a basis for improving accuracy of the flexible CMM.

Reliability Evaluation on Machining Center Based on Three-Parameter Weibull Distribution

2012 ◽  
Vol 430-432 ◽  
pp. 1645-1649 ◽  
Author(s):  
Gong Chang Ren ◽  
Zhi Wei Yang ◽  
Bo Min Meng
Keyword(s):  
Weibull Distribution ◽  
Goodness Of Fit ◽  
Location Parameter ◽  
Least Square Method ◽  
Optimization Method ◽  
Reliability Evaluation ◽  
Least Square ◽  
Distribution Model ◽  
Adaptive Genetic Algorithm ◽  
Machining Center

In order to improve the model accuracy of reliability evaluation, the Three-Parameter Weibull Distribution model of time between fault was established by introducing location parameters. The correlation coefficient optimization method based on the adaptive genetic algorithm was firstly applied to estimate the location parameter of the Three-Parameter Weibull Distribution. Shape parameter and scale parameter were obtained by the least square method. The time between failures of these series machining center submitting to three-parameter weibull Distribution was checked by the test hypothesis of goodness-of-fit distribution. Finally, the machining center was carried out reliability evaluation based on the Three-Parameter Weibull Distribution model.

scholarly journals FORMULATION OF MATHEMATICAL MODEL FOR PRODUCTION TURNOVER OF BIODIESEL PLANT BASED ON DIMENSIONAL ANALYSIS AND MULTIPLE REGRESSION

2012 ◽  
pp. 268-276
Author(s):  
ASHWIN S. CHATPALLIWAR ◽  
DR. VISHWAS S. DESHPANDE ◽  
DR. JAYANT P. MODAK ◽  
DR. NILESHSINGH V. THAKUR
Keyword(s):  
Mathematical Model ◽  
Multiple Regression ◽  
Dimensional Analysis ◽  
Least Square Method ◽  
Least Square ◽  
Design Data ◽  
Dimensionless Equation ◽  
Set Up ◽  
The Mathematical Model ◽  
Data Design

This paper presents the approach for the mathematical modeling of production turnover for the set up of new Biodiesel plant based on the dimensional analysis and multiple regression. Presented production turnover mathematical model is derived based on the generated design data. Design data is generated from the estimated design data. Estimation of design data is carried out based on the assumed plant layouts of different capacities. Dimensional analysis is used to make the independent and dependent variables dimensionless and to get dimensionless equation. Later, multiple regression analysis is applied to this dimensionless equation to obtain the index values based on the least square method. The mathematical model of production turnover is formulated using these obtained index values. Finally, the formulated model is evaluated on the basis of correlation and root mean square error between the computed values by model and the estimated values.

Study of Evaluation Method about the Presswork Quality of Digital Inkjet System

2014 ◽  
Vol 540 ◽  
pp. 512-517
Author(s):  
Chang Xian Cheng ◽  
Yan Mei Liang
Keyword(s):  
High Speed ◽  
Evaluation Method ◽  
Orthogonal Experiment ◽  
Least Square Method ◽  
Least Square ◽  
Affecting Factors ◽  
Print Head ◽  
Machine Communication ◽  
The Mathematical Model

At present, the productivity benefits of inkjet printing technology with high speed shows a rapid expanding trends, however, the precondition of which is its high quality presswork. Therefore, one of the top priorities now is to find better way to evaluate the presswork quality scientifically and effectively. A new parameter, ink dot fidelity, was introduced as an evaluation criterion to study the presswork quality in this paper. The four evident effect factors that fluctuated more during the printing process were chosen, such as the paper transmission speed, the print head (nozzle) voltage, the ink cartridge pressure and the distance between the print head and paper, to make the scientific orthogonal experiment design. The fluctuation rules of the ink dot fidelity corresponding to each effecting factors were obtained through intuitively analyzing of the orthogonal tables and the effect curves. Based on the experiment, the test data were fitted and optimized by using the mathematical analysis software of MATLAB and the least-square method. And then the mathematical model for ink dot fidelity and these affecting factors were created. Finally, the user interface (GUI) design platform was developed to improve the man-machine communication and the ink dot fidelity, or the presswork quality.

scholarly journals Evaluation on Nonholonomic Constraints and Rauch–Tung–Striebel Filter-Enhanced UWB/INS Integration

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Zhouzheng Gao ◽  
Lin Chen ◽  
Yu Min ◽  
Jie Lv ◽  
You Li
Keyword(s):  
Three Dimensional ◽  
Nonholonomic Constraints ◽  
Satellite System ◽  
Least Square ◽  
Precise Positioning ◽  
Global Navigation Satellite ◽  
Navigation Accuracy ◽  
The Impact ◽  
The Mathematical Model ◽  
Better Than

Precise and seamless positioning is becoming a basic requirement for the Internet of Things (IoT). However, there is a gap for precise positioning in Global Navigation Satellite System- (GNSS-) denied indoor areas. Thus, a multisensor integration system based on ultrawide-band (UWB), inertial navigation system (INS), nonholonomic constraints (NHCs), and Rauch–Tung–Striebel (RTS) smoother is proposed. In this system, the UWB performs as the major precise positioning system, while the INS bridges the UWB-degraded and UWB-denied periods. Meanwhile, the NHC restrains the drifts of INS, while the RTS smoother further upgrades the navigation accuracy. The contributions of this article are as follows. First, it presents the robust least square- (RLS-) based UWB positioning. The proposed method is effective in mitigating the impact of the effect of non-line-of-sight (NLOS), which is one of the most significant error sources for UWB positioning. Second, it derives the mathematical model of the UWB/INS/NHC/RTS integration, which is new compared to the existing approaches. Results illustrate that the proposed system can provide centimeter-level positioning accuracy, millimeter-level velocimetry accuracy, and accuracy of better than 0.05 and 0.15 degrees for horizontal and vertical attitude angles, respectively. Even in the scenario with short-term UWB outages (30 s), simulation results show that the three-dimensional position still can be better than 20 cm. Such accuracy values reach the state-of-the-art for indoor positioning using UWB and INS.

scholarly journals Numerical Analysis of Electrohydrodynamic Flow in a Circular Cylindrical Conduit by Using Neuro Evolutionary Technique

Energies ◽  
2021 ◽  
Vol 14 (22) ◽  
pp. 7774
Author(s):  
Naveed Ahmad Khan ◽  
Muhammad Sulaiman ◽  
Carlos Andrés Tavera Romero ◽  
Fawaz Khaled Alarfaj
Keyword(s):  
Numerical Solutions ◽  
Fitness Function ◽  
Least Square Method ◽  
Approximate Solutions ◽  
Least Square ◽  
Mean Absolute Deviation ◽  
Absolute Deviation ◽  
Evolutionary Technique ◽  
Generalized Normal Distribution ◽  
The Mathematical Model

This paper analyzes the mathematical model of electrohydrodynamic (EHD) fluid flow in a circular cylindrical conduit with an ion drag configuration. The phenomenon was modelled as a nonlinear differential equation. Furthermore, an application of artificial neural networks (ANNs) with a generalized normal distribution optimization algorithm (GNDO) and sequential quadratic programming (SQP) were utilized to suggest approximate solutions for the velocity, displacements, and acceleration profiles of the fluid by varying the Hartmann electric number (Ha2) and the strength of nonlinearity (α). ANNs were used to model the fitness function for the governing equation in terms of mean square error (MSE), which was further optimized initially by GNDO to exploit the global search. Then SQP was implemented to complement its local convergence. Numerical solutions obtained by the design scheme were compared with RK-4, the least square method (LSM), and the orthonormal Bernstein collocation method (OBCM). Stability, convergence, and robustness of the proposed algorithm were endorsed by the statistics and analysis on results of absolute errors, mean absolute deviation (MAD), Theil’s inequality coefficient (TIC), and error in Nash Sutcliffe efficiency (ENSE).

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