scholarly journals Human gait modelling and tracking based on motion functionalisation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ruxun Sun ◽  
Sanaa Sharaf ◽  
Basel Jamal Ali
Keyword(s):  
Least Square Method ◽  
Human Movement ◽  
Least Square ◽  
Human Gait ◽  
Mathematical Function ◽  
Movement Model ◽  
Motion Error ◽  
Fitting Method ◽  
Movement Parameters ◽  
The Mathematical Model

Abstract This paper proposes a mathematical function movement model based on the gait movement of the human body and, in particular, on the trajectory of the limbs during human movement. The article systematically measures and experimentally deals with the trajectory of the limbs of 40 students in the walking movement. The linear high-order polynomial fitting method eliminates the motion error. Simultaneously, the linear relationship least square method is used to obtain the expression of the limb motion function. Finally, the mathematical model of the limb motion trajectory is obtained. It is verified through experiments that the model proposed in the thesis can calculate the law of limb movement and movement parameters of any person under normal walking movement. This research has high research value for human movement rehabilitation and the design of wearable equipment.

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.

scholarly journals The Parameter Estimation of Double Exponential Pulse Based on a Least Infinity Norm Fitting Method

2021 ◽  
Vol 2083 (4) ◽  
pp. 042002
Author(s):  
Yuewu Shi ◽  
Wei Wang ◽  
Zhizhen Zhu ◽  
Xin Nie
Keyword(s):  
Estimation Error ◽  
Estimation Method ◽  
Maximum Amplitude ◽  
Least Square Method ◽  
Least Square ◽  
Physical Parameters ◽  
Infinity Norm ◽  
Fitting Method ◽  
Double Exponential ◽  
Exponential Pulse

Abstract This paper presents an estimation method of double exponential pulse (DEP) between the physical parameters rise time (t r), full width at half maximum amplitude (t FWHM) and the mathematical parameters α, β. A newly fitting method based on the least infinity norm criterion is proposed to deal with the estimation problem of DEP. The calculation process and equation of parameters of this method is proposed based on an m-th-order polynomial fitting model. This estimation method is compared with the least square method by the same data and fitting function. The results show that the maximum estimation error of parameters of double exponential pulse obtained by the least infinity norm method is 1.5 %.

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.

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.

scholarly journals Calculation and realization of new method grey residual error correction model

PLoS ONE ◽  
2021 ◽  
Vol 16 (7) ◽  
pp. e0254154
Author(s):  
Lifang Xiao ◽  
Xiangyang Chen ◽  
Hao Wang
Keyword(s):  
Prediction Model ◽  
Least Square Method ◽  
Residual Error ◽  
Least Square ◽  
Grey Model ◽  
Grey Prediction ◽  
Grey Prediction Model ◽  
True Value ◽  
Prediction Function ◽  
Fitting Method

Aiming at the problem of prediction accuracy of stochastic volatility series, this paper proposes a method to optimize the grey model(GM(1,1)) from the perspective of residual error. In this study, a new fitting method is firstly used, which combines the wavelet function basis and the least square method to fit the residual data of the true value and the predicted value of the grey model(GM(1,1)). The residual prediction function is constructed by using the fitting method. Then, the prediction function of the grey model(GM(1,1)) is modified by the residual prediction function. Finally, an example of the wavelet residual-corrected grey prediction model (WGM) is obtained. The test results show that the fitting accuracy of the wavelet residual-corrected grey prediction model has irreplaceable advantages.

Reliability and Usefulness of the Fitting of a Modified Gamma Function to Time-Activity Curves by Means of a Non-Linear Iterative Least-Square Method

1981 ◽  
Vol 20 (04) ◽  
pp. 195-197
Author(s):  
J. M. Fránquiz
Keyword(s):  
Gamma Function ◽  
Least Square Method ◽  
Least Square ◽  
Base Line ◽  
Time Activity ◽  
Appearance Time ◽  
Least Square Fitting ◽  
Fitting Method ◽  
Non Linear ◽  
Least Square Fitting Method

A non-linear iterative least-square fitting method is presented for calculating the parameters of a modified gamma function. The method permits the correction of the appearance time (AT) and the curve parameters in those situations in which AT cannot be estimated with accuracy. The reliability and accuracy of the method is studied in experimental and simulated curves by means of a computer, comparing the results with those obtained by the method of Starmer and Clark for different initial selections of AT and noise at the base line. The usefulness of the method is shown in situations where the curves are distorted in their initial part.

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.

A New Method for the Identification of Coulomb and Viscous Friction

Tribology ◽  
2005 ◽  
Author(s):  
Lilan Liu ◽  
Hongzhao Liu ◽  
Ziying Wu ◽  
Daning Yuan
Keyword(s):  
Damping Ratio ◽  
Viscous Friction ◽  
Least Square Method ◽  
Least Square ◽  
New Method ◽  
Exponential Fitting ◽  
Viscous Damping ◽  
Equivalent Viscous Damping ◽  
Fitting Method ◽  
Friction Parameters

In this paper, a new method for simultaneously estimating Coulomb and viscous friction parameters from the free vibration of a damped oscillator is put forward. In the method, the nonlinear vibration equation with Coulomb and viscous friction is transformed into a linear procedure with equivalent viscous damping which is a function of velocity. The proposed method works well with both the displacement and velocity response data, while the case of zero velocity is not considered. From the displacement decaying curve, the equivalent viscous damping ratios are obtained by means of the local exponential fitting method, and different velocities corresponding to the equivalent viscous damping ratios are also obtained from the velocity decaying curve. Then, according to the relationship between the equivalent viscous damping ratio and the velocity, the Coulomb friction and the viscous damping are achieved using the least square method. The validity and accuracy of the proposed method are demonstrated through good simulation results.

Improved modified moving average analysis of T-wave alternans using least squares-based curve fitting method

2014 ◽  
Vol 07 (04) ◽  
pp. 1450044 ◽  
Author(s):  
Xiang-Kui Wan ◽  
Kang-Hui Yan ◽  
Ang Li ◽  
Ming-Hu Wu
Keyword(s):  
Curve Fitting ◽  
Moving Average ◽  
Least Square Method ◽  
Least Square ◽  
T Wave ◽  
Fitting Method ◽  
Average Analysis ◽  
T Wave Alternans ◽  
Improved Performance ◽  
Curve Fitting Method

T-wave alternans (TWA) in surface electrocardiograph (ECG) signal is considered a marker of abnormal ventricular function which may be associated with ventricular tachycardia. Several methods have been developed in recent years to evaluate the important feature. One such method is known as modified moving average (MMA) analysis, which performs well for different levels of TWA, but it is sensitive to the noise in T-waves. In this paper we propose an improved MMA algorithm, which adds a stage of T-wave curve fitting for the MMA method before intermediate averaging. The curve fitting is performed by means of least square method technique. Our assessment study demonstrates the improved performance.

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.

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