Research on Flatness Error Measurement of Revolving Body End-Face

2010 ◽  
Vol 44-47 ◽  
pp. 4002-4006 ◽  
Author(s):  
Peng Guan ◽  
Tian Biao Yu ◽  
Wan Shan Wang
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Sampling Method ◽  
Evaluation Method ◽  
Least Squares Method ◽  
Error Measurement ◽  
Measurement Evaluation ◽  
Revolving Body ◽  
The Mathematical Model ◽  
Flatness Error

According to problems of flatness error measurement of revolving body end-face, sampling method and evaluation method are studied in this paper. First, spiral sampling method is presented, in order to meet the needs of flatness error measurement sampling of revolving body end-face. Second, combined with least squares method, mathematical model applied to flatness error measurement evaluation of revolving body end-face is proposed. Finally, through the simulation, the mathematical model is proved to be correct.

scholarly journals The identification of a device based on a Peltier element by the least squares method

2020 ◽  
pp. 17-27
Author(s):  
Vladimir Grinkevich ◽  
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Control Object ◽  
Object Identification ◽  
Model Parameters ◽  
Peltier Element ◽  
Transport Delay ◽  
Non Linear ◽  
The Mathematical Model

The evaluation of the mathematical model parameters of a non-linear object with a transport delay is considered in this paper. A temperature controlled stage based on a Peltier element is an identification object in the paper. Several input signal implementations are applied to the input of the identification object. The least squares method is applied for the calculation of the non-linear differential equitation parameters which describe the identification object. The least squares method is used due to its simplicity and the possibility of identification non-linear objects. The parameters values obtained in the process of identification are provided. The plots of temperature changes in the temperature control system with a controller designed based on the mathematical model of the control object obtained as a result of identification are shown. It is found that the mathematical model obtained in the process of identification may be applied to design controllers for non-linear systems, in particular for a temperature stage based on a Peltier element, and for self-tuning controllers. However, the least square method proposed in the paper cannot estimate the transport delay time. Therefore it is required to evaluate the time delay by temperature transient processes. Dynamic object identification is applied when it is required to obtain a mathematical model structure and evaluate the parameters by an input and output control object signal. Also, identification is applied for auto tuning of controllers. A mathematical model of a control object is required to design the controller which is used to provide the required accuracy and stability of control systems. Peltier elements are applied to design low-power and small- size temperature stage . Hot benches based on a Peltier element can provide the desired temperature above and below ambient temperature.

Mathematical modeling and parametric identification of a model using the example of a water-heating unit

2020 ◽  
Vol 42 (1) ◽  
pp. 103-109
Author(s):  
Sarsenbek Zhusupbekov ◽  
◽  
Laulasyn Abzhanova ◽  
Olzhas Nauryzbaev ◽  
◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Mimo System ◽  
Control Object ◽  
Real Object ◽  
Water Heating ◽  
Heating Unit ◽  
The Mathematical Model

The article is devoted to systemic issues related to the principles of mathematical modeling of technological objects, and the degree of adequacy of certain mathematical descriptions to real processes in these systems. In the article using the least squares method (least squares), a model of a water-heating unit is constructed as a MIMO system. The analysis of the process as a complex multi-connected control object. Based on the experimental data, a mathematical model is obtained in the state space of the water path. The adequacy of the mathematical model to the real object was established by directly comparing the output values of the object with the output values of the model. The results of a comparative assessment of the transition characteristics of the constructed mathematical model and the control object are presented. From the transient characteristics of the object and the mathematical model, it follows that the mathematical model fairly accurately and qualitatively describes the properties of the modeled object, i.e., it is adequate to the modeled object. The material presented allows you to teach a student to study processes by the method of mathematical modeling, including the preparation of a mathematical description, the choice of a solution method, software implementation of the model and verification of the model’s adequacy to a real object.

Research on Self-Calibration of Circular Artifacts

2013 ◽  
Vol 475-476 ◽  
pp. 167-172
Author(s):  
Xin Mei Liu ◽  
Yun Chen
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Random Noise ◽  
Poor Performance ◽  
Correlation Equation ◽  
System Error ◽  
Calibration Algorithm ◽  
The Impact ◽  
The Mathematical Model

In order to solve the problem of poor performance of the traditional calibration algorithm , the paper proposed a mathematical model under the constraints of nonrotating and nonscale error ,which solved the defects of inconvenience and expensiveness. Moreover, the mathematical model was obtained through the correlation equation based on the least squares method. Meanwhile , the paper discussed the impact of random noise on the model ,and it was simulated by Matlab. The result of the simulation shows that the model can separate the system error of circular artifacts accurately whether the existence of random noise or not. The result of this paper on expanding the application areas of selfcalibration is of great significance.

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 Method of determining the distance to the object by analyzing its image blur

Vestnik MGSU ◽  
2015 ◽  
pp. 140-151 ◽  
Author(s):  
Aleksey Alekseevich Loktev ◽  
Daniil Alekseevich Loktev
Keyword(s):  
Least Squares ◽  
Statistical Approach ◽  
Evaluation Method ◽  
Least Squares Method ◽  
Focal Length ◽  
Error Variance ◽  
Method Of Least Squares ◽  
Automated Control ◽  
Image Blur

In modern integrated monitoring systems and systems of automated control of technological processes there are several essential algorithms and procedures for obtaining primary information about an object and its behavior. The primary information is characteristics of static and moving objects: distance, speed, position in space etc. In order to obtain such information in the present work we proposed to use photos and video detectors that could provide the system with high-quality images of the object with high resolution. In the modern systems of video monitoring and automated control there are several ways of obtaining primary data on the behaviour and state of the studied objects: a multisensor approach (stereovision), building an image perspective, the use of fixed cameras and additional lighting of the object, and a special calibration of photo or video detector.In the present paper the authors develop a method of determining the distances to objects by analyzing a series of images using depth evaluation using defocusing. This method is based on the physical effect of the dependence of the determined distance to the object on the image from the focal length or aperture of the lens. When focusing the photodetector on the object at a certain distance, the other objects both closer and farther than a focal point, form a spot of blur depending on the distance to them in terms of images. Image blur of an object can be of different nature, it may be caused by the motion of the object or the detector, by the nature of the image boundaries of the object, by the object’s aggregate state, as well as by different settings of the photo-detector (focal length, shutter speed and aperture).When calculating the diameter of the blur spot it is assumed that blur at the point occurs equally in all directions. For more precise estimates of the geometrical parameters determination of the behavior and state of the object under study a statistical approach is used to determine the individual parameters and estimate their accuracy. A statistical approach is used to evaluate the deviation of the dependence of distance from the blur from different types of standard functions (logarithmic, exponential, linear). In the statistical approach the evaluation method of least squares and the method of least modules are included, as well as the Bayesian estimation, for which it is necessary to minimize the risks under different loss functions (quadratic, rectangular, linear) with known probability density (we consider normal, lognormal, Laplace, uniform distribution). As a result of the research it was established that the error variance of a function, the parameters of which are estimated using the least squares method, will be less than the error variance of the method of least modules, that is, the evaluation method of least squares is more stable. Also the errors’ estimation when using the method of least squares is unbiased, whereas the mathematical expectation when using the method of least modules is not zero, which indicates the displacement of error estimations. Therefore it is advisable to use the least squares method in the determination of the parameters of the function.In order to smooth out the possible outliers we use the Kalman filter to process the results of the initial observations and evaluation analysis, the method of least squares and the method of least three standard modules for the functions after applying the filter with different coefficients.

THE FLOW FIELD ACTING ON THE FLUTTERING PROFILE, KINEMATICS, FORCES AND TOTAL MOMENT

2013 ◽  
Vol 13 (07) ◽  
pp. 1340009 ◽  
Author(s):  
JAN KOZÁNEK ◽  
VÁCLAV VLČEK ◽  
IGOR ZOLOTAREV
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
High Speed ◽  
Least Squares Method ◽  
High Speed Camera ◽  
Aerodynamic Forces ◽  
Total Moment ◽  
Airfoil Surface ◽  
Measured System ◽  
Simplified Mathematical Model

A high speed camera was used for interferometry visualization (in different phases of the motion) of the fluttering NACA0015 profile supported in a translational and rotational manner. First, the simplified mathematical model of the support of investigated profile was identified from minimum least squares differences between modeled and measured system responses. A special graphical Matlab procedure was proposed for evaluation of interferograms. Kinematic analysis defining motion of the profile as a function of time was obtained by a regression using the least squares method. Numerical integration of pressure functions around the airfoil surface allows for calculation of the resulting aerodynamic forces and moments.

Sensorless Simultaneous Rotary-Translational Axis Motion Error Measurement and Trace Based on Virtual Bar

2010 ◽  
Author(s):  
Yuqing Zhou ◽  
Xuesong Mei ◽  
Gedong Jiang ◽  
Nuogang Sun ◽  
Bai Shao
Keyword(s):  
Mathematical Model ◽  
Feature Extraction ◽  
Wavelet Transform ◽  
Machine Tool ◽  
Error Measurement ◽  
Error Source ◽  
Spatial Error ◽  
Motion Error ◽  
Circular Test ◽  
The Mathematical Model

Simultaneous rotary-translational (R-T) axis motion error has significant influence on multi-axis machine tool precision. To improve multi-axis machine tool precision, axis motion error measurement and trace method are investigated in this study. A sensorless R-T axis motion error measurement and trace technology based on virtual bar is proposed. Firstly, the fundamental sensorless test principle is discussed. Then, the virtual-bar-based test path of a circular test though a rotary axis and two translational axes motion is scheduled. The mathematical model of motion error is established. Furthermore, to identify the error source, spatial error charts and some advanced signal processing and feature extraction technologies, such as wavelet transform and frequency analysis, are used. The analysis of experimental results shows that it is practical and efficient to use the virtual bar and the sensorless information to estimate motion error.

Model Parameter Identification and Simulation of Ship Power System Based on Recursive Least Squares Method

2012 ◽  
Vol 220-223 ◽  
pp. 482-486 ◽  
Author(s):  
Jin Hui Hu ◽  
Da Bin Hu ◽  
Jian Bo Xiao
Keyword(s):  
Mathematical Model ◽  
Power Systems ◽  
Parameter Identification ◽  
Least Squares ◽  
Least Squares Method ◽  
Recursive Least Squares ◽  
Design Parameters ◽  
Model Parameters ◽  
Model Parameter ◽  
Model Parameter Identification

According to the lack of the part of the equipment design parameters of a certain type of ship power systems, the algorithm of recursive least squares for model parameter identification is studied. The mathematical model of the propulsion motor is established. The model parameters are calculated and simulated based on parameter identification method of recursive least squares. The simulation results show that a more precise mathematical model can be simple and easily obtained by using of the method.

Optimization of the FSAE Car Steering Trapezoid

2012 ◽  
Vol 591-593 ◽  
pp. 196-200
Author(s):  
Ze Peng Liu ◽  
Gang Zhu ◽  
Jie Li ◽  
Shan Hu Yu
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Steering System ◽  
Vehicle Performance ◽  
Tire Wear ◽  
Special Circumstances

Steering system is important to the FSAE vehicle performance. And it’s necessary to optimize the steering trapezoid as well. According to the mentioned problem, the steering trapezoid is designed for the special circumstances of the track in this article. the steering mathematical model is established and optimized using the least squares method in the MATLAB Optimization Toolbox to improve the steering stability of the car. After manufacturing and testing the FSAE car prototype, the experimental and optimal results are compared, which indicates that the design of the steering trapezoid mechanism reduce tire wear and protect good steering and grip performance.

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