Application of the Least Squares Method to Estimate the Gain of the Mathematical Model of the Aircraft Structure Strength Test Bench

2021 ◽  
Author(s):  
Valery D. Yurkevich ◽  
Maksim V. Trubin ◽  
Vitaliy G. Trubin
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Test Bench ◽  
Least Squares Method ◽  
Strength Test ◽  
Aircraft Structure ◽  
Structure Strength ◽  
The Mathematical Model

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 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.

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.

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.

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.

scholarly journals Experimentalanalytical identification of a mathematical model of a dc motor using the least squares method

2019 ◽  
Vol 21 (4) ◽  
pp. 113-122
Author(s):  
N. A. Malev ◽  
A. I. Mukhametshin ◽  
O. V. Pogoditsky ◽  
A. G. Gorodnov
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Dynamic Properties ◽  
Dc Motor ◽  
High Accuracy ◽  
Electrical Machines ◽  
Analytical Assessment ◽  
Approximate Polynomial ◽  
Process Graphs

The urgency of the problem lies in the formation of mathematical models of electromechanical converters corresponding to the objects of study with high accuracy. An experimental-analytical assessment of transient modes of a DC motor based on an installation for the study of electrical machines has been carried out. Based on the results obtained, an approximation of transient process graphs was carried out using the least squares method and an approximate polynomial of the corresponding order was selected with the closest imminence to the dynamic properties of the object under study.

scholarly journals An Estimation of Dates Production Function in Karbala Governorate For The Agricultural Season 2020 (Al-jadual Al-gharby District A case Study)

2021 ◽  
Vol 923 (1) ◽  
pp. 012070
Author(s):  
Sadeq H. Hussein ◽  
Hayder Hamed Blaw
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Production Function ◽  
Returns To Scale ◽  
Ordinary Least Squares ◽  
Total Production ◽  
Logarithmic Function ◽  
The Mathematical Model

Abstract This study aimed to detect the most important factor that affects dates production. About 108 questionary forms collecttted palm orchard farmers in Karbala to estimate the dates production function in Karbala governorate for the agricultural season 2021 (the district of Al-jadual Al-Gharby). The study distributed those formmmsss for about 10% of the total palm orchards in Al-jadual Al-Gharby district of the holy governorate of Karbala. The study used the method of ordinary Least squares (OLS) to estimate the mathematical model of the function. The results showed that the double Logarithmic function in terms of its estimation of the estimated Coefficients by one unit leads to a corresponding change in the produced quality of dates and the same direction by 0.188 0.808) % respectively, and that the capital variable is more in fluently in production than the work variable. As for the total production elasticity (the sum of the partial elasticities of the resources used), which represents returns to scale, it amounted to about (0.996), which indicates a decrease in the return to scale.

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