Mathematical Model for Evaluating Cylindricity Errors by Minimum Zone Method

2011 ◽  
Vol 284-286 ◽  
pp. 434-438 ◽  
Author(s):  
Ping Liu ◽  
Hui Yi Miao
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Model ◽  
Dimensional Euclidean Space ◽  
Modern Theory ◽  
Minimal Point ◽  
Zone Method ◽  
Deviation Measurement ◽  
Minimum Zone ◽  
Theoretical Results

An unconstrained optimization model is established for assessing cylindricity errors by the minimum zone method based on radial deviation measurement. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory on convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on a subset of the four-dimensional Euclidean space. The minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Thus, any existing optimization algorithm, so long as it is convergent, can be applied to solve the objective function in order to get the wanted cylindricity errors by the minimun zone assessment. An example is given to verify the theoretical results presented.

Research on the Properties of Coaxality Error Objective Function

2009 ◽  
Vol 16-19 ◽  
pp. 1164-1168 ◽  
Author(s):  
Ping Liu ◽  
San Yang Liu
Keyword(s):  
Euclidean Space ◽  
Objective Function ◽  
Optimization Model ◽  
Dimensional Euclidean Space ◽  
Modern Theory ◽  
Minimal Point ◽  
Zone Method ◽  
Deviation Measurement ◽  
Minimum Zone ◽  
Theoretical Results

The unconstrained optimization model applying to radial deviation measurement is established for assessing coaxality errors by the positioned minimum zone method. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory of convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on the four-dimensional Euclidean space R4. Therefore, the global minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Thus, any existing optimization algorithm, as long as it is convergent, can be used to solve the objective function to get the wanted values of coaxality errors by the positioned minimum zone assessment. An example is given to verify the theoretical results presented.

Some Properties of Mathematical Model for Cylindricity Errors

2010 ◽  
Vol 37-38 ◽  
pp. 1214-1218 ◽  
Author(s):  
Ping Liu ◽  
Hui Yi Miao
Keyword(s):  
Mathematical Model ◽  
Euclidean Space ◽  
Convex Function ◽  
Objective Function ◽  
Optimization Model ◽  
Dimensional Euclidean Space ◽  
Modern Theory ◽  
Minimal Point ◽  
Deviation Measurement ◽  
Theoretical Results

An unconstrained optimization model, applicable to radial deviation measurement, is established for assessing cylindricity errors by the minimum circumscribed cylinder evaluation. The properties of the objective function in the optimization model are thoroughly investigated. On the basis of the modern theory of convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on the four-dimensional Euclidean space R4. Therefore, the minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Thus, any existing optimization algorithm, so long as it is convergent, can be used to solve the objective function to get the wanted values of cylindricity errors by the minimum circumscribed cylinder assessment. An example is given to verify the theoretical results presented.

Mathematical Model for Evaluating Roundness Errors by Minimum Circumscribed Circle Method

2011 ◽  
Vol 328-330 ◽  
pp. 380-383 ◽  
Author(s):  
Ping Liu ◽  
Hui Yi Miao
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Model ◽  
Circle Method ◽  
Dimensional Euclidean Space ◽  
Modern Theory ◽  
Two Dimensional ◽  
Minimal Point ◽  
Deviation Measurement ◽  
Theoretical Results

An unconstrained optimization model is established for assessing roundness errors by the minimum circumscribed circle method based on radial deviation measurement. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory on convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on the two-dimensional Euclidean space. The minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Any existing optimization algorithm, so long as it is convergent, can be used to solve the objective function in order to get the wanted roundness errors by the minimun circumscribed circle assessment. One example is given to verify the theoretical results presented.

Mathematical Model for Evaluating Roundness Errors by Maximum Inscribed Circle Method

2011 ◽  
Vol 314-316 ◽  
pp. 393-396 ◽  
Author(s):  
Ping Liu ◽  
Hui Yi Miao
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Model ◽  
Circle Method ◽  
Dimensional Euclidean Space ◽  
Modern Theory ◽  
Two Dimensional ◽  
Minimal Point ◽  
Deviation Measurement ◽  
Theoretical Results

An unconstrained optimization model is established for assessing roundness errors by the maximum inscribed circle method based on radial deviation measurement. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory on convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on the two-dimensional Euclidean space. The minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Any existing optimization algorithm, so long as it is convergent, can be used to solve the objective function in order to get the wanted roundness errors by the maximum inscribed circle assessment. One example is given to verify the theoretical results presented.

Mathematical Model for Evaluating Cylindricity Errors by Maximum Inscribed Cylinder

2011 ◽  
Vol 474-476 ◽  
pp. 1418-1422
Author(s):  
Ping Liu ◽  
Hui Yi Miao
Keyword(s):  
Mathematical Model ◽  
Euclidean Space ◽  
Convex Function ◽  
Objective Function ◽  
Optimization Model ◽  
Dimensional Euclidean Space ◽  
Modern Theory ◽  
Minimal Point ◽  
Deviation Measurement ◽  
Theoretical Results

An unconstrained optimization model applicable to radial deviation measurement is established for assessing cylindricity errors by the maximum inscribed cylinder evaluation. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory of convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on a subset of the four-dimensional Euclidean space. The minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Any existing optimization algorithm, so long as it is convergent, can be used to solve the objective function to get the wanted values of cylindricity errors by the maximum inscribed cylinder assessment. An example is given to verify the theoretical results presented.

COMPARISON OF TWO OPTIMIZATION MODELS FOR CONSTRUCTING PATTERNS IN THE METHOD OF LOGICAL ANALYSIS OF DATA

2020 ◽  
pp. 10-13
Author(s):  
Р.И. Кузьмич ◽  
А.А. Ступина ◽  
С.Н. Ежеманская ◽  
А.П. Шугалей
Keyword(s):  
Objective Function ◽  
Optimization Model ◽  
Logical Analysis ◽  
Optimization Models ◽  
Logical Analysis Of Data

Предлагаются две оптимизационные модели для построения информативных закономерностей. Приводится эмпирическое подтверждение целесообразности использования критерия бустинга в качестве целевой функции оптимизационной модели для получения информативных закономерностей. Информативность, закономерность, критерий бустинга, оптимизационная модель Comparison of two optimization models for constructing patterns in the method of logical analysis of data Two optimization models for constructing informative patterns are proposed. An empirical confirmation of the expediency of using the boosting criterion as an objective function of the optimization model for obtaining informative patterns is given.

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

Optimization Research on Dynamic Balance of Spatial Engine under Limiting Shaking Moment

2009 ◽  
Vol 626-627 ◽  
pp. 693-698
Author(s):  
Yong Yong Zhu ◽  
S.Y. Gao
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Kinetic Analysis ◽  
Optimization Design ◽  
Design Method ◽  
Dynamic Balance ◽  
Optimized Design ◽  
Design Variables ◽  
The Mathematical Model ◽  
Shaking Moment

Dynamic balance of the spatial engine is researched. By considering the special wobble-plate engine as the model of spatial RRSSC linkages, design variables on the engine structure are confirmed based on the configuration characters and kinetic analysis of wobble-plate engine. In order to control the vibration of the engine frame and to decrease noise caused by the spatial engine, objective function is choosed as the dimensionless combinations of the various shaking forces and moments, the restriction condition of which presents limiting the percent of shaking moment. Then the optimization design is investigated by the mathematical model for dynamic balance. By use of the optimization design method to a type of wobble-plate engine, the optimization process as an example is demonstrated, it shows that the optimized design method benefits to control vibration and noise on the engines and improve the performance practically and theoretically.

Fitting Spherical Surface and Evaluating Sphericity Error Based on the Minimum Zone Principle

2014 ◽  
Vol 687-691 ◽  
pp. 1373-1376 ◽  
Author(s):  
Lei Zhang ◽  
Li Li Liu ◽  
Chuan Hui Huang ◽  
Xing Hua Lu ◽  
Gen Sun
Keyword(s):  
Mathematical Model ◽  
Spherical Surface ◽  
Least Square ◽  
Model Based ◽  
Minimum Zone

To address the fitting spherical surface and evaluating sphericity error, a mathematical model based on the minimum zone principle is presented. And the presented model is answered by GA. An example shows the performance of the proposed method by comparison with the methods based on the least square principle.

A prey–predator model and control of a nematodes pest using control in banana: Mathematical modeling and qualitative analysis

2021 ◽  
pp. 2150089
Author(s):  
Sudhakar Yadav ◽  
Vivek Kumar
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Local Stability ◽  
Detection Method ◽  
Initial Release ◽  
Pest Detection ◽  
Predator Model ◽  
And Control ◽  
The Mathematical Model ◽  
Theoretical Results

This study develops a mathematical model for describing the dynamics of the banana-nematodes and its pest detection method to help banana farmers. Two criteria: the mathematical model and the type of nematodes pest control system are discussed. The sensitivity analysis, local stability, global stability, and the dynamic behavior of the mathematical model are performed. Further, we also develop and discuss the optimal control mathematical model. This mathematical model represents various modes of management, including the initial release of infected predators as well as the destroying of nematodes. The theoretical results are shown and verified by numerical simulations.

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