DEVELOPMENT OF A MATHEMATICAL MODEL OF THE FABRIC FINISHING PROCESS

Recently, systematic sampling on the circle and the sphere has been studied by Gual-Arnau and Cruz-Orive (2000) from a design-based point of view. In this note, it is shown that their mathematical model for the covariogram is, in a model-based statistical setting, a special case of the p-order shape model suggested by Hobolth, Pedersen and Jensen (2000) and Hobolth, Kent and Dryden (2002) for planar objects without landmarks. Benefits of this observation include an alternative variance estimator, applicable in the original problem of systematic sampling. In a wider perspective, the paper contributes to the discussion concerning design-based versus model-based stereology.

Download Full-text

27 years of the HIV epidemic amongst men having sex with men in the Netherlands: An in depth mathematical model-based analysis

Epidemics ◽

10.1016/j.epidem.2010.04.001 ◽

2010 ◽

Vol 2 (2) ◽

pp. 66-79 ◽

Cited By ~ 45

Author(s):

Daniela Bezemer ◽

Frank de Wolf ◽

Maarten C. Boerlijst ◽

Ard van Sighem ◽

T. Deirdre Hollingsworth ◽

...

Keyword(s):

Mathematical Model ◽

The Netherlands ◽

Model Based ◽

Hiv Epidemic ◽

Sex With Men ◽

Model Based Analysis

Download Full-text

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.687-691.1373 ◽

2014 ◽

Vol 687-691 ◽

pp. 1373-1376 ◽

Cited By ~ 1

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.

Download Full-text

Model-Based Design Approach to Improve Performance Characteristics of Hydrostatic Bearing Using Multivariable Optimization

Mathematics ◽

10.3390/math9040388 ◽

2021 ◽

Vol 9 (4) ◽

pp. 388

Author(s):

Waheed Ur Rehman ◽

Xinhua Wang ◽

Yiqi Cheng ◽

Yingchun Chen ◽

Hasan Shahzad ◽

...

Keyword(s):

Mathematical Model ◽

Feedback Control ◽

External Load ◽

Sliding Mode ◽

Feedforward Control ◽

Spindle Speed ◽

Performance Criteria ◽

Model Based ◽

Hydrostatic Bearings ◽

Robust Control Design

Research in the field of tribo-mechatronics has been gaining popularity in recent decades. The objective of the current research is to improve static/dynamics characteristics of hydrostatic bearings. Hydrostatic bearings always work in harsh environmental conditions that effect their performance, and which may even result in their failure. The current research proposes a mathematical model-based system for hydrostatic bearings that helps to improve its static/dynamic characteristics under varying conditions of performance-influencing variables such as temperature, spindle speed, external load, and clearance gap. To achieve these objectives, the capillary restrictors are replaced with servo valves, and a mathematical model is developed along with robust control design systems. The control system consists of feedforward and feedback control techniques that have not been applied before for hydrostatic bearings in the published literature. The feedforward control tries to remove a disturbance before it enters the system while feedback control achieves the objective of disturbance rejection and improves steady-state characteristics. The feedforward control is a trajectory-based controller and the feedback controller is a sliding mode controller with a PID sliding surface. The particle swarm optimization algorithm is used to tune the 6-dimensional vector of the tuning parameters with multi-objective performance criteria. Numerical investigations have been carried out to check the performance of the proposed system under varying conditions of viscosity, clearance gap, external load and the spindle speed. The comparison of our results with the published literature shows the effectiveness of the proposed system.

Download Full-text

Global Approximation: Performance Comparison of Different Methods, With an Application to Road Vehicle System Engineering

10.1115/imece1999-0329 ◽

1999 ◽

Author(s):

Massimiliano Gobbi ◽

Giampiero Mastinu

Keyword(s):

Neural Networks ◽

Mathematical Model ◽

Linear Interpolation ◽

Performance Comparison ◽

Pareto Optimal ◽

Approximation Methods ◽

Global Approximation ◽

Road Vehicle ◽

Pareto Optimal Set ◽

Design Variables

Abstract Optimisation of complex mechanical systems has often to be performed by resorting to global approximation. In usual global approximation practice, the original mathematical model is substituted by another mathematical model which gives approximately the same relationships between design variables and performance indexes. This is made to ensure much faster simulations which are of crucial importance to find optimal solutions. In this paper the performances of four global approximation methods (Neural Networks, Kriging, Quadratic Approximation, Linear Interpolation) are compared, with reference to an actual optimal design problem. The performances of a road vehicle suspension system are optimised by varying the system’s design variables. The Pareto-optimal set is derived symbolically. The performances of the different approximation methods taken into consideration are assessed by comparing the numerical- and the analytical-Pareto-optimal results. It is found that Neural Networks obtain the best accuracy.

Download Full-text

ANALYTICAL METHODS FOR CALCULATING FAN AERODYNAMICS

Acta Polytechnica ◽

10.14311/ap.2015.55.0373 ◽

2015 ◽

Vol 55 (6) ◽

pp. 373

Author(s):

Jan Dostal ◽

Jan Kuzel

Keyword(s):

Mathematical Model ◽

Analytical Methods ◽

Preliminary Design ◽

Computer Programme ◽

Aerospace Research ◽

Model Based ◽

The Creation ◽

The Mathematical Model ◽

Measuring Unit

This paper presents results obtained between 2010 and 2014 in the field of fan aerodynamics at the Department of Composite Technology at the VZLÚ aerospace research and experimental institute in Prague – Letnany. The need for rapid and accurate methods for the preliminary design of blade machinery led to the creation of a mathematical model based on the basic laws of turbomachine aerodynamics. The mathematical model, the derivation of which is briefly described below, has been encoded in a computer programme, which enables the theoretical characteristics of a fan of the designed geometry to be determined rapidly. The validity of the mathematical model is assessed continuously by measuring model fans in the measuring unit, which was developed and manufactured specifically for this purpose. The paper also presents a comparison between measured characteristics and characteristics determined by the mathematical model as the basis for a discussion on possible causes of measured deviations and calculation deviations.

Download Full-text

Movement Time to an Array of Controls

Proceedings of the Human Factors and Ergonomics Society Annual Meeting ◽

10.1177/154193129303700924 ◽

1993 ◽

Vol 37 (9) ◽

pp. 625-629 ◽

Cited By ~ 2

Author(s):

Errol R. Hoffmann

Keyword(s):

Mathematical Model ◽

Theoretical Result ◽

Movement Time ◽

Element Model ◽

Optimum Control ◽

Fitts Law ◽

Model Based ◽

Array Density

Two tasks in which subjects aim at an array of devices were considered: moving to one knob within an array and moving the finger on a numeric keypad. It was shown by a mathematical model based on Fitts' law, that when the array density is specified for the array of knobs or keys, there is an optimum control size for minimum movement time. The theoretical result was obtained by considering a two-element model of the movement, the first being a reach to the general location of the control and the second describing the insertion of the fingers into the space between adjacent controls. As the first element has a movement time that decreases with increase of control size and the second a time increasing with control size, there is an optimum control size where the movement time is a minimum.

Download Full-text

Temperature Prediction at the Blow End of the Converter via Control Model

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1025-1026.298 ◽

2014 ◽

Vol 1025-1026 ◽

pp. 298-301

Author(s):

Alexandre Furtado Ferreira

Keyword(s):

Mathematical Model ◽

Dynamic Control ◽

Control Model ◽

Mass Balances ◽

Temperature Prediction ◽

Oxygen Blow ◽

Model Based ◽

Gas Control ◽

Prediction Capability

In the present work, a technique and model for temperature prediction at the blow end are briefly discussed, along with their limitations and perspectives for application. As a result of this analysis, a mathematical model based in heat and mass balances has been developed with a view to evaluating the possibility of improving this prediction capability. The study here presented focuses the development of a semi-dynamic control model in the LD-KGC converter (Linz-Donawitz-Kawasaki Gas Control Converter). The control model enables one to predict the temperature of the blow end by solving both the energy and mass equations. The inputs to the control model are the load data of the LD-KGC converter at the blow beginning and the collected data by the lance to 89% of oxygen blow. The results obtained in the present work were compared to the data measured in steelmaking. The semi-dynamic control model results agree well with data for LD-KGC converters.

Download Full-text