Mathematical Models In Terms Research Articles

Minimizing the total tardiness for the tool change scheduling problem on parallel machines

This paper deals with the total tardiness minimization problem in a parallel machines manufacturing environment where tool change operations have to be scheduled along with jobs. The mentioned issue belongs to the family of scheduling problems under deterministic machine availability restrictions. A new model that considers the effects of the tool wear on the quality characteristics of the worked product is proposed. Since no mathematical programming-based approach has been developed by literature so far, two distinct mixed integer linear programming models, able to schedule jobs as well as tool change activities along the provided production horizon, have been devised. The former is an adaptation of a well-known model presented by the relevant literature for the single machine scheduling problem with tool changes. The latter has been specifically developed for the issue at hand. After a theoretical analysis aimed at revealing the differences between the proposed mathematical models in terms of computational complexity, an extensive experimental campaign has been fulfilled to assess performances of the proposed methods under the CPU time viewpoint. Obtained results have been statistically analyzed through a properly arranged ANOVA analysis.

Response Surfaces for Fresh and Hardened Properties of Concrete with E-Waste (HIPS)

The fresh and hardened properties of concrete with E-waste plastic, that is, high impact polystyrene (HIPS), as a partial replacement for coarse aggregate were analyzed using response surface methodology (RSM). Face-centred central composite response surface design was used in this study. The statistical models were developed between the factors (HIPS and water cement ratio) and their response variables (slump, fresh density, dry density, compressive strength, spilt tensile strength, and flexural strength). The Design-Expert 9.0.3 software package was used to analyze the experimental values. The relationships were established and final mathematical models in terms of coded factors from predicted responses were developed. The effects of factors on properties for all variables were seen visually from the response surface and contour plot. Validation of experiments has shown that the experimental value closely agreed with the predicted value, which validates the calculated response surface models with desirability = 1. The HIPS replacement influenced all the properties of concrete than water cement ratio. Even though all properties show the decline trend, the experimented values and predicted values give a hope that the E-waste plastic (HIPS) can be used as coarse aggregate up to certain percentage of replacement in concrete which successively reduces the hazardous solid waste problem and conserves the natural resources from exhaustion.

Modeling of Duck Density and Complex Stocking Time in Rice-Duck Agroecosystems in Terms of Economic and Ecological Benefits

Rice-duck integrated farming is an effective step under today’s sustainable development background. To make better economic and ecological benefits, a rice-duck agroecosystem is established and kept, in which the paddy field, rice, and the duck mutually promote one another. But the duck density and complex stocking time must be rationally selected. Aiming to attain quantitative assessment and optimal selection of the duck density and complex stocking time in this kind of systems, a methodology based on proposed mathematical models in terms of comparative economic and ecological benefits is addressed. Then the models are solved by a hybrid intelligent algorithmNN-GAthat integrates the Neural Networks (NN) and Genetic Algorithm (GA), making use of the fitting ability in nonlinear fitness context of Neural Networks and the optimization ability of the Genetic Algorithm. Besides, numerical examples are demonstrated in order to test the proposed models. Results reveal that the methodology is reasonable and feasible.

The Application of Boolean Algebra in Modelling of Leakage Condition of a Car Hydraulic Braking System

A general characteristics of a car hydraulic braking system (CHBS) is presented in this publication. A graphical model of properties-component objects is developed for the above-mentioned system. Moreover, four mathematical models in terms of logic, the set theory and the Boolean algebra of Boolean functions are developed. The examination is ended with a general model of the CHBS for n - Boolean variables and the construction and mathematical-technical interpretation of this model is presented.

Modeling, Simulation and Dynamics Analysis Issues of Electric Motor, for Mechatronics Applications, Using Different Approaches and Verification by MATLAB/Simulink

The accurate control of motion is a fundamental concern in mechatronics applications, where placing an object in the exact desired location with the exact possible amount of force and torque at the correct exact time is essential for efficient system operation. An accurate modeling, simulation and dynamics analysis of actuators for mechatronics motion control applications is of big concern. The ultimate goal of this paper addresses different approaches used to derive mathematical models, building corresponding simulink models and dynamic analysis of the basic open loop electric DC motor system, used in mechatronics motion control applications, particularly, to design, construct and control of a mechatronics robot arm with single degree of freedom, and verification by MATLAB/Simulink. To simplify and accelerate the process of DC motors sizing, selection, dynamic analysis and evaluation for different motion applications, different mathematical models in terms of output position, speed, current, acceleration and torque, as well as corresponding simulink models, supporting MATLAB m.file and general function block models are to be introduced. The introduced models were verified using MATLAB/ Simulink. These models are intended for research purposes as well as for the application in educational process.

Securing Superior Properties of Composite (PP+WF) through Central Composite Design

Due to numerous attractive properties, use of composites is in increasing trend. Efforts are being made to develop new composites securing their useful properties at optimum level for more demanding applications. The purpose of this project is to optimize the mechanical properties of composite (polypropylene + wood fiber) using Central Composite Design (CCD) technique. Accordingly experiments were conducted to develop mathematical models in terms of three process parameters - composition (percentage of PP and wood fiber), injection pressure (bar), and time (second) for functional characteristics such as tensile strength and water absorption. Design expert software was used for convenience to carry out the analysis with a view to identifying the optimum level of the processing parameters for securing the desirable properties of the composite.

Simple gene assembly as a rewriting of directed overlap-inclusion graphs

The simple intramolecular model for gene assembly in ciliates consists of three molecular operations, simple ld, simple hi and simple dlad. Mathematical models in terms of signed permutations and signed strings proved limited in capturing some of the combinatorial details of the simple gene assembly process. Brijder and Hoogeboom introduced a new model in terms of overlap-inclusion graphs which could describe two of the three operations of the model and their combinatorial properties. To capture the third operation, we extended their framework to directed overlap-inclusion (DOI) graphs in Azimi et al. (2011) [1]. In this paper we introduce DOI graph-based rewriting rules that capture all three operations of the simple gene assembly model and prove that they are equivalent to the string-based formalization of the model.

Comparison of central composite and orthogonal array designs for cutting force and surface roughness prediction modelling in turning

Development of empirical models in turning operation has been a major activity in metal cutting research. This paper presents an application of central composite face centred (CCF) and L18(21 × 37) orthogonal array designs for developing cutting force and surface roughness models in case of turning AISI 1015 steel with HSS tool. Three process parameters namely cutting speed, feed, depth of cut and three tool parameters namely side cutting edge angle, inclination angle, normal rake angle were considered in developing the cutting force and surface roughness models. Each parameter was set at three levels. Based on the experimental data, mathematical models in terms of process and tool parameters were developed using multiple linear regression. Finally, central composite and orthogonal array designs are compared with respect to effect analysis and empirical model building. Confirmation tests were performed to verify the predictability of the developed models.

Response Surface Methodology and Genetic Algorithm used to Optimize the Cutting condition for Surface Roughness Parameters in CNC Turning

In the present study, response surface methodology has been applied to determine the optimum cutting conditions leading to minimum surface roughness in CNC turning operation on EN-8 steel. The second order mathematical models in terms of machining parameters were developed for surface roughness prediction using response surface methodology (RSM) on the basis of experimental results. The experimentation was carried out with coated carbide tool for machining of EN-8 steel. The model selected for optimization has been validated with F-test. The adequacy of the models on surface roughness has been established with Analysis of Variance (ANOVA). An attempt has also been made to optimize the surface roughness prediction model using Genetic Algorithm to find optimum cutting parameters.

Optimization of cutting conditions for surface roughness in CNC end milling

The aim of this research is to develop an integrated study of surface roughness to model and optimize the cutting parameters when end milling of 6061 aluminum alloy with HSS and carbide tools under dry and wet conditions. A multiple regression analysis using analysis of variance is conducted to determine the performance of experimental measurements and to show the effect of cutting parameters on the surface roughness. The second-order mathematical models in terms of machining parameters have been developed for each of these conditions on the basis of experimental results. Genetic algorithm (GA) supported with the regression equation is utilized to determine the best combinations of cutting parameters providing roughness to the lower surface through optimization process. The value obtained from GA is compared with that of experimental value and found reliable. It is observed from the results that the developed study can be applied to other machining processes operating under different machining conditions.

Directed Overlap-inclusion Graphs as Representations of Ciliate Genes

The simple intramolecular model for gene assembly in ciliates consists of three molecular operations based on local DNA manipulations. It was shown to predict correctly the assembly of all currently known ciliate gene patterns. Mathematical models in terms of signed permutations and signed strings proved limited in capturing some of the combinatorial details of the simple gene assembly process. A different formalization in terms of overlap-inclusion graphs, recently introduced by Brijder and Hoogeboom, proved well-suited to describe two of the three operations of the model and their combinatorial properties. We introduce in this paper an extension of the framework of Brijder and Hoogeboom in terms of directed overlap-inclusion graphs where more of the linear structure of the ciliate genes is described. We investigate a number of combinatorial properties of these graphs, including a necessary property in terms of forbidden induced subgraphs.

The medium access control problem for wireless communication networks modelled as hybrid dynamical systems

The paper considers the medium access control problem for a class of wireless communication networks. We apply mathematical models in terms of hybrid dynamical systems to analyze such networks. We introduce the concept of stabilizability for such systems which guarantees that any data packet in the wireless network will reach its destination within finite time. We obtain conditions for a wireless communication network to be stabilizable.

Mathematical modeling of zone drawing process

To provide guidelines and a basic understanding of static and continuous zone drawing processes, we propose two different mathematical models in terms of the processing conditions and material parameters. Although the models are not finely tuned, because of assumptions made, they are still useful for the analysis of the process and for predicting the processibility.

A survey of fuzzy logic monitoring and control utilisation in medicine

Intelligent systems have appeared in many technical areas, such as consumer electronics, robotics and industrial control systems. Many of these intelligent systems are based on fuzzy control strategies which describe complex systems mathematical models in terms of linguistic rules. Since the 1980s new techniques have appeared from which fuzzy logic has been applied extensively in medical systems. The justification for such intelligent systems driven solutions is that biological systems are so complex that the development of computerised systems within such environments is not always a straightforward exercise. In practice, a precise model may not exist for biological systems or it may be too difficult to model. In most cases fuzzy logic is considered to be an ideal tool as human minds work from approximate data, extract meaningful information and produce crisp solutions. This paper surveys the utilisation of fuzzy logic control and monitoring in medical sciences with an analysis of its possible future penetration.

MATHEMATICAL MODELLING OF GAS-SOLID REACTIONS: EFFECT OF PORE STRUCTURE

Gas-solid reactions find importance in numerous processes including conventional ones, involving gasification and ore reduction, as well as newer ones related to ceramics and VLSI production. The mathematical modelling of gas solid reactions is therefore a subject of long standing interest now receiving renewed attention. This review presents the various mathematical models in terms of a unified framework that accommodates shrinking core reactions as well as the internal reaction-diffusion formulation with an arbitrary structural model. In the former case the effect of the narrow internal reaction-diffusion zone that always accompanies the shrinking front is discussed. The error associated with the neglect of this zone is not necessarily negligible under conditions of surface reaction or product layer diffusion control.

An Experiment to Identify the Structural Dynamics of a Portal Frame

This paper describes the application of sequential frequency domain techniques to the estimation of mass, stiffness, and damping parameters using measured frequency response functions from a portal frame rig. The theory of the method has been described in the authors’ previous publications. A portal frame is representative of many engineering structures. It is lightly damped and may be thought of as an element of several larger structures such as bridges, transmission towers, and the steel foundations of modern power generating plant. The results offered in this paper are thus of interest to a broad range of engineering problems where it is required to obtain mathematical models in terms of physical parameters.

Mathematical simulation and experimental verification for actinide accumulation in extraction stage of purex process.

Abstract Accumulation of the actinides in the extraction stage of the Purex process was investigated with mathematical models in terms of the U(VI)-loading effect, i.e. decrease of distribution ratios with increase of concentration of U(VI) in the organic phase. Time excursion of the accumulation profiles of U, Pu, Np and HNO2 under several flowsheet conditions was estimated for a mixer settler process with a simulation code. Process experiments using U(VI) and U(IV) were carried out with mixer settlers to verify the simulation results. The concentration profiles of U(IV) and U(VI) agreed fairly well between the experimental and the calculated. Behavior of the peaking position of U(IV) build-up, however, did not always agree well. The causes of the discrepancy were discussed in terms of mass balance of U(VI). Fluctuation of the volume ratio of the two phases in the extractor during operation, particularly during the transient, affects significantly the total mass of U(VI) present in the extractor and hence the concentration profile of the element accumulated. The role of the third phase of Pu(IV) to criticality safety was mentioned.

Adaptive Structural Identification

In this paper the synthesis of mathematical models in terms of parametric, argument and structural indefiniteness of plants with known laws of noises' probability distribution is discussed. An an optimality criterion of the structures the proposed method for adaptive structural identification uses the verification of the statistical hypothesis for the insignificance of the correlation ratio between the structures and the remainders, obtained after the parametric identification with the mean-root-square method. Increasing the complexity of the model structure does not lead to increasing the dimension of identified parameters. This method is applied for the synthesis of mathematical models in a class of transport processes.

Application of Bilinear Models to Biological Problems. An Approach to Mechanism Inference and Analysis

Volterra differential equations (i.e. bilinear autonomous models) are often used to modeling biological, and ecological systems. In the framework of a kinetic theory we find that only a subset of these equations is avalaible to explain such mathematical models in terms of mechanisms. A biological example is studied and shows how we are led to include complementary hypothesis to explain experimental data: “secret variables”.