Improving forecasting performance by employing the Taguchi method

To satisfy the volatile nature of today’s markets, businesses require a significant reduction in product development lead times. Consequently, the ability to develop precise product sales forecasts is of fundamental importance to decision-makers. Over the years, many forecasting techniques of varying capabilities have been introduced. The precise extent of their influences, and the interactions between them, has never been fully clarified, although various forecasting factors have been explored in previous studies. Accordingly, this study adopts the Taguchi method to calibrate the controllable factors of a forecasting model. An L₉(3⁴) inner orthogonal array is constructed for the controllable factors of data period, horizon length, and number of observations required. An experimental design is then performed to establish the appropriate levels for each factor. At the same time, an L₄(2³) outer orthogonal array is used to consider the inherited parameters of forecasting method as the noise factors of Taguchi method simultaneously. An illustrated example, employing data from a power company, serves to demonstrate the thesis. The results show that the proposed model permits the construction of a highly efficient forecasting model through the suggested data collection method.     

A web-based methodology for product design evaluation and optimisation

The authors have developed a methodology that takes advantages of the World Wide Web to analyse and develop optimal new product designs. This paper describes the methodology and illustrates its application to a case study involving the design of an actual Web site where music CDs are sold. The proposed methodology has the following features: (a) it is based on a design inspired by conjoint analysis; (b) it involves unobtrusive electronic measurement of the actual behavior of Web users who remain undisturbed by experimental factors; and (c) it utilises an integer programming approach to seek optimal Web site configurations. The methodology uses limited dependent variable methods to develop response models that provide the basis for the development of objective functions for an optimisation model. The optimisation model can consider either single or multiple objective functions by using a Pareto optimum approach.     

Diffusion of methylene blue in glass fibers – Application of the shrinking core model

Diffusion of mass in a solid cylinder with concentration dependent diffusivity (or temperature-dependent thermal conductivity in case of heat diffusion) does not admit of an analytical solution except in special cases. The ‘shrinking core model’ has been used to develop an approximate analytical solution in certain circumstances. The model, generally useful to describe heterogeneous solid–fluid reactions, is applied to theoretically analyze the adsorption–diffusion phenomena of methylene blue dye in a glass fiber in the present work. Theoretical equations have been derived for the case of diffusivity as an exponential function of concentration. The diffusivity parameters are evaluated by global minimization of the error between the experimental and the theoretical concentration history. Other forms of diffusivity, namely constant diffusivity and diffusivity varying linearly with concentration are found to involve larger errors. A parametric sensitivity analysis of the error has been done. The shrinking core model could satisfactorily interpret the experimental dye concentration profile in the substrate.     

Properties of an h-Bernstein-like basis and curves

Blossoming is a useful technique to study bases and curve representations in computer-aided geometric design. Recently Simeonov et al. (Comput Aided Geom Des 28:549–565, 2011) have used a blossom generalization, namely the h-blossom, to derive new results about the h-Bernstein basis and h-Bézier curves that have previously been studied in approximation theory and computer-aided geometric design. This paper introduces a basis related to the h-Bernstein basis. There is a close relationship between this new basis and the h-Bernstein basis, between the new basis and the h-blossom, and between the new basis and “progressive” curves. This paper explores these relationships and uses them to derive properties both of the new basis itself, and of curves represented in terms of the new basis.     

A vague multivalued data dependency

The work in this paper is an application of vague set theory in relational databases. It is well known that integrity constraints like functional dependency, multivalued dependency, etc. play a key role in any database design. In the present work, the authors introduce a new definition of vague multivalued dependency(VMVD), called α-VMVD, on the basis of α-equality of tuples as defined in the recent work on vague functional dependency [1] in 2012. Next, the definition has been shown to be consistent and finally a set of sound and complete inference axioms have been designed and verified for the α-VMVD.     

On optimization of the RBF shape parameter in a grid-free local scheme for convection dominated problems over non-uniform centers

Global optimization techniques exist in the literature for finding the optimal shape parameter of the infinitely smooth radial basis functions (RBF) if they are used to solve partial differential equations. However these global collocation methods, applied directly, suffer from severe ill-conditioning when the number of centers is large. To circumvent this, we have used a local optimization algorithm, in the optimization of the RBF shape parameter which is then used to develop a grid-free local (LRBF) scheme for solving convection–diffusion equations. The developed algorithm is based on the re-construction of the forcing term of the governing partial differential equation over the centers in a local support domain. The variable (optimal) shape parameter in this process is obtained by minimizing the local Cost function at each center (node) of the computational domain. It has been observed that for convection dominated problems, the local optimization scheme over uniform centers has produced oscillatory solutions, therefore, in this work the local optimization algorithm has been experimented over Chebyshev and non-uniform distribution of the centers. The numerical experiments presented in this work have shown that the LRBF scheme with the local optimization produced accurate and stable solutions over the non-uniform points even for convection dominant convection–diffusion equations.     

A family of new, high order NS-α models arising from helicity correction in Leray turbulence models

This report gives a reinterpretation of the NS-α model which leads to a family of high order NS-α-deconvolution models with NS-α as the zeroth order case. First, we show that the Navier-Stokes-α model arises by adding helicity correction to Leray-α model. Higher order Leray models have recently been proposed in [W. Layton, R. Lewandowski, A high accuracy Leray-deconvolution model of turbulence and its limiting behavior, Anal. Appl. 6 (1) (2008); W. Layton, C. Manica, M. Neda, L. Rebholz, Numerical analysis and computational testing of a high-accuracy Leray-deconvolution model of turbulence, Numer. Methods Partial Differential Equations, in press]: the so-called Leray-deconvolution models, that employ van Cittert approximate deconvolution to decrease consistency error. We use an analogous helicity correction idea to develop a family of higher order accurate NS-α type models, the NS-α-deconvolution models. We prove several mathematical and physical properties for this new family of models and discuss the design of efficient algorithms for them.     

The basis step in the construction of the principle of mathematical induction based on APOS theory

Using APOS theory as the framework along with a case study from a perspective within the methodological design of APOS theory, this study presents a cognitive model of the Principle of Mathematical Induction (PMI) in higher education. Based on evidence from university classrooms and the result of an initial measurement, the genetic decomposition designed by Dubinsky and Lewin for this concept was reformulated, introducing and defining the basis step in the PMI as a mental process. Using this reformulated genetic decomposition, the productions of four university students are analysed in order to support or refute the constructions it proposes. The results show that the reformulated genetic decomposition is viable and that the inclusion of the basis step as a mental process was seen in the cognitive model of the PMI shown by the students. The instruments used provide activities for a teaching sequence for the PMI at university level.     

Alternative formulations of a combined trip generation,trip distribution,modal split,and trip assignment model

The traditional four-step model has been widely used in travel demand forecasting by considering trip generation, trip distribution, modal split and traffic assignment sequentially in a fixed order. However, this sequential approach suffers from the inconsistency among the level-of-service and flow values in each step of the procedure. In the last two decades, this problem has been addressed by many researchers who have sought to develop combined (or integrated) models that can consider travelers’ choice on different stages simultaneously and give consistent results. In this paper, alternative formulations, including mathematical programming (MP) formulation and variational inequality (VI) formulations, are provided for a combined travel demand model that integrates trip generation, trip distribution, modal split, and traffic assignment using the random utility theory framework. Thus, the proposed alternative formulations not only allow a systematic and consistent treatment of travel choice over different dimensions but also have behavioral richness. Qualitative properties of the formulations are also given to ensure the existence and uniqueness of the solution. Particularly, the model is analyzed for a special but useful case where the probabilistic travel choices are assumed to be a hierarchical logit model. Furthermore, a self-adaptive Goldstein–Levitin–Polyak (GLP) projection algorithm is adopted for solving this special case.     

Omitting types theorem in hybrid dynamic first-order logic with rigid symbols

In the present contribution, we prove an Omitting Types Theorem (OTT) for an arbitrary fragment of hybrid dynamic first-order logic with rigid symbols (i.e. symbols with fixed interpretations across worlds) closed under negation and retrieve. The logical framework can be regarded as a parameter and it is instantiated by some well-known hybrid and/or dynamic logics from the literature. We develop a forcing technique and then we study a forcing property based on local satisfiability, which lead to a refined proof of the OTT. For uncountable signatures, the result requires compactness, while for countable signatures, compactness is not necessary. We apply the OTT to obtain upwards and downwards Löwenheim-Skolem theorems for our logic, as well as a completeness theorem for its constructor-based variant.     

Modeling of thermotransport phenomenon in metal alloys using artificial neural networks

Thermodiffusion in molten metals, also known as thermotransport, a phenomenon in which constituent elements of an alloy separate under the influence of non-uniform temperature field, is of significance in several applications. However, due to the complex inter-particle interactions, there is no theoretical formulation that can model this phenomenon with adequate accuracy. Keeping in mind the severe deficiencies of the present day thermotransport models and an urgent need of a reliable method in several engineering applications ranging from crystal growth to integrated circuit design to nuclear reactor designs, an engineering approach has been taken in which neurocomputing principles have been employed to develop artificial neural network models to study and quantify the thermotransport phenomenon in binary metal alloys. Unlike any other thermotransport model for molten metals, the neural network approach has been validated for several types of binary alloys, viz., concentrated, dilute, isotopic and non-isotopic metals. Additionally, to establish the soundness of the model and to highlight its potential as a unified computational analysis tool, it ability to capture several thermotransport trends has been shown. Comparison with other models from the literature has also been made indicating a superior performance of this technique with respect to several other well established thermotransport models.     

Computational fluid dynamics modelling of an entrained flow biomass gasifier

A mathematical model, based on the Computational Fluid Dynamics package CFX4, has been developed to study the flow within an entrained flow biomass gasifier. The gasifier is designed to convert sawdust and chopped cotton gin trash into a low calorific value gas which can be burned in a modified engine to run a generator. Calculations of the flowfield are performed using the standard k–ϵ model and a Differential Reynolds Stress Model (DSM). In line with current thinking, it is shown that the k–ϵ model gives unphysical results for complex swirling flows, whereas the DSM model performs well. Particle tracking was performed to determine typical trajectories for the biomass and char and the results used to determine means of avoiding slagging in the gasifier base. The simulations have proved to be very useful to the designers who are now using the model to optimise the design.     

Analysis of two-sample truncated data using generalized logistic models

Parallel to Cox's [JRSS B34 (1972) 187-230] proportional hazards model, generalized logistic models have been discussed by Anderson [Bull. Int. Statist. Inst. 48 (1979) 35-53] and others. The essential assumption is that the two densities ratio has a known parametric form. A nice property of this model is that it naturally relates to the logistic regression model for categorical data. In astronomic, demographic, epidemiological, and other studies the variable of interest is often truncated by an associated variable. This paper studies generalized logistic models for the two-sample truncated data problem, where the two lifetime densities ratio is assumed to have the form exp{α+φ(x;β)}. Here φ is a known function of x and β, and the baseline density is unspecified. We develop a semiparametric maximum likelihood method for the case where the two samples have a common truncation distribution. It is shown that inferences for β do not depend the nonparametric components. We also derive an iterative algorithm to maximize the semiparametric likelihood for the general case where different truncation distributions are allowed. We further discuss how to check goodness of fit of the generalized logistic model. The developed methods are illustrated and evaluated using both simulated and real data.     

Calculation of conjugate heat transfer problem with volumetric heat generation using the Galerkin method

A mathematical model of fluid flow across a rod bundle with volumetric heat generation has been built. The rods are heated with volumetric internal heat generation. To construct the model, a volume average technique (VAT) has been applied to momentum and energy transport equations for a fluid and a solid phase to develop a specific form of porous media flow equations. The model equations have been solved with a semi-analytical Galerkin method. The detailed velocity and temperature fields in the fluid flow and the solid structure have been obtained. Using the solution fields, a whole-section drag coefficient C_d and a whole-section Nusselt number Nu have also been calculated. To validate the developed solution procedure, the results have been compared to the results of a finite volume method. The comparison shows an excellent agreement. The present results demonstrate that the selected Galerkin approach is capable of performing calculations of heat transfer in a cross-flow where thermal conductivity and internal heat generation in a solid structure has to be taken into account. Although the Galerkin method has limited applicability in complex geometries, its highly accurate solutions are an important benchmark on which other numerical results can be tested.     

Scheduling independent jobs for torus connected networks with/without link contention

In this paper, we investigate the problem of how to schedule n independent jobs on an m × m torus based network. We develop a model to to quantify the effect of contention for communication links on the dilation of job execution time when multiple jobs share communication links; we then design an efficient algorithm to schedule a set of n independent jobs with different torus size requirements on a given torus with an objective to minimize the total schedule length. We also develop a feasibility algorithm for pre-emptively scheduling a given set of jobs on a torus of given size with a given deadline. We provide analysis for both the algorithms.     

A 3-D coupled Smoothed Particle Hydrodynamics and Coarse-Grained model to simulate drying mechanisms of small cell aggregates

Recently, meshfree-based computational modelling approaches have become popular in modelling biological phenomena due to their superior ability to simulate large deformations, multiphase phenomena and complex physics compared to the conventional grid-based methods. In this article, small plant cell aggregates were simulated using a three dimensional (3-D) Smoothed Particle Hydrodynamics (SPH) and Coarse-Grained (CG) coupled computational approach to predict the morphological behaviour during drying. The model predictions of these cell aggregate models have been compared qualitatively and quantitatively through comparisons with experimental findings. The results show that the shrinkage and wrinkling behaviour of cell cluster models are in fairly good agreement with real cellular structures. The agreement between the cell aggregate model predictions and the experimental findings are closer in the high and medium moisture content values (X/X₀ ≥ 0.3), than highly dried stages (X/X₀ < 0.3). Further, optimisation and sensitivity studies have been conducted on model parameters such as particle resolution, smoothing length, mass transfer characteristics and wall forces. Overall, the 3-D nature of this model allows it to predict real 3-D morphological changes more realistically compared to the previous meshfree based 2-D cellular drying models. The proposed 3-D modelling approach has a higher potential to be used to model larger plant tissues with complicated physical and mechanical interactions as well as their multiscale interactions.     

Numerical simulation of methane partial oxidation in the burner and combustion chamber of autothermal reformer

This study aims to model the methane partial oxidation process in the burner and combustion chamber of autothermal reactor. The numerical simulation based on this model offers a powerful tool that can assist in reactor design and optimization and scale up of the process saving expensive pilot work. The steady-state governing equations were solved using the SIMPLE algorithm and the effect of turbulence on the mean flow field was accounted for using the RNG k–ε model. A two-step reaction mechanism was used for the gas combustion with CO as the intermediate species. The reaction rates were modeled using an Eddy-Dissipation Model. In terms of the geometrical model, a 3D model for burner was developed while an axis-symmetric model for the combustion chamber was implemented to reduce the computational costs. The model formulated was validated against a currently operating autothermal reactor and then has been used to investigate different aspects of these reactors. Results show that effect of oxygen to methane ratio is more than that of feed temperature. It is demonstrated that a 60% increase in O₂/CH₄ ratio causes a 15.4% decrease and 42.7% increase in H₂/CO ratio and methane conversion, respectively. In contrast, a 60% increase in feed temperature does not have a significant effect on the process.     

Mathematical model and optimum design approach of sinusoidal pressure wave generator for downhole drilling tool

Mud pulse generators have been widely used for the real-time transmission of valuable directional and formation data from downholes with depths of thousands of meters. There have been numerous studies on the design of mud pulse generators in which the pressure waves were typically nonsinusoidal. Sinusoidal waves provide improved long-distance data transmission and signal noise suppression compared with nonsinusoidal waves. Although sinusoidal pressure wave generators have been studied in the published literature, the influence of the risks of clogging on the design of the generator for producing sinusoidal pressure waves has rarely been considered. To generate sinusoidal pressure waves and to reduce the risks of clogging, a mathematical model for the design of a sinusoidal pressure wave generator is developed in this paper. The effects of the axial and radial clearances between the rotor and stator on the design of the generator are considered in the model. An optimum design method for the generator is provided by combining the developed model and a computational fluid dynamics analysis. Finally, an experimental platform was built and experiments at frequencies 2 Hz and 10 Hz were conducted to validate the design result. The simulation and experimental results show that the optimized pressure waves closely approximate sine waves. Therefore, the developed mathematical model and optimization approach can be used to design a sinusoidal pressure wave generator.     

Comparison of turbulence models in simulating swirling pipe flows

Swirling flow is a common phenomenon in engineering applications. A numerical study of the swirling flow inside a straight pipe was carried out in the present work with the aid of the commercial CFD code fluent. Two-dimensional simulations were performed, and two turbulence models were used, namely, the RNG k–ε model and the Reynolds stress model. Results at various swirl numbers were obtained and compared with available experimental data to determine if the numerical method is valid when modeling swirling flows. It has been shown that the RNG k–ε model is in better agreement with experimental velocity profiles for low swirl, while the Reynolds stress model becomes more appropriate as the swirl is increased. However, both turbulence models predict an unrealistic decay of the turbulence quantities for the flows considered here, indicating the inadequacy of such models in simulating developing pipe flows with swirl.