# Applied Mathematical Modelling

Print ISSN: 0307-904X

## .css-10d2qir{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-box-flex:1;-webkit-flex-grow:1;-ms-flex-positive:1;flex-grow:1;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}Articles

Comparisons of two commercial computational fluid dynamics codes in modelling pulverised coal combustion for a 2.5 MW burner
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June 1999

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This paper reports an investigation into the performance of two commercial computational fluid dynamics (CFD) codes for pulverised coal combustion prediction. The two codes employed were FLUENT and FLOW3D 3.2 (now called CFX). The experimental case considered was a 2.5 MW Aerodynamically Air Staged Burner (AASB) fired in isolation into a rectangular furnace. Predictions were compared to velocity, temperature and species concentration experimental data. Some slight differences were noted between the two CFD codes predictions beyond one burner diameter downstream of the burner exit. Discrepancies between the predictions of the two CFD codes were concluded to be due to differences in the physical models used to describe devolatilisation and gaseous combustion. This paper therefore concludes that, for this case, the two commercial CFD codes were capable of predicting good `trend' answers.

Parametric modelling and numerical simulation of natural-convective transport of radon-222 from a phosphogypsum stack into open air

December 2006

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An existing finite-volume computational simulator for heat and mass transfer in media fully or partially filled with porous material has been adapted to predict radon-222 exhalation rates. For validation purposes, this paper numerically examines the extent of natural-convective effects on radon-222 steady-state transfer from a phosphogypsum stack into the surrounding atmosphere. The stack is approximated by a dry rectangular porous matrix having uniform porosity and isotropic permeability whereas the supposedly laminar buoyancy-driven air flow is modelled following Darcy–Brinkman–Boussinesq approach. Differential governing equations are cast in dimensionless form in order to encompass simultaneous effects from physical factors involved. Dimensionless groups related to decay and emanation processes are put forward apart from usual controlling parameters such as Prandtl, Schmidt, Darcy and Grashof numbers. Results are reported for 106 ⩽ Gr ⩽ 108 and 10−13 ⩽ Da ⩽ 10−7. Natural-convective effects on typical low-permeability phosphogypsum stacks proved to be of minor importance, as radon-222 transfer becomes diffusive dominant as expected.

Solvability of the 3D rotating Navier–Stokes equations coupled with a 2D biharmonic problem with obstacles and gradient restriction

June 2009

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A coupled system by the 3D rotating Navier–Stokes equations with a mixed boundary condition and a 2D biharmonic problem with two obstacles and the gradient restriction is investigated in this paper. Using the Schauder’s fixed point theorem, we show the existence of a strong solution for a sufficiently large viscosity ν and sufficiently small data.

Realization of non-Fourier phenomena in heat transfer with 2D transfer function

August 2011

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The present mainstream realizes that non-Fourier phenomena in heat transfer are arisen from the time-delay in heat diffusion; however, in this paper we mathematically prove this realization an untruth. The analysis is based on the construction of 2D transfer function for the parabolic equation with time-delayed Laplacian that governs the assumed non-Fourier heat transfer. There, functional representation of this spatio-temporal dynamics is performed by the composite of Laplace transform and Galerkin projection. With 2D transfer function, the heat-transfer dynamics is further represented by feedback interconnection of thermal capacitance and time-delayed diffusion, which makes it possible for Nyquist to perform stability and bifurcation analyses on this spatio-temporal dynamics. It comes out that the heat-transfer dynamics under investigation is unstable no matter how small the time-delay in heat diffusion is. That is, time-delayed heat diffusion contradicts the first law of thermodynamics and thus cannot be observed. This paper continues to show that the realization of thermal inertia by thermal inductance is supported by the principle of electro-thermal analogy and compatible with experimental observations.

Liu, B.: Fuzzy project scheduling problem and its hybrid intelligent algorithm. Applied Mathematical Modelling 34(2), 301-308

February 2010

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Project scheduling problem is to determine the schedule of allocating resources so as to balance the total cost and the completion time. This paper considers a type of project scheduling problem with fuzzy activity duration times. According to some management goals, three types of fuzzy models are built to solve the project scheduling problem. Moreover, the technique of fuzzy simulation and genetic algorithm are integrated to design a hybrid intelligent algorithm to solve the fuzzy models. Finally, some numerical examples are given to illustrate the effectiveness of the algorithm.

Gao, X.: Fuzzy weighted equilibrium multi-job assignment problem and genetic algorithm. Applied Mathematical Modelling 33(10), 3926-3935

October 2009

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In this paper, the equilibrium optimization problem is proposed and the assignment problem is extended to the equilibrium multi-job assignment problem, equilibrium multi-job quadratic assignment problem and the minimum cost and equilibrium multi-job assignment problem. Furthermore, the mathematical models of the equilibrium multi-job assignment problem and the equilibrium multi-job quadratic assignment problem with fuzzy parameters are formulated. Finally, a genetic algorithm is designed for solving the proposed programming models and some numerical examples are given to verify the efficiency of the designed algorithm.

Synchronous and asynchronous solution of a 3D transport model in a grid computing environment

July 2006

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Numerical simulation is a common approach to understand many phenomena, usually yielding a computationally intensive problem. To overcome insufficient computer capacity and computational speed, a grid computing environment is a suitable approach. In this paper we focus on the development of parallel algorithms to solve a 3D transport model in such a context. The solver is based on the multisplitting Newton method that provides a coarse-grained scheme. Algorithms are implemented using JACE, a grid-enabled Java Asynchronous Computing Environment. This programming environment allows users to design synchronous and asynchronous parallel iterative algorithms as well. Experiments are carried out on a heterogeneous grid environment in which the behaviour of both parallel iterative algorithms is analysed. The results allow us to draw some conclusions about the use of the programming library JACE and the design of parallel iterative algorithms in a grid computing environment.

A numerical model for predicting bubble formation in a 3D fluidized bed

December 1998

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Fluidized bed systems have the potential to be widely used in the power generation, mineral processing and chemical industries. One factor limiting their increased use is the lack of adequate design techniques for scaling such systems. A model has been developed for simulating gas–solid fluidized bed plant. The model uses a multiphase Eulerian–Eulerian technique to predict the transient behaviour of fluidized bed systems. The commercial CFD code CFX is used as the computational framework for solving the discretized equations. To overcome the problem of accurate geometrical representation experienced in previous models a body fitted grid system is employed. The model is used to predict isothermal flow in a three-dimensional bubbling fluidized bed. Predictions of the three-dimensional model show bubble formation with gas bubbles or voids preferentially moving along the centre of the bed. Predicted behaviour is qualitatively consistent with experimental observations.

DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge

February 2002

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While the discrete element method (DEM) is attracting increasing interest for the simulation of industrial granular flow, much of the previous DEM modelling has considered two-dimensional (2D) flows and used circular particles. The inclusion of particle shape into DEM models is very important and allows many flow features, particularly in hoppers, to be more accurately reproduced than was possible when using only circular particles. Elongated particles are shown here to produce flow rates up to 30% lower than for circular particles and give flow patterns that are quite different. The yielding of the particle microstructure resembles more the tearing of a continuum solid, with large-scale quasi-stable voids being formed and large groups of particles moving together. The flow becomes increasingly concentrated in a relatively narrow funnel above the hopper opening. This encourages the hope that DEM may be able to predict important problems such as bridging and rat-holing. Increasing the blockiness or angularity of the particles is also shown to increase resistance to flow and reduces the flow rates by up to 28%, but without having perceptible effect on the nature of the flow. We also describe our methodology for constructing and modelling geometrically complex industrial applications in three dimensions and present a series of industrially important three-dimensional (3D) case studies. The charge motion in a 5 m diameter ball mill and in a Hicom nutating mill, discharge from single- and four-port cylindrical hoppers, and particle size separation by a vibrating screen are demonstrated. For each case, plausible particle size distributions (PSDs) have been used. The results obtained indicate that DEM modelling is now sufficiently advanced that it can make useful contributions to process optimisation and equipment design. Finally the parallelisation of such a DEM code is described and benchmark performance results for a large-scale 2D hopper flow are presented.

Optimum selection of the dental implant diameter and length in the posterior mandible with poor bone quality – A 3D finite element analysis

January 2011

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This study aimed to evaluate continuous and simultaneous variations of dental implant diameter and length, and to identify their relatively optimal ranges in the posterior mandible under biomechanical consideration. A 3D finite element model of a posterior mandibular segment with dental implant was created. Implant diameter ranged from 3.0 to 5.0 mm, and implant length ranged from 6.0 to 16.0 mm. The results showed that under axial load, the maximum Von Mises stresses in cortical and cancellous bones decreased by 76.53% and 72.93% respectively, with the increasing of implant diameter and length; and under buccolingual load, by 83.97% and 84.93%, respectively. Under both loads, the maximum displacements of implant-abutment complex decreased by 58.09% and 75.53%, respectively. The results indicate that in the posterior mandible, implant diameter plays more significant roles than length in reducing cortical bone stress and enhancing implant stability under both loads. Meanwhile, implant length is more effective than diameter in reducing cancellous bone stress under both loads. Moreover, biomechanically, implant diameter exceeding 4.0 mm and implant length exceeding 12.0 mm is a relatively optimal combination for a screwed implant in the posterior mandible with poor bone quality.

A comparison between the parabolic and partially-parabolic solution procedures for 3D turbulent flows around ships' hulls
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• Full-text available

August 1979

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This paper is concerned with the prediction of three-dimensional turbulent flows around bodies of arbitrary shape, with particular emphasis on a ship's hull. Two solution methods are compared employing a non-orthogonal coordinate system, in which the surface of the body is arranged to coincide with a coordinate surface. The velocity components are solved for the axial, radial and circumferential components in the cylindrical-polar system from which the non-orthogonal coordinates are derived.The partial-differential equations governing the flows under consideration are solved by two finite-difference methods for three-dimensional, parabolic1and partially-parabolic2flows. Turbulence is accounted for through a two-equation model of turbulence developed by Harlow and Nakayama3and modelled by Launder and Spalding.4Solutions are presented for flow around a ship's hull which demonstrate the potential of the present methods.

3D modeling of crack growth in electro-magneto-thermo-elastic coupled viscoplastic multiphase composites

February 2009

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This work presents a time-domain hypersingular integral equation (TD-HIE) method for modeling 3D crack growth in electro-magneto-thermo-elastic coupled viscoplastic multiphase composites (EMTE-CVP-MCs) under extended incremental loads rate through intricate theoretical analysis and numerical simulations. Using Green’s functions, the extended general incremental displacement rate solutions are obtained by time-domain boundary element method. Three-dimensional arbitrary crack growth problem in EMTE-CVP-MCs is reduced to solving a set of TD-HIEs coupled with boundary integral equations, in which the unknown functions are the extended incremental displacement discontinuities gradient. Then, the behavior of the extended incremental displacement discontinuities gradient around the crack front terminating at the interface is analyzed by the time-domain main-part analysis method of TD-HIE. Also, analytical solutions of the extended singular incremental stresses gradient and extended incremental integral near the crack fronts in EMTE-CVP-MCs are provided. In addition, a numerical method of the TD-HIE for a 3D crack subjected to extended incremental loads rate is put forward with the extended incremental displacement discontinuities gradient approximated by the product of time-domain basic density functions and polynomials. Finally, examples are presented to demonstrate the application of the proposed method.

Electro-Thermo-Chemical Computational Models for 3D Heterogeneous Semiconductor Device Simulation

July 2013

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In this article we propose and numerically implement a mathematical model for the simulation of three-dimensional semiconductor devices characterized by an heterogeneous material structure. The model consists of a system of nonlinearly coupled time-dependent diffusion-reaction partial differential equations with convection terms describing the principal electrical, thermal and chemical phenomena that determine the macroscopic electrical response of the device under the action of externally applied electrical and thermal forces. The system is supplied with suitable initial, boundary and interface conditions that account for the interaction occurring among the various regions of the device with the surrounding environment. Temporal semi-discretization of the problem is carried out with the Backward Euler Method while a fixed-point iteration of Gummel type is used for system decoupling. Numerical approximation of the linearized subproblems is carried out using an exponentially fitted stabilized Finite Element Method on unstructured tetrahedral grids. Several computational experiments are included to validate the physical accuracy of the proposed computational algorithm in the study of realistic device structures.

A 3D non-linear k–ε turbulent model for prediction of flow and mass transport in channel with vegetation

April 2010

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The results from a 3D non-linear k–ε turbulence model with vegetation are presented to investigate the flow structure, the velocity distribution and mass transport process in a straight compound open channel and a curved open channel. The 3D numerical model for calculating flow is set up in non-orthogonal curvilinear coordinates in order to calculate the complex boundary channel. The finite volume method is used to disperse the governing equations and the SIMPLEC algorithm is applied to acquire the coupling of velocity and pressure. The non-linear k–ε turbulent model has good useful value because of taking into account the anisotropy and not increasing the computational time. The water level of this model is determined from 2D Poisson equation derived from 2D depth-averaged momentum equations. For concentration simulation, an expression for dispersion through vegetation is derived in the present work for the mixing due to flow over vegetation. The simulated results are in good agreement with available experimental data, which indicates that the developed 3D model can predict the flow structure and mass transport in the open channel with vegetation.

3D SPH flow predictions and validation for high pressure die casting of automotive components

November 2006

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The geometric complexity and high fluid speeds involved in high pressure die casting (HPDC) combine to give strongly three-dimensional fluid flow with significant free surface fragmentation and splashing. A Lagrangian simulation technique that is particularly well suited to modelling HPDC is smoothed particle hydrodynamics (SPH). Materials are approximated by particles that are free to move around rather than by fixed grids, enabling the accurate prediction of fluid flows involving complex free surface motion.Validation of isothermal SPH flow predictions for the casting of a servo piston head using water analogue experiments is presented. Comparison with MAGMAsoft predictions provides information of the relative strengths of these two approaches. The SPH simulations were better able to capture the key details of the fluid motion and splashing, particularly the relative rates of flow around sharp bends and through thin sections. Validation of flow predictions coupled to temperature and solidification using short shots are also presented. The bulk features of the final solid castings are in good agreement with the predictions.Several automotive examples of SPH simulated HPDC flows are presented, ranging from simple cases such as a servo piston to steering column components and a full engine rocker cover. These show unprecedented detail in the fluid free surfaces, particularly in the extent of fragmentation and void formation.These results together combine to demonstrate that SPH modelling of HPDC has now reached a level where both isothermal and thermal simulations can be performed in reasonable computation times for large scale automotive castings and provide a high degree of predictive accuracy.

Applying the combined integral method to one-dimensional ablation

January 2012

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In this paper the combined integral method is applied to a simple one-dimensional ablation problem. One of the drawbacks of heat balance integral methods is how to choose the approximating function. It is common to use a polynomial form but even then it is not clear what the power of the highest order term should be. Previous studies have determined exponents either from exact solutions or from expansions valid over short time scales; neither approach is satisfactory nor very accurate for larger times. We combine the heat balance and refined integral methods to determine this exponent as part of the solution process, and conclude that it is in fact time-dependent in the ablation stage. From comparing the approximate solutions with numerical and exact analytical solutions whenever possible, we show that this new method greatly improves the accuracy on standard methods, without overcomplicating the method.

On the derivation of fractional diffusion equation with an absorbent term and a linear external force

July 2009

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Recently, the generalized fractional reaction–diffusion equation subject to an external linear force field has been proposed to describe the transport processes in disordered systems. The solution of this generalized model can be formally expressed in closed form through the Fox function. For the sack of completeness, we dedicate this work to construct a neatly derivation of the generalized fractional reaction–diffusion equation. Remarkably, such derivation could in general offer some novel and inspiring inspection to the phenomena of anomalous transport. For instance, there is a strong evidence that the fractional calculus offers some physical insight into the origin of fractional dynamics for a systems which exhibit multiple trapping.

Long-range predictive control of an absorption packed column

January 1995

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This paper is concerned with modelling and long-range predictive control of an absorption packed column. The absorption column is used to decrease the concentration of CO2 in a gas mixture below a desired value. A solution of Diethanolamine (DEA) is used as the absorbent. The flow rate of the absorbent and the concentration of CO2 in the gas mixture are selected, respectively, as control and controlled variables. A physically based model has been developed from considerations of mass balances, of transport phenomena, and of chemical reaction in the liquid phase. It consists of three nonlinear partial differential equations. The control design is based on a simple low-order linear discrete model with unknown and possibly time-varying parameters. The parameters of this model are estimated using the least squares algorithm taking into account the requirements for long-term adaptive control. An extended horizon control policy, based on the minimization of a quadratic criterion function of the input and output tracking errors, is used for feedback control. Several simulation studies highlight the applicability of the involved adaptive control algorithm.

A decision support system for order acceptance/rejection in hybrid MTS/MTO production systems

March 2011

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In this paper, we present a novel decision support system for order acceptance/rejection in a hybrid Make-to-Stock/Make-to-Order production environment. The proposed decision support system is comprised of five steps. At the first step, the customers are prioritized based on a fuzzy TOPSIS method. Rough-cut capacity and rough-cut inventory are calculated in the second step and in case of unavailability in capacity and materials, some undesirable orders are rejected. Also, proper decisions are made about non-rejected orders. At the next step, prices and delivery dates of the non-rejected orders are determined by running a mixed-integer mathematical programming model. At the fourth step, a set of guidelines are proposed to help the organization negotiate over price and due date with the customers. In the next step, if the customer accepts the offered price and delivery date, the order is accepted and later considered in the production schedule of the shop floor, otherwise the order is rejected. Finally, numerical experiments are conducted to show the tractability of the applied mathematical programming model.

Introducing a modified gradient vector method for optimization of accident prediction non-linear functions

December 2011

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In this paper, a new optimization method has been proposed for accident prediction non-linear models. This has been achieved by eliminating the Hessian matrix from the equation of optimal pace length in the gradient vector method. One advantage is that it is independent of the starting point in optimization processes and it provides convergence at the highest top as well. This method has been tested on an accident prediction model and its preference over the gradient vector method has been proven.

August 2007

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Heavy metals like cadmium and arsenic have serious health consequences and ecosystem impacts. Due to various factors including the disposal of municipal and industrial wastes, application of fertilizers, atmospheric deposition and discharge of wastewater on land, has resulted in increase in the concentration of heavy metals in the soil. Crops and vegetables grown on such soil accumulate heavy metals, which leads to phyto-toxicity. For understanding and managing precious natural resources, mathematical models are increasingly being used. This paper describes a dynamic macroscopic numerical model for heavy metal transport and its uptake by vegetables in the root zone. The model is applied for simulating cadmium uptake by radish (Raphanus sativus), carrot (Daucos carota), spinach (Spinacia oleracea) and cabbage (Brassica oleracea) by using measured field data. The governing non-linear partial differential equations are solved numerically by an implicit finite difference method using Picard’s iterative technique and the source code is written in MATLAB.

The influence of sampling frequency, non-linear interaction, and frictional effects upon the accuracy of the harmonic analysis of tidal simulations

June 2005

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A two dimensional tidal model of the northwest European shelf is used to examine the influence of sampling rate, number of harmonic constituents analysed for, and length of data upon the accuracy of tidal constituents. Calculations show that in shallow water, where non-linear interactions give rise to higher harmonics, an accurate analysis can be obtained from a short span of data provided the higher harmonics are included in the analysis. In very shallow water where the tidal range is comparable to the water depth, asymmetry in the tidal signal due to substantial differences in friction at times of high and low water produces a number of semi-diurnal constituents in particular ν2 and L2 that must be included in the harmonic analysis. When these constituents together with the “classical” shallow water constituents are used in the harmonic analysis then an accurate analysis can be performed on a short span of data. The significant saving in computer time, particularly for a fine grid three dimensional model of using frequent sampling and analysing for a full set of constituents is stressed.

The accuracy of finite difference schemes for the numerical solution of the Navier-Stokes equations

June 1979

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Comparisons are made between various finite difference algorithms used for the numerical solution of two-dimensional viscous flow. Central difference algorithms recently developed by the authors are compared with the well established upwind difference algorithms. Some analytical solutions to the Navier-Stokes equations have been produced in order for meaningful comparisons to be made. On the basis of the results, the new central difference algorithms are recommended as being more accurate whilst requiring little additional computational effort. There is an upper limit on the grid Reynolds number for which these new methods will converge, but this will usually be when the flow would in practice be turbulent.

Order of Accuracy of QUICK and Related Convection-Diffusion Schemes

December 1993

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This paper explains significant differences in truncation error between finite-difference and finite-volume convection-diffusion schemes. Specifically, the order of accuracy of the QUICK scheme for steady-state convection and diffusion is discussed in detail. Other related convection-diffusion schemes are also considered. The original one-dimensional QUICK scheme written in terms of nodal-point values of the convected variable (with a -factor multiplying the “curvature” term) is indeed a third-order representation of the finite-volume formulation of the convection operator average across the control volume, written naturally in flux-difference form. An alternative single-point upwind difference scheme (SPUDS) using node values (with a -factor) is a third-order representation of the finite-difference single-point formulation; this can be written in a pseudo-flux-difference form. These are both third-order convection schemes; however, the QUICK finite-volume convection operator is 33% more accurate than the single-point implementation of SPUDS. Another finite-volume scheme, writing convective fluxes in terms of cell-average values, requires a -factor for third-order accuracy. For completeness, one can also write a single-point formulation of the convective derivative in terms of cell averages and then express this in pseudo-flux-difference form; for third-order accuracy, this requires a curvature factor of . Diffusion operators are also considered in both finite-difference and finite-volume formulations. Finite-volume formulations are found to be significantly more accurate. For example, classical second-order central differencing for the second derivative is exactly twice as accurate in a finite-volume formulation as it is in a finite-difference formulation.

Accurate bending analysis of rectangular plates with two adjacent edges free and the others clamped or simply supported based on new symplectic approach

January 2011

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The symplectic geometry approach is introduced for accurate bending analysis of rectangular thin plates with two adjacent edges free and the others clamped or simply supported. The basic equations for rectangular plates are first transferred into Hamilton canonical equations. Using the symplectic approach, the analytic solution of rectangular thin plate with two adjacent edges simply supported and the others slidingly supported is derived. Accurate bending solutions of title problems are then obtained using the superposition method. The approach used in this paper eliminates the need to pre-determine the deformation function and is hence more reasonable than conventional methods. Numerical results are presented to demonstrate the validity and efficiency of the approach as compared with those reported in other literatures.

Forecasting urban traffic flow by SVR with continuous ACO

March 2011

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Accurate forecasting of inter-urban traffic flow has been one of the most important issues globally in the research on road traffic congestion. Because the information of inter-urban traffic presents a challenging situation, the traffic flow forecasting involves a rather complex nonlinear data pattern. In the recent years, the support vector regression model (SVR) has been widely used to solve nonlinear regression and time series problems. This investigation presents a short-term traffic forecasting model which combines the support vector regression model with continuous ant colony optimization algorithms (SVRCACO) to forecast inter-urban traffic flow. Additionally, a numerical example of traffic flow values from northern Taiwan is employed to elucidate the forecasting performance of the proposed SVRCACO model. The forecasting results indicate that the proposed model yields more accurate forecasting results than the seasonal autoregressive integrated moving average (SARIMA) time series model. Therefore, the SVRCACO model is a promising alternative for forecasting traffic flow.

Computational aero-acoustic analysis of a passenger car with a rear spoiler

September 2009

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This study proposes an effective numerical model based on the Computational Fluid Dynamics (CFD) approach to obtain the flow structure around a passenger car with wing type rear spoiler. The topology of the test vehicle and grid system is constructed by a commercial package, ICEM/CFD. FLUENT is the CFD solver employed in this study. After numerical iterations are completed, the aerodynamic data and detailed complicated flow structure are visualized using commercial packages, Field View and Tecplot. The wind effect on the aerodynamic behavior of a passenger car with and without a rear spoiler and endplate is numerically investigated in the present study. It is found that the installation of a spoiler with an appropriate angle of attack can reduce the aerodynamic lift coefficient. Furthermore, the installation of an endplate can reduce the noise behind the car. It is clear that the vertical stability of a passenger car and its noise elimination can be improved. Finally, the aerodynamics and aero-acoustics of the most suitable design of spoiler is introduced and analyzed.

Reduced order fully coupled structural–acoustic analysis via implicit moment matching

November 2009

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A reduced order model is developed for low frequency, undamped, fully coupled structural–acoustic analysis of interior cavities backed by flexible structural systems. The reduced order model is obtained by applying a projection of the coupled system matrices, from a higher dimensional to a lower dimensional subspace, whilst preserving essential properties of the coupled system. The basis vectors for projection are computed efficiently using the Arnoldi algorithm, which generates an orthogonal basis for the Krylov Subspace containing moments of the original system. The key idea of constructing a reduced order model via Krylov Subspaces is to remove the uncontrollable, unobservable and weakly controllable, observable parts without affecting the transfer function of the coupled system. Three computational test cases are analyzed, and the computational gains and the accuracy compared with the direct inversion method in ANSYS.It is shown that the reduced order model decreases the simulation time by at least one order of magnitude, while maintaining the desired accuracy of the state variables under investigation. The method could prove as a valuable tool to analyze complex coupled structural–acoustic systems, and their subsequent optimization or sensitivity analysis, where, in addition to fast analysis, a fine frequency resolution is often required.

Studies of an infinite element method for acoustical radiation

July 2006

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Infinite element computations are very efficient for predicting the vibro-acoustic response and sensitivities of a vibrating structure for an exterior acoustic domain. In addition, domain decomposition methods are very powerful algorithms for solving large linear systems in parallel. In this paper, an infinite element method is proposed and analyzed for parallel computations purpose. An original formulation of this method with Lagrange multipliers defined on (semi-)infinite space is presented. The implementation aspects of this method in an industrial acoustic software (SYSNOISE) are discussed. New numerical results illustrate the efficiency of the proposed method for realistic acoustical radiation problems.

An indirect boundary element formulation for multi-valued impedance simulation in structural acoustics

June 1998

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The indirect boundary element method naturally allows the simultaneous modelling of acoustic domains on both sides of thin vibrating structures. To fully utilize the potential of this technique a formulation that permits the application of separate impedance on the surface of acoustic domains on each side of the vibrating structure is developed. The resulting integral equations are solved by using a variational approach. The formulation and the numerical implementation are validated by comparing the results from the present development to analytical solutions. The applicability of this procedure to the solution of a realistic engineering problem is also demonstrated.

Dynamical behaviors of a class of recurrent neural networks with discontinuous neuron activations

December 2009

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This paper investigates the dynamics of a class of recurrent neural networks where the neural activations are modeled by discontinuous functions. Without presuming the boundedness of activation functions, the sufficient conditions to ensure the existence, uniqueness, global exponential stability and global convergence of state equilibrium point and output equilibrium point are derived, respectively. Furthermore, under certain conditions we prove that the system is convergent globally in finite time. The analysis in the paper is based on the properties of M-matrix, Lyapunov-like approach, and the theories of differential equations with discontinuous right-hand side as introduced by Filippov. The obtained results extend previous works on global stability of recurrent neural networks with not only Lipschitz continuous but also discontinuous neural activation functions.

Dynamical behavior of delayed Hopfield neural networks with discontinuous activations

April 2009

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In this paper, a general class of neural networks with arbitrary constant delays is studied, whose neuron activations are discontinuous and may be unbounded or nonmonotonic. Based on the Leray–Schauder alternative principle and generalized Lyapunov approach, conditions are given under which there is a unique equilibrium of the neural network, which is globally asymptotically stable. Moreover, the existence and global asymptotic stability of periodic solutions are derived, where the neuron inputs are periodic. The obtained results extend previous works not only on delayed neural networks with Lipschitz continuous neuron activations, but also on delayed neural networks with discontinuous neuron activations.

Stability analysis of Cohen–Grossberg neural networks with discontinuous neuron activations

February 2010

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In this paper, we consider the dynamical behavior of delayed Cohen–Grossberg neural networks with discontinuous activation functions. Some sufficient conditions are derived to guarantee the existence, uniqueness and global stability of the equilibrium point of the neural network. Convergence behavior for both state and output is discussed. The constraints imposed on the interconnection matrices, which concern the theory of M-matrices, are easily verifiable and independent of the delay parameter. The obtained results improve and extend the previous results. Finally, we give an numerical example to illustrate the effectiveness of the theoretical results.

Stability analysis for neural networks with inverse Lipschitzian neuron activations and impulses

November 2008

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In this paper, a new concept called α-inverse Lipschitz function is introduced. Based on the topological degree theory and Lyapunov functional method, we investigate global convergence for a novel class of neural networks with impulses where the neuron activations belong to the class of α-inverse Lipschitz functions. Some sufficient conditions are derived which ensure the existence, and global exponential stability of the equilibrium point of neural networks. Furthermore, we give two results which are used to check the stability of uncertain neural networks. Finally, two numerical examples are given to demonstrate the effectiveness of results obtained in this paper.

Single-machine scheduling with a general sum-of-actual-processing-times-based and job-position-based learning effect

November 2010

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In this paper, we bring into the scheduling field a general learning effect model where the actual processing time of a job is not only a general function of the total actual processing times of the jobs already processed, but also a general function of the job’s scheduled position. We show that the makespan minimization problem and the sum of the kth power of completion times minimization problem can be solved in polynomial time, respectively. We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions.

Bending and vibration of an electrostatically actuated circular microplate in presence of Casimir force

May 2011

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The pull-in instability and the vibration for a prestressed circular electrostatically actuated microplate are investigated in consideration of the Casimir force. Based on von Kármán’s nonlinear bending theory of thin plates, the governing equations for the whole analysis are decomposed into two two-point boundary value problems. For static deformation of the plate, the geometric nonlinearity is involved and the pull-in parameters are obtained by using the shooting method through taking the applied voltage or Casimir parameter as an unknown. This algorithm is also used to study the small amplitude free vibration about the predeformed bending configuration following an assumed harmonic time mode, and the variation of the prestress and Casimir parameters dependent fundamental natural frequency with the applied voltage is presented. Several case studies are compared with available published simulations to confirm the proposed method. The influences of various parameters, such as the initial gap-thickness ratio, Casimir effect, prestress on the pull-in instability behavior and the natural frequency are examined.

Modelling of sloshing modulated angular momentum fluctuations actuated by gravity gradient associated with spacecraft slew motion

May 1996

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The mathematical formulation of orbital spacecraft sloshing dynamics for a partially filled cryogenic superfluid liquid helium II in a dewar container actuated by the gravity gradient acceleration associated with slew motion is studied. The Advanced X-Ray Astrophysics Facility-Spectroscopy (AXAF-S) spacecraft is chosen as a practical example in this study. Explicit mathematical expressions that manage orbital gravity gradient acceleration associated with the slew motion that is acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics is based on the noninertial frame spacecraft-bound coordinates and the solution of time-dependent three-dimensional formulations of partial differential equations subject to initial and boundary conditions. This study discloses the capillary effect of sloshing dynamics governed liquid-vapor interface fluctuations, angular momentum and moment fluctuations of fluid system, and also bubble mass center fluctuations driven by the gravity gradient acceleration associated with slew motion which affects the stability of the orbital spacecraft fluid system in a microgravity environment.

Static pull-in analysis of electrostatically actuated microbeams using homotopy perturbation method

January 2013

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In this study, static pull-in instability of electrostatically-actuated microbridges and microcantilevers is investigated considering different nonlinear effects. Galerkin’s decomposition method is utilized to convert the nonlinear differential equations of motion to nonlinear integro-algebraic equations. Afterward, analytic solutions to static deflections of the microbeams are obtained using the homotopy perturbation method. Results are in excellent agreement with those presented in the literature.

Detection, isolation and identification of multiple actuator and sensor faults in nonlinear dynamic systems: Application to a waste water treatment process

January 2011

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The goal in many fault detection and isolation schemes is to increase the isolation and identification speed. This paper, presents a new approach of a nonlinear model based adaptive observer method, for detection, isolation and identification of actuator and sensor faults. Firstly, we will design a new method for the actuator fault problem where, after the fault detection and before the fault isolation, we will try to estimate the output of the instrument. The method is based on the formation of nonlinear observer banks where each bank isolates each actuator fault. Secondly, for the sensor problem we will reformulate the system by introducing a new state variable, so that an augmented system can be constructed to treat sensor faults as actuator faults. A method based on the design of an adaptive observers’ bank will be used for the fault treatment. These approaches use the system model and the outputs of the adaptive observers to generate residues. Residuals are defined in such way to isolate the faulty instrument after detecting the fault occurrence. The advantages of these methods are that we can treat not only single actuator and sensor faults but also multiple faults, more over the isolation time has been decreased. In this study, we consider that only abrupt faults in the system can occur. The validity of the methods will be tested firstly in simulation by using a nonlinear model of waste water treatment process with and without measurement noise and secondly with the same nonlinear model but by using this time real data.

A biobjective optimization model for routing in mobile ad hoc networks

March 2009

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In this paper, the problem of finding optimal paths in mobile ad hoc networks is addressed. More specifically, a novel bicriteria optimization model, which allows the energy consumption and the link stability of mobile nodes to be taken into account simultaneously, is presented. In order to evaluate the validity of the proposed model, a greedy approach is devised. Some preliminary computational experiments have been carried out, in a simulation environment. The numerical results are very encouraging, showing the correctness of the proposed model. Indeed, the selection of a shorter route leads to a more stable route, but to a greater energy consumption. On the other hand, if longer routes are selected the route fragility is increased, but the average energy consumption is reduced.

Improved ad hoc interface conditions for Schwarz solution procedure tuned to highly heterogeneous media

May 2005

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In this paper, an improved method to derive efficient interface conditions for the Schwarz solution procedure tuned to highly heterogeneous media is presented. This method, based on two parameters optimization, involves new interface conditions specially designed to keep the heterogeneity between the subdomains on the interface. The mathematical analysis of these interface conditions is first presented. Then the asymptotic analysis upon the mesh size parameter together with the heterogeneity ratio is detailed. These interface conditions lead to better asymptotic convergence rate than other available interface conditions. Numerical experiments illustrate the dependence of the proposed method upon several parameters, and confirm the robustness and efficiency of the Schwarz algorithm when equipped with such interface conditions.

System identification and control using adaptive particle swarm optimization

March 2011

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This paper presents a methodology for finding optimal system parameters and optimal control parameters using a novel adaptive particle swarm optimization (APSO) algorithm. In the proposed APSO, every particle dynamically adjusts inertia weight according to feedback taken from particles’ best memories. The main advantages of the proposed APSO are to achieve faster convergence speed and better solution accuracy with minimum incremental computational burden. In the beginning we attempt to utilize the proposed algorithm to identify the unknown system parameters the structure of which is assumed to be known previously. Next, according to the identified system, PID gains are optimally found by also using the proposed algorithm. Two simulated examples are finally given to demonstrate the effectiveness of the proposed algorithm. The comparison to PSO with linearly decreasing inertia weight (LDW-PSO) and genetic algorithm (GA) exhibits the APSO-based system’s superiority.

Robust adaptive control of linear time-delay systems with point time-varying delays via multiestimation

February 2009

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This paper presents an adaptive pole-placement based controller for continuous-time linear systems with unknown and eventually time-varying point delays under uncertainties consisting of unmodeled dynamics and eventual bounded disturbances. A multiestimation scheme is designed for improving the identification error performance and then to deal with possibly errors between the true basic delay compared to that used in regressor vector of measurements of the adaptive scheme and also to prevent the closed-loop system against potential instability. Each estimation scheme in the parallel disposal possesses a relative dead-zone which freezes the adaptation process for small sizes of the adaptation error compared to the estimated size of the absolute value of the contribution of the uncertainties to the filtered output versus time. All the estimation schemes run in parallel but only that which is currently in operation parameterizes the adaptive controller to generate the plant input at each time. A supervisor chooses the appropriate estimator in real time which respects a prescribed minimum residence time at each estimation algorithm in operation. That strategy is the main tool used to ensure the closed-loop stability under estimates switching. The relative dead-zone in the adaptation mechanism prevents the closed-loop system against potential instability caused by uncertainties.

An adaptive network based fuzzy inference system–auto regression–analysis of variance algorithm for improvement of oil consumption estimation and policy making: The cases of Canada, United Kingdom, and South Korea

February 2011

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This paper presents an adaptive network based fuzzy inference system (ANFIS)–auto regression (AR)–analysis of variance (ANOVA) algorithm to improve oil consumption estimation and policy making. ANFIS algorithm is developed by different data preprocessing methods and the efficiency of ANFIS is examined against auto regression (AR) in Canada, United Kingdom and South Korea. For this purpose, mean absolute percentage error (MAPE) is used to show the efficiency of ANFIS. The algorithm for calculating ANFIS performance is based on its closed and open simulation abilities. Moreover, it is concluded that ANFIS provides better results than AR in Canada, United Kingdom and South Korea. This is unlike previous expectations that auto regression always provides better estimation for oil consumption estimation. In addition, ANOVA is used to identify policy making strategies with respect to oil consumption. This is the first study that introduces an integrated ANFIS–AR–ANOVA algorithm with preprocessing and post processing modules for improvement of oil consumption estimation in industrialized countries.

December 2000

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Shape optimal design of arch dams using an adaptive neuro-fuzzy inference system and improved particle swarm optimization

June 2010

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An efficient methodology is proposed to find the optimal shape of arch dams including fluid–structure interaction subject to earthquake ground motion. In order to reduce the computational cost of optimization process, an adaptive neuro-fuzzy inference system (ANFIS) is built to predict the dam effective response instead of directly evaluating it by a time-consuming finite element analysis (FEA). The presented ANFIS is compared with a widespread neural network termed back propagation neural network (BPNN) and it appears a better performance generality for estimating the dam response. The optimization task is implemented using an improved version of particle swarm optimization (PSO) named here as IPSO. In order to assess the effectiveness of the proposed methodology, the optimization of a real world arch dam is performed via both IPSO–ANFIS and PSO–BPNN approaches. The numerical results demonstrate the computational advantages of the proposed IPSO–ANFIS for optimal design of arch dams when compared with the PSO–BPNN approach.

Neuron phase shift adaptive to time delay in locomotor control

February 2009

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Based on neurophysiological evidence, theoretical studies have shown that walking can be generated by mutual entrainment of oscillations of a central pattern generator (CPG) and a body. However, it has also been shown that the time delay in the sensorimotor loop destabilizes mutual entrainment, and results in the failure to walk. Recently, it has been reported that if (a) the neuron model used to construct the CPG is replaced by physiologically faithful neuron model (Bonhoeffer–Van der Pol type) and (b) the mechanical impedance of the body (muscle viscoelasticity) is controlled depending on the angle between two legs, the phase relationship between CPG activity and body motion could be flexibly locked according to the loop delay and, therefore, mutual entrainment can be stabilized. That is, locomotor control adaptive to the loop delay can emerge from the coupling between CPG and body. Here, we call this mechanism flexible-phase locking. In this paper, we construct a system of coupled oscillators as a simplified model of a walking system to theoretically investigate the mechanism of flexible-phase locking, and to analyze the simplified model. The analysis suggests that the following are required as the essential mechanism: (i) an asymptotically stable limit cycle of the coupling system of CPG and body and (ii) a sign difference between afferent and efferent coupling coefficients.

Numerical solution of stiff and convection-diffusion equations using adaptive spline function approximation

February 1983

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The singular perturbation mathematical model plays an important role in modelling fluid processes which arise in applied mechanics. We have either, the stiff system of initial value problems or convection-diffusion problems. When conventional numerical methods are used to obtain the solution, the stepsize must be limited to small values. Any attempt to use a larger step-size results in the production of nonphysical oscillations in the solution.In this paper we have constructed an adaptive spline function to solve initial and boundary value problems of ordinary and partial differential equations. The numerical methods based on the spline relations when applied to the test models produce oscillation free solutions. The numerical results are presented and discussed.

Dynamic modelling of flexible robotic mechanisms and adaptive robust control of trajectory computer simulation––Part I

December 2002

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The purpose of this research is to design robust control for a flexible arm by a deterministic approach. This approach represents a new development in control theory and allows dealing with uncertain elements; which every dynamical system may contain, as well as with unknown or imperfectly know inputs and errors in state measurements. The obtained controller guarantees that all possible responses of the system behave in a desired fashion. The controllers, designed via this approach, are called “robust” or “deterministic”. The deterministic or robust principle of control is successfully applied to single input multiple-output system with a system matrix as large as 6×6 (in the case of one link flexible arm). Two different controllers are designed. The uncertain parameters appear here as a set of the natural frequencies of the system. The procedure for the design performed here, can also be applied (with some modifications) to multi-input multi-output system (MIMO), e.g., to a manipulator with several flexible links. Theoretical proof that the robust control may be applied to MIMO systems is available.

Error estimation, adaptivity and data transfer in enriched plasticity continua to analysis of shear band localization

June 2007

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