Showing papers in "Mathematical Problems in Engineering in 2013"

Review on Methods to Fix Number of Hidden Neurons in Neural Networks

Abstract: This paper reviews methods to fix a number of hidden neurons in neural networks for the past 20 years. And it also proposes a new method to fix the hidden neurons in Elman networks for wind speed prediction in renewable energy systems. The random selection of a number of hidden neurons might cause either overfitting or underfitting problems. This paper proposes the solution of these problems. To fix hidden neurons, 101 various criteria are tested based on the statistical errors. The results show that proposed model improves the accuracy and minimal error. The perfect design of the neural network based on the selection criteria is substantiated using convergence theorem. To verify the effectiveness of the model, simulations were conducted on real-time wind data. The experimental results show that with minimum errors the proposed approach can be used for wind speed prediction. The survey has been made for the fixation of hidden neurons in neural networks. The proposed model is simple, with minimal error, and efficient for fixation of hidden neurons in Elman networks.

Systems of Navier-Stokes equations on Cantor sets

Abstract: We present systems of Navier-Stokes equations on Cantor sets, which are described by the local fractional vector calculus. It is shown that the results for Navier-Stokes equations in a fractal bounded domain are efficient and accurate for describing fluid flow in fractal media.

Stability of Fractional Order Systems

Abstract: The theory and applications of fractional calculus (FC) had a considerable progress during the last years. Dynamical systems and control are one of the most active areas, and several authors focused on the stability of fractional order systems. Nevertheless, due to the multitude of efforts in a short period of time, contributions are scattered along the literature, and it becomes difficult for researchers to have a complete and systematic picture of the present day knowledge. This paper is an attempt to overcome this situation by reviewing the state of the art and putting this topic in a systematic form. While the problem is formulated with rigour, from the mathematical point of view, the exposition intends to be easy to read by the applied researchers. Different types of systems are considered, namely, linear/nonlinear, positive, with delay, distributed, and continuous/discrete. Several possible routes of future progress that emerge are also tackled.

Engineering Applications of Intelligent Monitoring and Control 2014

Abstract: 1 Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, Avenida Padre Tomas Pereira Taipa, Macao, China 2 School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China 3Department of Mechanical Engineering, The University of Auckland, 20 Symonds Street, Auckland, New Zealand 4Department of Bio-Industrial Mechatronics Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan

Mathematical Modeling of Heat and Mass Transfer in Energy Science and Engineering

Abstract: 1 School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110004, China 2 Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou, Zhejiang Province 310018, China 3 Faculty of Process and Environmental Engineering, Technical University of Lodz, 90-924 Lodz, Poland 4 Institute of Drying and Dewatering, College of Mechanical Engineering, Tianjin University of Science and Technology, 1038 Daguan Road, Hexi District, Tianjin 300222, China 5 Institute of Biology and Chemistry, Shenyang University, Shenyang 110044, China

Persistent Homology of Collaboration Networks

Abstract: Over the past few decades, network science has introduced several statistical measures to determine the topological structure of large networks. Initially, the focus was on binary networks, where edges are either present or not. Thus, many of the earlier measures can only be applied to binary networks and not to weighted networks. More recently, it has been shown that weighted networks have a rich structure, and several generalized measures have been introduced. We use persistent homology, a recent technique from computational topology, to analyse four weighted collaboration networks. We include the first and second Betti numbers for the first time for this type of analysis. We show that persistent homology corresponds to tangible features of the networks. Furthermore, we use it to distinguish the collaboration networks from similar random networks.

A Review of Piecewise Linearization Methods

Abstract: Various optimization problems in engineering and management are formulated as nonlinear programming problems. Because of the nonconvexity nature of this kind of problems, no efficient approach is available to derive the global optimum of the problems. How to locate a global optimal solution of a nonlinear programming problem is an important issue in optimization theory. In the last few decades, piecewise linearization methods have been widely applied to convert a nonlinear programming problem into a linear programming problem or a mixed-integer convex programming problem for obtaining an approximated global optimal solution. In the transformation process, extra binary variables, continuous variables, and constraints are introduced to reformulate the original problem. These extra variables and constraints mainly determine the solution efficiency of the converted problem. This study therefore provides a review of piecewise linearization methods and analyzes the computational efficiency of various piecewise linearization methods.

Recent Developments on Wireless Sensor Networks Technology for Bridge Health Monitoring

Abstract: Structural health monitoring (SHM) systems have shown great potential to sense the responses of a bridge system, diagnose the current structural conditions, predict the expected future performance, provide information for maintenance, and validate design hypotheses. Wireless sensor networks (WSNs) that have the benefits of reducing implementation costs of SHM systems as well as improving data processing efficiency become an attractive alternative to traditional tethered sensor systems. This paper introduces recent technology developments in the field of bridge health monitoring using WSNs. As a special application of WSNs, the requirements and characteristics of WSNs when used for bridge health monitoring are firstly briefly discussed. Then, the state of the art in WSNs-based bridge health monitoring systems is reviewed including wireless sensor, network topology, data processing technology, power management, and time synchronization. Following that, the performance validations and applications of WSNs in bridge health monitoring through scale models and field deployment are presented. Finally, some existing problems and promising research efforts for promoting applications of WSNs technology in bridge health monitoring throughout the world are explored.

Sales Forecasting for Fashion Retailing Service Industry: A Review

Abstract: Sales forecasting is crucial for many retail operations. It is especially critical for the fashion retailing service industry in which product demand is very volatile and product’s life cycle is short. This paper conducts a comprehensive literature review and selects a set of papers in the literature on fashion retail sales forecasting. The advantages and the drawbacks of different kinds of analytical methods for fashion retail sales forecasting are examined. The evolution of the respective forecasting methods over the past 15 years is revealed. Issues related to real-world applications of the fashion retail sales forecasting models and important future research directions are discussed.

A Computational Method for Two-Point Boundary Value Problems of Fourth-Order Mixed Integrodifferential Equations

Abstract: In this paper, reproducing kernel Hilbert space method is applied to approximate the solution of two-point boundary value problems for fourth-order Fredholm-Volterra integrodifferential equations. The analytical solution was calculated in the form of convergent series in the space with easily computable components. In the proposed method, the -term approximation is obtained and is proved to converge to the analytical solution. Meanwhile, the error of the approximate solution is monotone decreasing in the sense of the norm of . The proposed technique is applied to several examples to illustrate the accuracy, efficiency, and applicability of the method.

A Simple and Efficient Artificial Bee Colony Algorithm

Abstract: Artificial bee colony (ABC) is a new population-based stochastic algorithm which has shown good search abilities on many optimization problems. However, the original ABC shows slow convergence speed during the search process. In order to enhance the performance of ABC, this paper proposes a new artificial bee colony (NABC) algorithm, which modifies the search pattern of both employed and onlooker bees. A solution pool is constructed by storing some best solutions of the current swarm. New candidate solutions are generated by searching the neighborhood of solutions randomly chosen from the solution pool. Experiments are conducted on a set of twelve benchmark functions. Simulation results show that our approach is significantly better or at least comparable to the original ABC and seven other stochastic algorithms.

Quality-Related Process Monitoring Based on Total Kernel PLS Model and Its Industrial Application

Abstract: Projection to latent structures (PLS) model has been widely used in quality-related process monitoring, as it can establish a mapping relationship between process variables and quality index variables. To enhance the adaptivity of PLS, kernel PLS (KPLS) as an advanced version has been proposed for nonlinear processes. In this paper, we discuss a new total kernel PLS (T-KPLS) for nonlinear quality-related process monitoring. The new model divides the input spaces into four parts instead of two parts in KPLS, where an individual subspace is responsible in predicting quality output, and two parts are utilized for monitoring the quality-related variations. In addition, fault detection policy is developed based on the T-KPLS model, which is more well suited for nonlinear quality-related process monitoring. In the case study, a nonlinear numerical case, the typical Tennessee Eastman Process (TEP) and a real industrial hot strip mill process (HSMP) are employed to access the utility of the present scheme.

Levy-flight krill herd algorithm

Abstract: To improve the performance of the krill herd (KH) algorithm, in this paper, a Levy-flight krill herd (LKH) algorithm is proposed for solving optimization tasks within limited computing time. The improvement includes the addition of a new local Levy-flight (LLF) operator during the process when updating krill in order to improve its efficiency and reliability coping with global numerical optimization problems. The LLF operator encourages the exploitation and makes the krill individuals search the space carefully at the end of the search. The elitism scheme is also applied to keep the best krill during the process when updating the krill. Fourteen standard benchmark functions are used to verify the effects of these improvements and it is illustrated that, in most cases, the performance of this novel metaheuristic LKH method is superior to, or at least highly competitive with, the standard KH and other population-based optimization methods. Especially, this new method can accelerate the global convergence speed to the true global optimum while preserving the main feature of the basic KH.

LGMS-FOA: An Improved Fruit Fly Optimization Algorithm for Solving Optimization Problems

Abstract: Recently, a new fruit fly optimization algorithm (FOA) is proposed to solve optimization problems. In this paper, we empirically study the performance of FOA. Six different nonlinear functions are selected as testing functions. The experimental results illustrate that FOA cannot solve complex optimization problems effectively. In order to enhance the performance of FOA, an improved FOA (named LGMS-FOA) is proposed. Simulation results and comparisons of LGMS-FOA with FOA and other metaheuristics show that LGMS-FOA can greatly enhance the searching efficiency and greatly improve the searching quality.

UCAV Path Planning by Fitness-Scaling Adaptive Chaotic Particle Swarm Optimization

Abstract: Path planning plays an extremely important role in the design of UCAVs to accomplish the air combat task fleetly and reliably. The planned path should ensure that UCAVs reach the destination along the optimal path with minimum probability of being found and minimal consumed fuel. Traditional methods tend to find local best solutions due to the large search space. In this paper, a Fitness-scaling Adaptive Chaotic Particle Swarm Optimization (FAC-PSO) approach was proposed as a fast and robust approach for the task of path planning of UCAVs. The FAC-PSO employed the fitness-scaling method, the adaptive parameter mechanism, and the chaotic theory. Experiments show that the FAC-PSO is more robust and costs less time than elite genetic algorithm with migration, simulated annealing, and chaotic artificial bee colony. Moreover, the FAC-PSO performs well on the application of dynamic path planning when the threats cruise randomly and on the application of 3D path planning.

Controllability of Weighted and Directed Networks with Nonidentical Node Dynamics

Abstract: The concept of controllability from control theory is applied to weighted and directed networks with heterogenous linear or linearized node dynamics subject to exogenous inputs, where the nodes are grouped into leaders and followers. Under this framework, the controllability of the controlled network can be decomposed into two independent problems: the controllability of the isolated leader subsystem and the controllability of the extended follower subsystem. Some necessary and/or sufficient conditions for the controllability of the leader-follower network are derived based on matrix theory and graph theory. In particular, it is shown that a single-leader network is controllable if it is a directed path or cycle, but it is uncontrollable for a complete digraph or a star digraph in general. Furthermore, some approaches to improving the controllability of a heterogenous network are presented. Some simulation examples are given for illustration and verification.

Modeling and Control of Wind Turbine

Abstract: In recent years, the energy production by wind turbines has been increasing, because its production is environmentally friendly; therefore, the technology developed for the production of energy through wind turbines brings great challenges in the investigation. This paper studies the characteristics of the wind turbine in the market and lab; it is focused on the recent advances of the wind turbine modeling with the aerodynamic power and the wind turbine control with the nonlinear, fuzzy, and predictive techniques.

Mathematical and Metaheuristic Applications in Design Optimization of Steel Frame Structures: An Extensive Review

Abstract: The type of mathematical modeling selected for the optimum design problems of steel skeletal frames affects the size and mathematical complexity of the programming problem obtained. Survey on the structural optimization literature reveals that there are basically two types of design optimization formulation. In the first type only cross sectional properties of frame members are taken as design variables. In such formulation when the values of design variables change during design cycles, it becomes necessary to analyze the structure and update the response of steel frame to the external loading. Structural analysis in this type is a complementary part of the design process. In the second type joint coordinates are also treated as design variables in addition to the cross sectional properties of members. Such formulation eliminates the necessity of carrying out structural analysis in every design cycle. The values of the joint displacements are determined by the optimization techniques in addition to cross sectional properties. The structural optimization literature contains structural design algorithms that make use of both type of formulation. In this study a review is carried out on mathematical and metaheuristic algorithms where the effect of the mathematical modeling on the efficiency of these algorithms is discussed.

Recent Advances on Recursive Filtering and Sliding Mode Design for Networked Nonlinear Stochastic Systems: A Survey

Abstract: Copyright © 2013 Jun Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Homotopy Perturbation Method for Fractional Black-Scholes European Option Pricing Equations Using Sumudu Transform

Abstract: The homotopy perturbation method, Sumudu transform, and He’s polynomials are combined to obtain the solution of fractional Black-Scholes equation. The fractional derivative is considered in Caputo sense. Further, the same equation is solved by homotopy Laplace transform perturbation method. The results obtained by the two methods are in agreement. The approximate analytical solution of Black-Scholes is calculated in the form of a convergence power series with easily computable components. Some illustrative examples are presented to explain the efficiency and simplicity of the proposed method.

A Study of Nonlinear Fractional Differential Equations of Arbitrary Order with Riemann-Liouville Type Multistrip Boundary Conditions

Abstract: We develop the existence theory for nonlinear fractional differential equations of arbitrary order with Riemann-Liouville type boundary conditions involving nonintersecting finite many strips of arbitrary length. Our results are based on some standard tools of fixed point theory. For the illustration of the results, some examples are also discussed.

Model Reduction for Discrete-Time Markovian Jump Systems with Deficient Mode Information

Abstract: This paper investigates the problem of model reduction for a class of discrete-time Markovian jump linear systems (MJLSs) with deficient mode information, which simultaneously involves the exactly known, partially unknown, and uncertain transition probabilities. By fully utilizing the properties of the transition probability matrices, together with the convexification of uncertain domains, a new performance analysis criterion for the underlying MJLSs is first derived, and then two approaches, namely, the convex linearisation approach and iterative approach, for the model reduction synthesis are proposed. Finally, a simulation example is provided to illustrate the effectiveness of the proposed design methods.

A Hybrid Bat Algorithm with Path Relinking for the Capacitated Vehicle Routing Problem

Abstract: The capacitated vehicle routing problem (CVRP) is an NP-hard problem with both engineering and theoretical interests. In this paper, a hybrid bat algorithm with path relinking (HBA-PR) is proposed to solve CVRP. The HBA-PR is constructed based on the framework of the continuous bat algorithm, the greedy randomized adaptive search procedure (GRASP) and path relinking are effectively integrated into the bat algorithm. Moreover, in order to further improve the performance, the random subsequences and single-point local search are operated with certain loudness (a probability). In order to verify the effectiveness of our approach and its efficiency and compare with other existing methodologies, several classical CVRP instances from three classes of CVRP benchmarks are selected to test. Experimental results and comparisons show the HBA-PR is effective for solving CVRPs.

Mixed Static and Dynamic Optimization of Four-Parameter Functionally Graded Completely Doubly Curved and Degenerate Shells and Panels Using GDQ Method

Abstract: This study deals with a mixed static and dynamic optimization of four-parameter functionally graded material (FGM) doubly curved shells and panels. The two constituent functionally graded shell consists of ceramic and metal, and the volume fraction profile of each lamina varies through the thickness of the shell according to a generalized power-law distribution. The Generalized Differential Quadrature (GDQ) method is applied to determine the static and dynamic responses for various FGM shell and panel structures. The mechanical model is based on the so-called First-order Shear Deformation Theory (FSDT). Three different optimization schemes and methodologies are implemented. The Particle Swarm Optimization, Monte Carlo and Genetic Algorithm approaches have been applied to define the optimum volume fraction profile for optimizing the first natural frequency and the maximum static deflection of the considered shell structure. The optimization aim is in fact to reach the frequency and the static deflection targets defined by the designer of the structure: the complete four-dimensional search space is considered for the optimization process. The optimized material profile obtained with the three methodologies is presented as a result of the optimization problem solved for each shell or panel structure.

Firefly Algorithm for Explicit B-Spline Curve Fitting to Data Points

Abstract: This paper introduces a new method to compute the approximating explicit B-spline curve to a given set of noisy data points. The proposed method computes all parameters of the B-spline fitting curve of a given order. This requires to solve a difficult continuous, multimodal, and multivariate nonlinear least-squares optimization problem. In our approach, this optimization problem is solved by applying the firefly algorithm, a powerful metaheuristic nature-inspired algorithm well suited for optimization. The method has been applied to three illustrative real-world engineering examples from different fields. Our experimental results show that the presented method performs very well, being able to fit the data points with a high degree of accuracy. Furthermore, our scheme outperforms some popular previous approaches in terms of different fitting error criteria.

Boundary Layer Flow Past a Wedge Moving in a Nanofluid

Abstract: The problem of steady boundary layer flow past a stretching wedge with the velocity in a nanofluid and with a parallel free stream velocity is numerically studied. It is assumed that at the stretching surface the temperature and the nanoparticle fraction take the constant values and , respectively. The ambient values (inviscid fluid) of and are denoted by and , respectively. The boundary layer governing partial differential equations of mass, momentum, thermal energy, and nanoparticles recently proposed by Kuznetsov and Nield (2006, 2009), are reduced to ordinary differential equations along with the corresponding boundary conditions. These equations are solved numerically using an implicit finite-difference method for some values of the governing parameters, such as , , , , , and , which are the measure of the pressure gradient, moving parameter, Prandtl number, Lewis number, the Brownian motion parameter, and the thermophoresis parameter, respectively.

Analysis of Sandwich Plates by Generalized Differential Quadrature Method

Abstract: We combine a layer-wise formulation and a generalized differential quadrature technique for predicting the static deformations and free vibration behaviour of sandwich plates. Through numerical experiments, the capability and efficiency of this strong-form technique for static and vibration problems are demonstrated, and the numerical accuracy and convergence are thoughtfully examined.

Hydromagnetic Stagnation-Point Flow towards a Radially Stretching Convectively Heated Disk

Abstract: The steady stagnation-point flow and heat transfer of an electrically conducted incompressible viscous fluid are extended to the case where the disk surface is convectively heated and radially stretching. The fluid is subjected to an external uniform magnetic field perpendicular to the plane of the disk. The governing momentum and energy balance equations give rise to nonlinear boundary value problem. Using a spectral relaxation method with a Chebyshev spectral collocation method, the numerical solutions are obtained over the entire range of the physical parameters. Emphasis has been laid to study the effects of viscous dissipation and Joule heating on the thermal boundary layer. Pertinent results on the effects of various thermophysical parameters on the velocity and temperature fields as well as local skin friction and local Nusselt number are discussed in detail and shown graphically and/or in tabular form.

Markov Chain Models for the Stochastic Modeling of Pitting Corrosion

Abstract: The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure birth) Markov process is used to model external pitting corrosion in underground pipelines. A closed-form solution of the system of Kolmogorov's forward equations is used to describe the transition probability function in a discrete pit depth space. The transition probability function is identified by correlating the stochastic pit depth mean with the empirical deterministic mean. In the second model, the distribution of maximum pit depths in a pitting experiment is successfully modeled after the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time is simulated as the realization of a Weibull process. Pit growth is simulated using a nonhomogeneous Markov process. An analytical solution of Kolmogorov's system of equations is also found for the transition probabilities from the first Markov state. Extreme value statistics is employed to find the distribution of maximum pit depths.

Wavelet Packet Transform Based Driver Distraction Level Classification Using EEG

Abstract: We classify the driver distraction level (neutral, low, medium, and high) based on different wavelets and classifiers using wireless electroencephalogram (EEG) signals. 50 subjects were used for data collection using 14 electrodes. We considered for this research 4 distraction stimuli such as Global Position Systems (GPS), music player, short message service (SMS), and mental tasks. Deriving the amplitude spectrum of three different frequency bands theta, alpha, and beta of EEG signals was based on fusion of discrete wavelet packet transform (DWPT) and FFT. Comparing the results of three different classifiers (subtractive fuzzy clustering probabilistic neural network, -nearest neighbor) was based on spectral centroid, and power spectral features extracted by different wavelets (db4, db8, sym8, and coif5). The results of this study indicate that the best average accuracy achieved by subtractive fuzzy inference system classifier is 79.21% based on power spectral density feature extracted by sym8 wavelet which gave a good class discrimination under ANOVA test.