Showing papers by "Amirkabir University of Technology published in 2010"

A new operational matrix for solving fractional-order differential equations

Abstract: Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. For that reason we need a reliable and efficient technique for the solution of fractional differential equations. This paper deals with the numerical solution of a class of fractional differential equations. The fractional derivatives are described in the Caputo sense. Our main aim is to generalize the Legendre operational matrix to the fractional calculus. In this approach, a truncated Legendre series together with the Legendre operational matrix of fractional derivatives are used for numerical integration of fractional differential equations. The main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of algebraic equations thus greatly simplifying the problem. The method is applied to solve two types of fractional differential equations, linear and nonlinear. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.

Solving nonlinear fractional partial differential equations using the homotopy analysis method

Abstract: In this article, the homotopy analysis method is applied to solve nonlinear fractional partial differential equations. On the basis of the homotopy analysis method, a scheme is developed to obtain the approximate solution of the fractional KdV, K(2,2), Burgers, BBM-Burgers, cubic Boussinesq, coupled KdV, and Boussinesq-like B(m,n) equations with initial conditions, which are introduced by replacing some integer-order time derivatives by fractional derivatives. The homotopy analysis method for partial differential equations of integer-order is directly extended to derive explicit and numerical solutions of the fractional partial differential equations. The solutions of the studied models are calculated in the form of convergent series with easily computable components. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the new technique. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010

Fuzzy AHP to determine the relative weights of evaluation criteria and Fuzzy TOPSIS to rank the alternatives

Abstract: The aim of this study is to propose a Fuzzy multi-criteria decision-making approach (FMCDM) to evaluate the alternative options in respect to the user's preference orders. Two FMCDM methods are proposed for solving the MCDM problem: Fuzzy Analytic Hierarchy Process (FAHP) is applied to determine the relative weights of the evaluation criteria and the extension of the Fuzzy Technique for Order Preference by Similarity to Ideal Solution (FTOPSIS) is applied to rank the alternatives. Empirical results show that the proposed methods are viable approaches in solving the problem. When the performance ratings are vague and imprecise, this Fuzzy MCDM is a preferred solution.

Enhanced probabilistic neural network with local decision circles: A robust classifier

Abstract: In recent years the Probabilistic Neural Network (PPN) has been used in a large number of applications due to its simplicity and efficiency. PNN assigns the test data to the class with maximum likelihood compared with other classes. Likelihood of the test data to each training data is computed in the pattern layer through a kernel density estimation using a simple Bayesian rule. The kernel is usually a standard probability distribution function such as a Gaussian function. A spread parameter is used as a global parameter which determines the width of the kernel. The Bayesian rule in the pattern layer estimates the conditional probability of each class given an input vector without considering any probable local densities or heterogeneity in the training data. In this paper, an enhanced and generalized PNN (EPNN) is presented using local decision circles (LDCs) to overcome the aforementioned shortcoming and improve its robustness to noise in the data. Local decision circles enable EPNN to incorporate local information and non-homogeneity existing in the training population. The circle has a radius which limits the contribution of the local decision. In the conventional PNN the spread parameter can be optimized for maximum classification accuracy. In the proposed EPNN two parameters, the spread parameter and the radius of local decision circles, are optimized to maximize the performance of the model. Accuracy and robustness of EPNN are compared with PNN using three different benchmark classification problems, iris data, diabetic data, and breast cancer data, and five different ratios of training data to testing data: 90:10, 80:20, 70:30, 60:40, and 50:50. EPNN provided the most accurate results consistently for all ratios. Robustness of PNN and EPNN is investigated using different values of signal to noise ratio (SNR). Accuracy of EPNN is consistently higher than accuracy of PNN at different levels of SNR and for all ratios of training data to testing data.

New diagnostic EEG markers of the Alzheimer's disease using visibility graph

Abstract: A new chaos-wavelet approach is presented for electroencephalogram (EEG)-based diagnosis of Alzheimer's disease (AD) employing a recently developed concept in graph theory, visibility graph (VG). The approach is based on the research ideology that nonlinear features may not reveal differences between AD and control group in the band-limited EEG, but may represent noticeable differences in certain sub-bands. Hence, complexity of EEGs is computed using the VGs of EEGs and EEG sub-bands produced by wavelet decomposition. Two methods are employed for computation of complexity of the VGs: one based on the power of scale-freeness of a graph structure and the other based on the maximum eigenvalue of the adjacency matrix of a graph. Analysis of variation is used for feature selection. Two classifiers are applied to the selected features to distinguish AD and control EEGs: a Radial Basis Function Neural Network (RBFNN) and a two-stage classifier consisting of Principal Component Analysis (PCA) and the RBFNN. After comprehensive statistical studies, effective classification features and mathematical markers were discovered. Finally, using the discovered features and a two-stage classifier (PCA-RBFNN), a high diagnostic accuracy of 97.7% was obtained.

Incorporating location, routing and inventory decisions in supply chain network design

Abstract: This paper for the first time presents a novel model to simultaneously optimize location, allocation, capacity, inventory, and routing decisions in a stochastic supply chain system. Each customer’s demand is uncertain and follows a normal distribution, and each distribution center maintains a certain amount of safety stock. To solve the model, first we present an exact solution method by casting the problem as a mixed integer convex program, and then we establish a heuristic method based on a hybridization of Tabu Search and Simulated Annealing. The results show that the proposed heuristic is considerably efficient and effective for a broad range of problem sizes.

Investigation of particle size and amount of alumina on microstructure and mechanical properties of al matrix composite made by powder metallurgy

Abstract: Al matrix composite is well known, in which Al2O3 is the most widely used reinforcement. The aim of this study is to investigate the effect of alumina particle size and its amount on the relative density, hardness, microstructure, wear resistance, yield and compressive strength and elongation in Al–Al2O3 composites. To this end, the amount of 0–20 wt.% alumina with average particle sizes 48, 12 and 3 μm was used along with pure aluminum of average particle size of 30 μm. Powder metallurgy is a method used in the fabrication of this composite in which the powders were mixed using a planetary ball mill. Consolidation was conducted by axial pressing at 440 MPa. Sintering procedure was done at 550 °C for 45 min. The results indicated that as the alumina particle size is reduced, density raises at first, then, declines. Moreover, as the alumina particle size decreases, hardness, yield strength, compressive strength and elongation increase and factors such as wear resistance, microstructure grain size and distribution homogeneity in matrix decreases. For instance, as the alumina particle size gets smaller from 48 to 3 μm at 10 wt.% alumina, hardness rises from 50 to 70 BHN, compressive strength improves from 168 to 307 MPa and wear rate rises from 0.0289 to 0.0341 mm3/m. On the other hand, as the amount of alumina increases, hardness and wear resistance increase and relative density and elongation is decreased. However, compressive and yield strength rise at first, then drop. For example, if the amount of alumina with 12 μm particle size increases from 5 to 10 wt.%, hardness increases from 47 to 62 BHN and compressive strength rises from 190 to 273 MPa. Nevertheless, erosion rate after 300 m decreases from 0.0447 to 0.0311 mm3/m.

Double Flying Capacitor Multicell Converter Based on Modified Phase-Shifted Pulsewidth Modulation

Abstract: Multilevel converters are very interesting alternatives for medium and high-power applications. The main reason is the increase in the number of output voltage levels and its apparent frequency. This paper presents a new configuration of flying capacitor multicell (FCM) converter. The main advantages of the proposed converter, in comparison with FCM and stacked multicell converters, are doubling the rms and the number of output voltage levels, improving the output voltage frequency spectrum, and canceling the midpoint of dc source. This progress is achieved by adding only two low-frequency switches to the conventional configuration of FCM converter while the number of high-frequency switches and capacitors, voltage ratings of capacitors and switches, and the number of high-frequency switchings during a full cycle are kept constant. This converter is controlled by a modified phase-shifted pulsewidth modulation, therefore, the self-balancing property of the flying capacitor converter is maintained in the proposed converter. The circuit is simulated using power systems computer-aided design/electromagnetic transients in DC systems (EMTDC) software and simulation results are presented to validate the effectiveness and advantages of the proposed configuration as well as its control strategy. Additionally, measurements taken from an experimental setup are presented in order to study the practical configuration.

Fractality and a wavelet-chaos-neural network methodology for EEG-based diagnosis of autistic spectrum disorder.

Abstract: A method is presented for investigation of EEG of children with autistic spectrum disorder using complexity and chaos theory with the goal of discovering a nonlinear feature space. Fractal Dimension is proposed for investigation of complexity and dynamical changes in autistic spectrum disorder in brain. Two methods are investigated for computation of fractal dimension: Higuchi's Fractal Dimension and Katz's Fractal Dimension. A wavelet-chaos-neural network methodology is presented for automated EEG-based diagnosis of autistic spectrum disorder. The model is tested on a database of eyes-closed EEG data obtained from two groups: nine autistic spectrum disorder children, 6 to 13 years old, and eight non-autistic spectrum disorder children, 7 to 13 years old. Using a radial basis function classifier, an accuracy of 90% was achieved based on the most significant features discovered via analysis of variation statistical test, which are three Katz's Fractal Dimensions in delta (of loci Fp2 and C3) and gamma (of locus T6) EEG sub-bands with P < 0.001.

Wavelet-synchronization methodology: a new approach for EEG-based diagnosis of ADHD.

Abstract: A multi-paradigm methodology is presented for electroencephalogram (EEG) based diagnosis of Attention-Deficit/Hyperactivity Disorder (ADHD) through adroit integration of nonlinear science; wavelets, a signal processing technique; and neural networks, a pattern recognition technique. The selected nonlinear features are generalized synchronizations known as synchronization likelihoods (SL), both among all electrodes and among electrode pairs. The methodology consists of three parts: first detecting the more synchronized loci (group 1) and loci with more discriminative deficit connections (group 2). Using SLs among all electrodes, discriminative SLs in certain sub-bands are extracted. In part two, SLs are computed, not among all electrodes, but between loci of group 1 and loci of group 2 in all sub-bands and the band-limited EEG. This part leads to more accurate detection of deficit connections, and not just deficit areas, but more discriminative SLs in sub-bands with finer resolutions. In part three, a clas...

Reverse logistics network design using simulated annealing

Abstract: Reverse logistics is becoming more important in overall industry area because of the environmental and business factors. Planning and implementing a suitable reverse logistics network could bring more profit, customer satisfaction, and a nice social picture for companies. But, most of logistics networks are not equipped to handle the return products in reverse channels. This paper proposes a mixed integer linear programming model to minimize the transportation and fixed opening costs in a multistage reverse logistics network. Since such network design problems belong to the class of NP-hard problems, we apply a simulated annealing (SA) algorithm with special neighborhood search mechanisms to find the near optimal solution. We also compare the associated numerical results through exact solutions in a set of problems to present the high-quality performance of the applied SA algorithm.

Numerical solution of hyperbolic telegraph equation using the Chebyshev tau method

Abstract: In this article we propose a numerical scheme to solve the one-dimensional hyperbolic telegraph equation. The method consists of expanding the required approximate solution as the elements of shifted Chebyshev polynomials. Using the operational matrices of integral and derivative, we reduce the problem to a set of linear algebraic equations. Some numerical examples are included to demonstrate the validity and applicability of the technique. The method is easy to implement and produces very accurate results. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010