Search results for: linear algebraic method

Authors: Fatma Susilawati Mohamad, Azizah Abdul Manaf, Fadhillah Ahmad, Zarina Mohamad, Wan Suryani Wan Awang

Abstract:

A simple and robust multi-class linear classifier is proposed and implemented. For a pair of classes of the linear boundary, a collection of segments of hyper planes created as perpendicular bisectors of line segments linking centroids of the classes or part of classes. Nearest Neighbor and Linear Discriminant Analysis are compared in the experiments to see the performances of each classifier in discriminating ripeness of oil palm. This paper proposes a multi-class linear classifier using Linear Discriminant Analysis (LDA) for image identification. Result proves that LDA is well capable in separating multi-class features for ripeness identification.

Keywords: multi-class, linear classifier, nearest neighbor, linear discriminant analysis

Procedia PDF Downloads 518

Authors: S. H. Nasseri, A. Ebrahimnejad

Abstract:

Fuzzy set theory has been applied to many fields, such as operations research, control theory, and management sciences. In this paper, we consider two classes of fuzzy linear programming (FLP) problems: Fuzzy number linear programming and linear programming with trapezoidal fuzzy variables problems. We state our recently established results and develop fuzzy primal simplex algorithms for solving these problems. Finally, we give illustrative examples.

Keywords: fuzzy linear programming, fuzzy numbers, duality, sensitivity analysis

Procedia PDF Downloads 552

Authors: Abdel-Razzaq Mugdadi, Ruqayyah Sani

Abstract:

The Kernel Distribution Function Estimator (KDFE) method is the most popular method for nonparametric estimation of the cumulative distribution function. The kernel and the bandwidth are the most important components of this estimator. In this investigation, we replace the kernel in the KDFE with a linear combination of kernels to obtain a new estimator based on the linear combination of kernels, the mean integrated squared error (MISE), asymptotic mean integrated squared error (AMISE) and the asymptotically optimal bandwidth for the new estimator are derived. We propose a new data-based method to select the bandwidth for the new estimator. The new technique is based on the Plug-in technique in density estimation. We evaluate the new estimator and the new technique using simulations and real-life data.

Keywords: estimation, bandwidth, mean square error, cumulative distribution function

Procedia PDF Downloads 565

Authors: Deepshikha Verma, V. N. Rajasekharan Pillai

Abstract:

The present study reports the synthesis of cyclic PNC-28 peptides with solid-phase peptide synthesis method. In the first step, we synthesize the linear PNC-28 Peptide and in the second step, we cyclize (N-to-C or head-to-tail cyclization) the linear PNC-28 peptide. The molecular formula of cyclic PNC-28 peptide is C64H88N12O16 and its m/z mass is ≈1233.64. Elemental analysis of cyclic PNC-28 is C, 59.99; H, 6.92; N, 13.12; O, 19.98. The characterization of LC-MS, CD, FT-IR, and 1HNMR has been done to confirm the successful synthesis and cyclization of linear PNC-28 peptides.

Keywords: CD, FTIR, 1HNMR, cyclic peptide

Procedia PDF Downloads 121

Authors: Hazem M. Al-Mofleh, John E. Daniels, Joseph W. McKean

Abstract:

In this paper numerous robust fitting procedures are considered in estimating spatial variograms. In spatial statistics, the conventional variogram fitting procedure (non-linear weighted least squares) suffers from the same outlier problem that has plagued this method from its inception. Even a 3-parameter model, like the variogram, can be adversely affected by a single outlier. This paper uses the Hogg-Type adaptive procedures to select an optimal score function for a rank-based estimator for these non-linear models. Numeric examples and simulation studies will demonstrate the robustness, utility, efficiency, and validity of these estimates.

Keywords: asymptotic relative efficiency, non-linear rank-based, rank estimates, variogram

Procedia PDF Downloads 413

Authors: Thi Thi Zin, Pyke Tin, Ikuo Kobayashi, Yoichiro Horii

Abstract:

Today dairy farm experts and farmers have well recognized the importance of dairy cow Body Condition Score (BCS) since these scores can be used to optimize milk production, managing feeding system and as an indicator for abnormality in health even can be utilized to manage for having healthy calving times and process. In tradition, BCS measures are done by animal experts or trained technicians based on visual observations focusing on pin bones, pin, thurl and hook area, tail heads shapes, hook angles and short and long ribs. Since the traditional technique is very manual and subjective, the results can lead to different scores as well as not cost effective. Thus this paper proposes an algebraic geometric imaging approach for an automatic dairy cow BCS system. The proposed system consists of three functional modules. In the first module, significant landmarks or anatomical points from the cow image region are automatically extracted by using image processing techniques. To be specific, there are 23 anatomical points in the regions of ribs, hook bones, pin bone, thurl and tail head. These points are extracted by using block region based vertical and horizontal histogram methods. According to animal experts, the body condition scores depend mainly on the shape structure these regions. Therefore the second module will investigate some algebraic and geometric properties of the extracted anatomical points. Specifically, the second order polynomial regression is employed to a subset of anatomical points to produce the regression coefficients which are to be utilized as a part of feature vector in scoring process. In addition, the angles at thurl, pin, tail head and hook bone area are computed to extend the feature vector. Finally, in the third module, the extracted feature vectors are trained by using Markov Classification process to assign BCS for individual cows. Then the assigned BCS are revised by using multiple regression method to produce the final BCS score for dairy cows. In order to confirm the validity of proposed method, a monitoring video camera is set up at the milk rotary parlor to take top view images of cows. The proposed method extracts the key anatomical points and the corresponding feature vectors for each individual cows. Then the multiple regression calculator and Markov Chain Classification process are utilized to produce the estimated body condition score for each cow. The experimental results tested on 100 dairy cows from self-collected dataset and public bench mark dataset show very promising with accuracy of 98%.

Keywords: algebraic geometric imaging approach, body condition score, Markov classification, polynomial regression

Procedia PDF Downloads 146

Authors: Ismail Rahama Adam Hamid

Abstract:

This paper presents the development of a thermal model for a flat, double-sided linear generator designed for use in free-piston engines. The study conducted in this paper examines the influence of temperature on the performance of the permeant magnet linear generator, an integral and pivotal component within the system. This research places particular emphasis on the Neodymium Iron Boron (NdFeB) permanent magnet, which serves as a source of magnetic field for the linear generator. In this study, an internal combustion engine that tends to produce heat is connected to a generator. Considering the temperatures rise from both the combustion process and the thermal contributions of current-carrying conductors and frictional forces. Utilizing Computational Fluid Dynamics (CFD) method, a thermal model of the (NdFeB) magnet within the linear generator is constructed and analyzed. Furthermore, the temperature field is examined to ensure that the linear generator operates under stable conditions without the risk of demagnetization.

Keywords: free piston engine, permanent magnet, linear generator, demagnetization, simulation

Procedia PDF Downloads 36

Authors: Melvin Ballera, Aldrich Olivar, Mary Soriano

Abstract:

Digital computers nowadays must be able to have a utility that is capable of generating random numbers. Usually, computer-generated random numbers are not random given predefined values such as starting point and end points, making the sequence almost predictable. There are many applications of random numbers such business simulation, manufacturing, services domain, entertainment sector and other equally areas making worthwhile to design a unique method and to allow unpredictable random numbers. Applying stochastic simulation using linear congruential algorithm, it shows that as it increases the numbers of the seed and range the number randomly produced or selected by the computer becomes unique. If this implemented in an environment where random numbers are very much needed, the reliability of the random number is guaranteed.

Keywords: stochastic simulation, random numbers, linear congruential algorithm, pseudorandomness

Procedia PDF Downloads 302

Authors: A. M. Sagir

Abstract:

The aim of this paper is to investigate the performance of the developed linear multistep block method for solving first order initial value problem of Ordinary Differential Equations (ODEs). The method calculates the numerical solution at three points simultaneously and produces three new equally spaced solution values within a block. The continuous formulations enable us to differentiate and evaluate at some selected points to obtain three discrete schemes, which were used in block form for parallel or sequential solutions of the problems. A stability analysis and efficiency of the block method are tested on ordinary differential equations involving practical applications, and the results obtained compared favorably with the exact solution. Furthermore, comparison of error analysis has been developed with the help of computer software.

Keywords: block method, first order ordinary differential equations, linear multistep, self-starting

Procedia PDF Downloads 294

Authors: Cherifi Mehdi, Lahdir Mourad, Ameur Soltane

Abstract:

Image compression is used to reduce the number of bits required to represent an image. The Meteosat Second Generation satellite (MSG) allows the acquisition of 12 image files every 15 minutes. Which results a large databases sizes. The transform selected in the images compression should contribute to reduce the data representing the images. The Radon transform retrieves the Radon points that represent the sum of the pixels in a given angle for each direction. Linear predictive coding (LPC) with filtering provides a good decorrelation of Radon points using a Predictor constitute by the Symmetric Nearest Neighbor filter (SNN) coefficients, which result losses during decompression. Finally, Run Length Coding (RLC) gives us a high and fixed compression ratio regardless of the input image. In this paper, a novel image compression method based on the Radon transform and linear predictive coding (LPC) for MSG images is proposed. MSG image compression based on the Radon transform and the LPC provides a good compromise between compression and quality of reconstruction. A comparison of our method with other whose two based on DCT and one on DWT bi-orthogonal filtering is evaluated to show the power of the Radon transform in its resistibility against the quantization noise and to evaluate the performance of our method. Evaluation criteria like PSNR and the compression ratio allows showing the efficiency of our method of compression.

Keywords: image compression, radon transform, linear predictive coding (LPC), run lengthcoding (RLC), meteosat second generation (MSG)

Procedia PDF Downloads 402

Authors: Shouji Yujiro, Memei Dukovic, Mist Yakubu

Abstract:

Fields are important objects of study in algebra since they provide a useful generalization of many number systems, such as the rational numbers, real numbers, and complex numbers. In particular, the usual rules of associativity, commutativity and distributivity hold. Fields also appear in many other areas of mathematics; see the examples below. When abstract algebra was first being developed, the definition of a field usually did not include commutativity of multiplication, and what we today call a field would have been called either a commutative field or a rational domain. In contemporary usage, a field is always commutative. A structure which satisfies all the properties of a field except possibly for commutativity, is today called a division ring ordivision algebra or sometimes a skew field. Also non-commutative field is still widely used. In French, fields are called corps (literally, body), generally regardless of their commutativity. When necessary, a (commutative) field is called corps commutative and a skew field-corps gauche. The German word for body is Körper and this word is used to denote fields; hence the use of the blackboard bold to denote a field. The concept of fields was first (implicitly) used to prove that there is no general formula expressing in terms of radicals the roots of a polynomial with rational coefficients of degree 5 or higher. An extension of a field k is just a field K containing k as a subfield. One distinguishes between extensions having various qualities. For example, an extension K of a field k is called algebraic, if every element of K is a root of some polynomial with coefficients in k. Otherwise, the extension is called transcendental. The aim of Galois Theory is the study of algebraic extensions of a field. Given a field k, various kinds of closures of k may be introduced. For example, the algebraic closure, the separable closure, the cyclic closure et cetera. The idea is always the same: If P is a property of fields, then a P-closure of k is a field K containing k, having property, and which is minimal in the sense that no proper subfield of K that contains k has property P. For example if we take P (K) to be the property ‘every non-constant polynomial f in K[t] has a root in K’, then a P-closure of k is just an algebraic closure of k. In general, if P-closures exist for some property P and field k, they are all isomorphic. However, there is in general no preferable isomorphism between two closures.

Keywords: field theory, mechanic maths, supertech, rolltech

Procedia PDF Downloads 356

Authors: Arka Roy, Chandra Prakash Dubey

Abstract:

Inverse problem generally used for recovering hidden information from outside available data. Vertical component of gravity field we will be going to use for underneath density structure calculation. Ill-posing nature is main obstacle for any inverse problem. Linear regularization using Tikhonov formulation are used for appropriate choice of SVD and GSVD components. For real time data handle, signal to noise ratios should have to be less for reliable solution. In our study, 2D and 3D synthetic model with rectangular grid are used for gravity field calculation and its corresponding inversion for density reconstruction. Fine grid also we have considered to hold any irregular structure. Keeping in mind of algebraic ambiguity factor number of observation point should be more than that of number of data point. Picard plot is represented here for choosing appropriate or main controlling Eigenvalues for a regularized solution. Another important study is depth resolution plot (DRP). DRP are generally used for studying how the inversion is influenced by regularizing or discretizing. Our further study involves real time gravity data inversion of Vredeforte Dome South Africa. We apply our method to this data. The results include density structure is in good agreement with known formation in that region, which puts an additional support of our method.

Keywords: depth resolution plot, gravity inversion, Picard plot, SVD, Tikhonov formulation

Procedia PDF Downloads 198

Authors: Xu Runzhang, Yang Yanbing, Niu Yi, Zhang Mingyou, Liu Yu

Abstract:

For a class of semilinear parabolic equations with linear dynamical boundary conditions in a bounded domain, we obtain both global solutions and finite time blow-up solutions when the initial data varies in the phase space H1(Ω). Our main tools are the comparison principle, the potential well method and the concavity method. In particular, we discuss the behavior of the solutions with the initial data at critical and high energy level.

Keywords: high energy level, critical energy level, linear dynamical boundary condition, semilinear parabolic equation

Procedia PDF Downloads 426

Authors: W. R. Li, J. K. Xia, R. Q. Peng, Z. Y. Guo, L. Jiang

Abstract:

According to 3D magnetic circuit of the transverse flux PM linear machine, distribution law is presented, and analytical expression of axial end flux leakage is derived using numerical method. Maxwell stress tensor is used to solve detent force of mover. A 3D finite element model of the transverse flux PM machine is built to analyze the flux distribution and detent force. Experimental results of the prototype verified the validity of axial end flux leakage and detent force theoretical derivation, the research on axial end flux leakage and detent force provides a valuable reference to other types of linear machine.

Keywords: axial end flux leakage, detent force, flux distribution, transverse flux PM linear machine

Procedia PDF Downloads 431

Authors: Sachin Kumar

Abstract:

Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

Procedia PDF Downloads 184

Authors: Hyun-Woo Cho

Abstract:

Unexpected events may occur with serious impacts on industrial process. This work utilizes a data representation technique to model and to analyze process data pattern for the purpose of diagnosis. In this work, the use of triangular representation of process data is evaluated using simulation process. Furthermore, the effect of using different pre-treatment techniques based on such as linear or nonlinear reduced spaces was compared. This work extracted the fault pattern in the reduced space, not in the original data space. The results have shown that the non-linear technique based diagnosis method produced more reliable results and outperforms linear method.

Keywords: process monitoring, data analysis, pattern modeling, fault, nonlinear techniques

Procedia PDF Downloads 377

Authors: Sergio Haram Sarmiento, Arcady Ponosov

Abstract:

Based on appropriate multivariate statistical methodology, we suggest a generic framework for efficient parameter estimation for ordinary differential equations and the corresponding nonlinear models. In this framework classical linear regression strategies is refined into a nonlinear regression by a locally linear modelling technique (known as metamodelling). The approach identifies those latent variables of the given model that accumulate most information about it among all approximations of the same dimension. The method is applied to several benchmark problems, in particular, to the so-called ”power-law systems”, being non-linear differential equations typically used in Biochemical System Theory.

Keywords: principal component analysis, generalized law of mass action, parameter estimation, metamodels

Procedia PDF Downloads 501

Authors: S. Oudjemia, F. Alim, S. Seddiki

Abstract:

This paper shows the application of multifractal analysis for additional help in cancer diagnosis. The medical image processing is a very important discipline in which many existing methods are in search of solutions to real problems of medicine. In this work, we present results of multifractal analysis of brain MRI images. The purpose of this analysis was to separate between healthy and cancerous tissue of the brain. A nonlinear method based on multifractal detrending moving average (MFDMA) which is a generalization of the detrending fluctuations analysis (DFA) is used for the detection of abnormalities in these images. The proposed method could make separation of the two types of brain tissue with success. It is very important to note that the choice of this non-linear method is due to the complexity and irregularity of tumor tissue that linear and classical nonlinear methods seem difficult to characterize completely. In order to show the performance of this method, we compared its results with those of the conventional method box-counting.

Keywords: irregularity, nonlinearity, MRI brain images, multifractal analysis, brain tumor

Procedia PDF Downloads 431

Authors: Ibnorachid Zakaria, El Bikri Khalid, Benamar Rhali, Farah Abdoun

Abstract:

The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave like Euler-Bernoulli beams while the core layer like a Timoshenko beam. Based on Hamilton’s principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters for a clamped-clamped and simple supported-simple-supported beams. The effects of material properties and geometric parameters on the natural frequencies are also investigated.

Keywords: linear vibration, sandwich, shear deformation, Timoshenko zig-zag model

Procedia PDF Downloads 460

Authors: Yuchen Yang, Zhenming Wang, Jun Zhu, Ning Zhao

Abstract:

An easy-to-implement and robust finite volume multi-resolution Weighted Essentially Non-Oscillatory (WENO) scheme is proposed on adaptive cartesian grids in this paper. Such a multi-resolution WENO scheme is combined with the ghost cell immersed boundary method (IBM) and wall-function technique to solve Navier-Stokes equations. Unlike the k-exact finite volume WENO schemes which involve large amounts of extra storage, repeatedly solving the matrix generated in a least-square method or the process of calculating optimal linear weights on adaptive cartesian grids, the present methodology only adds very small overhead and can be easily implemented in existing edge-based computational fluid dynamics (CFD) codes with minor modifications. Also, the linear weights of this adaptive finite volume multi-resolution WENO scheme can be any positive numbers on condition that their sum is one. It is a way of bypassing the calculation of the optimal linear weights and such a multi-resolution WENO scheme avoids dealing with the negative linear weights on adaptive cartesian grids. Some benchmark viscous problems are numerical solved to show the efficiency and good performance of this adaptive multi-resolution WENO scheme. Compared with a second-order edge-based method, the presented method can be implemented into an adaptive cartesian grid with slight modification for big Reynolds number problems.

Keywords: adaptive mesh refinement method, finite volume multi-resolution WENO scheme, immersed boundary method, wall-function technique.

Procedia PDF Downloads 137

Authors: Jia Li, Huacong Li, Xiaobao Han

Abstract:

Due to the more variable geometry parameters of VCE (variable cycle aircraft engine), presents an adaptive controller method based on the full-state linear model of VCE and has simulated to solve the multivariate controller design problem of the whole flight envelops. First, analyzes the static and dynamic performances of bypass ratio and other state parameters caused by variable geometric components, and develops nonlinear component model of VCE. Then based on the component model, through small deviation linearization of main fuel (Wf), the area of tail nozzle throat (A8) and the angle of rear bypass ejector (A163), setting up multiple linear model which variable geometric parameters can be inputs. Second, designs the adaptive controllers for VCE linear models of different nominal points. Among them, considering of modeling uncertainties and external disturbances, derives the adaptive law by lyapunov function. The simulation results showed that, the adaptive controller method based on full-state linear model used the angle of rear bypass ejector as input and effectively solved the multivariate control problems of VCE. The performance of all nominal points could track the desired closed-loop reference instructions. The adjust time was less than 1.2s, and the system overshoot was less than 1%, at the same time, the errors of steady states were less than 0.5% and the dynamic tracking errors were less than 1%. In addition, the designed controller could effectively suppress interference and reached the desired commands with different external random noise signals.

Keywords: variable cycle engine (VCE), full-state linear model, adaptive control, by-pass ratio

Procedia PDF Downloads 306

Authors: Tunjo Perič, Marin Fatović

Abstract:

In this paper a new methodology for vendor selection and supply quotas determination (VSSQD) is proposed. The problem of VSSQD is solved by the model that combines revised weighting method for determining the objective function coefficients, and a multiple objective linear programming (MOLP) method based on the cooperative game theory for VSSQD. The criteria used for VSSQD are: (1) purchase costs and (2) product quality supplied by individual vendors. The proposed methodology is tested on the example of flour purchase for a bakery with two decision makers.

Keywords: cooperative game theory, multiple objective linear programming, revised weighting method, vendor selection

Procedia PDF Downloads 342

Authors: Carlos A. Vega-Posada, Jeisson Alejandro Higuita-Villa, Julio C. Saldarriaga-Molina

Abstract:

This paper presents a simplified analytical approach to conduct elastic stability and second-order lateral stiffness analyses of beam-column elements (i.e., piles) with generalized end-boundary conditions embedded on a homogeneous or non-homogeneous Pasternak foundation. The solution is derived using the well-known Differential Transformation Method (DTM), and it consists simply of solving a system of two linear algebraic equations. Using other conventional approaches to solve the governing differential equation of the proposed element can be cumbersome and the solution challenging to implement, especially when the non-homogeneity of the soil is considered. The proposed formulation includes the effects of i) any rotational or lateral transverse spring at the ends of the pile, ii) any external transverse load acting along the pile, iii) soil non-homogeneity, and iv) the second-parameter of the elastic foundation (i.e., shear layer connecting the springs at the top). A parametric study is conducted to investigate the effects of different modulus of subgrade reactions, degrees of non-homogeneities, and intermediate end-boundary conditions on the pile response. The same set of equations can be used to conduct both elastic stability and static analyses. Comprehensive examples are presented to show the simplicity and practicability of the proposed method.

Keywords: elastic stability, second-order lateral stiffness, soil-non-homogeneity, pile analysis

Procedia PDF Downloads 199

Authors: Ibrahim Ali, Adamu Danlami Ahmed

Abstract:

This study examines the impact of depreciation on taxable income and financial performance of consumer goods companies quoted on the Nigerian stock exchange. The study adopts ex-post factor research design. Data were collected using a secondary source. The findings of the study suggest that, method of depreciation adopted in any organization influence the taxable profit. Depreciation techniques can either be: depressive, accelerative and linear depreciation. It was also recommended that consumer goods should adjust their method of depreciation to make sure an appropriate method is adopted. This will go a long way to revitalize their taxable profit.

Keywords: accelerated, linear, depressive, depreciation

Procedia PDF Downloads 262

Authors: Mamyrbek A. Beisenbi, Nurgul M. Kissikova, Saltanat E. Beisembina, Salamat T. Suleimenova, Samal A. Kaliyeva

Abstract:

The paper proposes a method for constructing a self-organizing control system for unstable and deterministic chaotic processes in the class of catastrophe “hyperbolic umbilic” for objects with m-inputs and n-outputs. The self-organizing control system is investigated by the universal gradient-velocity method of Lyapunov vector functions. The conditions for self-organization of the control system in the class of catastrophes “hyperbolic umbilic” are shown in the form of a system of algebraic inequalities that characterize the aperiodic robust stability in the stationary states of the system.

Keywords: gradient-velocity method of Lyapunov vector-functions, hyperbolic umbilic, self-organizing control system, stability

Procedia PDF Downloads 125

Authors: Davood Rajabi, Mojgan Yazdani

Abstract:

Non-linear Muskingum model is an efficient method for flood routing, however, the efficiency of this method is influenced by three applied parameters. Therefore, efficiency assessment of Imperialist Competition Algorithm (ICA) to evaluate optimum parameters of non-linear Muskingum model was addressed through this study. In addition to ICA, Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) were also used aiming at an available criterion to verdict ICA. In this regard, ICA was applied for Wilson flood routing; then, routing of two flood events of DoAab Samsami River was investigated. In case of Wilson flood that the target function was considered as the sum of squared deviation (SSQ) of observed and calculated discharges. Routing two other floods, in addition to SSQ, another target function was also considered as the sum of absolute deviations of observed and calculated discharge. For the first floodwater based on SSQ, GA indicated the best performance, however, ICA was on first place, based on SAD. For the second floodwater, based on both target functions, ICA indicated a better operation. According to the obtained results, it can be said that ICA could be used as an appropriate method to evaluate the parameters of Muskingum non-linear model.

Keywords: Doab Samsami river, genetic algorithm, imperialist competition algorithm, meta-exploratory algorithms, particle swarm optimization, Wilson flood

Procedia PDF Downloads 492

Authors: Emad K. Jaradat, Ala’a Al-Faqih

Abstract:

Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two-dimensional Schrodinger equation

Procedia PDF Downloads 175

Authors: Ih-Ching Hsu

Abstract:

Inspired by the so called Jacobi Identity (x y) z + (y z) x + (z x) y = 0, the following class of functional equations EQ I: F [F (x, y), z] + F [F (y, z), x] + F [F (z, x), y] = 0 is proposed, researched and generalized. Research methodologies begin with classical methods for functional equations, then evolve into discovering of any implicit algebraic structures. One of this paper’s major findings is that EQ I, under two additional conditions F (x, x) = 0 and F (x, y) + F (y, x) = 0, proves to be a fundamental functional equation for Lie Algebras. Existence of non-trivial solutions for EQ I can be proven by defining F (p, q) = [p q] = pq –qp, where p and q are quaternions, and pq is the quaternion product of p and q. EQ I can be generalized to the following class of functional equations EQ II: F [G (x, y), z] + F [G (y, z), x] + F [G (z, x), y] = 0. Concluding Statement: With a major finding proven, and non-trivial solutions derived, this research paper illustrates and provides a new functional equation scheme for studies in two major areas: (1) What underlying algebraic structures can be defined and/or derived from EQ I or EQ II? (2) What conditions can be imposed so that conditional general solutions to EQ I and EQ II can be found, investigated and applied?

Keywords: fundamental functional equation, generalized functional equations, Lie algebras, quaternions

Procedia PDF Downloads 214

Authors: Ishapathik Das

Abstract:

The purpose of this article is to find a method of comparing designs for ordinal regression models using quantile dispersion graphs in the presence of linear predictor misspecification. The true relationship between response variable and the corresponding control variables are usually unknown. Experimenter assumes certain form of the linear predictor of the ordinal regression models. The assumed form of the linear predictor may not be correct always. Thus, the maximum likelihood estimates (MLE) of the unknown parameters of the model may be biased due to misspecification of the linear predictor. In this article, the uncertainty in the linear predictor is represented by an unknown function. An algorithm is provided to estimate the unknown function at the design points where observations are available. The unknown function is estimated at all points in the design region using multivariate parametric kriging. The comparison of the designs are based on a scalar valued function of the mean squared error of prediction (MSEP) matrix, which incorporates both variance and bias of the prediction caused by the misspecification in the linear predictor. The designs are compared using quantile dispersion graphs approach. The graphs also visually depict the robustness of the designs on the changes in the parameter values. Numerical examples are presented to illustrate the proposed methodology.

Keywords: model misspecification, multivariate kriging, multivariate logistic link, ordinal response models, quantile dispersion graphs

Procedia PDF Downloads 377

Authors: Jan-Tore H. Horn, Jørgen Juncher Jensen

Abstract:

Uncertainties related to fatigue damage estimation of non-linear systems are highly dependent on the tail behaviour and extreme values of the stress range distribution. By using a combination of the First Order Reliability Method (FORM) and Monte Carlo simulations (MCS), the accuracy of the fatigue estimations may be improved for the same computational efforts. The method is applied to a bottom-fixed, monopile-supported large offshore wind turbine, which is a non-linear and dynamically sensitive system. Different curve fitting techniques to the fatigue damage distribution have been used depending on the sea-state dependent response characteristics, and the effect of a bi-linear S-N curve is discussed. Finally, analyses are performed on several environmental conditions to investigate the long-term applicability of this multistep method. Wave loads are calculated using state-of-the-art theory, while wind loads are applied with a simplified model based on rotor thrust coefficients.

Keywords: fatigue damage, FORM, monopile, Monte Carlo, simulation, wind turbine

Procedia PDF Downloads 246