Master's/Ph.D Thesis

IDENTIFICATION OF OPTIMAL AUTOREGRESSIVE INTEGRATED MOVING AVERAGE MODEL FOR METEOROLOGICAL DATA

Sun, 11 Jul 2004 00:00:00 GMT

IDENTIFICATION OF OPTIMAL AUTOREGRESSIVE INTEGRATED MOVING AVERAGE MODEL FOR METEOROLOGICAL DATA OLUSOLA, SAMUEL MAKINDE Autoregressive Integrated Moving Average (ARIMA) model of various orders was presented, with a view to identifying the optimal model. In this study, ARIMA (p, d, q) model of various orders was presented in both causal and inverted forms, behavioural patterns of both causality and invertibility parameters were investigated, parameters of the models were estimated using Ordinary Least Square approach and optimal model from a class of models was identified using Normalized Bayesian Information Criterion (BIC) as model selection criterion. It was deduced that behaviour of causality parameter, ѱᵢ and invertibility parameter,π, depend on positive and negative values of auto regressive parameter ɸ and moving average parameter θ respectively. ѱᵢ is skewed to right and sinusoidal for positive and negative values of ɸ respectively. ѱᵢ of ARMA (1, q) model increases as the value of q increases for positive values of ɸ. Also, ѱ increases as ɸ increases as shown in Figure 2.4 for positive values of θ. Similarly, πᵢ, of ARIMA (p, d, 1) model for various integer values of d are sinusoidal for positive values of θ irrespective of ɸₙ's arrangement, [πᵢ] increases as d increases and the lower the integer value of d, the faster [πᵢ] converges to zero. For negative integer values of θ , πᵢ, of ARlMA (p, d, 1) model oscillates as the value of d increases with [πᵢ]d₌ ₖ < [πᵢ]d₌ ₖ ₊ ₂ for all even integer value k > 0 provided i ≥ 3 and I[πᵢ]d₌ ₖ > [πᵢ]d₌ ₖ ₊ ₂ for all odd integer value k > 0. Similarly, πᵢ, of ARIMA (p, d, I) model was found to be sinusoidal for p = 1,2,3 and 4 and d = 0 and 1 with[πᵢ] ᵨ ₌ ₄ > [πᵢ] ᵨ ₌ ₃ > [πᵢ] ᵨ ₌ ₂ > [πᵢ] ᵨ ₌ ₁ for all positive values of θ. For all negative values of θ, [πᵢ] ᵨ ₌ ₖ < [πᵢ] ᵨ ₌ ₖ ₊ ₂ for odd integer value k > 0 and [πᵢ] ᵨ ₌ ₖ < [πᵢ] ᵨ ₌ ₖ ₊ ₂ for even integer value k > 0. ARIMA (p, d, q) model was formulated for daily maximum meteorological temperature data of Ondo, Nigeria (07°06'27" N, 04°50'19" E) and Zaira, Nigeria (11°04'N, 07°42'E), daily rain amount of Calabar, Nigeria (07°06'27"N, 08°20'E) and Ondo, Nigeria (07°06'27"N, 04°50'19"E) and daily cloud of Warri, Nigeria (05°30'N, 05°41'E) and Benin City, Nigeria (07° 06'27" N, 05° 31' E) from January 1995 to December 2005. The choice of ARIMA model of orders p and q was intended to retain any persistence in natural process. To determine the performance of models, Normalized BIC was adopted. ARIMA (1, 1, 1) model was adequate-for modelling daily maximum temperature of On do, Nigeria and Zaira, Nigeria, parameters of the model was estimated and redundant variable was removed for each of the cities. Similarly for modelling daily rain amount of Calabar, Nigeria and Ondo, Nigeria, and daily cloud of Warri, Nigeria and Benin City, Nigeria, ARIMA (1, 0, 1) model was found adequate and parameters of the model were estimated. xii.: 130p.: ill.; 32cm.

DYNAMICAL ANALYSIS OF FINITE PRESTRESSED BERNOULLI-EULER BEAMS WITH GENERAL BOUNDARY CONDITIONS UNDERTRAVRLLING DISTRIBUTED LOADS

Tue, 31 Oct 2006 00:00:00 GMT

DYNAMICAL ANALYSIS OF FINITE PRESTRESSED BERNOULLI-EULER BEAMS WITH GENERAL BOUNDARY CONDITIONS UNDERTRAVRLLING DISTRIBUTED LOADS OGUNYEBI, SEGUN NATHANIEL This thesis presents the problems of dynamical analysis of finite prestressed Bernoulli-Euler beams with general boundary conditions under traveling distributed masses. The responses. of the elastic structures to moving distributed forces are special cases of such dynamical problems. The governing equation of this problem is a fourth order partial differential equation. The solution technique is based on generalized integral transforms, the use of the properties of Heaviside function H(x - ct) as the generalized derivative of the Dirac delta function 5(x - ct) in the distributed sense and a modification of the asymptotic method of Struble. By the use of this technique, one is able to obtain closed form' solutions for all variants of classical end conditions for this class of problems. The closed form solutions are analyzed and numerical analyses in plotted curves are presented. The results show that as the 'prestress value N and foundation modulli K increases, the response amplitude of the' dynamical system decreases. However, higher values of N and K are required for a more noticeable effect in the case of other boundary conditions than those of simply supported boundary condition. It is also found that for all the illustrative examples, the moving force solution is not an upper bound for the accurate solution of the moving masses problem of a uniform Bernoulli-Euler beam under the action of a uniform distributed load. This important result also agrees with similar problems that considered the moving load as a lump mass. Finally, in all the illustrative examples considered, for the same natural frequency, the critical speed for the moving mass problem is smaller than that of the moving force problem. Hence resonance is reached earlier in moving mass problem. ix.: 130p.: ill.; 32cm

DYNAMIC RESPONSE TO MOVING CONCENTRATED MASSES OF RAYLEIGH BEAMS ON VARIABLE WINKLER ELASTIC FOUNDATIONS

Thu, 31 Jul 2003 00:00:00 GMT

DYNAMIC RESPONSE TO MOVING CONCENTRATED MASSES OF RAYLEIGH BEAMS ON VARIABLE WINKLER ELASTIC FOUNDATIONS AWODOLA, THOMAS OLUBUNMI The response of Rayleigh beams carrying moving masses, resting on variable Winkler elastic foundations is investigated in this thesis. The problem is investigated for both cases of uniform and non-uniform Rayleigh beams. In each case, the governing equation is a fourth order partial differential equation. In order to solve this problem, the versatile Galerkin's method is used to reduce the governing fourth order partial differential equations with variable coefficients to a sequence of second order ordinary differential equations. For the solutions of these equations, a modification of the Struble's technique is employed. Numerical results in plotted curves are then presented. The results show that response amplitudes of the uniform Rayleigh beam decrease as the rotatory inertia correction factor R° increases for all variants of classical boundary conditions considered. These same results obtain for the non-uniform Rayleigh beams. Furthermore, for fixed value of R0,the displacements of both uniform and non-uniform Rayleigh beams resting on variable elastic foundations decrease as the foundation modulli K increases. ".' The results further show that, for fixed RO and K, the transverse deflections of both uniform and non-uniform Rayleigh beams under the actions of moving masses are higher than those when only the force effects of the moving load are considered. Therefore, the moving force solution is not a safe approximation to the moving mass problem. Hence safety is not guaranteed for a design based on the moving force solution. Also the analyses show that the response amplitudes of both moving force and moving mass problems decrease both with increasing Foundation constant and with increasing Rotatory inertia. Finally, the critical speed for the moving mass problem is reached prior to that of the moving force for both uniform and non-uniform Rayleigh beam problems in all variants of illustrative examples considered. x.: 110p.: ill.; 32cm.

DYNAMIC RESPONSE TO A MOVING LOAD OF A HIGHLY PRESTRESSED ISOTROPIC RECTANGULAR PLATE ON A BI-PARAMETRIC SUBGRADE

Mon, 07 Jul 2008 00:00:00 GMT

DYNAMIC RESPONSE TO A MOVING LOAD OF A HIGHLY PRESTRESSED ISOTROPIC RECTANGULAR PLATE ON A BI-PARAMETRIC SUBGRADE OGUNBAMIKE, OLUWATOYIN KEHINDE In this thesis, the dynamic response of a highly prestressed isotropic rectangular plate resting on a bi-parametric subgrade under the action of a moving load is investigated. In particular, the bi-parametric subgrade is the so called Pasternak foundation model. The equation of motion of the dynamical system which is a fourth order non-homogeneous partial differential equation is presented in a non-dimensionalized form. As a result of this, a small parameter E (the ratio-of bending stiffness to the axial prestress) multiplies the highest derivative in the governing partial differential equation. For an analytical solution to be obtained, the equation was subjected to Laplace transformation while the resulting partial differential equation was solved using the singular perturbation technique, specifically the Method of Matched Asymptotic Expansion (MMAE). The methods of integral transformations and the Cauchy residue theory were then used to solve the resulting partial differential equations to obtain a uniformly valid analytical solution in the entire domain of definition of the rectangular plate. Analysis of analytical solutions and numerical results in plotted curves were presented. The results show that the prestress, shear modulus and foundation stiffness affect the response to 0(£1) of the rectangular plate. Also, the critical velocities of the dynamical system increase with prestress, shear modulus and foundation stiffness. Thus, resonance is reached earlier for lower values of prestress, shear modulus and foundation stiffness. viii.: 108p.: ill.' 32cm.