In the steam boiler industrial sector, pressure and temperature of the water tube are the two main factors that affect the safety and efficiency of a steam boiler. Explosions may be occurring because of a sudden drop in pressure without a corresponding drop in temperature. Therefore, understanding the temperature distribution of the water tube boiler is essential to control the failure and explosion of the boiler. Once the temperature distribution is known than the limiting factors that affect the water tube life such as the maximum allowable pressure can be determined. ANSYS software will be used to determine the temperature distribution in the water tube of a utility boiler during operation at elevated inlet water and furnace temperature. The theory of axisymmetric has been utilized since the water- tube is cylindrical in shape. In axisymmetric theory, a three-dimensional cylindrical problem like a water tube can be reduced to two-dimensional by ignoring the circumferential Ө, while the r-axis and z-axis became x-axis and y-axis or Cartesian coordinate. Then two-dimensional rectangular elements meshing for the profile cross-section along the water tube in r and z axes were implemented in a computerized simulation using ANSYS 10 to find out the steady-state temperature distribution of the water tube.
The conditional, unconditional, or the exact maximum likelihood estimation and the least-squares estimation involve minimizing either the conditional or the unconditional residual sum of squares. The maximum likelihood estimation (MLE) approach and the nonlinear least squares (NLS) procedure involve an iterative search technique for obtaining global rather than local optimal estimates. Several authors have presented brief overviews of algorithms for solving NLS problems. Snezana S. Djordjevic (2019) presented a review of some unconstrained optimization methods based on the line search techniques. Mahaboob et al. (2017) proposed a different approach to estimate nonlinear regression models using numerical methods also based on the line search techniques. Mohammad, Waziri, and Santos (2019) have briefly reviewed methods for solving NLS problems, paying special attention to the structured quasi-Newton methods which are the family of the search line techniques. Ya-Xiang Yuan (2011) reviewed some recent results on numerical methods for nonlinear equations and NLS problems based on online searches and trust regions techniques, particularly on Levenberg-Marquardt type methods, quasi-Newton type methods, and trust regions algorithms. The purpose of this paper is to review some online searches and trust region's more well-known robust numerical optimization algorithms and the most used in practice for the estimation of time series models and other nonlinear regression models. The line searches algorithms considered are: Gradient algorithm, Steepest Descent (SD) algorithm, Newton-Raphson (NR) algorithm, Murray’s algorithm, Quasi-Newton (QN) algorithm, Gauss-Newton (GN) algorithm, Fletcher and Powell algorithm (FP), Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. While the only trust-region algorithm considered is the Levenberg-Marquardt (LM) algorithm. We also give some main advantages and disadvantages of these different algorithms.
Densities and viscosities of binary and ternary electrolytes solution have been determined experimentally at 298.15 K. The results obtained from density and viscosity measurement have been used to calculate apparent molar volume φv partial molar volume φov at infinite dilution, relative viscosities hrel, A and B coefficients, and free energies of activation of viscous flow of solvent Δ µ10# and solute Δ µ20. The results are discussed in terms of the dehydration effect of the weak ion-ion and strong ion-solvent interactions. The properties of these systems are discussed in terms of the charge, size, and hydrogen bonding effect.
We propose in this paper a fast and iterative algorithm for estimating the parameters of a Gaussian vector autoregressive-moving average (VARMA) model. This algorithm is a multivariate generalization of that suggested by Sabiti (1996) for estimating the parameters of a univariate ARMA(p,q) process. It is proposed, mainly for providing initial estimators for the iterative maximization of a log-likelihood function. Comparisons about the number of computations in terms of multiplication operations are made with a method that uses gradients to locate a maximum of the likelihood function and the fast method suggested by Spliid (1983).
