Automatic Formant Tracking by a Newton‐Raphson Technique

In real situations all observations and measurements are not exact numbers but more or less non-exact, also called fuzzy. So, in this paper, we use approximate non-Bayesian computational methods to estimate inverse Weibull parameters and reliability function with fuzzy data. The maximum likelihood and moment estimations are obtained as non-Bayesian estimation. The maximum likelihood estimators have been derived numerically based on two iterative techniques namely “Newton-Raphson” and the “Expectation-Maximization” techniques. In addition, we provide compared numerically through Monte-Carlo simulation study to obtained estimates of the parameters and reliability function in terms of their mean squared error values and integrated mean squared error values respectively.

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Axisymmetric flow near the critical point on the moving boundary

Proceedings of the Mavlyutov Institute of Mechanics ◽

10.21662/uim2010.1.016 ◽

2010 ◽

Vol 7 ◽

pp. 182-190

Author(s):

I.Sh. Nasibullayev ◽

E.Sh. Nasibullaeva

Keyword(s):

Fluid Flow ◽

Finite Difference ◽

Boundary Conditions ◽

Numerical Solution ◽

Axial Velocity ◽

Moving Boundary ◽

Axisymmetric Flow ◽

Boundary Motion ◽

Newton Raphson ◽

Raphson Method

In this paper the investigation of the axisymmetric flow of a liquid with a boundary perpendicular to the flow is considered. Analytical equations are derived for the radial and axial velocity and pressure components of fluid flow in a pipe of finite length with a movable right boundary, and boundary conditions on the moving boundary are also defined. A numerical solution of the problem on a finite-difference grid by the iterative Newton-Raphson method for various velocities of the boundary motion is obtained.

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A Class of Decision Processes Showing Policy-Improvement/Newton–Raphson Equivalence

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964800001261 ◽

1989 ◽

Vol 3 (3) ◽

pp. 397-403 ◽

Cited By ~ 1

Author(s):

P. Whittle

Keyword(s):

Optimality Condition ◽

Regularity Condition ◽

Decision Processes ◽

Policy Improvement ◽

Improvement Algorithm ◽

Newton Raphson ◽

Raphson Algorithm

A condition expressed in Eq. (7) is given which, with one simplifying regularity condition, ensures that the policy-improvement algorithm is equivalent to application of the Newton–Raphson algorithm to an optimality condition. It is shown that this condition covers the two known cases of such equivalence, and another example is noted. The condition is believed to be necessary to within transformations of the problem, but this has not been proved.

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A Generalized Compositional Approach for Reservoir Simulation

Society of Petroleum Engineers Journal ◽

10.2118/10516-pa ◽

1983 ◽

Vol 23 (05) ◽

pp. 727-742 ◽

Cited By ~ 84

Author(s):

Larry C. Young ◽

Robert E. Stephenson

Keyword(s):

Enhanced Recovery ◽

Gas Condensate ◽

Reservoir Modeling ◽

Pressure Equation ◽

Compositional Modeling ◽

Fluid Property ◽

Black Oil ◽

Fluid Properties ◽

Newton Raphson ◽

Raphson Method

A procedure for solving compositional model equations is described. The procedure is based on the Newton Raphson iteration method. The equations and unknowns in the algorithm are ordered in such a way that different fluid property correlations can be accommodated leadily. Three different correlations have been implemented with the method. These include simplified correlations as well as a Redlich-Kwong equation of state (EOS). The example problems considered area conventional waterflood problem,displacement of oil by CO, andthe displacement of a gas condensate by nitrogen. These examples illustrate the utility of the different fluid-property correlations. The computing times reported are at least as low as for other methods that are specialized for a narrower class of problems. Introduction Black-oil models are used to study conventional recovery techniques in reservoirs for which fluid properties can be expressed as a function of pressure and bubble-point pressure. Compositional models are used when either the pressure. Compositional models are used when either the in-place or injected fluid causes fluid properties to be dependent on composition also. Examples of problems generally requiring compositional models are primary production or injection processes (such as primary production or injection processes (such as nitrogen injection) into gas condensate and volatile oil reservoirs and (2) enhanced recovery from oil reservoirs by CO or enriched gas injection. With deeper drilling, the frequency of gas condensate and volatile oil reservoir discoveries is increasing. The drive to increase domestic oil production has increased the importance of enhanced recovery by gas injection. These two factors suggest an increased need for compositional reservoir modeling. Conventional reservoir modeling is also likely to remain important for some time. In the past, two separate simulators have been developed and maintained for studying these two classes of problems. This result was dictated by the fact that compositional models have generally required substantially greater computing time than black-oil models. This paper describes a compositional modeling approach paper describes a compositional modeling approach useful for simulating both black-oil and compositional problems. The approach is based on the use of explicit problems. The approach is based on the use of explicit flow coefficients. For compositional modeling, two basic methods of solution have been proposed. We call these methods "Newton-Raphson" and "non-Newton-Raphson" methods. These methods differ in the manner in which a pressure equation is formed. In the Newton-Raphson method the iterative technique specifies how the pressure equation is formed. In the non-Newton-Raphson method, the composition dependence of certain ten-ns is neglected to form the pressure equation. With the non-Newton-Raphson pressure equation. With the non-Newton-Raphson methods, three to eight iterations have been reported per time step. Our experience with the Newton-Raphson method indicates that one to three iterations per tune step normally is sufficient. In the present study a Newton-Raphson iteration sequence is used. The calculations are organized in a manner which is both efficient and for which different fluid property descriptions can be accommodated readily. Early compositional simulators were based on K-values that were expressed as a function of pressure and convergence pressure. A number of potential difficulties are inherent in this approach. More recently, cubic equations of state such as the Redlich-Kwong, or Peng-Robinson appear to be more popular for the correlation Peng-Robinson appear to be more popular for the correlation of fluid properties. SPEJ p. 727

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