Limited-Time Convergent ZNN for Computing Time-Dependent Complex-Valued Matrix Pseudoinverse

2019 ◽  
Author(s):  
Yihui Lei ◽  
Bolin Liao ◽  
Jialiang Chen
Keyword(s):  
Computing Time ◽  
Time Dependent ◽  
Limited Time ◽  
Complex Valued ◽  
Matrix Pseudoinverse

scholarly journals A Noise-Acceptable ZNN for Computing Complex-Valued Time-Dependent Matrix Pseudoinverse

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 13832-13841 ◽  
Author(s):  
Yihui Lei ◽  
Bolin Liao ◽  
Qingfei Yin
Keyword(s):  
Time Dependent ◽  
Complex Valued ◽  
Matrix Pseudoinverse

scholarly journals Noise-Resistant Discrete-Time Neural Dynamics for Computing Time-Dependent Lyapunov Equation

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 45359-45371 ◽  
Author(s):  
Qiuhong Xiang ◽  
Weibing Li ◽  
Bolin Liao ◽  
Zhiguan Huang
Keyword(s):  
Discrete Time ◽  
Computing Time ◽  
Lyapunov Equation ◽  
Time Dependent ◽  
Neural Dynamics

Analytic Wellbore Temperature Model for Transient Gas-Well Testing

2005 ◽  
Vol 8 (03) ◽  
pp. 240-247 ◽  
Author(s):  
A. Rashid Hasan ◽  
C. Shah Kabir ◽  
Dongqing Lin
Keyword(s):  
Steady State ◽  
Transient Analysis ◽  
Computing Time ◽  
Time Dependent ◽  
Well Testing ◽  
Fluid Temperature ◽  
Gas Wells ◽  
Gas Well ◽  
Gas Density ◽  
Analytic Expressions

Summary Questions arise whether bottomhole pressures (BHPs), derived from their wellhead counterpart (WHP), lend themselves to transient analysis. That is because considerable heat exchange may affect the wellbore-density profile, thereby making the WHP translation a nontrivial exercise. In other words, gas density is dependent on both spatial locations in the wellbore and time during transient testing. Fully coupled wellbore/reservoir simulators are available to tackle this situation. However, they are not readily adaptable for their numeric formulations. This paper presents analytic expressions, derived from first principles, for computing time-dependent fluid temperature at any point in the wellbore during both drawdown and buildup testing. The simplicity of the analytic expressions for Tf (z, t) is profound in that one can compute flowing or shut-in BHPs on a spreadsheet. Two tests were considered to verify the new analytic formulae. In one case, measurements were available at both sandface and surface, and partial wellhead information was available in the other case. We explored a parametric study to assess whether a given wellbore/reservoir system will lend itself to wellhead measurements for valid transient analysis. Reservoir flow capacity (kh) turned out to be the most influential variable. Introduction Gas-well testing is sometimes conducted by measuring pressures at the wellhead. Both cost and circumstance (high pressure/high temperature, or HP/HT)often necessitate WHP monitoring or running the risk of having no tests at all. Methods for computing BHP from wellhead pressures for steady flow in gas wells are well established in the literature. For dry-gas wells, the widely used method of Cullender and Smith is most accurate, as confirmed by subsequent studies. For wet gas, either a two-phase model, such as the one offered by Govier and Fogarasi, or the modified Cullender-Smith approach appears satisfactory. However, these methods apply to steady-state gas flow and implicitly presuppose that the wellbore is in thermal equilibrium with the formation. These assumptions may be tested during a transient test. That is because unsteady-state wellbore heat transfer occurs even after the cessation of the wellbore-fluid-storage period. Steady-state fluid flow ordinarily implies the absence of wellbore effects from the viewpoint of transient testing. Consequently, one needs to develop working equations by conserving mass, momentum, and energy in the wellbore to capture physical phenomena. Earlier, we presented a forward model and showed its capability to reproduce BHP, WHP, and wellhead temperature (WHT) given reservoir and wellbore parameters. However, translation of WHP to BHP was not demonstrated clearly. The intent of this work is to present a framework for rigorous computation of BHP from WHP. To achieve this objective, we developed analytic expressions for depth- and time-dependent fluid temperature during both flow and shut-in tests. These temperature relations, in turn, allow computation of gas density and, therefore, pressure at any point in the wellbore.

A Procedure for Comparing Groups of Time-Dependent Measurements

1979 ◽  
Vol 18 (02) ◽  
pp. 84-88 ◽  
Author(s):  
H. Prestele ◽  
W. Gaus ◽  
L. Horbach
Keyword(s):  
Spline Function ◽  
Computing Time ◽  
Smooth Curve ◽  
Cubic Spline ◽  
Repeated Measurements ◽  
Time Dependent ◽  
Longitudinal Methods ◽  
Time Points ◽  
Calculation Of Parameters ◽  
Natural Cubic Spline

A three stop procedure is proposed for the comparison of groups, where for each individual a process is investigated on the basis of repeated measurements (e.g. 3 up to about 15 time points).1. A natural cubic spline function is fitted to the time-dependent measurements of each individual. A cubic spline is a function which is composed of piecewise polynomials, continuous up to and including second derivatives; it has a minimal »curvature«, so that a »smooth« curve is generated.2. For each individual the value of a problem-oriented parameter is estimated from the spline function.3. The values of the problem-oriented parameter are evaluated with standard, not necessarily longitudinal methods for estimating and hypothesis testing.The proposed procedure requires neither an equal number of measurements for each individual, nor the same time points of measurement for all individuals, nor equal length of the time intervals. Splines can be fitted to very different patterns of curves. They can be used for a more exact calculation of parameters adequate to the problem concerned. The procedure necessitates the use of a computer; programs are available and do not demand excessive arithmetic precision and computing time.

A theoretical study on the response of a point elasto-hydrodynamic lubrication contact to a normal harmonic vibration under thermal and non-Newtonian conditions

2007 ◽  
Vol 221 (9) ◽  
pp. 1089-1110 ◽  
Author(s):  
P Yang ◽  
J Cui ◽  
J M Jin ◽  
D Dowson
Keyword(s):  
Steady State ◽  
Numerical Solutions ◽  
Hydrodynamic Lubrication ◽  
Computing Time ◽  
Harmonic Vibration ◽  
Time Dependent ◽  
Processing Unit ◽  
Infinite Plane ◽  
Shear Strain Rate ◽  
Newtonian Flow

Time-dependent thermal and non-Newtonian elastohydrodynamic lubrication of an elliptical point contact subjected to a normal harmonic vibration was studied numerically in this work. The contact was idealized as between an infinite plane and a spherical roller. The normal vibration of the roller was described by specifying the centre of the spherical roller to the infinite plane (without deformation) as a cyclic function of time. The shear-thinning rheological property of the lubricant was described by the Eyring model. The time-dependent numerical solution was achieved instant after instant in each period of a vibration. The periodic errors were checked at the end of each vibration cycle until the responses of variables such as pressure, film thickness, and temperature were all periodic functions with the same frequency of the roller's vibration. At each instant, the pressure field was solved with a multi-grid method, the surface deflection produced by pressure was determined with a multi-level multi-integration technique, the non-Newtonian flow of the lubricant was considered by using the equivalent viscosity calculated according to the shear-strain rate along the entrainment direction only, and the temperature field was evaluated with a finite-difference scheme through a column-by-column relaxation process. The computing time for a cyclic solution was 12–15 h on a personal computer with a 3.0 GHz central processing unit. The effects of both the amplitude and the frequency of the vibration were investigated. It was shown that the time-dependent solution is significantly different from the steady-state solution, especially when the amplitude of vibration is large and the frequency of vibration is high. Corresponding to a typical thermal and non-Newtonian case, numerical solutions were also obtained under isothermal and Newtonian, isothermal and non-Newtonian, and thermal and Newtonian conditions. Comparisons between these solutions indicate that, under time-dependent conditions, the effects of thermal and non-Newtonian flow are similar to those under steady-state conditions.

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