Fast Transient Stability Solution Approach Combining Taylor Series Expansion and Energy Function

1987 ◽  
Vol 20 (5) ◽  
pp. 13-18
Author(s):  
S. Iwamoto ◽  
S. Furuya ◽  
H. Suzuki
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Energy Function ◽  
Transient Stability ◽  
Taylor Series Expansion ◽  
Solution Approach ◽  
Fast Transient

Extraction of Dunham Coefficients from Murrell-Sorbie Parameters

2008 ◽  
Vol 63 (1-2) ◽  
pp. 1-6 ◽  
Author(s):  
Teik-Cheng Lim
Keyword(s):  
Potential Energy ◽  
Bond Length ◽  
Potential Function ◽  
Series Expansion ◽  
Taylor Series ◽  
Energy Function ◽  
Taylor Series Expansion ◽  
Potential Energy Function ◽  
Reliable Data ◽  
Equilibrium Bond Length

A set of relationships between parameters of the Dunham and Murrell-Sorbie potential energy function is developed. By employing Taylor series expansion and comparison of terms arranged in increasing order of bond length, a set of Dunham coefficients is obtained as functions of Murrell- Sorbie parameters. The conversion functions reveal the importance of factorials in extracting Dunham coefficients from Murrell-Sorbie parameters. Plots of both functions, based on parameters of the latter, reveal good correlation near the equilibrium bond length for a group of diatomic molecules. Potential function relations, such as that shown in this paper, are useful when the preferred/reliable data is based on a potential function different from that adopted in available computational software.

Full-Scale Bounds Estimation for the Nonlinear Transient Heat Transfer Problems with Interval Uncertainties

2021 ◽  
pp. 2150026
Author(s):  
Ruifei Peng ◽  
Haitian Yang ◽  
Yanni Xue
Keyword(s):  
Heat Transfer ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Transient Heat Transfer ◽  
High Fidelity ◽  
Interval Scale ◽  
Nonlinear Transient ◽  
Transfer Problems ◽  
Derivatives Of

A package solution is presented for the full-scale bounds estimation of temperature in the nonlinear transient heat transfer problems with small or large uncertainties. When the interval scale is relatively small, an efficient Taylor series expansion-based bounds estimation of temperature is stressed on the acquirement of first and second-order derivatives of temperature with high fidelity. When the interval scale is relatively large, an optimization-based approach in conjunction with a dimension-adaptive sparse grid (DSG) surrogate is developed for the bounds estimation of temperature, and the heavy computational burden of repeated deterministic solutions of nonlinear transient heat transfer problems can be efficiently alleviated by the DSG surrogate. A temporally piecewise adaptive algorithm with high fidelity is employed to gain the deterministic solution of temperature, and is further developed for recursive adaptive computing of the first and second-order derivatives of temperature. Therefore, the implementation of Taylor series expansion and the construction of DSG surrogate are underpinned by a reliable numerical platform. The parallelization is utilized for the construction of DSG surrogate for further acceleration. The accuracy and efficiency of the proposed approaches are demonstrated by two numerical examples.

scholarly journals Weighted Measurement Fusion Particle Filter for Nonlinear Systems with Correlated Noises

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3242 ◽  
Author(s):  
Ke Wei Zhang ◽  
Gang Hao ◽  
Shu Li Sun
Keyword(s):  
Nonlinear Systems ◽  
Particle Filter ◽  
Series Expansion ◽  
Taylor Series ◽  
Asymptotic Optimality ◽  
Taylor Series Expansion ◽  
Full Rank ◽  
Expansion Method ◽  
Least Square ◽  
Correlated Noises

The multi-sensor information fusion particle filter (PF) has been put forward for nonlinear systems with correlated noises. The proposed algorithm uses the Taylor series expansion method, which makes the nonlinear measurement functions have a linear relationship by the intermediary function. A weighted measurement fusion PF (WMF-PF) was put forward for systems with correlated noises by applying the full rank decomposition and the weighted least square theory. Compared with the augmented optimal centralized fusion particle filter (CF-PF), it could greatly reduce the amount of calculation. Moreover, it showed asymptotic optimality as the Taylor series expansion increased. The simulation examples illustrate the effectiveness and correctness of the proposed algorithm.

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