On the connection betweenS-matrix and the Neumann series expansion of the wave function

1964 ◽  
Vol 31 (4) ◽  
pp. 890-903 ◽  
Author(s):  
L. Favella
Keyword(s):  
Wave Function ◽  
Series Expansion ◽  
Neumann Series ◽  
Neumann Series Expansion

Stochastic Sensitivity Analysis of Structural Systems With Interval Uncertainties

2013 ◽  
Author(s):  
Giuseppe Muscolino ◽  
Roberta Santoro ◽  
Alba Sofi
Keyword(s):  
Sensitivity Analysis ◽  
Series Expansion ◽  
Neumann Series ◽  
Mean Value ◽  
Frame Structure ◽  
Young’S Moduli ◽  
Rational Series ◽  
Power Spectral ◽  
Stochastic Sensitivity Analysis ◽  
Neumann Series Expansion

Interval sensitivity analysis of linear discretized structures with uncertain-but-bounded parameters subjected to stationary multi-correlated Gaussian stochastic processes is addressed. The proposed procedure relies on the use of the so-called Interval Rational Series Expansion (IRSE), recently proposed by the authors as an alternative explicit expression of the Neumann series expansion for the inverse of a matrix with a small rank-r modification and properly extended to handle also interval matrices. The IRSE allows to derive approximate explicit expressions of the interval sensitivities of the mean-value vector and Power Spectral Density (PSD) function matrix of the interval stationary stochastic response. The effectiveness of the proposed method is demonstrated through numerical results pertaining to a seismically excited three-storey frame structure with interval Young’s moduli of some columns.

scholarly journals Biobjective Optimization Algorithms Using Neumann Series Expansion for Engineering Design

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Huan Guo ◽  
Yoshino Tatsuo ◽  
Lulu Fan ◽  
Ao Ding ◽  
Tianshuang Xu ◽  
...  
Keyword(s):  
Series Expansion ◽  
Optimization Problems ◽  
Neumann Series ◽  
Optimization Strategy ◽  
Weighted Sum Method ◽  
Car Crash ◽  
Engineering Problems ◽  
Biobjective Optimization ◽  
Neumann Series Expansion ◽  
Novel Algorithms

In this paper, two novel algorithms are designed for solving biobjective optimization engineering problems. In order to obtain the optimal solutions of the biobjective optimization problems in a fast and accurate manner, the algorithms, which have combined Newton’s method with Neumann series expansion as well as the weighted sum method, are applied to deal with two objectives, and the Pareto optimal front is achieved through adjusting weighted factors. Theoretical analysis and numerical examples demonstrate the validity and effectiveness of the proposed algorithms. Moreover, an effective biobjective optimization strategy, which is based upon the two algorithms and the surrogate model method, is developed for engineering problems. The effectiveness of the optimization strategy is proved by its application to the optimal design of the dummy head structure in the car crash experiments.

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