New method for efficient Monte Carlo–Neumann solution of linear stochastic systems

2015 ◽  
Vol 40 ◽  
pp. 90-96 ◽  
Author(s):  
C.R. Avila da S. ◽  
A.T. Beck
Keyword(s):  
Monte Carlo ◽  
Stochastic Systems ◽  
New Method ◽  
Linear Stochastic Systems

A Fast Convergence Parameter for Monte Carlo–Neumann Solution of Linear Stochastic Systems

2015 ◽  
Vol 1 (2) ◽  
Author(s):  
Cláudio R. Ávila da Silva ◽  
André Teófilo Beck
Keyword(s):  
Monte Carlo ◽  
Stochastic Systems ◽  
Uncertainty Propagation ◽  
Neumann Series ◽  
Fast Convergence ◽  
System Matrix ◽  
Convergence Parameter ◽  
Linear Stochastic Systems ◽  
Beam Bending ◽  
Distance Minimization

The Neumann series is a well-known technique to aid the solution of uncertainty propagation problems. However, convergence of the Neumann series can be very slow, often making its use highly inefficient. In this article, a fast convergence parameter (λ) convergence parameter is introduced, which yields accurate and efficient Monte Carlo–Neumann (MC-N) solutions of linear stochastic systems using first-order Neumann expansions. The λ convergence parameter is found as a solution to the distance minimization problem, for an approximation of the inverse of the system matrix using the Neumann series. The method presented herein is called Monte Carlo–Neumann with λ convergence, or simply the MC-N λ method. The accuracy and efficiency of the MC-N λ method are demonstrated in application to stochastic beam-bending problems.

UGR CALCULATION BASED ON THE LUMINANCE SPATIAL-ANGULAR DISTRIBUTION

2020 ◽  
Vol 2020 (4) ◽  
pp. 25-32
Author(s):  
Viktor Zheltov ◽  
Viktor Chembaev
Keyword(s):  
Monte Carlo ◽  
Angular Distribution ◽  
Monte Carlo Method ◽  
Visual Task ◽  
New Method ◽  
Lighting System ◽  
Preliminary Assessment ◽  
System A ◽  
The Monte Carlo Method

The article has considered the calculation of the unified glare rating (UGR) based on the luminance spatial-angular distribution (LSAD). The method of local estimations of the Monte Carlo method is proposed as a method for modeling LSAD. On the basis of LSAD, it becomes possible to evaluate the quality of lighting by many criteria, including the generally accepted UGR. UGR allows preliminary assessment of the level of comfort for performing a visual task in a lighting system. A new method of "pixel-by-pixel" calculation of UGR based on LSAD is proposed.

The stochastic observability for noisy non-linear stochastic systems†

1975 ◽  
Vol 22 (4) ◽  
pp. 461-480 ◽  
Author(s):  
YOSHIFUMI SUNAHARA ◽  
SHIN'ICHl AIHARA ◽  
MASAYUKI SHIRAIWA
Keyword(s):  
Stochastic Systems ◽  
Linear Stochastic Systems ◽  
Non Linear
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