References in raw/Page_2.html

• Modified affine arithmetic is more accurate than centered interval arithmetic or affine arithmetic
  H Shou, H Lin, R Martin, G Wang - Mathematics of surfaces, 2003 - Springer
  ... Test results show that modified affine arithmetic is not only more accurate but also much faster than standard affine arithmetic. We thus suggest that modified affine arithmetic is the ...
  

• A generalization of p-boxes to affine arithmetic
  O Bouissou, E Goubault, J Goubault-Larrecq, S Putot - Computing, 2012 - Springer
  ... In this article, we define a new arithmetic that combines affine arithmetic to propagate the linear relations between random variables and p-box arithmetic to overapproximate the ...
  

• A novel affine arithmetic method to solve optimal power flow problems with uncertainties
  M Pirnia, CA Cañizares... - IEEE Transactions on ..., 2014 - ieeexplore.ieee.org
  An affine arithmetic (AA) method is proposed in this paper to solve the optimal power flow (OPF) problem with uncertain generation sources. In the AA-based OPF problem, all the state ...
  

• An affine arithmetic-based energy management system for isolated microgrids
  D Romero-Quete, CA Cañizares - IEEE Transactions on Smart ..., 2018 - ieeexplore.ieee.org
  This paper presents a mathematical formulation of an energy management system (EMS) for isolated microgrids, which addresses uncertainty using the affine arithmetic (AA) method. ...
  

• Floating-point error analysis based on affine arithmetic
  CF Fang, T Chen, RA Rutenbar - 2003 IEEE International ..., 2003 - ieeexplore.ieee.org
  ... We present a novel approach based on affine arithmetic, a recent development in range ... Based on the affine arithmetic (AA) model in range arithmetic, we present our AA-based ...
  

• Uncertainty tracing of distributed generations via complex affine arithmetic based unbalanced three-phase power flow
  S Wang, L Han, L Wu - IEEE Transactions on Power Systems, 2014 - ieeexplore.ieee.org
  ... This paper proposes a complex affine arithmetic based unbalanced three-phase power flow solution to explore the impacts of DG uncertainties on distribution systems. Based on the ...
  

• True worst-case circuit tolerance analysis using genetic algorithms and affine arithmetic
  N Femia, G Spagnuolo - ... Transactions on Circuits and Systems I ..., 2000 - ieeexplore.ieee.org
  ... It is based on the joint use of genetic algorithms (GAs) and affine arithmetic (AA). The GAs are ... , it is shown that the problem can be afforded more efficiently using the Affine Arithmetic. ...
  

• An affine arithmetic-based algorithm for radial distribution system power flow with uncertainties
  W Gu, L Luo, T Ding, X Meng, W Sheng - International Journal of Electrical ..., 2014 - Elsevier
  ... Concepts of affine arithmetic In affine arithmetic, a quantity x is represented by an expression of the form(1) x ˆ = x 0 + x 1 ε 1 + ⋯ + x n ε n which is an affine expression of noise symbols ...
  

• An affine arithmetic-based framework for uncertain power flow and optimal power flow studies
  A Vaccaro, CA Canizares - IEEE Transactions on Power ..., 2016 - ieeexplore.ieee.org
  This paper proposes a unified framework based on affine arithmetic for computing reliable enclosures of uncertain power flow (PF) and optimal power flow (OPF) solutions. The main ...
  

• Fast ray tracing of arbitrary implicit surfaces with interval and affine arithmetic
  A Knoll, Y Hijazi, A Kensler, M Schott... - Computer Graphics ..., 2009 - Wiley Online Library
  ... Ray tracing algorithms employing interval arithmetic (IA) or affine arithmetic (AA) for root-... , as well as an inclusion-preserving reduced affine arithmetic (RAA) for faster ray-surface ...