Numerical Computation for MRE (Magnetic Resonance Elasticity) by Applying Numerical Differentiation Method

2008 ◽  
Keyword(s):  
Magnetic Resonance ◽  
Numerical Computation ◽  
Numerical Differentiation ◽  
Differentiation Method

Case studies of choosing a numerical differentiation method under uncertainty

1996 ◽  
Vol 31 (3) ◽  
pp. 9-26
Author(s):  
Andrei M. Finkelstein ◽  
Misha Koshelev
Keyword(s):  
Case Studies ◽  
Numerical Differentiation ◽  
Differentiation Method

A numerical differentiation method and its application to reconstruction of discontinuity

2002 ◽  
Vol 18 (6) ◽  
pp. 1461-1476 ◽  
Author(s):  
Y B Wang ◽  
X Z Jia ◽  
J Cheng
Keyword(s):  
Numerical Differentiation ◽  
Differentiation Method

Bond graph model-based fault detection using residual sinks

2008 ◽  
Vol 223 (3) ◽  
pp. 337-352 ◽  
Author(s):  
W Borutzky
Keyword(s):  
Fault Detection ◽  
Numerical Computation ◽  
Graph Model ◽  
Numerical Differentiation ◽  
Equation System ◽  
Bond Graph ◽  
Engineering System ◽  
Differential Algebraic Equation ◽  
Symbolic Form ◽  
Model Based

In this paper, residual sinks are used in bond graph model-based quantitative fault detection for the coupling of a model of a faultless process engineering system to a bond graph model of the faulty system. By this way, integral causality can be used as the preferred computational causality in both models. There is no need for numerical differentiation. Furthermore, unknown variables do not need to be eliminated from power continuity equations in order to obtain analytical redundancy relations (ARRs) in symbolic form. Residuals indicating faults are computed numerically as components of a descriptor vector of a differential algebraic equation system derived from the coupled bond graphs. The presented bond graph approach especially aims at models with non-linearities that make it cumbersome or even impossible to derive ARRs from model equations by elimination of unknown variables. For illustration, the approach is applied to a non-controlled as well as to a controlled hydraulic two-tank system. Finally, it is shown that not only the numerical computation of residuals but also the simultaneous numerical computation of their sensitivities with respect to a parameter can be supported by bond graph modelling.

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