Using Krylov-Padé model order reduction for accelerating design optimization of structures and vibrations in the frequency domain

2012 ◽  
Vol 90 (10) ◽  
pp. 1207-1232 ◽  
Author(s):  
Yao Yue ◽  
Karl Meerbergen
Keyword(s):  
Design Optimization ◽  
Frequency Domain ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Model Order

scholarly journals Rational Approximations of Arbitrary Order: A Survey

2021 ◽  
Vol 5 (4) ◽  
pp. 267
Author(s):  
José Daniel Colín-Cervantes ◽  
Carlos Sánchez-López ◽  
Rocío Ochoa-Montiel ◽  
Delia Torres-Muñoz ◽  
Carlos Manuel Hernández-Mejía ◽  
...  
Keyword(s):  
Frequency Domain ◽  
Approximation Method ◽  
Model Order Reduction ◽  
Reduction Method ◽  
Arbitrary Order ◽  
Order Reduction ◽  
Synthesis Process ◽  
Rational Approximations ◽  
Model Order ◽  
Advantages And Disadvantages

This paper deals with the study and analysis of several rational approximations to approach the behavior of arbitrary-order differentiators and integrators in the frequency domain. From the Riemann–Liouville, Grünwald–Letnikov and Caputo basic definitions of arbitrary-order calculus until the reviewed approximation methods, each of them is coded in a Maple 18 environment and their behaviors are compared. For each approximation method, an application example is explained in detail. The advantages and disadvantages of each approximation method are discussed. Afterwards, two model order reduction methods are applied to each rational approximation and assist a posteriori during the synthesis process using analog electronic design or reconfigurable hardware. Examples for each reduction method are discussed, showing the drawbacks and benefits. To wrap up, this survey is very useful for beginners to get started quickly and learn arbitrary-order calculus and then to select and tune the best approximation method for a specific application in the frequency domain. Once the approximation method is selected and the rational transfer function is generated, the order can be reduced by applying a model order reduction method, with the target of facilitating the electronic synthesis.

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