Advanced Model-Order Reduction Techniques for Large Scale Dynamical Systems

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Nouri, Seyed Behzad




Model Order Reduction (MOR) has proven to be a powerful and necessary tool for various
applications such as circuit simulation. In the context of MOR, there are some unaddressed
issues that prevent its efficient application, such as “reduction of multiport networks” and
“optimal order estimation” for both linear and nonlinear circuits. This thesis presents the
solutions for these obstacles to ensure successful model reduction of large-scale linear and
nonlinear systems.
This thesis proposes a novel algorithm for creating efficient reduced-order macromodels
from multiport linear systems
(e.g. massively coupled interconnect structures). The new
algorithm addresses the difficulties associated with the reduction of networks with large
numbers of input/output terminals, that often result in large and dense reduced-order models.
The application of the proposed reduction algorithm leads to reduced-order models
that are sparse and block-diagonal in nature. It does not assume any correlation between
the responses at ports; and thereby overcomes the accuracy degradation that is normally associated
with the existing (Singular Value Decomposition based) terminal reduction
Estimating an optimal order for the reduced linear models is of crucial importance to ensure
accurate and efficient transient behavior. Order determination is known to be a challenging
task and is often based on heuristics. Guided by geometrical considerations, a novel and
efficient algorithm is presented to determine the minimum sufficient order that ensures the
accuracy and efficiency of the reduced linear models.
The optimum order estimation for nonlinear MOR is extremely important. This is mainly
due to the fact that, the nonlinear functions in circuit equations should
be computed in the
original size within the iterations of the transient analysis. As a result, ensuring both accuracy
and efficiency becomes a cumbersome task. In response to this reality, an efficient
algorithm for nonlinear order determination is presented. This is achieved by adopting the
geometrical approach to nonlinear systems, to ensure the accuracy and efficiency in transient
Both linear and nonlinear optimal order estimation methods are not dependent on any specific
order reduction algorithm and can work in conjunction with any intended reduced
modeling technique.


Engineering - Electronics and Electrical




Carleton University

Thesis Degree Name: 

Doctor of Philosophy: 

Thesis Degree Level: 


Thesis Degree Discipline: 

Engineering, Electrical and Computer

Parent Collection: 

Theses and Dissertations

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