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New strategies in model order reduction of trajectory piecewise‐linear models
Author(s) -
Mohseni Seyed Saleh,
Yazdanpanah Mohammad Javad,
Ranjbar N. Abolfazl
Publication year - 2015
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.2131
Subject(s) - projection (relational algebra) , reduction (mathematics) , linearization , model order reduction , matrix (chemical analysis) , weighting , piecewise linear function , linear model , mathematical optimization , mathematics , nonlinear system , computer science , trajectory , algorithm , statistics , medicine , physics , geometry , materials science , quantum mechanics , astronomy , composite material , radiology
Abstract Model order reduction based on trajectory piecewise linearization (TPWL) is a beneficial technique for approximating nonlinear models. One efficient method for building projection matrix in TPWL reduction is by aggregation of projection matrices of linearization points (LPs). However, in this method, the size of projection matrix will also grow up by increasing the number of LPs, which yield the increment of the size of reduced model. In other words, the size of reduced model will depend on the number of LPs. In this paper, we will address this issue and propose two new strategies for obviating this problem. Contrarily to former works in TPWL modeling, we established a model via TWPL based on output weighting of parallel linear models. Then, we proposed two reduction strategies for suggested TPWL model. The first algorithm inspires from former works in this field but in a parallel structure that enable segregation of projection matrices whereas the second algorithm remedies the problem by considering the high‐order TPWL model as a unit linear model and reduces this model like a linear model but uses back projection method for constructing different outputs. The efficiency of methods is shown by comparison with former TPWL methods through vast simulations. Copyright © 2015 John Wiley & Sons, Ltd.