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Set-membership nonlinear regression approach to parameter estimation
File(s)
Author(s)
Peric, Nikola
Paulen, Radoslav
Villanueva, Mario E
Chachuat, B
Type
Journal Article
Abstract
This paper introduces set-membership nonlinear regression (SMR), a new approach to nonlinear regression under uncertainty. The problem is to determine the subregion in parameter space enclosing all (global) solutions to a nonlinear regression problem in the presence of bounded uncertainty on the observed variables. Our focus is on nonlinear algebraic models. We investigate the connections of SMR with (i) the classical statistical inference methods, and (ii) the usual set-membership estimation approach where the model predictions are constrained within bounded measurement errors. We also develop a computational framework to describe tight enclosures of the SMR regions using semi-infinite programming and complete-search methods, in the form of likelihood contour and polyhedral enclosures. The case study of a parameter estimation problem in microbial growth is presented to illustrate various theoretical and computational aspects of the SMR approach.
Date Issued
2018-10-01
Date Acceptance
2018-04-09
Citation
Journal of Process Control, 2018, 70, pp.80-95
URI
URL
DOI
ISSN
0959-1524
Publisher
Elsevier
Start Page
80
End Page
95
Journal / Book Title
Journal of Process Control
Volume
70
Copyright Statement
© 2018 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
License URL
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Identifier
https://www.sciencedirect.com/science/article/pii/S0959152418300647?via=ihub
Grant Number
EP/K503381/1
Subjects
Science & Technology
Technology
Automation & Control Systems
Engineering, Chemical
Engineering
Parameter estimation
Nonlinear regression
Set-membership estimation
Statistical inference
Semi-infinite programming
Complete-search methods
DETERMINISTIC GLOBAL OPTIMIZATION
CONFIDENCE-REGIONS
INTERVAL-ANALYSIS
MODEL
DESIGN
UNCERTAINTY
OBSERVERS
Chemical Engineering
0904 Chemical Engineering
Publication Status
Published
Date Publish Online
2018-09-25