Interval predictor model: Difference between revisions

Revision as of 13:33, 8 August 2022

Revision as of 17:40, 31 July 2023

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Interval Predictor Models are sometimes referred to as a [[nonparametric regression]] technique, because a potentially infinite set of functions are contained by the IPM, and no specific distribution is implied for the regressed variables.

Multiple-input multiple-output IPMs for multi-point data commonly used to represent functions have been recently developed.<ref>{{cite journalbook | doi=10.1109/CDC45484.2021.9683582 | chapter=Interval Predictor Models for Robust System Identification | title=2021 60th IEEE Conference on Decision and Control (CDC) | year=2021 | last1=Crespo | first1=Luis G. | last2=Kenny | first2=Sean P. | last3=Colbert | first3=Brendon K. | last4=Slagel | first4=Tanner |title pages=Interval872–879 Predictor| Models for Robust System Identificationisbn=978-1-6654-3659-5 |journal=IEEE CDC 2021 |dates2cid=December246479771 2021}}</ref> These IPM prescribe the parameters of the model as a path-connected, semi-algebraic set using sliced-normal <ref>{{cite journal |last1=Crespo |first1=Luis |last2=Colbert |first2=Brendon |last3=Kenny |first3=Sean |last4=Giesy |first4=Daniel |title=On the quantification of aleatory and epistemic uncertainty using Sliced-Normal distributions |journal=Systems and Control Letters |date=2019 |volume=34 |page=104560 |doi=10.1016/j.sysconle.2019.104560 |s2cid=209339118 |url=https://doi.org/10.1016/j.sysconle.2019.104560}}</ref> or sliced-exponential distributions.<ref>{{cite journalbook | doi=10.1109/CDC45484.2021.9683584 | chapter=Robust Estimation of Sliced-Exponential Distributions^⋆ | title=2021 60th IEEE Conference on Decision and Control (CDC) | year=2021 | last1=Crespo | first1=Luis G. | last2=Colbert | first2=Brendon K. | last3=Slager | first3=Tanner | last4=Kenny | first4=Sean P. |title pages=Robust6742–6748 Estimation| of Slicedisbn=978-Exponential Distributions1-6654-3659-5 |journal=IEEE CDC |dates2cid=December246476974 2021}}</ref> A key advantage of this approach is its ability to characterize complex parameter dependencies to varying fidelity levels. This practice enables the analyst to adjust the desired level of conservatism in the prediction.

As a consequence of the theory of [[scenario optimization]], in many cases rigorous predictions can be made regarding the performance of the model at test time.<ref name="CampiCalafiore2009">{{cite journal|last1=Campi|first1=M.C.|last2=Calafiore|first2=G.|last3=Garatti|first3=S.|title=Interval predictor models: Identification and reliability|journal=Automatica|volume=45|issue=2|year=2009|pages=382–392|issn=0005-1098|doi=10.1016/j.automatica.2008.09.004}}</ref>

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Initially, [[scenario optimization]] was applied to robust control problems.<ref name="CampiGaratti2009">{{cite journal|last1=Campi|first1=Marco C.|last2=Garatti|first2=Simone|last3=Prandini|first3=Maria|author3-link= Maria Prandini |title=The scenario approach for systems and control design|journal=Annual Reviews in Control|volume=33|issue=2|year=2009|pages=149–157|issn=1367-5788|doi=10.1016/j.arcontrol.2009.07.001}}</ref>

Crespo (2015) and (2021) applied Interval Predictor Models to the design of space radiation shielding <ref name="CrespoKenny2016a">{{cite book|last1=Crespo|first1=Luis G.|title=18th AIAA Non-Deterministic Approaches Conference|last2=Kenny|first2=Sean P.|last3=Giesy|first3=Daniel P.|last4=Norman|first4=Ryan B.|last5=Blattnig|first5=Steve|chapter=Application of Interval Predictor Models to Space Radiation Shielding|year=2016|doi=10.2514/6.2016-0431|isbn=978-1-62410-397-1|hdl=2060/20160007750|s2cid=124192684 }}</ref> and to system identification.<ref>{{cite journalbook | doi=10.1109/CDC45484.2021.9683582 | chapter=Interval Predictor Models for Robust System Identification | title=2021 60th IEEE Conference on Decision and Control (CDC) | year=2021 | last1=Crespo | first1=Luis G. | last2=Kenny | first2=Sean P. | last3=Colbert | first3=Brendon K. | last4=Slagel | first4=Tanner |title pages=Interval872–879 Predictor Models for Robust| System Identification |journalisbn=IEEE978-1-6654-3659-5 CDC| 2021 |dates2cid=December246479771 2021}}</ref>

In Patelli (2017), Faes (2019), and Crespo (2018), Interval Predictor models were applied to the [[structural reliability]] analysis problem.<ref name="PatelliBroggi2017">{{cite book|last1=Patelli|first1=Edoardo|title=Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2017)|last2=Broggi|first2=Matteo|last3=Tolo|first3=Silvia|last4=Sadeghi|first4=Jonathan|year=2017|pages=212–224|doi=10.7712/120217.5364.16982|chapter=Cossan Software: A Multidisciplinary and Collaborative Software for Uncertainty Quantification|isbn=978-618-82844-4-9}}</ref>