Inferring the Size of Stochastic Systems from Partial Measurements

Alain Boldini, Maurizio Porfiri

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Inferring the size of a complex system from partial measurements of some of its units is a common problem in engineering, with significant applications in the field of structural health monitoring (SHM), where one may attempt at relating system size (number of degrees of freedom) to the integrity of the structure. Here, we demonstrate the possibility of inferring the size of a stochastic system by assembling measurements of its response into a detection matrix. In deterministic systems, the rank of the detection matrix (number of non-zero singular values) equals the size of the largest observable system component. We extend this framework to reconstruct the number of states of an unknown Markov chain, where we cannot distinguish between two or more states. In this case, we only have access to an estimate of the detection matrix, but with a larger rank, since stochasticity generates a series of non-zero singular values. We establish conditions for the correct inference of system size, relating the number of realizations and the smallest true singular value. Our work highlights connections between SHM, system identification, and control theory, paving the way for new cross-disciplinary inquiries.

Original languageEnglish (US)
Title of host publicationEuropean Workshop on Structural Health Monitoring, EWSHM 2022, Volume 3
EditorsPiervincenzo Rizzo, Alberto Milazzo
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages8
ISBN (Print)9783031073212
StatePublished - 2023
Event10th European Workshop on Structural Health Monitoring, EWSHM 2022 - Palermo, Italy
Duration: Jul 4 2022Jul 7 2022

Publication series

NameLecture Notes in Civil Engineering
Volume270 LNCE
ISSN (Print)2366-2557
ISSN (Electronic)2366-2565


Conference10th European Workshop on Structural Health Monitoring, EWSHM 2022


  • Markov chains
  • Networked systems
  • Stochastic systems

ASJC Scopus subject areas

  • Civil and Structural Engineering


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