Auto-regressive model based input and parameter estimation for nonlinear finite element models

Juan Castiglione, Rodrigo Astroza*, Saeed Eftekhar Azam, Daniel Linzell

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


A novel framework to accurately estimate nonlinear structural model parameters and unknown external inputs (i.e., loads) using sparse sensor networks is proposed and validated. The framework assumes a time-varying auto-regressive (TAR) model for unknown loads and develops a strategy to simultaneously estimate those loads and parameters of the nonlinear model using an unscented Kalman filter (UKF). First, it is confirmed that a Kalman filter (KF) allows to estimate TAR parameters for a measured, earthquake, acceleration time-history. The KF-based framework is then coupled to an UKF to jointly identify unmeasured inputs and nonlinear finite element (FE) model parameters. The proposed approach systematically assimilates different structural response quantities to estimate TAR and FE model parameters and, as a result, updates the FE model and unknown external excitation estimates. The framework is validated using simulated experiments on a realistic three-dimensional nonlinear steel frame subjected to unknown seismic ground motion. It is demonstrated that assuming relatively low order TAR model for the unknown input leads to precise reconstruction and unbiased estimation of nonlinear model parameters that are most sensitive to measured system response.

Original languageEnglish
Article number106779
JournalMechanical Systems and Signal Processing
StatePublished - Sep 2020

Bibliographical note

Funding Information:
The authors acknowledge the support from the Chilean National Commission for Scientific and Technological Research (CONICYT), FONDECYT project No. 11160009, and from the Universidad de los Andes – Chile through FAI initiatives. SEA and DL would like to also acknowledge the support provided by NSF Award # 1762034 BD Spokes: MEDIUM: MIDWEST: Smart Big Data Pipeline for Aging Rural Bridge Transportation Infrastructure (SMARTI).

Publisher Copyright:
© 2020 Elsevier Ltd


  • Auto-regressive model
  • Finite element model
  • Input estimation
  • Kalman filter
  • Model updating


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