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\begin{document}

\title{Robust adaptive Kalman filter for structural health monitoring}



\author[1]{Shenglun Yi}%
\author[2]{Tingli Su}%
\author[3]{ZhenYun Tang}%
\affil[1]{Universita degli Studi di Padova Dipartimento di Ingegneria Dell'Informazione}%
\affil[2]{Beijing Technology and Business University}%
\affil[3]{Beijing University of Technology}%


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  \date{June 15, 2024}


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\begin{abstract}
Health monitoring is critical for the maintenance and risk management of
reinforced concrete (RC) structures. In this paper, a robust adaptive
Kalman filter is proposed for an interstory drift estimation problem to
show the health condition of RC structures in the case that the
statistics or internal dynamics describing the signals and measurements
are not known precisely. More precisely, we build an adaptive current
Jerk model (ACJM) where the model parameters are updated in each time
step to presuppose the statistics characterization of the RC dynamic,
while the unknown measurement noise covariance is adapted based on a
fixed-lag innovation with respect to measurements. Moreover, a robust
adaptive Kalman filter is designed for the modeling mismatch in each
time increment by solving a minimax game: one ``hostile'' player tries
to select a worst model far from the proposed ACJM with an exponential
decay tolerance, while an optimum filter is designed by minimizing the
estimation error according to this worst model. Finally, some simulation
and experimental results show the effectiveness of the proposed
algorithm.%
\end{abstract}%



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