RESEARCH ARTICLE Adaptive constrained unscented Kalman filtering for real‐time nonlinear structural system identification Andrea Calabrese 1 | Salvatore Strano 2 | Mario Terzo 2 1 Civil Engineering and Construction Engineering Management (CECEM), California State University, Long Beach, CA, USA 2 Department of Industrial Engineering, University of Naples Federico II, Naples 80125, Italy Correspondence Salvatore Strano, Department of Industrial Engineering, University of Naples Federico II, Naples 80125, Italy. Email: salvatore.strano@unina.it Summary The unscented Kalman filter (UKF) is often used for nonlinear system identifi- cation in civil engineering; nevertheless, the application of the UKF to highly nonlinear structures could not provide accurate results. In this paper, an improvement of the UKF algorithm has been adopted. This methodology can consider state constraints, and it can estimate the measurement noise covari- ance matrix. The results obtained adopting a modified UKF have been com- pared to the ones obtained using the UKF for parameter estimation of a single degree of freedom nonlinear hysteretic system. The second part of this work shows results of an experimental activity on a base‐isolated prototype structure. Both numerical and experimental results underline that the adopted algorithm produces better state estimation and parameter identification than the UKF, being capable of taking into account parameter boundaries. The adopted algorithm is more robust than the standard UKF in the case of measur- ing noise variation. KEYWORDS adaptive Kalman filter—nonlinear system identification, constrained unscented Kalman filter, hysteresis, structural dynamics 1 | INTRODUCTION The identification of nonlinear structural systems is a common task in civil engineering. For example, several methods for damage detection and monitoring of civil engineering structures are based on parametric identification algorithms suitable for nonlinear structural elements. [1–3] Various techniques have been developed for nonlinear structural system identification, including least squares estimation, Monte Carlo filter, extended Kalman filter (EKF), unscented Kalman filter (UKF), and others. [4–11] The time‐domain methods, such as the least squares estimation, perform an optimization for parameters such as stiffness and damping through a minimization of the errors between the measured and the sim- ulated responses, [12] but the procedure is time consuming and it is generally considered not suitable for real‐time appli- cations of structural health monitoring and damage detection. Monte Carlo filter often requires a very large number of sample points, being high computationally demanding. Among the different methods, the UKF is the most adopted tech- nique for structural dynamics identification with many successful applications. [13–18] Despite the fact that the UKF outperforms the other methods, especially in presence of very noisy measurements, some deficiencies still remain. One of the most important deficiencies of UKF is the impossibility of taking into account bounds and other constraints on state variables. The constraints can be useful as a remediation for inaccurate system modeling, which often happens in real‐world applications. As a consequence, many approaches have been developed Received: 18 November 2016 Revised: 1 June 2017 Accepted: 20 July 2017 DOI: 10.1002/stc.2084 Struct Control Health Monit. 2017;e2084. https://doi.org/10.1002/stc.2084 Copyright © 2017 John Wiley & Sons, Ltd. wileyonlinelibrary.com/journal/stc 1 of 17