## 5 Conclusions and Topics for Future Study  
In this paper, a novel methodology was proposed to track sudden damage of structural system under dynamic excitations using sparse measurements. First, the state-space model often used for the purpose of parameter estimation was modified to handle time-variant system parameters. The regularization term was also introduced to avoid divergence of estimation caused by sparse noisy measurements. Second, the master-slave Kalman filter for measurement noise estimation (MS-KF\({}_{\text{ME}}\)) was utilized to adapt to time-varying status of the target system. The unscented Kalman filter (UKF) as master filter estimates the status of target system parameters while a linear Kalman filter (LKF) as slave filter estimates the covariance of artificial measurement noise in UKF through a covariance-matching technique. Lastly, particle swarm optimization (PSO) was exploited to tune the artificial noises of MS-KF\({}_{\text{ME}}\) with practical considerations. To test the proposed methodology, sets of structural response data were simulated for a shear-building system subjected to two real earthquake ground motion time histories. Several damage scenarios were introduced based on the simulated data such as peak values of inter-story drifts. For comparison purposes, the normal-UKF and adaptive UKF, which control artificial process noise, were conducted with sparse noisy measurements. Unlike the other two methods, the  
Figure 12: Estimation by MS-KF\({}_{\text{ME}}\): Scenario 3\({}^{\prime}\) with RMS-noise 5%.  
Figure 13: Estimation by MS-KF\({}_{\text{ME}}\): Scenario 4\({}^{\prime}\) with RMS-noise 5%.  
proposed method provided accurate estimation of sudden damage in system parameters even if the corresponding parameter's response was missing. These results demonstrated the potential of the proposed method for practical applications.  
In general, it is critical to tune filter methods to obtain near-optimal estimation results. Especially, the tuning process of MS-KFME is known to be sensitive to choices of covariance matrices of artificial noises for master and slave filter. Even if the number of tuning parameters is reduced to just two parameters through the recommended assumptions, it is impossible to determine the tuning parameters empirically. To this end, this paper utilizes particle swarm optimization (PSO). The PSO-based tuning process is affected by choice of boundary conditions, and thus it is essential to perform PSO repeatedly to find the best tuning parameters.  
It is recommended to further explore the use of an efficient global optimization method to avoid assumptions that were introduced to reduce the number of tuning parameters. If so, a tuning process of dual adaptive filter will be more flexible to adapt to practical applications. In addition, the slave filter in this paper used the covariance-matching technique as a state-space model. The matching technique depends on differences between actual and theoretical covariance while structural knowledge is not exploited. Because of this limited capability of covariance-matching technique from SI point of view, some important structural information may not be revealed accurately, which causes slow convergence into accurate values or biased estimations. To infer meaningful information appropriately from sparse noisy measurements, the latest machine-learning techniques and Bayesian methods could provide a suitable state-space model for the slave filter.  
[PERSON]-[PERSON] designed this paper, and performed numerical investigations; [PERSON] reviewed and edited the manuscript. All authors read and approved this manuscript.  
This research was funded by the National Research Foundation of Korea, grant number 0583-20190026.  
The second author would like to acknowledge the support by the Institute of Construction and Environmental Engineering at Seoul National University.  
The authors declare no conflict of interest.