Optimal Sensor Placement for Structural Health Monitoring of Buildings Using a Kalman Filter-Based Approach

This study proposes a Kalman filter-based method to optimize the placement of accelerometers in buildings, formulated as a multi-objective problem that simultaneously minimizes the number of sensors and the state estimation error. State-space equations of 3-, 9-, 15-, and 30-story buildings were developed from a simplified continuous beam model, allowing the method to be evaluated across different structural conditions. The trace of the state error covariance matrix (Tr(P)) was employed as the performance metric, showing a strong correlation with the signal-to-noise ratio (SNR) and the normalized absolute estimation error. The results highlight that measurement noise critically affects sensor placement. As the noise covariance increases, estimation uncertainty grows, and more sensors are required, often concentrated in specific structural regions. Conversely, high-sensitivity low-noise sensors reduce uncertainty, though at a higher sensor unit cost. Maintaining an SNR above 10 dB proved essential to ensure reliable operational modal analysis. Optimal layouts tended to concentrate on upper floors, where accelerations and SNR are higher, avoiding redundant sensors at modal nodes or lower levels. Validation under real and synthetic excitations, including the 2010 Concepción ground motion record and band-limited white noise, confirmed that the method can accurately identify the fundamental frequencies of the structures. These findings demonstrate the effectiveness of the proposed Kalman filter-based methodology for optimizing sensor layouts in structural health monitoring applications under realistic operational conditions.