Dynamic Deformation Analysis of Super High-Rise Buildings Based on GNSS and Accelerometer Fusion

To accurately capture the dynamic displacement of super-tall buildings under complex conditions, this study proposes a data fusion algorithm that integrates NRBO-FMD optimization with Adaptive Robust Kalman Filtering (ARKF). The NRBO-FMD method preprocesses GNSS and accelerometer data to mitigate GNSS multipath effects, unmodeled errors, and high-frequency noise in accelerometer signals. Subsequently, ARKF fuses the preprocessed data to achieve high-precision displacement reconstruction. Numerical simulations under varying noise conditions validated the algorithm's accuracy. Field experiments conducted on the Hairong Square Building in Changchun further demonstrated its effectiveness in estimating three-dimensional dynamic displacement. Key findings are as follows: (1) The NRBO-FMD algorithm significantly reduced noise while preserving essential signal characteristics. For GNSS data, the root mean square error (RMSE) was reduced to 0.7 mm for the 100 s dataset and 1.0 mm for the 200 s dataset, with corresponding signal-to-noise ratio (SNR) improvements of 3.0 dB and 6.0 dB. For accelerometer data, the RMSE was reduced to 3.0 mm (100 s) and 6.2 mm (200 s), with a 4.1 dB SNR gain. (2) The NRBO-FMD-ARKF fusion algorithm achieved high accuracy, with RMSE values of 0.7 mm (100 s) and 1.9 mm (200 s). Consistent PESD and POSD values demonstrated the algorithm's long-term stability and effective suppression of irregular errors. (3) The algorithm successfully fused 1 Hz GNSS data with 100 Hz accelerometer data, overcoming the limitations of single-sensor approaches. The fusion yielded an RMSE of 3.6 mm, PESD of 2.6 mm, and POSD of 4.8 mm, demonstrating both precision and robustness. Spectral analysis revealed key dynamic response frequencies ranging from 0.003 to 0.314 Hz, facilitating natural frequency identification, structural stiffness tracking, and early-stage performance assessment. This method shows potential for improving the integration of GNSS and accelerometer data in structural health monitoring. Future work will focus on real-time and predictive displacement estimation to enhance monitoring responsiveness and early-warning capabilities.