Xiao Xingxing, Han Houzeng, Wang Jian, Li Dong, Chen Cai, Wang Lei
School of Geomatics and Urban Spatial Informatics, Beijing University of Civil Engineering and Architecture, Beijing 102616, China.
Research Center for Urban Big Data Applications, Beijing University of Civil Engineering and Architecture, Beijing 100044, China.
Sensors (Basel). 2025 Apr 23;25(9):2659. doi: 10.3390/s25092659.
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.
为了准确捕捉复杂条件下超高层建筑的动态位移，本研究提出了一种将NRBO - FMD优化与自适应鲁棒卡尔曼滤波（ARKF）相结合的数据融合算法。NRBO - FMD方法对全球导航卫星系统（GNSS）和加速度计数据进行预处理，以减轻GNSS多径效应、未建模误差以及加速度计信号中的高频噪声。随后，ARKF对预处理后的数据进行融合，以实现高精度的位移重建。在不同噪声条件下的数值模拟验证了该算法的准确性。在长春海容广场大厦进行的现场实验进一步证明了其在估计三维动态位移方面的有效性。主要发现如下：（1）NRBO - FMD算法在保留基本信号特征的同时显著降低了噪声。对于GNSS数据，100秒数据集的均方根误差（RMSE）降至0.7毫米，200秒数据集的RMSE降至1.0毫米，相应的信噪比（SNR）分别提高了3.0分贝和6.0分贝。对于加速度计数据，RMSE降至3.0毫米（100秒）和6.2毫米（200秒），SNR增益为4.1分贝。（2）NRBO - FMD - ARKF融合算法实现了高精度，RMSE值为0.7毫米（100秒）和1.9毫米（200秒）。一致的位置误差标准差（PESD）和位置标准差（POSD）值证明了该算法的长期稳定性以及对不规则误差的有效抑制。（3）该算法成功地将1赫兹的GNSS数据与100赫兹的加速度计数据进行了融合，克服了单传感器方法的局限性。融合后的RMSE为3.6毫米，PESD为2.6毫米，POSD为4.8毫米，显示出精度和鲁棒性。频谱分析揭示了关键动态响应频率范围为0.003至0.314赫兹，有助于识别固有频率、跟踪结构刚度和进行早期性能评估。该方法在改善结构健康监测中GNSS和加速度计数据的融合方面显示出潜力。未来的工作将集中在实时和预测性位移估计上，以提高监测响应能力和预警能力。
