###### Abstract  
Structural monitoring is crucial for assessing structural health, and high-precision deformation prediction can provide early warnings for safety monitoring. To address the issue of low prediction accuracy caused by the non-stationary and nonlinear characteristics of deformation sequences, this paper proposes a similarity clustering (SC) deformation prediction model based on GNSS/accelerometer time-frequency analysis. First, the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) algorithm is used to decompose the original monitoring data, and the time-frequency characteristic correlations of the deformation data are established. Then, similarity clustering is conducted for the monitoring sub-sequences based on their frequency domain characteristics, and clustered sequences are combined subsequently. Finally, the Long Short-Term Memory (LSTM) model is used to separately predict GNSS displacement and acceleration with clustered time series, and the overall deformation displacement is reconstructed based on the predicted GNSS displacement and acceleration-derived displacement. A shake table simulation experiment was conducted to validate the feasibility and performance of the proposed CEEMDAN-SC-LSTM model. A duration of 5 s displacement prediction is analyzed after 153 s of monitoring data training. The results demonstrate that the root mean square error (RMSE) of predicted displacement is 0.011 m with the proposed model, which achieves an improvement of 64.45% and 61.51% in comparison to the CEEMDAN-LSTM and LSTM models, respectively. The acceleration predictions also show an improvement of 96.49% and 95.58%, respectively, the RMSE of the predicted acceleration-reconstructed displacement is less than 1 mm, with a reconstruction similarity of over 99%. The overall displacement reconstruction similarity can reach over 95%. CEEMDAN; similarity clustering; LSTM; GNSS/accelerometer; deformation prediction; deformation reconstruction +
Footnote †: journal: Applied  
Article  
A Similarity Clustering Deformation Prediction Model Based on GNSS/Accelerometer Time-Frequency Analysis [PERSON] et al. (2020), [PERSON] et al. (2020), [PERSON] et al. (2020), [PERSON] et al. synchronously obtain high-precision three-dimensional deformation information, making it a primary method for high-precision dynamic deformation monitoring [7]. However, GNSS signal can be seriously blocked by factors such as buildings and trees, resulting in significant multipath error and positioning accuracy degradations, making it difficult to obtain accurate and reliable deformation monitoring results. Accelerometers can operate independently of external environmental factors, exhibiting characteristics such as short-term high accuracy and strong stability [8]. However, the inherent errors of these inertial sensors accumulate over time, leading to a gradual divergence in the calculated results. Therefore, the integration of accelerometer and GNSS can create effective redundancy and complementarity, contributing to more continuous and reliable monitoring results. Many researchers have applied them in fields such as bridge structure monitoring [9] and high-rise building vibration monitoring [10], achieving favorable results. In practical monitoring scenarios, GNSS monitoring sequences exhibit nonlinear and non-stationary characteristics due to the influence of multipath. Traditional decomposition methods, such as Empirical Mode Decomposition (EMD) [11] and Ensemble Empirical Mode Decomposition (EEMD) [12], reveal significant advantages in multi-scale monitoring sequence time-frequency analysis. but they are prone to problems such as modal aliasing and incomplete decomposition. The improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) [13] algorithm, which is used to analyze nonlinear and non-stationary time series, has a series of advantages such as more thorough decomposition, smaller reconstruction errors, and shorter computational time.