The deformation of arch dams represents a highly complex nonlinear process governed simultaneously by internal structural conditions and diverse external environmental factors, making accurate prediction and continuous monitoring indispensable for ensuring structural safety assessment. In the existing study, single prediction models or two‐stage ensemble models exhibit significantly insufficient generalization capability under the coupled effects of complex environmental factors. Moreover, directly inputting the residual series into the model for correction often overlooks the dependency between residuals and environmental factors, leading to a correction process that lacks physical interpretability. Furthermore, dam deformation monitoring data are generally affected by instrumental noise and random environmental disturbances, which further reduces prediction accuracy. To address and overcome these limitations, this study introduces a multiorder machine learning fusion framework enhanced with environmentally influenced residual clustering correction. The proposed framework integrates several complementary algorithms, including the Sparrow Search Algorithm (SSA)–optimized Long Short‐Term Memory (LSTM) network, a Whale Optimization Algorithm (WOA)–driven Variational Mode Decomposition (VMD) noise suppression module, and a K‐means clustering–based grouping strategy for second‐order residuals using key environmental variables such as water level and temperature. In the first stage, an SSA‐optimized LSTM is utilized to generate first‐order deformation predictions. In the second stage, WOA‐optimized VMD decomposes the first‐order prediction sequence into multiple modal components, and the component most correlated with the first‐order prediction sequence is identified using Pearson correlation analysis. This selected component, when combined with environmental variables such as water level, temperature, and time, is subsequently input into an ELM for second‐order prediction. In the third stage, K‐means clustering is applied to classify second‐order residuals under different environmental conditions, thereby revealing heterogeneity in residual patterns. Rolling predictions for each residual cluster are then performed using SSA‐LSTM. By integrating residual predictions with second‐order outputs, third‐order deformation fitting values are obtained, enabling dynamic, adaptive, and highly precise monitoring. Application to a real‐world concrete arch dam demonstrates that the proposed framework achieves superior accuracy, robustness, and adaptability across multiple modeling stages, offering a comprehensive and practical solution for deformation safety monitoring under complex and variable environmental conditions.
Qiu et al. (Thu,) studied this question.