| 06 Aug 2026
Development and application of a physics-constrained adaptive decomposition model for displacement sequences of step-like landslide
Abstract. Addressing the nonlinear evolution of step-like landslides in China's Three Gorges Reservoir area, which is driven by the strong coupling of reservoir water level fluctuations and rainfall pulses, this paper proposes a highly adaptive and physics-constrained displacement decomposition framework. First, a Chebyshev-Lévy flight-enhanced sparrow search algorithm (CLF-SSA) is developed to adaptively optimize the core parameters of variational mode decomposition (VMD). Concurrently, an integrated objective function—incorporating mathematical sparsity (envelope entropy) and a physical correlation penalty for the periodic component—is constructed. This framework ensures that the decomposition process is mechanistically-driven from its foundational level, maintaining a strictly physics-constrained architecture. Secondly, a multi-dimensional quantitative reconstruction strategy for intrinsic mode functions (IMFs) is established, integrating central frequencies, correlations with multi-source environmental factors (reservoir water level, rainfall, and elevation), and seasonal energy distribution. This strategy enables the robust decoupling of cumulative displacement sequences into distinct trend, periodic, and random components, effectively mitigating the phenomenon of mode mixing. Finally, the surface displacement of a representative step-like landslide in the TGR area was decomposed using the proposed framework. The results demonstrate that the model achieves sub-millimeter reconstruction precision, with an average root mean square error (RMSE) of approximately 0.5 mm. Notably, the decoupled periodic components exhibit exceptional consistency with geomechanical responses, achieving a maximum correlation gain of 4283.60 %. By incorporating the PyLith continuous-slip numerical model for physical validation, this study effectively elucidates the displacement step-triggering mechanism induced by seepage pressure during reservoir drawdown. This transition from statistical identification to mechanistic interpretation provides robust physical support for overcoming the pervasive time-lag bottlenecks in landslide early warning engineering. Future research will focus on integrating this physics-constrained decomposition framework with deep learning models to enhance the real-time predictive capability for diverse landslide types.
The manuscript presents a physics-constrained displacement decomposition framework based on CLF-SSA and VMD for step-like landslides. The topic is relevant and the manuscript provides a relatively complete methodology and case study. The results are generally convincing. I recommend minor revision. The following issues should be addressed:
The authors are encouraged to provide a brief explanation of the selection of the main parameters involved in the proposed method, particularly the physical constraint weight λ in the joint fitness function and the criteria used to classify the decomposed modes into trend, periodic, and stochastic components. A short description of the parameter-setting procedure or the corresponding decision criteria would improve the clarity and reproducibility of the study.
Some of the reported results, such as the very large percentage increase in correlation, would benefit from a brief explanation of how these values are calculated and interpreted. In addition, when discussing the relationships between displacement components and environmental factors, the authors should use slightly more cautious wording to distinguish statistical correlation from physical causation.
The authors should ensure that the literature review adequately reflects recent research related to landslide displacement decomposition, VMD-based methods, and physics-informed approaches. At the same time, all in-text citations and reference entries should be checked for consistency with the journal's required format. Overall, some of the literature are relatively outdated, please update with some latest relevant literature.
Several grammatical, typographical, and formatting issues remain throughout the manuscript. The authors should carefully check the English expression, abbreviations, mathematical symbols, figure and table captions, equation formatting, and terminology consistency. Some sentences are relatively lengthy and could be simplified to improve readability. A thorough proofreading of the entire manuscript before resubmission is recommended.
Overall, the manuscript is generally well structured and the proposed approach is interesting. The above issues are mainly related to clarification, presentation, and formatting, and can be addressed through revision without substantial changes to the current methodology. Therefore, I recommend publication after minor revision.