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.