Abstract: The dynamic response of ship hull structures subjected to underwater explosions is conventionally bifurcated into early-stage and late-stage responses. The early-stage response, which directly induces structural damage, exhibits pronounced nonlinear and non-stationary characteristics. This response phase demonstrates extreme sensitivity to variations in system parameters, initial conditions, and environmental factors, leading to complex dynamical phenomena such as bifurcation and mutation in response trajectories. Consequently, the output manifests significant uncertainty, complicating precise prediction and analysis. To address these challenges, this study proposes a novel analytical framework integrating phase space reconstruction techniques, parabolic mapping methodologies, and symbolic dynamics theory. This hybrid approach aims to decode the spatiotemporal evolution patterns of the early-stage dynamic response and establish predictive capabilities within the parametric neighborhood of the system. The research methodology commenced with the development of a scaled experimental model based on a stiffened cylindrical shell structure. Systematic tests were conducted across a spectrum of impulse factor conditions to investigate the nonlinear, non-stationary dynamic response characteristics under varied loading regimes. Advanced signal processing and uncertainty quantification techniques were employed to characterize the inherent variability in these responses. Subsequently, the research scope was expanded to include full-scale cabin segment structures and floating impact platforms modeled after actual naval vessel configurations. These experiments were designed to validate the proposed methodology's applicability under more complex boundary conditions and loading scenarios, thereby demonstrating its universality and robustness. The analytical framework leverages phase space reconstruction to transform complex time-domain response signals into multi-dimensional geometric representations. This transformation facilitates the identification of underlying dynamic patterns and attractors. Parabolic mapping techniques are then applied to establish explicit relationships between successive states in the phase space trajectory, capturing transient response features with high fidelity. Symbolic dynamics theory provides a mechanistic framework to encode continuous dynamic processes into discrete symbolic sequences, enabling quantitative analysis of system complexity and uncertainty propagation. The experimental campaign revealed that the proposed methodology successfully characterized the nonlinear response evolution across different structural configurations and loading conditions. Statistical analyses of the experimental data demonstrated that the technique could predict response thresholds and variability within the parametric design space. These findings hold significant implications for naval architecture and marine engineering, providing enhanced capabilities for assessing structural integrity under extreme dynamic loads. The methodology's demonstrated effectiveness across multiple scales and configurations underscores its potential for broader application in complex nonlinear dynamic systems beyond naval engineering.