<p>The dynamic response of the hull structure under transient strong impact loads exhibits nonlinear behavior influenced by multi-physical field coupling. This response is highly sensitive to coefficient parameters and boundary conditions. Even small disturbances can lead to bifurcations and abrupt changes in the response, resulting in chaotic behavior within the dynamic system. Therefore, accurately predicting the dynamic response of similar hull structures becomes challenging, limiting the identification of damage modes and the design of impact-resistant hull structures. In this study, an impact test of a stiffened cylindrical shell under underwater explosion loads is conducted. The deviation index of adjacent moving orbits of the shell’s dynamic response in the time domain is calculated, revealing the chaotic characteristics of the impact response system. The concept of a maximum predictable critical time for the response system is proposed. Range analysis indicates that the evolution of structural dynamic motion response exhibits scale invariance. Based on generalized Brownian motion, a mathematical framework for a dynamic response scaling theory for hull structures subjected to explosive loading is established. Finally, impact tests on model structures at different scales are performed. Test results show that the dynamic response of large-scale, similar model structures can be accurately predicted using the scaling equation derived from the impact response system, with an error margin controlled within 10%.</p>