<p>The dynamic response of hull grillage structures subjected to the initial shock wave loading of an underwater explosion is influenced by factors such as initial conditions, boundary conditions, and system parameters. The system dynamics exhibit strong nonlinearity and non-stationary characteristics. Model test results guided by classical similarity theory struggle to accurately predict prototype behavior. This paper addresses the similarity conversion problem for under underwater explosion hull grillage structure model tests. Utilizing phase space reconstruction and parabolic mapping theory, we characterize the evolutionary behavior of the system’s dynamic response in phase space. By introducing renormalization group theory and self-similarity theory, the scaling relationship between the scale ratio and the amplitude of the superstable periodic orbit is revealed. Two similarity conversion methods for model tests guided by renormalization group theory are established. Taking the local grillage structures of the main deck, transverse bulkhead, and double bottom of a 10 000-ton class hull as the prototype, a series of model tests were designed based on period-doubling bifurcation characteristics and the scaling relationship with superstable periodic orbit amplitude. The effectiveness and universality of the two similarity conversion methods derived from the renormalization group framework were thoroughly validated. The results demonstrate that the similarity conversion methods established within the renormalization group theory framework can effectively solve the problem of converting model test results with distortion effects to prototype predictions.</p>