<p>The response of ship structure under underwater explosion loads is a strong nonlinear dynamic response behavior under the coupling action of multiple physical fields. Because of the variety of distortions and the sensitivity of structural response to initial conditions and boundary conditions, the system dynamics behavior will bifurcate when there is a small disturbance, and the accurate transformation between model and prototype cannot be realized. For distortion effects and strong nonlinear characteristics in model experiments, based on the classical second law of similarity, a similarity transformation method for nonlinear dynamical systems is proposed in this paper. By using the phase space reconstruction method, the high-dimensional nonlinear dynamic system is mapped to a low-dimensional phase space, and the mapping function of acceleration response evolution in phase space is constructed. Based on the differential homeomorphism principle of mapping functions of nonlinear dynamic systems, a conjugate transformation function of similar systems is established to realize accurate transformation from a nonlinear dynamic similar model experiment to a prototype experiment. Finally, the comparison between the theoretical inversion results with high-fidelity numerical outcomes demonstrates that the conjugate similarity transformation method effectively reproduces the motion evolution orbits of a nonlinear dynamic system, thereby validating the accuracy of the structural response similarity transformation for a stiffened cylindrical shell model subjected to strong impact loads.</p>