Ship–ship collisions continue to occur regardless of efforts to prevent them. The collisions involve highly nonlinear characteristics associated with structural crashworthiness, including crushing and fracture as well as buckling and plastic collapse. When applying nonlinear finite element analysis (NLFEA) to solve these problems, a reliable critical fracture strain accounting for strain-rate effects due to collision speed must be implemented. This study proposes a practical method to estimate the dynamic fracture strain to be used for the structural crashworthiness analysis associated with the collisions. For this purpose, the strain-rate characteristics in struck ship were investigated by NLFEA, in which the striking vessel was assigned various velocities in the range of practical ship speeds. Based on computations, an empirical formula was developed to calculate the strain rate at a given collision speed, allowing for a practical estimation of the dynamic fracture strain. The formula is validated by a comparison with experiment.

Ship–ship collision accidents continue to occur regardless of the continuous efforts to prevent them, and they essentially involve highly nonlinear problems associated with structural crashworthiness due to crushing and fracture. The nonlinear finite-element method is one of the most powerful techniques to solve the problems. In industry practice, the bow structure of a striking ship is often modelled as a rigid body as it is usually much stiffer than the side structure of a struck ship. However, reality is that the initial kinetic energy in a ship–ship collision accident can be absorbed by the damages of not only the struck ship's side structures but also the striking ship's bow structures because the striking ship bow structure is actually deformable. The aim of the present study is to examine the effects of a deformable striking ship's bow on the structural crashworthiness in ship–ship collisions. In the present study, two scenarios are considered where the side structure of a VLCC class double hull oil tanker is collided by the bow structure of a VLCC class double hull oil tanker or a SUEZMAX class double hull oil tanker. All of the ships considered are real ships in operation. The structural crashworthiness in terms of the collision force–penetration relation and the collision energy–penetration relation is then studied with two cases in which the striking ship's bow structures are either rigid or deformable. It is concluded that the striking ship's bow may be modelled as a rigid body in minor collisions at a collision angle of about 90° where the initial kinetic energy is entirely consumed before the inner hull structure is ruptured, but it should be modelled as a deformable body in a major collision accident or at an inclined collision angle where the maximum penetration can be greater than the double side breadth.

This study proposes a hybrid deep learning framework for predicting vehicle crash frequency (F_i) using nationwide traffic accident and traffic volume data from the United States (2019–2022). Crash frequency is defined as the product of exposure frequency ($N_a$) and crash risk rate ($\lambda$), a structure widely adopted for its ability to separate physical exposure from the crash likelihood. $N_a$ was computed using an extended Safety Performance Function (SPF) that incorporates roadway traffic volume, segment length, number of lanes, and traffic density, while $\lambda$ was estimated using a multilayer perceptron-based deep neural network (DNN) with inputs such as impact speed, road surface condition, and vehicle characteristics. The DNN integrates rectified linear unit (ReLU) activation, batch normalization, dropout layers, and the Huber loss function to capture nonlinearity and over-dispersion beyond the capability of traditional statistical models. Model performance, evaluated through five-fold cross-validation, achieved R² = 0.7482, MAE = 0.1242, and MSE = 0.0485, demonstrating a strong capability to identify high-risk areas. Compared to traditional regression approaches such as Poisson and negative binomial models, which are often constrained by equidispersion assumptions and limited flexibility in capturing nonlinear effects, the proposed framework demonstrated substantially improved predictive accuracy and robustness. Unlike prior studies that loosely combined SPF terms with machine learning, this study explicitly decomposes F_i into $N_a$ and $\lambda$, ensuring interpretability while leveraging DNN flexibility for crash risk estimation. This dual-layer integration provides a unique methodological contribution by jointly achieving interpretability and predictive robustness, validated with a nationwide dataset, and highlights its potential for evidence-based traffic safety assessments and policy development.