# A Novel Deep Learning Model to Predict Ultimate Strength of Ship Plates under Compression
## 1 Introduction  
Due to the increasing number of ships constructed every year, the international maritime traffic has grown rapidly. Curved plates are one of the basic structural elements of hulls. However, in recent years, owing to the reduction in the weight of ships, extremely thin curved plates have become vulnerable to buckling and corrosion [1]. Therefore, it is important to analyze buckling and collapse of structural elements such as curved plates. The curved plates used in ship construction must be able to withstand repeated axial and complex loads; hence, its stability is confirmed by estimating the ultimate strength. The transverse compressive force is generated by the difference between the hydrostatic pressure of the ship and the pressure due to the weight of the cargo. Generally, the magnitude of the transverse compressive force is smaller than that of the longitudinal compressive force [2]. However, during the transverse and combined loading states, a physical behavior occurs which is different from that of the longitudinal loading. This acts as a factor influencing the ultimate strength, which is an essential part of this research. Therefore, in this study, curved plates subjected to transverse compressive loads were used as the research subjects. There are three strategies through which the ultimate strength can be estimated: a finite element method (FEM) universal analysis program, an experimental approach, and an empirical formula derived from the experimental results [3]. However, a new analysis must be conducted when the dimensions or materials of the plate are changed during the design stage. For instance, in the case of the empirical formula method, the ultimatestrength of the curved plate differs from the actual analysis result if the usable range is limited or if the curved plate undergoes nonlinear behavior, resulting in low reliability. It is an advantage of a deep learning model to be able to find regularity through statistical analysis of parameters and result values within the data. Using this, the ultimate strength considering nonlinear behavior is estimated, and the appropriateness and necessity of the deep learning model are suggested compared with the empirical equations presented from previous studies [4]. In a previous study, [PERSON] and [PERSON] [5] developed a model for predicting the ultimate strength of a plate with a single-hidden-layer perceptron neural network. Upon comparing the model with the existing empirical formula, the predicted result using the neural network yielded a value closer to the actual experimental value. This result confirms that the deep learning-based model can be useful during the initial design stage; however, the neural network used was a single-layer perceptron neural network, and a relatively small number of cases were used with 143 training datasets. In this study, based on a deep neural network, the ultimate strength of the curved plate was predicted over a wider range under a transverse load in various scenarios. These results indicate the ability of the deep neural network to efficiently estimate the ultimate strength to acquire the optimal design of the ship and cost reduction in the initial design stage. Several studies have been conducted to predict the ultimate strength of structural members using ANN. [PERSON] et al. [6] estimated the ultimate strength of stiffened aluminum plates with flat-bar stiffeners under in-plane longitudinal compression loads using an ANN. When comparing this value with the ultimate strength obtained using empirical equations, it was confirmed that the model prediction was close to the FEM result. However, the number of cases in this study was limited (42 datasets). Thus, these results cannot be considered sufficiently robust, since prediction models require a large variety of datasets to perform effectively over a wide range of applications. [PERSON] et al. [7] developed an ANN model to predict the ultimate strength of circular concrete-filled steel tube columns under concentric loading.