1. Introduction
Taiwan has recently developed wind-based renewable energy on a growing scale. However, its mountainous terrain and limited plains make offshore wind farms an increasingly attractive option. As offshore wind energy installations increase, the demand for crew transfer vessels (CTVs) transporting personnel and equipment also rises [
1], as CTVs are vital for supporting wind turbine operation and maintenance. Small waterplane area twin hull (SWATH) vessels are commonly preferred as CTVs due to their superior seakeeping performance, but their low wave-induced forces, while advantageous, can lead to poor longitudinal stability [
2]. Pontoon resistance is the most dominant component of the total resistance of a SWATH vessel. The pontoon’s shape influences pressure distribution, creating the Munk moment that brings longitudinal instability. While optimizing pontoon design can improve both resistance and stability, effective design methods are still limited, with only a few numerical studies available [
3,
4,
5]. To counteract longitudinal instability, SWATH vessels typically use fin stabilizers that generate lift to balance Munk moments, especially at high speeds. This method enhances stability but increases total resistance [
6], making fin stabilizer placement a key design factor. Computational fluid dynamics (CFD) software [
7] is now widely used for ship design and performance analysis, providing advantages over physical model tests. However, accurately predicting ship resistance with free-surface effects remains computationally expensive, driving the need for simplified methods. In addition to simplifying computational methods, this study utilizes artificial intelligence techniques, particularly deep neural networks (DNNs), to aid in design optimization. DNNs, as a branch of artificial intelligence, can effectively model the nonlinear correlation between hull form and resistance, enabling the identification of optimal design parameters within a defined range. Although there have been numerous studies applying neural networks to SWATH hull optimization [
8,
9], no research focuses on a parameterized hull form design optimization for total resistance reduction. Hence, the main objective of this study is to propose a DNN model to address this research gap.
The concept of SWATH vessels has been under development since the 1970s. Over the decades, several successful applications of SWATH vessels have been realized, including oceanographic research vessels, such as the Ferdinand R. Hassler operated by the National Oceanic and Atmospheric Administration (NOAA) [
10], offshore patrol vessels [
11], and naval vessels, such as the Sea Shadow [
12]. A SWATH vessel comprises two primary structural components. The first is the submerged pontoon, located below the free surface, which provides most of the vessel’s buoyancy. The second is the strut, which pierces the free surface and serves as the connection between the deck and the pontoon. SWATH vessels are known for superior seakeeping in high sea states compared to conventional ships [
13]. Advantages include low resistance at high speeds, reduced wave-induced forces, and a large deck area. However, drawbacks remain, such as increased viscous resistance from the wetted surface, limited longitudinal restoring force due to the small waterplane area, the Munk moment of the pontoon, and the flow–structure interaction from hull-mounted fin stabilizers [
14,
15,
16]. Reliable resistance estimates are to be obtained for conventional modern fast ferries to enable the evaluation of current energy use and emissions. Engineering accuracy is to be obtained for the resistance of hulls at reduced draft, representing foil supported operation or the take-off phase of hydrofoil catamarans [
17]. As the pontoon largely contributes to both resistance and instability [
18,
19,
20], this study focuses on optimizing its hull form.
Traditional hull form optimization often relies on statistical analysis of existing ships to correlate hydrodynamic performance with geometric parameters [
21,
22]. However, methods like linear regression can be highly constrained when the relationship between variables is not explicitly defined. As a result, advanced approaches such as neural networks are increasingly employed for hull form optimization. Neural networks have been widely and successfully applied in naval architecture. In hull form resistance optimization, studies such as [
23,
24] used free-form deformation techniques, while [
25] applied principal component analysis (PCA) to reduce hull form parameters, which were then input into deep neural networks (DNNs) for resistance prediction. In [
26], pressure distribution, free-surface elevation, and wake images were used to train a convolutional neural network (CNN) to predict hydrodynamic performance. Neural networks have also been used to account for sea conditions and ship motions: [
27,
28] predicted short-term sea states using wave descriptors, while [
29] trained models to estimate seakeeping performance. Additionally, refs. [
30,
31] developed models to predict short-term ship motions. In structural analysis, refs. [
32,
33] employed neural networks to estimate the ultimate strength and fatigue failure of transverse structures. For engine power prediction, refs. [
34,
35] used hull form, environmental data, and ship speed, while [
36] modeled fuel consumption using data from the engine, propulsion system, flow field, and cargo load. Finally, ref. [
37] predicted the energy efficiency operational indicator (EEOI) using publicly available ship, engine, and meteorological data. Various types of neural networks exist, including recurrent neural networks (RNNs), long short-term memory (LSTM), convolutional neural networks (CNNs), and deep neural networks (DNNs). Among them, DNNs are classic feed-forward networks where data flows directly from input to output without recurrence. Since the hull form design parameters in this study are neither sequential nor spatial (e.g., image-like), a DNN model seems to be an appropriate choice.
This study proposes a pontoon design optimization process. First, the total resistance of the SWATH vessel is linearized into its main components. Next, a parametric pontoon model is created in Grasshopper3D using key design parameters. Resistance analyses of the pontoon, strut, and fin stabilizer are then performed independently with STAR-CCM+ 2302. The numerical results train a deep neural network (DNN) model, which is used to predict optimized design parameters. Finally, the optimized vessel’s total resistance is validated through CFD simulations.
7. Conclusions
This study proposes a parameterized SWATH underwater pontoon design method, integrating resistance analysis and deep neural network (DNN) modeling to identify an optimized design with reduced total resistance and Munk moment at a high Froude number. To simplify calculations, the resistance of the SWATH vessel is decomposed into contributions from the pontoon, strut, superstructure, and fin stabilizers. The pontoon is identified as the largest resistance contributor and is thus the primary target for optimization. The pontoon design is based on an axisymmetric body defined by fore- and aft-lengths and body angles. After optimizing pontoon resistance using the DNN model, computational fluid dynamics (CFD) simulations are conducted to predict the total resistance of the SWATH in a full three-dimensional flow field, serving as the final validation step. The DNN model employed comprises five hidden layers with six, eight, nine, eight, and seven neurons, respectively, achieving a mean absolute percentage error (MAPE) of 0.19%. The optimized design parameters suggested by the model include a fore-body length of 7.8 m, an aft-body length of 6.8 m, a fore-angle of 10°, and an aft-angle of 35°. The longitudinal center of buoyancy () of the optimized design shifts closer to the stern compared to the baseline design. Correspondingly, the longitudinal moment is reduced by 127.8%, and the fin stabilizer’s angle of attack decreases by 121.7%. After accounting for the resistance contributions of all components via CFD, the total resistance of the optimized SWATH is reduced by 2.2% relative to the baseline. Performance evaluation across different speeds reveals that the optimized design exhibits better resistance characteristics at high Froude numbers, primarily due to the significant reduction in the Munk moment, which allows for a smaller stabilizer angle and reduced fin drag. In summary, minimizing the Munk moment during pontoon design is critical not only to enhance vessel stability and prevent capsizing but also to reduce overall resistance. The optimized design also offers the advantage of lower construction costs and higher payload capacity. This integrated approach combining DNN-based optimization with CFD validation offers an effective framework for designing high-performance SWATH vessels.