Application of Dynamic Space Reduction Method Based on Partial Correlation Analysis in Hull Optimization
Authors: Zheng Qiang , Chang Hai-Chao , Liu Zu-Yuan , Feng Bai-Wei 
Published: January 2021

Hull optimization design based on computational fluid dynamics (CFD) is a highly computationally intensive complex engineering problem. Because of reasons such as many variables, spatially complex design performance, and huge computational workload, hull optimization efficiency is low. To improve the efficiency of hull optimization, a dynamic space reduction method based on a partial correlation analysis is proposed in this study. The proposed method dynamically uses hull-form optimization data to analyze and reduce the range of values for relevant design variables and, thus, considerably improves the optimization efficiency. This method is used to optimize the wave-making resistance of an S60 hull, and its feasibility is verified through comparison.
1. Introduction
In recent years, to promote the rapid development of green ships, hull optimization methods based on computational fluid dynamics (CFD) have been widely used by many researchers, such as Tahara et al. (2011), Peri and Diez (2013), Kim and Yang (2010), Yang and Huang (2016), Chang et al. (2012), and Feng et al. (2009). However, hull optimization design is a typically complex engineering problem. It requires many numerical simulation calculations, and the design performance space is complex, which has resulted in low optimization efficiency and difficulty in obtaining a global optimal solution. Commonly used solutions include 1) efficient optimization algorithms, 2) approximate model techniques, and 3) high-performance cluster computers. However, these methods still cannot satisfy the engineering application requirements in terms of efficiency and quality of the solution.
To solve the problem of low optimization efficiency and difficulty in obtaining an optimal solution in engineering optimization problems, many scholars have conducted research on design space reduction technology. Reungsinkonkarn and Apirukvorapinit (2014) applied the search space reduction (SSR) algorithm to the particle swarm optimization (PSO) algorithm, eliminating areas in which optimal solutions may not be found through SSR to improve the optimization efficiency of the algorithm. Chen et al. (2015) and Diez et al. (2014, 2015) used the Karhunen–Loeve expansion to evaluate the hull, eliminating the less influential factors to achieve space reduction modeling with fewer design variables. Further extensions to nonlinear dimensionality reduction methods can be found in D'Agostino et al. (2017) and Serani et al. (2019). Jeong et al. (2005) applied space reduction techniques to the aerodynamic shape optimization of the vane wheel, using the rough set theory and decision trees to extract aerofoil design rules to improve each target. Gao et al. (2009) and Wang et al. (2014) solved the problem of low optimization efficiency in the aerodynamic shape optimization design of an aircraft, by using analysis results of partial correlation, which reduced the range of values of relevant design variables to reconstruct the optimized design space. Li et al. (2013) divided the design space into several smaller cluster spaces using the clustering method, which is a global optimization method based on an approximation model, thus achieving design space reduction. Chu (2010) combined the rough set theory and the clustering method for application to the concept design stage of bulk carriers, thus realizing the exploration and reduction of design space. Feng et al. (2015) applied the rough set theory and the sequential space reduction method to the resistance optimization of typical ship hulls to achieve the reduction of design space. Wu et al. (2016) used partial correlation analysis to reduce the design space of variables of a KCS container ship to improve optimization efficiency. Most of the above space reduction methods need to sample and calculate the original design space in the early stage of optimization and then obtain the reduced design space through data mining. This process increases the computational cost of sampling, making it difficult to control optimization efficiency.