Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Nonlinear Design-Space Dimensionality Reduction in Shape Optimization
Zhiqiang Liu1, Jian Wang2, Decheng Wan1*
1

Computational Marine Hydrodynamics Lab (CMHL), School of Naval Architecture, Ocean and Civil Engineering,
Shanghai Jiao Tong University, Shanghai, China
2Marine Design and Research Institute of China, Shanghai, China*Corresponding author

problem (D’Agostino, 2017; Reddy, 2020). SBDO consists of three mainelements as shown in Fig. 1: (1) hull form deformation tools; (2) thehydrodynamic performance evaluation; (3) high-efficiency optimization
algorithms. The dimensionality reduction is applied in pre-processing ofhull form modification. The types of dimensionality methods are divided
into linear dimensionality (Cunningham, 2015) and non-linear
dimensionality method(DeMers, 1993). The difference is whether thelinear conversion is used in the dimensionality reduction process.

ABSTRACT
Many design variables are often required for the optimization design of
the whole hull, thus numerous new sample hulls need to be calculated.
The dimensionality reduction of design space is essential for theoptimization of whole ship design, which can save the consumption of
calculation resources. In this paper, a nonlinear dimensionality reduction
method called Auto Encoder (AE) based on the neural network is used
to optimize the total resistance of the DTMB hull under Fr=0.18 in calm
water. Firstly, based on the radius basis function modification method in
in-house hull form optimization software—OPTShip-SJTU, a series ofhull forms can be obtained under the high-dimensional design space.
Then the neural network model is established and trained based on thesehull forms. And the low dimensionality space information can be gotten
after training. The new hull forms are gotten by the trained neuralnetwork. And then the viscous solver naoe-FOAM-SJTU is applied tocalculate the resistance of new hull forms. The Kriging theory is used toconstruct the surrogate model, and the single-objective genetic algorithm
is applied to get the lowest total drag hull based on the Kriging surrogate
model. Finally, it shows the nonlinear dimensionality reduction method
has the capacity for dimensionality reduction in hull form optimization.
And we also can obtain optimization results under reduceddimensionality design space compared with initial high design space.

Fig. 1The flowchart of hull form optimization based on dimensionality
reduction
In the past few years, many scholars focus on the dimensionality
reduction application in hull form optimization. In the aspect of linear
dimensionality reduction, Liu (2021) used a linear dimensionality
reduction method called principal components analysis (PCA) todecrease the number of design variables and achieved multi-physics fieldlearning based on proper orthogonal decomposition. Diez (2015)
suppose the Karhunen–Loève expansion (KLE) method in
dimensionality reduction and conduct an off-line dimensionality
reduction method for single- and multi-disciplinary shape optimization
based on the Karhunen–Loève expansion technique, which is also a
linear dimensionality reduction method(Diez, 2016). D’Agostino (2020)
used an off-line dimensionality reduction method based on theKarhunen–Loève expansion to optimize a DTMB model. Khan (2021)
combined geometry- and physics-informed principal component
analysis and the active subspace method in shape optimization. In anaspect of the non-linear dimensionality method, D’Agostino (2017)
compared several non-linear dimensionality reduction methods. The
dimensionality reduction methods are Kernel Principle Analysis(KPAC), Local Principle Analysis (LPA), and Deep Auto Encoder(DAE). They concluded that the Deep Autoencoder showed the best

KEY WORDS: CFD; nonlinear dimensionality reduction; AE;
OPTShip-SJTU; total drag optimization;
INTRODUCTION
Simulation-based design optimization (SBDO) becomes the maintechnique for the design optimization process(Lin, 2018; Liu, 2018a;
Nazemian, 2021) in recent years. And the gradient-free methods are also
widely used in many fields(Liu, 2020; Park, 2015). Although thegradient-free methods have a wide range, it faces huge time-consuming
and curse-of-dimensionality when the design variables increase. Design
space dimensionality reduction is an effective measure to solve this3495