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Many-objective optimization for a deep-sea aquaculture vessel based on an improved RBF neural network surrogate model

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Abstract

Many-objective optimization refers to the optimization aiming at four or more objectives. More complex than multi-objective optimization, which copes with two or three objectives, many-objective optimization represents a challenging problem due to the complex trade-off relationships among the optimization objectives. In this study, a four-objective optimization system was proposed for reducing the resistance and the non-uniformity of wake flow of a deep-sea aquaculture vessel at design speed in full load and ballast conditions. The numerical optimization system was mainly composed of the uniform design (UD), free-form deformation method (FFD), radial basis neural network (RBFNN) and a series of genetic algorithms (GAs). During the optimization process, nine design variables were selected to reconstruct the hull geometry. UD and FFD were utilized to generate a series of derivative ship forms. According to CFD calculation results of all derivative ship forms, four surrogate models were constructed, using RBFNN optimized by the particle swarm optimization (PSO), to replace direct numerical calculations. To verify the prediction accuracy advantage of improved RBFNN-based surrogate models based on small sample size, the accuracy comparison was made among surrogate models based on RBFNN, kriging and support vector regression (SVR). Moreover, Sobol' method was employed to analyze the influence of design variables on the optimization objectives. GAs were applied to perform from single-objective to four-objective optimization of the resistance and non-uniformity of wake flow. Eventually, the optimal ship form was selected from the Pareto front of four-objective optimization. Numerical results of the optimized shape showed that the resistance and the non-uniformity of wake flow in full load and ballast conditions were reduced, and the results of the verification and validation (V&V) procedure proved the validation of the many-objective optimization system.

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Abbreviations

V s :

Actual ship speed (Kn)

V d :

Ship design speed (Kn)

V m :

Ship speed for model scale (m/s)

L OA :

Overall length (m)

L wl :

Designed waterline length (m)

L pp :

Length between perpendiculars (m)

S.d:

Scantling draft (m)

B.d:

Ballast draft (m)

D :

Diameter of the propeller (m)

\(\nu\) :

Kinematic viscosity coefficient (m2/s)

Re :

Reynolds number, \({\text{Re}} = \frac{{VL_{pp} }}{\nu }\)

Fr :

Froude number, \(Fr = \frac{V}{{\sqrt {gL_{pp} } }}\)

\(\lambda\) :

Scale ratio

1 + k :

Form factor

\(\Delta\) :

Displacement (MT)

S :

Wet-surface area for actual scale (m2)

R tm :

Total resistance for model scale (N)

R fm :

Frictional resistance for model scale (N)

C tm :

Total resistance coefficient for model scale, \(C_{tm} = \frac{{R_{tm} }}{{\frac{1}{2}\rho V_{m}^{2} S_{m} }}\)

C fm :

Frictional resistance coefficient for model scale, \(C_{fm} = \frac{{R_{fm} }}{{\frac{1}{2}\rho V_{m}^{2} S_{m} }}\)

S m :

Wet-surface area for model scale (m2)

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Acknowledgements

This work was supported by the Shanghai Science and Technology Commission [Grant No. 15DZ1202100]. The authors appreciate the academic exchange and discussion from the State Key Laboratory of Ocean Engineering (SKLOE) of Shanghai Jiao Tong University.

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Authors and Affiliations

  1. State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Penghui Wang, Zuogang Chen & Yukun Feng

  2. Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration (CISSE), Shanghai, 200240, China

    Zuogang Chen

  3. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Penghui Wang, Zuogang Chen & Yukun Feng

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  1. Penghui Wang
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Correspondence to Zuogang Chen.

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Wang, P., Chen, Z. & Feng, Y. Many-objective optimization for a deep-sea aquaculture vessel based on an improved RBF neural network surrogate model. J Mar Sci Technol 26, 582–605 (2021). https://doi.org/10.1007/s00773-020-00756-z

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