Design of Underwater Robot Lines Based on a Hybrid Automatic Optimization Strategy

College of Mechanical Engineering and Automation, Fuzhou University, Fujian 350108, China

Design of Underwater Robot Lines Based on a Hybrid Automatic Optimization Strategy

Wenjing Lyu and Weilin Luo＊

College of Mechanical Engineering and Automation, Fuzhou University, Fujian 350108, China

:In this paper, a hybrid automatic optimization strategy is proposed for the design of underwater robot lines. Isight is introduced as an integration platform. The construction of this platform is based on the user programming and several commercial software including UG6.0, GAMBIT2.4.6 and FLUENT12.0. An intelligent parameter optimization method, the particle swarm optimization, is incorporated into the platform. To verify the strategy proposed, a simulation is conducted on the underwater robot model 5470, which originates from the DTRC SUBOFF project. With the automatic optimization platform, the minimal resistance is taken as the optimization goal; the wet surface area as the constraint condition; the length of the fore-body, maximum body radius and after-body’s minimum radius as the design variables. With the CFD calculation, the RANS equations and the standard turbulence model are used for direct numerical simulation. By analyses of the simulation results, it is concluded that the platform is of high efficiency and feasibility. Through the platform, a variety of schemes for the design of the lines are generated and the optimal solution is achieved. The combination of the intelligent optimization algorithm and the numerical simulation ensures a global optimal solution and improves the efficiency of the searching solutions.

hybrid optimization strategy; automatic optimization platform; underwater robot lines; hydrodynamic numerical simulation; computational fluid dynamics

1 Introduction

Rapidity is one of the most important hydrodynamic performance aspects of underwater robots, which not only has a close relationship with the underwater exploration in the harsh marine environment, but also determines the amount of energy and costs of a carrier (Antonelliet al., 2008). Resistance and propulsion are two key factors of rapidity. The design of the lines plays an important role in improving the rapidity of an underwater robot (Yanget al., 2001). Traditionally, the lines are designed by means of repeated selection, calculation and modification, which results in the low efficiency. Also, the optimal solution is difficult to obtain because of the limitation of selection and the lack of required design experience. Yanget al. (2002) presented a resistanceoptimization for a multi-hull ship, which was mainly concerned with the influence of the center and outer hull forms in achieving a fairly large reduction of wave drag. To obtain the optimal solution, 48678 schemes were performed by using the CFD method. This kind of process is the so-called "manual optimization". Such an optimization is a tedious process because of the huge repeated calculation and analysis involved.

With the development of the process integration, it is possible to run the repeated manual operation automatically. By computer, one can set up a platform to deal with the complex engineering problem. In the platform, CAD/CAE/CAM can be combined together. CAD modeling and CFD analysis were applied to design the Boeing 777, which exemplifies the process integration (Birtleset al., 1998). Cho and Korwi (2004) integrated the CAD modeling, meshing and CFD simulation to design the shape of the engine cylinder. In the shipping industry, the process integration is also developed. Combining SHIPFLOW with OCTOPUS, Jason and Larsson (1997) achieved an automatic optimization of the ship hull lines.

An interesting possibility is to combine a numerical simulation and a mathematical optimization together for design and optimization of the hull lines (Alexandrov and Lewis, 2002). The whole procedure is fully automatic and user interference is not required during the optimization. It is an "automatic optimization" system (McAIiisteret al., 2002). The process of the "automatic optimization" can be described as follows. First, based on the information exchange among the software, the system makes use of the computer to do orderly and repetitive work. The entire optimization process runs automatically. Second, based on the optimal theory and the various constraints, the system explores the design space deeply and comprehensively. The globally optimal solution of the design space can be achieved.

In this paper, a hybrid automatic optimization strategy is proposed. Isight is introduced as an integration platform. The construction of this platform is based on the user programming and several different types of commercial software, including UG6.0, GAMBIT2.4.6 and FLUENT12.0. The DTRC′s SUBOFF project is taken as an example (Groveset al., 1989; Roddyet al., 1990). With the automatic optimization platform, the minimal resistance is chosen as the optimization goal, the wet surface area of an underwater robotas the constraint condition, the length of the fore-body, maximum body radius, and the after-body′s minimum radius as the design variables in the integration. An artificial intelligence technique, particle swarm optimization (PSO), is also introduced in the platform (Panda and Padhy, 2008, Ethniet al., 2009). Through the optimization, a variety of the lines design schemes are generated and the optimal solution is obtained. The combination of the intelligent optimization algorithm and the numerical simulation ensures a global optimal solution and improves the efficiency of solution-searching.

2 The Isight integration platform

The optimization of the lines of an underwater robot is based on the Isight integration platform. Isight is a powerful, practical and effective integration tool (Lai and Jiang, 2012). It not only has the ability to read CAD/CAE/author-edited-programming input/output files, but it can also implement the parametric integration. In this paper, for the sake of creating an automatic optimization platform, three different kinds of software are integrated, including UG6.0, GAMBIT2.4.6, and FLUENT12.0. The simcode components of Isight are used. The automatic optimization is illustrated in Figs. 1, 2 and 3. The main procedure includes:

1) Parametric Modeling. Based on the lines of an underwater robot, UG6.0 is used to create the model through the expression offered. Then a Parasolid file is exported.

2) Model partitioning and meshing. The Parasolid file is imported into GAMBIT2.4.6. Computational domains are determined and meshing is conducted. A mesh file is generated in this step.

3) Hydrodynamic numerical simulation. The numerical computation is performed with FLUENT12.0 after the mesh file is imported. In this step, the resistance and wet surface area of the model are achieved.

4) Modification of the lines. The hybrid optimization is carried out in this step. By changing the design variables and calculating the error precision, the optimal lines are gained.

5) Above processes repeated.

Fig.1 The flow chart of automation optimization

Fig. 2 Data process

Fig. 3 The platform based on Isight

3 The hydrodynamic numerical simulation mode

3.1 An underwater robot model

This paper studies the SUBOFF project model 5470, originated from the Defense Advanced Research Program (DARPA). This model has been widely used to analyze hydrodynamic forces and flow fields. During the last decades, experiments and numerical simulations were performed widely. The available hydrodynamic data include the speed, pressure, friction, and Reynolds stresses, etc. In this paper, the experimental drag data are used in the optimization for a comparative study.

Figure 4 presents the SUBOFF project model 5470. As can be seen, this model is a body of revolution, with the total length being 4.356m, the turning diameter 0.508m, the length of the fore-body 1.016m, the length of the mid-ship 2.229m, and the after-body’s length 1.111m.

Fig. 4 SUBOFF MODEL5470

3.2 Numerical methods

The numerical simulation takes the RANS equation as a control equation and the standardkε- equations are taken as the turbulence models (Jiyuanet al., 2007).

The Navier-Stokes equations can be expressed in terms of the tensor notation (for an incompressible Newtonian fluid),

whereiuandjuare velocity components,ρthe fluid density,pthe pressure,μthe dynamic viscosity coefficient,iSthe source item.

It requires modeling of the Reynold′s stress to close the RANS equation. This paper adopts the standardkε- turbulence models to calculate the Reynold’s stress.

The exactkε- equation contains many unknown and unmeasurable terms. For a much more practical approach, the standardkε- turbulence model is used which is based on our best understanding of the relevant processes, thus minimizing unknowns and presenting a set of equations which can be applied to a large number of turbulent applications (Launder and Spalding, 1974).

For turbulent kinetic energyk

For dissipationε

whereuirepresents the velocity component in the corresponding direction,Gkrepresents the component of the rate of deformation,tμrepresents the eddy viscosity with

The equations also consist of some adjustable constants, i.e.1Gε,2Gε,Cμ,kσandεσ. The values of these constants have been arrived at by numerous iterations of data fitting for a wide range of turbulent flows. These are as follows.

The finite volume method was applied for discretization. SIMPLE was used for pressure correction. For the pressure, the standard discretization scheme was employed, while for momentum, turbulence kinetic energy and the turbulence dissipation rate, the second-order upwind scheme was used. The under-relaxation factor read the default value.

3.3 Computational domain and meshing

Usually with numerical simulations, the larger the computational domain is, the higher the level of precision there will be. However, the increase of the computational domain leads to an increase of the calculation burden, moreover, the demand of workstation equipment also becomes higher. On the contrary, too small a computational domain causes the boundary conditions and calculation results to be unmatched with the experiments. To alleviate the contradiction between the efficiency and accuracy, this paper determines the computational domain shown as in Fig. 5. The computational domain consists of a semi-sphere and a cylinder. The inlet boundary is around a length of the model away from the model’s top, while the flow region’s radius is of the equivalent length, and the outlet boundary away from the model’s end is about two lengths. The surfaces of the semi-sphere and cylinder are set as the velocity inlet while the round face is the pressure outlet with the reference pressure set to zero. The turbulent intensity and turbulent viscosity ratio are respectively set at 2% and 2, in both the inlet and outlet. The model’s wall is defined as no slip wall. The wall function method is used in the near wall treatment. The longitudinal section is defined as the symmetry plane. Thetechnique of block division is used in the meshing (Thompsonet al., 1985). The entire flow region is divided into 14 pieces. The structural grid is applied in the meshing. The entire meshes in the computational domain amount to 121,840. The meshes are shown in Fig. 6.

Fig. 5 Computational domain

Fig. 6 Meshing adopted for calculation

3.4 Hydrodynamic numerical simulation results

Table 1 presents the resistance results from the experiment and numerical simulation. The DARPA had already published the experimental resistance results of the SUBOFF model (Liu and Huang, 1998). In Table 1, the drag coefficients as well as the errors between the CFD calculation and experiment were also calculated. As can be seen, the calculation results agree well with the experiments results.

Fig. 7 presents the comparison of the drag coefficients between the CFD calculations and the results from the experiments. As can be seen, in the case ofv=13.92kn, the error is the smallest, with only 2.22%. To make the optimization more accurate, in this study thev=13.92kn is taken as optimization.

y+values are shown in Fig. 8. As can be seen, the satisfying results vary in the range of 30 to 60. The values ofy+fluctuate around the pointy=50.

Table 1 Direct numerical simulation results

Fig. 7 Comparison of drag coefficients between CFD and experiments

Fig. 8y+ values

4 Hybrid optimization strategy

Generally, optimization includes finding the "best available" values of some objective function given a defined domain, including a variety of different types of objective functions and different types of domains. The search processes or rules include intelligent algorithms andnumerical algorithms. Intelligent algorithms are inspired by the mechanism of the evolution, and proposed for solving complex optimization problems (Noesis Solutions, 2006). Modern intelligent algorithms include the evolutionary algorithm (EA), neural networks (NN), particle swarm optimization (PSO) and so forth. Usually, these intelligent optimal algorithms have the global convergence; however, the shortcoming is the low efficiency, which means a lot of time would be needed for one optimal process. Numerical algorithms use the derivative of the function, gradient and other mathematical characteristics to optimize engineering problems, e.g. the nonlinear continuous problem (Noesis Solutions, 2006). Common numerical algorithms refer to the modified method of feasible direction (MMFD) and sequential quadratic programming (SQP),etc. The advantage of the numerical algorithm is the high optimization efficiency; however, it is easier to fall into the local optimal solution when it comes to a complex optimization model. To obtain the global optimal solution with high efficiency, this paper combines two kinds of optimization algorithms, i.e. PSO and MMFD.

Initially, the PSO was applied to the optimization of the underwater robot lines. The PSO is originally attributed to Kennedyet al.(1995) and was first intended for simulating social behaviour (Shi, 1998), as a stylized representation of the movement of organisms in a flock of birds. The principle of the PSO is simple and it is easy to implement the PSO in complex engineering optimization. It neither requires too many parameters to be adjusted, nor differentiation operations. The PSO has been widely applied to optimization.

The PSO optimizes a problem by having a population of candidate solutions, dubbed particles, and moving these particles around in the search-space according to simple mathematical formulae over the particle′s position and velocity. Each particle′s movement is influenced by its local best known position and is also guided toward the best known positions in the search-space, which are updated as better positions are found by other particles. This is expected to move the swarm toward the best solutions. The algorithm of PSO can be described as follows.

whereωis the inertia weight,1cand2cthe acceleration constants,1rand2rrandom values varying in the range of [0, 1],dthe dimension of particle,idpthe individual optimal position,dgpthe global optimal position,idvthe velocity,idxthe position. The first term in the right hand side of (5) is named inertia force, which allows the particles to expand the searching space. The second one is called “cognition part”, which makes the particles to improve the direction by themselves. The third term, named by “social part”, aims to share optimal information between particles.ωis the inertia weight, while1cand2care the acceleration constants. 1rand2rare random values, which vary in the range of [0, 1].

The update process of PSO is summarized as follow:

The PSO update process

Secondly, the modified method of feasible direction (MMFD) method is used. It utilizes the direction-finding sub-problem from the method of feasible direction to find a search direction without requiring the addition of a large number of slack variables associated with inequality constraints. It is possible to obtain the optimal solution when starting from a feasible design point. The purpose of utilizing MMFD in the second step is to continue a quick and local precision search so as to obtain a globally optimal solution after an approximate globally optimal solution has been derived from the first step.

5 The automatic optimization results

As aforementioned, the SUBOFF project model 5470 has been taken as the example for the automatic optimization platform. Table 2 presents the optimization results. The least resistance is taken as the optimization goal. Wet surface area is set as the constraint condition, named as area in the table. The length of fore-bodyxaa, the coefficient of the maximum radiusk, and the minimum coefficient of after-body’s radiusrh, are taken as the design variables.

In the hybrid optimization, MMDF takes the PSO’s optimum design point as its starting design point, while in PSO, it starts with the SUBOFF’s original type in the case of velocityv=13.92 kn. The optimization of lines is based on the hybrid optimization strategy. The number of feasible designs is 52 (PSO employs 40, while the MMDF occupies the rest,i.e. 12). In the scheme design phase, the designers can choose them as a feasible scheme. The optimal solutions are listed in Table 3. The original resistance is 461.527N. After the optimization by PSO, the resistance reduces to 434.179N. With the help of MMFD, the optimal solution is further reduced to 431.525N.

In Fig. 9, the comparison between the original lines and the optimal lines of the model 5470 is shown. As can be seen, the optimal lines are of more streamline pattern.

Table 2 Optimization results

Fig. 9 The comparison between the original lines and the optimal lines of the model 5470

6 Conclusions

In this paper, the SUBOFF project model 5470 is adopted in the automatic optimization platform. Using the hybrid optimization search strategy, the globally optimal solution and the optimality are improved. The use of process integration makes the design, analysis and calculation process automatically run. Through the platform, the automatic design and analysis of the hydrodynamic performances of underwater robots can be achieved. Simulation results demonstrate the validity of the optimization strategy proposed. It is concluded that the proposed automatic platform improves the efficiency of selection in the scheme design phase.

In this paper, only resistance and underwater robot’s hull are taken into account. In the future work, more aspects in the hydrodynamic performances will be considered, e.g. propulsion and more complicated manoeuvring such as zigzag manoeuvres, turning circles,etc. More efforts will also be devoted to the optimization of a complex underwater robot, e.g. a hull with fairwater, stern appendages (rudder and/or propeller).

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Author biography

Weilin Luowas born in 1973. He earned the Dr.-Ing. degree in Design and Manufacture of Naval Architecture and Ocean Structure from Shanghai Jiao Tong University (SJTU), China, in 2009. Since 2011, he has been an Associate Professor in the College of Mechanical Engineering and Automation, Fuzhou University, China. He was a postdoctoral fellow in the Centre for Marine Technology and Engineering (CENTEC), Instituto Superior Técnico, University of Lisbon, Portugal from July 2012 to July 2013. His current research interests include ship maneuvering and control, underwater robotics, and artificial intelligent techniques.

1671-9433(2014)03-0274-07

Received date: 2013-10-09.

Accepted date: 2014-05-09.

＊Corresponding author Email: wlluo@fzu.edu.cn

? Harbin Engineering University and Springer-Verlag Berlin Heidelberg 2014