Design of a Toy Submarine Using Underwater Vehicle ... - IEEE Xplore
Design of a Toy Submarine Using Underwater Vehicle Design Optimization Framework Khairul Alam, Tapabrata Ray and Sreenatha G. Anavatti School of Engineering and Information Technology University of New South Wales Australian Defence Force Academy UNSW@ADFA, Canberra, ACT 2600, Australia Telephone: +61 2 6268 8479, Fax: +61 2 6268 8276 Email: [email protected], [email protected], [email protected]
Abstract—This paper presents a framework for optimum design of a small, low-cost, light-weight toy submarine for recreational purposes. Two state of the art optimization algorithms namely Non-dominated sorting genetic algorithm (NSGA-II) and Infeasibility driven evolutionary algorithm (IDEA) have been used in this study to carry out optimization of the toy submarine design. Single objective formulation of the toy submarine design problem is considered in this paper to identify designs with minimum drag and internal clash free assembly. The flexibility of the proposed framework and its ability to identify optimum preliminary designs of a toy submarine are demonstrated. Design identified through the process of optimization is compared with an existing toy submarine to highlight the benefits offered by the present approach.
N OMENCLATURE D d dt l lm ln lt LA1 LA2 nn nt s ZB ZC ZL ZV
Drag Maximum body diameter Smaller diameter of the tail Length overall Length of the parallel middle body Length of the nose Length of the tail Length of the first lever arm Length of the second lever arm Shape variation coefficient of the nose Shape variation coefficient of the tail Longitudinal distance between CB and CG Z-coordinate of the battery unit Z-coordinate of the controller Z-coordinate of the propeller unit for lateral movement Z-coordinate of the propeller unit for vertical movement I. I NTRODUCTION
Unmanned underwater vehicles (UUVs) have received worldwide attention and been widely used in ocean exploration, military and industrial applications [1], [2]. The wide range of applications have resulted in development of hundreds of UUVs with a variety of shapes, sizes, working depth limits, sources of energy, means of propulsion and ways of control. Such vehicles include glider (unpropelled underwater vehicles
978-1-4244-9976-2/11/$26.00 ©2011 IEEE
gliding down in depth and using buoyancy to surface), Remotely Operated Vehicles (ROVs), Autonomous Surface Vehicles (ASVs) and Autonomous Underwater Vehicles (AUVs). In particular, the UUVs have been promoted as a prominent option and tool in oceanographic exploration and exploitation programs. Traditionally, the UUV design process has been largely ‘ad hoc’ with designs governed by experience and rules of thumb [3]. The application of formal optimization methods to the drag minimization or to evaluate optimum design of UUVs have not gained much attention by the researchers so far [4]. It is important to highlight that the use of efficient optimization tools leads to better product quality and improved functionality [5]. In the recent years, some works have considered the problem of finding the optimum hull form for UUVs which include the works of [3], [6]–[8] to minimize drag. Small improvement in drag can result in a substantial saving in thrust requirement. However, much work still needs to be done in terms of optimizing the hull form design to minimize drag and increase propulsion efficiency [9]. Although a number of present works have been devoted to find the optimum hull form for UUVs, limited attention has been paid towards the optimum ‘clash-free’ placement of the internal components and factors affecting controllability, i.e. the centre of gravity (CG) and centre of buoyancy (CB) effects. This paper presents a framework for design optimization of a toy submarine that represents a class of torpedo-shaped underwater vehicles by simultaneously considering both internal clash-free arrangement of on-board components and external size and shape for given design requirements. The objective is to find an appropriate hull shape to minimize drag and optimum clash-free placement of the internal objects for optimal CG/CB separation thereby ensuring better controllability of a vehicle moving submerged near the free surface while fulfilling the design constraints. The organization of this paper is as follows. Section II provides a framework for the design optimization of the toy submarine. Thereafter, the details of the numerical experiment are described in Section III. The numerical results are presented in Section IV. Finally, conclusions are made in
Section V. II. O PTIMIZATION FRAMEWORK This work presents an optimization framework for the design of a toy submarine with minimum drag consideration. The framework incorporates geometry and configuration modules, a hydrodynamics module, several accepted maritime performance and characteristics estimation methods and a suite of optimization algorithms. Shown in Fig. 1 is the flowchart of the optimization framework. The framework facilitates the communication of data from one application to the next, producing an automated multidisciplinary design environment.
1) Hull Geometry and Material Selection: The hull size of the toy submarine is constrained by the space for the onboard instruments that needs to be carried, and the hull shape is constrained by the hydrodynamic characteristics for minimization of drag. Axisymmetric body of revolution moving submerged near to the free surface is considered in this study. Illustration of the parameterization for the hull geometry is shown in Fig. 2, where the body is seen to comprise a nosesection of variable length ln , a mid-section of variable length lm , and a tail-section of variable length lt , making up the total body length of l units.
Fig. 2: Parameterization of the hull geometry The nose radius follow from the Eq. (1), n 1 ln − xn n nn 1 rn = d 1 − 2 ln
(1)
where d is the maximum body diameter in m, which may be varied, and nn is the shape variation coefficient of the nose which may also be varied to give different shapes, as shown in Fig. 3.
Fig. 1: Detail flowchart of the optimization framework A. Geometry and Configuration Modules The basic design concept of the toy submarine employed herein is based on the development of a small, light-weight vehicle that can be easily launched, recovered and operated without any special handling equipments capable of working at snorkeling depth. The design requirements chosen in this study are: • Speed is 0.5 m/s • No longer than 400 mm • Total weight be less than or equal to 450 g • The vehicle to be propelled by one rear propeller and two propellers each for vertical and lateral movements • Cost effective Considering the basic design requirements, the geometry and system configurations for the toy submarine are formulated as follows.
Fig. 3: Parameterization of the nose geometry For the capability of housing the rear propeller and ease of fabrication a long tapered tail cone is used in this study. This shape follows the fluid flow lines and as the contraction is still occurring at the nozzle exit, the velocity of the fluid is still increasing as it leaves the nozzle. The materials for the design vehicle should have the following properties: • good resistance to corrosion • high strength but relatively lightweight • ease of fabrication: can the vehicle be manufactured easily with the chosen material? • cheap • availability
Fig. 4: Parameterization of the tail geometry
The Polyvinyl chloride (PVC) water pipe for it’s intrinsic properties fits best for all the above requirements, and therefore, has been chosen for this study. 2) Propulsion System: The propulsion of the toy submarine under consideration is achieved through the use of three propeller units, one of which is used for vertical movement, i.e. to move the vehicle up and down. Another propeller unit is used to steer the vehicle left and right, and the remaining propeller is used to propel the vehicle forward and backward in the water, as illustrated in Fig. 5.
parts of the toy submarine for optimal CG position. The term clash-free, is defined as the placement of the internal components such as controller, propellers and battery compartment in their respective positions without any overlapping as well as keeping appropriate clearance among them. Practically, the components considered here are irregular in shape. However, for simplicity of the clash-free mechanism, we considered minimum bounding box dimensions of those components in this study. Once the internal parts are placed in a clash free state, the parallel middle body is generated automatically covering the internal arrangement, and then nose, rear propeller and tail cone are attached along with the mid-body, thereby generating the whole toy submarine shape. In the present study, Matlab is used for geometry manipulation, and interfacing with CATIA is done using VBScript macros for the vehicle design within this framework. B. Hydrodynamics Module: Drag Estimation The hull for the design vehicle has been optimized for minimum drag that eventually reduces the submerged vehicle power requirements [4]. For drag estimation, the following formula has been used: D=
Fig. 5: Configuration of the propulsion system To achieve the required design speed of 0.5 m/s, optimization of the entire vehicle needs to be done to reduce drag to a minimum while increasing thrust to a maximum to improve the efficiency of the propellers. Therefore, the position of the propeller units for vertical and lateral movements as illustrated in Fig. 5, are not fixed, but are rather free to move within the entire mid-section. During optimization process, the optimizer chooses the optimal positions of those propeller units while designing the vehicle. 3) Power Source: Most underwater vehicles in use today are powered by low cost rechargeable batteries. A few of the larger vehicles are powered by solid Polymer Electrolyte Fuel Cell (PEFC) [10], aluminium/oxygen fuel cell [11] and by solar energy [12] where endurance is a keen issue. However, they require substantial maintenance and expensive refills for continuous deployment. Due to simplicity and commercial availability, the AA size alkaline batteries with nominal voltage of 1.5 V and energy density of 140 Whr/kg have been selected in this study. These batteries are attractive as they are cheap, small and usually safe. 4) Clash-free Mechanism: A remarkable point of this work is to apply ‘clash-free’ mechanism while arranging the internal
1 2 ρV CV S 2
(2)
where ρ is the density of the fluid in kg/m3 , V is the velocity in m/s, S is the wetted surface area of the vehicle in m2 , and CV is the coefficient of viscous resistance for the smooth bare hull. Three methods- Virginia Tech (VT) [3], MIT [13] and G&J method [14] are employed in this study to measure the coefficient of viscous resistance (CV ) in three different ways to ensure uniformity in drag estimation of the design vehicle. C. Optimization Modules In this framework, two state of the art optimization algorithms, NSGA-II and IDEA are used. The algorithms are written in Matlab and are integrated with CATIA along with VBScript to automate the whole design process. • NSGA-II: Non-dominated Sorting Genetic Algorithm II (NSGA-II) proposed by Deb et al. [15], is one of the most popular population based optimization algorithms that has been successfully used in a number of real life applications. The main steps of NSGA-II are outlined in Algorithm 1. It uses Simulated Binary Crossover (SBX) and polynomial mutation for generating off-springs. Individual solutions in a population are ranked based on their fitness value. Feasible solutions are considered better than infeasible solutions and are ranked higher. Feasible and infeasible solutions are ranked separately. For single objective optimization feasible solutions are sorted based on the objective value while for multi-objective optimization the solutions are ranked based on non-dominance. • IDEA: Solutions to real-life constrained optimization problems often lie on constraint boundaries. In reality,
Algorithm 1 Non-dominated Sorting Genetic Algorithm II (NSGA-II) Require: NG > 1 {Number of Generations} 1: Initialize (P1 ) {Create an initial population of solutions} 2: Evaluate (P1 ) 3: Rank (P1 ) {Assign ranks to each solution} 4: for i = 2 to NG do 5: Ci = Evolve (Pi−1 ) {Create child solutions from parents of previous generation} 6: Evaluate Ci {Compute the performance of the child solutions} 7: Rank (Pi−1 + Ci ) {Assign ranks to each solution} 8: Pi = Reduce (Pi−1 + Ci ) {Identify parents for the next generation} 9: end for
a designer is interested to look at the solution that might be marginally infeasible. NSGA-II and most other optimization algorithms intrinsically prefer a feasible solution over an infeasible solution during its course of search. However, Infeasibility Driven Evolutionary Algorithm (IDEA) introduced by Singh et al. [16], suggests that preservation of marginally infeasible solutions during the course of search can expedite the rate of convergence. Since the Pareto optimal solutions for a constrained problem usually lie on a constraint boundary, IDEA tries to focus the search near the constraint boundaries by maintaining a set of infeasible solutions (in addition to feasible solutions) near the constraint boundary during the search. The main steps of IDEA are outlined in Algorithm 2. IDEA ranks the infeasible solutions higher than the feasible solutions to provide a selection pressure to create better infeasible solutions resulting in an active search through the infeasible search space. Interested readers are referred to Ray et al. [17] for a comparison of IDEA with other state of the art optimization algorithms. Algorithm 2 Infeasibility Driven Evolutionary Algorithm (IDEA) Require: N {Population Size} Require: NG > 1 {Number of Generations} Require: 0 < α < 1 {Proportion of infeasible solutions} 1: Ninf = α ∗ N 2: Nf = N − Ninf 3: pop1 = Initialize() 4: Evaluate(pop1 ) 5: for i = 2 to NG do 6: childpopi−1 = Evolve(popi−1 ) 7: Evaluate(childpopi−1 ) 8: (Sf , Sinf ) = Split(popi−1 + childpopi−1 ) 9: Rank(Sf ) 10: Rank(Sinf ) 11: popi = Sinf (1, Ninf ) + Sf (1, Nf ) 12: end for
III. N UMERICAL E XPERIMENT In this section, the optimization problem formulation is presented. Based on the design requirements, the following problem has been formulated. Single objective optimization The single objective optimization problem is posed as the identification of a vehicle hull form with minimum drag as well as ‘clash-free’ optimal placement of the internal objects subject to the constraints on lever arms and CG/CB separation. The first (LA1 ) and second (LA2 ) lever arms are the longitudinal distances of the propellers from the centre of buoyancy respectively. The higher value of lever arm produces higher pitching and turning moments that lead to better diving and heading changes. The CG/CB separation (s) is the longitudinal distance of the centre of gravity from centre of buoyancy. The lower the value of s, the closer the position of the CG and CB that leads to better stability of the vehicle. Minimization of drag is important because minimum drag leads to least power consumption for propulsion, and corresponding savings in the operating costs. The objective function, constraints and design variables are listed in the Eq. (3). Minimize: f (1) = D Constraints: g (1) = LA1 ≥ 45 mm; g (2) = LA2 ≥ 90 mm g (3) = s ≤ 4 mm
(3)
Design variables: 0 ≤ ZC ≤ 300 mm; 0 ≤ ZV ≤ 300 mm 0 ≤ ZB ≤ 300 mm; 0 ≤ ZL ≤ 300 mm 35 ≤ dt ≤ 50 mm; 80 ≤ lt ≤ 150 mm 1.5 ≤ nn ≤ 3; 45 ≤ ln ≤ 100 mm The above formulated problem is solved using NSGA-II and IDEA. Multiple runs are performed varying parameterscrossover probability, mutation probability, crossover distribution index and mutation distribution index. The values of the parameters are listed in Table I, and for each parameter combination, both the algorithms are run with two different random seeds. TABLE I: Parameters used for NSGA-II and IDEA Parameter Crossover probability Mutation probability Crossover distribution index Mutation distribution index
Value 0.9 0.1 10 20
A population size of 500 is evolved for 300 generations, resulting in 150,000 function evaluations for each run. Twenty independent runs are done using NSGA-II and IDEA. For IDEA, infeasibility ratio (α) of 0.2 is used.
0.22
IV. R ESULTS AND D ISCUSSION A. Single Objective Optimization Results
0.16 NSGA−II IDEA
0.18 Drag (N)
Shown in Fig. 6 is the result of the best run for the single objective drag minimization problem using NSGA-II and IDEA.
0.15
NSGA−II IDEA
0.2
0.16 0.14 0.12
0.14 0.1 Drag (N)
0.13 0.08 0
0.12 0.11
5 10 Function evaluations
15 4
x 10
Fig. 7: Progress plot of median design for single objective drag minimization using NSGA-II and IDEA
0.1 0.09 0.08 0
5 10 Function evaluations
15 4
x 10
Fig. 6: Progress plot of the best design for single objective drag minimization using NSGA-II and IDEA It can be observed that both optimization algorithms are able to achieve near optimal value of drag in approximately 37000 function evaluations. The statistics of results computed across 20 runs for each algorithm is reported in Table II. It is seen that the best, median and the average objective values obtained by IDEA are better than NSGA-II. In addition, the standard deviation across the multiple runs is much less than NSGA-II, indicating that it is able to achieve better objective values more consistently. This is also reflected in the median runs as shown in Fig. 7, where IDEA is seen to converge faster than NSGA-II.
Fig. 8: CATIA model of the resulting optimized toy submarine Nose
Propeller unit for vertical movement
Controller unit
Propeller unit for lateral movement
Battery compartment
Tail
Propeller unit for longitudinal movement
Fig. 9: Configuration of the resulting optimized toy submarine
TABLE II: Single objective drag minimization results Design Best Mean Median Worst SD
NSGA-II 0.084003 0.086081 0.0859657 0.087465 0.000937534
IDEA 0.082177 0.083828 0.0841192 0.086806 0.000892474
B. Results of Optimum Toy Submarine Design Based on the results obtained by carrying out optimization of drag, Figs. 8-10 show the optimal shape and internal configurations of the optimized toy submarine. The resulting performance criteria of the optimized toy submarine are listed in Table III. The values of the lever arms and CG/CB separation as reported in Table III, clearly indicate that the design constraints are satisfied while achieving minimum drag. An example of similar existing toy submarine available in the market is USS Dallas RC toy submarine. This model
Fig. 10: Longitudinal section of the resulting optimized toy submarine
submarine has independent propellers to allow it to ascend, descend, turn and move forward and backward. Configuration of the internal components of the toy submarine is shown in Fig. 12. The specifications and performance criteria measured for this toy submarine are also listed in Table III. It can be observed that the performance criteria of the resulting optimized toy submarine are close to the results measured for the existing toy submarine. In addition, the length of the first lever arm of the optimized toy submarine is higher and also the value of CG/CB separation is lower than that of the existing toy submarine; thereby ensuring better
Fig. 11: USS Dallas RC toy submarine Nose
Propeller unit for vertical movement
Controller unit
Propeller unit for lateral movement
Battery compartment
Tail
Propeller unit for longitudinal movement
Fig. 12: Configuration of the USS Dallas RC toy submarine TABLE III: Performance criteria of the existing USS Dallas RC and optimized toy submarines Vehicle particulars Nose length Parallel middle body length Tail length Length overall Maximum diameter Length to diameter ratio Maximum dimension of the inner square Wetted surface area Displacement volume Mass of the displaced water Total mass of the vehicle Length of the first lever arm Length of the second lever arm X-coordinate of CG Y-coordinate of CG Z-coordinate of CG X-coordinate of CB Y-coordinate of CB Z-coordinate of CB Longitudinal distance between CB and CG Nominal speed Drag (VT method) Drag (G&J method) Drag (MIT method)
USS Dallas RC 45 mm 210 mm 95 mm 350 mm 60 mm 5.8 39.6 mm
Optimized 49 mm 231 mm 80 mm 360 mm 58 mm 6.2 38 mm
0.082385 m2 0.000437 m3 437 g 430 g 45 mm 90 mm -0.981462 mm -0.210313 mm 167.083 mm 0 0 163.375 mm 3.705 mm
0.082624 m2 0.000433 m3 433 g 428 g 48 mm 90 mm -0.982488 mm -0.210533 mm 172.734 mm 0 0 169.906 mm 2.828 mm
0.5 m/s 0.0792024 N 0.0800956 N 0.0825858 N
0.5 m/s 0.0789568 N 0.0798317 N 0.0821771 N
performance and controllability of the designed vehicle over the existing one. It is also reflected that the drag of the optimized toy submarine is lower than that of the existing toy submarine for the same marginal speed. V. C ONCLUSIONS Introduced in this paper is an optimization framework for the preliminary design of a small-scale, low-cost, lightweight toy submarine for recreational purposes. The use of an
efficient integrated analysis/design system comprising highend mathematical (Matlab) and CAD package (CATIA), the framework is able to generate an optimized geometry of the toy submarine based on given design requirements. A single objective constrained optimization formulation of the toy submarine design problem is considered in this paper and solved using two state of the art optimization algorithms NSGA-II and IDEA. The study demonstrated the benefits of preserving marginally infeasible solutions in IDEA that accounts for superior performance of IDEA over NSGA-II for constrained optimization problems. It is emphasized that the modularity and catalogue driven structure of the proposed framework allows for design of underwater vehicles of various sizes, propulsions and power systems. With the final optimum design, more and more refined analysis can be performed using external tools as a post-process. The integration of computational fluid dynamics (CFD) tool for better drag estimation, and an analysis module that could assist in vehicle dynamics and control analysis remain to be performed in future works. ACKNOWLEDGEMENTS The authors would like to thank Dr. Amitay Isaacs, Mr. Hemant K. Singh and Mr. Ahmad F. Ayob for their support in programming the methods. R EFERENCES [1] W. Wang, X. Chen, A. Marburg, J. Chase, and C. Hann, “A low-cost unmanned underwater vehicle prototype for shallow water tasks,” in Proceedings of the IEEE/ASME International Conference on Mechatronic and Embedded Systems and Applications, MESA 2008, Beijing, China, 2008, pp. 204–209. [2] K. Mohseni, “Pulsatile vortex generators for low-speed maneuvering of small underwater vehicles,” Ocean Engineering, vol. 33, pp. 2209–2223, 2006. [3] M. A. Martz, “Preliminary design of an autonomous underwater vehicle using a multiple-objective genetic optimizer,” Master’s thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, United States, May 27 2008. [4] J. S. Parsons, R. E. Goodson, and F. R. Goldschmied, “Shaping of axisymmetric bodies for minimum drag in incompressible flow,” J. Hydronautics, vol. 8, no. 3, pp. 100–107, 1974. [5] M. Diez and D. Peri, “Robust optimization for ship conceptual design,” Ocean Engineering, vol. 37, pp. 966–977, 2010. [6] T. Lutz and S. Wagner, “Numerical shape optimization of natural laminar flow bodies,” in Proceedings of 21st ICAS Congress, Melbourne, Australia, 1998. [7] V. Bertram and A. Alvarez, “Hydrodynamic aspects of AUV design,” in The Fifth Conference on Computer and IT Applications in the Maritime Industries (COMPIT), Oegstgeest, Netherlands, 2006, pp. 45–53. [8] A. Alvarez, V. Bertram, and L. Gualdesi, “Hull hydrodynamic optimization of autonomous underwater vehicles operating at snorkeling depth,” Ocean Engineering, vol. 36, pp. 105–112, 2009. [9] T. Joung, K. Sammut, F. He, and S.-K. Lee, “A study on the design optimization of an AUV by using computational fluid dynamic analysis,” in Proceedings of the Nineteenth (2009) International Offshore and Polar Engineering Conference, Osaka, Japan, 2009. [10] T. Hyakudome, T. Aoki, T. Murashima, S. Tsukioka, H. Yoshida, H. Nakajoh, T. Ida, S. Ishibashi, and R. Sasamoto, “Key technologies for AUV URASHIMA,” in Oceans Conference Record (IEEE), vol. 1, 2002, pp. 162–166. [11] K. Vestgard, R. Hansen, B. Jalving, and O. Pedersen, “The HUGIN 3000 survey AUV - design and field results,” in Proceedings of the Eleventh (2001) International Offshore and Polar Engineering Conference, Stavanger, Norway, vol. 4, 2001, pp. 679–684.
[12] J. Jalbert, J. Baker, J. Duchesney, P. Pietryka, W. Dalton, D. Blidberg, S. Chappell, R. Nitzel, and K. Holappa, “A solar-powered autonomous underwater vehicle,” in Oceans Conference Record (IEEE), vol. 2, 2003, pp. 1132–1140. [13] H. Jackson, MIT Professional Summer Course Submarine Design Trends, 1992. [14] T. Gillmer and B. Johnson, Introduction to Naval Architecture, 2nd ed. US Naval Institute Press, 1982. [15] K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” Evolutionary Computation,
IEEE Transactions on, vol. 6, pp. 182–197, 2002. [16] H. K. Singh, A. Isaacs, T. Ray, and W. Smith, “Infeasibility driven evolutionary algorithm (IDEA) for engineering design optimization,” in 21st Australasian Joint Conference on Artificial Intelligence: Advances in Artificial Intelligence, Auckland, NewZealand (2008), Springer-Verlag Berlin Heidelberg, no. LNAI 5360, 2008, pp. 104–115. [17] T. Ray, H. K. Singh, A. Isaacs, and W. Smith, Infeasibility Driven Evolutionary Algorithm for Constrained Optimization, E. Mezura-Montes, Ed. Constraint Handling in Evolutionary Optimization, Studies in Computational Intelligence Series 198, 2009.
Abstract—This paper presents a framework for optimum design of a small, low-cost, light-weight toy submarine for recreational purposes. Two state of the art optimization algorithms namely Non-dominated sorting genetic algorithm (NSGA-II) and Infeasibility driven evolutionary algorithm (IDEA) have been used in this study to carry out optimization of the toy submarine design. Single objective formulation of the toy submarine design problem is considered in this paper to identify designs with minimum drag and internal clash free assembly. The flexibility of the proposed framework and its ability to identify optimum preliminary designs of a toy submarine are demonstrated. Design identified through the process of optimization is compared with an existing toy submarine to highlight the benefits offered by the present approach.
N OMENCLATURE D d dt l lm ln lt LA1 LA2 nn nt s ZB ZC ZL ZV
Drag Maximum body diameter Smaller diameter of the tail Length overall Length of the parallel middle body Length of the nose Length of the tail Length of the first lever arm Length of the second lever arm Shape variation coefficient of the nose Shape variation coefficient of the tail Longitudinal distance between CB and CG Z-coordinate of the battery unit Z-coordinate of the controller Z-coordinate of the propeller unit for lateral movement Z-coordinate of the propeller unit for vertical movement I. I NTRODUCTION
Unmanned underwater vehicles (UUVs) have received worldwide attention and been widely used in ocean exploration, military and industrial applications [1], [2]. The wide range of applications have resulted in development of hundreds of UUVs with a variety of shapes, sizes, working depth limits, sources of energy, means of propulsion and ways of control. Such vehicles include glider (unpropelled underwater vehicles
978-1-4244-9976-2/11/$26.00 ©2011 IEEE
gliding down in depth and using buoyancy to surface), Remotely Operated Vehicles (ROVs), Autonomous Surface Vehicles (ASVs) and Autonomous Underwater Vehicles (AUVs). In particular, the UUVs have been promoted as a prominent option and tool in oceanographic exploration and exploitation programs. Traditionally, the UUV design process has been largely ‘ad hoc’ with designs governed by experience and rules of thumb [3]. The application of formal optimization methods to the drag minimization or to evaluate optimum design of UUVs have not gained much attention by the researchers so far [4]. It is important to highlight that the use of efficient optimization tools leads to better product quality and improved functionality [5]. In the recent years, some works have considered the problem of finding the optimum hull form for UUVs which include the works of [3], [6]–[8] to minimize drag. Small improvement in drag can result in a substantial saving in thrust requirement. However, much work still needs to be done in terms of optimizing the hull form design to minimize drag and increase propulsion efficiency [9]. Although a number of present works have been devoted to find the optimum hull form for UUVs, limited attention has been paid towards the optimum ‘clash-free’ placement of the internal components and factors affecting controllability, i.e. the centre of gravity (CG) and centre of buoyancy (CB) effects. This paper presents a framework for design optimization of a toy submarine that represents a class of torpedo-shaped underwater vehicles by simultaneously considering both internal clash-free arrangement of on-board components and external size and shape for given design requirements. The objective is to find an appropriate hull shape to minimize drag and optimum clash-free placement of the internal objects for optimal CG/CB separation thereby ensuring better controllability of a vehicle moving submerged near the free surface while fulfilling the design constraints. The organization of this paper is as follows. Section II provides a framework for the design optimization of the toy submarine. Thereafter, the details of the numerical experiment are described in Section III. The numerical results are presented in Section IV. Finally, conclusions are made in
Section V. II. O PTIMIZATION FRAMEWORK This work presents an optimization framework for the design of a toy submarine with minimum drag consideration. The framework incorporates geometry and configuration modules, a hydrodynamics module, several accepted maritime performance and characteristics estimation methods and a suite of optimization algorithms. Shown in Fig. 1 is the flowchart of the optimization framework. The framework facilitates the communication of data from one application to the next, producing an automated multidisciplinary design environment.
1) Hull Geometry and Material Selection: The hull size of the toy submarine is constrained by the space for the onboard instruments that needs to be carried, and the hull shape is constrained by the hydrodynamic characteristics for minimization of drag. Axisymmetric body of revolution moving submerged near to the free surface is considered in this study. Illustration of the parameterization for the hull geometry is shown in Fig. 2, where the body is seen to comprise a nosesection of variable length ln , a mid-section of variable length lm , and a tail-section of variable length lt , making up the total body length of l units.
Fig. 2: Parameterization of the hull geometry The nose radius follow from the Eq. (1), n 1 ln − xn n nn 1 rn = d 1 − 2 ln
(1)
where d is the maximum body diameter in m, which may be varied, and nn is the shape variation coefficient of the nose which may also be varied to give different shapes, as shown in Fig. 3.
Fig. 1: Detail flowchart of the optimization framework A. Geometry and Configuration Modules The basic design concept of the toy submarine employed herein is based on the development of a small, light-weight vehicle that can be easily launched, recovered and operated without any special handling equipments capable of working at snorkeling depth. The design requirements chosen in this study are: • Speed is 0.5 m/s • No longer than 400 mm • Total weight be less than or equal to 450 g • The vehicle to be propelled by one rear propeller and two propellers each for vertical and lateral movements • Cost effective Considering the basic design requirements, the geometry and system configurations for the toy submarine are formulated as follows.
Fig. 3: Parameterization of the nose geometry For the capability of housing the rear propeller and ease of fabrication a long tapered tail cone is used in this study. This shape follows the fluid flow lines and as the contraction is still occurring at the nozzle exit, the velocity of the fluid is still increasing as it leaves the nozzle. The materials for the design vehicle should have the following properties: • good resistance to corrosion • high strength but relatively lightweight • ease of fabrication: can the vehicle be manufactured easily with the chosen material? • cheap • availability
Fig. 4: Parameterization of the tail geometry
The Polyvinyl chloride (PVC) water pipe for it’s intrinsic properties fits best for all the above requirements, and therefore, has been chosen for this study. 2) Propulsion System: The propulsion of the toy submarine under consideration is achieved through the use of three propeller units, one of which is used for vertical movement, i.e. to move the vehicle up and down. Another propeller unit is used to steer the vehicle left and right, and the remaining propeller is used to propel the vehicle forward and backward in the water, as illustrated in Fig. 5.
parts of the toy submarine for optimal CG position. The term clash-free, is defined as the placement of the internal components such as controller, propellers and battery compartment in their respective positions without any overlapping as well as keeping appropriate clearance among them. Practically, the components considered here are irregular in shape. However, for simplicity of the clash-free mechanism, we considered minimum bounding box dimensions of those components in this study. Once the internal parts are placed in a clash free state, the parallel middle body is generated automatically covering the internal arrangement, and then nose, rear propeller and tail cone are attached along with the mid-body, thereby generating the whole toy submarine shape. In the present study, Matlab is used for geometry manipulation, and interfacing with CATIA is done using VBScript macros for the vehicle design within this framework. B. Hydrodynamics Module: Drag Estimation The hull for the design vehicle has been optimized for minimum drag that eventually reduces the submerged vehicle power requirements [4]. For drag estimation, the following formula has been used: D=
Fig. 5: Configuration of the propulsion system To achieve the required design speed of 0.5 m/s, optimization of the entire vehicle needs to be done to reduce drag to a minimum while increasing thrust to a maximum to improve the efficiency of the propellers. Therefore, the position of the propeller units for vertical and lateral movements as illustrated in Fig. 5, are not fixed, but are rather free to move within the entire mid-section. During optimization process, the optimizer chooses the optimal positions of those propeller units while designing the vehicle. 3) Power Source: Most underwater vehicles in use today are powered by low cost rechargeable batteries. A few of the larger vehicles are powered by solid Polymer Electrolyte Fuel Cell (PEFC) [10], aluminium/oxygen fuel cell [11] and by solar energy [12] where endurance is a keen issue. However, they require substantial maintenance and expensive refills for continuous deployment. Due to simplicity and commercial availability, the AA size alkaline batteries with nominal voltage of 1.5 V and energy density of 140 Whr/kg have been selected in this study. These batteries are attractive as they are cheap, small and usually safe. 4) Clash-free Mechanism: A remarkable point of this work is to apply ‘clash-free’ mechanism while arranging the internal
1 2 ρV CV S 2
(2)
where ρ is the density of the fluid in kg/m3 , V is the velocity in m/s, S is the wetted surface area of the vehicle in m2 , and CV is the coefficient of viscous resistance for the smooth bare hull. Three methods- Virginia Tech (VT) [3], MIT [13] and G&J method [14] are employed in this study to measure the coefficient of viscous resistance (CV ) in three different ways to ensure uniformity in drag estimation of the design vehicle. C. Optimization Modules In this framework, two state of the art optimization algorithms, NSGA-II and IDEA are used. The algorithms are written in Matlab and are integrated with CATIA along with VBScript to automate the whole design process. • NSGA-II: Non-dominated Sorting Genetic Algorithm II (NSGA-II) proposed by Deb et al. [15], is one of the most popular population based optimization algorithms that has been successfully used in a number of real life applications. The main steps of NSGA-II are outlined in Algorithm 1. It uses Simulated Binary Crossover (SBX) and polynomial mutation for generating off-springs. Individual solutions in a population are ranked based on their fitness value. Feasible solutions are considered better than infeasible solutions and are ranked higher. Feasible and infeasible solutions are ranked separately. For single objective optimization feasible solutions are sorted based on the objective value while for multi-objective optimization the solutions are ranked based on non-dominance. • IDEA: Solutions to real-life constrained optimization problems often lie on constraint boundaries. In reality,
Algorithm 1 Non-dominated Sorting Genetic Algorithm II (NSGA-II) Require: NG > 1 {Number of Generations} 1: Initialize (P1 ) {Create an initial population of solutions} 2: Evaluate (P1 ) 3: Rank (P1 ) {Assign ranks to each solution} 4: for i = 2 to NG do 5: Ci = Evolve (Pi−1 ) {Create child solutions from parents of previous generation} 6: Evaluate Ci {Compute the performance of the child solutions} 7: Rank (Pi−1 + Ci ) {Assign ranks to each solution} 8: Pi = Reduce (Pi−1 + Ci ) {Identify parents for the next generation} 9: end for
a designer is interested to look at the solution that might be marginally infeasible. NSGA-II and most other optimization algorithms intrinsically prefer a feasible solution over an infeasible solution during its course of search. However, Infeasibility Driven Evolutionary Algorithm (IDEA) introduced by Singh et al. [16], suggests that preservation of marginally infeasible solutions during the course of search can expedite the rate of convergence. Since the Pareto optimal solutions for a constrained problem usually lie on a constraint boundary, IDEA tries to focus the search near the constraint boundaries by maintaining a set of infeasible solutions (in addition to feasible solutions) near the constraint boundary during the search. The main steps of IDEA are outlined in Algorithm 2. IDEA ranks the infeasible solutions higher than the feasible solutions to provide a selection pressure to create better infeasible solutions resulting in an active search through the infeasible search space. Interested readers are referred to Ray et al. [17] for a comparison of IDEA with other state of the art optimization algorithms. Algorithm 2 Infeasibility Driven Evolutionary Algorithm (IDEA) Require: N {Population Size} Require: NG > 1 {Number of Generations} Require: 0 < α < 1 {Proportion of infeasible solutions} 1: Ninf = α ∗ N 2: Nf = N − Ninf 3: pop1 = Initialize() 4: Evaluate(pop1 ) 5: for i = 2 to NG do 6: childpopi−1 = Evolve(popi−1 ) 7: Evaluate(childpopi−1 ) 8: (Sf , Sinf ) = Split(popi−1 + childpopi−1 ) 9: Rank(Sf ) 10: Rank(Sinf ) 11: popi = Sinf (1, Ninf ) + Sf (1, Nf ) 12: end for
III. N UMERICAL E XPERIMENT In this section, the optimization problem formulation is presented. Based on the design requirements, the following problem has been formulated. Single objective optimization The single objective optimization problem is posed as the identification of a vehicle hull form with minimum drag as well as ‘clash-free’ optimal placement of the internal objects subject to the constraints on lever arms and CG/CB separation. The first (LA1 ) and second (LA2 ) lever arms are the longitudinal distances of the propellers from the centre of buoyancy respectively. The higher value of lever arm produces higher pitching and turning moments that lead to better diving and heading changes. The CG/CB separation (s) is the longitudinal distance of the centre of gravity from centre of buoyancy. The lower the value of s, the closer the position of the CG and CB that leads to better stability of the vehicle. Minimization of drag is important because minimum drag leads to least power consumption for propulsion, and corresponding savings in the operating costs. The objective function, constraints and design variables are listed in the Eq. (3). Minimize: f (1) = D Constraints: g (1) = LA1 ≥ 45 mm; g (2) = LA2 ≥ 90 mm g (3) = s ≤ 4 mm
(3)
Design variables: 0 ≤ ZC ≤ 300 mm; 0 ≤ ZV ≤ 300 mm 0 ≤ ZB ≤ 300 mm; 0 ≤ ZL ≤ 300 mm 35 ≤ dt ≤ 50 mm; 80 ≤ lt ≤ 150 mm 1.5 ≤ nn ≤ 3; 45 ≤ ln ≤ 100 mm The above formulated problem is solved using NSGA-II and IDEA. Multiple runs are performed varying parameterscrossover probability, mutation probability, crossover distribution index and mutation distribution index. The values of the parameters are listed in Table I, and for each parameter combination, both the algorithms are run with two different random seeds. TABLE I: Parameters used for NSGA-II and IDEA Parameter Crossover probability Mutation probability Crossover distribution index Mutation distribution index
Value 0.9 0.1 10 20
A population size of 500 is evolved for 300 generations, resulting in 150,000 function evaluations for each run. Twenty independent runs are done using NSGA-II and IDEA. For IDEA, infeasibility ratio (α) of 0.2 is used.
0.22
IV. R ESULTS AND D ISCUSSION A. Single Objective Optimization Results
0.16 NSGA−II IDEA
0.18 Drag (N)
Shown in Fig. 6 is the result of the best run for the single objective drag minimization problem using NSGA-II and IDEA.
0.15
NSGA−II IDEA
0.2
0.16 0.14 0.12
0.14 0.1 Drag (N)
0.13 0.08 0
0.12 0.11
5 10 Function evaluations
15 4
x 10
Fig. 7: Progress plot of median design for single objective drag minimization using NSGA-II and IDEA
0.1 0.09 0.08 0
5 10 Function evaluations
15 4
x 10
Fig. 6: Progress plot of the best design for single objective drag minimization using NSGA-II and IDEA It can be observed that both optimization algorithms are able to achieve near optimal value of drag in approximately 37000 function evaluations. The statistics of results computed across 20 runs for each algorithm is reported in Table II. It is seen that the best, median and the average objective values obtained by IDEA are better than NSGA-II. In addition, the standard deviation across the multiple runs is much less than NSGA-II, indicating that it is able to achieve better objective values more consistently. This is also reflected in the median runs as shown in Fig. 7, where IDEA is seen to converge faster than NSGA-II.
Fig. 8: CATIA model of the resulting optimized toy submarine Nose
Propeller unit for vertical movement
Controller unit
Propeller unit for lateral movement
Battery compartment
Tail
Propeller unit for longitudinal movement
Fig. 9: Configuration of the resulting optimized toy submarine
TABLE II: Single objective drag minimization results Design Best Mean Median Worst SD
NSGA-II 0.084003 0.086081 0.0859657 0.087465 0.000937534
IDEA 0.082177 0.083828 0.0841192 0.086806 0.000892474
B. Results of Optimum Toy Submarine Design Based on the results obtained by carrying out optimization of drag, Figs. 8-10 show the optimal shape and internal configurations of the optimized toy submarine. The resulting performance criteria of the optimized toy submarine are listed in Table III. The values of the lever arms and CG/CB separation as reported in Table III, clearly indicate that the design constraints are satisfied while achieving minimum drag. An example of similar existing toy submarine available in the market is USS Dallas RC toy submarine. This model
Fig. 10: Longitudinal section of the resulting optimized toy submarine
submarine has independent propellers to allow it to ascend, descend, turn and move forward and backward. Configuration of the internal components of the toy submarine is shown in Fig. 12. The specifications and performance criteria measured for this toy submarine are also listed in Table III. It can be observed that the performance criteria of the resulting optimized toy submarine are close to the results measured for the existing toy submarine. In addition, the length of the first lever arm of the optimized toy submarine is higher and also the value of CG/CB separation is lower than that of the existing toy submarine; thereby ensuring better
Fig. 11: USS Dallas RC toy submarine Nose
Propeller unit for vertical movement
Controller unit
Propeller unit for lateral movement
Battery compartment
Tail
Propeller unit for longitudinal movement
Fig. 12: Configuration of the USS Dallas RC toy submarine TABLE III: Performance criteria of the existing USS Dallas RC and optimized toy submarines Vehicle particulars Nose length Parallel middle body length Tail length Length overall Maximum diameter Length to diameter ratio Maximum dimension of the inner square Wetted surface area Displacement volume Mass of the displaced water Total mass of the vehicle Length of the first lever arm Length of the second lever arm X-coordinate of CG Y-coordinate of CG Z-coordinate of CG X-coordinate of CB Y-coordinate of CB Z-coordinate of CB Longitudinal distance between CB and CG Nominal speed Drag (VT method) Drag (G&J method) Drag (MIT method)
USS Dallas RC 45 mm 210 mm 95 mm 350 mm 60 mm 5.8 39.6 mm
Optimized 49 mm 231 mm 80 mm 360 mm 58 mm 6.2 38 mm
0.082385 m2 0.000437 m3 437 g 430 g 45 mm 90 mm -0.981462 mm -0.210313 mm 167.083 mm 0 0 163.375 mm 3.705 mm
0.082624 m2 0.000433 m3 433 g 428 g 48 mm 90 mm -0.982488 mm -0.210533 mm 172.734 mm 0 0 169.906 mm 2.828 mm
0.5 m/s 0.0792024 N 0.0800956 N 0.0825858 N
0.5 m/s 0.0789568 N 0.0798317 N 0.0821771 N
performance and controllability of the designed vehicle over the existing one. It is also reflected that the drag of the optimized toy submarine is lower than that of the existing toy submarine for the same marginal speed. V. C ONCLUSIONS Introduced in this paper is an optimization framework for the preliminary design of a small-scale, low-cost, lightweight toy submarine for recreational purposes. The use of an
efficient integrated analysis/design system comprising highend mathematical (Matlab) and CAD package (CATIA), the framework is able to generate an optimized geometry of the toy submarine based on given design requirements. A single objective constrained optimization formulation of the toy submarine design problem is considered in this paper and solved using two state of the art optimization algorithms NSGA-II and IDEA. The study demonstrated the benefits of preserving marginally infeasible solutions in IDEA that accounts for superior performance of IDEA over NSGA-II for constrained optimization problems. It is emphasized that the modularity and catalogue driven structure of the proposed framework allows for design of underwater vehicles of various sizes, propulsions and power systems. With the final optimum design, more and more refined analysis can be performed using external tools as a post-process. The integration of computational fluid dynamics (CFD) tool for better drag estimation, and an analysis module that could assist in vehicle dynamics and control analysis remain to be performed in future works. ACKNOWLEDGEMENTS The authors would like to thank Dr. Amitay Isaacs, Mr. Hemant K. Singh and Mr. Ahmad F. Ayob for their support in programming the methods. R EFERENCES [1] W. Wang, X. Chen, A. Marburg, J. Chase, and C. Hann, “A low-cost unmanned underwater vehicle prototype for shallow water tasks,” in Proceedings of the IEEE/ASME International Conference on Mechatronic and Embedded Systems and Applications, MESA 2008, Beijing, China, 2008, pp. 204–209. [2] K. Mohseni, “Pulsatile vortex generators for low-speed maneuvering of small underwater vehicles,” Ocean Engineering, vol. 33, pp. 2209–2223, 2006. [3] M. A. Martz, “Preliminary design of an autonomous underwater vehicle using a multiple-objective genetic optimizer,” Master’s thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, United States, May 27 2008. [4] J. S. Parsons, R. E. Goodson, and F. R. Goldschmied, “Shaping of axisymmetric bodies for minimum drag in incompressible flow,” J. Hydronautics, vol. 8, no. 3, pp. 100–107, 1974. [5] M. Diez and D. Peri, “Robust optimization for ship conceptual design,” Ocean Engineering, vol. 37, pp. 966–977, 2010. [6] T. Lutz and S. Wagner, “Numerical shape optimization of natural laminar flow bodies,” in Proceedings of 21st ICAS Congress, Melbourne, Australia, 1998. [7] V. Bertram and A. Alvarez, “Hydrodynamic aspects of AUV design,” in The Fifth Conference on Computer and IT Applications in the Maritime Industries (COMPIT), Oegstgeest, Netherlands, 2006, pp. 45–53. [8] A. Alvarez, V. Bertram, and L. Gualdesi, “Hull hydrodynamic optimization of autonomous underwater vehicles operating at snorkeling depth,” Ocean Engineering, vol. 36, pp. 105–112, 2009. [9] T. Joung, K. Sammut, F. He, and S.-K. Lee, “A study on the design optimization of an AUV by using computational fluid dynamic analysis,” in Proceedings of the Nineteenth (2009) International Offshore and Polar Engineering Conference, Osaka, Japan, 2009. [10] T. Hyakudome, T. Aoki, T. Murashima, S. Tsukioka, H. Yoshida, H. Nakajoh, T. Ida, S. Ishibashi, and R. Sasamoto, “Key technologies for AUV URASHIMA,” in Oceans Conference Record (IEEE), vol. 1, 2002, pp. 162–166. [11] K. Vestgard, R. Hansen, B. Jalving, and O. Pedersen, “The HUGIN 3000 survey AUV - design and field results,” in Proceedings of the Eleventh (2001) International Offshore and Polar Engineering Conference, Stavanger, Norway, vol. 4, 2001, pp. 679–684.
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