Research on Multidisciplinary Design Optimization Methods for Cylindrical Underwater Vehicle

SU Yu-ming,CUI Tong,ZHU Wei,CAO Jian,YANG Zhuo-yi

(1.State Key Laboratory of Autonomous Underwater Vehicle,Harbin Engineering University,Harbin 150001,China;

2.Military Delegate Office of Navy,Hudong-Zhonghua Shipbuilding(Group)Co.,Ltd,Shanghai 200129,China)

Research on Multidisciplinary Design Optimization Methods for Cylindrical Underwater Vehicle

SU Yu-ming1,CUI Tong1,ZHU Wei2,CAO Jian1,YANG Zhuo-yi1

(1.State Key Laboratory of Autonomous Underwater Vehicle,Harbin Engineering University,Harbin 150001,China;

2.Military Delegate Office of Navy,Hudong-Zhonghua Shipbuilding(Group)Co.,Ltd,Shanghai 200129,China)

Based on Isight software,a study of the multidisciplinary design optimization(MDO)techniques for cylindrical underwater vehicle was carried out.This cylindrical underwater vehicle was divided into four disciplines involving resistance,structure,energy,and propulsion,and detailed modeling and analysis of each subject were conducted.Then based on the Sequential Quadratic Programming,Hooke-Jeeves Direct Search Method as well as Multi-island Genetic Algorithm,a single disciplinary optimization was operated.When getting the optimization results,the most suitable optimization algorithm for each subsystem is determined.The coupling relations of the four disciplines were studied,and multidisciplinary design optimization models based on Collaborative Optimization(CO)and Simultaneous Analysis and Design(AAO)were built respectively.These two multi-disciplinary optimization methods combined with above three optimization algorithms were applied to the multidisciplinary design optimization of cylindrical underwater vehicle,and satisfactory optimization results were obtained.Finally,a MDO scheme suitable for cylindrical underwater vehicle was summarized.

underwater vehicle;MDO;CO;AAO;optimization algorithm

1 Introduction

1.1 Problem statement

Autonomous Underwater Vehicle(AUV)is a typical complex engineering system involving many coupling disciplines[1].The design of AUV is essentially a multi-disciplinary problem.The methods of traditional ocean structure design are a kind of serial design patterns,that is,at different design stages,designers can choose different key subjects to design and optimize.This design process artificially separated these subjects including hydrodynamic,propulsion,structure and control which will affect overall properties of the ocean structure at the same time.It will not make full use of the synergies effect generated by the mutual coupling among the various disciplines and reduce the system overall optimality and performance.Therefore,the introduction of multi-disciplinary design optimization method to the design of ocean structures will have a very broad development space and realistic significance.With this background,re-search and application of multidisciplinary design optimization technology to a cylindrical underwater vehicle were carried out in this paper,aiming at providing a theoretical basis and technical support for future underwater vehicle design.

1.2 A brief review of the existing research

In 2000,Pennsylvania State University,Louisiana State University together with other related departments carried out the application research of the multidisciplinary optimization method in the underwater vehicle design[2-3].Charles and Mc Allister et al[4]applied MDO to the intelligent system design of submersible to test its optimization effect.Their research focused on these four aspects:analysis of subject approximation model,uncertainty modeling,optimization algorithm and the solving process visualization.With Individual Discipline Feasible method[5]used to this process,they obtained satisfactory results.And in the subsequent study,they realized the optimization of the AUV system in the collaborative optimization framework combined with linear programming,and proved that in spite of increasing in the computational complexity when executing system level consistent constraint conditions,the convergence of algorithm was very good[6].In 2002,the Office of U.S.Naval Research launched the project“Undersea Weapon Design and Optimization(UWDO)”and pointed out its future development direction[7].In 2010,Lahopoulos and Hart[8]in the University of Michigan studied the application of MDO method in the submarine concept design.According to each subject’s characteristic in the conceptual design stage,they set up executable calculation model,and summarized the content of the work for the future.In addition,Researchers in China introduced MDO technology into the submersible design process,such as torpedoes[9],manned submersibles[10-12]and AUVs[13],and also made some achievements.

1.3 MDO methods

For the application of MDO on underwater vehicle,Dr.Yang[14]at Harbin Engineering U-niversity proved the efficiency of Simultaneous Analysis and Design method.While as one of the most common MDO methods,Collaborative Optimization is widely applied to many engineering areas,especially in marine structures design.This paper focuses on these two MDO methods which are described as follows.

1.3.1 Collaborative Optimization

Collaborative Optimization method(CO)[15]was first proposed by Kroo et al in aircraft preliminary optimization design in 1998.It is a typical two-level optimization method.This method decomposes a MDO problem for a complex system into a system-level and a number of subsystem-level optimization problems.For subsystem-level optimization,each sub-discipline not only needs to be analyzed,also needs to be optimized.This process should be conducted according to the accurate model of this discipline.Their design variables involve only variables related to this subject and the coupling variables between this subject and other ones.Their constraints also need to only satisfy this discipline,and the goal is generally to ensure the conformance between sub-discipline optimization results and the whole system optimization objectives.Calculations operated in each discipline are paralleled and independent which do not exit any relations,while inconsistencies generated by different sub-disciplines optimization are submitted to the system-level to coordinate.There are two tasks for system-level optimization:coordinating inconsistency among different sub-disciplines and making the system reach the optimal solutions.Finally,through continuous iterations between system-level and subsystem level optimization,the inconsistencies between the various disciplines gradually reduced and a group of best results meeting the convergence conditions are eventually obtained.

The mathematical model of Collaborative Optimization method based on constraint relaxation used in this paper is expressed as follows:System-level optimizer:

where XDand X are design variable and state variable,respectively,XDijand xijare coupled design variable and state variable in subsystem,respectively,N is the number of disciplines,U（X ） is output variable,Jiis interdisciplinary consistency constraint,and ε is a relaxation factor which is a positive small value,often selected as 0.01,0.001,0.000 1,etc according to different optimization conditions.Within a certain range,the relaxation factor can speed up the convergence rate of the optimization process and improve computational efficiency.

A general view of CO method is shown in Fig.1.

Fig.1 General view of CO method

1.3.2 Simultaneous Analysis and Design

Simultaneous Analysis and Design,also known as the All At Once(AAO),are a simple and efficient single-level optimization method[16].This method extracts all the variables including the system design variables,interdisciplinary coupling variables and the state variables of each discipline to system-level optimizer which completes all optimization contents.On every iteration,each sub-discipline calculates concurrently and independently,and disciplinary order and disciplinary feasibility do not need to be considered until the system-level optimization is completed.Consistency between different sub-disciplines can be ensured by introducing supplemental constraints,that is,supplemental constraints related to itself should be calculated for each subject,and the objective function under the condition of meeting the system constraints and supplemental constraints should be calculated by system-level optimizer.Supplemental constraints are set to zero during the whole optimization process to ensure the consistency of the interdisciplinary solutions.The mathematical model of AAO expressed as follows:

where Jiis the residual of subject analysis i.

AAO frame diagram method is shown in Fig.2.

Fig.2 General view of AAO method

1.4 Optimization algorithms

For an established optimization problem(given the design variables,constraints,objective function),we need to choose an optimization algorithm to automatically iterate and search the goal in the design space,so as to obtain the optimal design solutions.

The selection of the optimization algorithms is a critical step in the optimization process which has a negligible impact on the optimization results[17].A suitable optimization algorithm can not only get satisfied optimization results,but also improve the efficiency of the optimization process.Optimization algorithms used in engineering are usually divided into three categories:Gradient Optimization Algorithm,Direct Search Algorithm,and Global Optimization Algorithm.In this paper,three representative optimization algorithms are selected from each category,which are Sequential Quadratic Programming(NLPQL),Hooke-Jeeves Direct Search Method(HJ),and Multi-Island Genetic Algorithm(MIGA),respectively.They will be applied to all levels of optimizers to make a comparative analysis.

2 Single subject analysis,modeling and optimization

2.1 Resistance

The main body of cylindrical underwater vehicle can be divided into four parts,in front-to-back order are the bow,the control cabin,the energy cabin and the stern in turn.The bow and stern parts are respectively formed by the nosecone and tailcone both connected with a parallel middle body,while the central pressure cabin is divided into the control cabin and energy cabin which are both standard cylindrical rotary body.Nosecone and tailcone are formed by the rotation of Myring curves which is accepted internationally.The structure of cylindrical underwater vehicle is shown in Fig.3.

Fig.3 Structure of cylindrical underwater vehicle

Myring’s equations for nose and tail curves are shown as follows,respectively:Nose curve:

where a is the length of nosecone,b is the length of pressure cabin(energy cabin and control cabin),c is the length of tailcone,d is diameter,θ is angle of departure(radians),n is sharpness of entry factor.

In this discipline,empirical formulas are used to calculate resistance.

For the vehicle sailing underwater,if its depth is greater than its length,the impact of the wave resistance can be ignored,so the total resistance under the cruising speed is:

where R is total resistance,Rfis frictional resistance,RPVis form resistance,RAPis resistance of appendage,Cfis frictional resistance coefficient,ΔCfis roughness compensation coefficient,CPVis form resistance coefficient,CAPis appendage resistance coefficient,ρ is seawater density,Velis cruising speed,S is wetted surface area.

Estimation methods for each resistance coefficient are as follows:

(1)Frictional resistance coefficient Cf,can be solved by ITTC recommended formula:

where Reynolds number Re=VL/ν,L is characteristic length,V is speed,ν is water sports viscosity coefficient assigned by 1.307×10-6m/s2.

(2)Roughness compensation coefficient ΔCf,is 0.4×10-3.

(3)Form resistance coefficient CPV,can be obtained by the test value of similar shape underwater vehicle.Under low-speed conditions,when length diameter ratio of cylindrical underwater vehicle is in a certain range,form resistance coefficient of design vehicle can be regarded as the same to mother vehicle’s approximately.

(4)Appendage resistance coefficient CAP.Appendages of cylindrical underwater vehicle contain radio,GPS antenna,USBL transducer,rudder,side-scan sonar transducer and DVL.Appendage resistance coefficient can be estimated by Eqs.(3-5):

Thus,appendage resistance is about 0.3 times the bare hull resistance[18].

Wetted surface area S consists of three parts:nosecone wetted surface area,parallel middle body wetted surface area and tailcone wetted surface area.The parallel middle body is a standard cylindrical shell whose wetted surface area is easy to get.While the nosecone and tailcone are not standard shapes,they need to integrate the Matlab software,in which Gaussian integral is adopted to calculate the two wetted surface areas formed by the rotation of Myring curves.

Through the analysis,for the resistance subject model,five variables are set including diameter and length of nosecone,energy cabin,control cabin and tailcone.In order to make the vehicle body shape not too stubby or elongate,a constraint variable-length to diameter ratio is introduced,and simultaneity,a constraint range is set to the total length of pressure cabin.The optimization target is to minimize the total resistance under the cruising speed.The resistancedisciplinary optimization parameters are shown in Tab.1.

Tab.1 Input and output parameters of resistance discipline

Based on NLPQL,HJ and MIGA,resistance discipline is optimized.The results of three kinds of optimization algorithm are shown in Tab.2.

Tab.2 Results of resistance discipline

As can be seen from Tab.2,the result based on NLPQL is the best and gotten fastest,and HJ followed.In contrast,the result of MIGA is the worst,which is not suitable for single discipline optimization also due to too many iterations.Therefore,NLPQL is adopted as the most suitable optimization algorithm for resistance discipline.

2.2 Structure

In view of the maximum depth of this cylindrical underwater vehicle is 100 m,its pressure cabin strength can be checked by“Regulations of submersible system and submersible classification and construction[19]”.Pressure cabin is divided into a control cabin and an energy cabin,both of which adopt LF6 high-strength aluminum alloy material.Although two cabins have the same diameter,their length,shell thickness and other parameters are not consistent,so their strength need to be checked respectively.

After strength check,the mass of the pressure cabin(including ribs)can be obtained according to the density of the material and the geometric parameters of control and energy cabins.As the volume of pressure cabin can not be infinitesimal,an assumption that all electrical equipments in the vehicle are to be placed in the control cabin is introduced.Thus the volume of the electrical equipments(constant)should be less than the volume of control cabin.Taking the shape diversity of the electrical equipments into account,in order to make the results more practical,the volume of control cabin is multiplied by a coefficient of 0.75,which must satisfy the following requirements:

where Vkzis the volume of control cabin,Vdqis the volume of the electrical equipments,Vlcis the difference between them.

For the structure subject model,eleven variables and twelve constraints are set.The optimization target is to minimize the mass of the pressure cabin.The structure-disciplinary optimization parameters are shown in Tab.3.

Based on NLPQL,HJ and MIGA,structure discipline is optimized.The results are shown in Tab.4.

Tab.3 Input and output parameters of structure discipline

Tab.4 Results of structure discipline

As can be seen from Tab.4,the result based on NLPQL is the best and gotten fastest.Therefore,NLPQL is adopted as the most suitable optimization algorithm for structure discipline.

2.3 Energy

Energy of cylindrical underwater vehicle is divided into two parts:energy for control system which provides power to electrical equipments and energy for dynamical systems.Their selection of lithium battery is the same,whose energy density is 232 994.08 wh/m3,ampere-hour density is 70 604.27 Ah/m3,and weight density is 2 061.65 kg/m3.

(1)Energy for control system

When all electrical equipments in cylindrical underwater vehicle are fully open,the maximum current is 6.2A.Along with minimum working hours for 12h and the discharge efficiency of 90%,the capacity of batteries for control system is 82.67 Ah.

So the volume of batteries for control system is:

(2)Energy for dynamical systems

This cylindrical underwater vehicle has a maximum range of 100 km and maximum speed of 4 kns.So the sailing time of this vehicle in maximum range with maximum speed is 13.5h.

Effective power of propeller is:

where Vmaxis maximum speed,Rmaxis resistance at maximum speed,can be obtained by empirical formulas in resistance discipline.

Main motor power of the vehicle is:

where η1is propeller efficiency,can be assigned by initial value 0.529 31, η2is electric efficiency,can be assigned by empirical value 0.75.

In consideration of the discharge efficiency of 90%,so the volume of batteries for dynamical system is,

where ρewhis energy density with the value of 232 994.08 wh/m3.Overall,the total mass of batteries is,

where ρeis weight density with the value of 2 061.65 kg/m3.

An assumption that all batteries in the vehicle are to be placed in the cabin should be introduced,thus the volume of all batteries should be less than the volume of energy cabin.Taking the actual layout of batteries into account,in order to make the results more practical,the volume of energy cabin is multiplied by a coefficient of 0.7,which must satisfy the following requirements:

where Vdccis the volume of energy cabin,Vldis the volume difference between batteries and energy cabin.

As the maximum resistance calculation is necessary for energy subject,like resistance subject,the Matlab software needs to be integrated to calculate wetted surface area in the model of energy subject.Through the analysis of energy subject,eight variables and two constraints are set.The optimization target is to minimize the total mass of batteries.The energy-disciplinary optimization parameters are shown in Tab.5.

Tab.5 Input and output parameters of energy discipline

Continue Tab.5

Based on NLPQL,HJ and MIGA,energy discipline is optimized.The results of three kinds of optimization algorithm are shown in Tab.6.

Tab.6 Results of energy discipline

As can be seen from Tab.6,the result based on NLPQL is the best and gotten fastest.Therefore,NLPQL is adopted as the most suitable optimization algorithm for energy discipline.

2.4 Propulsion

Propeller propulsion form is used for cylindrical underwater vehicle.In order to calculate the propeller efficiency,a propeller calculation program compiled by surface element method is integrated[20],which can calculate some propeller performance parameters(advance coefficient,thrust coefficient,torque coefficient,efficiency)according to four variables(propeller diameter,area ratio,pitch,rotating speed).

The calculation process of this program is slow,and it will delay the overall optimization process when it is integrated in Isight software,so another key optimization technologyapproximate model is introduced instead of this analysis module to enhance the overall optimization efficiency.Approximate model technology mainly includes two parts:Design of Experiments(DOE)and Modeling methods.For DOE,Optimal Latin Hypercube Design method is adopted to select the sample points,while Radial Basis Function Neural Network(RBF)is chosen for modeling.

Fig.4 shows relations of propeller efficiency to area ratio and diameter,while Fig.5 shows relations of propeller efficiency to pitch and rotating speed in the RBF model.

After the approximate model is built up,the propeller needs to be matched with the cylindrical underwater vehicle.Three matching conditions are shown as follows:

Fig.4 Efficiency-area ratio-diameter 3D diagram

Fig.5 Efficiency-pitch-rotating speed 3D diagram

(1)Propeller thrust should be greater than the maximum resistance of the vehicle,thus

where

And ρ is density of seawater,Ktis thrust coefficient,M is rotating speed,Dpis propeller diameter.

(2)Propeller power should be less than main motor power of the vehicle,

where

And Kqis torque coefficient,Q is torque.

(3)Propeller diameter should not be greater than 0.8 times the diameter of the vehicle,thus

In single discipline optimization,main motor power,maximum resistance and diameter of the vehicle are all constant,which can be respectively assigned by initial value,Ps=253.57 W,Rmax=55.46 N,d=0.26 m.

According to propulsion discipline model,four variables and three constraints are set.The optimization target is to maximize the propeller efficiency.The propulsion-disciplinary optimization parameters are shown in Tab.7.

Based on NLPQL,HJ and MIGA,propulsion discipline is optimized.The results of three kinds of optimization algorithm are shown in Tab.8.

Tab.7 Input and output parameters of propulsion discipline

Tab.8 Results of propulsion discipline

As can be seen from Tab.8,the result based on HJ is the best and gotten fastest.Therefore,HJ is adopted as the most suitable optimization algorithm for structure discipline.

In addition,Tab.8 also shows the propeller actual efficiency values corresponding to the three groups of propeller parameters respectively based on three kinds of optimization algorithms.Through comparison,the accuracy of propulsion discipline approximation model is further verified.

3 MDO for cylindrical underwater vehicle

3.1 Based on CO

Based on Collaborative Optimization method,the diagram of multidisciplinary optimization design to cylindrical underwater vehicle is shown in Fig.6.

With CO method based on constraint relaxation,multidisciplinary design optimization of cylindrical underwater vehicle is conducted in this section.The goal is to minimize the total mass of the vehicle.However,it is assumed that the mass of electrical equipments is constant,thereby the mass of pressure cabin and batteries becomes the most important part of total mass.So the objective of this MDO problem is to minimize the mass of pressure cabin and batteries,thus

Fig.6 Structure of CO method for cylindrical underwater vehicle

According to the idea of collaborative optimization,coupling variables of each sub-discipline should be selected,and then their corresponding system-level variables can be set in the system-level optimizer.In addition,two parameters:main motor power Psand maximum resistance Rmaxgotten from energy subject need to be submitted to propulsion subject for matching the propeller,while the propeller efficiency Ceq need to be submitted to energy subject for the calculation of main motor power Ps.However,these two subjects are independent mutually and unable to transfer the data,so all the above three parameters are also selected as the system-level variables.For easy to distinguish,the system-level variables all add a letter s after its variable symbol.For example,the system-level variable symbol of diameter is ds.

Through the above analysis,the consistency constraints of each discipline can be determined as:

Resistance subject:

In summary,with the CO method,the system-level parameters of MDO to cylindrical underwater vehicle are shown in Tab.9.

Only after single-disciplinary optimization,can each subject pass the results to the system level.Settings of subsystem involving input variables,constraints and suitable optimization algorithm are consistent with single-disciplinary modeling and analysis described in the previous section.After this,the data transfer directions need to be set to associate system-level optimizer with subsystem-level optimizers.

The established Collaborative Optimization framework in Isight is shown in Fig.7.

Based on NLPQL,HJ and MIGA in systemlevel optimizer,the cylindrical underwater vehicle is optimized with CO method.The results are shown in Tab.10.

Fig.7 Collaborative Optimization framework

Tab.9 System-level parameters

Tab.10 Results of CO method

Continue Tab.10

3.2 Based on AAO

AAO is a kind of single-level optimization method.Compared with the multi-level optimization methods,it is easier to understand and build.This method extracts all the design variables,and constraints of each discipline to system-level optimizer.Settings of variables and constraints of system-level optimizer are the same to single disciplinary optimization(and not explained here).The optimization objective is still to minimize the total mass of the pressure cabin and batteries.By setting the data transfer directions:system-level optimizer inputs design variables to sub-disciplines,and sub-disciplines output calculated results to system-level optimizer.

The established Simultaneous Analysis and Design framework in Isight is shown in Fig.8.

Based on NLPQL,HJ and MIGA in system-level optimizer,the cylindrical underwater vehicle is optimized with AAO method.The results are shown in Tab.11.

Fig.8 Simultaneous analysis and design framework

Tab.11 Results of AAO method

4 Results analysis

Comprehensive comparison is made among the results obtained from CO and AAO methods respectively based on NLPQL,HJ and MIGA.It can be seen that,the optimal solutions under two MDO methods are very close,so both CO and AAO can be thought as suitable methods for cylindrical underwater vehicle multidisciplinary Design Optimization.For CO methods,difference of three results respectively based on three optimization algorithms is extremely small,while three results under AAO method are quite different,so CO method has stronger inclusiveness for different optimization algorithms than AAO.But,in contrast,the result of AAO method based on NLPQL is the best.Meeting all the requirements of the task,this set of method reduces the total mass of pressure cabin and all the batteries by 32.42%.

Collaborative Optimization is a two-level optimization method.Its various sub-disciplines coupled variables need to be coordinated by introducing consistency constraints,and the ultimate goal is to make the same variable of each discipline exactly equal.But in this process,due to introduction of relaxation constraints,the results will be slightly different.While as a single-level optimization method,Simultaneous Analysis and Design method will not generate this problem.At the same time,relatively speaking,multidisciplinary design optimization for cylindrical underwater vehicle is not very complex.When applying a simple optimization algorithm to its system-level optimizer,AAO can fully withstand calculation burden of this magnitude.If the optimization problem is more complicated,then CO can reflect its superiority in multidisciplinary design optimization.

About optimization algorithms,it can be found that the result of AAO method based on MIGA is poorer.The reason may lie in the high requirement of MIGA.In theory,MIGA can get the global optimal solution in all cases.But for AAO method,too much design variables are all in system-level optimizer,and MIGA as a global optimization algorithm,can make the calculation too complex.Coupled with computer hardware limitations,MIGA often makes the results difficult to converge.Moreover,the parameters set in MIGA are too much,so changing any parameters will have a great influence on the results.The result of AAO method based on HJ is also different from the optimal solution.Except for its sensitivity to the initial value,HJ can also easily make results into local optimal solution when being applied to complex optimization problems.

In addition,it can be seen from the results,the vehicle structure form changes greatly and the target mass drops significantly.There are some reasons for these:Some other subjects like general arrangement and maneuverability are not taken into account;a lot of assumptions are made in modeling and analysis of each subject;approximate empirical formula method is adopted instead of accurate simulation software and so on.All of above will have impacts on the results.However,the conclusions still have positive significance.

In summary,there is reason to believe,the method of AAO based on NLPQL can be regarded as the first choice for multidisciplinary design optimization of cylindrical underwater ve-hicle.Values of input and output variables after optimization are shown in Tab.12.

Tab.12 Input and output variables of the optimal AUV

Before and after multidisciplinary optimization,an obvious change happened in the main body of cylindrical underwater vehicle,as shown in Fig.9.

In addition,compared with the results of previous single subject optimization,it is clear that the results of multidisciplinary optimization design are more effective,which can reflect the rationality and superiority of MDO.

Fig.9 Comparison diagram for main body of cylindrical underwater vehicle before and after optimization

5 Summary and conclusions

Taking Isight software as the optimization integration platform,a study of the multidisciplinary design optimization techniques for cylindrical underwater vehicle was carried out,and satisfactory results were obtained.In the meantime,through the analysis of the MDO methods and optimization algorithms,a MDO scheme suitable for cylindrical underwater vehicle was summarized,which has certain theoretical significance and practical value.The summary of the work in this paper is as follows:

(1)Each sub-discipline of the cylindrical underwater vehicle was studied.Firstly,the cylindrical underwater vehicle system is divided into four disciplines involving resistance,structure,energy,and propulsion.Then detailed modeling and analysis of each subject were conducted,in which,design variables,constraints and objective function of each discipline were determined.Based on the Sequential Quadratic Programming,Hooke-Jeeves Direct Search Method as well as Multi-island Genetic Algorithm,each single discipline was optimized.When getting the optimization results,the most suitable optimization algorithm for each subsystem was determined.For resistance,structure and energy subjects,the most suitable optimization algorithm for them was NLPQL,while HJ method can be adopted to get the optimal solution of propulsion subject.

(2)The application of Multidisciplinary Design Optimization techniques to cylindrical underwater vehicle was researched.The interdisciplinary couplings of the four disciplines were studied,and then MDO models based on Collaborative Optimization and Simultaneous Analysis and Design methods were built respectively.Based on two MDO methods(CO and AAO)and three optimization algorithms(NLPQL,HJ,MIGA),the multidisciplinary design optimization of cylindrical underwater vehicle was conducted,and satisfactory results has been obtained.The results show that CO and AAO methods are both effective,but AAO based on NLPQL is the best method for MDO of cylindrical underwater vehicle.

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圓柱形水下航行器多學(xué)科優(yōu)化設(shè)計(jì)方法研究

蘇玉民1，崔 桐1，朱 煒2，曹 建1，楊卓懿1

（1哈爾濱工程大學(xué) 智能水下機(jī)器人技術(shù)國(guó)防科技重點(diǎn)實(shí)驗(yàn)室，哈爾濱150001；
2海軍駐上海滬東中華造船（集團(tuán)）有限公司軍事代表室，上海 200129）

基于Isight軟件，對(duì)圓柱形水下航行器開(kāi)展了多學(xué)科設(shè)計(jì)優(yōu)化技術(shù)的研究。首先將圓柱形水下航行器劃分為阻力、結(jié)構(gòu)、能源和推進(jìn)四個(gè)學(xué)科，對(duì)每一個(gè)學(xué)科進(jìn)行了詳細(xì)的建模與分析，然后基于序列二次規(guī)劃法，霍克-吉維斯直接搜索法以及多島遺傳算法三種優(yōu)化算法對(duì)每個(gè)學(xué)科進(jìn)行了單學(xué)科優(yōu)化，在得到優(yōu)化結(jié)果的同時(shí)，確定了最適合每個(gè)子系統(tǒng)的優(yōu)化算法。接著確定了四個(gè)學(xué)科的耦合關(guān)系，完成了協(xié)同優(yōu)化框架和同時(shí)分析與設(shè)計(jì)框架下多學(xué)科優(yōu)化模型的構(gòu)建?；谶@兩個(gè)多學(xué)科優(yōu)化框架，分別在系統(tǒng)級(jí)優(yōu)化器中采用上述三種優(yōu)化算法，對(duì)圓柱形水下航行器進(jìn)行了多學(xué)科設(shè)計(jì)優(yōu)化，得到了滿意的優(yōu)化結(jié)果。最后總結(jié)出了一套適用于微小型水下航行器的多學(xué)科設(shè)計(jì)優(yōu)化方案。

水下航行器；多學(xué)科設(shè)計(jì)優(yōu)化；協(xié)同優(yōu)化；同時(shí)分析與設(shè)計(jì)；優(yōu)化算法

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蘇玉民（1960-），男，哈爾濱工程大學(xué)教授，博士生導(dǎo)師；

楊卓懿（1983-），女，哈爾濱工程大學(xué)講師。

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10.3969/j.issn.1007-7294.2013.09.011

1007-7294（2013）09-1076-20

date：2013-04-11

Weapon Equipments Advanced Research Foundation of China(9140C270305120C2701)

Biography：SU Yu-ming(1960-),male,professor/tutor of Harbin Rngineering University;CUI Tong(1988-),male,master student of Harbin Engineering University,E-mail:cuitong_06011417@126.com.

崔 桐（1988-），男，哈爾濱工程大學(xué)碩士生；

朱 煒（1979-），男，工程師；

曹 建（1984-），男，哈爾濱工程大學(xué)博士研究生；