Robust-based Opti­miza­tion of the Hull Internal Layout of an Oil Tanker

This blog post is part of our CAESES Student Award 2020 com­pe­ti­tion about the use of CAESES in academia, where we showcase exciting material sub­mit­ted to us by students who use CAESES in their research. Many students from high school to PhD make use of CAESES to reach their project goals. If you are one of them, we encour­age you to send us an article about your project and how CAESES has helped you. Inter­est­ing articles will be posted reg­u­larly in our blog, along with some infor­ma­tion about the author, and at the end of February 2021, we will select the best author, who will win some exciting prizes. 

Intro­duc­tion

The size and location of the internal spaces are estab­lished in the early stage of ship design. For oil tankers, the internal hull layout design can be defined as an opti­miza­tion problem to improve ship per­for­mance during the life cycle. The internal layout of oil tankers can be opti­mized tar­get­ing the improve­ment of the economic returns and the safety and pre­ven­tion of envi­ron­men­tal pol­lu­tion. The promi­nent indi­ca­tors of these objec­tives are iden­ti­fied as the cargo capacity, induced bending moment to the ship hull and oil outflow per­for­mance for a fixed hull shape. This work deals with the improve­ment of the design of the internal layout of oil tankers, tar­get­ing safety and economic feedback and con­sid­er­ing the incor­po­rated uncertainty.

Def­i­n­i­tion of Opti­miza­tion Problem

Design Para­me­ters

The ship hull shape is assumed to be fixed. There­fore, the main chal­lenge of the problem is defined by the deter­mi­na­tion of the dimen­sions of the internal com­part­ments and tanks to approach the optimum of the interest functions.

Con­straints

The majority of con­straints are of inequal­ity type due to reg­u­la­tions of SOLAS (2012; Inter­na­tional Con­ven­tion for the Safety of Life at Sea, Inter­na­tional Maritime Orga­ni­za­tion, London, Chapter II) and MARPOL (2006, Inter­na­tional Con­ven­tion for the Pre­ven­tion of Pol­lu­tion from Ships, Annex I. Inter­na­tional Maritime Orga­ni­za­tion, London.). However, they can be trans­lated to equality con­straints. For instance, intact sta­bil­ity criteria include inequal­ity lim­i­ta­tions for trans­verse and lon­gi­tu­di­nal sta­bil­i­ties. Even­tu­ally, all those con­straints can be trans­lated to an equality con­straint of intact sta­bil­ity reg­u­la­tions with two options of pass (equal to 1) or not pass (not equal to 1). A com­bi­na­tion of the two approaches was applied to con­straints to simplify the cat­e­go­riza­tion of the limits. Espe­cially, the approach is helpful during the iden­ti­fi­ca­tion of the pri­or­i­ties for con­straint con­ver­sion to robust-based approach. To model the uncer­tainty of oil outflow due to possible damages, the reg­u­la­tory con­straint is replaced by using a 3‑sigma for­mu­la­tion. So, a tol­er­ance between is defined for the solu­tions and the original constraints.

Objec­tive Functions

The main aims of the opti­miza­tion problem are defined by increas­ing safety and economic func­tions. Thus, the fol­low­ing objec­tives are defined for the opti­miza­tion problem:

1. Max­i­miza­tion of the Cargo Capacity
2. Min­i­miza­tion of the Maximum Hogging Still Water Bending Moment
3. Min­i­miza­tion of the Maximum Sagging Still Water Bending Moment

The maximum still water bending moment (SWBM) is induced to this ship hull in the hogging con­di­tion, however, the sagging has a more impor­tant effect on the safety and envi­ron­ment pro­tec­tion objec­tives. This is because the sagging extreme values are in the full load con­di­tion, while, the extreme values of hogging are usually hap­pen­ing in the full ballast con­di­tions. Thus, the min­i­miza­tion of maximum sagging and hogging loading was defined as two separate objec­tives. The uncer­tainty of SWBM is modelled by normal dis­tri­b­u­tions. The expected values and standard devi­a­tions of the dis­tri­b­u­tions of the sagging and hogging are cal­cu­lated sep­a­rately. The robust objec­tives of sagging and hogging are replaced using the 3‑sigma method:

Opti­miza­tion Procedure

The opti­miza­tion pro­ce­dure includes:

• updating the model accord­ing to the design parameters
• applying the pre­de­fined loading con­di­tions and damage sce­nar­ios to the model
• per­form­ing the intact and damage sta­bil­ity analysis
• updating the uncer­tainty model
• eval­u­at­ing the objec­tive and constraints
• checking the criteria
• running the multi-objec­tive genetic algo­rithm (MOGA) for optimization
• repeat­ing the above stages until reaching the stopping criteria

Results and Discussion

The evo­lu­tion direc­tion of the obtained solu­tions can be rec­og­nized toward the Pareto solu­tions, which includes the higher value of cargo capacity and smaller values of maximum sagging SWBM. The ref­er­ence design is approx­i­mately in the middle range of the objec­tives’ values for the obtained solu­tions. Globally, plenty of solu­tions had better values of the men­tioned objec­tives relative to the ref­er­ence design. Even locally, the ref­er­ence design can be improved from the aspect of the cargo capacity and maximum hogging and sagging SWBM. 
The con­straint values are at an accept­able level relative to the allow­able oil outflow para­me­ter for the designs. The marginal distance of each design relative to the allow­able value is depen­dent on the uncer­tainty term. The distance increased for those solu­tions that have a higher standard devi­a­tion of oil outflow.

Decision-making for Final Design Selection

The final optimal solution can be selected by a trade-off between con­flict­ing objec­tive func­tions. Thus, the selec­tion of final designs can be defined as a Multi-Attribute Decision Making (MADM) problem. So, the Pareto solu­tions can be judged by the MADM methods and the superior design can be iden­ti­fied among the avail­able alter­na­tives. For this purpose, the degree of impor­tance of objec­tives needs to be spec­i­fied by assign­ing a weight to each objec­tive function.

Here, two alter­na­tive sce­nar­ios are presented:

• alter­na­tive 1 is selected by defining equal weight for criteria,
• alter­na­tive 2 is defined by ded­i­cat­ing higher impor­tance to the cargo capacity relative to other criteria.

Con­clu­sions

The interest func­tions are improved for the obtained solu­tions based on a robust-based method, besides the solu­tions are limited to the designs that are in the reliable region of criteria limits. The ref­er­ence design can have a con­sid­er­able improve­ment in the induced loads to the ship struc­ture, even if the cargo capacity remains unchanged. The obtained solu­tions provide a wide range of diver­si­ties for the designer to have free hand for design selections.

About the Author

Special thanks to Hamidreza Jafarye­ganeh from the Insti­tuto Superior Técnico in Lisboa, Portugal. It is always inspir­ing to see your enthu­si­asm and ded­i­ca­tion to opti­miza­tion tasks with the help of CAESES.

Hamidreza is a research assis­tant at Insti­tuto Superior Técnico. He has expe­ri­ences in the fields of hydro­dy­namic sim­u­la­tion, modeling uncer­tain­ties, damage sta­bil­ity analysis, opti­miza­tion of struc­tures and decision-making for design selec­tion. He also benefits from working expe­ri­ences of the detail and basic design in offshore industries.

More Infor­ma­tion

The full version of this con­tri­bu­tion can be found here.