Optimization of a Floating Platform Mooring System Based on Genetic Algorithm

8/11/2019 Optimization of a Floating Platform Mooring System Based on Genetic Algorithm

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Sesam Users Conference 03.Dec.2012

Optimization of a FloatingPlatform Mooring System Based

on a Genetic Algorithm

Aidin Rezvani Sarabi

Nelson Szilard Galgoul

NSG Engenharia, Projetos e

Representacao Comercial Ltda.

1


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Objective

Optimization of the platform heading

Optimization of the mooring pattern

Searching for the tension or length of themooring lines

Choosing the optimum line material and size


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Choosing an Optimization

Method

Many optimization problems in practical

engineering are quite hard to be solved by

conventional optimization techniques.

So there has been an increasing interest in

solving such hard optimization problems by

imitating the behavior of living beings.


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Choosing Optimization Method

Simulating the natural evolutionary process of

living beings results in stochastic optimization

techniques called evolutionary algorithms.

The most widely developed type of

evolutionary algorithms are known today as

Genetic Algorithms (GAs).


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Genetic Algorithm Fundamentals

GAs work with a coding of the solution set, not

the solutions themselves

GAs search for a population of solutions, not a

single solution

Genetic Algorithms use payoff information

(Fitness Functions), not derivatives or other

auxiliary knowledge

GAs use probabilistic transition rules, not

deterministic rules


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Analysis of Mooring System

using Mimosa

First, Mimosadetermines an equilibrium

position by applying a numerical procedure

that solves the equation below:

The solution to this equation is the

equilibrium position that defines theplatform coordinates and heading under

static loads

06216

,2

,1

=+++ xwa

fxwi

Fxcu

Fxxxmo

F


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Analysis of the Mooring System

using Mimosa

The actual platform motions are computed

by performing a dynamic analysis, where the

corresponding responses are categorized as

high frequency (HF) and low frequency (LF)motions

The HF responses are calculated using alinear spectral analysis.


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Analysis of Mooring System

using Mimosa

The LF responses are horizontal motions

(Surge, Sway and Yaw) which result from the

solution of equation below:

LFLFLFLF FKxxCxM =++


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Analysis of the Mooring System

using Mimosa

In order to calculate the extreme values for

the combinations of HF and LF motions,

Mimosa uses a heuristic equation which is

based on model tests and simulation studiesas given in the equation below for one

variable

+

+=

HF

ext

LF

Sign

LF

ext

HF

Sign

tot

ext

xx

xx

x max


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Objective Function Formulation

Each floating unit has six degrees of freedom(DOF) which include surge, sway, yaw, roll,pitch and heave. The mooring system is onlycapable of controlling the surge, sway and yaw

responses i.e. horizontal responses.

To reduce roll, pitch and heave, i.e. verticalresponses, the vessel shape and dimensionsmay be optimized.


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Here optimization of the mooring design,means to minimize the surge and swayresponses. Surge and sway are platformlongitudinal and transverse displacements


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Minimizing the horizontal translationalresponse (Platform Offset) is our optimizationproblem objective function.

The objective function of the mooring design

optimization problem, the optimizationparameter boundaries and the problemconstraints could be defined as:

( ) ( ) ( )( )[ ]=

+=

=

m

i iyix

i

am

i ii

aMinimize

1

22

1

2.:

( )

=

=

pk

k

g

njjjj

toSubjected

,...1,67.1

,...1,maxmin

:


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Penalty Function Formulation

The sequence presented in the previous slidehas led to a constrained optimization problemwhich now must be solved

The penalizing strategy is chosen to handle the

constraints. So a constrained problem istransformed into an unconstrained problem bypenalizing unfeasible solutions. The penaltyfunction is described as below:

( )

==


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Fitness Function Formulation

Fitness is a quality value that is a measure ofthe reproducing efficiency of individuals in apopulation.

A potential solution with a higher fitness value

will have greater probability of being selectedas a parent in the reproduction process.Therefore, the minimization problem must betransformed into a maximization problem of a

fitness function, using the followingexpressions:

2

2

avg

ii

=

i

i

i PF .1max

=


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Genetic Algorithms

As already mentioned above GAs differ fromconventional optimization methods andsearch procedures in several fundamentalways. A GAs basic execution cycle can be

described by the following steps:

Step 1:Reproduction

Step 2:Recombination

Step 3:Replacement

If some convergence criteria is satisfied,

Stop

Otherwise, go to step 1


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Implementation Details 1- Coding Design Variable

Design variables were coded using a fixed-length

binary-digit {0,1} string

2- Decoding

To obtain the real values of the design variables in thedomain region, each chromosome must be decoded

3- Offset Computation

Dynamic analyses are carried out in the frequency

domain using Mimosa

4- Fitness Function Calculation

The fitness value of each chromosome is computed by

considering offset values obtained from Mimosa


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Implementation Details 5- Selection

Chromosomes are selected as parents to produce

children and this selection depends on fitness values

6- Crossover Operator

The two-point crossover operator (2X), has been

adopted herein, for example 000000 and 111111

make 001100 and 110011

7- Mutation Operator

This operator changes the bit from 1 to 0 or vice versa 8- Generation Gap

It is a parameter that controls percentage of the

population that will be replaced in each generation


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Computational Procedure 1- Start

Initialize parameters: population size, crossover and

mutation probabilities

2- Seeding

Initial population is generated randomly Initial population is decoded

Fitness value of each individual is computed by using

the Mimosa software applying fitness equation

3- Reproduction Chromosomes are selected as parents

Application of the crossover operator

Application of the mutation operator


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Computational Procedure 4- Updating

The new offspring chromosomes substitute the worst

chromosomes of the current population

5- Evaluation

The new chromosomes are decoded Fitness of the new chromosomes is computed

6- Stopping Criterion Satisfied

If so, then go to step 7; else, go back to step 3 (Here

maximum number of 8000 iterations is considered

7- Repeat

8- End


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Case Study

The procedure described in the previoussections, has been implemented in acomputer program (based on Matlab) whichhas been written to solve a mooring design

optimization problem usingMimosa

.

As a case study, a

floating unit anchored

by 10 mooring lines,

was considered.


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Case Study

The 10 lines were divided into 4 groups withside constraints, as given in the Table below:

The floating unit is subjected to a set of

environmental conditions that are combined

according to a collinear approach, i.e. with

currents, winds and waves acting

simultaneously in the same direction.


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Case Study In this case study, eight combinations have

been considered. The JONSWAP spectrum for

the Caspian Sea conditions was used to

calculate wave HF responses, while the API

spectrum was used for determining the timevarying part of the wind forces.


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Case Study The total number of iterations considered

here was 8000 and the minimum value of the

objective function was reached at the 43rd

generation in offspring 4269.

The next table presents the final results of themooring design optimization problem

including azimuths of each line, anchor

position, line length, line size and line

material. Also the platform heading is 180 deg.

relative to true North.


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Case Study


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Case Study The optimized mooring pattern is illustrated

below. Line size and material in the ordinarycase is 3.5 chain and 4 chain in the optimized

design.


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Case Study The responses are reduced by the optimized

mooring design to up to 3.5 times less than in anordinary design. This matter has a great effect on

platform workability because of the reduction of

down-time.

Optimization of a Floating Platform Mooring System Based on Genetic Algorithm

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