An Automatic PipeArrangement Algorithm
Considering Elbows and Bends
Dept. of Marine System Engineering, Kyushu University
Yuto Ando
Hajime Kimura

1

Outline
1. Background and Purpose- Previous Research
2. Routing Algorithm Including Bends- Approach- Outline of “Bends”- Outline of Pipe-rack Area and Aisle Space- Experiments
3. Conclusion and Challenges
2

Background
Pipe Arrangement requires …
 Keeping to regulations

ex.
- Not to set fuel oil pipelines
near to electrical equipment.

http://www.cadpipe.com/industrial3D.html
3Background
Pipe Arrangement requires …
 Keeping to regulations

 Meeting demands
ex.
- To shorten the total length- To set along with the ship hull

http://www.cadpipe.com/industrial3D.html
4Background
Pipe Arrangement requires …
 Keeping to regulations

 Meeting demands
 Originality by each ship

http://www.cadpipe.com/industrial3D.html
5Background
Pipe Arrangement requires …
 Keeping to regulations

 Meeting demands
 Originality by each ship

Experiences of skilled designers
http://www.cadpipe.com/industrial3D.html
6Background
Pipe Arrangement requires …
 Keeping to regulations

 Meeting demands
 Originality by each ship

Experiences of skilled designers
http://www.cadpipe.com/industrial3D.html

Automatic Design System7

Purpose
Previous Researches

Problems are …

Our Proposal

We try for …

Optimization of piping routes  Solving these problems
Searching of piping routes

 High performance system

Constraints

 Full automatic design8Previous Research

Goal Point

Approach by Asmara and Nienhuis
 Looking on the pipe arrangement problem asa routing problem in a directed and weightedgraphObstacle

Obstacle

Solved by “Dijkstra’s method”

Disadvantage is …
- The mesh size is restricted to be larger thana pipe’s diameter
Especially in large pipe’s diameter

Strong Constraint!

Start Point

9Previous Research

Goal Point

Approach by Martins and Lobo
 To set cost value in each cell
 To set area for pipes : Low Cost Zone
 Routing algorithm is based on G.A.

Disadvantages are…

- Uncertainty of optimal routing- The mesh size is restricted

Start Point

Low Cost Zone10

Outline
1. Background and Purpose- Previous Research
2. Routing Algorithm Including Bends- Approach- Outline of “Bends”- Outline of Pipe-rack Area and Aisle Space- Experiments
3. Conclusion and Challenges
11Approach
New Layout of Equipment

Main System
Equipment Layout

Operability of Valves

Valve
Evaluation
SystemRouting
SystemTotal Length
Num. of Bending
12

Approach of Routing
Problems of Previous Researches- Uncertainty of the route with minimum costs- Demanding of the mesh size on the diameter

Our Approach Using “Dijkstra’s method”

 Improvement the routing algorithm Using not only elbows but “bends”
13Approach of Routing
Problems of Previous Researches- Uncertainty of the route with minimum costs- Demanding of the mesh size on the diameter

Our Approach Using “Dijkstra’s method”

 Improvement the routing algorithm Using not only elbows but “bends”
14Approach of Routing
Problems of Previous Researches- Uncertainty of the route with minimum costs- Demanding of the mesh size on the diameter

Our Approach Using “Dijkstra’s method”

variable mesh size!

 Improvement the routing algorithm Using not only elbows but “bends”
15

Approach of Routing
Problems of Previous Researches- Uncertainty of the route with minimum costs- Demanding of the mesh size on the diameter

Our Approach using “Dijkstra’s method”

 improvement the routing algorithm Using not only elbows but “bends”
16Approach Design Space: Box for pipe arrangement

 Start and Goal

: Coordinates and vectors

 Target Pipeline: Pipes not including any branches
17

Approach Design Space: Box for pipe arrangement

 Start and Goal

: Coordinates and vectors

 Target Pipeline: Pipes not including any branches
18Approach Design Space: Box for pipe arrangement

 Start and Goal

: Coordinates and vectors

 Target Pipeline: Pipes not including any branches
19Approach
Pipe Arrangement

Routing Problem

Equipment Layout
ProblemSubject ofthis research Design Space: box for pipe arrangement

 Start and Goal

: coordinates and vectors

 Target Pipeline: Pipes not including any branches
20Approach Obstacle: Structures and equipments
in ships

 Aisle Space: Space for passages

 Pipe-rack Area

: Space for pipelines
21

Approach Obstacle: Structures and equipments
in ships

 Aisle Space: Space for passages

 Pipe-rack Area

: Space for pipelines
22Approach Obstacle: Structures and equipments
in ships

 Aisle Space: Space for passages

 Pipe-rack Area

: Space for pipelines
23

Dijkstra’s Method
This method can …
 Find the shortest path in a directed and weighted graph Guarantee a path with minimum costs
Where is the path with minimum costs
between C1 and C2?
C4
77C23565C1C73C5
10
7C3
8
8C6

The answer is …

75C1

10C2

63C3

C4

minimum costs
735C516C7788C624

Design Objectives
Pipe-rackObstacleAisle

 To minimize the total length of pipes
Sum Up To minimize the number of elbows and bends
 To avoid aisles as possible
 To pass through pipe-rack areas as possible25

Design Objectives
Obstacle

Cost of 1 Mesh = 1
Cost of Elbows = 0.1

Total Costs = Cost of Total Length +Cost of Elbows and Bends
Total Costs = 12 + 0.1×4
Total Costs = 12.426

Routing Algorithm
Goal Point
Obstacle

Start Point

Obstacle
Obstacle

Pipe’s Diameter < Mesh Size

27

Routing Algorithm
Obstacle

Obstacle
Obstacle

Pipe’s Diameter > Mesh Size

28Searching of Straight Pipes

StraightElbow
Next node

Next node
Current node

Current node

Bends

Next node29

Searching of Straight Pipes

Pipe’s Diameter ＞ Mesh Size

Recording Costs
Next node

Current node
Diameter：R

30

Searching of Elbows

d2≧R/2

Temporarynode
dd1
1≧
 R/2
R

Current node

Diameter：R

31

Searching of Elbows

Pipe’s Diameter ＞ Mesh Size
Recording Costs

Next node

Current node32

Outline of Bends“Bends” are …
 Pipe parts to take the form of gentle S-shape Connectors for gaps within the pipe’s diameter

33from “NAMURA TECHNICAL REVIEW No.13, 2010”

Outline of Bends
Goal Point

Start Point
11Total length : 1934

Outline of Bends

11Total length : 2235

Outline of Bends

11Total length : 2218.7

36

Searching of Bends

Constraints of Bending Machine

System user sets a value of 1,  2, dex. 1  5,  2  0, d  R d  2  1 R 2  1
  arcsin   arcsin 22 (2  1)  ( 2)  (2  1) 2  ( 2) 2 L  (2 1 R  sin  )  ( 2  R  cos  )L : the minimum vertical length of the bend
37

Searching of Bends

L : the minimum vertical length

Temporarynoded2≧L
d1<R
Current node

Diameter：R38

Searching of Bends
Next node

Recording Costs

Current node39

Interference Check

Straight

Elbow

Check coordinates of circumscribed boxes

Bend40Pipe-rack Area
Pipe-rack : Supporter of pipes
Objectives…
 To bundle pipes
 To progress workability
 To progress maintainability

In the routing system…

Cost Discounting Area
41

Pipe-rack Area
Pipe-rack Area
L4L3:

CtotalCost of an Elbow:

CE

Total Cost

Length of Pipe : L1~L4
Discount Rate : VD < 1L2Diameter：R

CTotal = (L1+L2+L3 X VD+L4
L1+ (1+VD) X CE) X R
42

Pipe-rack Area

Experiments
Design Space ：Size X 3.0m, Size Y 2.5m, Size Z 2.0m
Mesh Size：Size X 0.25m, Size Y 0.25m, Size Z 0.25m

Start Point：( 0.5m, 2.0m, 0.5m), x+

Goal Point：( 2.75m, 2.0m, 0.5m), xDiscount Rate : 0.3
Pipe-rack Area

43

Aisle Space
Aisle Space : Passage for CrewObjective…
 To improve safety
 To progress maintainability

In the routing system…

Cost Increasing Area
44

Aisle Space
Aisle SpaceL5L4L3L2:

CtotalCost of an Elbow:

CE

Total Cost

Length of Pipe : L1~L5
Extra Rate

: VP > 1Diameter：R

CTotal = (L1+(L2+L3+L4) X VP+L5
L145+ (1+VP) X CE ) X R

Aisle SpaceExperiment
Design Space ：Size X 3.0m, Size Y 2.5m, Size Z 2.0m
Mesh Size：Size X 0.25m, Size Y 0.25m, Size Z 0.25m

Start Point：( 0.5m, 0.5m, 1.5m), z-Goal Point：( 2.75m, 0.5m, 0.5m), z+

Extra rate: 3.0Aisle Space46

Simulations
ObjectiveTo verify the useful of the algorithm through drawing pipes
in a part of a ballast pomp room

Test Case Setting
Design Space ：Size X 8.0m, Size Y 12.0m, Size Z 4.0m

Mesh Size：Size X 0.25m, Size Y 0.25m, Size Z 0.25m

Discount Rate of Pipe-rack Area : 0.5
Extra Rate of Aisle Space : 2.047

From the largest
Simulation
To the thinnest

From the longest
To the shortest

Pipe No.

Diameter[m]Length[m]Order1

Order2

Pipe10.9

12.0

13

Pipe20.7

12.3

22

Pipe30.5

11.7

34

Pipe40.3

13.1

41

Start 2

Goal 4

Start 3

Goal 3

Start 1

Goal 2Start 4

Goal 148

Experiments

Diameter：Rd1

Cost of a Straight Pipe : 1 X R per 1m49

Experiments
d2
d1

Diameter：R

Cost of a Elbow : (d1 + d2 + 0.1) X R
50

Experiments
d2
d1

Diameter：R

Cost of a Bend : (d1 + d2 + 0.3) X R
51

Results
Order1 : From the largest

Order2 : From the longest

Total Cost : 13.95

Total Cost : 5.452

Results
Order1 : From the largest

Total Cost : 23.42

Order2 : From the longest

Total Cost : 11.90

53

Results
Order1 : From the largest

Total Cost : 29.95

Order2 : From the longest

Total Cost : 30.08

54

Results
Order1 : From the largest

Total Cost : 35.22

Order2 : From the longest

Total Cost : 37.78

55

Discussion
Order1 : From the largest

Order2 : From the longest

 The algorithm succeeded finding routes with bends.
 Simulated routes passed the pipe-rack area.
 Last design demands on the order of routing.
 The system often drew pipes those are difficult to assemble.
56

Discussion
As a result in other test case…

Especially in very
narrow space

An obtained route interfered with itself!
57

Outline
1. Background and Purpose- Previous Research
2. Routing Algorithm Including Bends- Approach- Outline of “Bends”- Outline of Pipe-rack Area and Aisle Space- Experiments
3. Conclusion and Challenges
58Conclusions
Advantages of the algorithm
 The mesh size is free.
 The algorithm generates practical designs with bends.
 The algorithm draws each pipe with optimum costs.
 The drawing pipes are considered pipe-rack-area andaisle space.

59

Future Works
We need to …
 Improve the routing algorithm Associate the routing system withthe equipment layout system
 Make better the interference check algorithm
 Investigate best order of routingThis system will be opened for free at
http://sysplan.nams.kyushu-u.ac.jp/gen/index.html
60

Thank You.

This system will be opened for free at
http://sysplan.nams.kyushu-u.ac.jp/gen/index.html

61