Submarine Cable Path Planning Presenter: Elias TAHCHI EGS (Asia) - - PowerPoint PPT Presentation

Cost Effective and Survivable Submarine Cable Path Planning

Presenter: Elias TAHCHI

EGS (Asia) Limited, Hong Kong, China

Authors: Q. Wang1, Z. Wang2, E. Tahchi3, Y. Wang4, G. Wang5, J. Yang6, F. Cucker7, J. Manton8, B. Moran8 and M. Zukerman1 Credit: the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU8/CRF/13G)

• 1. Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China
• 2. School of Automation, Northwestern Polytechnical University, Xi’an, China
• 3. EGS (Asia) Limited, Hong Kong, China
• 4. Department of Architecture and Civil Engineering, City University of Hong Kong, Hong Kong, China
• 5. Department of Civil and Environmental Engineering, Hong Kong University of Science and Technology, Hong Kong, China
• 6. Department of Civil Engineering, The University of Hong Kong, Hong Kong, China
• 7. Department of Mathematics, City University of Hong Kong, Hong Kong, China
• 8. Department of Electrical and Electronic Engineering, The University of Melbourne, Melbourne, Australia

Contents

• Motivation
• Models
• Problems
• Solutions
• Applications
• Results
• Conclusion

Content 2

Cost Effective and Survivable Submarine Cable Path Planning

Hengchun (Taiwan) Earthquake 2006

Credit: TeleGeography Credit: U.S. Geological Survey

• Severe disruption of Internet and phone services in south

east Asia (for several weeks from 26-Dec.)

• Switzerland – (ETH 2005) – reduction of over 1% GDP

per week of Internet blackout.

Motivation 3

Faults caused by earthquakes and subsequent events (source: EGS database)

Mediterranean Area

Credit: TeleGeography Credit: University of Malta Credit: U.S. Geological Survey

Motivation 4

Faults <y 2004. Credit: EGS Database

West Coast USA

Credit: TeleGeography Credit: U.S. Geological Survey

Motivation 5

• Faults. Credit: EGS Database

Curving cables can improve cable survivability

Conflict between cost and cable survivability

Motivation 6

To develop a methodology and working tools for cost effective design of a survivable planned cable taking into account topography, ground motion information, and various other considerations and restrictions

Main aim 7

Main Aim

Back to the Hengchun earthquake

 Hengchun earthquake, 20:26 Dec. 26, 2006 (M7.0)  APCN, APCN-2, C2C, China-US CN, EAC, FLAG

FEA, FNAL/RNAL and SMW3, CH-US(W2), SMW3(S1.8) break at 20:27

 Southwestern Ryukyu Islands earthquake,

05:49 Aug. 17, 2009 (M6.7 + Tsunami Warning)

new cable systems: TPE and TGN

Motivation

Map of cables around Taiwan, source: TeleGeography Submarine Cable Map

Without consequences !!!!!

8

Other Problematic Areas

Environmental factors

Very hard seabed, https://i.ytimg.com/ High slope, http://smashingtops.com/ Marine protected areas, https://www.artisanathai.com/ Reef and seagrass, http://www.great- barrier-reef.com/blog/reef-on-tour.html9

Human activities

Fishing activities, http://dkcpc-kort.dk/

Other Problematic Areas

Anchors, https://www.fs.com/blog/things-you- probably-didnt-know-about-submarine-cables.html Offshore renewable energy generation and hydrocarbon exploitation, http://www.industrytap.com/ Existing cables and pipelines, http://www.divingco.com.au/

10

Landform Model

Models

• Approximate the Earth’s surface by a closed, triangulated

piecewise-linear 2-D manifold in , uniquely represented by a continuous, single-valued function z = ξ(x, y) ℝ3

• A cable is laid/buried on the surface of land or the sea

bed

11

Laying Cost Model

Models

• Different locations may have different cost, e.g. rock,

sand

• Cost function h(x, y, z), z = ξ(x, y)
• γ is the (Lipschitz) continuous path of a cable
• is laying cost of the cable
• Laying cost is cumulative,
• Set the cost of the cable in problematic areas to be

infinity to avoid the areas ℍ(γ)

12

Risk Model

Models

• Direct losses: repair cost, more serious cable damage (at

multiple points), higher repair cost

• Indirect losses: interruption of network services, more

serious cable damage, longer delays of the service

• Index: A number to represent the level of damage

“expected” which is considered as total number of failures (or repairs) over the lifetime of the cable or in an earthquake event?

• Index principal is widely used to assess reliability of

water supply networks and gas distribution networks

• 2006 Taiwan earthquake, 8 cable systems, 18 failures, 7

days for repairing on each fault (Index value is high)

• Repair (failure) rate function: g(x, y, z), z = ξ(x, y)
• The number of repairs is cumulative,

13

Seismic Hazard Risk

Repair rate

• Failure rate g(x, y, ξ(x, y )) is a function of the cable material,

diameter and movement (e.g. PGV).

• American Lifelines Alliance:

Many potential earthquakes CA, USA Taiwan earthquake 2006

• Ground motion intensity, PGV (Peak Ground Velocity), PGA

(Peak Ground Acceleration), SA (Spectral Acceleration) etc.

13

𝑕 𝑌 = 0.002416 ∙ 𝐿 ∙ 𝑄𝐻𝑊(𝑌) K is a coefficient determined by the cable material and

• diameter. g(X) is expressed in 1/km and PGV is given in

cm/s.

Problem

Mathematical Formulation

• A multi-objective variational optimization problem
• Linear scalarization: 𝑑 ∈ 𝑆+

1

• A single objective variational problem
• If γ* is optimal for 𝑛𝑗𝑜𝛿Φ(𝛿), then it is Pareto
• ptimal for
• Therefore, we need to solve the variational problem

min

𝛿 Φ 𝛿 = න 𝑚(𝛿)

𝑔 𝑌 𝑡 𝑒𝑡 14 min

𝛿 Φ(𝛿) = (ℍ 𝛿 , 𝔿(𝛿))

min(ℍ 𝛿 , 𝔿(𝛿)) min

𝛿 Φ(𝛿) = න 𝑚(𝛿)

𝑑 ∙ ℎ 𝑌 𝑡 + 𝑕 𝑌 𝑡 𝑒𝑡 = න

𝑚(𝛿)

𝑔(𝑌(𝑡)) 𝑒𝑡

׬

• Discrete optimization methods, such as Dijkstra algorithm,

is inconsistent with the underlying continuous problem.

• Fast Marching Method (FMM) converges to the

continuous physical solution as the grid step size tends to zero.

• FMM has the same computational complexity as the

Dijkstra algorithm., i.e., O(N log N)

Solutions

• Variational problem:
• This is a continuous problem!
• The solution paths (a path for each node) that minimize

the integral are the minimum cost paths.

15

𝑔 𝑌 𝑡 = 𝑑 ∙ ℎ 𝑌 𝑡 + 𝑕(𝑌(𝑡))

• Define a new cost function
• 𝜚 𝑇 is the solution of the Eikonal equation
• 𝜚 𝑇 = 𝑏 is a level set, i.e., a curve composed of all

points can be reached from the point A with minimal cost equal to a.

• Construct the optimal path by tracking backwards from S

to A, solving the following ordinary differential equation. i.e., orthogonal to the level curves.

Solutions 16

𝑔 𝑌 𝑡 = 𝑑 ∙ ℎ 𝑌 𝑡 + 𝑕(𝑌(𝑡))

𝜚(𝑇) = min

𝛾 න 𝑚(𝛾)

𝑔 𝑌 𝑡 𝑒𝑡 , 𝑌 0 = 𝑌𝐵, 𝑌 𝑚 𝛾 = 𝑌𝑇 | 𝛼𝜚 𝑇 | = 𝑔(𝑇) 𝑒𝑌(𝑡) 𝑒𝑡 = −𝛼𝜚, 𝑕𝑗𝑤𝑓𝑜 𝑌 0 = 𝑇

S can be any node on the objective manifold and A is the source, 𝛾 is the path between S and A.

Framework

Framework 17

𝑔 𝑌 𝑡 = 𝑑 ∙ ℎ 𝑌 𝑡 + 𝑕(𝑌(𝑡)) 𝜚(𝑇) = min

𝛾 න 𝑚(𝛾)

𝑔 𝑌 𝑡 𝑒𝑡 | 𝛼𝜚 𝑇 | = 𝑔(𝑇) 𝑒𝑌(𝑡) 𝑒𝑡 = −𝛼𝜚 𝑕 𝑌 = 0.002416 ∙ 𝐿 ∙ 𝑄𝐻𝑊(𝑌)

Applications

• USGS earthquake hazard assessment data (PGA, 2% in 50 years)
• Realistic landform
• Objective area: From (40.23°,-124.30 °) to (32.60 °,-114.30 °)
• Aim: Cable path from Davis and Los Angeles

US Example

• Geography. Source: Google Earth.

18

• Convert PGA to PGV by

𝑚𝑝𝑕10 𝑄𝐻𝑊 = 1.0548 × 𝑚𝑝𝑕10 𝑄𝐻𝐵 − 1.1556

• Convert PGV to failure rate

Applications 19

PGV map (unit: cm/s) 𝑕 𝑌 = 0.002416 ∙ 𝐿 ∙ 𝑄𝐻𝑊(𝑌)

• Elevation data: spatial resolution 0.05 °
• PGA data: spatial resolution 0.05 °
• Coordinate transformation: From latitude and

longitude coordinate to Universal Transverse Mercator coordinate

• Triangulated manifold approximation: 60, 800

faces

Applications 20

• Lay a cable from Los Angles (34.05°,-118.25°) to

Davis (38.53°,-121.74°)

• Weight 0.0252 (plus), 0.2188 (triangle) and 10

(circle)

Applications 21

𝑔 𝑌 𝑡 = 𝑑 ∙ ℎ 𝑌 𝑡 + 𝑕(𝑌(𝑡))

 Weight 10-3 ~10  The Pareto optimal values concentrate on a narrow range

Results 22

 Lay a cable from (21.00°, 119.00°) to (22.270°, 120.652°)

Taiwan Example

Applications 23

 Weight 10-3 ~ 10-1  The Pareto front

Results 24

Cable structure, https://en.wikipedia.org/wiki/Submarine_com munications_cable

Protection

• In practice, there are several types of cables (e.g. light

weight cable, single armored, double armored.) can be chosen depending on the laying environment and realistic topography.

• We consider both the path planning and the non-

homogeneous construction of the cable to provide special shielding or extra protection as appropriate to strengthen the cable in sensitive areas.

Modern telecommunication fiber

• ptical cables, Photograph

courtesy of L. Hagadorn

Cable Protection

25

Models

• The Earth’s surface is modeled by triangulated

irregular network---a graph G = (V, E)

• Laying cost model:
• ℎ′(𝑌, 𝑚) represents the cable unit laying cost of

protection level l at location (x, y, z);

• For an edge e = (v,w) ∈ E,

ℎ𝑚 𝑓 =

ℎ′ 𝑌 𝑤 , 𝑚 +ℎ′ 𝑌 𝑥 , 𝑚 2

𝑒(𝑤, 𝑥)

• For a path γ = (v0, l0, v1, l1, … , vp-1, lp-1, vp),

ℍ γ = Σ0

𝑞−1ℎ𝑚𝑗(𝑓𝑗)

• Cable repair model:
• 𝑕′(𝑌, 𝑚) represents the repair rate corresponding

to protection level l at location (x, y, z);

• For an edge e = (v,w) ∈ E,

𝑕𝑚 𝑓 =

𝑕′ 𝑌 𝑤 , 𝑚 +𝑕′ 𝑌 𝑥 , 𝑚 2

𝑒(𝑤, 𝑥)

• For a path γ = (v0, l0, v1, l1, … , vp-1, lp-1, vp),

𝔿 γ = Σ0

𝑞−1𝑕𝑚𝑗(𝑓𝑗)

26

• A label setting based exact algorithm (Algorithm 1 in

later slides): spreads from an existing label (ℍ𝑤

𝑙, 𝔿𝑤 𝑙)

• n a particular vertex v to the neighbours of this

particular vertex with lexicographic ordering. It can find all the exact solutions but it is time consuming and needs a huge storage memory.

• An interval-partition-based approximate algorithm:

partition the label sets as arrays of polynomial size in

• rder to avoid keeping all non-dominated solutions
• An evolutionary algorithm: Strength Pareto

Evolutionary Algorithm 2 (SPEA2)

Algorithms

• The multi-objective optimization problem, start point

s, end point t.

27

e act a huge

Results

(Approximate) Pareto front.

31

 Objective area: 2°× 2°(California State)  Lay cables from A (33.55°, -117.65°) to B (35.00°, -

116.00°)

 Two design levels (low design level means no

protection and high design level means with protection)

The mean logarithmic PGV of

• bjective area

Applications

CA Example

• Geography. Source: Google Earth.

28

ℍ (γ*) (w/p) 𝔿(γ*) (w/p) ℍ1(γ*) (wo/p) 𝔿1(γ*) (wo/p) 248.47 37.56 230.75 41.92

 ℍ(γ*) is the total laying cost  𝔿(γ*) is the total number of repairs  ℍ1(γ*) and 𝔿1 (γ*) are for the same paths in the case

when all the segments are without any shielding protection.

Applications 29

Applications

ℍ (γ*) (w/p) 𝔿(γ*) (w/p) ℍ1(γ*) (wo/p) 𝔿1(γ*) (wo/p) 271.72 33.27 227.49 43.10

 ℍ(γ*) is the total laying cost  𝔿(γ*) is the total number of repairs  ℍ1(γ*) and 𝔿1 (γ*) are for the same paths in the case

when all the segments are without any shielding protection.

30

32

A Large Region Example----US Central

• Objective area: central US (6°× 6°);
• Lay cables from A (33.00°, -93.00°) to B

(39.00°, -87.00°);

• Two design levels (low design level means no

protection and high design level means with protection);

New Madrid faultline. Source: Google Earth. The mean logarithmic PGV of

• bjective area

Applications

34 Results

Approximate Pareto front.

Algorithm 1 can not be used because of the constraints

• f computational time and storage memory.

Conclusions

1. The Internet as a human right is becoming essential to our daily lives and we can make it 100% reliable. 2. Groundbreaking path design of cables includes considerations of topography, problematic areas, earthquake and other risks, and shielding. 3. Diffrent approach for route planning and cable route engineering. 4. Our approach based on trianguated manifolds has potential for cost saving relative to other approaches. 5. Synergy and partnership with submarine cable stakeholders 6. Diversity and alternative solutions for path planning

Conclusions 35

1.

• Z. Wang, Q. Wang, M. Zukerman, J. Guo, Y. Wang, G. Wang, J.

Yang, and B. Moran, “Multiobjective path optimization for critical infrastructure links with consideration to seismic resilience,” Computer-Aided Civil and Infrastructure Engineering, vol. 32, no. 10, pp. 836–855, Oct. 2017. 2.

• Z. Wang, Q. Wang, M. Zukerman, and B. Moran, “A seismic

resistant design algorithm for laying and shielding of optical fiber cables,” IEEE/OSA Journal of Lightwave Technology, vol. 35, no. 14, pp. 3060–3074, Jul. 2017. 3.

• C. Cao, Z. Wang, M. Zukerman, J. Manton, A. Bensoussan, and Y.
• Wang. Optimal cable laying across an earthquake fault line

considering elliptical failures. IEEE Transactions on Reliability. 65(3): 1536-1550, 2016. Publications

Publications

34

Thank you!

38

Back up slides

Pareto Optimal

39 Definition: Pareto optimal is a state of allocation of resources from which it is impossible to reallocate so as to make any one individual or preference criterion better off without making at least one individual or preference criterion worse off. Alternatively, An allocation is not Pareto optimal if there is an alternative allocation where improvements can be made to at least one participant's well-being without reducing any other participant's well-being.

The red points are examples of Pareto-optimal choices of production. Points off the frontier, such as N and K, are not Pareto-efficient.