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 Cost Effective and Survivable Content Submarine Cable Path Planning Contents • Motivation • Models • Problems • Solutions • Applications • Results • Conclusion 2 Hengchun (Taiwan) Earthquake 2006 Motivation

Faults caused by earthquakes and subsequent events (source: EGS database) 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. 3 Mediterranean Area Motivation

Credit: TeleGeography Credit: U.S. Geological Survey

Faults

Credit: TeleGeography Credit: U.S. Geological Survey

Faults. Credit: EGS Database 5 Curving cables can improve Motivation cable survivability

Conflict between cost and cable survivability 6 Main aim Main Aim

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

7 Back to the Hengchun earthquake

Motivation  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

Without consequences !!!!!

Map of cables around Taiwan, source: TeleGeography Submarine Cable Map 8 Other Problematic Areas Environmental factors

Very hard seabed, https://i.ytimg.com/ High slope, http://smashingtops.com/

Marine protected areas, Reef and seagrass, http://www.great- barrier-reef.com/blog/reef-on-tour.html https://www.artisanathai.com/ 9 Other Problematic Areas Human activities

Anchors, https://www.fs.com/blog/things-you- Fishing activities, http://dkcpc-kort.dk/ probably-didnt-know-about-submarine-cables.html

Offshore renewable energy generation Existing cables and pipelines, and hydrocarbon exploitation, http://www.divingco.com.au/ http://www.industrytap.com/ 10 Landform Model Models • A cable is laid/buried on the surface of land or the sea bed • Approximate the Earth’s surface by a closed, triangulated piecewise-linear 2-D manifold in ℝ 3, uniquely represented by a continuous, single-valued function z = ξ(x, y)

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 • ℍ(γ) 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

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 • Ground motion intensity, PGV (Peak Ground Velocity), PGA Repair rate (Peak Ground Acceleration), SA (Spectral Acceleration) etc.

Many potential earthquakes CA, USA Taiwan earthquake 2006 • Failure rate g(x, y, ξ(x, y )) is a function of the cable material, diameter and movement (e.g. PGV). • American Lifelines Alliance: 푔 푋 = 0.002416 ∙ 퐾 ∙ 푃퐺푉(푋) 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. 13 Mathematical Formulation Problem • A multi-objective variational optimization problem min Φ(훾) = (ℍ 훾 , 픾(훾)) 훾 1 • Linear scalarization: 푐 ∈ 푅+ 푙(훾) 푙(훾) min Φ(훾) = න 푐 ∙ ℎ 푋 푠 + 푔 푋 푠 푑푠 = න 푓(푋(푠)) 푑푠 훾 0 0 • A single objective variational problem

• If γ* is optimal for 푚𝑖푛훾Φ(훾), then it is Pareto optimal for min(ℍ 훾 , 픾(훾))

Therefore, we need to solve the variational problem ׬ •

푙(훾) min Φ 훾 = න 푓 푋 푠 푑푠 훾 0 14 Solutions • Variational problem: 푓 푋 푠 = 푐 ∙ ℎ 푋 푠 + 푔(푋(푠))

• This is a continuous problem! • The solution paths (a path for each node) that minimize the integral are the minimum cost paths. . 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) 15 • Define a new cost function 푓 푋 푠 = 푐 ∙ ℎ 푋 푠 + 푔(푋(푠)) Solutions 푙(훽) 휙(푆) = min න 푓 푋 푠 푑푠 , 푋 0 = 푋퐴, 푋 푙 훽 = 푋푆 훽 0 S can be any node on the objective manifold and A is the source, 훽 is the path between S and A. • 휙 푆 is the solution of the Eikonal equation | 훻휙 푆 | = 푓(푆) • 휙 푆 = 푎 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. 푑푋(푠) = −훻휙, 푔𝑖푣푒푛 푋 0 = 푆 푑푠 i.e., orthogonal to the level curves. 16 Framework 푔 푋 = 0.002416 ∙ 퐾 ∙ 푃퐺푉(푋)

푓 푋 푠 = 푐 ∙ ℎ 푋 푠 + 푔(푋(푠))

푙(훽) 휙(푆) = min න 푓 푋 푠 푑푠 훽 0

| 훻휙 푆 | = 푓(푆)

푑푋(푠) = −훻휙 푑푠

Framework

17 US Example 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

Geography. Source: Google Earth. 18 Applications • Convert PGA to PGV by 푙표푔10 푃퐺푉 = 1.0548 × 푙표푔10 푃퐺퐴 − 1.1556 • Convert PGV to failure rate 푔 푋 = 0.002416 ∙ 퐾 ∙ 푃퐺푉(푋)

PGV map (unit: cm/s) 19 Applications

• 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

20 Applications • 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) 푓 푋 푠 = 푐 ∙ ℎ 푋 푠 + 푔(푋(푠))

21 -3 Results  Weight 10 ~10  The Pareto optimal values concentrate on a narrow range

22 Taiwan Example Applications  Lay a cable from (21.00°, 119.00°) to (22.270°, 120.652°)

23 Results  Weight 10-3 ~ 10-1

 The Pareto front

24 Cable Protection 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 Cable structure, optical cables, Photograph https://en.wikipedia.org/wiki/Submarine_com courtesy of L. Hagadorn munications_cable 25 • The Earth’s surface is modeled by triangulated Models irregular network---a graph G = (V, E) • Laying cost model: • ℎ′(푋, 푙) represents the cable unit laying cost of protection level l at location (x, y, z); • For an edge e = (v,w) ∈ E, ℎ′ 푋 푣 , 푙 +ℎ′ 푋 푤 , 푙 ℎ 푒 = 푑(푣, 푤) 푙 2 • For a path γ = (v0, l0, v1, l1, … , vp-1, lp-1, vp), 푝−1 ℍ γ = Σ0 ℎ푙푖(푒𝑖) • Cable repair model: • 푔′(푋, 푙) represents the repair rate corresponding to protection level l at location (x, y, z); • For an edge e = (v,w) ∈ E, 𝑔′ 푋 푣 , 푙 +𝑔′ 푋 푤 , 푙 푔 푒 = 푑(푣, 푤) 푙 2 • For a path γ = (v0, l0, v1, l1, … , vp-1, lp-1, vp), 픾 γ = Σ푝−1푔 (푒 ) 0 푙푖 𝑖 26 Algorithms • The multi-objective optimization problem, start point s, end point t.

To solve this problem, we propose approximate algorithms. The exact • A label setting based exact algorithm (Algorithm 1 in 푘 푘 later slides): spreads from an existing label (ℍ푣, 픾푣) time consuming and needs a huge on 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 order to avoid keeping all non-dominated solutions • An evolutionary algorithm: Strength Pareto Evolutionary Algorithm 2 (SPEA2) 27 Results

(Approximate) Pareto front.

31 CA Example Applications  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)

Geography. Source: Google Earth. The mean logarithmic PGV of objective area 28  ℍ(γ*) is the total laying cost Applications  픾(γ*) is the total number of repairs  ℍ1(γ*) and 픾1 (γ*) are for the same paths in the case when all the segments are without any shielding protection.

ℍ (γ*) (w/p) 픾(γ*) (w/p) ℍ1(γ*) (wo/p) 픾1(γ*) (wo/p) 248.47 37.56 230.75 41.92 29  ℍ(γ*) is the total laying cost Applications  픾(γ*) is the total number of repairs  ℍ1(γ*) and 픾1 (γ*) are for the same paths in the case when all the segments are without any shielding protection.

ℍ (γ*) (w/p) 픾(γ*) (w/p) ℍ1(γ*) (wo/p) 픾1(γ*) (wo/p) 271.72 33.27 227.49 43.10

30 A Large Region Example----US Central Applications • 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. The mean logarithmic PGV of Source: Google Earth. objective area 32 Results

Approximate Pareto front.

Algorithm 1 can not be used because of the constraints of computational time and storage memory. 34 Conclusions 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 35 Publications Publications

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.

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.