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. Wang 1 , Z. Wang 2 , E. Tahchi 3 , Y. Wang 4 , G. Wang 5 , J. Yang 6 , F. Cucker 7 , J. Manton 8 , B. Moran 8 and M. Zukerman 1 Credit: the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU8/CRF/13G) 2. School of Automation, Northwestern Polytechnical University, Xi’an, China 1. Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China 4. Department of Architecture and Civil Engineering, City University of Hong Kong, Hong Kong, China 3. EGS (Asia) Limited, 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 Credit: TeleGeography Credit: U.S. Geological Survey subsequent events (source: EGS database) • 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 <y 2004 . Credit: EGS Database 4 Credit: University of Malta

West Coast USA Motivation Credit: TeleGeography Credit: U.S. Geological Survey 5 Faults . Credit: EGS Database

Curving cables can improve cable survivability Motivation 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/ Reef and seagrass, http://www.great- Marine protected areas, barrier-reef.com/blog/reef-on-tour.html 9 https://www.artisanathai.com/

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/ 10 http://www.industrytap.com/

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 ℝ 3 piecewise-linear 2-D manifold in , 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 • Direct losses: repair cost, more serious cable damage (at Models 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. Taiwan earthquake 2006 Many potential earthquakes CA, USA • Failure rate g ( x , y , ξ ( x , y )) is a function of the cable material, diameter and movement (e.g. PGV). • American Lifelines Alliance: 𝑕 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. 13

Mathematical Formulation Problem • A multi-objective variational optimization problem min 𝛿 Φ(𝛿) = (ℍ 𝛿 , 𝔿(𝛿)) 1 • Linear scalarization: 𝑑 ∈ 𝑆 + 𝑚(𝛿) 𝑚(𝛿) min 𝛿 Φ(𝛿) = න 𝑑 ∙ ℎ 𝑌 𝑡 + 𝑕 𝑌 𝑡 𝑒𝑡 = න 𝑔(𝑌(𝑡)) 𝑒𝑡 0 0 • A single objective variational problem • If γ * is optimal for 𝑛𝑗𝑜 𝛿 Φ(𝛿) , then it is Pareto optimal for min(ℍ 𝛿 , 𝔿(𝛿)) • Therefore, we need to solve the variational problem ׬ 𝑚(𝛿) min 𝛿 Φ 𝛿 = න 𝑔 𝑌 𝑡 𝑒𝑡 0 14

• Variational problem: Solutions 𝑔 𝑌 𝑡 = 𝑑 ∙ ℎ 𝑌 𝑡 + 𝑕(𝑌(𝑡)) • 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 𝑔 𝑌 𝑡 = 𝑑 ∙ ℎ 𝑌 𝑡 + 𝑕(𝑌(𝑡)) 𝑚(𝛾) Solutions 𝜚(𝑇) = min 𝛾 න 𝑔 𝑌 𝑡 𝑒𝑡 , 𝑌 0 = 𝑌 𝐵 , 𝑌 𝑚 𝛾 = 𝑌 𝑇 0 S can be any node on the objective manifold and A is the source, 𝛾 is the path between S and A. • 𝜚 𝑇 is the solution of the Eikonal equation | 𝛼𝜚 𝑇 | = 𝑔(𝑇) • 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. 𝑒𝑌(𝑡) = −𝛼𝜚, 𝑕𝑗𝑤𝑓𝑜 𝑌 0 = 𝑇 𝑒𝑡 i.e., orthogonal to the level curves. 16

Framework 𝑕 𝑌 = 0.002416 ∙ 𝐿 ∙ 𝑄𝐻𝑊(𝑌) 𝑔 𝑌 𝑡 = 𝑑 ∙ ℎ 𝑌 𝑡 + 𝑕(𝑌(𝑡)) 𝑚(𝛾) 𝜚(𝑇) = min 𝛾 න 𝑔 𝑌 𝑡 𝑒𝑡 0 | 𝛼𝜚 𝑇 | = 𝑔(𝑇) 𝑒𝑌(𝑡) = −𝛼𝜚 𝑒𝑡 Framework 17

US Example • USGS earthquake hazard assessment data (PGA, 2% in 50 years) Applications • 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

• Convert PGA to PGV by Applications 𝑚𝑝𝑕 10 𝑄𝐻𝑊 = 1.0548 × 𝑚𝑝𝑕 10 𝑄𝐻𝐵 − 1.1556 • Convert PGV to failure rate 𝑕 𝑌 = 0.002416 ∙ 𝐿 ∙ 𝑄𝐻𝑊(𝑌) 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

• Lay a cable from Los Angles (34.05 ° ,-118.25 ° ) to Applications Davis (38.53 ° ,-121.74 ° ) • Weight 0.0252 (plus), 0.2188 (triangle) and 10 (circle) 𝑔 𝑌 𝑡 = 𝑑 ∙ ℎ 𝑌 𝑡 + 𝑕(𝑌(𝑡)) 21

 Weight 10 -3 ~10 Results  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

 Weight 10 -3 ~ 10 -1 Results  The Pareto front 24

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