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Cost Effective and Survivable Submarine Cable Path Planning Presenter: Elias TAHCHI EGS (Asia) Limited, Hong Kong, China

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Cost Effective and Survivable Submarine Cable Path Planning Presenter: Elias TAHCHI EGS (Asia) Limited, Hong Kong, China 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 <y 2004. Credit: EGS Database Credit: University of Malta 4 West Coast USA Motivation 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 푚푛훾Φ(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, 푔푣푒푛 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(푒) • 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, ′ 푋 푣 , 푙 +′ 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 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.
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