科研之友
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摘要
This paper provides a method for optimal shielding design and path planning of a long-haul optical fiber cable between two locations on the Earth's surface. The method allows minimization of the cable laying cost including material and labor and the risks of future cable break associated with laying the cable through various areas, including earthquake-prone or other risky areas. Both costs per unit length and risk of cable damage may be different at different locations. Expensive shielding may be important in certain high-risk areas and unnecessary in lower risk areas. We use ground motion intensity to estimate future cable repair rate (our measure of earthquake-related cable damage risk), and a triangulated manifold to represent the surface of the Earth. With laying cost and expected total number of repairs of the cable as the two objectives, we formulate the problem as a multiobjective variational optimization problem. This formulation incorporating multiple design levels for cable shielding is converted into a single objective variational optimization problem by assigning different weights to each objective. The solution path of the later problem is obtained by using the Fast Marching Method (FMM) with an additional minimization step. A new proof of the optimality of FMM for the problem is provided. Numerical results demonstrate that the FMM-based method outperforms existing raster-based algorithms. With billions of US dollars spent yearly on new cables, the potential savings are substantial. Furthermore, the computational complexity of the FMM-based method is O(N log(N)), making it applicable to cables of realistic length.
