Patent Application
20230061400
A portion of the disclosure of this patent document contains material, which is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the Patent and Trademark Office patent file or records, but otherwise reserves all copyright rights whatsoever.
The present invention generally relates to cable path planning. More specifically, the present invention relates to weight selection of design considerations for submarine cable path planning.
With recent technology push and demand pull mainly linked to the introduction of 5G technology and the COVID-19 outburst, there is continuous growth in global data and network traffic and it is challenging to sustain capacity growth of submarine cables. However, the laying and maintenance of submarine cables are costly and vast submarine cable systems are prone to faults. To design a cost-effective and resilient submarine cable network, it is required to consider various factors that may cause the submarine cable to break, including natural and anthropological activities. In reality, a resilient and cost-effective submarine cable's path design is achievable by considering a range of factors. Industry experts conduct multiple routes and engineering surveys and constantly modify the cable path meter by meter manually to balance the various considerations. This process is highly time-consuming and expensive.
There has also significant fundamental research done on submarine cable path planning. Most of the existing work on path planning of submarine cables focuses on path optimization under a specific factor. In addition to the earthquake factor that is usually considered, there are many other factors that may affect the cost and reliability of submarine cables that should be considered.
Therefore, there is an unmet need for a cable path planning method which can take into account various considerations that may affect the cost and reliability of submarine cables so as to produce cost-effective and reliable real-life submarine cable path design within an acceptable time frame.
According to one aspect of the present invention, the present invention provides a method for cable path planning. The method comprises: deriving an optimal set of weights of design considerations from an optimal virtual cable path generated between a reference start point and a reference end point in a reference manifold under an objective of minimizing a life-cycle cost modelled with one or more design considerations and minimizing a discrete Fréchet distance with respect to a reference cable path; and determining an optimal path arrangement for the infrastructure cable over the target terrain based on the derived optimal set of weights of design considerations.
According to another aspect of the present invention, the present invention provides a cable planning method using a fast marching method (FMM) based on simulated annealing (SA) (FMM/SA) algorithm. In the FMM/SA algorithm, FMM is used to obtain the optimal submarine cable path with the lowest life-cycle cost, and SA algorithm is used to continuously adjust the weight of each design consideration with the aim to achieve an optimal cable path that is as close as possible to a real-life cable path which has a history of cost-effectiveness and resilience. The set of weights contributed to the optimal cable path is then used as an optimal set of weights of design considerations for cable path planning.
Compared with other types of FMM algorithms such as the FMM algorithm based on random-restart hill-climbing (FMM/RRHC) and the FMM algorithm based on Monte Carlo's idea (FMM/MC), the FMM/SA algorithm based cable planning method can provide a computationally effective approach which has lower computation costs and better performance in generating cable paths with optimal life-cycle cost and reliability.
The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.
Embodiments of the invention are described in more detail hereinafter with reference to the drawings, in which:
In the following description, a method and a system for optimizing a cable path design and the likes are set forth as preferred examples. Specific details may be omitted so as not to obscure the invention; however, the disclosure is written to enable one skilled in the art to practice the teachings herein without undue experimentation.
Preferably, the reference cable path is a real-life cable between two geographic locations and with a history of resilience and cost-effectiveness. The reference start point and the reference end point are the two geographic locations, respectively. The reference manifold may be obtained by modelling an earth surface between the two geographic locations into a triangulated piecewise-linear two-dimensional manifold M in R3. Each point on M is denoted by a three-dimensional coordinate (x, y, z), where z=ξ(x, y) is the elevation corresponding to a geographic location (x, y).
In addition to basic construction cost consideration (including cable length) as well as considerations for cable resilience (including geological hazards like earthquakes and volcano eruptions, anthropological hazards like fishing and anchoring activities), there are other cable design considerations that are taken into account in cable path planning. Such considerations include but not limited to restricted/protected areas, existing cables/pipelines, seabed slope, water depth, shield level for cables.
The reference cable path may be denoted as U and represented by a sequence of points {u1, u2, . . . , up}, where p is the number points in U. A virtual cable path may be denoted as V and represented by a sequence of points {v1, v2, . . . , vq}, where q is the number of points in U. Without loss of generality, it is assumed that the number of points in U is larger than the number of points in V, namely, p>q.
The virtual path curve V with the minimal total life-cycle cost may be obtained by solving a first optimization problem:
where C(V) is the life-cycle cost function for the virtual cable path V.
The total life-cycle cost for the virtual cable path V may be given by:
C(V)=∫0l(V)C(X(t))dt,
where l(V) is the total length of the virtual cable path V, c(X(t)) is a life-cycle cost function per unit length at a location X(t) formulated with a length t of a very small arc segment of the cable path V.
The life-cycle cost function per unit length may be constructed based on a K number of design considerations and given by:
C(X)=Σk=1Kwkck(X),
where ck (X) represent the cost function of design consideration k at location X and wk is the weight of design consideration k, and k=1, 2, . . . , K.
Then, the optimal virtual cable path can be obtained by solving a second optimization problem defined as:
where δdF(U, V) represents the discrete Fréchet distance of the virtual cable path with respect to the reference cable path, and W represents sets of weights of design considerations used for obtaining the discrete Fréchet distance, and R+K is the feasible solution space for the sets of weights of design considerations.
The discrete Fréchet distance may be given by:
where s={(ui, vai)} represents a sequence of pairs of points generated based on the rules: (1) for any two points ui and uj in U, if i<j, then ai≤aj; (2) every point vj in V should be used to form a pair; S is a set of all possible sequences of pairs of points (ui, vk) paired with points from U and V respectively; and d(ui, va
The annealing temperature may be defined by a function:
T(r)=Toφr
where T(r) is the annealing temperature, r is the number of temperature attenuation, D is the dimension of the state space and φ is a non-negative real number. In various embodiments, the dimension of the state space D is equal to 1 or 2, and non-negative real number φ has a value ranging from 0.7 to 1, inclusive of 0.7 and 1, i.e. 0.7≤φ≤1.
502: obtaining a new virtual path having a minimal total life-cycle cost under a new set of weights of design considerations generated by perturbating a current set of weights of design considerations which is obtained in a previously performed iteration;
504: calculating a new discrete Fréchet distance for the new virtual path with respect to the reference cable path;
506: determining whether the new discrete Fréchet distance is smaller than a current discrete Fréchet distance which is calculated in a previously performed iteration; going to a step 508 if the new discrete Fréchet distance is smaller than the current discrete Fréchet distance; and going to a step 510 if the new discrete Fréchet distance is not smaller than the current discrete Fréchet distance.
Referring to
Referring to
The processing unit 702 is a processor such as a CPU, an MCU or electronic circuitries including but not limited to application specific integrated circuits (ASIC), field programmable gate arrays (FPGA), and other programmable logic devices configured or programmed according to the teachings of the present disclosure.
The memory unit 704 may include a volatile memory unit (such as RAM), a non-volatile unit (such as ROM, EPROM, EEPROM and flash memory) or both, or any type of media or devices suitable for storing instructions, codes, and/or data.
Preferably, the apparatus 700 further includes one or more input devices 706 such as a keyboard, a mouse, a stylus, a microphone, a tactile input device (e.g., touch sensitive screen) and a video input device (e.g., camera). The apparatus 700 may further include one or more output devices 708 such as one or more displays, speakers, disk drives, and printers. The displays may be a liquid crystal display, a light emitting display or any other suitable display that may or may not be touch sensitive. The apparatus 700 may further include one or more disk drives 712 which may encompass solid state drives, hard disk drives, optical drives and/or magnetic tape drives. A suitable operating system may be installed in the apparatus 700, e.g., on the disk drive 712 or in the memory unit 704 of the apparatus 700. The memory unit 704 and the disk drive 712 may be operated by the processing unit 702.
The apparatus 700 also preferably includes a communication module 710 for establishing one or more communication links (not shown) with one or more other computing devices such as a server, personal computers, terminals, wireless or handheld computing devices. The communication module 710 may be a modem, a Network Interface Card (NIC), an integrated network interface, a radio frequency transceiver, an optical port, an infrared port, a USB connection, or other interfaces. The communication links may be wired or wireless for communicating commands, instructions, information and/or data.
Preferably, the processing unit 702, the memory unit 704, and optionally the input devices 706, the output devices 708, the communication module 710 and the disk drives 712 are connected with each other through a bus, a Peripheral Component Interconnect (PCI) such as PCI Express, a Universal Serial Bus (USB), and/or an optical bus structure. In one embodiment, some of these components may be connected through a network such as the Internet or a cloud computing network. A person skilled in the art would appreciate that the apparatus 700 shown in
In some embodiments, the method in the invention may also be implemented in distributed computing environments and/or Cloud computing environments, wherein the whole or portions of machine instructions are executed in distributed fashion by one or more processing devices interconnected by a communication network, such as an intranet, Wide Area Network (WAN), Local Area Network (LAN), the Internet, and other forms of data transmission medium.
This section illustrates an application example of the present invention by using a first real-life existing submarine cable path as the reference cable path for deriving an optimal set of weights of design considerations and demonstrating whether an optimal path arrangement determined with the derived optimal set of weights of design considerations for a second real-life existing submarine cable is consistent with the realistic cable path arrangement. In addition, the performance of the FMM/SA algorithm is compared to those of the FMM algorithm based on random-restart hill-climbing (the FMM/RRHC algorithm) and the FMM algorithm based on Monte Carlo's idea (the FMM/MC algorithm).
The first real-life existing submarine cable path is from the Southern Cross NEXT located in the Pacific Ocean and comprising a Trans-Pacific trunk route linking Coogee Beach, Australia with Hermosa Beach, Calif. USA, and branches to Takapuna Beach, New Zealand, to Suva, to Savusavu, to Apia, to Tokelau, and also a link to Kiribati.
The second real-life existing submarine cable path is from the South America-1 (SAm-1) cable network located in Latin America, connecting the United States, Puerto Rico, Brazil, Argentina, Chile, Peru and Guatemala.
In calculating the life-cycle cost of each point X (x, y, z) on a submarine cable path, the following design considerations that contribute to the total life-cycle cost of the submarine cable path are taken into account (Notice that the units “dollars ($)” representing the total life-cycle cost should not be taken as the actual prediction for the cable cost, because they are a measure obtained as a summary cost function which is based on the various costs associated with the design considerations and their weights (that are subjective measures of importance)):
1) Basic construction cost c1 (X). It involves the laying, maintenance and removal cost of submarine cables. By way of example and not limitation, c1(X) may be defined as constant number, that is, c1(X)=27,000 $.
2) Geological hazards c2(X), specifically, earthquakes with magnitudes greater than 4.5 and volcanic eruption. By way of example and not limitation, assuming that there are p earthquakes and q volcanic eruptions in total in target region T, the cost c2 (X) may be defined as:
c
2(X)=Σi
where ce(X, ie) and cv(X, iv) are the cost caused by earthquake ie and a volcanic eruption iv.
The cost ce(X, ie) may be given by:
c
e(X,ie)=a1e1.3 ln PGV(X)−7.21, and
PGV(X)=2.04+0.422×(Mw−6)−0.0373×(Mw−6)2−log10 i d(X,ie),
which represents the peak ground velocity (PGV) at location X,
where Mw and d(X, ie) are the earthquake magnitude of ie and the distance between point X and earthquake ie, respectively.
The cost cv(X, iv) may be given by:
where a2 is a very large number for avoiding these volcanos and d(X, iv) is the distance between point X and volcano iv, respectively.
3) Seabed slope c3(X). By way of example and not limitation, the cost c3(X) may be defined as:
where a3 is a very large number for avoiding steep areas and l1(X) is the slope at location X.
4) Water depth c4(X). By way of example and not limitation, the cost c4(X) may be defined as:
where a4 is a very large number for avoiding placing cable on the land and l2 (X) is the water depth at location X. Note that l2(X)<0 means that the location X is underwater.
5) Anthropological hazards c5(X), specifically, fishing and anchoring activities. By way of example and not limitation, the cost c5(X) may be defined as:
c
5(X)=cf(X)+ca(X),
where cf(X) and ca(X) are the cost caused by fishing and anchoring activities, respectively.
The cost cf(X) may be defined as:
and the cost ca(X) may be defined as:
where a5 is a very large number for avoiding the shallow water area.
6) Protected areas c6(X), specifically, seagrass and coral areas. By way of example and not limitation, the cost c6(X) may be defined as:
where a6 is a very large number for avoiding these protected areas.
Accordingly, the importance (weights) of the design considerations (1)-(6) above may be denoted as W={w1, w2, w3, w4, w5, w6}. By implementing these weights, the life-cycle cost per unit length of the cable passing through location X may be represented as C(X)=Σi=16 wici(X). In this application example, the initial set of weights W0 is set to be {0.28, 0.091, 0.35, 0.091, 0.09, 0.0981}. The numbers a1, a2, a3, a4, a5, a6 are all set to be 3×106$.
Data of the design considerations for the two real-life existing submarine cable paths can be obtained from public data sources or web-based mapping software. For example, geological data (that is, longitude, latitude, and elevation) at each point on the paths can be obtained from worldwide submarine cable map (e.g., Infrapedia, https://www.infrapedia.com/app/subsea-cable/). The global terrain data for ocean and land is available in the General Bathymetric Chart of the Oceans (GEBCO, https://www.gebco.net) at 15 arc-second intervals. This data can provide a triangulated manifold model M with the distance between two adjacent grid points in the range of 350 to 650 meters. The seabed slope data and water depth data are calculated from the global terrain data. The earthquake data is provided by United States Geological Survey (USGS, https://earthquake.usgs.gov/). The information on volcano eruptions is obtained from National Oceanic and Atmospheric Administration (NOAA, https://www.ngdc.noaa.gov/). The protected areas for seagrass and corals are derived from World Conservation Monitoring Centre (WCMC, https://data.unep-wcmc.org/datasets/).
The parameter setting of cooling schedule of the FMM/SA algorithm is shown in Table 1. A sufficiently high initial temperature (T0=500) is selected to avoid falling into the local optimum. A sufficiently low termination temperature (Tf=5) is selected to avoid poor accuracy. The dimension of the state space D is set to be 2, and non-negative real number φ is set to be 0.8 such that the annealing temperature function is given by: T(r)=T0*0.8r
Under an International Cable Protection Committee Ltd (“ICPC”) Recommendation (https://www.iscpc.org/publications/recommendations/), the cable path generated by the FMM/SA algorithm is set to march in only the 50-degree fan-shaped range in front of the current direction during the marching process as shown in
Table II provides the detailed Fréchet distances and total lengths of minimal life-cycle cost paths (denoted as Cables 1-4) generated by the FMM/SA algorithm under different sets of weights of design considerations obtained at different running times. Cable 1 is the optimal cable path obtained while Cables 2-4 are the intermediate results. All the results are obtained using a Dell G7-7590 laptop (32 GB RAM, 2.60 GHz Intel® Core™ i7-9750H CPU) for running the codes in Matlab R2017b.
It can be seen from Table 2 that, as time used to assess the weights increases, the closer our cable path is to Cable SX, but the time required to make further improvements in getting closer to Cable SX will increase greatly.
A partially enlarged view of
Tables 3 and 4 show numerical results for the cable paths generated by FMM/SA algorithm (Cable 1), the FMM/RRHC algorithm (Cable 5) and the FMM/MC algorithm (Cable 6) compared with the data of Cable SX, respectively. Noted that the total life-cycle cost for Cable SX is different in Table 3 and 4 because these two tables use different W derived by FMM/RRHC and FMM/MC, respectively.
It can be clearly seen that FMM/SA algorithm can better solve this problem within the limited time. Given the data of a submarine cable path in the real world and the cost functions of all the design considerations, FMM/SA algorithm can continuously approach the actual submarine cable curve (Cable SX) at a faster speed. In contrast, FMM/MC algorithm takes nearly 50,000 seconds to find the path result (Cable 6), which is comparable with Cable 3 by FMM/SA algorithm taking only 75 seconds. Although FMM/RRHC algorithm obtains a path result (Cable 5) closer to that of FMM/SA algorithm (Cable 1), it takes much more time to obtain the results.
Based on the optimal set of weights of design considerations derived with the first real-life existing submarine cable, Cable SX, an optimal path arrangement on the second real-life existing submarine cable, Cable SAm, is determined and compared with the realistic cable path arrangement.
Table 6 provides the detailed Fréchet distances and total lengths of the cable paths generated under the optimal set of weights of design considerations obtained by the FMM/SA algorithm, the FMM/RRHC algorithm (Cable 8) and FMM/MC algorithm, respectively. Cable 7 is the cable path generated under the optimal set of weights of design considerations obtained by the FMM/SA algorithm. Cable 8 is the cable path generated under the optimal set of weights of design considerations obtained by the FMM/RRHC algorithm. Cable 9 is the cable path generated using weights of design considerations obtained by the FMM/MC algorithm. Note that in Table 6, total life-cycle costs are normalized by setting the total life-cycle cost for Cable SAm to 1 for easy comparison among Paths 7, 8, and 9.
From the results shown in Table 6 and
The above application example demonstrates that learning the weights of design considerations from the 5,351.1 kilometer-long (with over 9,000 data points) Cable SX in one part of the world (Pacific Ocean), and then using these weights for cable path planning between the end-points of the 1,791.2 kilometers-long Cable SAm in a different part of the world (Latin America) can provide a path (Path 7) that is very close to the actual real-life path of Cable SAm derived based on the traditional approach.
The foregoing description of the present invention has been provided for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many modifications and variations will be apparent to the practitioner skilled in the art.
The embodiments were chosen and described in order to best explain the principles of the invention and its practical application, thereby enabling others skilled in the art to understand the invention for various embodiments and with various modifications that are suited to the particular use contemplated.
