Cellular Simulation for Distributed Sensing over Complex Terrains
1.1. Related Work
1.2. A Characterization of Terrain Complexity
1.3. Designing for Long-Distance Radio Coverage
1.4. Observing Physical Phenomena
2. Mapping Geographic Space into Cell Systems
2.1. Geographic Map and User Interfaces
2.2. Definition of Cells
- Cell locations are bounded to geometric locations on maps, in relation to tile containers, and when possible to geographical locations.
- Basic cell contents are extracted from the map or image fragment as supported by the browser tool.
- Cell content extensions are obtained from external databases. Most of the cases are digital elevations, and also climate, or weather characteristics and historical data.
- Cell size is chosen to match a particular physical phenomenon or sensing requirements.
- Cell behaviors are local procedures operating on a cell state. They need to be programmed to produce simulation data that in turn can be sent back to databases, or displayed on tiles.
2.3. Cellular Automata Principles
2.3.1. Synchronous Systems
- The cellular space is represented by an assembly of similar cells. A common notion of neighborhoods defines local communications following observed physical dependencies. The spatial organization can be either regular or irregular, possibly with disconnected subsystems as shown in Figure 11, item 3.
- The evolution of each cell is defined in a set of states as observed in a real system (quantities, colors, boolean). Change of states are operated by procedures associated with representing transition rules from step to step: .
- The neighborhood represents physical dependencies, for example, signal propagation, or downward flooding. These dependencies are connectivities from cell to neighbor cells. Common neighborhoods are Von Neumann and Moore with four and eight cardinal directions, respectively. Item “Process architecture” in Figure 11 illustrates a Moore neighborhood.
- The transition rule defines the behavior of each cell evolution under influence of its neighborhood and local sensed influences. The state of the whole cell system synchronously changes, time step by time step.
2.3.2. Variability in Large Systems and Asynchronism
2.4. Cellular Automata Parallel Execution Models
- The synchronous distributed messaging model  can support parallel computation by associating cells with communicating processes. In this case, process progress by locked steps, based on messages being sent and received to or from neighbor nodes. The steps are split into two phases, one for communications with the neighborhood, the other to execute the transition rule. Figure 12 shows an internal node representation and the outside connection with three input and output links. This model does not need to specify the relative speed of processes, and can therefore be used for multi-cores or supercomputers.
- Another way to take advantage of parallelism is to use data parallel Single Instruction Multiple Data (SIMD) processors to execute a group of processes simultaneously. Current graphics accelerators propose solutions up to two thousand processors working concurrently, and exchanging data synchronously in shared memory. State spaces must be copied to the accelerator memory. Then, a loop of steps can be run completely on the acceleration, which is very efficient.
2.5. Cellular Systems Workflow Organization
- Zone selection is done by moving a graphical window anywhere, with any level of zoom. The tool extracts graphic tiles, and displays the contents.
- Cell segmentation is obtained by splitting the view into rectangles of a given size specified as a width × height value. Cells will carry an image and a geographical location from the underlying image.
- Binding cell together and producing a cell system implies the choice of a connectivity (Moore, Von Neumann), and possibly filtering cells by colors or elevation. This step also injects external values from a variety of sources, including elevation.
- Adding behavior programs the cellular system at the local level, given a cell system architecture that step 3 (Figure 11) automatically produces.
3. Heavy Rain Simulation on a Complex Terrain
3.1. Managing Space
- Millimeters of water falling on the ground. For this simulation, we admit that the quantity can vary over time, but will remain uniform.
- Water disappearing locally for reasons such as absorption or evaporation.
- Water passed locally from cell to cell according to elevation differences.
3.2. Transition Rule
- t: time t represented by a step number,
- : water quantity in a center cell at the beginning of time step t,
- : rainfall at time t,
- : percentage of water remaining on each cell after each step,
- : elevation value of ,
- : elevation value of center cell,
- : the difference of elevation between neighbor and the center cell,
- : sum of all elevation differences,
- : amount of water out coming from center cell to neighbor ,
- : amount of water in coming to center cell from neighbor .
4. Parallel Algorithms for Cellular Long-Range Coverage Computations
4.1. General Idea
|Algorithm 1 Setup visible nodes from emitter based on the LoS condition.|
4.2. Vertical Model
4.3. Horizontal Model and Directed Breadth-First Search
5. Radio Signal Propagation on Complex Terrains
5.1. Free Space Path Loss Model
- : transmitted power,
- : received power,
- : transmitter antenna gain,
- : receiver antenna gain,
- d: distance between transmitter and receiver in meters,
- L: system loss factor,
- : wavelength in meters.
|Algorithm 2 Received signal power in the Free Space Path Loss Model.|
|1: procedure SignalPower|
|2: Input: txPower, waveLength, distance|
|3: Output: receivedPower|
|4: for each neighbor of do|
|5: if neighbor.visible then|
|6: receivedPower ← txPower × (SQR(waveLen /(4.0 ))× SQR(1/distance))|
|7: end if|
|8: end for|
|9: end procedure|
5.2. Single Knife-Edge Diffraction Model
|Algorithm 3 Received signal power in the Single Knife-Edge Diffraction Model.|
| 1: procedure diffractionLoss|
2: Input: fsplPower, h, ,
3: Output: diffPower
4: v = h * SQRT((valuePi/2)×((1/) + (1/)))
5: if v < 0 then
6: diffLoss ← 0
8: if v < 2.4 then
9: diffLoss ← 6 + (9 × v) + (1.27 × SQR(v))
11: diffLoss ← 13 + 20×
12: end if
13: end if
14: diffPower = fsplPower - diffLoss
15: end procedure
5.3. Okumura–Hata Model
- : center carrier frequency of transmission band in MHz.
- : antenna height of base station in meter,
- : antenna height of mobile node in meter,
- : distance in kilometers,
- for each type of area and K, see Table 2.
5.4. Correctness of the Different Radio Communication Models
- Synthesizing long-range mesh radio networks would allow for covering very large surfaces and require optimization of relay placement. Powerful parallel algorithms can help to overcome the coverage problem complexity.
- Line-of-sight propagation and water spreading are examples of common spatial behaviors found in nature. Many biological, mechanical or physical processes have similar properties. Sensing of environment could take benefits from generic frameworks helping to develop and compose such simulations.
- Applicability for large problems available for the public can be obtained by publishing web interfaces to services dependent on two separated concerns: zone selection and cell resolution, and cellular system libraries.
Conflicts of Interest
Appendix A.1. A Study of a Flash Flood Event
Appendix A.2. Experimental Measurements of Radio Coverage
|Area Name||Description||Resolution||Actual Size||Range||Match||Mismatch||% Error|
|Albert 1er||Urban area||pixels||24 m||3 km||64||13||20.21%|
|Plougastel||River and its banks||pixels||96 m||9 km||129||4||3.10%|
|Trevezel||mountain area||pixels||191 m||11 km||45||8||17.78%|
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|Type of Area||a||K|
|Free space path loss||19,537|
|Single knife-edge diffraction||22,305|
|Weather broadcast||2D/3D||3000 (https://www.ncdc.noaa.gov/data-access/model-data/model-datasets/numerical-weather-prediction)|
|Coastal ocean||2D/3D||1200 (https://pdfs.semanticscholar.org/55be/a487827c28aaaf713017c499e4f33aed62fd.pdf)|
|Earth magnetic||2D/3D||3700 (http://www.sciencedirect.com/science/article/pii/S0377042798002465)|
|Ocean acoustics||2D/3D||2500 (https://www.ngdc.noaa.gov/geomag/emag2.html)|
|0.5 (Peter Wille. Chapter 5: The Sea Floor—Natural Formations.|
|Road traffic noise||2D/3D||In Sound Images of the Ocean: in Research and Monitoring.|
|Springer-Verlag Berlin Heidelberg, 2005. ISBN 978-3-540-27910-5)|
|Processes||Number of Rounds||Time (s)|
|Compute ruggedness index||1||0.026|
|Resolution (Pixels)||Number of Cells||820M||GTX 680||PGTX 1070|
|3 × 3||58,725||28.168 (ms)||6.5269 (ms)||1.3373 (ms)|
|5 × 5||21,060||10.411 (ms)||2.1728 (ms)||518.64 (s)|
|10 × 10||5226||2.5234 (ms)||454.59 (s)||83.696 (s)|
|15 × 15||2340||1.1155 (ms)||181.48 (s)||65.916 (s)|
|20 × 20||1287||602.47 (s)||171.19 (s)||62.085 (s)|
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Truong, T.P.; Pottier, B.; Huynh, H.X. Cellular Simulation for Distributed Sensing over Complex Terrains. Sensors 2018, 18, 2323. https://doi.org/10.3390/s18072323
Truong TP, Pottier B, Huynh HX. Cellular Simulation for Distributed Sensing over Complex Terrains. Sensors. 2018; 18(7):2323. https://doi.org/10.3390/s18072323Chicago/Turabian Style
Truong, Tuyen Phong, Bernard Pottier, and Hiep Xuan Huynh. 2018. "Cellular Simulation for Distributed Sensing over Complex Terrains" Sensors 18, no. 7: 2323. https://doi.org/10.3390/s18072323