Example of fuzzy alfa-cut method on river hydraulics

River Jadar runs through west of Serbia and Montenegro state. Since the landuse is highly variable and not the same over years, due to urbanisation and diferent agrycultural plans, it is required to analyse risk of flooding under influence of uncertain Manning coeficient in the main channel and in flood plains. Representation of uncertain parameters is choosen to be represented as fuzzy sets.

Grafical representation of mathematical model of river Jadar

River Jadar is modeled from the bridge in Osecina to cross section 1650 m upstream. It was divided in 15 crossections. As flow is subcritical, critical depth in the most dounstream cross section is assumed as boundary condition. The discharge was Q=147 m3/s.

Schematic representation of main channel and inundation areas.

Main characteristics of the example:

  • Water head is monotonic on Manning value - no need for optimization methods
  • Input fuzzy sets are triangular - there is no need to have more than one a cut (support of a fuzzy set)
  • Subcritical flow - the influences are transmitted upstream so the boundaries conditions are downstream (critical depth under the bridge)

After dividing input fuzzy sets on 4 alfa cuts, the result is presented on picture below:

Fuzzy output - water level

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The exercise on fuzzy set analysis