FloodingSensitivity

class FloodingSensitivity

Class to define a Flooding sensitivity benchmark problem.

Methods

getFirstOrderIndices()

Returns the first order Sobol' sensitivity indices.

getFunction()

Returns the function.

getInputDistribution()

Returns the input distribution.

getName()

Returns the name of the problem.

getTotalOrderIndices()

Returns the total order Sobol' sensitivity indices.
__init__()

Create a Flooding sensitivity problem.

The function is defined by the equation:

g(x) = (\frac{Q}{K_s B \sqrt{\frac{Z_m-Z_v}{L}}})^{\frac{3}{5}}+Z_v-Z_b-H_d

with:

  • Q : maximum annual flowrate (m3/s)

  • Ks : Strickler coefficient

  • Zv : downstream riverbed level (m)

  • Zm : upstream riverbed level (m)

  • L : Length of the river in meters

  • B : Width of the river in meters

  • Hd : height of the dyke (m)

  • Zb : the height of the bank (m)

The input random variables are independent.

Parameters:
None.

Notes

The dimension of this problem cannot be changed.

The model was first introduced in (Iooss, 2015).

The analysis is the following.

  • The model has almost no interactions.

  • The most important variable is Q, with first order indice approximately equal to 0.4.

  • The variables L and B are insignificant.

The reference Sobol’ indices were computed from a sparse polynomial chaos. A Sobol’ low discrepancy design of experiments was generated with 1000 training points. The sparse polynomial chaos expansion used an hyperbolic enumeration rule and a polynomial degree 8. The coefficients were estimated from regression. With 1000 points in the validation set, the Q2 was greater than 99.9%. There are 2 significant digits in the reference results.

References

  • Iooss, B., Lemaître, P. A review on global sensitivity analysis methods. In: Meloni, C., Dellino, G. (eds.) Uncertainty Management in Simulation-Optimization of Complex Systems. Algorithms and Applications. Springer, New York (2015)

  • “OpenTURNS: An industrial software for uncertainty quantification in simulation”. Baudin, M., Dutfoy, A., Looss, B., Popelin, A.-L. 2017. Handbook of Uncertainty Quantification. pp. 2001-2038

Examples

>>> import otbenchmark as otb
>>> problem = otb.FloodingSensitivity()
getFirstOrderIndices()

Returns the first order Sobol’ sensitivity indices.

Parameters:
None.
Returns:
firstOrderIndices: ot.Point

The first order sensitivity indices.

getFunction()

Returns the function.

Parameters:
None.
Returns:
function: ot.Function

The function.

getInputDistribution()

Returns the input distribution.

Parameters:
None.
Returns:
distribution: ot.Distribution

The distribution.

getName()

Returns the name of the problem.

Parameters:
None.
Returns:
name: str

The name.

getTotalOrderIndices()

Returns the total order Sobol’ sensitivity indices.

Parameters:
None.
Returns:
totalOrderIndices: ot.Point

The total order sensitivity indices.