BoreholeSensitivity¶
- class BoreholeSensitivity¶
Class to define a Borehole sensitivity benchmark problem.
Methods
Returns the first order Sobol' sensitivity indices.
Returns the function.
Returns the input distribution.
getName
()Returns the name of the problem.
Returns the total order Sobol' sensitivity indices.
- __init__()¶
Create a Borehole sensitivity problem.
The function is defined by the equation:
g(x) = (2*pi_*Tu*(Hu-Hl))/(ln(r/rw)*(1+(2*L*Tu)/(ln(r/rw)*rw^2*Kw)+Tu/Tl))
where:
r_w: radius of borehole (m)
r: radius of influence (m)
T_u: transmissivity of upper aquifer (m^2/yr)
H_u: potentiometric head of upper aquifer (m)
T_l: transmissivity of lower aquifer (m^2/yr)
H_l: potentiometric head of lower aquifer (m)
L: length of borehole (m)
K_w: hydraulic conductivity of borehole (m/yr)
The input random variables are independent.
- Parameters:
- None.
Notes
The dimension of this problem cannot be changed.
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 6. 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
Worley, B. A. (1987). Deterministic uncertainty analysis (No. CONF-871101-30). Oak Ridge National Lab., TN (USA).
Morris, M. D., Mitchell, T. J., & Ylvisaker, D. (1993). Bayesian design and analysis of computer experiments: use of derivatives in surface prediction. Technometrics, 35(3), 243-255.
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.