Probabilistic Tutorials

Contents:

• Tutorial 1: Deriving Lognormal statistics from measurements
  • Step 1: Importing the dataset, and interpreting the data.
  • Step 2: Sample mean and sample standard deviation of the data set
    • Step 2a: Calculate the mean and standard deviation of the ‘real’ values
    • Step 2b: Calculate the mean and standard deviation of the logarithmic values
  • Step 3: Fitted Lognormal Distribution using method of moments (MoM)
    • Step 3c: Visual inspection of the results
    • Optional step 3d: Derive parameters for a shifted Lognormal distribution, with all values shifted to 14
  • Step 4: Characteristic values
    • Step 4a: Calculate the characteristic value with the Student-T factor.
    • Step 4b: Calculate the characteristic value with and without spatial avaraging
    • Step 4c: Visually checking the results
  • Step 5: Get the inputs for D-Stability, taking into account the statistical uncertainty
    • Step 5a: For the uncertainty in the point values
    • Step 5b: For the uncertainty in the regional average
    • Step 5c: For the uncertainty in the spatial average
    • Step 5d: Visualize the results
• Tutorial 2: Fit an extreme value distribution for the water level
  • Step 1: Importing packages and data
  • Step 2: Importing the data from external source
  • Step 3: Preprocessing of the data.
  • Step 4: Visually checking the data
  • Step 5: Fitting a Generalized Extreme Value (GEV) distribution
  • Step 6: Optimizing the distribution parameters using Python
  • Step 7: Plot the result
  • Step 8: Force fitting a Gumbel distribution
• Tutorial 3: Integrating the fragility curve with the PDF of the waterlevel
  • Step 1: Create base class DStabilityFragilityCurve for fragility curve operations
  • Step 2: Specify the fragility curve names and locations
  • Step 3: Plot the fragility points and the extrapolated fragility curve
  • Step 4: integrate the fragility curve with the probability density of water level
  • Step 5: Calculate the probability of exceedence
• Tutorial 4: Combining 2 fragility curves for different scenario’s.
  • Import necessary python packages
  • Load base class for Fragility curve operations
  • Code for plotting
    • Load fragility curves, create DStabilityFragilityCurve objects, and save in list
  • Plot the fragility points
  • Extrapolate fragility curves linearly along the given range, with the given discretisation
  • Plot the extrapolated fragility curves
  • Load the water level dependent scenario probability and densify and extrapolate
  • Sanity checks:
  • Plot the scenario probabilities
  • The combination of 2 fragility curves
  • Plot the combined fragility curve
  • Save the combined fragility curve to json (e.g. to import in the Probabilistic Toolkit)