Running a single calculation

In this example, we demonstrate how to perform a single model run using the library.

First, we import the necessary classes:

from probabilistic_library import RunProject, RunValuesType, DistributionType, ReliabilityProject
import matplotlib.pyplot as plt
import numpy as np

Let’s consider the Hunt’s model for wave run-up with three output parameters:

from utils.models import hunt_3_outputs

We define a project using the RunProject() class and specify the model to be used:

project = RunProject()
project.model = hunt_3_outputs

project.model.print()

Model hunt_3_outputs:
Input parameters:
  t_p
  tan_alpha
  h_s
  h_crest
  h
Output parameters:
  Z
  xi
  r_u

We define the input variables as follows:

project.variables["t_p"].distribution = DistributionType.log_normal
project.variables["t_p"].mean = 6
project.variables["t_p"].deviation = 2

project.variables["tan_alpha"].distribution = DistributionType.deterministic
project.variables["tan_alpha"].mean = 0.333333

project.variables["h_s"].distribution = DistributionType.log_normal
project.variables["h_s"].mean = 3
project.variables["h_s"].deviation = 1

project.variables["h_crest"].distribution = DistributionType.log_normal
project.variables["h_crest"].mean = 10
project.variables["h_crest"].deviation = 0.05

project.variables["h"].distribution = DistributionType.exponential
project.variables["h"].shift = 0.5
project.variables["h"].scale = 1

Running model

It is possible to run a model assuming that the input parameters are based on one of the following:

• Mean values

• Median values

• Design values

• Values derived from a Reliability Project

These types are explained below.

Mean values

This is configured using RunValuesType.mean_values, and the model results are stored in project.realization.output_values. When printing the result, the first array corresponds to the input parameters and the second array to the output parameters, which were displayed by using project.model.print().

project.settings.run_values_type = RunValuesType.mean_values

project.run()
project.realization.print()

[6, 0.3333, 3, 10, 1.5] -> [4.172, 1.443, 4.328]

Median values

This is set using RunValuesType.median_values.

project.settings.run_values_type = RunValuesType.median_values

project.run()
project.realization.print()

[5.692, 0.3333, 2.846, 10, 1.193] -> [4.807, 1.405, 4]

Design values

This is set using RunValuesType.design_values.

Two attributes of the input variables are relevant here: design_quantile and design_factor. The default values for these parameters are \(0.5\) and \(1.0\), respectively, which lead to the same results as option median_values.

project.settings.run_values_type = RunValuesType.design_values

project.run()
project.realization.print()

[5.692, 0.3333, 2.846, 10, 1.193] -> [4.807, 1.405, 4]

Below, we define the design_quantile and design_factor attributes for two input parameters: h_crest and h.

project.variables["h_crest"].design_quantile = 0.65
project.variables["h_crest"].design_factor = 0.95

project.variables["h"].design_quantile = 0.95
project.variables["h"].design_factor = 1.05

project.run()
project.realization.print()

[5.692, 0.3333, 2.846, 10.55, 3.329] -> [3.218, 1.405, 4]

Values derived from a Reliability Project

It is also possible to perform a single run using a model that has already been defined in a reliability project:

reliability_project = ReliabilityProject()
reliability_project.model = hunt_3_outputs

reliability_project.variables["t_p"].distribution = DistributionType.log_normal
reliability_project.variables["t_p"].mean = 6
reliability_project.variables["t_p"].deviation = 2

reliability_project.variables["tan_alpha"].distribution = DistributionType.deterministic
reliability_project.variables["tan_alpha"].mean = 0.333333

reliability_project.variables["h_s"].distribution = DistributionType.log_normal
reliability_project.variables["h_s"].mean = 3
reliability_project.variables["h_s"].deviation = 1

reliability_project.variables["h_crest"].distribution = DistributionType.log_normal
reliability_project.variables["h_crest"].mean = 10
reliability_project.variables["h_crest"].deviation = 0.05

reliability_project.variables["h"].distribution = DistributionType.exponential
reliability_project.variables["h"].shift = 0.5
reliability_project.variables["h"].scale = 1

project = RunProject()
project.model = reliability_project.model
project.settings.run_values_type = RunValuesType.mean_values

project.run()
project.realization.print()

[6, 0.3333, 3, 10, 1.5] -> [4.172, 1.443, 4.328]

Loop

It is possible to loop over different input-parameter values:

h_crest_values = np.arange(0.5, 11.0, 0.5)
z_value = []

for val in h_crest_values:
    reliability_project.variables["h_crest"].mean = val

    project.run()
    z_value.append(project.realization.output_values[0])

plt.figure()
plt.plot(h_crest_values, z_value)
plt.grid()
plt.xlabel("h crest [m]")
plt.ylabel("z value [-]")
plt.show()