convergence_probability_failure

This function calculates the convergence rate of a given column in a data frame. This function is used to check the convergence of the probability of failure or reliability index.

div, m, ci_l, ci_u = convergence_probability_failure(df, column)

Input variables

Name	Description	Type
df	DataFrame containing the data with indicator function column	DataFrame
column	Name of the column to be used for calculating the convergence rate	String

Output variables

Name	Description	Type
div	List containing sample sizes	List
m	List containing the mean values of the column. pf value rate	List
ci_l	List containing the lower confidence interval values of the column	List
ci_u	List containing the upper confidence interval values of the column	List

Example 1

Use convergence_probability_failure function is used to determine the convergence rate of the failure probability of the limit state function I_0.

# Libraries
import pandas as pd
pd.set_option('display.max_columns', None)

from parepy_toolbox import sampling_algorithm_structural_analysis, convergence_probability_failure
from obj_function import nowak_collins_example

# Check structural reliability 
f = {'type': 'normal', 
    'parameters': {'mean': 40.3, 'sigma': 4.64}, 
    'stochastic variable': False, 
    }

p = {'type': 'gumbel max',
    'parameters': {'mean': 10.2, 'sigma': 1.12}, 
    'stochastic variable': False, 
    }

w = {'type': 'lognormal',
    'parameters': {'mean': 0.25, 'sigma': 0.025}, 
    'stochastic variable': False, 
    }
var = [f, p, w]
setup = {
             'number of samples': 100000, 
             'numerical model': {'model sampling': 'mcs'}, 
             'variables settings': var, 
             'number of state limit functions or constraints': 1, 
             'none variable': None,
             'objective function': nowak_collins_example,
             'name simulation': 'nowak_collins_example',
        }
results, pf, beta = sampling_algorithm_structural_analysis(setup)

# Convergence rate
x, m, l, u = convergence_probability_failure(results, 'I_0')

We can construct the convergence rate chart using the results m, ci_l, and ci_u. We using x in x-axis.

Figure 1. Failure probability - convergence rate.