Line Sampling

Line Sampling#

TODO#

Todo

Write this section.

Syntax#

flx.perform_Line_Sampling()#
Syntax:

flx.perform_Line_Sampling(LSF, U_STAR, SAMPLER, CONFIG)

Description:

Perform a line sampling (structural reliability analysis).

Parameters:

  • LSF (flxPara) – The limit-state function (that depends on the input random variables of sampler SAMPLER).

  • U_STAR (numpy.ndarray) – The base-vector for performing the line sampling. Ideally, this point is the design point of the structural reliability problem.

  • SAMPLER (flx.sampler) – A sampler for a set (or multiple sets) of random variables.

  • CONFIG (dict) –

    A configuration dictionary. The following keys are allowed in CONFIG:

    • n_ls (int, default: 10): The total number of line searches to perform. Value must be positive.

    • ls_max_iter (int, default: 10): The maximum number of iterations per line-search. Value must be positive.

    • ls_tol (float, default: 0.001): Tolerance parameter for performing the line search. Value must be positive.

    • use_bisec (bool, default: False): Specifies the line-search algorithm. True: bisection method; False: regula falsi / secant method

    • extended_ls (bool, default: False): If True, the algorithm searches for multiple roots per line-search.

    • verboseLog (bool, default: False): Verbose logging.

    • show_progress (bool, default: True): Show progress bar.

    • data_box (type flx.dataBox): A flx.dataBox to store/post-process all evaluations of the limit-state function performed by the line sampling algorithm.

Returns:

A Python dict with the following information is returned:

  • pf (float): The probability of failure estimated by line-sampling.

  • N_lsf_calls (int): The total number of times the limit-state function was evaluated.

  • calls_per_line_search (int): The average number of limit-state function calls per line-search.

  • n_ls (int): The total number of line searches performed.

Return type:

dict

Application Example#

import fesslix as flx
flx.load_engine()

Random Number Generator: MT19937 - initialized with rand()=884715071;
Random Number Generator: MT19937 - initialized with 1000 initial calls.

0

## ==============================================
## Generate input model
## ==============================================
config_rv_R = { 'name':'R', 'type':'logn', 'mu':6., 'sd':1. }
config_rv_S = { 'name':'S', 'type':'normal', 'mu':1., 'sd':1. }
rv_set = flx.rv_set( {'name':'rv_set', 'allow_x2y':True}, [ config_rv_R, config_rv_S ] )
sampler = flx.sampler(['rv_set'])

## ==============================================
## Limit-state function
## ==============================================
lsf_expr = "rbrv(rv_set::R)-rbrv(rv_set::S)"

## ==============================================
## Set up dataBox
## ==============================================
dBox = flx.dataBox(2,1)
pp_rel = dBox.register_post_processor({ 'type':'counter' })

## ==============================================
## FORM solution
## ==============================================
config = { 'verboseLog':True, 'opt_method':'HLRF', 'fdstep':5e-2, 'data_box':dBox }
form_res = flx.perform_FORM(lsf_expr, sampler, config)
print(form_res)
print(pp_rel.eval())

{'FORM_alpha': array([-0.5658187 ,  0.82452968]), 'FORM_beta': 3.8105978475448645, 'FORM_pf': 6.931556382892316e-05, 'pf_upper_bound': '7.028775e-4', 'dzdy': array([ 0.13952447, -0.20331966]), 'FORM_x': array([4.14195278, 4.14195104]), 'FORM_u': array([-2.15610752,  3.14195104]), 'N_lsf_calls': 16, 'N_iter': 5}
{'N': 6}

## ==============================================
## Line sampling
## ==============================================
config = { 'n_ls':10000, 'extended_ls':True, 'use_bisec':False, 'data_box':dBox }
ra_ls_res = flx.perform_Line_Sampling(lsf_expr, form_res['FORM_u'], sampler, config)
print(ra_ls_res)
print(pp_rel.eval())

{'pf': 6.175684236913863e-05, 'N_lsf_calls': 60004, 'calls_per_line_search': 6.0, 'n_ls': 10000}
{'N': 60010}
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