Reliability Analysies

The methods

Several reliability methods was implementrd in Numpress system :

  • Monte Carlo
  • First Order Rliability Method (FORM)
  • Second OrderReliability Method (SORM)
  • Importance Sampling
  • Adaptive Importance Sampling
  • Mean-Value First-Order (MVFO)

Reliability methods managing using main tree

To create reliability analysis (as well as other analysis) just right click on the "Reliability analysis" item. Context menu with reliability analysies methods will appear. Click on choosen method. New analysis will appear on the tree. Clicking on the sub items subitems of the analysis user can set up parameters of the analysis. It will be described more preciselly below. To start computations rightclick on the analysis item. context menu will apeearr with "start analysis" option. Last item of each analysis is "Result" item. Color of this item reflects status of the analysis. Lack of the item means the computations wasn't started yed. Disabled state means the files with results was deleted. Red color means the computations failed or interrupted. Green color states the computations finished correctly and all results are available to view.

"Random variables table"

Setting parameters of reliability analysis

Some parameters are common for several analyses some are unique. Detailed description of dialogs are presented below

Variable selection

Determination of set of random variables is curcial for reliability problem statement. Often fast reduction of random variables set is needed. Excluded variable is replaced by constant. Doe exclude variable form analysis click on "variables" tree subitem. Desribed below dialog box will apear:

"Random variables table"

if particular variable is selected it will be used in the analysis. If not constant value will be used taken from secong column.Note that: Set of dependent random variables is setermined automatically by selecting limit state function. This window will be empty if no function is selected. So user can eliminate a variable only. To add a variable, definition of limit state function have to be enriched. Variable selection is applicable to all reliability methods.

Limit state function selection

User can select limit state by clicking "LSF" tree subitem. Selection dialog is opened:

"Random variables table"

Selection of LSF determines also set of variables to be used in the analysis. All tree items in tree window displays variable dependece after limit state function selection.selection. Limit state function selection is required by all reliability methods.

Design point search algorithm selection.

To select design point search algorithm select proper tab in dialog box depicted below:

"Random variables table"

Numpress Explore has implemented four design point search methods:

  • HLRF
  • ARF
  • Adaptive response surface
  • Gong and Yi (2011)

Selecting tab user can also change parameters for given algorithm. Selection of design point search algorithm is applicable in methods :FORM, SORM, Importance Sampling.

Starting point

Starting point gives possibility to determine point algorithms starts. It is importand especially in DPSA based methods (FORM, SORM, IS). In some cases (complex shape of limit state function) it may help to determine design point if starting point is entered manually by user. If not mean values point is used as starting point. Coordinates of starting point user can ender in dialog box showed below:

"Random variables table"

Dialog box gives also possibility to choose space for starting point: oryginal (X) or standard normal (U).

Sampling setup

Two sampling method are implemented in Numpress Explore: Random sapmling and Latin Hypercube sampling. Selection is made in Sampling setub dialod by choosing proper tab:

Random sampler

"Sampling setup"

Parameters of random sampler: Sample size is numper odf points to be use in simulations. "Pf estimator target cov." sampling will cntinue while target cov. level is reached.

Latin hypercube sampler:

"Sampling setup"

Parameters of random sampler: Sample size is numper odf points to be use in simulations. "Optimal" option means tat the Optimal Latin Hypercube will be used. If data base of OLH cubes is missing Numpress Explore will optimize LH. It may take some time so if user don't have database it is tecomented to use LH.

Applicable in Monte Carlo and Importannt Sampling methods.