Probabilistic Methods

There are generally two types of probabilistic methods: Sampling based Methods and Analytical Methods. Sampling based methods generally generate a set of random values based on the joint PDF of the design variables (input random variables) and compute Z-function values. These methods thus are highly accurate if high enough number of samples can be performed. These methods generally are suitable in case that the Z-function evaluation takes very less time. Very low probability values, high computation time for Z-function can render these methods almost unusable. Analytical methods are the ones which generally approximate the response function. Analytical methods require very few response function evaluations and can compute rare event probabilities economically. These methods can be of two types namely Most Probable Point (MPP) based methods and Surrogate based methods. MPP based methods try and find the high probability of occurrence point. The success of the MPP based methods is generally based on how good the approximation of the response function is and whether they can point out a good MPP. Once MPP is found they perform fast probability integration to compute probability of failure and probabilistic sensitivity as by product. Surrogate based methods try and come up with an approximation of the response function by sampling some training points and doing some curve fitting. Once there is a response surface built, these methods then perform sampling on it to compute probabilities.

CENTAUR

Probabilistic Analysis Tool now has some more probabilistic methods other than Monte Carlo. Analyzer now provides some probabilistic methods from Southwest Research Institute (SwRI), a leader in the field of probabilistic and reliability. Probabilistic methods from SwRI are well tested and industry standard in most cases. SwRI provides a probabilistic analysis tool called NESSUS. NESSUS was initially developed by SwRI for NASA to perform probabilistic analysis of space shuttle main engine components. SwRI continues to develop and apply NESSUS to a diverse range of problems including aerospace structures, automotive structures, biomechanics, gas turbine engines, geomechanics, nuclear waste packaging, offshore structures, pipelines, and rotordynamics. NESSUS is used for performing reliability analysis all over the world. CENTAUR is the underlying library for NESSUS. CENTAUR (Collection of ENgineering Tools for Analyzing Uncertainty and Reliability) is a software library that contains an array of methods for solving various types of problems, with an emphasis on non-deterministic analysis. Thus through CENTAUR, Probabilistic Analysis Tool now provides efficient analytical methods to perform reliability analysis. The analytical methods generally provide very efficient analysis relative to the standard Monte Carlo. The selection of an appropriate method should be guided by several considerations, including required computational time, which strongly depends on the complexities of the performance functions for example finite element models versus closed form equations. The solution accuracy is also important which depends on the non-linearity and smoothness of the performance functions. The Method Selection Wizard tries to point out the most suitable method based on problem setup and a few responses.

List of probabilistic methods available in the Probabilistic Analysis Tool:

References:1. SwRI CENTAUR homepage: http://www.nessus.swri.org/centaur