Efficient Probabilistic Analysis Methods for Complex Numerical Models with Large Numbers of Random Variables, 20-9190

Principal Investigators
Sitakanta Mohanty
Michael P. Enright
Y-T (Justin) Wu (consultant)

Inclusive Dates: 04/01/00 - 05/01/02

Background - Physics-based probabilistic reliability/risk analysis of engineered and natural systems is emerging as a less expensive alternative to field and laboratory test-based methods. New challenges exist,  however,  because highly complicated physics-based models are computationally intensive and require a large number of variables to conduct accurate system-level analyses. The Total-System Performance Assessment code developed with assistance from the Center for Nuclear Waste Regulatory Analyses (a division of the Southwest Research Institute) to evaluate a high-level radioactive waste (HLW) disposal facility and the codes for reliability-based motor vehicle design involving hundreds of input variables are typical examples. These problems cannot be solved efficiently and accurately by the existing methods that have been successfully used for problems with a small number of variables.

Approach - The objective of the project is to develop and demonstrate a fast and accurate method to tackle risk/reliability problems involving computationally intensive and numerically complex models with large numbers of parameters. The hybrid method combines the sampling approach that explores the parameter space and the advanced reliability methods that focus the analysis at the tail of the probability distribution. Probabilistic sensitivity measures that can most effectively identify the most important random variables are being developed. The method is being extended to combine the low-probability, high-consequence scenarios with the most likely scenarios to obtain a single performance measure. An efficient reliability analysis method and an efficient reliability-based design optimization method are being developed. The demonstration examples include nuclear waste management, oil and gas exploration and transportation, and automotive applications.

Accomplishments - This research made significant advances in developing a methodology for probabilistic analysis of complex systems characterized by time-consuming analyses and a large number of random variables. The following is a summary of the key accomplishments.

• Developed and formalized an efficient sampling-based screening procedure and demonstrated through a multi-linear response function example that (i) the ranking is more easily identified at the tails of the distribution; (ii) the mean-sensitivity (response CDF with respect to mean) has a generally better discriminating power in identifying influential variables than the sigma-sensitivity (response CDF with respect to standard deviation), particularly when the CDF is close to the median (i.e., CDF = 0.5) where S_s is not useful; and (iii) the deviation at the tail end is not due to the nonlinearity of the performance function.
• Developed confidence interval or acceptance limit-based criteria that most definitely groups and simplifies the variables that are not important with specified confidence level.
• Developed and demonstrated five new sensitivity measures: (i) two of these (i.e., sample mean-mean and sample mean-sigma sensitivities) are particularly suitable for conducting analyses consistent with the United States high-level waste disposal regulatory criterion; (ii) another two are average sensitivity measures developed to facilitate comparison of the CDF sensitivity method with the results from other methods; and (iii) a mean-sigma-based sensitivity measure that combines the power of mean and sigma sensitivity measures proposed in the past.
• Combined the low-probability high-consequence scenarios with the most likely scenarios to obtain a single performance measure. The approach is based on the probabilistic sensitivity and failure cost ratio associated with each random variable and provides for visualization of not only the most influential variables, but also the scenarios that contribute most to this influence.
• Developed a methodology for efficient reliability analysis of problems with large numbers of random variables in which an "approximate response function" is constructed based on the important variables identified by the sampling-based screening procedure.
• Developed and demonstrated an approximate method to include the remaining (unimportant) variables identified by the sampling-based screening procedure (the remaining variables are grouped into a single term and added to the approximate response function for reliability computations).
• Investigated efficient reliability-based design optimization method for problems with large numbers of random variables and identified computational improvements for design problems in which the reliability constraints are inactive.
• Developed an integrated oil and gas production system model that combined reservoir depletion drive model, multiphase flow wellbore pressure losses, production economic model, and the CDF sensitivity method to identify parameters that define the economic viability of producing from a given reservoir.

(a)

(b)

Important variables identified by (a) and (b) sensitivity measures for an example problem with 246 random variables. The figure clearly differentiates between significant and insignificant variables with a 95% accuracy or acceptance level. (Note: LHS - Latin Hypercube Sampling)

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