Description
Different nondeterministic methods have differing support for uncertain variable distributions. Tables 5.37, 5.38, and 5.39 summarize the uncertain variables that are available for use by the different methods, where a "-" indicates that the distribution is not supported by the method, a "U" means the uncertain input variables of this type must be uncorrelated, a "C" denotes that correlations are supported involving uncertain input variables of this type, and an "A" means the appropriate variables must be specified as active in the variables specification block. For example, if one wants to support sampling or a stochastic expansion method over both continuous uncertain and continuous state variables, the specification active
all
must be listed in the variables specification block. Additional notes include:
- we have four variants for stochastic expansions (SE), listed as Wiener, Askey, Extended, and Piecewise which draw from different sets of basis polynomials. The term stochastic expansion indicates polynomial chaos and stochastic collocation collectively, although the Piecewise option is only currently supported for stochastic collocation. Refer to polynomial_chaos and stoch_collocation for additional information on these three options.
- methods supporting the epistemic interval distributions have differing approaches:
sampling
and the lhs
option of global_interval_est
model the interval basic probability assignments (BPAs) as continuous histogram bin distributions for purposes of generating samples; local_interval_est
and the ego
option of global_interval_est
ignore the BPA details and models these variables as simple bounded regions defined by the cell extremes; and local_evidence
and global_evidence
model the interval specifications as true BPAs.
Table 5.37
Summary of Distribution Types supported by Nondeterministic Methods, Part I (Continuous Aleatory Types)
Distribution Type | Sampling | Local Reliability | Global Reliability | Wiener SE | Askey SE | Extended SE | Piecewise SE | Local Interval | Global Interval | Local Evidence | Global Evidence |
Normal | C | C | C | C | C | C | - | - | - | - | - |
Bounded Normal | C | U | U | U | U | U | U | - | - | - | - |
Lognormal | C | C | C | C | C | U | - | - | - | - | - |
Bounded Lognormal | C | U | U | U | U | U | U | - | - | - | - |
Uniform | C | C | C | C | U | U | U | - | - | - | - |
Loguniform | C | U | U | U | U | U | U | - | - | - | - |
Triangular | C | U | U | U | U | U | U | - | - | - | - |
Exponential | C | C | C | C | U | U | - | - | - | - | - |
Beta | C | U | U | U | U | U | U | - | - | - | - |
Gamma | C | C | C | C | U | U | - | - | - | - | - |
Gumbel | C | C | C | C | C | U | - | - | - | - | - |
Frechet | C | C | C | C | C | U | - | - | - | - | - |
Weibull | C | C | C | C | C | U | - | - | - | - | - |
Continuous Histogram Bin | C | U | U | U | U | U | U | - | - | - | - |
Table 5.38
Summary of Distribution Types supported by Nondeterministic Methods, Part II (Discrete Aleatory Types)
Distribution Type | Sampling | Local Reliability | Global Reliability | Wiener SE | Askey SE | Extended SE | Piecewise SE | Local Interval | Global Interval | Local Evidence | Global Evidence |
Poisson | C | - | - | - | - | - | - | - | - | - | - |
Binomial | C | - | - | - | - | - | - | - | - | - | - |
Negative Binomial | C | - | - | - | - | - | - | - | - | - | - |
Geometric | C | - | - | - | - | - | - | - | - | - | - |
Hypergeometric | C | - | - | - | - | - | - | - | - | - | - |
Discrete Histogram Point | C | - | - | - | - | - | - | - | - | - | - |
Table 5.39
Summary of Distribution Types supported by Nondeterministic Methods, Part III (Epistemic, Design, and State Types)
Distribution Type | Sampling | Local Reliability | Global Reliability | Wiener SE | Askey SE | Extended SE | Piecewise SE | Local Interval | Global Interval | Local Evidence | Global Evidence |
Interval | U | - | U,A | U,A | U,A | U,A | U,A | U | U | U | U |
Continuous Design | U,A | - | U,A | U,A | U,A | U,A | U,A | - | - | - | - |
Discrete Design Range, Int Set, Real Set | U,A | - | - | - | - | - | - | - | - | - | - |
Continuous State | U,A | - | U,A | U,A | U,A | U,A | U,A | - | - | - | - |
Discrete State Range, Int Set, Real Set | U,A | - | - | - | - | - | - | - | - | - | - |
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