Page 116 - Using ANSYS for Finite Element Analysis Dynamic, Probabilistic, Design and Heat Transfer Analysis

probabilistic Design analysis • 103
• Gradient information is local information only. It does not take
into account that the output parameter may react more or less with
respect to variation of input parameters at other locations in the
input parameter space. However, the probabilistic approach not
only takes the slope at a particular location into account, but also all
the values the random output parameter can have within the space
of the RVs.
• Deterministic sensitivities are typically evaluated using a finite-dif-
ferencing scheme (varying one parameter at a time while keeping
all others fixed). This neglects the effect of interactions between
input parameters. An interaction between input parameters exists if
the variation of a certain parameter has a greater or lesser effect if
at the same time one or more other input parameters change their
values as well. In some cases interactions play an important or even
dominant role. This is the case if an input parameter is not sig-
nificant on its own but only in connection with at least one other
input parameter. Generally, interactions play an important role in
10 percent to 15 percent of typical engineering analysis cases (this
figure is problem dependent). If interactions are important, then a
deterministic sensitivity analysis can give you completely incorrect
results. However, in a probabilistic approach, the results are always
based on Monte Carlo simulations, either directly performed using
your analysis model or using response surface equations. Inher-
ently, Monte Carlo simulations always vary all RVs at the same
time; thus if interactions exist then they will always be correctly
reflected in the probabilistic sensitivities.

To display sensitivities, the PDS first groups the RVs into two groups:
those having a significant influence on a particular random output param-
eter and those that are rather insignificant, based on a statistical signif-
icance test. This tests the hypothesis that the sensitivity of a particular
random input variable is identical to zero and then calculates the proba-
bility that this hypothesis is true. If the probability exceeds a certain sig-
nificance level (determining that the hypothesis is likely to be true), then
the sensitivity of that random input variable is negligible. The PDS will
plot only the sensitivities of the RVs that are found to be significant. How-
ever, insignificant sensitivities are printed in the output window. You can
also review the significance probabilities used by the hypothesis test to
decide which group a particular random input variable belonged to the
PDS allows you to visualize sensitivities either as a bar chart, a pie chart,
or both. Sensitivities are ranked so the random input variable having the
highest sensitivity appears first.