Page 112 - Using ANSYS for Finite Element Analysis Dynamic, Probabilistic, Design and Heat Transfer Analysis

probabilistic Design analysis • 99
3.5.1 STATiSTiCAL PoSTPRoCeSSing

Statistical postprocessing allows you several options for reviewing your
results.

3.5.1.1 Sample history

The most fundamental form of postprocessing is directly reviewing the
simulation loop results as a function for the number of simulation loops.
Here, you can review the simulation values, the mean, minimum, or max-
imum values, or the standard deviations.
It is most helpful to review the mean values and standard deviation
history for Monte Carlo Simulation results if you want to decide if the
number of simulation loops was sufficient. If the number of simulation
loops was sufficient, the mean values and standard deviations for all RPs
should have converged. Convergence is achieved if the curve shown in the
respective plots approaches a plateau. If the curve shown in the diagram
still has a significant and visible trend with increasing number of simula-
tion loops then you should perform more simulation loops. In addition, the
confidence bounds plotted for the requested history curves can be inter-
preted as the accuracy of the requested curve. With more simulation loops,
the width of the confidence bounds is reduced.

3.5.1.2 histogram

A histogram plot is most commonly used to visualize the scatter of a prob-
abilistic design variable. A histogram is derived by dividing the range
between the minimum value and the maximum value into intervals of
equal size. Then the PDS determines how many samples fall within each
interval, that is, how many “hits” landed in the intervals.
Most likely, you will use histograms to visualize the scatter of your RPs.
The ANSYS PDS also allows you to plot histograms of your RVs so you
can double check that the sampling process generated the samples according
to the distribution function you specified. For RVs, the PDS not only plots
the histogram bars, but also a curve for values derived from the distribution
function you specified. Visualizing histograms of the RVs is another way to
make sure that enough simulation loops have been performed. If the number
of simulation loops is sufficient, the histogram bars will:

• Be close to the curve that is derived from the distribution function.
• Be “smooth” (without large “steps”).
• Not have major gaps.