HS5020: Stochastic Study of a Cantilever Ibeam
In this tutorial, you will complete a simple Stochastic study to investigate uncertain parameters of a cantilever Ibeam model defined with four variables and four functions.
Run a Stochastic Study
In this step, you will run a Stochastic study and review the evaluation scatter.
In this study, you will consider w_th, f_l and f_th as Random parameters (uncertain, not controllable by design) and h as Design with Random parameter (uncertain but controllable by design).

Add a Stochastic.

Modify input variables.
 Go to the step.
 In the work area, set the Mode to Simple Random.

In the Settings tab, change the Number of Runs to
500.
 Click Apply.
 Go to the step.

Click Evaluate Tasks.
The evaluations are randomly sampled in the space and the designs are evaluated.
 Click the Evaluation Scatter tab.

Review the scatter plots for Total Height and Web Thick.
The Evaluation scatter shown in Figure 4 presents the sampling for Total Height and Web Thick. Due to the Design with Random distribution role the sampling for Total Height is truncated to only samples which fall between the upper and lower bounds.
Review PostProcessing Results
In this step, you will review the evaluation results within the PostProcessing step.
 Go to the step.
 Click the Distribution tab.
 From the Channel Selector, click Histogram.

Review the histograms of the stochastic results.
Figure 5 shows the histograms of Total Height and Web Thick values distributions. Each blue bin represents the frequency of runs yielding a subrange of response values. Notice the Total Height histogram has no tails at the extremities because of the truncated sampling. The probability densities (red curves) indicate the relative likelihoods of the variables to take particular values. A higher value indicates that the values are more likely to occur. The cumulative distributions (green curves) indicate what percentage of the data falls below the value threshold.
 From the Channel Selector, click Box Plot.

Identify the eventual outliers.
Note: There are no outliers for Total Height because of the truncated sampling.
 Click the Reliability tab.

Add a reliability.
 Click Add Reliability.
 Set Response to ly (r_1).
 Set Bound Type to >=.
 For Bound Value, enter 75.596800.

Create another reliability by repeating step 8 with the following
changes:
 Set Response to lz (r_2).
 Set Bound Type to >=.
 For Bound Value, enter 14.404800.

Create another reliability by repeating step 8 with the following
changes:
 Set Response to Disp (r_4).
 Set Bound Type to <=.
 For Bound Value, enter 4.41e05.
 Click the Reliability Plot tab.

Review the graphs.
Figure 8 show the reliabilities for the values Web Thick and Total Height could take.