Reliability Analysis of a Damped Oscillator

This tutorial allows you to complete a reliability analysis of a single degree-of-freedom system excited with initial kinetic energy.

This tutorial uses the robust optimum found in the iterative robust design optimization procedure in the previous tutorial.

The reliability criterion for omega_damped will be evaluated.

Mass m, damping ratio D, stiffness k and initial kinetic energy E_kin are taken as normally distributed random variables.

Task Description

This tutorial demonstrates how to do the following:

Incorporate the results of the robust design optimization
Define the limit state for damped eigen frequency
Compute the probability of failure (the probability of exceeding the limit) by Adaptive Response Surface Method and Importance Sampling

You must complete the Robustness Evaluation of a Damped Oscillator tutorial before starting this one.

The best design of the iterative robust design optimization is used as the reference for the reliability analysis.

To set up and run the tutorial, perform the following steps:

Start optiSLang.
From the Start screen, click Open.
Browse to the location of the damped oscillator optimization project you used in the previous tutorial and click Open.

Drag the Robustness wizard onto the AMOP_Step2 system and let it drop.
At the bottom of the Parametrize Inputs table, click Import parameter.
From the Select system pane, select Robustness_Step2.
To highlight all of the parameters in the table, do one of the following:
- Click the name of the first parameter, press Shift, and then click the name of the parameter the last row.
- Click the name of the first parameter, then with the mouse key pressed, pull down to the last parameter and release the mouse key.
Click OK.
The selected parameters are imported.
Click Next.
To delete the existing criteria, select all the values in the Criteria list then right-click the selection and select Remove selected criteria from the context menu.
At the prompt, click Yes.
Drag omega_damped to the Limit State Less icon.
Change the omega_damped Limit field to 8.5.
Click Next.
From the Uncertainty knowledge list, select Qualified.
The Adaptive Response Surface Method (ARSM-DS) is automatically selected.
Move the Desired sigma level slider to 4.5σ
Click Next.
Do not adjust the additional options settings.
Click Finish.
The ARSM-DS system is added to the Scenery pane.

To save the project, click .
To run the project, click .
The results of the ARSM-DS reliability evaluation are displayed. You can observe:
- Failure probability is about 10^-6
- Corresponding reliability index is about 4.7 which fulfills the robustness requirements
- In the m-k-anthill plot, a clearly separated unsafe domain can be observed

Drag the Robustness wizard onto the ARSM-DS system and let it drop.
Do not adjust or add to the currently displayed values for parameters, responses, and criteria.
Click Next.
From the Uncertainty knowledge list, select Qualified.
Move the Desired sigma level slider to 4.5σ
Select Importance Sampling using Design Point (ISPUD).
Click Next.
Do not adjust the additional options settings.
Click Finish.
The ISPUD system is added to the Scenery pane.

To save the project, click .
To run the project, click .
The results of the ISPUD reliability evaluation are displayed. You can observe:
- The design point search converges within five iterations
- Failure probability is about 10^-6
- Corresponding reliability index is about 4.7 which fulfills the robustness requirements
- The ARSM-DS results are verified
Open the Reliability Importance plot.
You can observe:
- Parameter k and m are most important with respect to the failure probability
- Ekin and D have neglectable influence