This tutorial demonstrates how to perform a reliability-based optimization on a finite element model defined for RADIOSS.
Before running this tutorial, you must complete tutorial HS-4220: Size Optimization Study on an Impact Simulation using RADIOSS or you can import the archive file HS-4220.hstx, available in <hst.zip>/HS-4405/.
In the initial optimization problem, as stated in tutorial HS-4220, the objective is to minimize the mass of the beam under the following two constraints: the internal energy must be more than 450, and the resulting reaction force must be less than 75. The input variables are the thicknesses of the four components defined in the input deck boxbeam1_0000.rad via the /PROP/SHELL entries. They are combined into two input variables. The thickness should be between 0.5 and 2.0; the initial thickness is 1.0.
The reliability is added in this study through the definition of uncertainties on the input variables and probability targets for the constraints.
The thicknesses follow a normal distribution, with mean 1.0 and coefficient of variation 0.10.
The constraints are expressed as follows:
Prob(internal energy > 450) > 0.98
Prob(reaction force < 75) > 0.98
This means: Taking into account possible variations created by the random parameters; we want the 98th percentile of the reaction force distribution to be less than 75.
The ARSM-SORA optimization engine is used in this tutorial. SORA (Sequential Optimization and Reliability Assessment) is an algorithm that makes it possible to manage random variables and set reliability targets on constraints. ARSM-SORA takes advantage of the response surface based approach to reduce the computational effort needed in such problems
| 2. | Perform all steps in tutorial HS-4220. |
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| 1. | In the Explorer, right-click on Optimization 1 and select Copy Approach from the context menu. |
| 2. | In the Copy - HyperStudy dialog, click OK. A copy of Optimization 1 opens in the Explorer. |
| 3. | Go to the Select Input Variables step. |
| 4. | Review and edit the probabilistic properties by right-clicking in the Select Input Variables table and selecting Columns > Show All from the context menu. All of the columns available appear in the work area. |
| 5. | In the Distribution Role column of both input variables, select Design with Random. |
| 6. | Go to the Select Output Responses step. |
| a. | Click the Constraints tab. |
| b. | Define both constraints. |
| • | For CDF Limit, enter 98.00. |
| 9. | Go to the Specifications step. |
| 10. | In the work area, set the Mode to ARSM based SORA (SORA_ARSM). |
| Note: | Only the methods that are valid for the problem formulation are enabled. |
| 12. | Go to the Evaluate step. |
| 13. | Click Evaluate Tasks to launch the Optimization. |
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When using the SORA or ARSM-SORA engines, additional information is displayed for each of the Random type constraints. These are the percentile values (labeled _PV) and they are related to the CDF Limits.
For a constraint of the form Prob(g > b) > R , the constraint is satisfied in the probabilistic way if the Rth-Percentile value of g is greater than b. R stands for the target probability, and b stands for the bound value.
For a constraint of the form Prob(g < b) > R, the constraint is satisfied in the probabilistic way if the Rth-Percentile value of g is smaller than b.
When using SORA or ARSM-SORA, the history table displays, as the first iteration, the result of the deterministic optimization (i.e. without taking the random parameters into account). The following iterations are successive iterations made to satisfy the probabilistic constraints.
| 1. | Click the Iteration History tab to review the SORA_ARSM history. Iteration 1 is the outcome of the deterministic optimization. Iterations 2 to 6 summarize the probabilistic steps. The two constraints match the probabilistic target: constraint_2_PV = 75.08. This indicates that the 98th percentile value of constraint 2 (reaction force) satisfies the 75.0 upper bound you defined. |
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See Also:
HyperStudy Tutorials
