Learning Forum

[Torben T.]

I want to solve a reliability problem with 4 parameters using ARSM-DS. The limited state function is given by g(x)=f(x1, x2, x3) - f(x4). Solving f(x1, x2, x3) is very time consuming. 

I need to calculate the failure probability for different scenarios, only the input parameter x4 will differ. As the paremeters x1 to x3 are the same for every scenario, it would be usefull to only calculate f(x1, x2, x3) for the first scenario and reuse the solutions for f(x1,x2,x3) in the following scenarios.

Is it possible to keep the already sampled values for x1 to x3 (to reuse the solution of f(x1,x2,x3) and only sample new values for x4? 

[Veit Bayer]

Hi Torben,

so I understand correctly, that x1~x3 are the random variables, while x4 is varied systematically to control the scenario? 

Generally, all advanced reliability algorithms in optiSLang aim to explore the failure domain to do an efficient sampling and reduce the efforts compared to plain Monte Carlo. Since the failure domain will change with the scenario, it is not possible to "recycle" existing samples. 

My proposal would be, to first create a metamodel and then do the reliability analysis using the MOP Solver instead of the physical solver. But be aware, that even the best metamodel is an approximation. Hence you can proceed fast in the stage of developing the best design, but you need to do a final reliability analysis without approximations, dimension reductions etc. to proof the result.

To do so I recommend to use AMOP for creating the metamodel.

• Incorporate all x1~x4 in the model. Define all parameters as Optimization or Opt.+Stoch. type. Provide a sensible range for the random parameters, as mean plusminus n times sigma, where n is somewhat more than the expected sigma level. E.g., for an expected failure probability of 1E-6 ~ 4.75sigma, choose n=6.
• Edit the AMOP system after setup and open the advanced settings. Choose Local strategy, use the sliders to assign most budget to local CoP and some to sample density (to avoid whitespace), e.g. 80% and 20%. Be generous with the computational budget, you'll save efforts later.
• Edit the MOP tab in AMOP or append a MOP node after AMOP. Edit the MOP advanced settings, set both CoP tolerance values to 0.001, add more sophisticated models e.g. Anisotropic Kriging and DIM-GP
• You cannot drag the Robustness wizard onto a MOP node or AMOP system. But you can use the Solver wizard and choose MOP Solver there. 
• Then apply the Rob. wizard on the such created parametric system. Operating on the MOP, you can afford a more extensive algorithm like Adaptive Sampling.

Still, ARSM-DS is one of the most efficient yet accurate reliability algorithms. Maybe use this for the final proof.

Best regards,

Veit