Ramon C. Kuczera, Z. P. Mourelatos, E. Nikolaidis

[Steve Yenisch]

Paper: www.mae.ufl.edu/nkim/ISSMO/MourelatosPaper.pdf
Presentation: www.mae.ufl.edu/nkim/ISSMO/MourelatosPresentation.ppt

A Simulation-Based RBDO Method Using Probabilistic Re-Analysis and a Trust-Region Approach
Ramon C. Kuczera
Mechanical Engineering Department
Oakland University, Rochester, MI 48309
Email : [e-mail]

Zissimos P. Mourelatos
Mechanical Engineering Department
Oakland University, Rochester, MI 48309
Phone: [phone]
Fax: [phone]
Email: [e-mail]

Efstratios Nikolaidis
Mechanical, Industrial and Manufacturing Engineering Department
The University of Toledo, Toledo, OH 43606
Email: [e-mail]

ABSTRACT
A simulation-based, system reliability-based design optimization (RBDO) method is presented which can handle problems with multiple failure regions. The method uses a Probabilistic Re-Analysis (PRRA) approach in conjunction with a trust-region optimization approach. PRRA calculates very efficiently the system reliability of a design by performing a single Monte Carlo (MC) simulation. Although PRRA is based on MC simulation, it calculates “smooth” sensitivity derivatives, allowing therefore, the use of a gradient-based optimizer. The PRRA method is based on importance sampling. It provides accurate results, if the support (set of all values for which a function is non zero) of the sampling PDF contains the support of the joint PDF of the input random variables and, if the mass of the input joint PDF is not concentrated in a region where the sampling PDF is almost zero. A sequential, trust-region optimization approach satisfies these two requirements. The potential of the proposed method is demonstrated using the design of a vibration absorber, and the system RBDO of an internal combustion engine.

[haftka]

I must protest again against the notion that deterministic design leads to high probability of failure. I guess you do not fly airplanes because they are designed by deterministic optimization!

If anything, probabilistic optimization is more dangerous, since the statistical data for calculating probabilities is often bogus. See the space shuttle, for example.

[FNWEI1S]

May 19, 2009 8:34:26 GMT -5 haftka said:

I must protest again against the notion that deterministic design leads to high probability of failure. I guess you do not fly airplanes because they are designed by deterministic optimization!

If anything, probabilistic optimization is more dangerous, since the statistical data for calculating probabilities is often bogus. See the space shuttle, for example.

Rafi, you are right. The paper gives the impression that a deterministc designer pushes the design to the limit of the feasible domain. The authors of the paper forgot that there are safety factors and design allowables. It will not happen again (in a paper in which I am a coauthor).

[Stratos]

May 19, 2009 8:34:26 GMT -5 haftka said:

I must protest again against the notion that deterministic design leads to high probability of failure. I guess you do not fly airplanes because they are designed by deterministic optimization!

If anything, probabilistic optimization is more dangerous, since the statistical data for calculating probabilities is often bogus. See the space shuttle, for example.

Rafi,
Although I agree that deterministic design does not generally lead to higher failure probability, I disagree that probabilistic designs are more dangerous. Deterministic approaches have a disadvantage in design of series systems. Deterministic tools (safety factors and allowables) cannot alert a designer that a system with many components in series is more dangerous than a design with one component.

The prob em with space shuttle is not because designers used probabilistic tools, but rather that they did not account for epistemic uncertainty.

[haftka]

I certainly do not want to imply that there is something wrong with probabilistic tools. Just that we have much less experience in getting the data needed to get good results from them.

[Mourelatos]

May 19, 2009 8:34:26 GMT -5 haftka said:

I must protest again against the notion that deterministic design leads to high probability of failure. I guess you do not fly airplanes because they are designed by deterministic optimization!

If anything, probabilistic optimization is more dangerous, since the statistical data for calculating probabilities is often bogus. See the space shuttle, for example.

We are sorry for the confusion. We did not claim that "airplanes" or any other structures are designed by deterministic optimization and simultaneously account for uncertainty. Yes, you are right that even probabilistic design may be "dangerous" if we use a "wrong" uncertainty quantification. As we know, people have been using safety factors to account for uncertainty in design. In doing so, a less "optimum" than the deterministic design is obtained with the premise that it considers uncertainty which in general, may not be quantified accurately. How though we determine the "right" safety factors? To account for uncertainty, we may overdesign. This paper, simply presents a simulation-based RBDO method. RBDO is simply another tool to design "safer" structures without "overdesigning." I hope I answered the question.

[haftka]

Indeed. Probabilistic optimizatin holds the promise of more efficient design, and this is the way it should be presented.

Rafi