N. Kogiso, Young S. Yang, Bong-Jae Kim, Jae-Ohk Le

[Steve Yenisch]

Paper: www.aero.osakafu-u.ac.jp/as/lab3/rbdo_net_conf_2009/MSLSV.pdf
Presentation: www.aero.osakafu-u.ac.jp/as/lab3/rbdo_net_conf_2009/presen.pdf

Modified Single-Loop-Single-Vector Method for Stability and Efficiency Improvement in Reliability-Based Design Optimization
Nozomu Kogiso^a, Young-Soon Yang^b, Bong-Jae Kim^b, and Jae-Ohk Lee^c,

(a) Department of Aerospace Engineering, Graduate School of Engineering,
Osaka Prefecture University, Sakai, Osaka 599-8531 Japan
(b) Department of Naval Architecture and Ocean Engineering, College of Engineering,
Seoul National University, Seoul, 151-742 Republic of Korea
(c) Structure Research Department, Hyundai Maritime Research Institute,
Hyundai Heavy Industry, Ulsan, 682-792 Republic of Korea

ABSTRACT
Single-Loop-Single-Vector (SLSV) method is to resolve the excessive computational cost problem in reliabilitybased design optimization (RBDO) by decoupling the nested iteration loops. The key idea of the method is that the reliability constraint is replaced to the deterministic constraint by approximating the most probable point (MPP) obtained from the previous iteration. However, the practical use of SLSV method is limited by the instability or inaccuracy of the method since it often diverges or converges to a wrong solution. Thus, in this paper, a new modified-SLSV method is proposed to improve its convergence capability effectively by utilizing Inactive Design and Active MPP Design together with modified-HMV (Hybrid Mean Value) method. The usefulness of the proposed method is verified through some numerical examples.
Keywords: RBDO, Modified SLSV Method, Modified HMV Method, Inactive Design, Active MPP Design

[haftka]

I have two minor questions that will help me understand the logic of the different methodologies.

First, what the "single" in the single-vector terminology. From the description of the method, it would appear that it should be called "previous vector" rather than "single vector?"

Second, why are the design variables limited to the means of the design variables? We can have deterministic design variables, and we can also have design variables that control the standard deviation (like manufacturing tolerances).

[Kogiso]

Thank you for watching our paper.

Reply for First Question:
From my understanding, "single vector" indicates that the design variable vector considered for the iteration loop is limited to only the design vector (in this case, the mean value) and the random variables are not included in the iteration loop.
I think that the "previous vector" is preferred to indicate the design variable updated equation.

Reply for Second Question:
We have not considered the case that the standard deviations are treated as design variables.
I would like to consider the case as a future problem.

Thank you for your comments.

[Ikjin Lee]

I have couple of questions regarding your presentation.

1. In page 13 of your presentation material, you mentioned 'inactive design'. Usually, we say 'inactive constraint' not 'inactive design'. What is exact definition of 'inactive design'?

2. In page 17, standard deviations are 0.3 and 0.6, respectively. However, in page 18, they are 0.03 and 0.06. Which one is correct?

3. In examples, you compared your proposed method and PMA in terms of efficiency and accuracy. For the efficiency comparison, you use NFE. I want to know how you count the NFE because the NFE number seems to be somewhat large for PMA. For the accuracy comparison, you use error (%). What is the definition of the error?

Thank you.

[Kogiso]

Thank you for your questions.

1. "Inactive Design" is defined as the design that the deterministic optimum design with "active" constraints will correspond to MPP for the target reliability index.
If the deterministic design has multiple active constraints, the Inactive Design is obtained as a kind of average of the constraints.

I think that "inactive constraint" is generally used as the design that satisfies inequality constraints with large slacks.

2. p. 17 is correct. sigma-s are 0.3 and 0.6.
I am sorry for my wrong description in p. 18.

3. NFE is the number of performance function evaluations.
We evaluated NFE in our developed code for each approach.
For PMA, the number of NFE is affected by the stopping criteria
of the inner loop.
So, our criteria might be stronger than your expectation.
However, we believe that the difference of NFE is not so large.

[Definition of %Error]
I am sorry that the definition of %Error is not included.
That is the difference between the target reliability index and the true reliability index of the obtained optimum design evaluated by FORM divided by the target reliability index.


Thank you very much for watching our paper.