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Structural and Multidisciplinary Optimization

, Volume 57, Issue 3, pp 1079–1091 | Cite as

Convergence control of single loop approach for reliability-based design optimization

  • Zeng Meng
  • Dixiong Yang
  • Huanlin Zhou
  • Bo Ping Wang
RESEARCH PAPER

Abstract

For solution of reliability-based design optimization (RBDO) problems, single loop approach (SLA) shows high efficiency. Thus SLA is extensively used in RBDO. However, the iteration solution procedure by SLA is often oscillatory and non-convergent for RBDO with nonlinear performance function. This prevents the application of SLA to engineering design problems. In this paper, the chaotic single loop approach (CLSA) is proposed to achieve the convergence control of original iterative algorithm in SLA. The modification involves automated selection of the chaos control factor by solving a novel one-dimensional optimization model. Additionally, a new oscillation-checking method is constructed to detect the oscillation of iterative process of design variables. The computational capability of CLSA is demonstrated through five benchmark examples and one stiffened shell application. The comparison of numerical results indicates that CSLA is more efficient than the double loop approach and the decoupled approach. CSLA also solves the RBDO problems with highly nonlinear performance function and non-normal random variables stably.

Keywords

Reliability-based design optimization Iterative computation Convergence control Chaotic single loop approach Oscillation-checking method 

Nomenclature

RBDO

Reliability-based design optimization

FORM

First order reliability method

RIA

Reliability index approach

PMA

Performance measure approach

AMV

Advanced mean value

HMV

Hybrid mean value method

CGA

Conjugate gradient analysis

CC

Chaos control

MCC

Modified chaos control method

SORA

Sequential optimization and reliability assessment

SLSV

Single loop single vector

SLA

Single loop approach

RDS

Reliable design space

CSLA

Chaotic single loop approach

U-space

Standard normal space

MPTP

Most probable target point

C

Objective function

g

Performance function

d

Design variables

dL

Low bounds of design variables

dU

Upper bounds of design variables

x

Random design variables

μx

Mean of random design variables

\( {\boldsymbol{\upmu}}_{\mathbf{x}}^L \)

Low bounds of random variables

\( {\boldsymbol{\upmu}}_{\mathbf{x}}^U \)

Upper bounds of random variables

σx

Standard deviation variables

p

Random variables

μp

Mean of random variables

σp

Standard deviations of random variables

Pt

Admissible failure probability

βt

Target reliability index

Pf

Failure probability

fx , p(x, p)

joint probability density function

u

Normalized random variable

λ

Chaos control factor

C

Involutory matrix

f

Response function vector

k

Iterative step number

g

Performance function

G

Performance function in U-space

xg

Sensitivities of performance function with respect to random design variables x

pg

Sensitivities of performance function with respect to random variables p

Notes

Acknowledgements

The supports of the National Natural Science Foundation of China (Grant Nos. 11602076 and 51605127), the Natural Science Foundation of Anhui Province (No. 1708085QA06) and the Fundamental Research Funds for the Central Universities of China (No JZ2016HGBZ0751) are much appreciated. The authors also thank Dr. Yuxue Pu for his comments and discussion.

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of Civil EngineeringHefei University of TechnologyHefeiPeople’s Republic of China
  2. 2.Department of Engineering Mechanics, State Key Laboratory of Structural Analyses for Industrial EquipmentDalian University of TechnologyDalianPeople’s Republic of China
  3. 3.Department of Mechanical and Aerospace EngineeringUniversity of Texas at ArlingtonArlingtonUSA

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