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

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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.

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Abbreviations

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

d L :

Low bounds of design variables

d U :

Upper bounds of design variables

x :

Random design variables

μ x :

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

σ x :

Standard deviation variables

p :

Random variables

μ p :

Mean of random variables

σ p :

Standard deviations of random variables

P t :

Admissible failure probability

β t :

Target reliability index

P f :

Failure probability

f x , 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

∇ x g :

Sensitivities of performance function with respect to random design variables x

∇ p g :

Sensitivities of performance function with respect to random variables p

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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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Authors and Affiliations

  1. School of Civil Engineering, Hefei University of Technology, Hefei, 230009, People’s Republic of China

    Zeng Meng & Huanlin Zhou

  2. Department of Engineering Mechanics, State Key Laboratory of Structural Analyses for Industrial Equipment, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Dixiong Yang

  3. Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, Arlington, TX, 76019, USA

    Bo Ping Wang

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  1. Zeng Meng
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  2. Dixiong Yang
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Correspondence to Zeng Meng.

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Meng, Z., Yang, D., Zhou, H. et al. Convergence control of single loop approach for reliability-based design optimization. Struct Multidisc Optim 57, 1079–1091 (2018). https://doi.org/10.1007/s00158-017-1796-z

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  • DOI: https://doi.org/10.1007/s00158-017-1796-z

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