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Limited descent-based mean value method for inverse reliability analysis

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Abstract

The robustness and efficiency of inverse reliability methods are important issues in reliability-based design optimization (RBDO) using performance measure approach (PMA). The adaptive modified chaos control (ACC), step length adjustment (SA), and relaxed mean value (RMV) methods were recently implemented to improve the robustness and efficiency of PMA. In this paper, a limited descent mean value (LDMV) method is proposed to improve robustness and efficiency of inverse reliability analysis for either convex or concave probabilistic constraints. The LDMV formula is dynamically adjusted by an adaptive step size based on the advanced mean value method (AMV). The robustness and efficiency of the ACC, SA, RMV, and proposed LDMV methods are compared through six nonlinear performance functions. The results illustrated a similar robust performance between LDMV against RMV and FSL methods and superior to the ACC method. The proposed LDMV improves the robustness and efficiency of the inverse first-order reliability method in comparison with existing reliability methods.

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Abbreviations

AMV:

Advanced mean value

ACC:

Adaptive modified chaos control

LDMV:

Limited descent mean value

RMV:

Relaxed mean value

CC:

Chaos control

SMCC:

Self-adaptive modified chaos control

SA:

Step length adjustment

SMV:

Self-adjusted mean value

MMV:

Modified mean value

CMV:

Conjugate mean value

\({{\varvec{d}}^{\text{L}}}\) :

Lower bound of the design vector

\({{\varvec{d}}^{\text{U}}}\) :

Lower bound of the design vector

SL:

Single-loop approach

DLA:

Double loop approach

HMV:

Hybrid mean value

HMV+ :

Enhanced hybrid mean value

\(f\) :

Objective or cost function

FORM:

First-order second-moment method

\({f_{\varvec{X}}}(x)\) :

Joint probability density function of the basic random variables \({\varvec{X}}\)

\(k\) :

Number of iterations

MCC:

Modified chaos control

MPFP:

Most probable failure point

\({\widetilde {{\varvec{U}}}^{{\text{DMV}}}}\) :

Descent search direction vector

\(p\) :

Number of performance functions

\({P_{\text{f}}}\) :

Acceptable failure probability

PMA:

Performance measure approach

RBDO:

Reliability-based design optimization

RIA:

Reliability index approach

\({\varvec{X}}\) :

Random variables in original space

\({\varvec{U}}\) :

Independent standard normal random variable

\({{\varvec{U}}^*}\) :

Most probable failure point

\(\beta\) :

Reliability index

\(\beta _{{\text{t}}}^{{\text{j}}}\) :

Target reliability index of the jth probabilistic constraint

\(\delta\) :

Adjusted parameter

\(\rho\) :

Limited step size

\(\Phi\) :

Standard normal cumulative distribution function

\({\varvec{\sigma}_{\varvec{x}}}\) :

Standard deviations

\(\varvec{\mu}_{{\varvec{x}}}^{{\text{L}}}\) :

Lower mean of the random design vector

\(\varvec{\mu}_{{\varvec{x}}}^{{\text{U}}}\) :

Upper mean of the random design vector

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Acknowledgements

The authors thank the financial support by the University of Zabol with grant number UOZ-GR-9517-3.

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Authors and Affiliations

  1. Sustainable Developments in Civil Engineering Research Group, Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Zaher Mundher Yaseen

  2. Department of Civil Engineering, University of Zabol, Zabol, P.O. Box 9861335-856, Iran

    Behrooz Keshtegar

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  1. Zaher Mundher Yaseen
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Correspondence to Behrooz Keshtegar.

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Yaseen, Z.M., Keshtegar, B. Limited descent-based mean value method for inverse reliability analysis. Engineering with Computers 35, 1237–1249 (2019). https://doi.org/10.1007/s00366-018-0661-z

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