Abstract
Reliability-based design optimization under fuzzy and interval variables is important in engineering practice. The interval Monte Carlo simulation (IMCS), extremum method, and saddlepoint approximation (SPA) can be used for reliability optimization issues contain only interval variables. Thus, how to deal with the fuzzy variables is critical for system reliability analysis and optimization design. The α-level cut method can be applied to deal with fuzzy variables but it is complex and computationally expensive. Therefore, an equivalent conversion method based on entropy theory is proposed in this paper, which can convert the fuzzy variables to the normal random variables to avoid the complex integral process. According to the equivalent conversion method, the entropybased sequential optimization and reliability assessment (E-SORA) is developed in combination with the worst case analysis (WCA) for reliability-based design optimization under fuzzy and interval variables. A numerical example about the reliability design of the crank-link mechanism under fuzzy and interval variables is solved by the E-SORA, double-loops method, and α-level cut algorithm, respectively, is used to demonstrate the accuracy and efficiency, and the results show that the proposed method is feasible for reliability-based design optimization under fuzzy and interval variables
Highlights
Reliability-based design optimization is a probabilistic design method which has been successfully applied into engineering fields
The fuzzy entropy of a fuzzy variable is defined, and the fuzzy variables can be equivalently converted to normal random variables
The reliability-based design optimization under the mixture of fuzzy variables and interval variables can be changed to a model with normal random variables and interval variables
Summary
Reliability-based design optimization is a probabilistic design method which has been successfully applied into engineering fields. Awruch et al [1] applied fuzzy α - level cut method for optimization analysis under uncertainties He et al [11] introduced the fuzzy set theory, changing failure probability function and dynamic fuzzy subset into Bayesian Networks method for the reliability analysis of multi-state system reliability analysis with fuzzy and dynamic information. These models are very complex and computation expensive. Different types of uncertainty variables are existing in engineering, and there are many solutions for reliability-based design optimization, the reliability analysis or optimization design methods under fuzzy and interval variables, are complex and computationally expensive.
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