Reliability Methods for Bimodal Distribution with First-Order Approximation1
In traditional reliability problems, the distribution of a basic random variable is usually unimodal; in other words, the probability density of the basic random variable has only one peak. In real applications, some basic random variables may follow bimodal distributions with two peaks in their probability density. When binomial variables are involved, traditional reliability methods, such as the first-order second moment (FOSM) method and the first-order reliability method (FORM), will not be accurate. This study investigates the accuracy of using the saddlepoint approximation (SPA) for bimodal variables and then employs SPA-based reliability methods with first-order approximation to predict the reliability. A limit-state function is at first approximated with the first-order Taylor expansion so that it becomes a linear combination of the basic random variables, some of which are bimodally distributed. The SPA is then applied to estimate the reliability. Examples show that the SPA-based reliability methods are more accurate than FOSM and FORM.
Z. Hu and X. Du, "Reliability Methods for Bimodal Distribution with First-Order Approximation1," ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, vol. 5, no. 1, American Society of Mechanical Engineers (ASME), Mar 2019.
The definitive version is available at https://doi.org/10.1115/1.4040000
Mechanical and Aerospace Engineering
Keywords and Phrases
Probability density function; Probability distributions; Random variables; Structural analysis, Bimodal distribution; First order reliability methods; First order second moment method; First-order approximations; Limit state functions; Probability densities; Reliability problems; Saddle-point approximation, Reliability
International Standard Serial Number (ISSN)
Article - Journal
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