Reliability sensitivity-based correlation coefficient calculation in structural reliability analysis
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- Yang, Z., Zhang, Y., Zhang, X. et al. Chin. J. Mech. Eng. (2012) 25: 608. doi:10.3901/CJME.2012.03.608
The correlation coefficients of random variables of mechanical structures are generally chosen with experience or even ignored, which cannot actually reflect the effects of parameter uncertainties on reliability. To discuss the selection problem of the correlation coefficients from the reliability-based sensitivity point of view, the theory principle of the problem is established based on the results of the reliability sensitivity, and the criterion of correlation among random variables is shown. The values of the correlation coefficients are obtained according to the proposed principle and the reliability sensitivity problem is discussed. Numerical studies have shown the following results: (1) If the sensitivity value of correlation coefficient ρ is less than (at what magnitude 0.000 01), then the correlation could be ignored, which could simplify the procedure without introducing additional error. (2) However, as the difference between ρs, that is the most sensitive to the reliability, and ρR, that is with the smallest reliability, is less than 0.001, ρs is suggested to model the dependency of random variables. This could ensure the robust quality of system without the loss of safety requirement. (3) In the case of |Eabs|>0.001 and also |Erel|>0.001, ρR should be employed to quantify the correlation among random variables in order to ensure the accuracy of reliability analysis. Application of the proposed approach could provide a practical routine for mechanical design and manufactory to study the reliability and reliability-based sensitivity of basic design variables in mechanical reliability analysis and design.