A Reliability Analysis Methodology for Mechanical Systems with Uncertain and Correlated Variables

The operation of mechanical systems frequently occurs under complex load and environmental conditions. Such systems typically involve multiple inherently interrelated uncertain parameters, rendering reliability assessment crucial for ensuring structural safety and functional stability. This study employs a multivariate joint L-moment transformation to analyses nonlinear systems featuring correlated non-normal variables. Firstly, a joint polynomial mapping is constructed based on L-moments and correlation coefficients, thereby preserving consistency between marginal distributions and correlation structures while enabling transformation from physical space to standard normal space. This approach is applied to both a nonlinear benchmark case and an engineering example concerning the yield reliability of high-pressure gas storage tanks. Compared to conventional reliability analysis techniques, results demonstrate that this framework significantly reduces computational effort while maintaining high accuracy and stability. This research also provides an alternative reliability analysis framework for complex engineering systems under conditions of uncertainty.