Bivariate safety assessment for welded AA5083 aluminium alloys by the Gaidai multivariate reliability method and the Belyaev formulation

This study integrates experimental welding data with benchmarking of the novel reliability assessment methodology for nonlinear nonstationary dynamic systems and nonlinear materials, subjected to stochastic non-stationary environmental loadings. The proposed design approach employs multivariate structural reliability approach, based on Vickers Hardness (HV) measurements. This case study advocates novel material-based multivariate design concept, that bridges welding optimization with advanced probabilistic design for a wide range of engineering applications. Figure a) Failure probability P F h H V extrapolated to selected level P F = 10 - 0.8 , (star). Two dotted lines represent the estimated 95% Confidence intervals (CI). b) Bivariate 4-parameter Weibull copula fit. • A new reliability-informed framework establishes the first direct linkage between experimental weld material properties and structural failure probabilities. • Probabilistic modeling of correlated hardness and load capacity enables realistic safety margin predictions even from limited experimental datasets. • Optimized rotational speeds and dwell times achieve maximum load capacities exceeding seven kilonewtons and hardness values near two hundred Vickers. • Bivariate statistical extrapolation demonstrates that integrating weld performance with reliability analysis significantly improves structural design safety. This study addresses the need for reliability-informed assessment of welded joints by linking experimentally measured weld properties to structural failure risk. Friction spot welding experiments were conducted on AA5083 aluminium alloy under varying rotational speeds and dwell times to obtain hardness and load capacity datasets. These properties were treated as correlated stochastic variables within a multivariate probabilistic reliability framework. Optimal welding conditions near 900 rpm and 1–5 s dwell time produced maximum loads exceeding 7 kN and hardness values approaching 200 HV. The coupled variability of these parameters was used to construct a bivariate failure surface and extrapolate survival probabilities using advanced statistical modelling. Results demonstrate that integrating weld material performance with probabilistic reliability analysis enables realistic prediction of safety margins, even with limited datasets. The proposed framework establishes a direct linkage between welding parameter optimization and structural design reliability, offering a practical tool for safety–critical marine and engineering applications.