Belief reliability modeling and analysis of electrical connectors with hyperboloid contact structure considering multi-source aleatory and epistemic uncertainty

Electrical connectors with hyperboloid grid structures (HGEC) are widely used in high-current and miniaturized applications, yet their reliability remains difficult to assess due to the complex coupling among mechanical, electrical and thermal (MET) behaviors, and the many aleatory and epistemic uncertainties affecting design, manufacturing and operation. This paper develops a comprehensive belief reliability modeling framework for HGEC that integrates multidisciplinary physical principles, experiment-based degradation characterization and chance theory. Mathematical equations are established to quantify the physical influence of material properties, structural parameters and external stresses on MET performance. A series of experiments are then conducted to identify the non-monotonic force degradation and resistance growth, based on which Wiener process and Liu process degradation models are formulated. Multi-source uncertainties — including material inconsistency, manufacturing tolerance, stress fluctuation, threshold ambiguity and time-dependent degradation — are jointly represented as uncertain random variables within chance theory. Finally, a Monte-Carlo-based algorithm for belief reliability evaluation is developed to evaluate the reliability over the lifespan. The results reveal distinct degradation stages and dominant failure mechanisms, and the sensitivity analysis identifies the most influential factors for initial, early and long-term reliability. The proposed approach provides a systematic and quantitative solution for reliability evaluation of HGEC under uncertain environments.