Generating function approach to reliability analysis of structural systems

The generating function approach is an important tool for performance assessment in multi-state systems. Aiming at strength reliability analysis of structural systems, generating function approach is introduced and developed. Static reliability models of statically determinate, indeterminate systems and fatigue reliability models are built by constructing special generating functions, which are used to describe probability distributions of strength (resistance), stress (load) and fatigue life, by defining composite operators of generating functions and performance structure functions thereof. When composition operators are executed, computational costs can be reduced by a big margin by means of collecting like terms. The results of theoretical analysis and numerical simulation show that the generating function approach can be widely used for probability modeling of large complex systems with hierarchical structures due to the unified form, compact expression, computer program realizability and high universality. Because the new method considers twin loads giving rise to component failure dependency, it can provide a theoretical reference and act as a powerful tool for static, dynamic reliability analysis in civil engineering structures and mechanical equipment systems with multi-mode damage coupling.