Calculating the Time-Variant System Reliability of Trusses Based on an Explicit Performance Function

Evaluating time-variant structural system reliability is vital for the life-cycle design and health monitoring of trusses. However, the numerous failure modes inherent in highly redundant trusses make calculating their system reliability extremely challenging. In this work, a constructed structural pseudostiffness matrix is employed to characterize the possible system failure of trusses induced by member failures. Its advantage lies in avoiding the search for failure modes and enabling the minimum eigenvalue of the matrix to serve as an explicit performance function for identifying truss failure. Considering the time-dependent nature of the structural parameters, a generalized density evolution equation for this minimum eigenvalue is established. To improve the efficiency of solving the equation, an analytical expression for the time derivative of the minimum eigenvalue is derived based on sensitivity analysis of the eigenvalues with respect to time-dependent structural parameters. Neumann expansion is also employed to efficiently approximate the inverse of the time-dependent tangent stiffness matrix. Additionally, a numerical strategy for calculating the time-variant system reliability of trusses is proposed, and three numerical examples are employed to validate the accuracy and efficiency of the proposed method by comparing the results with those of Monte Carlo simulation, the single-loop kriging surrogate model method, and the time-dependent adaptive support vector machine method.