Non-probabilistic convex model process: A new method of time-variant uncertainty analysis and its application to structural dynamic reliability problems

In this paper, we propose a method for time-variant uncertainty analysis, namely, the “non-probabilistic convex model process”, which provides an effective mathematical tool for the analysis of structural dynamic uncertainty when lacking relevant information. In the convex model process, we express the variables at any time with intervals and establish the corresponding auto-covariance function and correlation coefficient function to depict the correlation between variables at different times. We also define several important characteristic parameters for the uni- and bi-dimensional convex model processes, including the mid-value function, variance function, auto-covariance function, and cross-covariance function; we provide the definition for the stationary convex model process and its ergodicity. Then, by combining the convex model process with the first-passage failure mechanism, we propose a non-probabilistic analysis model of structural dynamic reliability and formulate the solving algorithm based on Monte Carlo simulation. Finally, through the analysis of numerical examples, we verify the effectiveness of the convex model process and the model of dynamic reliability analysis proposed in this paper.