Multi-level, multi-variate, non-stationary, random field modeling and fragility analysis of engineering systems

Engineering systems can often be represented considering models at multiple levels. Different properties within each level are typically inhomogeneous in space and cross-correlated, while properties of different levels are physically dependent on each other. In addition, system properties usually vary in time due to effects of external environmental conditions. Current analysis techniques cannot model the spatially inhomogeneous, infra-level correlated, inter-level dependent, and temporally varying system properties. This paper proposes a random field-based formulation for the modeling of engineering systems that overcome the limitation. To consider the inhomogeneous spatial variability and infra-level correlation, we propose a multi-variate non-stationary random field formulation. To consider the inter-level dependency, we propose a multi-level formulation that considers lower-level properties as regressors in the random field of higher-level properties. To consider the temporal variability, we use a state-dependent model that enables the updating of the multi-level random fields over time. As a special case, the paper shows that the proposed formulation can be used in system fragility analysis, considering capacities and demands, and fragilities as levels. The paper implements the proposed formulation in the modeling of a deteriorating transportation system considering six different levels. The first three levels are defined by state variables at different scales, while the last three levels are defined by bridge capacities and demands, bridge fragilities, and network fragilities. The results are significantly different from those obtained by using non-random field models.