Analysis and computation with hybrid random set stochastic models

• Uncertainty analysis of engineering structures with intervals and probability.
• Combining stochastic processes and imprecise probability.
• Monte Carlo simulations with imprecise probability models.
• Sensitivity analysis at no additional computational cost.

Engineering structures are usually modelled as input–output maps: the response is a function of input parameters and driving forces, both being nondeterministic and uncertain. The paper addresses and advertises recent methods combining stochastic processes and imprecise probability, namely random fields for the description of loads and random sets for the description of uncertain input parameters. This approach covers interval analysis, fuzzy sets, Dempster–Shafer structures and random variables and their hybrid combination with stochastic processes. The methods are demonstrated using an example from geotechnics, including an application to sensitivity analysis.