Reliability bounds through random sets: Non-parametric methods and geotechnical applications

Random sets form a well-established, general tool for modelling epistemic uncertainty in engineering. They can be seen as encompassing probability theory, fuzzy sets and interval analysis. Random set models for data uncertainty are typically used to obtain robust upper and lower bounds for the reliability of structures in engineering models. The goal of this paper is to show how random set models can be constructed from measurement data by non-parametric methods using inequalities of Tchebycheff type. Relations with sensitivity analysis will also be high-lighted. We demonstrate the application of the methods in an FE-model for the excavation of a cantilever sheet pile wall.