Uncertainty representation and quantification for a nonlinear rotor/stator system with mixed uncertainties

A rotor-to-stator coupled system usually exhibits complicated dynamic behaviors due to its nonlinear nature. Moreover, the inherent uncertainty (aleatory uncertainty) and many undetermined factors either brought by manufacturing process or due to the lack of knowledge (epistemic uncertainty) make the analysis of system response a challenging task. Existing studies on rotor uncertainties are mostly focused on the stochastic variables, yet pay less attention to other forms of uncertain variables such as intervals. However, some physical parameters (e.g. friction coefficient) can be hardly assigned one specific probability distribution and often available in interval forms. To deal with this, the concept of likelihood is extended from classical discrete point value to interval variable in the presence of mixed uncertainties. A likelihood-based approach is carried out for the mixed uncertainties representation and quantification. In addition, a new single loop sampling algorithm is developed to reduce the computation cost. This framework could be applied in the field of industry manufacturing and mounting, especially take effect in risk assessment and product maintaining. A series of numerical cases are demonstrated for validation and comparison.