Li, C. and Mahadevan, S., "Uncertainty Quantification of System Model Parameters with Component Level and Sub-System Level Tests," SAE Int. J. Mater. Manf. 9(2):345-354, 2016, doi:10.4271/2016-01-0287.
An essential step in predicting the output of a complicated system is the calibration of model parameters, but this step cannot be conducted directly if the data at the system-level are not available. In such a situation, a reasonable route is to quantify the system model parameters using tests at lower levels of complexity which share the same model parameters with the system, and propagate the results through the computational model at the system level. For such a multi-level problem, this paper proposes a methodology to quantify the uncertainty in the system-level model parameters by integrating model calibration, model validation and sensitivity analysis at different levels. The proposed approach considers the validity of the models used for parameter estimation at lower levels, as well as the relevance at the lower level to the prediction at the system level. The model validity is evaluated using a model reliability metric, which is extended to handle the uncertainty in model validity and models with multivariate output. The relevance is quantified by comparing Sobol indices at the lower level and system level, thus measuring the extent to which a lower level test represents the characteristics of the actual system so that the calibration results can be reliably used in the system level. Finally a roll-up method is proposed to integrate the results of calibration, validation and relevance analysis and predict the system output.