A hierarchical framework for statistical model calibration in engineering product development

As the role of computational models has increased, the accuracy of computational results has been of great concern to engineering decision-makers. To address a growing concern about the predictive capability of the computational models, this paper proposes a hierarchical model calibration procedure with a statistical model calibration technique. The procedure consists of two activities: (1) calibration planning (top-down) and (2) calibration execution (bottom-up). In the calibration planning activity, engineers define either physics-of-failure (PoF) mechanisms or system performances of interest. Then, an engineered system can be decomposed into subsystems or components of which computational models are better understood in terms of PoF mechanisms or system performances of interest. The calibration planning activity identifies vital tests and predictive models along with both known and unknown model input variable(s). The calibration execution activity takes a bottom-up approach, which systematically improves the predictive capability of the computational models from the lowest level to the highest using the statistical calibration technique. This technique compares the observed test results with the predicted results from the computational model. A likelihood function is used for the comparison metric. In the statistical calibration, an optimization technique is integrated with the eigenvector dimension reduction (EDR) method to maximize the likelihood function while determining the unknown model variables. As the predictive capability of a computational model at a lower hierarchy level is improved, this enhanced model can be fused into the model at a higher hierarchical level. The calibration execution activity is then continued for the model at the higher hierarchical level. A cellular phone is used to demonstrate the hierarchical calibration framework of the computational models presented in this paper. It is concluded that the proposed hierarchical model calibration can effectively enhance the ability of the computational model to predict the system reliability of the cellular phone system.