Clustered parameters of calibrated models when considering both fidelity and robustness

In computer modeling, errors and uncertainties inevitably arise due to the mathematical idealization of physical processes stemming from insufficient knowledge regarding accurate model forms as well as the precise values of input parameters. While these errors and uncertainties are quantifiable, compensations between them can lead to multiple model forms and input parameter sets exhibiting a similar level of agreement with available experimental observations. Such nonuniqueness makes the selection of a single, best computer model (i.e. model form and values for its associate parameters) unjustifiable. Therefore, it becomes necessary to evaluate model performance based not only on the fidelity of the predictions to available experiments but also on a model’s ability to sustain such fidelity given the incompleteness of knowledge regarding the model itself, such an ability will herein be referred to as robustness. In this paper, the authors present a multiobjective approach to model calibration that accounts for not only the model’s fidelity to experiments but also its robustness to incomplete knowledge. With two conflicting objectives, the multi-objective model calibration results in a family of nondominated solutions exhibiting varying levels of fidelity and robustness effectively forming a Pareto front. The Pareto front solutions can be grouped depending on their nature of compromise between the two objectives, which can in turn help determine clusters in the parameter domain. The knowledge of these clusters can shed light on the nature of compensations as well as aid in the inference of uncertain input parameters. To demonstrate the feasibility and application of this new approach, we consider the computer model of a structural steel frame with uncertain connection stiffness parameters under static loading conditions.