Robust model development for evaluation of existing structures.

摘要

In the context of scientific computing, validation aims to determine the worthiness of a model in supporting critical decision making. This determination must occur given the imperfections in the mathematical representation resulting from the unavoidable idealizations of physics phenomena. Uncertainty in parameter values furthers the validation problems due to the inevitable lack of information about material properties, boundary conditions, loads, etc. which must be taken into account in making predictions about structural response. The determination of worthiness then becomes assessing whether an unavoidably imperfect mathematical model, subjected to poorly known input parameters, can predict sufficiently well in its intended purpose. The maximum degree of uncertainty in the model's input parameters which the model can tolerate and still produce predictions within a predefined error tolerance is termed as robustness of the model. A trade-off exists between a model's robustness to unavoidable uncertainty and its agreement with experiments, i.e. fidelity. This dissertation introduces the concept of satisfying boundary to evaluate such a trade-off. This boundary encompasses the model predictions that meet prescribed error tolerances. Decisions regarding allocation of resources for additional experiments to reduce uncertainty, relaxation of error tolerances, or the required confidence in the model predictions can be arrived at with the knowledge of this trade-off. This new approach for quantifying robustness based on satisfying boundaries is demonstrated on an application to a nonlinear finite element model of a historic masonry monument Fort Sumter.