Using Statistical Learning Theory to Rationalize System Model Identification and Validation Part I: Mathematical Foundations

Existing procedures for model validation have been deemed inadequate for many engineering systems. The reason of this inadequacy is due to the high degree of complexity of the physical mechanisms that govern these systems. It is proposed in this paper to shift the attention from modeling the engineering system itself to modeling the uncertainty that underlies its behavior. A mathematical framework for modeling the uncertainty in complex engineering systems is developed. This framework uses the results of computational learning theory. It is based on the premise that a system model is a learning machine.