Investigation of Model Falsification Using Error and Likelihood Bounds with Application to a Structural System

Abstract

Models are used to represent and characterize physical phenomena. When there are many plausible models for a particular phenomenon, the modeler can exploit the computational tool called model falsification to systematically eliminate models that do not reasonably fit measured data. Model falsification typically compares measurements and their predictions by different models, and rejects a model if some metric of the difference between them is outside some prescribed bounds. This paper compares two model falsification approaches: a conventional bounds on residual errors and a proposed bounds on a model’s prediction of the likelihood of the residual errors. The bounds in both approaches are selected based on two error control criteria: the more commonly used familywise error rate (FWER) and—proposed herein for model falsification—the false discovery rate (FDR). Because FDR control significantly increases the likelihood of rejecting an invalid model when there are many measurements, FDR provides advantages over FWER in exploratory studies. A variant of the second approach, using likelihood bounds specified by a constant probability mass contained within those bounds, is also investigated. Unlike many model falsification studies, the focus herein is on systems with many measurements, spread across spatial and/or temporal dimensions, such as dynamical systems. An elementary example is used to show the principles of each approach. A second example considers a series of four-degree-of-freedom models of a structure subjected to an earthquake excitation. The results from these examples show that FDR does indeed increase the number of falsified models, whereas the use of likelihood bounds additionally gives unfalsified models confidence values, which can also be used for maximum likelihood parameter estimation.