Machine Learning for Inverse Structural-Dynamical Problems: From Bayesian Non-Parametrics, to Variational Inference, and Chaos Surrogates

Abstract

To ensure that the design of a structure is both robust and efficient, engineers often investigate inverse dynamical modeling problems. In particular, there are three archetypal inverse modeling problems which arise in the context of structural engineering. These are respectively: (i) The eigenvalue assignment problem, (ii) Bayesian model updating, and (iii) Operational modal analysis. It is the intent of this dissertation to investigate all three aforementioned inverse dynamical problems within the broader context of modern machine learning advancements.

Firstly, the inverse eigenvalue assignment problem will be investigated via performing eigenvalue placement with respect to several different mass-spring systems. It will be shown that flexible, and robust inverse design analysis is possible by appealing to black box variational methods. Secondly, stochastic model updating will be explored via an in-house, physical T-tail structure. This will be addressed through the careful consideration of polynomial chaos theory, and Bayesian model updating, as a means to rapidly quantify structural uncertainties, and perform model updating between a finite element simulation, and the physical structure. Finally, the monitoring phase of a structure often represents an important and unique challenge for engineers. This dissertation will explore the notion of operational modal analysis for a cable-stayed bridge, by building upon a Bayesian non-parametric approach. This will be shown to circumvent the need for many classic thresholds, factors, and parameters which have often hindered analysis in this area.

Ultimately, this dissertation is written with the express purpose of critically assessing modern machine learning algorithms in the context of some archetypal inverse dynamical modeling problems. It is therefore hoped that this dissertation will act as a point of reference, and inspiration for further work, and future engineers in this area.