Technical Event
Tutorial: Applications of Uncertainty Analysis in Smart Materials and Adaptive Structures
icon_in-person.svgIn person: 7 March 2022 • 10:30 AM - 3:00 PM 
Instructors: Ralph Smith, North Carolina State Univ. (United States) and William Oates, Florida State Univ. (United States)

The purpose of this hands-on tutorial is to expose participants to statistical and numerical techniques that will allow them to quantify the accuracy of multi-physics models and simulation codes for active materials and structures when one accounts for uncertainty or errors in models, parameters, numerical simulation codes, and data.

In the first part of the tutorial, we will provide an overview of Bayesian statistics and numerical algorithms necessary to propagate input uncertainties through simulation codes. We will consider several case studies to illustrate these techniques for a variety of materials and smart structure applications. These include models for piezoelectric macro-fiber composites, shape memory alloys, viscoelastic polymers, graphene thermoacoustics, quantum-informed ferroelectric continuum models, and Rietveld analysis. In this part of the tutorial, we will provide participants with algorithms that quantify the uncertainties in model parameters, such as piezoelectric constants, when they are calibrated from experimental data. To illustrate the uncertainty propagation techniques, we will demonstrate the construction of 95% prediction intervals for PZT models at a given applied field.

As part of the tutorial, participants will have the opportunity to run case studies using MATLAB, if they have a local license on their laptop. These studies will include models and data provided by the instructors, but participants are also encouraged to bring their own models and data for testing during the tutorial, based on their specific problem(s) of interest. All tutorial code will be available online for later use by participants not having a local MATLAB license.

This introductory tutorial is intended for graduate students, industrial practitioners, and academic professionals who are interested in quantifying uncertainty in material and structural models in light of experiments or higher fidelity model predictions.

The tutorial is open to all registered attendees on a first-come first-serve basis. Seating is limited.



Ralph Smith is a distinguished professor of Mathematics at North Carolina State University, who has expertise in mathematical modeling, uncertainty and sensitivity analysis, and control of smart materials and structures. He has written books on both smart materials and structures as well as uncertainty quantification and sensitivity analysis. He has investigated the role of uncertainty quantification in the context of macro-fiber composites and shape memory alloys including the use of uncertainty quantification to improve robust control design.





William Oates is an associate professor in the Department of Mechanical Engineering at Florida State University. His research includes constitutive model development, structural analysis, and experimental characterization of smart materials and adaptive structures. He has utilized Bayesian statistics to analyze smart materials and systems including quantum informed ferroelectric modeling, graphene thermoacoustics, piezoelectric composites, and multi-functional polymer constitutive model development.