Measuring uncertainty

How can one estimate the unknown? Arizona State University researcher Marc Mignolet has spent his career taking on the hefty task of modeling uncertainty in engineered structures to promote safety and performance.

To recognize his body of work in this area, Mignolet received an International Association for Structural Safety and Reliability, or IASSAR, Distinguished Research Award. 

The award is conferred every four years to two senior researchers who promote the study, research and application of the scientific principles of probability, safety, risk and reliability in the design, construction, maintenance and operations of structures and other engineered systems.

Mignolet, a professor and graduate program chair of mechanical and aerospace engineering in the School for Engineering of Matter, Transport and Energy, part of the Ira A. Fulton Schools of Engineering at ASU, earned the award for his contributions to the modeling of uncertainty in structural dynamic systems and their effects. 

This work includes the development of efficient and accurate models for complex structures like bladed disks, such as those used in the turbine engines of aircrafts, and panels of hypersonic vehicles. These structures are often subject to uncertainties in geometry, material properties and other factors.

“The goal is to be able to identify and propagate possible uncertainties that exist in the field due to manufacturing or operation in a simple way and assess their effects, in particular to determine if changes in behavior occur,” Mignolet says.

Experiments in labs are usually conducted meticulously with all parameters precisely measured, but the outside world contains vast amounts of variance. 

For instance, manufacturers of aircraft need to predict the performance and durability of their designs. To do so, they must first have the geometric specifications, such as length and thickness, of all of the aircraft’s components.

However, manufacturing is never perfect, and there will be variance among the size of a structure’s parts. For example, one aircraft and another that was manufactured immediately after will have slightly different dimensions. 

The crux of Mignolet’s research lies in putting these variations into a probabilistic setting, performing a statistical modeling of a structure’s geometric properties and synthesizing them with modern computational abilities available at ASU. These models are not only valuable to assess performance when the design and manufacturing is completed, but they can also assess the tolerance of a design to uncertainties prior to its construction and establish permissible tolerances in the manufacturing process. A component will pass inspection only if it is within the acceptable tolerance limits.

“The benefit of all this modeling is to give a range of values of prediction that can be used to avoid early product failures and effectively produce a component, whatever it is, that’s going to meet expectations even with existing uncertainties,” Mignolet says.

Roger Ghanem, a professor of engineering at the University of Southern California, nominated Mignolet after working in the field of structural uncertainty for many years.

“Tackling these problems and producing engineering solutions of practical significance requires keen engineering insight and mastery of mathematical constructs,” Ghanem says. “Professor Mignolet has made seminal contributions at the confluence of stochastic mechanics (the study of uncertainty in mechanical engineering), nonlinear dynamics and operational feasibility.”

Ghanem understands firsthand the impact that Mignolet has had on the community.

“In addition to his impactful research contributions in the area of rotating machinery, Professor Mignolet has been a thought leader in framing and solving complex problems in stochastic mechanics,” he says. “He has made lasting contributions to the simulation of stochastic processes and to the characterization of parametric and model uncertainties for complex linear and nonlinear dynamical systems. He has organized dozens of workshops and minisymposia on these topics over the past 30 years.”

These key contributions to the study of uncertainty from Mignolet’s research group include explaining and accurately predicting the worst maximum response in bladed disks due to uncertainties. His group was the first to efficiently optimize these disks against uncertainties by combining two different types of blades. 

They were also the first group to effectively model uncertainties in structures undergoing large deformations and the first to effectively model uncertainties in rotordynamics, which characterizes the behavior of rotating mechanical parts. In another innovative development, Mignolet’s group recently published a novel model of uncertainties that has great potential to solve very large computational problems.

For Mignolet, this award is confirmation of a successful career.

“Receiving the award is a wonderful feeling,” he says. “It is the satisfaction that the hard work that my group and I have put in for the last 35 years has been appreciated by the community. It is like getting an 'A' at the end of a hard class, except that the class has not lasted for a semester, but for 35 years.”