Public Release: 

NSF grant to Wayne State aims to develop new ways to calculate odds of structural failure

Wayne State University - Office of the Vice President for Research

Current approaches to calculating failure probability in complex engineering structures can be inefficient and result in inconsistency, but a Wayne State University researcher is working to change that.

Christopher Eamon, associate professor of civil and environmental engineering, recently received a three-year, $250,000 grant from the National Science Foundation to develop an accurate and efficient method for calculating failure probability (reliability analysis) for computationally and probabilistically complex structural engineering problems, with the goal of achieving greater levels of consistency within a structure.

He believes his work will advance structural safety analysis for a variety of complex, high-fidelity problems such as crash, impact and blast analysis; metal forming; and complex structural system evaluation in various engineering disciplines.

Some current approaches, based on simulation, can yield accurate results for difficult problems, Eamon said. However, computational costs can be severe for highly complex problems, which often require many simulations to run an analysis and can be very time consuming, depending on the complexity level. One such approach, known as Monte Carlo simulation, might take over a million simulations or computations to accurately determine failure probability.

"Even if a computation takes a minute, that adds up to a lot of time," he said.

For example, car crash models that project material deformation levels are very computationally intensive, he said, and can run for hours and hours, if not days. If uncertainty analysis is introduced as well, Eamon said, repeating the analysis many, many times is often unfeasible, even on a supercomputer.

Another approach involves beta-based methods, which yield approximate solutions for most problems and exact ones for a very small set of theoretical problems. The advantage to such methods is that they are extremely fast, Eamon said, but often give very poor results for complicated problems.

A beta-based, analytical approach might take about 100 computations for a moderately complex problem. Eamon's approach will involve somewhere near 1,000 computations, depending on the structure, but hopefully approach the accuracy of the Monte Carlo method.

What's needed, he said, is a method that can produce reasonably accurate solutions while still having feasible computational costs. That way, engineers can better assess the safety levels of structures in order to avoid inconsistencies.

"If you don't get the safety factors right, you can get very inconsistent results in terms of safety level from one structure to the next because of different levels of uncertainty, different loads, components and so on," Eamon said. "If you're expending limited resources, it makes no sense to have one structure 10 times as safe as another if they're the same level of importance. We're trying to get the level of safety to be more evenly distributed and more consistent."

A side benefit of Eamon's work is that in addition to increased efficiency, it could serve to increase the number of students who become involved in research as undergraduates. Because much of that work involves monitoring computer calculations, he said, it can be done by students who are relatively new to the research experience, inspiring their interest in continuing on to graduate education.

As computational power increases, Eamon said, researchers can come up with more and more sophisticated models.

"We then need some way to evaluate the uncertainties with those models," Eamon said, "and that's another layer of complexity. We're looking for a better-than-approximate solution.

"The hope with this particular method I'm investigating is that we can actually solve these complex kinds of problems and get some feasible result."

Those results could have wide-ranging implications, he said. While most failure analysis tends to take place within the civil engineering realm, Eamon said, his work potentially could be applied to any electrical, mechanical, computing or medical problem where such analysis is needed.

"There are lots of different possibilities," he said.


Wayne State University is one of the nation's pre-eminent public research universities in an urban setting. Through its multidisciplinary approach to research and education, and its ongoing collaboration with government, industry and other institutions, the university seeks to enhance economic growth and improve the quality of life in the city of Detroit, state of Michigan and throughout the world. For more information about research at Wayne State University, visit

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