Did you know math could help NASA travel faster and farther? Worcester Polytechnic Institute (WPI) mathematician Randy Paffenroth has been combining machine learning with 19th-century mathematics to make NASA spacecraft lighter and more damage tolerant.

His goal is to detect imperfections in carbon nanomaterials used to make composite rocket fuel tanks and other spacecraft structures by using an algorithm he developed. The algorithm allows for higher resolution scans that provide more accurate images of the material's uniformity and potential defects.

Paffenroth searches for imperfections in MiralonĀ® yarns. These yarns are wrapped around structures like rocket fuel tanks, giving them the strength to withstand high pressures.

They are made by Nanocomp. The firm uses a modified scanning system that scans the nanomaterial for mass uniformity and imperfections.

Now, Paffenroth and his team are using machine learning to train algorithms to increase the resolution of these images. They have developed an algorithm that has increased the resolution by nine times.

## The Fourier Transform

This novel algorithm is based on the Fourier Transform, a mathematical tool devised in the early 1800s that can be used to break down an image into its individual components. "We take this fancy, cutting-edge neural network and add in 250-year-old mathematics and that helps the neural network work better," said Paffenroth.

"The Fourier Transform makes creating a high-resolution image a much easier problem by breaking down the data that makes up the image. Think of the Fourier Transform as a set of eyeglasses for the neural network. It makes blurry things clear to the algorithm. We're taking computer vision and virtually putting glasses on it.

"It's exciting to use this combination of modern machine learning and classic math for this kind of work," he added.

MiralonĀ® has already been used successfully in space. It was wrapped around structural supports in NASA's Juno probe orbiting the planet Jupiter and has been used to make and test prototypes of new carbon composite pressure vessels.

Now, Nanocomp is trying to make MiralonĀ® yarns that are three times stronger for a contract with NASA. Paffenroth and his team are helping with that goal.

"Randy is helping us achieve this goal of tripling our strength by improving the tools in our toolbox so that we can make stronger, better, next-generation materials to be used in space applications," said Bob Casoni, Quality Manager at Nanocomp.

"If NASA needs to build a new rocket system strong enough to get to Mars and back, it has a big set of challenges to face. Better materials are needed to allow NASA to design rockets that can go farther, faster and survive longer."

Casoni added that with WPI's new algorithm, Nanocomp can see patterns in its materials that they couldn't detect before.

"We can not only pick up features, but we also have a better idea of the magnitude of those features," he said.

"Before, it was like seeing a blurry satellite image. You might think you're seeing the rolling hills of Pennsylvania, but with better resolution you see it's really Mount Washington or the Colorado Rockies. It's pretty amazing stuff."