By Dave DeFusco
A small amount of carefully designed noise could help computer models better capture the complex motion experienced by energy-harvesting devices in real-world environments, according to research presented by Penghui Han, a student in the Katz School's Ph.D. in Mathematics, at the 2026 Symposium on Science, Technology and Health.
Han's project, 鈥淨uasiperiodic Noise For Bifurcation Mapping And Optimization: Numerical Study of Voltage Output in a Nonlinear Energy Harvester,鈥 examines a type of energy-harvesting device that converts vibrations into electrical power. Such technology could help power sensors, wearable devices and other electronics without relying as heavily on batteries.
The device Han studied behaves in complex ways. Depending on how it starts, it can settle into different patterns of motion, some of which produce much more electricity than others. This makes it difficult for researchers to identify the best operating conditions.
鈥淥ne of the biggest challenges is that the system can behave very differently even when the operating conditions stay the same,鈥 said Han. 鈥淎s a result, traditional methods can miss some of the most productive states.鈥
Researchers often use visual maps to track how a device responds as conditions change. If they begin with only one starting point, however, they may overlook important behaviors and underestimate the system's true potential.
To solve this problem, Han added a tiny amount of quasiperiodic noise鈥攁 gentle disturbance made up of several frequencies. The goal was not to change the device's behavior dramatically but to help it explore hidden operating states.
鈥淲e wanted to determine whether a very small and realistic disturbance could reveal behaviors that would otherwise remain hidden while still preserving strong energy output,鈥 said Han.
The results showed that the added noise helped uncover previously unseen operating states and provided a more complete picture of the system. It also expanded the range of conditions under which the device produced high levels of electrical power.
Han also found that combining the noise with a mathematical smoothing technique made it easier for computer algorithms to search for the best operating settings. Most important, the improvements came without reducing performance.
鈥淭he best solutions found with the added noise produced essentially the same amount of power as the best solutions found without it,鈥 said Han.
Marian Gidea, Han's advisor and a professor of mathematics, the study demonstrates how mathematical tools can help engineers design better technologies.
鈥淭his work shows that small, carefully designed disturbances can reveal important system behaviors that might otherwiseremain hidden,鈥 said Gidea. 鈥淭hose insights can help researchers find more efficient ways to harvest energy from the world around us.鈥
