Identifying Chaotic Behavior in Non-linear Vibration Energy Harvesting Systems

Large amplitude inter-well oscillations in bi-stable energy harvesters made them a proper energy harvesting choice due to high energy generation. However, the co-existence of the chaotic attractor in these harvesters could essentially decrease their efficiency. In this paper, an algorithm for detecting chaos in bi-stable energy harvesters based on a data-gathering algorithm and estimating the largest Lyapunov exponent is investigated. First, a simple model of axially loaded non-linear energy harvesters is derived. This model is derived using the Euler-Bernoulli beam theory and the Assumed Mode method considering the Von-Karman non-linear strain-displacement equation. The harvester's numerical simulation results are used to test the algorithm's efficiency and accuracy in identifying chaotic response. The results showed the algorithm's success in detecting chaos in such systems with minimum possible calculation cost. The effect of noise on the algorithm's performance has been investigated, and the results showed the excellent robustness of the algorithm to noise. It can diagnose the harvester's chaotic or harmonic behavior with noise-contaminated data, with 10 percent noise density. The comparison between this algorithm and Wolf's method showed relatively less computation time, up to 80 percent, to detect chaos with reasonable accuracy.