Identifying Chaotic Behavior in Non-linear Vibration Energy Harvesting Systems

Large amplitude inter-well oscillations in bi-stable energy harvesters have made them a proper energy harvesting choice due to a high energy generation. However, the co-existence of the chaotic attractor in these harvesters could essentially decrease their efficiency. In this work, an algorithm for detecting chaos in bi-stable energy harvesters based on a data-gathering algorithm and estimating the largest Lyapunov exponentis 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 in order to test the algorithm s efficiency and accuracy in identifying the chaotic response. The results obtained show the algorithm s success in detecting chaos in such systems with a minimum possible calculation cost. The effect of noise on the algorithm s performance is also investigated, and the results obtained show an excellent robustness of the algorithm to noise. It can diagnose the harvester s chaotic or harmonic behavior with noise-contaminated data with 10% noise density. The comparison between this algorithm and the Wolf s method show a relatively less computation time (up to 80%) to detect chaos with a reasonable accuracy.