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.