# Probabilistic maps on bistable vibration energy harvesters

## TL;DR

This paper studies how uncertainties in parameters affect the energy harvesting efficiency of bistable vibrational systems, using probabilistic modeling and polynomial chaos to analyze different regimes and parameter variations.

## Contribution

It introduces a probabilistic framework combining maximum entropy and polynomial chaos to analyze parametric uncertainties in bistable energy harvesters.

## Key findings

- Higher probability of increased power in intrawell motion with higher excitation frequency.
- Increased excitation amplitude boosts power in chaotic regimes.
- Greater piezoelectric coupling enhances power during interwell motion.

## Abstract

This paper analyzes the impact of parametric uncertainties on the dynamics of bistable energy harvesters, focusing on obtaining statistical information about how each parameter's variability affects the energy harvesting process. To model the parametric uncertainties, we use a probability distribution derived from the maximum entropy principle, while polynomial chaos is employed to propagate uncertainty. Conditional probabilities and probability maps are obtained to investigate the effect of uncertainty on harvesting energy. We consider different models of bistable energy harvesters that account for nonlinear piezoelectric coupling and asymmetries. Our findings suggest a higher probability of increasing harvested power in the intrawell motion regime as the excitation frequency increases. In contrast, increasing the excitation amplitude and piezoelectric coupling are more likely to increase power in the chaotic and interwell motion regimes, respectively. An illustrative example is presented to emphasize the importance of investigating the influence when all parameters vary simultaneously.