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Enhancing the performance of a bistable energy harvesting device via the cross-entropy method

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Abstract

This work deals with the solution of a non-convex optimization problem to enhance the performance of an energy harvesting device, which involves a nonlinear objective function and a discontinuous constraint. This optimization problem, which seeks to find a suitable configuration of parameters that maximize the electrical power recovered by a bistable energy harvesting system, is formulated in terms of the dynamical system response and a binary classifier obtained from 0 to 1 test for chaos. A stochastic solution strategy that combines penalization and the cross-entropy method is proposed and numerically tested. Computational experiments are conducted to address the performance of the proposed optimization approach by comparison with a reference solution, obtained via an exhaustive search in a refined numerical mesh. The obtained results illustrate the effectiveness and robustness of the cross-entropy optimization strategy (even in the presence of noise or in moderately higher dimensions), showing that the proposed framework may be a very useful and powerful tool to solve optimization problems involving nonlinear energy harvesting dynamical systems.

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Code availability

To facilitate the reproduction of this paper results, as well as to popularize the CE method use by the community of nonlinear dynamical systems, the code used in the simulations is available in the following repository: https://americocunhajr.github.io/HarvesterOpt

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Acknowledgements

Including noise into the objective function is an idea given to the author for the first time in a conference at Morocco by Prof. Luca Gammaitoni (University of Perugia), and more recently by one of the anonymous reviewers. The noisily test case proved to be very useful to illustrate the robustness of the framework presented here. The author is very grateful to both of them for this suggestion. He is also indebted to Dr. Welington de Oliveira (MINES ParisTech), for the fruitful discussions about the mathematical technicalities related to the optimization problem addressed in this work.

Funding

This research received financial support from the Brazilian agencies Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—Finance Code 001, and the Carlos Chagas Filho Research Foundation of Rio de Janeiro State (FAPERJ) under the following Grants: 211.304/2015, 210.021/2018, 210.167/2019, and 211.037/2019.

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    Americo Cunha Jr

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Cunha, A. Enhancing the performance of a bistable energy harvesting device via the cross-entropy method. Nonlinear Dyn 103, 137–155 (2021). https://doi.org/10.1007/s11071-020-06109-0

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