Data-driven identification of time-delayed hybrid energy harvesting system under non-Gaussian noise

In engineering applications, the strongly nonlinear multistable hybrid vibration energy harvester (HVEH) with time delay poses significant challenges for stochastic dynamic modeling due to its non-Markovian characteristics and non-Gaussian noise. This difficulty is particularly pronounced in time-delayed systems driven by non-Gaussian noise, where conventional modeling approaches often fail to yield accurate results. From a machine learning perspective, we devise a data-driven identification method to identify the time-delayed non-Gaussian governing equation of HVEH. Leveraging the nonlocal Kramers-Moyal formulas and sparse identification, we first obtain a delay-free approximation from trajectory data. The complete time-delayed equation is then identified by applying Laplace transform algebra. To validate the proposed method, we compare the probability density functions of the identified systems with the original system. Results demonstrate that the identified time-delayed system achieves about 14 % higher precision than the identified delay-free system. Furthermore, we develop a dynamic analysis framework for energy harvesting performance based on the identified time-delayed system. This work advances data-driven modeling and dynamic analysis of HVEH in practical engineering.