Abstract: With the increasing complexity and systematization of engineering research objects, it is difficult for mechanical modeling methods that rely solely on prior knowledge to meet the increasingly complex system modeling needs. In contrast, the data-driven system obtains a mathematical model that accurately reflects the current motion state of the system through big data processing methods, which reflects the development trend of data science integrating into the fields of basic and applied science. In particular, the emergence of sparse identification of nonlinear dynamical systems (SINDy) has solved the difficult problem of directly constructing nonlinear mathematical model and realized the direct transition from experimental data to nonlinear control equations. However, due to the significant influence of noise data and the difficulty of accurate analysis of singular matrix, the reliability of SINDy in practical application still needs to be strengthened. In view of this, based on the existing SINDy algorithm, this paper puts forward the enhanced sparse identification of nonlinear dynamical systems (ESindy) algorithm, improves the data filtering module to strengthen its processing ability for noisy signals, and changes the cyclic function body of the original algorithm to improve its ability to identify singular problems, making it more suitable for analyzing the common problems such as strong noise and high singularity in engineering signals. As an application, a kind of electromagnetic vibration energy harvester (EMH) with double-layer membrane structure is studied. The dynamic equation of the harvester is established by combining theoretical modeling with ESINDy method, and the theoretical results are verified by experiments and simulations. The results show that compared with SINDy algorithm, ESINDy algorithm can identify the information of the dynamic system more accurately and describe the complex vibration behavior contained in the system. The good consistency of theoretical, experimental and simulation results reflects the effectiveness of the improved algorithm in improving the identification accuracy of actual nonlinear systems, strengthens the engineering application value of data-driven modeling method, and provides a feasible analysis method for signal processing in practical engineering problems.