Deep-learning enabled parametric identification method of vibration-based energy harvesters with piezoelectric nonlinearity

Abstract With the introduction of nonlinearities in structures, circuits, and materials, vibration-based piezoelectric energy harvesters have become increasingly complex, making parameter identification more challenging. To address this challenge, this paper proposes a deep-learning-based parameter identification method for piezoelectric energy harvesting systems. The proposed method consists of the following steps: First, a comprehensive dataset encompassing system parameters and their corresponding frequency-voltage responses is generated based on theoretical models and approximate analytical solutions. Subsequently, an inverse neural network surrogate model is trained using the frequency-voltage responses as input and the system parameters (including the effective mass, linear damping, linear stiffness, nonlinear damping coefficient, nonlinear stiffness, and electromechanical coupling coefficients) as output. Finally, the trained inverse neural network model is employed to identify system parameters from measured frequency-voltage responses, followed by a study of the identification accuracy. To evaluate the performance of the proposed method, numerical simulations were conducted to assess the identification accuracy. Results indicated that the well-trained inverse neural network can accurately identify both the linear and nonlinear parameters. It was found that the identification errors for linear parameters (effective mass, linear damping, linear stiffness, and electromechanical coupling coefficient) were generally lower than those for nonlinear parameters (nonlinear damping and stiffness). It was also observed that the parameter identification accuracy was influenced by the parameter range of the training dataset. Specifically, as the parameters approached the boundaries of the parameter range, the identification accuracy decreased significantly. Finally, experimental data from a piezoelectric cantilever beam energy harvester with piezoelectric nonlinearities were used to validate the feasibility and accuracy of the proposed method.