NOM-optimized CNN-LSTM model for dynamic response prediction of a nonlinear piezoelectric energy harvester

As the strong nonlinearity and highly complex of piezoelectric energy harvesters (PEH), accurately predicting the dynamic response using mathematical models remains challenging. This study introduces a CNN-LSTM (Convolutional Neural Network, Long Short Term Memory) combined with a neural optimization machine (NOM) to predict the nonlinear dynamics of the PEH. CNN extracts local patterns from inputs related to incentives, while LSTM layer captures their temporal evolution. NOM uses a differentiable surrogate model to automatically optimize the hyperparameters of the CNN-LSTM, thereby improving the predicting accuracy. The proposed framework avoids explicit dynamic modeling, computationally numerical simulation, and repetitive parameter identification. The framework was then applied to predict the dynamic responses (including tip displacement, adaptive rotation angle and output voltage) of a nonlinear, directional self-adaptive PEH, and the results showed that the determination coefficients ( R 2 ) of all three responses exceeded 0.998, and the root mean square errors (RMSE) of tip displacement, adaptive rotation angle, and output voltage were 0.1156 mm, 0.2736°, and 0.2313 V respectively. There was good consistency between the predicted and measured responses, validating the effectiveness of the proposed method and opening up opportunities for accurately predicting the dynamic characteristics of highly complex and/or strongly nonlinear energy harvesting systems.