From state observer to deep neural network: design, optimization, and application in bearing dynamics modeling

Neural networks have been widely applied in system dynamics modeling. However, traditional neural networks still encounter limitations in capturing long-term dynamics, nonlinear modeling, and interpretability. To address these challenges, this study proposes a novel neural network architecture, Deep Stacked State-observer based Neural Network (DSSO-NN). Firstly, the state-space representation is introduced, integrating discretized state-space equations into the neural network design to leverage both system state information and deep learning capabilities. Subsequently, two optimization measures are employed to enhance the network's nonlinear modeling ability with activation functions and the state observer, respectively. Finally, DSSO-NN is validated using the Case Western Reserve University bearing dataset. Experimental results demonstrate that activation functions provide minimal improvement to model performance. In contrast, the incorporation of the state observer significantly enhances the DSSO-NN's ability to capture system dynamics behaviors and improves modeling accuracy. DSSO-NN exhibits higher precision and greater stability, offering a novel perspective on using the state observer as an alternative to traditional activation functions.