Deep stacked state-observer based neural network (DSSO-NN): A new network for system dynamics modeling and application in bearing

System dynamics modeling holds significant importance in engineering, especially for high-dimensional, non-linear, and time-varying systems. Traditional methods often encounter challenges such as poor interpretability, low computational efficiency, and limited generalization capabilities. To address these issues, this paper proposes a novel framework for dynamics modeling, Deep Stacked State-observer based Neural Network (DSSO-NN). This framework integrates the Extended State Observer (ESO) with state–space equations, leveraging the efficient state estimation of ESO and the powerful fitting capabilities of neural networks. Firstly, based on the system’s state–space equations, an ESO is constructed and then discretized to obtain neurons tailored for system modeling. Subsequently, serial and parallel structures are explored and compared to determine the optimal structure for validation, culminating in the construction of the DSSO network. Furthermore, critical factors influencing DSSO-NN performance, including ESO hyperparameter ($\delta$), system order, and the number of layers, are optimized. Experimental results on Case Western Reserve University and FEMTO datasets demonstrate that DSSO-NN effectively captures system dynamics and achieves superior performance. This study showcases the robust performance and broad application potential of DSSO-NN in bearing dynamics modeling, providing a novel approach for complex dynamics modeling.