State-Integration Neural Network for Modeling of Forced-Vibration Systems

Dynamic analysis of forced-vibration systems could be computationally inefficient or even difficult to converge if the systems are highly complicated. Rapid advances in machine learning make it possible to establish surrogate models for forced-vibration systems using neural networks. However, the existing data-driven neural network models usually require the data sampling frequency and time duration to be fixed, and they typically contain large amounts of learnable hyper-parameters which tend to cause overfitting issues. To overcome these limitations, we develop the state-integration neural network (SINN) modeling approach by combining the ideas of the state-space method and neural ordinary differential equations. The SINN model has two sets of independent neural networks aimed to compute the state derivative and system response, respectively. Integration on the state derivative at the current time step is executed to obtain the state at the next time step using the explicit 4th-order Runge Kutta method. The SINN model has strong adaptability because it is not restricted to the pre-designated sampling frequency and input data length. A numerical illustrative example is conducted in this paper.