Modeling of forced-vibration systems using continuous-time state-space neural network

Dynamic analysis of forced-vibration systems in civil engineering could be computationally inefficient or even hard to converge if the systems are stiff or highly complicated. Rapid advances in machine learning make it possible to formulate surrogate models for forced-vibration systems using neural networks. The widely used neural networks such as the convolutional neural network (CNN), recurrent neural network (RNN), etc., usually require a constant sampling rate and data length, thus they are difficult to be implemented for real-time calculation of the dynamic system with varying sampling rates. Recently, the continuous-time state-space neural network (CSNN) has shown the capability to lift these restrictions and has been drawing growing attention from the community. In this paper, we propose a generalized CSNN model for various forced-vibration systems (linear and nonlinear). The CSNN model comprises two sets of independent neural networks aiming to compute the state derivative and system response, respectively. Both neural networks adopt linear and nonlinear layers in parallel, instead of only fully connected nonlinear layers as adopted in the literature. This configuration is aimed to enhance the CSNN model with its capability to recognize the linear and nonlinear behaviors of systems. Additionally, the bias options in the CSNN model are all turned off to improve the stability of the model in the long-term time-series forecast, premised on the assumption that the forced-vibration systems are dissipative systems without drift, which is the most common case in civil engineering. 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. Both numerical and experimental illustrative examples are provided, demonstrating that the CSNN model can achieve high performance and training efficiency with a few hyper-parameters, and thus is highly promising for engineering applications.