SLIDE: A machine-learning based method for forced dynamic response estimation of multibody systems

In computational engineering, enhancing the simulation speed and efficiency is a perpetual goal. To fully take advantage of neural network (NN) techniques and hardware, we present the SLiding-window Initially-truncated Dynamic-response Estimator (SLIDE), a deep-learning based method designed to estimate output sequences of mechanical systems and multibody systems, in particular, which are subject to forced excitation. A key advantage of SLIDE is its ability to estimate the dynamic response of damped systems without requiring the full system state to be known, making it particularly effective for flexible multibody systems. The method truncates the output window based on the decay of initial effects due to damping, which is approximated by the complex eigenvalues of the system's linearized equations and is only limited by the lack of transfer of internal states between evaluations. In addition, a second NN is trained to assess the accuracy of the surrogate model by estimating the error during inference, further enhancing the method's applicability. The method is applied to a diverse selection of systems, including the Duffing oscillator, a flexible slider-crank system, and an industrial 6R manipulator, mounted on a flexible socket. Our results demonstrate significant speedups from the simulation up to several millions, exceeding real-time performance substantially.