Adjusting a torsional vibration damper model with physics-informed neural networks

Abstract

In this work, we implement a framework for adjusting the outputs of a torsional vibration damper (TVD) model to experimental data using physics-informed neural networks. TVDs are devices used to passively control vibration; and here are commonly modeled through reduced-order physics. Within the TVD model, the material properties of the viscoelastic rubber used in the device are characterized through previously performed coupon tests. Even so, when the TVD is experimentally tested, there are significant discrepancies in the frequency response function (FRF), due to simplifications and model assumptions. Here, we implement the FRF as a deep neural network using a direct graph. The model elements, such as storage and loss moduli, stiffness and damping coefficients are nodes of this graph. Then, we add data-driven nodes (implemented as multilayer perceptrons) to correct the outputs of the stiffness and damping coefficients. This way, the gap between predicted and observed FRF can be closed. With this framework, we can build hybrid models that merge the original computer model (or at least, a reduced-order representation of it) with the neural network through a graph. This allows us to estimate the model-form uncertainty even for hidden nodes of the graph. In the TVD application, we studied the performance of our framework both in interpolation (when the model predicts the FRF between observations) and extrapolation (when the model predicts the FRF outside the observation range). The results demonstrate the ability to perform simultaneous estimation of discrepancy at reasonable computational cost.