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.

在这项工作中，我们实现了一个框架，该框架使用物理信息神经网络将扭振阻尼器（TVD）模型的输出调整为实验数据。TVD是用于被动控制振动的设备。通常是通过降阶物理建模的。在TVD模型中，通过先前执行的试样测试来表征设备中使用的粘弹性橡胶的材料性能。即使这样，当对TVD进行实验测试时，由于简化和模型假设，频率响应函数（FRF）仍存在显着差异。在这里，我们使用直接图将FRF实现为深度神经网络。该模型的节点包括存储和损耗模量，刚度和阻尼系数等模型元素。然后，我们添加了数据驱动的节点（实现为多层感知器）以校正刚度和阻尼系数的输出。这样，可以缩小预测和观察到的FRF之间的差距。有了这个框架，我们可以建立混合模型，通过图形将原始计算机模型（或至少是其降阶表示形式）与神经网络合并。这使我们甚至可以为图的隐藏节点估计模型形式的不确定性。在TVD应用程序中，我们研究了框架在插值（模型预测观测值之间的FRF）和外推（模型预测观测值范围外的FRF）方面的性能。结果表明以合理的计算成本执行差异的同时估计的能力。