Speaker
Description
Understanding structural vibrations is critical for the design of mechanical structures such as airplanes or cars. In the context of vibroacoustic design the dynamical response of the system in the frequency domain is central. Such frequency response functions are usually computed using discretization techniques such as the finite element method. To this end, potentially large linear systems have to be solved at each queried frequency. For tasks like design space exploration, optimization or uncertainty quantification, the system has to be evaluated many times, quickly resulting in a prohibitive computational burden. Neural network surrogate models offer a promising alternative to traditional numerical simulation. These models can be evaluated rapidly but require large datasets for training. Our work focuses on enhancing the data efficiency of deep learning approaches by incorporating physical knowledge into the network architecture.
In this work, we consider harmonically excited plates with beadings as a benchmark dynamical system. The beading patterns define a geometry modification which affects the local stiffness of the plate and consequently the frequency response function (FRF). Our network is trained to predict the FRF given a beading pattern.
We propose a physically inspired final network layer. Specifically, our network represents the FRF as a (weighted) sum of rational basis functions derived from the FRF of a single mass oscillator model. This design ensures smooth predictions and allows the network to directly predict the eigenfrequency, height, and damping coefficient per peak. Using these parameters, we define a novel loss function that incorporates their contribution explicitly. During training, we have to account for its special numerical properties.
We compare our physics-constrained architecture to a generic architecture that directly predicts the FRFs trained on the same data. Our method predicts the eigenfrequencies more accurately, especially in the low data regime. However, the generic method achieves a smaller FRF mean squared error in the high data regime. Potential future work includes generalizing our method to predict velocity fields, where generic networks currently outperform. Overall, our approach offers a tradeoff: improved eigenfrequency prediction and physical interpretability at the cost of a more complicated architecture and training process.
