Multi-frequency superposed vortex-induced vibration modeling based on multiple Fourier features physics-informed neural network

Abstract

In scenarios involving coupled excitations from multiple forces, structures exhibit complex vibrational patterns with superimposed high and low-frequency. This is particularly evident in thin-walled structures such as submarine pipelines, where the coupling of internal and external flows leads to more intricate superimposed vibrations compared to scenarios with only internal flow excitation. However, neural networks encounter challenges in capturing these superimposed vibrations due to inherent spectral bias. To address this, the multiple Fourier features physics-informed neural network (MFF-PINN) is proposed. Through multiple Fourier mappings for refined multi-scale and multi-frequency decomposition, facilitating PINN in accurately capturing multi-frequency superposed vibrations. Additionally, the correspondence between hyperparameters and eigenvector frequencies is established, while the effects of different hyperparameters and number of mappings on the network is analyzed. The MFF-PINN with multiple mapping decomposition outperforms single mapping in synchronizing the learning of high and low-frequency, improving convergence speed and enhancing the ability to handle multi-frequency superposition. It provides an effective solution for modeling and simulating multi-frequency superposed problems in science and engineering.