Deep learning-based investigation of an innovative rail damper using particle damping technology for noise and vibration control

Abstract

Particle damping is a passive vibration control strategy that possesses various pronouncing merits in field application due to its straightforward mechanism. This technology is achieved by a granular material-filled enclosure that dissipates vibration energy through the collision and friction effects between the particles inside the cavity. To address the noise and vibration issue induced by the urban railway system, a novel rail particle damper (RPD) was developed to alleviate the vibration of the rail track. However, the intricate motion of the particle bed renders the modeling of particle dampers (PDs) a daunting challenge. This study aims to establish the surrogate particle damping models under the deep learning (DL) framework. The data-driven approach circumvents the time-consuming attempt that models the movement of all particles inside a PD, and directly gets to the desired target. The investigation of the PD is carried out progressively in this thesis, i.e., from a simple case to the field application of the rail particle dampers, and a few issues of exploiting DL will be settled during the procedure. Finally, the developed RPDs will be systematically evaluated. The first thing to learn about a PD is its energy dissipation ability. Various parameters influence the performance of a PD. A series of tests on simple cylindrical-shaped PDs were conducted to obtain their energy loss factor corresponding to different particle properties, damper cavity properties, and external excitation properties. The collected data was utilized for the training of the neural network (NN) surrogate model. Inductive transfer learning (TL) is applied here to remedy the lack of expensive high-fidelity experimental data, as the training of NNs is data hungry. The TL can leverage the low-fidelity knowledge from an approximate governing/constitutive equation to facilitate the learning in the target task, which forms a multi-fidelity approach for the modeling of PDs. Moving one step further, exploring the response of a PD helps to understand its mechanism. For example, the response force of a PD exhibits hysteretic behavior under dynamic excitation. However, there is a long-standing pathology called spectra bias that hampers NNs from reproducing the complex hysteresis loops of a PD. Analyzing the NN through the neural tangent kernel’s (NTK) perspective reveals why NNs are perplexed in recognizing high-frequency features. The Fourier features are thus embedded to extricate NNs from the shackle of spectra bias. The Fourier features-embedded NN (ffNN) is then combined with the TL-incorporated PINN (TLPINN) to enhance its performance. With these treatments, it is proved that the proposed ff-TLPINN can reconstruct the hysteresis loops of a PD under various excitation levels in a broad frequency band. However, the limitation of ff-TLPINN is that it can only model the response force of one PD. Introducing more parameters related to PD configurations into the model will make the task too bulky for the NN. The developed RPDs are equipped with cavities of different sizes, so the models for PDs with different configurations are required. Here, a divide-and-conquer strategy is applied. The basic model is firstly established on one PD with ff-TLPINN, the models for other PDs are then extended from the basic model. The mc-ESDN is proposed for this model extension. The recurrent neural network (RNN) based ESDN aims to decode the sequential information from the experimental data, and the imposition of multi-dimensional and multi-scale convolutions ameliorates the feature extraction performance of the proposed method. With the mc-ESDN, the surrogated models for the developed RPDs of different cavity sizes can be established. The effectiveness of the novel RPDs was thoroughly evaluated through experiments from laboratory to field. Numerous types of filling materials were investigated through the single-bay rail test, and the modal analysis on the RPD studied the movement of the damper cavity relative to the rail. The selected filling materials were further tested on a 6 m rail testbed to identify the optimum type of particle and its filling ratio. A noise-sensitive urban metro line was selected to evaluate the PRDs’ performance on noise and vibration control of the railway system. Through the in-situ test, the vibration of the track and surrounding noise were compared before and after the installation of RPDs. The vibration wave propagation is a critical factor in evaluating the noise emission of the track. This factor was measured and predicted by a periodic track-damper coupled model with the aid of the DL surrogate model of the RPD. Results show that RPDs are functional in suppressing the vibration of rail tracks.