The classical wake oscillator model is capable of predicting the vortex-induced vibration response of a cylinder at high mass-damping ratios, but it fails to perform satisfactorily at low mass-damping ratios. A modified wake oscillator model is presented in this paper. The modification method involves analyzing the variation law of the add mass coefficient of the cylinder versus reduced velocity and expressing the reference lift coefficient C_L0 as a function of the add mass coefficient. The modified wake oscillator model has been demonstrated to have better accuracy in capturing maximum amplitudes and flow velocity at low mass-damping ratios. However, the modified model at present form is unable to accurately predict the vortex-induced vibration response at high damping ratios. The purpose of this paper is to propose a new modification idea. In order to achieve better results when applying this modification idea to particular objects, it may be necessary to first understand the response law of these kinds of objects.

In response to the increasingly severe issue of anthropogenic carbon dioxide (CO₂) emissions, CO₂ hydrate storage presents a promising method for reducing atmospheric pollution and mitigating climate change. This study proposes a machine learning model based on the Convolutional-Kolmogorov-Arnold (CKAN) neural network, aiming to accurately predict the phase equilibrium temperatures of CO₂ hydrates in systems containing salts, various promoters, and inhibitors. This study utilized 1909 experimentally measured equilibrium data points of hydrate temperatures, covering systems with salts and thermodynamic agents. After preprocessing, 1527 data points were selected for model training, and 382 data points were used for model validation. The CKAN model involves 29 input variables and 1 output variable. Its predictive accuracy was evaluated using various statistical error metrics, and its effectiveness and interpretability were examined using methods such as Shapley additive explanations (SHAP) to identify features with significant positive or negative impacts on the model’s predictions. Compared to the traditional convolutional neural (CNN) network and multi-layer perceptron (MLP) models, long short-term memory (LSTM) networks, light gradient boosting machine (LightGBM) model, and natural gas hydrate (NGH) phase equilibrium calculation software, the CKAN model exhibits a significant accuracy advantage. The CKAN model can serve as a reliable tool for predicting the phase equilibrium curves of CO₂ hydrates in pure water, single-salt brine, multi-salt brine, and under various conditions.