The challenge of monitoring gas-handling processes in gas-insulated power equipment stems from the fact that operating signals vary over time. Traditional fixed-threshold methods may have poor detection sensitivity or high false alarm rate as operating condition changes. This paper proposes a predictive monitoring approach based on adaptive statistical modeling combined with sequential learning, as a Random Forest model estimates an adaptive threshold reflecting expected behavior across different operating states, whereas a Bidirectional Gated Recurrent Unit network models temporal patterns in multivariate monitoring signals and forecasts its future evolution. Persistence-based decision rule checks deviation between predicted signal and the adaptive threshold. The framework achieves stable prediction performance and reliable abnormality detection even under changing operating conditions such as evacuation and refilling process. Results show that combining adaptive threshold estimation with sequential prediction can be an effective solution for intelligent monitoring of gas-handling processes in gas-insulated power equipment.