Missing microseismic data imputation in tunnel monitoring using a transformer model with an integrated Gaussian mixture model

Microseismic (MS) monitoring is essential for early warning and evaluation of structural safety in tunnel engineering. However, data loss due to environmental interference often compromises the reliability of such systems. To address this challenge, a data imputation model that integrates the Gaussian Mixture Model (GMM) with a transformer-based neural network, referred to as the GMM–Transformer model, was developed. Its performance was evaluated using real-world MS monitoring data from a deep-buried tunnel project in southwestern China. The proposed method achieves high accuracy in reconstructing missing data, with the imputed results closely matching observed values across multiple characteristic parameters. By leveraging the probabilistic nature of the Gaussian mixture distribution and Monte Carlo Dropout, the model can also quantify predictive uncertainty, yielding narrow confidence intervals that reinforce its reliability. The influence of missing data duration on the imputation quality was examined. The results imply that a missing window of approximately 3.5 h yields optimal results. A comparison between direct and indirect imputation strategies indicates that the direct approach significantly reduces reconstruction errors, from 25.73 % to 13.37 %. Additionally, benchmark comparisons with models such as random forest and long short-term memory networks show that the proposed model offers superior accuracy in recovering spatial characteristic critical to MS analysis. Overall, the GMM–Transformer model provides an effective, robust solution for dealing with data loss in MS monitoring. This work provides a forward-looking methodology and theoretical foundation for advancing artificial intelligence–based MS monitoring technologies in complex tunnel environments.