Missing microseismic data imputation in tunnel monitoring using a transformer model with an integrated Gaussian mixture model - Kuang, Zhihao; Li, Shaojun; Qiu, Shili; Huang, Yong; Chang, Shuaipeng (Engineering applications of artificial intelligence, 2026)
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. •A novel GMM-Transformer data imputation model is proposed to address the challenge of missing or discontinuous microseismic (MS) data caused by environmental or human factors. This model combines the Gaussian Mixture Model (GMM) and Transformer for more accurate imputation.•The GMM-Transformer model showed strong performance, with imputed MS data maintaining a high level of consistency with observed data in various feature parameters.•The study revealed that the duration of missing data significantly affects the imputation model's performance. The best results were observed when the missing data duration was around 3.5 h.•A comparative analysis demonstrated that the direct prediction imputation method outperforms indirect methods, reducing data errors from 25.73 % to 13.37 %, leading to more accurate MS event data reconstruction.•The GMM-Transformer model outperformed the Transformer model alone in predicting the spatial distribution of MS events, validating its superior capability in handling complex data imputation tasks related to MS monitoring.