Copula-based generation of synthetic multivariate time-series for underground mine gas concentrations

Fatal incidents in underground coal mines are often linked to hazardous gas accumulation–methane ( \(CH_4\) ), carbon dioxide ( \(CO_2\) ), and oxygen ( \(O_2\) ) imbalances–posing risks of explosion, asphyxiation, and hypoxia. Predictive models require large volumes of continuous data, rarely available where monitoring is sparse and manual. This study introduces a fully statistical framework that fits a Gaussian multivariate copula to real, twice-daily \(CH_4\) , \(CO_2\) , and \(O_2\) measurements collected under safe-entry conditions from a Norte de Santander underground coal mine, generating 9 360 synthetic records at one-minute resolution without hyperparameter tuning. To make the output a genuine time series rather than independent draws, the copula is coupled with a first-order vector-autoregressive latent process (a meta-Gaussian construction) that captures the short-range autocorrelation and lagged cross-gas dependence observed in the sparse real series. The synthetic series preserve marginal distributions and cross-gas dependencies reflective of safe-entry conditions; hazardous-concentration episodes were inaccessible during collection and are not represented. Representativeness was validated by extending the TRTR–TRTS–TSTR protocol with 300 GRU runs per gas under a block temporal split, paired Wilcoxon signed-rank tests, and effect-size reporting; for \(CH_4\) and \(CO_2\) , models trained only on synthetic data achieved lower MAE than the real-data baseline in our experiments. Marginal fidelity was confirmed via Kuiper’s test (Bonferroni-adjusted) and joint distributional alignment via maximum mean discrepancy (MMD) across multiple kernel bandwidths. A UMAP sensitivity analysis complemented standard PCA and t-SNE projections. The resulting pipeline produces interpretable synthetic data for augmenting scarce normal-operation time-series in safety-critical settings, with applicability beyond mining to industrial monitoring, energy systems, and healthcare analytics.