Dynamic forecasting of beef freshness using multi-step time series analysis of electronic nose signals

The preservation of microbial quality in meat products represents a fundamental challenge in contemporary food supply chain management due to the highly perishable nature of these commodities. Although modern testing techniques, particularly electronic nose (E-nose), have shown considerable promise in real-time assessment of freshness status, most applications remain limited to static evaluation rather than dynamic forecasting of future quality trajectories, constraining proactive decision-making processes. To overcome this diagnostic-predictive gap, we propose a framework that integrates E-nose sensing with multi-step time-series forecasting, thereby transforming meat quality monitoring from real-time diagnosis to predictive modeling. In particular, we design an enhanced dual stage attention-based recurrent neural network tailored to microbial growth dynamics and the specific characteristics of E-nose signals, such as limited sample sizes, non-stationary temporal patterns, and gradual signal evolution. Furthermore, the proposed model is further validated on twelve beef regions to ensure robust generalization across heterogeneous tissue-specific spoilage patterns. The experimental results demonstrate that the model is capable of multi-step Total Viable Count (TVC) forecasting across horizons from 1 to 9 h. For 1-h short-term prediction, the model can achieve a mean R² of 0.950 with an RMSE of 0.097, while for long-term forecasting (9 h), it still maintained an R² above 0.859 across 12 tissues, demonstrating both superior predictive accuracy and sustained temporal stability. In summary, this work establishes a time-series forecasting framework that leverages sensor-derived signal trajectories to capture microbial growth dynamics and the evolution of TVC within beef. By advancing freshness evaluation from static detection to predictive modeling with hour-level resolution, the approach enables reliable estimation of remaining shelf life and provides a quantitative paradigm for meat quality management.