Artificial signal prediction

Industrial monitoring systems require reliable sensor data for condition monitoring, fault diagnosis, and predictive maintenance. This study proposes an integrated virtual-sensing framework for reconstructing rotational speed from torque measurements when speed signals are unavailable. The method combines industrial data preprocessing, speed calculation, interpolation-based temporal synchronization, Exponential Moving Average (EMA) filtering, min–max normalization, and Recursive Least Squares (RLS) prediction. The framework was evaluated on the Multi-mode Fault Diagnosis Dataset of Gearbox Under Variable Working Conditions using a chronological 70/30 train–test split across four independent gearbox measurements. Its performance was compared with Linear Regression (LR), Support Vector Regression (SVR), and Multi-Layer Perceptron (MLP) models. The proposed EMA + RLS approach achieved the best overall results, with a mean R 2 of 0.9391 ± 0.0427, RMSE of 81.0466 ± 83.5874 RPM, and MAE of 56.1234 ± 47.0097 RPM. Analysis of the EMA smoothing parameter showed that low-to-moderate smoothing provides an effective trade-off between noise reduction and prediction accuracy. These results demonstrate that combining industrial preprocessing with adaptive recursive estimation enables accurate, transparent, and computationally efficient speed-signal reconstruction from torque data under controlled signal-unavailability conditions.