A VMD-Prior-Guided Adaptive Learning Method for Multi-step Industrial Time Series Forecasting

Multi-step industrial time series forecasting is crucial for production scheduling and predictive maintenance. However, industrial data often contain noise, nonstationarity, and multiscale patterns, which make accurate prediction more difficult. Although signal decomposition is an effective approach to address this issue, its practical application faces a dilemma: offline decomposition may cause data leakage and violate deployment constraints, while online rolling decomposition is computationally expensive and prone to boundary effects, reducing predictive accuracy. To address these challenges, this paper proposes a Variational Mode Decomposition (VMD) prior-guided adaptive prediction network (VPALNet). The model uses VMD to construct modal anchors as physical supervision signals. Combined with frequency alignment loss and time-frequency orthogonality constraints, it guides the network to learn implicit mode decomposition. Based on this, the model first uses a shared encoder to integrate window-level statistical features. Then, multiple prediction heads capture the dynamic characteristics of different modes. Finally, a gating network adaptively fuses the predictions from all modes. This approach enables efficient, reliable industrial time series forecasting without online decomposition. Experiments on three real-world industrial datasets across multiple forecasting horizons show that VPALNet achieves superior forecasting accuracy in most cases, reducing MSE by up to 22.6% compared to state-of-the-art baselines.