Adaptive Wavelet Normalization Network for Soft Sensor Modeling in Nonstationary Industrial Processes

In industrial processes, accurate, real-time soft sensor modeling of key product indices is essential for optimal process control and improved product quality. However, the nonstationary characteristics inherent in industrial data, i.e., data distribution drift over time, cause significant challenges to soft sensor modeling. Existing normalization methods in the modeling procedure often rely on global static statistics, which fail to represent local statistical variations and result in poor predictive performance for soft sensor models in nonstationary environments. To overcome this limitation, we propose a novel plug-and-play normalization method named adaptive wavelet normalization network (AWNN) for soft sensor modeling in nonstationary industrial processes. Our method first utilizes the wavelet transform to identify nonstationary points and adaptively slices the input time series. Subsequently, fine-grained normalization is applied to each segment based on its local statistical properties. Finally, an attention-based BiLSTM predicts the statistical properties of the corresponding output window. This prediction enables accurate adaptive denormalization of the soft sensor model’s output. Extensive experiments validated AWNN’s effectiveness, demonstrating its ability to significantly improve the predictive performance across diverse soft sensor architectures. Moreover, it consistently outperforms traditional normalization methods when dealing with nonstationary data. Its plug-and-play nature facilitates seamless integration, offering a versatile and effective solution for improving soft sensor reliability under complex industrial environments.