Deep Koopman Kalman Filter for Nonlinear Model-Free Industrial Process Data Denoising and Its Soft Sensing Application

Data-driven modeling of industrial processes is fundamental for predictive maintenance of key equipment and optimization of process operations, playing a crucial role in ensuring high quality production. However, the harsh environments of industrial settings often result in process data being heavily contaminated with noise, significantly impairing the accuracy of modeling. Unfortunately, existing denoising methods are predominantly developed for scenarios with well-defined models. This renders them ineffective for complex industrial processes. To address this problem, this article proposes a deep Koopman Kalman filter (DKKF) for nonlinear model-free industrial process data denoising. First, DKKF defines a discrete dynamic system capable of conducting explicit Kalman filtering. This discrete system models the dynamics via the Koopman operator. Transition noise represents the approximation error of the Koopman operator, while observation noise is directly estimated from the observations. Then, the explicit implementation of the Kalman filter by the DKKF, both during training and inference phases, significantly enhances the accuracy and interpretability of the model. Moreover, a three-stage training strategy is defined for DKKF, which effectively addresses issues of slow training speed and gradient explosion. Finally, the effectiveness of the proposed method is validated on the Lorenz system and a real-world industrial process dataset. Notably, the denoised industrial process data is used for soft sensor modeling, resulting in more accurate prediction results compared to some existing representative methods.