Granger causality has emerged as a valuable tool in comprehending industrial processes and facilitating data modeling by unveiling the inherent relationships within the data. However, the characteristic of causality discovery tasks results in a lack of validation sets, making hyperparameter tuning reliant solely on intuition. Existing nonlinear Granger causality discovery methods suffer from insufficient accuracy and robustness due to the significant impact of hyperparameters. Hence, this article proposes an attribution-aided nonlinear Granger causality discovery method (Attri-NGC) for accurate and robust inference of Granger causality. Attri-NGC comprises two stages. In the first stage, a novel strategy is proposed to assess whether the variability in contributions, derived from deep learning-based attribution, can significantly reflect causality. This assessment transfers the robust advantage of attribution to causal discovery. In the second stage, a sparsity-inducing penalty targeted at ambiguous causality is defined to fine-tune the deep networks used for attribution. Our method transforms the paradigm of Granger causality discovery from a challenging deep networks training problem to a fine-tuning problem, leading to a substantial enhancement in the accuracy and robustness of causality discovery. The effectiveness of the proposed method is comprehensively validated on four public datasets and two industrial process datasets. The superior performance of Attri-NGC in supporting industrial process modeling effectively promotes the integration of Granger causality into practical applications for more interpretable process modeling.

In cloud manufacturing of industrial processes, the accurate online prediction of product quality is the basis for realizing decision-making and control of the manufacturing process. However, frequent fluctuations in working conditions and data noise restrict the application of data-driven methods in industrial sites. In addition, the constrained resources on edge devices limit their ability to automatically update or deploy complex models. To address these issues, this study proposes a Koopman-constrained hierarchical deep state-space model (KHSSM) and incorporates it into the innovative cloud-edge collaboration framework for industrial quality prediction. First, KHSSM integrates a state-space model, leveraging its advantage in modeling noisy dynamic data. Second, the Koopman operator is introduced to constrain the latent variables in the measurement space, enabling it to interpretably reflect the evolution dynamics of the system. In addition, novel strategies for model mismatch detection and model simplification are designed and deployed to improve the predictive accuracy and real-time efficiency of the cloud-edge collaboration framework. Finally, the effectiveness of the proposed method is verified by extensive experiments in a numerical simulation and a real-world industrial process.