Cointegration analysis [1,2], as an effective method of time series analysis in econometrics, has been introduced to non-stationary processes monitoring in recent years [3]. Traditional cointegration analysis, which relies on linear combinations to eliminate non-stationarity, faces significant limitations when confronts with complex industrial features, including nonlinear interactions [4], long-term memory effects, and multi-order integration properties. Nonlinear cointegration extends the linear cointegration by incorporating nonlinear mappings to extract nonlinear long-term equilibrium relationships and considering the long memory of time series [5]. To address the limitation of traditional cointegration analysis, a nonlinear cointegration-based monitoring framework, leveraging a Long Short-Term Memory [6] (LSTM)-based encoder-decoder model is proposed in this work. By imposing stationarity and short memory constraints on latent variables, the model ensures complex feature extraction effectively while preserving nonlinear long-term equilibrium properties. The extracted features are then utilized to construct monitoring statistics, enabling effective process monitoring. The proposed method is evaluated by both a numerical case and an industrial case, demonstrating its effectiveness in enhancing process monitoring performance compared to conventional non-stationary process monitoring approaches.
References:
[1] Engle, R. F.; Granger, C. W. Co-integration and error correction: representation, estimation, and testing. Econometrica: journal of the Econometric Society.1987, 251-276.
[2] Granger, C. W. Some properties of time series data and their use in econometric model specification. Journal of econometrics.1981, 16(1), 121-130.
[3] Chen, Q., Kruger, U., & Leung, A. Y. Cointegration testing method for monitoring nonstationary processes. Industrial & Engineering Chemistry Research. 2009, 48(7), 3533-3543.
[4] Lou S, Yang C, Zhang X, et al. Blast furnace ironmaking process monitoring with time-constrained global and local nonlinear analytic stationary subspace analysis[J]. IEEE Transactions on Industrial Informatics, 2023, 20(3): 3163-3176.
[5] Escanciano, J. C., & Escribano, A. Econometrics: Non-linear Cointegration. 2009.
[6] Greff, K., Srivastava, R. K., Koutník, J., Steunebrink, B. R., & Schmidhuber, J. (2016). LSTM: A search space odyssey. IEEE transactions on neural networks and learning systems. 2016, 28(10), 2222-2232.
