Neural Cointegration With Relaxed Integration Orders and Stationarity Guarantees for Nonstationary Rotating Machinery Monitoring

Rotating machinery often operates under time-varying conditions. This can result in nonstationary behavior that violates the stationarity assumption underlying many fault monitoring methods. Cointegration analysis can address nonstationarity but assumes that all monitored variables are linearly related and integrated of order one. To overcome these limitations, this study reformulates the cointegration model in a functional-coefficient form. The coefficients therein are parameterized using neural networks to capture nonlinear relationships and accommodate variables with arbitrary integration orders. An iterative Bayesian inference algorithm is developed to estimate model parameters, with a stationarity constraint imposed on the cointegration error during estimation. This constraint mitigates overfitting to noise and enforces a consistent cointegration structure across varying noise levels. A heuristic fault isolation strategy is further introduced to eliminate the need for manual regularization. The effectiveness of the proposed method is validated through numerical simulations and two real-world cases involving large-scale rotating machinery.