A Cross-Condition Time–Frequency Measurement Modeling Framework for Health State Estimation in Nonstationary Industrial Systems
Abstract
Measurement signals in industrial systems are often affected by nonstationarity, making reliable health state estimation challenging. These signals exhibit temporal dynamics reflecting sequential variations and spectral patterns associated with periodic behaviors. Across operating conditions, the distributions of these measurement signals may shift, reducing the reliability of measurement interpretation and health state estimation. In this work, we model historical multivariate sensor measurements to estimate future values of monitored variables. For prognostic tasks, these measurements characterize degradation evolution, with remaining useful life (RUL) serving as a degradation-related quantity for health state estimation. To this end, we propose a dual-branch time–frequency interaction network (DTFINet) for robust measurement-signal modeling and estimation under nonstationary and cross-condition settings. The proposed framework consists of three key components: 1) a temporal structural encoding (TSE) module to capture local dynamic variations; 2) an adaptive frequency-band selection (AFS) mechanism to identify task-relevant spectral components; and 3) a learnable cross-domain fusion (LCF) strategy to enhance interaction between temporal and spectral representations. These designs enable effective modeling of both periodic and transient characteristics in measurement signals, improving robustness under varying operating conditions. Across seven public benchmarks, DTFINet achieves the lowest mean squared error (mse) or mean absolute error (MAE) in 41 of 56 comparisons. On C-MAPSS, DTFINet reduces the average root mse (RMSE) for RUL estimation by 26.2 % relative to the taskwise best external baselines over 12 cross-condition tasks. On PHM2012, it reduces the average RMSE for RUL estimation by 13.0 % relative to the best external baseline in terms of average RMSE over six cross-condition tasks.