Hybrid approaches that combine data-driven learning with physics-based insight have shown promise for improving the reliability of industrial condition monitoring. This work develops a hybrid condition monitoring framework that integrates primary sensor measurements, lagged temporal features, and physics-informed residuals derived from nominal surrogate models. Two hybrid integration strategies are examined. The first is a feature-level fusion approach that augments the input space with residual and temporal information. The second is a model-level ensemble approach in which machine learning classifiers trained on different feature types are combined at the decision level. Both hybrid approaches of the condition monitoring framework are evaluated on a continuous stirred-tank reactor (CSTR) benchmark using several machine learning models and ensemble configurations. Both feature-level and model-level hybridization improve diagnostic accuracy relative to single-source baselines, with the best model-level ensemble achieving a 2.9% improvement over the best baseline ensemble. To assess predictive reliability, conformal prediction is applied to quantify coverage, prediction-set size, and abstention behavior. The results show that hybrid integration enhances uncertainty management, producing smaller and well-calibrated prediction sets at matched coverage levels. These findings demonstrate that lightweight physics-informed residuals, temporal augmentation, and ensemble learning can be combined effectively to improve both accuracy and decision reliability in nonlinear industrial systems.
Figures & tables
Fig. 1: The framework of the proposed method (icons from Flaticon)
Fault ID
Description
Value of δ
Interpretation
1
a=a0exp(−δt)
0.004
Catalyst decay
2
b=b0exp(−δt)
0.005
Heat transfer fouling
3
Ci=Ci,0+δt
0.005
Sensor shift
4
Ti=Ti,0+δt
0.1
Sensor shift
5
Tci=Tci,0+δt
0.1
Sensor shift
6
C=C0+δt
0.005
Sensor shift
TABLE I: Fault scenarios of the CSTR process
Models
Model
Accuracy
Precision
Recall
F1-score
ML Models
RF
0.9549
0.9597
0.9549
0.9562
XGBoost
0.9587
0.9621
0.9587
0.9597
CatBoost
0.9560
0.9608
0.9560
0.9574
MLP
0.9507
0.9620
0.9507
0.9533
Ensemble
Soft Voting
0.9596
0.9644
0.9596
0.9608
Weighted Soft Voting
0.9596
0.9644
0.9596
0.9608
TABLE II: Performance Comparison of Base and Ensemble Models on the Primary Data
Feature Set
Accuracy
Precision
Recall
F1-score
Base
0.9605
0.9652
0.9605
0.9615
Base + Lag
0.9834
0.9848
0.9834
0.9837
Base + Residual
0.9789
0.9806
0.9789
0.9793
Base + Lag + Residual
0.9894
0.9900
0.9894
0.9896
TABLE III: Fault classification performance using feature-level hybrid enhancement (Stacking (LogR)). Residuals and lagged measurements are integrated directly into the feature space.
Ensemble
Model
Accuracy
Precision
Recall
F1-score
Feature-Level
Soft Voting
0.9884
0.9894
0.9884
0.9886
Weighted Soft Voting
0.9884
0.9894
0.9884
0.9886
Hard Voting
0.9865
0.9880
0.9865
0.9869
Stacking (LogR)
0.9894
0.9900
0.9894
0.9896
Stacking (RF)
0.9891
0.9895
0.9891
0.9892
Parallel
Soft Voting
0.9810
0.9834
0.9810
0.9816
TABLE IV: Performance Comparison of Different Ensemble Models of Model-based and Data-driven methods.
Fig. 2: Accuracy comparison of different ensemble models
Fig. 3: Confidence and prediction set size comparison using stacking (LogR) ensemble
Representation
α=0.1
α=0.01
Cov.
∣C(x)∣
Cov.
∣C(x)∣
Base
0.9103
0.9231
0.9919
1.2277
Base + Lag
0.9034
0.9047
0.9896
1.0312
Base + Residual
0.9149
0.9174
0.9939
1.1502
Base + Lag + Res
0.9072
0.9073
0.9911
1.0037
Parallel
0.9050
0.9054
0.9927
1.0127
TABLE V: Conformal prediction performance at different miscoverage levels. Coverage (Cov.) and average prediction set size ( ∣C(x)∣ ) quantify uncertainty behavior.
Department of Chemical and Biological Engineering University of British Columbia Vancouver, BC, Canada · School of Computing and Artificial Intelligence Jiangxi University of Finance and Economics Nanchang, China · School of Automation Chongqing University Chongqing, China +2
School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, China · Research Center, East Hope Group Co., Ltd, Shanghai, China
Department of Information Engineering, University of Padova, Padova, Italy · Newtwen S.r.l., Padova, Italy · Infineon Technologies Dresden GmbH & Co. KG, Dresden, Germany +1