Drift-Aware Online Dynamic Learning for Nonstationary Multivariate Time Series: Application to Sintering Quality Prediction
Authors: Yumeng Zhao, Shengxiang Yang, Xianpeng Wang
Organizations: the National Frontiers Science Center for Industrial Intelligence and Systems Optimization, Northeastern University, Shenyang, China · De Montfort University, Leicester, U.K. · Innovative Artificial Intelligence Cluster, Digital Future Institute, De Montfort University, Leicester, U.K. · Key Laboratory of Data Analytics and Optimization for Smart Industry (Northeastern University), Ministry of Education, Shenyang, China
Accurate prediction of nonstationary multivariate time series remains a critical challenge in complex industrial systems such as iron ore sintering. In practice, pronounced concept drift compounded by significant label verification latency rapidly degrades the performance of offline-trained models. Existing methods based on static architectures or passive update strategies struggle to simultaneously extract multi-scale spatiotemporal features and overcome the stability-plasticity dilemma without immediate supervision. To address these limitations, a Drift-Aware Multi-Scale Dynamic Learning (DA-MSDL) framework is proposed to maintain robust multi-output predictive performance via online adaptive mechanisms on nonstationary data streams. The framework employs a multi-scale bi-branch convolutional network as its backbone to disentangle local fluctuations from long-term trends, thereby enhancing representational capacity for complex dynamic patterns. To circumvent the label latency bottleneck, DA-MSDL leverages Maximum Mean Discrepancy (MMD) for unsupervised drift detection. By quantifying online statistical deviations in feature distributions, DA-MSDL proactively triggers model adaptation prior to inference. Furthermore, a drift-severity-guided hierarchical fine-tuning strategy is developed. Supported by prioritized experience replay from a dynamic memory queue, this approach achieves rapid distribution alignment while effectively mitigating catastrophic forgetting. Long-horizon experiments on real-world industrial sintering data and a public benchmark dataset demonstrate that DA-MSDL consistently outperforms representative baselines under severe concept drift. Exhibiting strong cross-domain generalization and predictive stability, the proposed framework provides an effective online dynamic learning paradigm for quality monitoring in nonstationary environments.
Figures & tables
Fig. 1: Schematic diagram of the sintering process.
Fig. 2: Overall architecture of the DA-MSDL framework. The pipeline integrates Data Preprocessing (Step 1), Drift Detection and Adaptive Fine-tuning (Step 2), and MS-BCNN Feature Extraction (Step 3), supported by the Dynamic Memory Queue and Stable Error Fine-tuning modules.
Describe the raw-material composition and blending conditions before sintering
Process & Thermal Parameters
Ignition temperature; exhaust gas temperature; burn-through point (BTP); main-line and furnace negative pressures; coal-gas flow rate and pressure; air flow rate and pressure
Reflect combustion intensity, heat-transfer behavior, and airflow dynamics
Equipment & Environment
Sintering machine speed; pallet speed; bed height; finished-product weight; production output
Indicate equipment operating status and system-level production conditions
Output Targets
TFe, FeO, SiO 2 , CaO, basicity
Key chemical quality indicators obtained from laboratory assays
TABLE I: Feature categories and representative variables in the sintering dataset.
Fig. 5: MMD-based drift trend during the online detection stage.
Model
NMSE
NMAE
MAPE (%)
DA-MSDL
0.2423±0.1542
0.3052±0.1521
1.09±0.04
OB-ISSID
0.3044±0.2006
0.3809±0.1353
1.31±0.07
Ventingformer
0.2793±0.1989
0.3656±0.1364
1.25±0.07
Transformer
0.4564±0.1766
0.4829±0.1028
1.65±0.17
LSTM
0.3803±0.2204
0.4213±0.1419
1.44±0.08
GRU-PLS
0.4618±0.1707
0.5120±0.0821
1.74±0.08
TABLE II: Overall predictive performance on the shuffled dataset (mean ± standard deviation).
Model
Label
MSE
MAE
MAPE (%)
R2
DA-MSDL
TFe
0.060832 ± 0.006063
0.180206 ± 0.008479
0.320033 ± 0.015002
−0.26131±0.125718
FeO
0.118038 ± 0.006595
0.246699 ± 0.008104
2.682173 ± 0.089205
0.077400 ± 0.051546
SiO 2
0.006607 ± 0.001714
0.056760 ± 0.006537
1.028868 ± 0.117734
0.662256 ± 0.087604
CaO
0.036010 ± 0.003603
0.129945 ± 0.007947
1.092134 ± 0.067053
0.466945 ± 0.053337
Basicity
0.000536 ± 0.000036
0.016871 ± 0.000561
0.784819 ± 0.026099
0.212011 ± 0.053578
Overall Mean
0.768453 ± 0.318736
0.612549 ± 0.145467
1.181605 ± 0.063019
0.231459 ± 0.074357
TABLE III: Predictive performance comparison on the five quality targets (mean ± standard deviation).
Fig. 6: Error scatter distribution illustrating the prediction stability across labels.
Fig. 7: Time-series prediction comparison: true values vs. predicted values for the five quality targets on the test set across different models.
Model
NMSE
NMAE
MAPE (%)
DA-MSDL
0.7693±0.1328
0.5502±0.1954
0.55±0.03
OB-ISSID
1.3479±0.4521
0.6145±0.2545
0.63±0.04
Ventingformer
1.7582±0.9545
0.8336±0.7451
0.85±0.10
Transformer
4.3388±1.5265
1.6894±1.6541
1.71±0.24
LSTM
0.9525±0.4536
0.6247±0.2654
0.64±0.04
GRU-PLS
1.3018±0.5562
0.7286±0.2684
0.74±0.05
TABLE IV: Overall predictive performance on the Water Treatment Plant dataset (mean ± standard deviation).
Fig. 8: Online MAE of MS-BCNN (static) and DA-MSDL (dynamic) on real-world production sequences. Dashed lines mark detected concept drift events where online adaptation is triggered.
Fig. 9: Error difference ( ΔError ) between MS-BCNN and DA-MSDL over time. Persistent positive values indicate consistent gains from dynamic adaptation.
Fig. 10: Component-wise ablation of DA-MSDL measured by overall NMSE. The results show how each component affects prediction performance under nonstationary conditions.
Fig. 11: Recovery-time distribution under different drift severity levels.
Fig. 12: Sensitivity analysis of DA-MSDL with respect to key hyperparameters.
Online Time Series Forecasting (OTSF) requires models to continuously adapt to concept drift. However, existing methods often treat concept drift as a monolithic phenomenon. To address this limitation, we first redefine concept drift by categorizing it into two distinct types: Recurring Drift, where previously seen patterns reappear, and Emergent Drift, where entirely new patterns emerge. We then propose DynaME (Dynamic Multi-period Experts), a novel hybrid framework designed to effectively address this dual nature of drift. For Recurring Drift, DynaME employs a committee of specialized experts that are dynamically fitted to the most relevant historical periodic patterns at each time step. For Emergent Drift, the framework detects high-uncertainty scenarios and shifts reliance to a stable, general expert. Extensive experiments on several benchmark datasets and backbones demonstrate that DynaME effectively adapts to both concept drifts and significantly outperforms existing baselines.
Seungha Hong, Sukang Chae, Suyeon Kim +2
Pohang University of Science and Technology, Pohang, Republic of Korea · Kyungpook National University, Daegu, Republic of Korea
Real-world datasets often exhibit evolving distributions, known as concept drift. Ignoring drift degrades predictive performance, while reliance on fixed hyperparameters further limits model adaptability under changing conditions. Adaptive learning addresses this challenge by continuously updating models online, allowing them to incrementally adjust and remain effective as data distributions evolve. This paper presents the Stream Cruise Control Method (SCCM), a comprehensive framework for drift detection and adaptation in online regression. SCCM enables automated adaptation through early-response, pre-update drift detection, drift magnitude quantification, KPI-window-based thresholding for local false-alarm mitigation, dynamic hyperparameter tuning, and model recalibration. SCCM also adopts an in-memory design for real-time adaptability, unlike purely reactive methods that typically activate adaptation only after performance degradation is observed. By using dynamic thresholding and remaining agnostic to data distributions, SCCM supports KPI-based monitoring across varying data streams, including high-dimensional and large-scale settings. SCCM is integrated with four online regression models and evaluated on 18 synthetic datasets covering abrupt, incremental, and alternating gradual drift, together with eight real-world datasets. The evaluation uses both R2 and MSE and compares against eight detector--adaptation baselines. Results show improved predictive performance and effective drift handling across the evaluated online regression settings.
Mohammad Abu-Shaira, Weishi Shi
Department of Computer Science and Engineering, University of North Texas, 1155 Union Circle #311366, Denton, 76203, Texas, USA
Machine learning models deployed in real-world settings must operate under evolving data distributions and constrained computational resources. This challenge is particularly acute in non-stationary domains such as energy time series, weather monitoring, and environmental sensing. To remain effective, models must support adaptability, continuous learning, and long-term knowledge retention. This paper introduces a oblivious tree-based model with Hoeffding bound controlling its growth. It seamlessly integrates rapid learning and inference with efficient memory management and robust knowledge preservation, thus allowing for online learning. Extensive experiments across energy and environmental sensing time-series benchmarks demonstrate that the proposed framework achieves performance competitive with, and in several cases surpassing, existing online and batch learning methods, while maintaining superior computational efficiency. Collectively, these results demonstrate that the proposed approach fulfills the core objectives of adaptability, continual updating, and efficient retraining without full model retraining. The framework provides a scalable and resource-aware foundation for deployment in real-world non-stationary environments where resources are constrained and sustained adaptation is essential.
Daniel Bretsko, Piotr Walas, Devashish Khulbe +3
Masaryk University, Brno, Czech Republic · Warsaw University of Technology, Warsaw, Poland · Mycroft Mind, Brno, Czech Republic +2