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Industrial heating significantly contributes to global greenhouse gas emissions, accounting for a substantial portion of annual emissions. The transition to fossil-free operations in the heating industry is closely linked to advancements in industrial electrical heating systems, especially those using resistance heating wires. In this context, Prognostics and Health Management is crucial for enhancing system reliability and sustainability through predictive maintenance strategies. The integration of machine learning technologies into Prognostics and Health Management has significantly improved the precision and applicability of Remaining Useful Life modeling. This improvement enables more accurate predictions of component lifespans, optimizes maintenance schedules, and enhances operational efficiency in industrial heating applications. These developments are essential for reducing greenhouse gas emissions in the sector. This paper serves as a guide for conducting Remaining Useful Life modeling for industrial batch processes. It evaluates and compares two methodologies: deep learning-based approaches using full time-series data, such as recurrent neural networks and their variants, and feature-engineering-based methods, including random forest regression and support vector machines. Our results show that the feature-oriented approach performs better overall in terms of predictive accuracy and computational efficiency. The study includes a detailed sensitivity analysis and hyperparameter estimation for each method, providing valuable insights into developing robust and transparent Prognostics and Health Management systems. These systems are crucial in supporting the heating industry’s move towards more sustainable and emission-free operations. The findings reveal that feature-oriented methods are both performant and robust, particularly excelling in handling outliers. The random forest regression model, in particular, demonstrated the highest performance on the test dataset according to the chosen evaluation metrics. Conversely, trajectory-oriented methods exhibited less bias across varying levels of degradation, a helpful characteristic for Prognostics and Health Management systems. While feature-oriented methods tend to systematically underestimate Remaining Useful Life at high true values and overestimate it at low actual values, this issue is less pronounced in trajectory-oriented models. Overall, these insights highlight the strengths and limitations of each approach, guiding the development of more effective and reliable predictive maintenance strategies.

In industrial machine learning, predictive performance alone is insufficient to ensure reliable deployment, as model behaviour may vary across different regions of the input space under limited data and evolving process conditions. This work investigates whether such variation can be systematically analysed through post-hoc methods. A model-agnostic framework is proposed in which interpretability metrics, including residuals and feature attributions, are embedded into a low-dimensional space and approximated using a continuous surrogate model. This representation enables the analysis of model behaviour as a structured landscape, rather than as isolated pointwise explanations. The approach is applied to ceramic heating element production, where two distinct regimes are identified. One corresponds to a stable region with consistent and accurate predictions, while the other reflects a transitional regime associated with increased ambiguity and sensitivity to feature interactions. These regimes are shown to align with known process conditions and temporal variation. The results demonstrate that model behaviour can be organised into coherent regions that are not observable through aggregate performance metrics alone. This provides a structured basis for post-hoc analysis, supporting targeted interpretation and further investigation of model reliability in industrial settings.

The paradigm change of Industry 4.0 brings attention to data-driven modeling and the incentive to apply machine learning methods in the process industry. Further, capitalizing on a great deal of data available is an adverse task. For batch processes, the dataset is in a threeway format (Batch × Sensor × Time). Depending on the process and the goal of the analysis, it might be necessary to aggregate batches together. For this reason, a campaign unfolding structure is applied. By grouping the batches under new labels relevant to the analytical goal, campaigns are created. These labels can be created from periodical occurrences, such as refurbishing the refractory lining in the case of the case study. In order to utilize the three-way batch format, it is necessary to align the batches. In order to address this, the feature-oriented approach Statistical Pattern Analysis (SPA) is applied. SPA derives statistics, e.g., mean, skewness and kurtosis from the time series, consequently aligning the batches. The SPA and the campaign approach create a dataset consisting of select statistics instead of an irregular three-way array. Functional data analysis (FDA) is used to smooth and extract first- and second-order derivative information from the sensors in which functional behavior can be observed before creating features. Principal Component Analysis (PCA) is used to examine the final dataset. Further, industrial processes are notoriously nonlinear, and even more so batch processes. Therefore, kernel-based principal component analysis (KPCA) is used to review the final dataset. The KPCA can accommodate different underlying characteristics by modifying the kernel function used. 

In this work, cost-sensitive decision support was developed. Using Batch Data Analytics (BDA) methods of the batch data structure and feature accommodation, the batch process property and sensor data can be accommodated. The batch data structure organises the batch processes' data, and the feature accommodation approach derives statistics from the time series, consequently aligning the time series with the other features. Three machine learning classifiers were implemented for comparison: Logistic Regression (LR), Random Forest Classifier (RFC), and Support Vector Machine (SVM). It is possible to filter out the low-probability predictions by leveraging the classifiers' probability estimations. Consequently, the decision support has a trade-off between accuracy and coverage. Cost-sensitive learning was used to implement a cost matrix, which further aggregates the accuracy-coverage trade into cost metrics. Also, two scenarios were implemented for accommodating out-of-coverage batches. The batch is discarded in one scenario, and the other is processed. The Random Forest classifier was shown to outperform the other classifiers and, compared to the baseline scenario, had a relative cost of 26%. This synergy of methods provides cost-aware decision support for analysing the intricate workings of a multiprocess batch data system.

This study conducts a sensitivity analysis to evaluate the influence of varying datavolumes on model performance within multi-product batch processes in the iron and steelindustry. Nine machine learning models, encompassing both ensemble and parametric methods,were rigorously tested using a data withholding approach. The results demonstrate thatensemble models, particularly Random Forest and Gradient Boosting, consistently outperformedparametric models across different data volumes, showcasing superior generalisation androbustness to outliers. These findings underscore the importance of careful model selection andcomprehensive data preprocessing in enhancing model performance and suggest that ensemblemethods are particularly well-suited for complex industrial applications where data quality andvolume are critical.

This paper applies a post-hoc analytical framework to investigate degradation behaviour in industrialelectrical heating systems. A feature-based representation of resistance trajectories is used to train aremaining useful life (rul) model, after which interpretability metrics are mapped onto a reduced latentspace to examine model confidence, systematic deviation and lifetime-dependent structure. The analysisreveals distinct operational regimes corresponding to early, middle and late degradation phases, andhighlights how local and global statistical descriptors contribute differently to the separation of thesephases. The results demonstrate how post-hoc model analysis can support the extraction of processrelevant mechanisms and provide structured guidance for model interpretation in industrial settings.