Comparing Feature and Trajectory-Based Remaining Useful Life
Modeling of Electrical Resistance Heating Wires
Simon M
¨
ahlkvist
1
, Wilhelm S
¨
oderkvist Vermelin
2
, Thomas Helander
3
, and Konstantinos Kyprianidis
4
1,3
Kanthal AB, Hallstahammar, V
¨
astmanland, 734 27, Sweden
simonmkvst@gmail.com
2
RISE Research Institutes of Sweden, M
¨
olndal, V
¨
astra G
¨
otaland, 431 53, Sweden
wilhelm.soderkvist.vermelin@ri.se
1,2,4
M
¨
alardalens University, V
¨
aster
˚
as, V
¨
astmanland, 721 23, Sweden
ABSTRACT
Industrial heating significantly contributes to global green-
house 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 reliabil-
ity and sustainability through predictive maintenance strate-
gies.
The integration of machine learning technologies into Prog-
nostics and Health Management has significantly improved
the precision and applicability of Remaining Useful Life
modeling. This improvement enables more accurate predic-
tions of component lifespans, optimizes maintenance sched-
ules, 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 Use-
ful Life modeling for industrial batch processes. It evaluates
and compares two methodologies: deep learning-based ap-
proaches using full time-series data, such as recurrent neural
networks and their variants, and feature-engineering-based
methods, including random forest regression and support vec-
tor machines. Our results show that the feature-oriented ap-
proach 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 sys-
Simon M
¨
ahlkvist et al. This is an open-access article distributed under the
terms of the Creative Commons Attribution 3.0 United States License, which
permits unrestricted use, distribution, and reproduction in any medium, pro-
vided the original author and source are credited.
tems. 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 out-
liers. 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 vary-
ing levels of degradation, a helpful characteristic for Prog-
nostics and Health Management systems. While feature-
oriented methods tend to systematically underestimate Re-
maining 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 main-
tenance strategies.
1. INTRODUCTION
Industrial heating is a significant green house gas (GHG)
emitter, contributing to approximately 22% of annual global
emissions (Yoro & Daramola, 2020). Resistance heating
wires play a crucial role in industrial electrical heating sys-
tems and offer a substantial opportunity for the heating in-
dustry’s transition towards fossil-free operations.
In the prognostics and health management (PHM) field, the
focus on maintaining industrial processes is continuously
evolving. Specifically, within PHM, predictive maintenance
strategies leverage data-driven modeling techniques, leading
to the development of remaining useful life (RUL) prediction
models.
The advent of machine learning (ML) technologies has sig-
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