Mean Variance Estimation Neural Network Particle Filter for
Predicting Battery Remaining Useful Life
Francesco Cancelliere
1
, Sylvain Girard
2
, Jean-Marc Bourinet
3
, Piero Baraldi
4
, Enrico Zio
5
1,2
PHIMECA, Paris, 75012, France
cancelliere@phimeca.com
girard@phimeca.com
1,3
SIGMA Clermont University, Aubiere, 63178 , France
jean-marc.bourinet@sigma-clermont.fr
4,5
Politecnico di Milano, Milano, 20161 , Italy
piero.baraldi@polimi.it
enrico.zio@polimi.it
5
MINES Paris, PSL Research University, 06904 Sophia Antipolis, France
ABSTRACT
Traditional remaining useful life (RUL) prediction methods
based on particle filter (PF) require the manual tuning of hy-
perparameters, such as process or measurement noise, which
poses challenges, particularly in real-life applications where
external and operating conditions may change, potentially lead-
ing to large errors in the predictions. We address this issue
by replacing the measurement equation of a PF with a mean
variance estimation neural network that estimates the mean
and the variance of the output distribution. As a result, the
measurement noise is automatically estimated by the neural
network and does not require manual setting. Through sim-
ulations and comparative analyses with state-of-the-art meth-
ods, the proposed mean variance estimation neural network
particle filter (MVENN-PF) is shown to provide more stable
and accurate RUL predictions, thereby potentially enhancing
the robustness of battery health management systems based
on it. Additionally, by eliminating the need to manually set a
model hyperparameter (the measurement noise) the proposed
method simplifies the modeling process, making it more ac-
cessible and adaptable to various battery systems.
1. INTRODUCTION
Predicting the remaining useful life of batteries allows op-
timizing maintenance schedules, and, therefore, reducing
downtime and avoiding unexpected failures (Tran et al.,
Francesco Cancelliere et al. This is an open-access article distributed un-
der the terms of the Creative Commons Attribution 3.0 United States Li-
cense, which permits unrestricted use, distribution, and reproduction in any
medium, provided the original author and source are credited.
2022). This is a fundamental step for ensuring the longevity
and optimal performance of batteries (Hu, Xu, Lin, & Pecht,
2020), which is a key element for the safety, cost effi-
ciency, and sustainability of several industrial systems, such
as electric vehicles and renewable energy storage (Chen et al.,
2021).
Traditional model-based methods for RUL prediction rely
heavily on physical models, which are not always available
or accurately reflective of real-world conditions (Zio, 2022).
Considering battery degradation, they may struggle to adapt
to the stochastic nature of the process, which is influenced
by numerous factors, including usage patterns, environmental
conditions, and manufacturing variations. Particle filters (PF)
(Kantas, Doucet, Singh, & Maciejowski, 2009) have been
widely used for state estimation in dynamic systems. They
suffer from issues such as particle degeneracy and the need of
setting the hyperparameters process and measurement noise.
Data-driven approaches based on machine learning tech-
niques use signal measurements to predict component present
and future state of health and RUL (Wu, Fu, & Guan, 2016).
They have been shown able to learn complex degradation pat-
terns from historical data (Wang et al., 2021). Also, they are
more adaptable and accurate in case of variation of external
and operating conditions. However, they typically require
large amounts of data to generalize effectively and struggle
to describe unseen situations.
Hybrid methods such as physics-informed neural networks
(PINNs) (Nascimento, Corbetta, Kulkarni, & Viana, 2021)
and the combination of filter algorithms with machine learn-
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