Collaborative Training of Data-Driven Remaining Useful Life Prediction Models Using Federated Learning

Abstract

Remaining useful life prediction models are a central aspect of developing modern and capable prognostics and health management systems. Recently, such models are increasingly data-driven and based on various machine learning techniques, in particular deep neural networks. Such models are notoriously “data hungry”, i.e., to get adequate performance of such models, a substantial amount of diverse training data is needed. However, in several domains in which one would like to deploy data-driven remaining useful life models, there is a lack of data or data are distributed among several actors. Often these actors, for various reasons, cannot share data among themselves. In this paper a method for collaborative training of remaining useful life models based on federated learning is presented. In this setting, actors do not need to share locally held secret data, only model updates. Model updates are aggregated by a central server, and subsequently sent back to each of the clients, until convergence. There are numerous strategies for aggregating clients’ model updates and in this paper two strategies will be explored: 1) federated averaging and 2) federated learning with personalization layers. Federated averaging is the common baseline federated learning strategy where the clients’ models are averaged by the central server to update the global model. Federated averaging has been shown to have a limited ability to deal with non-identically and independently distributed data. To mitigate this problem, federated learning with personalization layers, a strategy similar to federated averaging but where each client is allowed to append custom layers to their local model, is explored. The two federated learning strategies will be evaluated on two datasets: 1) run-to-failure trajectories from power cycling of silicon-carbide metal-oxide semiconductor field-effect transistors, and 2) C-MAPSS, a well-known simulated dataset of turbofan jet engines. Two neural network model architectures commonly used in remaining useful life prediction, long short-term memory with multi-layer perceptron feature extractors, and convolutional gated recurrent unit, will be used for the evaluation. It is shown that similar or better performance is achieved when using federated learning compared to when the model is only trained on local data.

Full text

Collaborative Training of Data-Driven Remaining Useful Life
Prediction Models Using Federated Learning
Wilhelm S¨
oderkvist Vermelin1, Madhav Mishra2, Mattias P. Eng3, Dag Andersson4, and Konstantinos Kyprianidis5
1, 2, 3, 4 RISE Research Institutes of Sweden, M¨
olndal, V¨
astra G¨
otaland, 431 53, Sweden
wilhelm.soderkvist.vermelin@ri.se
madhav.mishra@ri.se
mattias.eng@ri.se
dag.andersson@ri.se
1, 5 M¨
alardalen University, V ¨
aster˚
as, V¨
astmanland, 722 18, Sweden
konstantinos.kyprianidis@mdu.se
ABSTRACT
Remaining useful life prediction models are a central aspect
of developing modern and capable prognostics and health
management systems. Recently, such models are increasingly
data-driven and based on various machine learning techniques,
in particular deep neural networks. Such models are noto-
riously “data hungry”, i.e., to get adequate performance of
such models, a substantial amount of diverse training data is
needed. However, in several domains in which one would like
to deploy data-driven remaining useful life models, there is a
lack of data or data are distributed among several actors. Of-
ten these actors, for various reasons, cannot share data among
themselves. In this paper a method for collaborative training
of remaining useful life models based on federated learning is
presented. In this setting, actors do not need to share locally
held secret data, only model updates. Model updates are aggre-
gated by a central server, and subsequently sent back to each
of the clients, until convergence. There are numerous strate-
gies for aggregating clients’ model updates and in this paper
two strategies will be explored: 1) federated averaging and
2) federated learning with personalization layers. Federated
averaging is the common baseline federated learning strategy
where the clients’ models are averaged by the central server
to update the global model. Federated averaging has been
shown to have a limited ability to deal with non-identically
and independently distributed data. To mitigate this problem,
federated learning with personalization layers, a strategy simi-
lar to federated averaging but where each client is allowed to
append custom layers to their local model, is explored. The
Wilhelm S
¨
oderkvist Vermelin 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, provided the original author and source are credited.
two federated learning strategies will be evaluated on two
datasets: 1) run-to-failure trajectories from power cycling of
silicon-carbide metal-oxide semiconductor field-effect tran-
sistors, and 2) C-MAPSS, a well-known simulated dataset of
turbofan jet engines. Two neural network model architectures
commonly used in remaining useful life prediction, long short-
term memory with multi-layer perceptron feature extractors,
and convolutional gated recurrent unit, will be used for the
evaluation. It is shown that similar or better performance is
achieved when using federated learning compared to when the
model is only trained on local data.
1. INTRODUCTION
1.1. Background
A central aspect of robust and reliable preventive maintenance
systems is the ability to predict the failure of a component
ahead of time. This is often referred to as predictive main-
tenance (PdM)(Meriem, Nora, & Samir, 2023). One such
way to predict the end-of-life of a component is to develop
systems that can predict the remaining useful life (RUL) of a
component. The RUL is defined as the remaining time (mea-
sured in some appropriate unit) a system has left until it has
failed (Pecht & Kang, 2018). Here failure does not necessarily
mean critical failure, which is when the system has failed irre-
versibly such that one or several subcomponents are broken
beyond repair. Failure in this context can also mean either that
system degradation has progressed beyond the point that it
cannot reliably deliver the specified functionality, or that some
measured value has exceeded (or fallen below) some specifi-
cation threshold. RUL prediction models are either physical;
based on mathematical modeling of the physics of the system,
data-driven; meaning that the model is developed using data
International Journal of Prognostics and Health Management, ISSN2153-2648, 2024 1
https://doi.org/10.36001/IJPHM.2024.v15i2.3821

INTERNATIONAL JOURNAL OF PROGNOSTICS AND HEALTH MANAGEMENT
collected from the system, or hybrid; which means that the
model uses some combination of the two former. This pa-
per focuses on data-driven models, specifically deep learning
models, a type of machine learning models, designed for the
prediction of RUL.
Machine learning (and especially deep learning models) can
achieve good performance on a wide range of tasks, given suf-
ficient access to diverse training data (Hestness et al., 2017).
However, in many prognostics problems data availability is
an issue, limiting the applicability of deep learning models.
Another challenge is that when data are available, they are
often distributed among several actors. For decentralized and
heterogeneous data, it is common that data are sensitive and
not possible to share with a third party for prognostics model
development. When data sharing is not viable among actors
it can hinder the use of machine learning as each individual
actor may have insufficient data in the sense of dataset size
and diversity. In this scenario, cooperative training of the ma-
chine learning model can serve as a means for overcoming
the problem of sharing sensitive data. Cooperative training
of machine learning models can be achieved through Feder-
ated Learning (FL), a decentralized machine learning training
method. Despite the growing interest in FL, owing much to
its privacy-enhancing features as reported in Kairouz et al.
(2021), its adoption in the industrial domain, which includes
many PHM applications, is still relatively slow. This paper
will evaluate FL for PHM in two cases of RUL prediction;
simulated turbofan jet engines, and power electronics.
1.2. Federated Learning
FL is a framework for decentralized training of machine learn-
ing models. FL is used when, for various reasons, data cannot
be centralized at a single location, meaning traditional ma-
chine learning training is not possible. The basic structure of
FL involves a central server and a group of clients forming a
so-called federation. Each client has a local private partition
of data referred to as
Pk
, where
k
is one of
K
clients. The size
of the local partition is
→Pk→=nk
. The full global dataset
is denoted as
S
such that
S={Pk}K
k=1
. In the first step, the
global model is initialized with random parameters (referred to
as weights),
w0
, and then communicated to each client. Then,
each client trains their model on their own local, private, data
(
Pk
) for
E
epochs, and thus obtains an updated local model.
The updated local models are then communicated back to the
central server, which in turn aggregates all updated models
from all clients which forms the new global model. Finally,
the server communicates the new global model to all clients.
This is repeated until the global model has converged. FL has
the advantage that no client explicitly has to share their local
data, which enhances privacy, and has been used at scale in
several domains with good success, as reported in Q. Li et al.
(2023).
The algorithm governing aggregation of local updates at the
central server is called the FL strategy. There are numer-
ous notable strategies, which have different benefits depend-
ing on the dataset, model, and objectives (Moshawrab, Adda,
Bouzouane, Ibrahim, & Raad, 2023). The first strategy, pre-
sented by the original authors of FL, is called federated av-
eraging (FedAvg)(McMahan, Moore, Ramage, Hampson, &
Arcas, 2017). In this strategy, model updates from the clients
communicated to the server are aggregated by averaging the
results. The pseudocode for this algorithm is presented in
Algorithm 1.
Algorithm 1 Federated Averaging (FedAvg) algorithm. There
are
K
clients indexed by
k
,
m
is the batch size and
E
is
the number of local epochs.
nk
is the size of the local data
partition
Pk
,
L(w;b)
is the loss function for optimizing the
model, and ωis the learning rate.
Server executes:
Initialize w0
for each round t=1,2,...,T do
s↑max (C↓K, 1)
St↑(random set of sclients)
for each client k↔Stin parallel do
wk
t↑CLIENTUPDATE(wk
t→1,k)
st↑!k↑Stnk
wt↑!k↑St
nk
stwk
t
endfor
end for
function CLIENTUPDATE(w,k)εRun on client k
B↑(split Pkinto batches of size m)
for each local epoch ito Edo
for each batch b↔Bdo
w↑w↗ω↘L(w;b)
end for
end for
return w
end function
The FedAvg strategy is a good baseline strategy and performs
well on a wide range of problems and datasets. However,
the FedAvg strategy is known to be sensitive to highly non-
Independent and Identically Distributed (non-IID) data. This
poses a potential issue when applied to RUL prediction as
it is not uncommon that clients’ assets operate under vastly
different operating conditions, leading to local data partitions
with distributions that are not representative of the population
distribution. To ameliorate the performance of FedAvg on non-
IID data, several strategies have been proposed. For example,
a strategy referred to as Federated Learning with Personaliza-
tion Layers (FedPer), initially introduced and described by
Arivazhagan, Aggarwal, Singh, and Choudhary (2019). This
strategy is similar to FedAvg but with the addition that each
client can append custom (personalized) layers to the neural
network model which are not communicated with the central
server. The weights in the personalized layers for the
k
:th
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INTERNATIONAL JOURNAL OF PROGNOSTICS AND HEALTH MANAGEMENT
client are denoted as
wPk
, see Algorithm 2. In this paper, the
FedPer algorithm will be implemented as originally described,
without any major adaptations.
Algorithm 2 Federated Learning with Personalization Layers
(FedPer) algorithm. There are
K
clients indexed by
k
,
m
is
the batch size and
E
is the number of local epochs.
nk
is the
size of the local data partition
Pk
,
L(w;b)
is the loss function
for optimizing the model, and ωis the learning rate.
Initialize each client’s personal weights:
for each client k=1,2,...,K do
Initialize personal weights wPk,0
end for
Server executes:
Initialize base weights wB,0
for each round t=1,2,...,T do
s↑max (C↓K, 1)
St↑(random set of sclients)
for each client k↔Stin parallel do
wk
B,t ↑CLIENTUPDATE(wk
B,t→1,k)
st↑!k↑Stnk
wB,t ↑!k↑St
nk
stwk
B,t
endfor
end for
function CLIENTUPDATE(w,k)εRun on client k
B↑(split Pkinto batches of size m)
for each local epoch ito Edo
for each batch b↔Bdo
(wB,w
Pk)↑(wB,w
Pk)↗ω↘L(wB,w
Pk;b)
end for
end for
return wB
end function
The FedPer algorithm is also presented visually in Figure 1.
In the figure, each model consists of a “backbone” and a pre-
diction “head”. The backbone is the foundation of the model
and shared among all clients, whereas the prediction head
constitute the personalized layers. In the FedPer strategy, only
model backbones are communicated to the server, prediction
heads are not shared and stay at each client.
1.3. Related Work
To explore what research has been performed in the area of
federated learning for PHM and RUL prediction, a small-scale
literature review has been conducted using the Elsevier Scopus
database. To find relevant documents, the following search
string was used
TITLE-ABS-KEY({federated learning})
AND (TITLE-ABS-KEY ("prognos*")
OR TITLE-ABS-KEY("pred*maint*"))
AND TITLE-ABS-KEY ({remaining useful
life})
This search yielded nine results, where seven were published
in 2023, and the two other were published in 2021 and 2022,
Client
Local training
data
Server
Local Model
Backbone Head
Upload
Client
Local training
data
Local Model
Backbone Head
Upload
Download
.
.
.
Figure 1. A visual representation of the FedPer algorithm.
Each client’s model consists of a backbone and a head. The
FedPer algorithm relaxes the constraint that the entire model
is communicated to the server, and in this protocol only the
model backbone is shared.
respectively. Some of the retrieved documents will be dis-
cussed below.
Although the research area has not received a lot of attention
so far (only nine search results), there is clear evidence for the
potential of federated learning in various applications related
to PHM, predictive maintenance, and remaining useful life
prediction. For example,Dhada, Parlikad, and Palau (2020)
proposes the use of federated learning for predicting failures
in a simulated turbofan fleet, showing the effectiveness of the
(FedAvg) algorithm.
In Arunan, Qin, Li, and Yuen (2023), the authors address data
heterogeneity among edge devices, stemming from dissimilar
degradation mechanisms and unequal dataset sizes, which
poses a critical statistical challenge for developing accurate
FL-models. To mitigate this problem the authors propose a
FL-based health prognostic model which feature a similarity
matched parameter aggregation algorithm.
Similarly,Vibhorpandhare, Jia, and Lee (2021) use federated
learning to collaboratively train a federated learning model
based on Gaussian mixture models.
The article authored by Bemani and Bj
¨
orsell (2022) presents
two FL algorithms for predictive maintenance applications,
evaluated using C-MAPSS. The federated learning methods
demonstrate enhanced accuracy in anomaly detection and RUL
prediction compared to traditional centralized approaches,
while preserving privacy via local training.
One paper, by Kamei and Taghipour (2023), explores alterna-
tive federated learning strategies to mitigate data heterogeneity
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INTERNATIONAL JOURNAL OF PROGNOSTICS AND HEALTH MANAGEMENT
in clients’ local data partitions. In particular, the authors use
the so called FedProx strategy, first developed in Sahu et al.
(2018). The article analyzes prognostics approaches for net-
works of centralized assets by utilizing sensor data. The paper
compares a localized model with both FedAvg and FedProx
and using both LSTM and Transformer (Vaswani et al., 2017)
architectures to predict RUL, for both centralized and decen-
tralized scenarios using C-MAPSS data, with the Transformer
architecture outperforming LSTM overall. The paper explores
the effect of the number of clients in the federation on model
performance. A separate federation per CMAPSS data sub-
sets (FD001, FD002, FD003, FD004) is evaluated, and the
model is trained using one (central training), two, five, and
ten clients in the federation. The authors conclude that model
performance only slightly degraded in the federated setting,
showing that FL is promising for RUL prediction. Their main
contribution is showing that FL can still be effective while the
number of clients is large (and therefore, the local datasets are
small).
In the paper by Du et al. (2023), the authors also investigate
the transformer architecture and evaluated its performance for
RUL prediction on the C-MAPSS dataset. In addition, the
authors proposed a hyperparameter search scheme based on
Bayesian optimization.
In the paper by Guo et al. (2023), the authors propose sev-
eral FL strategies to train feature extraction models based on
convolutional autoencoders (CAE). The CAEs are trained to
extract low-level features from the data and subsequently each
client trains their own local RUL prediction model using local
data. In this way only the CAE are trained using FL and the
RUL prediction models are trained locally.
In the paper by Abdelli, Cho, and Pachnicke (2021) the authors
focused on the collaboration aspect of federated learning, and
applied federated learning to RUL estimation of a laser device.
During the development of this manuscript, a paper by X. Chen,
Wang, Lu, Xu, and Yan (2023) was published, exploring an
idea similar to FedPer for PHM. In this paper, the authors de-
velop a RUL prediction model based on the C-MAPSS dataset,
where each clients’ model has two parts, a feature extractor
(which they refer to as a “local health degradation representa-
tion” (LHDR)) and a “unique super-structure module”. The
LHDR is trained in a federated manner while the unique su-
per
-
structure module are kept private at each client and not
shared with the rest of the federation. This strategy is similar
to FedPer in that the “backbone” of the model is shared within
the federation, but personalized layers, also called model head,
is not shared with the federation. The paper also has a similar
setup where clients in the federation are the different subsets
of the C-MAPSS dataset. Their paper is limited to investiga-
tions on the C-MAPSS dataset, whereas this paper extends the
investigation to a dataset from a completely different domain.
As this paper also deals with PHM for electronics, a corre-
sponding focused literary analysis was conducted to investi-
gate the current state of research within this area.
Regarding PHM for electronics, there has been some work on
PHM for MOSFETs. For example,Ren et al. (2022), used a
Long Short-Term Memory (LSTM) model to predict the RUL
of thermally stressed MOSFETs. In particular, their approach
was evaluated on the public dataset for MOSFET prognos-
tics, introduced in Celaya, Saxena, Saha, and Goebel (2011).
Similarly,Haris, Hasan, Jahanzeb Hussain Pirzada, and Qin
(2020) applied a Bayesian optimized LSTM for prognostics of
thermally aged MOSFETs. In Demus et al. (2019), the authors
obtained MOSFET junction temperature measurements and
trained a support vector machine to predict the junction temper-
ature, as a proxy for system degradation. However, research
on PHM for electronics in a federated setting is lacking.
1.4. Contribution
The main contributions of this paper are twofold.
Firstly, this paper addresses federated learning in a PHM set-
ting where the clients are expected to have non-IID data. To
explore and mitigate this challenge this paper evaluates the
performance of the traditional FedAvg aggregation strategy
in compared to the FedPer strategy. To the authors’ knowl-
edge, there has been few or no works exploring personalization
layers in federated learning for PHM.
Secondly, this paper investigates federated learning and PHM
for electronics, in particular, power electronics in the form of
SiC MOSFET devices, an area that has not been extensively
explored earlier.
1.5. Datasets
This paper will explore the scenario where the actors (or
clients) are companies that have safety critical components
that need to be monitored to ensure that they are operating as
expected. Specifically, two RUL prediction problems will be
addressed; accelerated aging of silicon carbide (SiC) metal-
oxide-semiconductor field-effect transistors (MOSFETs) and
turbofan jet engines via the C-MAPSS dataset as introduced
by Saxena, Goebel, Simon, and Eklund (2008). In each case,
the scenario where a company has a local dataset with some
number of assets operating under various operating conditions
is simulated. In this scenario, each company is interested in
modeling the RUL of their assets using deep neural networks,
but no company is willing to share data outside their organi-
zation. However, they are willing to share models trained on
their local data, making the FL strategy an optimal solution.
This paper will explore if there are any performance gains
when collaboratively training the RUL prediction model using
federated learning, versus limiting model training to locally
held data.
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1.5.1. SiC MOSFET Accelerated Aging Dataset
As complexity in modern electronic devices increases, the
risk of failure is also increasing. To ensure reliability and
safety of systems and components, monitoring of electronics
is becoming more and more important. However, gathering
health monitoring data from electronic devices in real-world
settings has been linked with inherent risks and substantial
expenses. In an effort to mitigate this challenge and stimulate
research in the field of PHM for electronic devices, a dataset
comprising the degradation histories of 33 wire-bonded SiC
MOSFETs subjected to accelerated aging by power cycling un-
til failure was meticulously created. To create a diverse dataset,
the SiC MOSFETs were cycled at different currents and on-
times (operating conditions), leading to a varying degree of
aging rate and hence substantial variation in degradation and
life length. More details on this dataset can be found in the
paper describing the dataset and its use in data-driven RUL
prediction:S
¨
oderkvist Vermelin, L
¨
ovberg, Misiorny, P. Eng,
and Brinkfeldt (2023).
Devices Under Test (DUTs), i.e., the SiC MOSFETs, were
cycled until one of the two failure conditions were met:
• measured ON-state voltage is higher than 8 V, or
•
recorded MOSFET casing temperature is higher than 100
↓C.
The settings for experiment rounds one through five are com-
piled in Table 1.
Exp. no. Current DUTs ON OFF
(#) (A) (#) (s) (s)
1 25 A 5 10 10
2 23 A 10 10 10
3 24 A 10 10 10
4 28 A 8 10 10
5 25 A 10 15 10
Table 1. SiC MOSFETs dataset, indexed by experiment num-
ber.
Recorded data from a typical on/off-cycle, represented by a
DUT in round 1, is shown in Figure 2.
Key characteristics for were extracted from the data, resulting
in a final dataset consisting of 18 features recorded per cycle.
For example, the cycle count is the number of cycles the DUT
has been cycled and the life percentage is the fractional life
left until failure (bounded in the interval [0,1]).
Life Percentage (LP) is defined as the amount of life consumed
at each point in time:
LP(t)= t
T,(1)
such that at time
t= 0 LP(t= 0) = 0
, and at end-of-life
t=T
,
LP(t=T) = 100%
. LP is related to RUL (measured
Figure 2. A cycle of data from power cycling, at steady-state
and significant degradation has yet to occur. The MOSFET-
case temperature is shown in green, and the voltage is shown
in red. The average temperature is showed as a vertical dashed
line. The cycle has an initial ON-time of 10 seconds where
voltage is increasing, and a subsequent OFF-time for 10 sec-
onds (no current is passed and hence no voltage).
in time/cycles) according to
RUL(t)= t
LP(t)↗t(2)
where at
t=0
,
RUL(t= 0) = T
. Life percentage is also
sometimes referred to as lifetime percentage (Ben Ali, Chebel-
Morello, Saidi, Malinowski, & Fnaiech, 2015; Lallart, Wu, Li,
& Qiu, 2017; Mahamad, Saon, & Hiyama, 2010; Singh, Darpe,
& Singh, 2020; Tian, 2009; Tian, Wong, & Safaei, 2010; Wu,
Gebraeel, Lawley, & Yih, 2007; Xia et al., 2019; Zhu, Chen, &
Shen, 2020). LP is often used for bearing RUL prediction, but
has also been used for railway switches (Q. Chen, Nicholson,
Ye, Zhao, & Roberts, 2020), and crack-growth in aluminum
lugs (T. Li, 2024).
Life percentage can then be translated into so-called Remain-
ing Useful Life Percentage (RULP) (Huang, Zhu, Han, & Peng,
2022; Xu, Duan, Chen, Wang, & Fan, 2022) which is defined
as
RULP(t)=1↗LP(t).(3)
LP and RULP prediction, are well established niches in the
PHM literature, often used for assets with high variability
in life spans and life lengths that span multiple orders of
magnitude.
For a detailed description of each feature please refer to the
corresponding paper authored by S
¨
oderkvist Vermelin et al.
(2023). A summary of the derived features is shown in Table 2.
The dataset of derived features was used to train a model on
the RULP prediction task.
The degradation progression is shown in Figure 3. In this
figure, the initial voltage at each cycle is shown, for each DUT
in round 1.
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Feature Unit
Cycles unitless
Life percentage unitless
End voltage V
End resistance m!
Residual resistance m!
Cleaned residual resistance m!
Min temperature →C
Max temperature →C
Min block temperature 1 →C
Max block temperature 1 →C
Min block temperature 2 →C
Max block temperature 2 →C
Min water inlet temperature →C
Max water inlet temperature →C
Min water outlet temperature →C
Max water outlet temperature →C
Mean block temperature →C
End resistance from
mean block temperature m!
Residual end resistance from
mean block temperature m!
Cleaned residual end resistance from
mean block temperature m!
Table 2. Derived features dataset.
Figure 3. The plot shows the first recorded voltage in each
cycle for each DUT in round 1.
For training the machine learning models, devices from each
round is randomly selected for training and testing, such that
approximately
80 %
is allocated to the training dataset, and
the rest to the test dataset. In Table 3, the training/testing split,
operating conditions and fault modes are shown.
Dataset Train Val. Test Op. Con. Fault modes
Round 1 2111 Wire-bond lift-off
Round 2 6221 Wire-bond lift-off
Round 3 6221 Wire-bond lift-off
Round 5 6221 Wire-bond lift-off
Table 3. SiC MOSFET dataset details. Op. Con. means
“operating condition”. Wire-bond lift-off as failure mechanism
has not been experimentally verified, but the collected data
indicates this fault mode.
When assuming LP is zero at time zero (or equivalently, RULP
is one at time zero), one is implicitly assuming there is no
initial wear in the devices. Note that RULP prediction is
only performed for the SiC MOSFET dataset, whereas RUL
prediction is used for the C-MAPSS dataset. The reason no
initial wear in the SiC MOSFETs is assumed is because the
devices are unused and recently manufactured at the start of
the power cycling experiments. Of course, there could be
manufacturing defects, and other problems with the devices
before they are used, which may affect the life span. Prior to
some of the power cycling experiments, a subset of the devices
have been analyzed using a Scanning Acoustic Microscope
(SAM), to assess the die attach quality in the chips. The
hypothesis is that the die attach quality would shorten the life
span, however, the results did not show any strong connection
between die attach quality and life span. If there had been
a link between die attach quality and life length, one could
account for it such that initial RULP would be slightly less
than one. In general, it is hard to know a priori what will affect
the life length of the devices, and as such additional research is
needed to assess the “initial wear” of SiC MOSFETs prior to
use. In light of this, and the fact that the devices are unused and
newly manufactured at the start of experiments LP is defined
as zero at time zero for each device. In this case, RULP is
interpreted as the device specific initial life capacity, going
from 100% to 0% as time progresses. When viewed in this
way, the initial wear can be included in the initial life capacity,
since it does not stem from operation, but external factors.
1.5.2. C-MAPSS Dataset
The Commercial Modular Aero-Propulsion System Simulation
(C-MAPSS) dataset, first presented and developed in Saxena
et al. (2008), consists of full run-to-failure trajectories using
simulated degradation of turbofan jet engines. The dataset
consists of flight cycles with recordings from 24 sensors. In
addition, it comprises four cohorts of turbofan engines (re-
ferred to as subsets) and contain various operating conditions
and fault modes. The authors have split the data into training
and testing data, where the first are used to develop the models
and the latter are used to evaluate the model performance. A
summary of the data is shown in Table 4.
Dataset Train Val. Test Op. Con. Fault modes
FD001 80 20 100 1 HPC degradation
FD002 208 52 259 6 HPC degr.
FD003 80 20 100 1 HPC and fan degr.
FD004 199 50 248 6 HPC and fan degr.
Table 4. C-MAPSS dataset details. Here HPC means high
pressure compressor.
For the C-MAPSS dataset, RUL is measured in actual cycles.
Due to low initial degradation in the engines, it is common to
clip RUL to a certain max value. The most common choices
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INTERNATIONAL JOURNAL OF PROGNOSTICS AND HEALTH MANAGEMENT
are setting maximum RUL to 120 or 130 cycles (Doulamis
et al., 2020; Zheng, Ristovski, Farahat, & Gupta, 2017). The
RUL of the engines in the test dataset remain unchanged,
RUL clipping is only performed on the training and validation
datasets.
2. METHODOLOGY
In this section the methodology for training and evaluating the
models, both using federated learning and local, is described.
2.1. Data-Driven Remaining Useful Life Prediction
RUL prediction involves finding a mapping between sensor
measurements Sand RUL, y,
f:S≃⇐ y. (4)
Here
S
is a time series dataset meaning that it is a collection
of multivariate sensor readings.
S
consists of multiple sub-
datasets for each asset
i=1,2,...,N
, where
N
is the total
number of assets in the dataset, such that
S={Di}N
i=1.(5)
Di={X(i)
t}Ti
t=0
where
X(i)
t
are
s
sensor readings at time
t
between starting time
t=0
and end time
t=Ti
for asset
i
,
where
i=1,2,...,N
.
Ti
is also referred to the end-of-life
or life-span for asset
i
. This means for each asset indexed
by
i
that
X(i)
t↔Rs
for
t=0,1,...,T
i
. When the sensor
measurements in
S
are run-to-failure histories, the mapping
f
in Equation
(4)
can be learned using supervised machine
learning. This means that a new dataset
T
can be constructed,
containing tuples of sensor measurements and the correspond-
ing remaining useful life, for each asset:
T="#X(i)
t,y
(i)
t$Ti
t=0%N
i=1
.(6)
Here, again
X(i)
t↔Rs
is an
s
-dimensional vector containing
sensor measurements, and
y(i)
t
is the RUL at time
t
for asset
i
. RUL can be scaled such that for each asset
i
,
y(i)
t↔[0,1]
for
t=0,1,...,T
i
, with
y(i)
0=1
and
y(i)
Ti=0
. This is
often done for assets that have long lifespans that cover sev-
eral orders of magnitude (as is the case for the devices in the
SiC MOSFET dataset). When this scaling is performed, the
new quantity is referred to as remaining useful life percentage
(RULP) (Huang et al., 2022; Xu et al., 2022), closely related
to the concept of life percentage (LP). Life percentage is men-
tioned in the derived features summary, cf. Table 2. RULP and
RUL measured in actual time or cycles can be transformed
using the below formula:
y(i)
T; t=ty(i)
S; t
1↗y(i)
S; t
,(7)
where
y(i)
T; t
is RUL, i.e.,
y(i)
T; t↔[0,T
i]
and
y(i)
S; t
is RULP,
i.e.,
y(i)
S; t↔[0,1]
. At
t=0
, RUL is
Ti
, i.e.,
y(i)
T; t=0 =Ti
and Equation (7) cannot be used. For the rest of the text, all
descriptions and discussions regarding RUL will apply to both
RUL and RULP, unless explicitly stated. For the C-MAPSS
dataset, it is conventional to work in terms of RUL, and this
paper will adhere to this convention. For the MOSFET dataset,
it is more convenient to work in terms of LP/RULP since
the devices have so large life spans, covering many orders of
magnitude.
If the mapping
f
is parameterized by
ϑ
, the supervised learning
problem can be formulated as follows:
min
ωϖ(X,y;ϑ),(8)
where
X
and
y
is shorthand notation for the full sensor dataset
and RUL, for all times and all assets;
X={{X(i)
t}Ti
t=0}N
i=1
,
y={{y(i)
t}Ti
t=0}N
i=1, respectively.
To train the data-driven models, in a classical non-federated
setting, the optimization problem in
(8)
, is approximately
solved using gradient descent
ϑk+1 =ϑk↗ω↘
ωϖ(X,y;ϑk).(9)
and when
ϑk
are the parameters in a neural network, this algo-
rithm is referred to as backpropagation (Goodfellow, Bengio,
& Courville, 2016).
2.2. Model Architectures
In this paper two model architectures are explored, one for
each dataset. The application of deep neural networks on the
C-MAPSS dataset has been studied extensively, and several
architectures have been proposed. One such architecture is
described in the paper by Chaoub, Voisin, Cerisara, and Iung
(2021), the current state-of-the-art architecture for RUL pre-
diction on the C-MAPSS dataset. The proposed architecture
is called MLP-LSTM-MLP, consisting of a multilayer per-
ceptron (MLP), a Long Short-Term Memory recurrent neural
network (Hochreiter & Schmidhuber, 1997), and finally an-
other MLP outputting the predicted RUL. This model will be
described in detail in Section 2.2.1.
For the MOSFET dataset, the Convolutional Gated Recurrent
Unit (ConvGRU)(Ballas, Yao, Pal, & Courville, 2016) neural
network model is used.
2.2.1. MLP-LSTM-MLP Model
The MLP-LSTM-MLP model described in the paper by Chaoub
et al. (2021) has two basic building blocks; the MLP and the
LSTM. An MLP consists an input layer, a number of fully
connected hidden layers, and an output layer. It is one of the
fundamental model architectures, the simplest instance of a
neural network with hidden layers.
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The LSTM is a type of Recurrent Neural Network (RNN) that
is capable of learning long-term dependencies in data. It is
commonly used for natural language processing and speech
recognition tasks, where the context of the current input de-
pends on the previous inputs.
The basic building block of an LSTM cell is a memory state
that keeps track of the information from previous time steps.
This memory state is updated at each time step based on the
new input and the previous memory state. The update rule
takes into account the importance of the previous memory
state and the new input, which is determined by a gating
mechanism.
There are three main gates in an LSTM cell: the input gate,
the forget gate, and the output gate. The input gate controls
how much new information from the current input should be
passed to the memory state. The forget gate decides how much
of the previous memory state should be retained or forgotten.
The output gate controls how much of the updated memory
state should be passed to the next time step.
The LSTM model has a series of connected cells, where each
cell processes a portion of the input sequence. The outputs
of the cells are combined to produce the final output of the
model.
One of the key advantages of LSTMs over traditional RNNs
is their ability to learn long-term dependencies by allowing
information to persist in the memory state for longer periods.
This enables them to better capture the context of the current
input and make more accurate predictions. In addition, LSTMs
are capable of learning which information to retain and which
to discard through the gating mechanism.
LSTMs have been applied extensively within the area of RUL
prediction, and in particular the C-MAPSS dataset, see e.g.,Al-
Dulaimi, Zabihi, Asif, and Mohammadi (2019); Che, Wang,
Fu, and Ni (2019); Wang, Wen, Yang, and Liu (2019); Zhang,
Wang, Yan, and Gao (2018).
The MLP-LSTM-MLP model is, as the name suggests, an
MLP, LSTM, and finally MLP in sequence. The first MLP
takes as input the sensor readings at time
t
for asset
i
:
x(i)(t)
,
and consists of a series of hidden layers, applying nonlinear
mappings of the input, and finally an output layer of some
dimensionality,
dout
. The output of the first MLP is fed into
the LSTM model which returns the updated hidden state of
the LSTM at each time step
ht
. The hidden state at each time
step is fed into the final MLP which has an one-dimensional
output layer, interpreted as the predicted RUL at time
t
:
ˆy(i)(t)
.
A full description of the model is presented in Chaoub et al.
(2021). The MLP-LSTM-MLP model is shown in Figure 4.
Figure 4. An overview of the MLP-LSTM-MLP model archi-
tecture. The sensor readings at time
t
for asset
i
(
x(i)(t)
) is
fed into the first MLP. The output of the first MLP is fed into
the LSTM, which updates its hidden state. The hidden state is
fed into the final MLP which outputs the predicted RUL.
2.2.2. Convolutional Gated Recurrent Unit Model
The Convolutional Gated Recurrent Unit (ConvGRU) model
consists of multiple GRU layers, an encoder, and an output
layer.
The encoder takes in a slice of time series data (with a predeter-
mined sequence length) and applies a series of convolutional
operations to reduce the dimensionality of the data while pre-
serving its important features. After each convolution in the
encoder, the output is passed through the Exponential Lin-
ear Unit (ELU) activation function (Clevert, Unterthiner, &
Hochreiter, 2016) to introduce nonlinearity into the feature
extraction procedure. The ELU activation function is defined
as follows:
ELU(x;ϱ)="xif x⇒0
ϱ(exp(x)↗1) if x⇑0,(10)
where ϱwas chosen such that ϱ=1.
The output of the encoder is then fed into the GRU layers.
The GRU layers consists of several GRU cells, each of which
represents one layer in the model. Each GRU cell takes in an
input tensor and returns an output tensor based on its internal
state. The cells are connected in a way that allows them to
update their internal states and outputs as they receive new
input data.
The output layer is a fully connected feed-forward neural
network with one hidden layer, which takes the output from
the GRU layers as input. The hidden activation is the ReLU
activation function (Agarap, 2018), defined as:
ReLU(x) = max (0,x).(11)
The output from the output layer is the predicted RULP (a
single value). The architecture of the ConvGRU model is
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illustrated in Figure 5.
Figure 5. The ConvGRU model architecture.
x
represents the
input time series data. For each sequence, in the time series,
the convolutional encoder is applied. The encoded sequence
z
is then fed into the GRU layers, which can consists of several
GRU cells. In this figure, the sequence length is
s
. For each
sequence, the RULP is predicted for the last time step of the
sequence. In the final step, the last RULP is predicted.
The ConvGRU has a number of hyperparameters specific to
the architecture. In particular, the length of the sequences
fed into the encoder, the hidden size of the GRU cells, the
number of GRU cells, and the hidden size of the MLP RULP
prediction head. In addition, there are hyperparameters spe-
cific to the training of the models, such as learning rate, and
weight decay for the AdamW optimizer. The hyperparame-
ters are tuned using hyperparameter tuning through the Ray
Tune library (Liaw et al., 2018). Tuning is performed for each
client for local training, see Section 2.3.2, and globally for
the central training, see Section 2.3.3. For the federated learn-
ing models, hyperparameter tuning is not used, the best local
hyperparameter settings are used.
2.3. Experimental Setup
The experimental setup takes advantage of the natural parti-
tioning present in both datasets. This partitioning is used to
artificially create clients in the federation, while also being
more realistic than random partitioning of the datasets.
2.3.1. Data Partitioning
The MOSFET dataset consist of four experimental rounds
(round 4 is omitted due to too highly accelerated testing) where
each experimental round is used to represent a client in the
federation. In this scenario, each client has a set of assets
operating with some operating conditions. The operating con-
ditions vary among clients but not within the cohort of assets
for each client. This is a good proxy for assets within differ-
ent companies; a company is likely to operate all their assets
similarly, whereas another company might operate their assets
differently. So in the experimental setup, various experimental
rounds represent companies operating their assets. This setup
ensures that the clients’ data are highly non-IID, as driving
current and ON/OFF time is different among clients, see Ta-
ble 1. The non-IID nature of the clients’ data can be seen
in Figure 6 where the lifespans of the MOSFET devices are
plotted by each experiment round (client).
Figure 6. Lifespans of the SiC MOSFETs. It can be observed
that there is great variability in lifespans, leading to clients
with non-IID data, when each round is used as a client in the
FL setup.
The C-MAPSS dataset consists of four “subsets” (FD001,
FD002, FD003, and FD004). These subsets are again utilized
to create four clients, each with aero engines being operated at
different conditions. Since the subsets have different operating
conditions, this again leads to clients with non-IID data. For
example, the distribution of values for “sensor 12” which is
ratio of fuel flow to Ps30, is shown in Figure 7. Here, it can be
observed that data is differently distributed among the different
subsets, leading to clients with non-IID data.
2.3.2. Local Training
To benchmark the federated learning models, central training
and local training will be used. Central training is described
in Section 2.3.3.
Each client in the federation (represented by different experi-
mental rounds in the dataset) has a number of assets, that is
referred to the client’s local assets. As these assets are operated
they produce data that will be called the local data.
To benchmark the federated learning approach, each client will
also train a model only using their local data, representing a
baseline for comparison. The model development is performed
on a subset of the local data, called the development set, and
is a randomly chosen subset of all assets. The development
dataset will also be partitioned into two datasets; the training
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Figure 7. Distribution of “sensor 12” (ratio of fuel flow to
Ps30) among the different subsets in the C-MAPSS dataset.
A variation among subsets is observed, thus leading to clients
with non-IID when subsets are used as clients in FL.
and validation datasets. The training dataset will be used for
training the model, and the validation dataset will be used
for monitoring the training. A third dataset called the evalua-
tion/testing dataset will be used to evaluate the trained model
and is used for comparing locally trained models and mod-
els trained using federated learning. In Figure 8 a schematic
overview of the partitioning of each client’s data is shown. For
Client data
Development
data
Training data
Validation
data
Evaluation
(Testing) Data
Training assets
Validation assets
Evaluation assets
Figure 8. Each client’s data are split into development data and
evaluation/testing data. The development data are split into
training data, data used for training the model, and validation
data, used for monitoring the training. The test/evaluation data
are held out during training and only used for evaluating the
performance of the trained model.
the SiC MOSFET dataset, each device in every experiment
round is randomly allocated to either, training, validation or
testing datasuch that 60
%
is used for training, 20
%
is used
for validation, and the last 20 %is used for testing.
For the C-MAPSS dataset, a test dataset is provided for each
subset and is used for model evaluation. The remaining data is
split such that 80
%
is used for training and 20
%
is used for
validation.
Model Component MLP-LSTM-MLP ConvGRU
Batch Size 14 1
Sequence Length - 200
LSTM/GRU Cells 128 32
No. Layers - 1
Kernel Size - 9
Learning Rate 0.0002 0.0002
Weight Decay 0.001 0.01
Table 5. Hyperparameter settings for the ConvGRU and MLP-
LSTM-MLP models.
The models are updated using gradient descent on the loss
function (LeCun, Bengio, & Hinton, 2015), where the loss
function used are common loss functions used in regression
problems, explained in Section 2.4. The weight update opti-
mizer chosen is the so-called AdamW optimizer (Loshchilov &
Hutter, 2019). It is a variation of the Adam optimizer (Kingma
& Ba, 2015) with decoupled weight decay regularization. Both
models are trained for 300 epochs, and the best models (in
terms of validation loss) is selected. In Table 5, the hyperpa-
rameters for the ConvGRU and MLP-LSTM-MLP models are
presented.
2.3.3. Central Training
Central machine learning, or (centralized machine learning)
refers to a system of machine learning in which data is col-
lected and processed in a single, central location (Abdulrah-
man et al., 2020). This approach is frequently used when
working with large datasets that cannot be easily distributed
across multiple machines or when real-time predictions are
required.
In a central machine learning system, raw data are typically
gathered from various sources and sent to a central server or
cluster of servers for processing. The data is then cleaned,
transformed, and prepared for training, after which a machine
learning model is trained on the data using specialized algo-
rithms and hardware. Once the model has been trained, it can
be deployed in the same central location to make predictions
on new data as it comes in.
Central machine learning has several advantages, including:
•
Improved performance: By processing large datasets in a
single location, central machine learning systems can take
advantage of powerful hardware and software optimiza-
tions that would not be possible with distributed systems.
This can lead to faster training times and more accurate
predictions.
•
Greater control: Centralizing the machine learning pro-
cess allows for greater control over the data and models
being used. This can help ensure compliance with reg-
ulatory requirements and minimize the risk of errors or
inconsistencies in the training process.
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•
Scalability: Central machine learning systems are often
more scalable than distributed systems, as they can easily
accommodate larger datasets and more complex models
as needed.
However, central machine learning also has some limitations,
including:
•
Data privacy concerns: Collecting and processing large
amounts of data in a central location can raise privacy
concerns, particularly if the data includes sensitive infor-
mation.
•
Dependence on infrastructure: Central machine learning
systems are dependent on the reliability and availability
of the underlying infrastructure. If the central server or
cluster goes down, the entire system may be unavailable
until it is restored.
•
Latency issues: Central machine learning systems can
introduce latency in the prediction process, particularly
if the data must be transmitted over long distances or
through congested networks.
In this study, central training as a limiting benchmark. Given
the proper training and hyperparameters, the central model
should perform at least equally well or better than the federated
models.
In the scenario where clients are different companies training
models on their own private data, central training is often
infeasible. Companies often have sensitive data and often
unable to share data between departments, let alone a third
party. In this case, central training should not be considered a
realistic alternative to federated learning, but it is an interesting
benchmark from a model evaluation perspective, which is why
it is included here.
Regarding the implementation details for central training, the
same setup as for local training is used (in terms of hyperpa-
rameters). One could argue that hyperparameter search should
be performed for central training and these are the hyperpa-
rameters that should be used in local training, so the proposed
procedure needs some justification. The hyperparameters from
local training are used for two main reasons. First, an exten-
sive hyperparameter search for the different subsets yielded
a small difference in hyperparameters, meaning the choice of
hyperparameters found in local training can be used for each
client. Secondly, in the real-world scenario, where compa-
nies are engaging in FL, central training is infeasible, for the
reasons stated earlier. If central training is infeasible, so is
central hyperparameter search (since data would need to be
pooled to perform central hyperparameter search). In spirit of
staying true to the goal of highlighting the difference between
local and FL training, the training procedure should adhere
as much as possible to the scenario targeted, meaning central
hyperparameter search is omitted in favor of results obtained
from local hyperparameter search.
In summary, central training is performed for each dataset
separately, by pooling all the subsets for each dataset and
training a model based on the pooled data, as one would do in
traditional machine learning training.
2.3.4. Federated Training
The federated training is performed using the FedAvg and
FedPer algorithms (see Algorithm 1 and Algorithm 2, respec-
tively). As in the previous section, the local model updates
are obtained using the local data training dataset. Then the
updates are sent to the central server which uses some aggrega-
tion to create a new global model. In this case, aggregation is
accomplished through the process of averaging the weights of
the clients’ models. When a new global model is created, it is
distributed to each of the clients which resumes local training.
An overview of the federated training is illustrated in Figure 9.
Server
Global Model
Local Model
Private
Data
Local assets Local Model
Private
Data
Local assets
...
Global Model
Global Model
Locally trained modelLocally trained model
...
Figure 9. Conceptual illustration of the federated training
setup. Each client
1,2,...,K
has their local data based on
their local assets and trains their local model on this data. This
model is sent to the global server which aggregates the local
models to form a new global model. The global model is then
sent to each of the clients. The above procedure is repeated
until convergence.
Federated training has a few hyperparameters specific to fed-
erated learning. Namely, one can choose how many epochs
are trained locally before communicating the model to the
server, referred to as “local epochs”. In addition, the number
of communications between the server and the clients can
be set, called the “federated learning rounds”. In this paper,
each client trained for a single local epoch, and the number of
federated learning rounds was set to 200, to give the models
sufficient time to converge.
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2.4. Model Evaluation
To evaluate the model performance, various metrics are used.
For the MOSFET dataset two loss components are used, Mean
Squared-Error (MSE) and ϖ↔-loss. MSE loss is defined as
ϖMSE (ˆy, y)= 1
N
N
&
i=1
(ˆyi↗yi)2,(12)
and ϖ↔-loss is defined as
ϖ↔(ˆy, y) = max |ˆy↗y|.(13)
Hence, the total loss function is given by
ϖ(ˆy, y)=ϖMSE(ˆy, y)+ϖ↔(ˆy, y).(14)
The MSE loss term is commonly used in regression problems.
The
ϖ↔
-loss term is used to penalize the largest output error
of the model, leading to a more conservative model with fewer
prediction outliers.
For the C-MAPSS dataset, two different metrics are used to
monitor and evaluate model performance. To train the model,
MSE is used. In the literature, it is common to report the
performance of models on C-MAPSS using two metrics, root
mean-squared error (RMSE) and a scoring function. RMSE is
the square root of MSE:
ϖRMSE (ˆy, y)='
(
(
)
1
N
N
&
i=1
(ˆyi↗yi)2.(15)
The other common evaluation metric is a scoring function de-
fined in the paper introducing the C-MAPSS dataset (Saxena
et al., 2008). The scoring metric penalizes overestimation of
RUL more than underestimation. The rationale is that overesti-
mation of RUL is worse since the model is too optimistic about
the remaining time left until failure, which means one is at risk
of delaying maintenance action until it is too late. On the other
hand, a conservative model that tends to underestimate RUL
minimizes the risk of failure in favor of excess maintenance
which is in many cases better. The scoring function is defined
as follows:
ϖs(ˆy, y)=

!N
i=1 exp #↗di
a1$↗1for di<0
!N
i=1 exp #di
a2$↗1for di⇒0.(16)
where
di=ˆyi↗yi,i=1,2,...,N
,
N
is the number of
assets under test, and a1= 10,a2= 13.
2.5. Implementation
The models and training framework were developed using the
Python programming language (Van Rossum & Drake, 2009).
In particular, the deep learning framework PyTorch (Paszke et
al., 2019) and a high level wrapper for PyTorch called PyTorch
Lightning (Falcon & team, 2019) was used to train the models.
For the training the federated learning models, the Flower
framework was used (Beutel et al., 2020).
3. RESULTS AND DISCUSSION
In this section, the results on each dataset will be presented
in a corresponding subsection. The results include tables
illustrating the relative overall performance on the datasets
using the various metrics discussed in Section 2.4. In addition,
plots of predicted RUL/RULP vs. true RUL/RULP will be
presented to show the accuracy and spread in predictions by
the various models.
3.1. MOSFET Dataset Results
The results on the MOSFET dataset are presented below. In
Table 6 the resulting loss (as given by Equation (14)) is pre-
sented, showing that FL, in particular the FedPer strategy, is
most performant. A notable exception is round 1 where local
is performing the best. In Figure 10 and Figure 11, the pre-
dicted vs. actual RULP for round 2, device 6 and device 10
are plotted, respectively.
Round Central Local FedAvg FedPer
1 0.3547 0.0070 0.0823 0.0149
2 0.0482 0.0341 0.0771 0.0126
30.0286 0.0455 0.1519 0.0695
50.0386 0.0949 0.0664 0.0552
Mean 0.1174 0.0454 0.0944 0.0381
Table 6. Local, FedAvg, and FedPer test set loss on the MOS-
FET dataset. The best (minimal) loss is highlighted in bold.
The last row is the mean of the loss.
Additional results are presented in the Appendix, see Fig-
ures 13 to 17.
3.2. C-MAPSS Dataset Results
In Table 7 RMSE is calculated per subset on the evaluation
dataset (defined in Equation (15)). Similarly, in Table 8,
the score according to the scoring function defined in Equa-
tion (16) is shown.
Subset Central Local FedAvg FedPer
FD001 13.38 14.36 13.60 13.44
FD002 23.49 24.20 23.10 23.13
FD003 13.14 12.99 12.71 14.24
FD004 24.72 33.15 24.11 24.16
Mean 18.68 21.18 18.38 18.74
Table 7. Local, FedAvg, and FedPer test set RMSE on the
C-MAPSS dataset. The best (minimal) RMSE is highlighted
in bold.
Additional results are presented in the Appendix, see Fig-
ures 18 to 20.
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(a) Central model. (b) Local model.
(c) FedAvg model. (d) FedPer model.
Figure 10. RUL prediction results on device 6 in round 2 from
models trained locally, using FedAvg, and using FedPer. The
number of cycles is shown on the horizontal axis, and the
vertical axis shows the RULP. The true RULP is shown in blue
and the predicted RULP is shown in orange.
(a) Central model. (b) Local model.
(c) FedAvg model. (d) FedPer model.
Figure 11. SiC MOSFET dataset RULP predictions for round
2, device 10.
3.3. Discussion
When analyzing the results of the paper, the following guiding
principles were used:
•
central training is expected to outperform FL in general,
as central training is a special case of FL with only one
client. Therefore, in this work, central training serves as
a “benchmark”, and
•
the difference between local training and FL is the most
Subset Central Local FedAvg FedPer
FD001 343.90 309.78 364.65 368.68
FD002 4300.42 5036.62 4147.94 3924.87
FD003 350.36 434.39 304.16 566.55
FD004 5073.86 11803.64 3370.73 3375.74
Mean 2517.13 4396.11 2046.87 2058.96
Table 8. Local, FedAvg, and FedPer test set score on the C-
MAPSS dataset. The best (minimal) score is highlighted in
bold.
(a) Central model. (b) Local model.
(c) FedAvg model. (d) FedPer model.
Figure 12. RUL prediction results on subset FD002 from
models trained locally, using FedAvg, and using FedPer. The
engine ID are shown on the horizontal axis, sorted in descend-
ing manner by highest actual RUL. The true RUL is shown as
a red line, whereas the predicted RUL is shown as blue points.
important result, as this represent the realistic dilemma
companies are faced with: is there a performance gain of
using FL over just training the model locally on private
data?
With these principles in mind, the results show that various
federated learning approaches are, in general, performing bet-
ter than only training on local data. In particular, it is observed
that the FedAvg strategy is performing well, especially on the
C-MAPSS dataset. This is probably because the subsets in the
C-MAPSS dataset, while still having different operating con-
ditions for each subset, are quite similar (especially regarding
lifespans), leading to the FedAvg strategy working well. One
should also note that the FedPer strategy works almost as well
as the FedAvg algorithm on the C-MAPSS dataset, with results
close to (and even exceeding) central training. The FedPer
strategy has a consistently high performance on both datasets,
especially the MOSFET dataset. One plausible reason is that
when using the FedPer strategy, each client is allowed to use
personalized layers in the model, which gives the local models
more flexibility to handle non-IID data. As discussed earlier,
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INTERNATIONAL JOURNAL OF PROGNOSTICS AND HEALTH MANAGEMENT
the MOSFET dataset is quite diverse among the devices in the
different rounds, and the FedPer strategy’s ability to cope with
heterogeneous data could explain the observed results. As
companies are likely to have assets that experience a variety
of degradation processes and therefore collect highly heteroge-
neous data, it is important for the federated strategy to handle
this in a robust manner.
Central training is the worst performer on the MOSFET dataset,
which is an unexpected result. However, the low performance
of central training can be attributed to a large incorrect predic-
tion on round 1. Due to the low number of DUTs in round 1,
only one device is assigned to the testing dataset (see Table 3).
Weighting the prediction results with the number of devices
in the testing dataset for each round one can observe that the
performance of the central training is not as bad as it seems at
first glance and the large contribution of round 1 is more clear
(see Table 6).
One can also note that local training is working well and for
some clients this model is the top performer. One explanation
for this is that the models used were small, in the sense of
total number of trainable parameters. Smaller models are less
prone to overfitting and can therefore can perform relatively
well on smaller datasets.
Regarding the SiC MOSFET dataset results, one can observe
in Table 6 that FedPer is outperforming local training except
for round 1 and 3 where local training is the best performer,
and FedPer is a close second. One possible explanation is
that round 1 contains the fewest number of devices, thereby
as a client in the federation, is contributing less in the weight-
update of the federated learning algorithm, see Algorithm 1
and Algorithm 2.
In addition, one can observe that the models perform well
on the device with the longest life span, see Figure 11, but
they are less accurate when the life span is shorter. This
can occur if the training dataset contains more longer-lived
devices, as compared to the test dataset. Indeed, as can be
seen in Figure 6, there is a large spread in life-spans and most
short-lived devices originate from round 1, which contains the
fewest number of devices.
In particular, one interesting observation regarding round 2
(the round with the lowest accelerated aging) is that the local
model is preforming well on device 10 which has a long life-
span, see Figure 11. The federated learning algorithms have
comparable, albeit slightly worse, performance on this device.
However, the local model performs poorly on the shorter-lived
device 6, see Figure 10, whereas the federated models perform
better. This is an indication that the federated models have
learned “short-lived” behavior from other clients in the feder-
ation, since such examples are more numerous and common
among other the other rounds/clients.
For the results on the C-MAPSS dataset, it can be observed
in Table 7 and Table 8 that federated learning is performing
better, especially FedAvg. In general, it is observed that RUL
predictions are quite poor when the remaining life is large,
see e.g., Figure 12. This is because, RUL is clipped at 130
cycles in the testing and validation datasets. At high RUL little
or no degradation is present in the system, leading to large
uncertainty in RUL predictions, and RUL clipping is therefore
used in training to stabilize the training process. Naturally, as
the model never receives samples with RUL exceeding 130
cycles, it will never predict RUL higher than the clipping value.
Of course, the RUL of the test devices are not clipped and RUL
values exceeding the threshold will be underestimated close to
the clipping threshold. This leads to poor results at high RUL,
especially RMSE. As time progresses, the degradation signal
in the data becomes more pronounced and consequently, the
RUL predictions are more accurate. This is what is observed,
the predictions at low RUL are far more accurate than at high
RUL.
4. CONCLUSIONS
In this paper, a method for collaborative training of Remaining
Useful Life (RUL) prediction models using federated learning
was explored, developed, and evaluated. Two federated learn-
ing strategies were compared, Federated Averaging (FedAvg)
and Federated Learning with Personalized Layers (FedPer), to
each other and the baseline case of training models on private
locally held data. The results show that the models trained
collaboratively using federated learning have similar or better
performance as compared to the baseline case.
Future research can further explore and optimize the appli-
cation of federated learning in this domain to unlock its full
potential. Specifically, bridging the gap between hybrid mod-
els (machine learning models combined with physics of fail-
ure models) with federated learning is a worthwhile future
endeavor. Incorporating physical knowledge in machine learn-
ing models is a crucial step for regularizing and enhancing
data-driven PHM applications. Furthermore, investigating ad-
ditional privacy enhancing features such as differential privacy
is interesting and may help bring federated learning for RUL
prediction to safety-critical and privacy-sensitive applications.
Overall, the results suggest that federated learning is a promis-
ing avenue for companies and organizations seeking to en-
hance the overall performance of their prognostics models,
collaboratively. The adoption of federated learning techniques
in training RUL prediction models holds the potential to im-
prove the accuracy and reliability of predictive maintenance
systems, ultimately leading to more effective and efficient
maintenance practices in various industrial sectors.
ACKNOWLEDGMENT
This research is supported by the Chips Joint Undertaking and
its members, including the top-up funding by the national Au-
14

INTERNATIONAL JOURNAL OF PROGNOSTICS AND HEALTH MANAGEMENT
thorities of Germany, Belgium, Spain, Sweden, Netherlands,
Austria, Italy, Greece, Latvia, Finland, Hungary, Romania and
Switzerland, under grant agreement number 101096387. Co-
funded by European Union. In particular, the authors thank
the Swedish funding authority Vinnova for support. This
research work has been funded by the Knowledge Founda-
tion within the framework of the INDTECH (Grant Number
20200132) Research School project, participating companies
and M
¨
alardalen University. The authors also give their thanks
to the RISE internal project DIGIPROD for supporting this
work. Research was supported by XPRES (Centre of Excel-
lence in Production Research) — a strategic research area in
Sweden. The authors thank Andreas L
¨
ovberg for his input in
the initial stage of this research.
REFERENCES
Abdelli, K., Cho, J. Y., & Pachnicke, S. (2021). Secure
collaborative learning for predictive maintenance in op-
tical networks [Conference paper]. Lecture Notes in
Computer Science (including subseries Lecture Notes
in Artificial Intelligence and Lecture Notes in Bioinfor-
matics),13115 LNCS, 114 – 130. (Cited by: 0) doi:
10.1007/978-3-030-91625-1 7
Abdulrahman, S., Tout, H., Ould-Slimane, H., Mourad, A.,
Talhi, C., & Guizani, M. (2020, 10). A survey on
federated learning: The journey from centralized to dis-
tributed on-site learning and beyond. IEEE Internet of
Things Journal,PP. doi: 10.1109/JIOT.2020.3030072
Agarap, A. F. (2018). Deep learning using rectified linear
units (relu). Retrieved from
http://arxiv.org/
abs/1803.08375
(cite arxiv:1803.08375Comment:
7 pages, 11 figures, 9 tables)
Al-Dulaimi, A., Zabihi, S., Asif, A., & Mohammadi, A.
(2019). A multimodal and hybrid deep neural network
model for remaining useful life estimation [Article].
Computers in Industry,108, 186 – 196. (Cited by: 167)
doi: 10.1016/j.compind.2019.02.004
Arivazhagan, M. G., Aggarwal, V., Singh, A. K., & Choud-
hary, S. (2019). Federated learning with personaliza-
tion layers. CoRR,abs/1912.00818. Retrieved from
http://arxiv.org/abs/1912.00818
Arunan, A., Qin, Y., Li, X., & Yuen, C. (2023). A fed-
erated learning-based industrial health prognostics for
heterogeneous edge devices using matched feature ex-
traction [Article]. IEEE Transactions on Automation
Science and Engineering, 1–15. (Cited by: 2; All
Open Access, Green Open Access) doi: 10.1109/
TASE.2023.3274648
Ballas, N., Yao, L., Pal, C., & Courville, A. C. (2016).
Delving deeper into convolutional networks for learn-
ing video representations. In Y. Bengio & Y. LeCun
(Eds.), 4th international conference on learning repre-
sentations, ICLR 2016, san juan, puerto rico, may 2-4,
2016, conference track proceedings. Retrieved from
http://arxiv.org/abs/1511.06432
Bemani, A., & Bj
¨
orsell, N. (2022). Aggregation strategy
on federated machine learning algorithm for collabora-
tive predictive maintenance [Article]. Sensors,22(16).
(Cited by: 11; All Open Access, Gold Open Access,
Green Open Access) doi: 10.3390/s22166252
Ben Ali, J., Chebel-Morello, B., Saidi, L., Mali-
nowski, S., & Fnaiech, F. (2015). Accurate
bearing remaining useful life prediction based
on weibull distribution and artificial neural net-
work. Mechanical Systems and Signal Processing,
56-57, 150-172. Retrieved from
https://
www.sciencedirect.com/science/
article/pii/S0888327014004087
doi:
https://doi.org/10.1016/j.ymssp.2014.10.014
Beutel, D. J., Topal, T., Mathur, A., Qiu, X., Parcollet, T.,
& Lane, N. D. (2020). Flower: A friendly federated
learning research framework. CoRR,abs/2007.14390.
Retrieved from https://arxiv.org/abs/2007
.14390
Celaya, J. R., Saxena, A., Saha, S., & Goebel, K. F. (2011).
Prognostics of power mosfets under thermal stress
accelerated aging using data-driven and model-based
methodologies. In (Vol. 3, p. 1995). doi: 10.36001/
phmconf.2011.v3i1.1995
Chaoub, A., Voisin, A., Cerisara, C., & Iung, B. (2021).
Learning representations with end-to-end models for
improved remaining useful life prognostics. CoRR,
abs/2104.05049. Retrieved from
https://arxiv
.org/abs/2104.05049
Che, C., Wang, H., Fu, Q., & Ni, X. (2019). Combining
multiple deep learning algorithms for prognostic and
health management of aircraft [Review]. Aerospace
Science and Technology,94. (Cited by: 87) doi: 10
.1016/j.ast.2019.105423
Chen, Q., Nicholson, G., Ye, J., Zhao, Y., & Roberts, C.
(2020). Estimating residual life distributions of com-
plex operational systems using a remaining mainte-
nance free operating period (rmfop)-based methodol-
ogy. Sensors,20(19). Retrieved from
https://
www.mdpi.com/1424-8220/20/19/5504
doi:
10.3390/s20195504
Chen, X., Wang, H., Lu, S., Xu, J., & Yan, R. (2023).
Remaining useful life prediction of turbofan engine
using global health degradation representation in
federated learning. Reliability Engineering & System
Safety,239, 109511. Retrieved from
https://
www.sciencedirect.com/science/
article/pii/S0951832023004258
doi:
https://doi.org/10.1016/j.ress.2023.109511
Clevert, D.-A., Unterthiner, T., & Hochreiter, S. (2016).
Fast and accurate deep network learning by ex-
ponential linear units (elus). In Y. Bengio
15

INTERNATIONAL JOURNAL OF PROGNOSTICS AND HEALTH MANAGEMENT
& Y. LeCun (Eds.), Iclr (poster). Retrieved
from
http://dblp.uni-trier.de/db/conf/
iclr/iclr2016.html#ClevertUH15
Demus, J., Sysoeva, V., Cheng, Q., Boubin, M., Siraj, A., &
Scott, M. (2019). Mosfet junction temperature measure-
ments using conducted electromagnetic emissions and
support vector machines [Conference paper]. In (p. 2973
– 2978). Institute of Electrical and Electronics Engineers
Inc. (Cited by: 0) doi: 10.1109/ECCE.2019.8912938
Dhada, M. H., Parlikad, A. K., & Palau, A. S. (2020).
Federated learning for collaborative prognosis.. Re-
trieved from
https://api.semanticscholar
.org/CorpusID:235049866
Doulamis, A. D., Hou, G., Xu, S., Zhou, N., Yang, L.,
& Fu, Q. (2020). Remaining useful life esti-
mation using deep convolutional generative adver-
sarial networks based on an autoencoder scheme.
Computational Intelligence and Neuroscience,2020,
9601389. Retrieved from
https://doi.org/
10.1155/2020/9601389
doi: 10.1155/2020/
9601389
Du, N. H., Long, N. H., Ha, K. N., Hoang, N. V., Huong, T. T.,
& Tran, K. P. (2023). Trans-lighter: A light-weight
federated learning-based architecture for remaining
useful lifetime prediction. Computers in Indus-
try,148, 103888. Retrieved from
https://
www.sciencedirect.com/science/
article/pii/S0166361523000386
doi:
https://doi.org/10.1016/j.compind.2023.103888
Falcon, W., & team, T. P. L. (2019, 3). Pytorch lightning. Re-
trieved from
https://www.pytorchlightning
.ai doi: 10.5281/zenodo.3828935
Goodfellow, I., Bengio, Y., & Courville, A. (2016).
Deep learning. MIT Press. (
http://www
.deeplearningbook.org)
Guo, L., Yu, Y., Qian, M., Zhang, R., Gao, H., & Cheng, Z.
(2023). Fedrul: A new federated learning method for
edge-cloud collaboration based remaining useful life
prediction of machines. IEEE/ASME Transactions on
Mechatronics,28(1), 350-359. doi: 10.1109/TMECH
.2022.3195524
Haris, M., Hasan, M. N., Jahanzeb Hussain Pirzada, S., &
Qin, S. (2020). Bayesian optimized long-short term
memory recurrent neural network for prognostics of
thermally aged power mosfets [Conference paper]. In
S. M., M. M.A., & N. S. (Eds.), . Institute of Electrical
and Electronics Engineers Inc. (Cited by: 2) doi: 10
.1109/RAEECS50817.2020.9265738
Hestness, J., Narang, S., Ardalani, N., Diamos, G. F., Jun, H.,
Kianinejad, H., . . . Zhou, Y. (2017). Deep learning scal-
ing is predictable, empirically. CoRR,abs/1712.00409.
Retrieved from
http://arxiv.org/abs/1712
.00409
Hochreiter, S., & Schmidhuber, J. (1997). Long short-term
memory. Neural computation,9(8), 1735–1780.
Huang, C.-G., Zhu, J., Han, Y., & Peng, W. (2022). A novel
bayesian deep dual network with unsupervised domain
adaptation for transfer fault prognosis across different
machines. IEEE Sensors Journal,22(8), 7855-7867.
doi: 10.1109/JSEN.2021.3133622
Kairouz, P., McMahan, H. B., Avent, B., Bellet, A., Bennis,
M., Bhagoji, A. N., . . . Zhao, S. (2021).
Kamei, S., & Taghipour, S. (2023). A comparison study
of centralized and decentralized federated learning ap-
proaches utilizing the transformer architecture for esti-
mating remaining useful life [Article]. Reliability En-
gineering and System Safety,233. (Cited by: 6) doi:
10.1016/j.ress.2023.109130
Kingma, D. P., & Ba, J. (2015). Adam: A method for
stochastic optimization. In Y. Bengio & Y. LeCun
(Eds.), 3rd international conference on learning rep-
resentations, ICLR 2015, san diego, ca, usa, may 7-9,
2015, conference track proceedings. Retrieved from
http://arxiv.org/abs/1412.6980
Lallart, M., Wu, B., Li, W., & Qiu, M.-q. (2017). Remain-
ing useful life prediction of bearing with vibration sig-
nals based on a novel indicator. Shock and Vibration,
2017, 8927937. Retrieved from
https://doi.org/
10.1155/2017/8927937
doi: 10.1155/2017/
8927937
LeCun, Y., Bengio, Y., & Hinton, G. (2015).
Deep learning. Nature,521(7553), 436–444.
Retrieved from
https://doi.org/10.1038/
nature14539 doi: 10.1038/nature14539
Li, Q., Wen, Z., Wu, Z., Hu, S., Wang, N., Li, Y., . .. He, B.
(2023, apr). A survey on federated learning systems:
Vision, hype and reality for data privacy and protection.
IEEE Transactions on Knowledge; Data Engineering,
35(04), 3347-3366. doi: 10.1109/TKDE.2021.3124599
Li, T. (2024). Particle filter-based fatigue damage
prognosis using prognostic-aided model updat-
ing. Mechanical Systems and Signal Process-
ing,211, 111244. Retrieved from
https://
www.sciencedirect.com/science/
article/pii/S0888327024001420
doi:
https://doi.org/10.1016/j.ymssp.2024.111244
Liaw, R., Liang, E., Nishihara, R., Moritz, P., Gonzalez, J. E.,
& Stoica, I. (2018). Tune: A research platform for
distributed model selection and training. arXiv preprint
arXiv:1807.05118.
Loshchilov, I., & Hutter, F. (2019). Decoupled weight
decay regularization. In International conference on
learning representations. Retrieved from
https://
openreview.net/forum?id=Bkg6RiCqY7
Mahamad, A. K., Saon, S., & Hiyama, T. (2010).
Predicting remaining useful life of rotating ma-
chinery based artificial neural network. Com-
puters & Mathematics with Applications,60(4),
16

INTERNATIONAL JOURNAL OF PROGNOSTICS AND HEALTH MANAGEMENT
1078-1087. Retrieved from
https://www
.sciencedirect.com/science/article/
pii/S0898122110002555
(PCO’ 2010) doi:
https://doi.org/10.1016/j.camwa.2010.03.065
McMahan, B., Moore, E., Ramage, D., Hampson, S., & Ar-
cas, B. A. y. (2017, 20–22 Apr). Communication-
efficient learning of deep networks from decentral-
ized data. In A. Singh & J. Zhu (Eds.), Proceed-
ings of the 20th international conference on artificial
intelligence and statistics (Vol. 54, pp. 1273–1282).
PMLR. Retrieved from
https://proceedings
.mlr.press/v54/mcmahan17a.html
Meriem, H., Nora, H., & Samir, O. (2023). Pre-
dictive maintenance for smart industrial sys-
tems: A roadmap. Procedia Computer Sci-
ence,220, 645-650. Retrieved from
https://
www.sciencedirect.com/science/
article/pii/S1877050923006178
(The
14th International Conference on Ambient Sys-
tems, Networks and Technologies Networks
(ANT) and The 6th International Conference on
Emerging Data and Industry 4.0 (EDI40)) doi:
https://doi.org/10.1016/j.procs.2023.03.082
Moshawrab, M., Adda, M., Bouzouane, A., Ibrahim,
H., & Raad, A. (2023). Reviewing federated
learning aggregation algorithms; strategies, contribu-
tions, limitations and future perspectives. Electron-
ics,12(10). Retrieved from
https://www.mdpi
.com/2079-9292/12/10/2287
doi: 10.3390/
electronics12102287
Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J.,
Chanan, G., . . . Chintala, S. (2019). Pytorch: An im-
perative style, high-performance deep learning library.
In Advances in neural information processing systems
32 (pp. 8024–8035). Curran Associates, Inc. Retrieved
from
http://papers.neurips.cc/paper/
9015-pytorch-an-imperative-style
-high-performance-deep-learning
-library.pdf
Pecht, M., & Kang, M. (2018). Prognostics and health
management of electronics : fundamentals, machine
learning, and internet of things (Second edition. ed.).
Hoboken, New Jersey: John Wiley & Sons.
Ren, H., Du, X., Yu, Y., Wang, J., Zhou, J., & Peng, Y.
(2022). Power mosfet lifetime prediction method based
on optimized long short-term memory neural network
[Conference paper]. Institute of Electrical and Elec-
tronics Engineers Inc. (Cited by: 0) doi: 10.1109/
ECCE50734.2022.9947640
Sahu, A. K., Li, T., Sanjabi, M., Zaheer, M., Talwalkar, A.,
& Smith, V. (2018). On the convergence of feder-
ated optimization in heterogeneous networks. CoRR,
abs/1812.06127. Retrieved from
http://arxiv
.org/abs/1812.06127
Saxena, A., Goebel, K., Simon, D., & Eklund, N. (2008).
Damage propagation modeling for aircraft engine run-
to-failure simulation. In 2008 international conference
on prognostics and health management (p. 1-9). doi:
10.1109/PHM.2008.4711414
Singh, J., Darpe, A. K., & Singh, S. P. (2020, may). Bear-
ing remaining useful life estimation using an adap-
tive data-driven model based on health state change
point identification and k-means clustering. Measure-
ment Science and Technology,31(8), 085601. Re-
trieved from
https://dx.doi.org/10.1088/
1361-6501/ab6671
doi: 10.1088/1361-6501/
ab6671
S
¨
oderkvist Vermelin, W., L
¨
ovberg, A., Misiorny, M., P. Eng,
M., & Brinkfeldt, K. (2023). Data-driven remain-
ing useful life estimation of discrete power elec-
tronic devices. In Proceedings of the 33rd euro-
pean safety and reliability conference (esrel 2023)
(Vol. 33). European Safety and Reliability Conference.
Retrieved from
https://urn.kb.se/resolve
?urn=urn:nbn:se:ri:diva-67109
doi: 10
.3850/978-981-18-8071-1-4procd
Tian, Z. (2009). An artificial neural network approach for
remaining useful life prediction of equipments subject
to condition monitoring. In 2009 8th international con-
ference on reliability, maintainability and safety (p. 143-
148). doi: 10.1109/ICRMS.2009.5270220
Tian, Z., Wong, L., & Safaei, N. (2010). A neu-
ral network approach for remaining useful life
prediction utilizing both failure and suspension
histories. Mechanical Systems and Signal Processing,
24(5), 1542-1555. Retrieved from
https://
www.sciencedirect.com/science/
article/pii/S088832700900377X
(Spe-
cial Issue: Operational Modal Analysis) doi:
https://doi.org/10.1016/j.ymssp.2009.11.005
Van Rossum, G., & Drake, F. L. (2009). Python 3 reference
manual. Scotts Valley, CA: CreateSpace.
Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J.,
Jones, L., Gomez, A. N., . . . Polosukhin, I. (2017).
Attention is all you need. In I. Guyon et al.
(Eds.), Advances in neural information processing
systems (Vol. 30). Curran Associates, Inc. Re-
trieved from
https://proceedings.neurips
.cc/paper files/paper/2017/file/
3f5ee243547dee91fbd053c1c4a845aa
-Paper.pdf
Vibhorpandhare, Jia, X., & Lee, J. (2021). Col-
laborative prognostics for machine fleets using
a novel federated baseline learner.. Retrieved
from
https://api.semanticscholar.org/
CorpusID:244645140
Wang, J., Wen, G., Yang, S., & Liu, Y. (2019). Remaining
useful life estimation in prognostics using deep bidi-
17

INTERNATIONAL JOURNAL OF PROGNOSTICS AND HEALTH MANAGEMENT
rectional lstm neural network [Conference paper]. In
D. P., L. C., Y. S., D. P., & S. R.-V. (Eds.), (p. 1037 –
1042). Institute of Electrical and Electronics Engineers
Inc. (Cited by: 121) doi: 10.1109/PHM-Chongqing
.2018.00184
Wu, S.-j., Gebraeel, N., Lawley, M. A., & Yih, Y. (2007). A
neural network integrated decision support system for
condition-based optimal predictive maintenance policy.
IEEE Transactions on Systems, Man, and Cybernetics
- Part A: Systems and Humans,37(2), 226-236. doi:
10.1109/TSMCA.2006.886368
Xia, M., Li, T., Shu, T., Wan, J., de Silva, C. W., & Wang,
Z. (2019). A two-stage approach for the remaining
useful life prediction of bearings using deep neural net-
works. IEEE Transactions on Industrial Informatics,
15(6), 3703-3711. doi: 10.1109/TII.2018.2868687
Xu, J., Duan, S., Chen, W., Wang, D., & Fan, Y. (2022).
Sacgnet: A remaining useful life prediction of bear-
ing with self-attention augmented convolution gru net-
work. Lubricants,10(2). Retrieved from
https://
www.mdpi.com/2075-4442/10/2/21
doi: 10
.3390/lubricants10020021
Zhang, J., Wang, P., Yan, R., & Gao, R. X. (2018). Long short-
term memory for machine remaining life prediction
[Article]. Journal of Manufacturing Systems,48, 78 –
86. (Cited by: 302) doi: 10.1016/j.jmsy.2018.05.011
Zheng, S., Ristovski, K., Farahat, A., & Gupta, C. (2017).
Long short-term memory network for remaining useful
life estimation. In 2017 ieee international conference on
prognostics and health management (icphm) (p. 88-95).
doi: 10.1109/ICPHM.2017.7998311
Zhu, J., Chen, N., & Shen, C. (2020). A new data-
driven transferable remaining useful life prediction
approach for bearing under different working
conditions. Mechanical Systems and Signal Process-
ing,139, 106602. Retrieved from
https://
www.sciencedirect.com/science/
article/pii/S0888327019308234
doi:
https://doi.org/10.1016/j.ymssp.2019.106602
APPENDIX
(a) Central model. (b) Local model.
(c) FedAvg model. (d) FedPer model.
Figure 13. SiC MOSFET dataset RULP predictions for round
1, device 4.
(a) Central model. (b) Local model.
(c) FedAvg model. (d) FedPer model.
Figure 14. SiC MOSFET dataset RULP predictions for round
3, device 1.
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INTERNATIONAL JOURNAL OF PROGNOSTICS AND HEALTH MANAGEMENT
(a) Central model. (b) Local model.
(c) FedAvg model. (d) FedPer model.
Figure 15. SiC MOSFET dataset RULP predictions for round
3, device 4.
(a) Central model. (b) Local model.
(c) FedAvg model. (d) FedPer model.
Figure 16. SiC MOSFET dataset RULP predictions for round
5, device 1.
(a) Central model. (b) Local model.
(c) FedAvg model. (d) FedPer model.
Figure 17. SiC MOSFET dataset RULP predictions for round
5, device 2.
(a) Central model. (b) Local model.
(c) FedAvg model. (d) FedPer model.
Figure 18. C-MAPSS dataset RUL predictions for FD001
subset.
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INTERNATIONAL JOURNAL OF PROGNOSTICS AND HEALTH MANAGEMENT
(a) Central model. (b) Local model.
(c) FedAvg model. (d) FedPer model.
Figure 19. C-MAPSS dataset RUL predictions for FD003
subset.
(a) Central model. (b) Local model.
(c) FedAvg model. (d) FedPer model.
Figure 20. C-MAPSS dataset RUL predictions for FD004
subset.
20