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Data-Driven Approaches to Diagnostics and State of Health
Monitoring of Maritime Battery Systems
Erik Vanem1, 2, Qin Liang1, Carla Ferreira1, Christian Agrell1, Nikita Karandikar1, Shuai Wang1, Maximilian Bruch 3, Clara
Bertinelli Salucci2, Christian Grindheim2, Anna Kejvalova2, Øystein Åsheim Alnes 4, Kristian Thorbjørnsen5, Azzeddine
Bakdi5, Rambabu Kandepu5
1DNV Group Research & Development, Høvik, Norway
Erik.Vanem@dnv.com
Qin.Liang@dnv.com
Carla.Ferreira@dnv.com
Christian.Agrell@dnv.com
Nikita.Karandikar@dnv.com
Shuai.Wang@dnv.com
2Department of Mathematics, University of Oslo, Oslo, Norway
erikvan@math.uio.no
clarabe@math.uio.no
chrgrindheim@gmail.com
annakej@student.ikos.uio.no
3Fraunhofer ISE, Freiburg, Germany
maximilian.bruch@ise.fraunhofer.de
4DNV Maritime, Høvik, Norway
oystein.alnes@dnv.com
5Corvus Energy, Porsgrunn, Norway
kthorbjornsen@corvusenergy.com
abakdi@corvusenergy.com
rkandepu@corvusenergy.com
ABS TR ACT
Battery systems are increasingly being used for powering
ocean going ships, and the number of fully electric or hybrid
ships relying on battery power for propulsion and maneuver-
ing is growing. In order to ensure the safety of such electric
ships, it is important to monitor the available energy that can
be stored in the batteries, and classification societies typically
require that the state of health (SOH) can be verified by in-
dependent tests. However, this paper addresses data-driven
approaches to state of health monitoring of maritime bat-
tery systems based on operational sensor data. Results from
various approaches to sensor-based, data-driven degradation
Erik Vanem 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.
monitoring of maritime battery systems will be presented, and
advantages and challenges with the different methods will
be discussed. The different approaches include cumulative
degradation models and snapshot models. Some of the mod-
els need to be trained, whereas others need no prior training.
Moreover, some of the methods only rely on measured data,
such as current, voltage and temperature, whereas others rely
on derived quantities such as state of charge (SOC). Mod-
els include simple statistical models and more complicated
machine learning techniques. Different datasets have been
used in order to explore the various methods, including pub-
lic datasets, data from laboratory tests and operational data
from ships in actual operation. Lessons learned from this ex-
ploration will be important in establishing a framework for
data-driven diagnostics and prognostics of maritime battery
systems within the scope of classification societies.
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1. INTRODUCTION
The safety of battery-powered ships is important, and this is
verified and ensured by classification services. Fire and ex-
plosion are obvious risks, but another central aspect is ensur-
ing that the available energy stored in the batteries is suffi-
cient to cover the required propulsion or manoeuvring power
demand (Hill et al., 2015). Loss of propulsion power in a crit-
ical situation can lead to serious accidents such as collision
or grounding. Therefore, reliable estimation and prediction
of the actual available energy of a battery is crucial for ship
safety.
Battery systems are aging, meaning that the energy storage
capacity degrades by calendar time and by charge/discharge
cycles (Pop et al., 2008). The aging process affects both the
amount of charge that can be stored and the available power.
Most maritime battery systems are designed with an expected
lifetime of 10 years and end of life is typically defined as State
of Health (SOH) = 70-80%, where SOH stands for the ratio
of remaining capacity to initial capacity (in %). Ships, on the
other hand, are typically design for 25-30 years. Hence, bat-
teries are expected to approach their end of useful life (EOL)
long before the end of the operational life of the vessels. In
such a context, reliable estimation of SOH will become in-
creasingly important as the battery systems approaches its
EOL and making correct decisions on remaining useful life
(RUL) will have great financial and safety implications.
Currently within the maritime Industry, the governing
methodology for evaluating the real-time capacity of a bat-
tery system on board a fully electric or battery-hybrid vessel
is by considering the State of Charge (SOC) and the State
of Health (SOH) in the following simplistic way: Available
energy = Initial Capacity x SOC x SOH. A major part of such
an estimation will be a reliable evaluation of the battery State
of Health. Currently, battery suppliers are required to have
an SOH estimation algorithm and to verify the SOH annually
through in-situ capacity testing. From a practical point of
view, the annual capacity test is time consuming and typically
requires that the ship is taken out of operation for one full
day. Moreover, the accuracy of the test is questionable due
to several factors influencing the results, such as variability
in loads, temperatures and Depth of Discharge (DOD). As
ship-to-shore connectivity has improved immensely over the
past few years it is natural to evaluate whether a sensor-based
monitoring system can both reduce downtime for the operator
and improve the quality of the SOH verification.
This paper summarizes and presents several approaches to
data-driven modeling of state of health of maritime battery
systems. The overall idea is to use sensor data from batteries
to learn the degradation state of the batteries without the need
for specific testing or characterization cycles. If successful,
data-driven approaches may replace the need for annual ca-
pacity testing to verify SOH according to class rules.
A review of different approaches for data-driven diagnos-
tics of maritime battery systems were presented in Vanem,
Bertinelli Salucci, et al. (2021); Vanem, Alnes, & Lam
(2021). According to this review, data-driven methods for
estimating battery capacity can be categorized into a few
generic type of approaches. Additionally, a distinction was
made between models that rely on the complete loading his-
tory of the batteries in order to estimate current state of health
and what was referred to as snapshot methods, where state
of health and capacity can be estimated based on only snap-
shots of the data. In this paper, the exploration of different ap-
proaches and methods will be outlined, including both snap-
shot methods and cumulative methods.
It is important to note that different approaches set different
requirements for the data. For example, most approaches re-
quire training data to train the data-driven models, whereas
some approaches can do without training data. If training
data are required, they obviously need to be representative of
typical operational data, and should preferably correspond to
identical cells as the system it should be applied to. This is
among the considerations that need to be made when com-
paring and recommending which models to use for data-
driven classification of the batteries. Other factors to con-
sider, apart from the predictive performance, include amount
of data needed, the sensitivity to missing data and the compu-
tational costs.
2. BAT TE RY DATASE TS
Different sets of data have been available for analysis and
modeling in the project. These include laboratory data gen-
erated by the project, proprietary data from actual ships in
operation and some publicly available data.
2.1. Laboratory Test Data
Three different types of battery cells have been subject to
cycling tests at Fraunhofer’s laboratory in order to generate
degradation data for the cells. Two types of cylindrical 18650
cells, i.e. energy cells (henceforth denoted DDE; nominal
capacity 3.5 Ah) and power cells (henceforth denoted DDP;
nominal capacity 2.5 Ah), and one type of pouch cells (hence-
forth denoted DDF; nominal capacity 64 Ah) have been cy-
cled according to specified test matrices. Individual cells have
been cycled within specified lower and upper voltage limits,
with specified charge and discharge currents, and at speci-
fied controlled temperatures. Varying these parameters yields
different degradation rates. This continuous cycling is inter-
rupted at regular intervals to perform check-ups and capac-
ity measurements, i.e. pulse tests and charge and discharge
capacity measurements by way of Coulomb counting over
deep cycles at low current rates. Hence, capacities will be
measured at certain points in time for all cells. Results are
illustrated in Figure 1, which show estimated capacity as a
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Figure 1. Capacity versus equivalent full cycles from Fraunhofer laboratory tests; DDE (left), DDP (middle) and DDF cells
function of the number of equivalent full cycles (EFC) for the
three types of cells. EFC has been calculated based on cur-
rent integration compared to the nominal capacity. It is noted
that some of the DDF cells have not been cycled - they are
simply stored over time. Hence, a significant drop in capac-
ity is observed without any increase in EFC for some of the
DDF cells, and this is due to calendar aging (rightmost plot
in Figure 1).
Values of current, voltage and temperature are sampled con-
tinuously, resulting in time-series of these variables through-
out the experiment. From these raw measurements, different
derived variables can be calculated as well, such as cumu-
lative throughputs, cycle counts and equivalent full cycles.
Measurements are obtained from a total of 81 individual cells;
35 DDE cells, 30 DDP cells and 16 DDF cells. The cells in
this experiments have been charged and discharged according
to a constant-current-constant voltage (CCCV) scheme: the
cells are charged/discharged with constant current until the
cut-off voltage, where the cells continue to charge/discharge
at constant voltage with a current that gradually decreases to-
wards zero.
A similar set of data from cycling tests performed on the same
cell types but at a different lab at Corvus’ has been made
available. Two types of cylindrical cells have been tested, cor-
responding to energy cells and power cells, which are similar
to the DDE and DDP cells tested at Fraunhofer. Again, the
cells have been subject to repeated cycling, with regular ca-
pacity measurements by Coulomb counting. Figure 2 shows
the measured remaining capacity as a function of equivalent
full cycles (EFC) for the energy (E) and power (P) cells, re-
spectively. The figures indicate both charge and discharge ca-
pacities, measured during charging and discharging tests, and
these are very similar, with only slightly higher values for the
charge capacity. The regular cycling in these tests are slightly
different from the tests performed at Fraunhofer. That is, the
regular cycling consists of repeatedly charging the cells with
a constant current - constant voltage scheme (CCCV), then
discharging with a constant power, with small pauses in be-
tween.
Some additional data have been available from DNV’s lab
testing facilities, on battery cells of similar types as the ones
used in the operational data. For some applications, these
have been used as training data to train the data-driven mod-
els.
2.2. Operational Data From Ships in Service
Field data from electric ships with a battery system of pouch
cells of type DDF have been analyzed in this study. These
battery systems are designed with a 4-layer structure; individ-
ual cell-pairs connected in series make up modules, modules
connected in series form packs and several packs connected
in parallel make up an array. A ship may have one or more ar-
rays connected in parallel as independent energy storage sys-
tems that do not communicate directly, and any combination
of packs in an array can be powered off during operation.
Raw data from these systems include the pack voltage and
current for all packs as well as the cell voltage, temperature
and State of Charge (SOC) for all cells (or rather, cell-pairs).
Since modules and cell-pairs are connected in series within
a pack, the current will be the same for all series elements
in that pack. However, it will not be possible to distribute
this current over the two cells in a series element. Hence, for
all practical purposes, the cell-pairs will be considered the
smallest entities of the system, i.e. cells. Moreover, whereas
currents, voltages and temperatures are measured directly by
sensors, SOC is a derived quantity that needs to be calcu-
lated from the other raw sensor measurements. An example
of time-series from this system is shown in Figure 3.
Operational data from 6 different ships with the same battery
system on board have been available for this study. These
ships include both hybrid and all-electric solutions and with
different configurations (different number of arrays and packs
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Figure 2. Capacity as a function of equivalent full cycles from Corvus laboratory tests; energy (left) and power (right) cells
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Current
SOC
Temperature
Voltage
Operation Data
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Figure 3. Example of time-series from the onboard battery
system; pack current (top), cell SOC (2nd row), cell temper-
ature (3rd row) and cell voltage (bottom)
per array). All of these systems are relatively new, without
having experienced extensive degradation. Results from an-
nual capacity tests are available, and all vessels had under-
gone at least two such tests by the time of this study. The
ships battery system configuration can be found in Table 1.
Trace plots of the operational data from one cell on Vessel C
is shown in Figure 4. It is observed that there is a rather long
gap in the data, and also that this system started doing fast-
charging at some point, with a sudden occurrence of higher
maximum currents.
Additional data from an older battery system have been ana-
lyzed in this study. These have different types of battery cells,
but with the benefit of longer time histories. However, data
quality is somewhat lower, and there are more and longer data
gaps compared to the newer system. Data from these systems
Table 1. Ships battery system configuration
Ship ID Battery # arrays # packs # Annual
system per array tests
Ship A Hybrid 2 4 2
Ship B Hybrid 1 12 3
Ship C All-electric 2 9 2
Ship D All-electric 2 9 2
Ship E All-electric 2 9 2
Ship F Hybrid 2 13 3
are referred to as Site A, Site B and Site C and include data
from three different vessels.
2.3. Publicly Available Datasets
There are a number of publicly available datasets from vari-
ous types of batteries (dos Reis et al. (2021)). Some of these
contain degradation data from cycling tests, and has been uti-
lized in this study.
Several battery datasets have been made publicly available by
the NASA Ames Prognostics Center of Excellence (PCoE),
of which a randomized battery usage dataset has be analyzed
in this study Bole et al. (2014)1. It consist of aging data of
18650 lithium-ion batteries under randomly generated usage
profiles. The loading of these batteries contain two regimes:
reference discharges and random walk steps. The reference
discharge step is a controlled full discharge cycle following a
controlled full charge cycle. This is used to estimate the cell
capacity periodically. Both the charge and the discharge in
these cycles follow the CCCV principle. During the random
walk steps, a charge or discharge current is randomly sampled
from a set of current values, and then kept constant for a pre-
determined period of time or until a voltage limit is reached.
Then, a new current is drawn and this continues until a new
1Bole, B. and Kulkarni, C. and Daigle, M. Randomized Battery Us-
age Data Set. NASA Arnes Prognostics Data Repository. URL:
http://ti.arc.nasa.gov/project/prognostic-data-repository
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Figure 4. Raw data from one cell from Vessel C
reference cycle is performed at pre-determined intervals. At
all times, values of temperature, current and voltage are mea-
sured. For more details on these data, reference is made to
Bole et al. (2014), see also Bertinelli Salucci et al. (2022).
3. DATA- DR IV EN STATE O F HEA LTH ESTIMATION
In this section of the paper, a description of various data-
driven approaches that have been explored in this study will
be presented. They include both cumulative damage models,
snapshot methods and other approaches, and are applied to
different datasets.
3.1. Cumulative Degradation Methods
3.1.1. Battery.ai
Battery AI is an artificial intelligence driven, semi-empirical
battery analytics platform (Xue et al. (2022))2. It provides
real-time battery health analysis considering both cycling and
calendar aging. The aim of this case study is to test the capa-
bility, functionality and prediction accuracy of Battery AI on
real operational data. Battery AI uses a combination of ma-
chine learning and semi-empirical methods to model battery
behavior under various real-world conditions. The platform
can analyze complex duty cycles in real-world operating con-
ditions and determining the constituent abuse factors. The
impact of these abuse factors is then modeled to predict total
degradation. In short, a semi-empirical function on the form
y= 100 −A×T O p+C(1)
2Battery.AI; url: https://www.dnv.com/services/battery-ai-35181
Battery AI on Veracity; url: https://store.veracity.com/battery-ai
is fitted to degradation data, where T O denotes turnover and
C is a calibration factor. The exponent pis estimated from
empirical degradation curves, and Amodels the contribution
from the combined effect of the various stress factors by way
of a neural network trained on cycling test data. Detailed
description of this tool is out of scope of this paper, but ref-
erences is made to Xue et al. (2022); see also an extended
description of this case study in Liang et al. (2022, 2023).
Figure 5 shows an example of results from this method on
one cell from one of the vessels investigated in this study.
Results are reasonably good, with deviations from the annual
capacity tests in the order of 3% after one and a half year.
Note also that estimated SOH > 100% means that the esti-
mated capacity is greater than the nominal capacity. Results
for the other vessels are similar, but it is stressed that verifi-
cation is difficult without longer time series of data and more
degradation.
Figure 5. Example of SOH predictions from battery.AI com-
pared to annual test
One critical step in analyses using the battery.AI tool is the
pre-processing of the data to get it on the required input for-
mat. This includes cycle decomposition of the raw data to
identify cycles and assign stress factor to these. These are
then combined in a cumulative way, where degradation con-
tributions from the individual cycles are added together. As
elaborated in Liang et al. (2023), this is both time-consuming
and expensive when the amount of data grows large. For large
maritime battery systems, which contains several thousand
cells, and are operated over several years, it was found that
the amount of data handling and pre-processing is a signif-
icant barrier to practical large-scale implementation of this
tool. Moreover, since it is a cumulative method, it relies on
the complete data stream and do not handle gaps in the data
very well. Nevertheless, results from this case study indi-
cate that the battery.AI tool might be able to predict battery
degradation reasonably well. Notwithstanding, the practical
limitations with regards to the data handling and the fact that
it is a cumulative method that requires complete time series is
a barrier for widespread implementation on a fleet of ships.
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3.1.2. Probabilistic cumulative models
This section describes a way to model the battery state of
health (SOH) for varying loading conditions, using data from
controlled laboratory experiments as training data and applied
to predict SOH on operational data from ships. In the con-
trolled laboratory experiments, cells are cycled under fixed
loading conditions, and the SOH as a function of the number
of cycles is estimated. A loading condition is represented by
the following five parameters: 1) Charge C-rate, 2) Discharge
C-rate, 3) Upper state of charge, 4) Lower state of charge, and
5) Temperature.
We consider inputs of the form (x, n)where x∈R5and n∈
N. Here x= (x1, . . . , x5)represents a loading scenario (’C-
rate charge’, ’C-rate discharge’, ’SOC upper’, ’SOC lower’,
’Temp’), and nis the number of cycles. Hence, (x, n)means
that ncycles are performed under condition x. Assume that
the cell is subjected to n1cycles under condition x1, followed
by n2cycles under condition x2, and so on. We will write
this as (X,n)where X= (x1, . . . xk)and n= (n1, . . . , nk).
Hence, (X,n)represents a total of Pk
i=1 nicycles under the
kdifferent conditions x1, . . . , xk.
Let fx(n)denote the SOH after ncycles under condition x.
We assume that all cells start with 100% SOH, i.e. fx(0) = 1
for all x. Let S(X,n)denote the SOH after loading (X,n).
That is, the SOH after the cell has been subjected to n1cycles
under condition x1, followed by n2cycles under condition x2,
and so on. We have that S(·,0)≡1. We will also define the
reduction in SOH which we denote ∆f. Let ∆f(s, x, n)be
the reduction in SOH after starting at SOH =sand then run
ncycles under condition x. When the condition xis fixed, we
have that
∆f(s, x, n) = s−fxf−1
x(s) + n.(2)
To model the SOH in this way, we rely on a "Markovian"
assumption of path independence, i.e. we assume that the
total reduction in SOH corresponding to the variable loading
(X,n)is the sum of the SOH reductions corresponding to the
individual scenarios (x1, n1), . . . , (xk, nk). That is,
S(X,n) = 1 −
k
X
i=1
∆si,(3)
where
∆si= ∆f(si−1,xi, ni), s0= 1,
si−1= 1 −(∆s1+· · · + ∆si−1).(4)
From Ncontrolled experiments we obtain a dataset D=
{(xi,ni,si)}N
i=1. Here xiis the fixed loading condition for
the i-th experiment, and (ni,si)contains a finite set of SOH
measurements where s(j)
iis the SOH after cycle n(j)
i. The
general approach to model SOH under dynamic loading is as
follows:
1. Use machine learning to estimate either
a) ˆ
fx(n)≈fx(n) : R5×[0,∞)→[0,1], or
b) c
∆f(s, x, n)≈∆f(s, x, n) : [0,1]×R5×[0,∞)→
[0,1].
2. Use (3) and (4) to compute the SOH for a new set of
cycles nwith dynamic loading X.
An important aspect is that both ˆ
fand c
∆fwill be subject
to uncertainty due to the limited number of experiments that
can be performed in practice. This is a "small data" machine
learning problem where uncertainty quantification is impor-
tant. We can use probabilistic machine learning to quantify
uncertainty regarding ˆ
fand/or c
∆fand propagate this uncer-
tainty to the quantity of interest S(X,n)by Monte Carlo sim-
ulation . In this study, two different approaches for how to es-
timate ˆ
fx(n)with probabilistic machine learning is explored:
non-parametric using Gaussian process regression (see e.g.
Rasmussen & Williams (2006); Agrell & Dahl (2021)) and
parametric using Bayesian neural network (see e.g. Bingham
et al. (2018)).
These models have been trained on experimental data with
static loading (42 experiments with 21 duplicated unique
loading conditions) and applied to predict SOH on opera-
tional data with dynamic loading from one ship (Vessel C).
The operational data have been converted to a table of half-
cycles by cycle counting, and it is assumed that the SOH re-
duction from one half-cycle is half the reduction of a corre-
sponding full cycle. This assumption might not be entirely
true and adds uncertainties to the model predictions. Exam-
ples of model predictions against pairs of experiments that
were held out during training are shown in Figure 6 (LOO
denotes leave one out).
Figure 6. SOH as predicted by the Gaussian process model
(left) and the Bayesian neural network (right) compared to
two identical experiments (excluded from training)
The degree of uncertainty shown in Figure 6 illustrates one
main challenge with this approach. For most loading scenar-
ios (excluding those the model has been trained on), the SOH
degradation can vary a lot. If such cycles are encountered, the
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uncertainty will be propagated and increased further in future
cycles and may "blow up". This is indeed what is observed
when these models are applied on the operational data; in all
cases the final SOH estimate was affected by this behavior,
both with the Gaussian process and the Bayesian neural net-
work alternative.
The main conclusion from this exercise is that high-quality
data and a good machine learning model is crucial for the
proposed method to work, since uncertainty will accumulate
in a cumulative model. Two main challenges was encoun-
tered in this study, i.e. that the training data did not cover the
operational cycles well, and that there are too little degrada-
tion in the operational data in order to really evaluate model
performance well.
3.1.3. Sequential and Non-Sequential Machine Learning
A set of sequential and non-sequential statistical and machine
learning models were applied to the NASA randomized usage
dataset based on summaries of the cumulative load profiles.
I.e., features are extracted in terms of histograms or buckets of
experienced conditions to predict capacity degradation. For
further details of these analyses, reference is made to Grind-
heim (2022), and in the following a brief summary will be
presented.
The main difference between non-sequential and sequential
methods is that sequential methods take the temporal infor-
mation into account, i.e. they work on time series, whereas
non-sequential methods regard data as independent in time.
The non-sequential methods explored in this study include
linear regression without penalization (OLS) and with differ-
ent types of penalization (ridge regression and lasso), gra-
dient boosted regression trees and support vector regression
(see e.g. Hastie et al. (2009) for an introduction to such
methods). The sequential methods include recurrent neu-
ral networks (RNN), long short-term memory (LSTM) mod-
els, transformers and temporal convolutional neural networks
(TCN), see e.g. Hochreiter & Schmidhuber (1997); Vaswani
et al. (2017); Oord et al. (2016).
For the non-sequential methods, features are extracted from
the random walk steps in terms of so-called buckets or his-
tograms of times spent in different current profiles and with
different bins of voltage and temperature. Interaction ef-
fects are included in the form of 2-dimensional buckets for
current-voltage and for current-temperature as well as a 3-
dimensional bucket for the time spent in different combina-
tions of voltage, temperature and current. Additional covari-
ates are introduced for the rest time and the temperature of
the batteries as well as data from the last nsteps prior to a
reference cycle. The idea is that the buckets explains the cu-
mulative degradation of the batteries, whereas the additional
covariates representing the usage just prior to the reference
cycles account for the stress of the battery when the refer-
ence cycles are performed. Different model alternatives that
include different subsets of the histogram features – different
data formats – are compared in terms of root mean square er-
ror (RMSE). The models are trained on the combined data for
all cells, but where the cell to be predicted is left out.
For the sequential methods, sequential data are used as in-
put. Two types of sequence formats are used based on the
raw data: long sequences correspond to down-sampled initial
time-series and short sequences include summary statistics
from each random walk step. In addition, static covariates
for the estimated capacity for the previous cycle and the tem-
perature during the reference discharge are included. Some
examples of predicted capacity deterioration from two of the
non-sequential models and two of the sequential models are
shown in Figure 7 for some of the data formats.
Ridge SVR
LSTM TCN
Figure 7. Predicted capacity degradation for some non-
sequential methods and data format; from Grindheim (2022)
The average RMSE for the best performing models are sum-
marized in Table 2. This summary indicate that the non-
sequential penalized linear regression models – ridge regres-
sion – performs best. On second place, different models such
as lasso, transformers and support vector regression, perform
almost equally good on average for the four cells. These re-
sults indicate that relatively simple linear models may outper-
form more complicated deep learning architectures.
This exercise has illustrated that it is possible to predict bat-
tery degradation using rather simple statistical models based
on buckets or histograms of operating conditions. As such
it would be a cumulative damage type of model, since the
complete loading history is needed in order to construct the
histogram-features. Even though the data size may be sig-
nificantly reduced since only summaries of the raw data are
needed it is questionable how well such methods scale to
large battery systems with very many battery cells, and the
histograms might also be biased if there are large data-gaps
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Table 2. Models ranked by lowest average RMSE score for
the four batteries; from Grindheim (2022)
model average RMSE
Ridge 0.067
Lasso 0.096
Transformer 0.097
SVR 0.099
TCN 0.108
xgboost 0.109
LSTM 0.117
in the sensor data. These are serious limitations of such types
of approaches and further study would be needed in order to
recommend such models for monitoring actual battery sys-
tems onboard ships.
3.1.4. Semi-Supervised Learning Approach
Access to relevant and high-quality data is a prerequisite for
data-driven estimation of state of health. Some models need
to be trained on a representative set of data to be applied on
other battery systems, and getting access to such training data
is a major challenge. For example, operational data will typi-
cally contain time series of several explanatory variables, but
will very seldom include information of capacity or state of
health. Typically, there will be high-resolution data of the co-
variates, but only few recorded values of the response from
whenever the system has performed a capacity test. In such
a situation, semi-supervised learning might be useful, if the
limited amount of labeled data can be exploited to generate
additional labels. Such an approach has been explored in
Bertinelli Salucci et al. (2023), and a brief summary of this
work is presented in the following.
Data from three vessels with the older battery system are used
in this study and the analysis is performed on pack-level. The
overall idea is to exploit the information that is in the opera-
tional data for one of the vessels to train a data-driven model
to predict state of health on the two others. The data are
continuous measurements of current, temperature and state
of charge, and the data for Site A include results from three
annual capacity tests. Hence, there are three cycles with la-
bels. The idea is assume a time window of constant SOH
around the annual test, and generate labels for other cycles
within this window. This idea is illustrated by Figure 8. The
pseudo-capacity corresponding to the cycles can be calcu-
lated by Coulomb counting of the incomplete cycles.
To generate labels, the data are clustered to identify groups
of cycles with similar conditions. Hence, the data are filtered
and clustered according to the depth of discharge (DoD), state
of charge, C-rate, and temperature. Groups of similar cycles
within the constant SoH-windows are regarded as reference
cycles, which would get labels from the annual test results. A
set of simple linear models is applied to estimate the battery
capacity based on the pseudo capacity and other characteris-
tics of the cycles. Cycles with similar characteristics are then
identified in the target data, i.e., data from outside these con-
stant SOH windows. Different cycle characteristics give rise
to different groups of cycles, and SOH can be estimated in-
dependently for different groups. An illustration of the SOH
estimates based on the different groups of cycles is shown in
Figure 9, where different colors distinguish between different
cycle groups. These estimates are for a different vessel than
the one providing the training data. Final SOH estimates can
be obtained by averaging the estimates from the different cy-
cle groups, and weights are introduced reflecting the degree
of uncertainty of the different groups.
An additional optional supervised learning step is suggested
in Bertinelli Salucci et al. (2023), where cumulative model-
ing can be performed on data with the newly created SOH
labels. Hence, multivariable fractional polynomial regression
models are trained to model the change in SOH over time.
This method predicts a reasonable overall decreasing trend
in battery capacity, although individual estimates are some-
what uncertain. However, when a vessel is used to generate
training data to predict SOH of other vessels, it is question-
able to what extent such a method can be used to estimate a
larger extent of degradation for the target vessels compared
to what the reference vessel has experienced. Hence, training
data should in principle always come from the battery system
with the lowest state of health, something that could be diffi-
cult to guarantee from a fleet of vessels. Notwithstanding, it is
demonstrated that it is possible to extend labels of SOH from
a few capacity tests to other cycles within a constant SOH
window and to use this to estimate capacity degradation.
Figure 8. Data for depth of discharge for a battery pack on one
of the vessels. Colored dots indicate reference cycles where
SOH is observed; black dots are cycles within a window of
assumed constant SOH and grey dots are cycles outside these
windows. (from Bertinelli Salucci et al. (2023)).
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Figure 9. SOH estimates for one pack from a target vessel
from different groups of cycles.
3.2. Snapshot Methods
3.2.1. Regression on Features Extracted from Charge
and Discharge Curves
Results from a number of relatively simple regression mod-
els for remaining capacity based on features extracted from
charge and discharge curves from the Fraunhofer laboratory
data were presented in Vanem et al. (2022). This work was
extended by fusing data from both Fraunhofer and Corvus lab
tests in Vanem et al. (2023). In the following, a brief summary
will be given.
After some initial filtering of the data, features are extracted
from the charge and discharge curves from individual cycles
close to the capacity measurement. Examples of extracted
charge and discharge curves for an arbitrary DDE-cell are
shown in Figure 10. The different colours correspond to dif-
ferent regular cycling periods, and it is clearly seen that these
curves are changing as the battery degrades. The measured
capacity preceding each period of regular cycling is also in-
dicated in the figures, and "no = 2" indicates that these results
are based on the second charge/discharge cycles in the regular
cycling periods.
From the selected cycles, the mean, minimum and maximum
temperature as well as the mean current are used as covari-
ates. Moreover, the total charge throughputs between voltage
ranges in steps of 0.1 V are used as additional explanatory
variables. It is noted that features have only been extracted
from the constant-current phase in this study. One reason for
this is that these are the features deemed most likely to be
found in data from battery systems in actual operation on-
board ships. In total up to 44 features are collected and the
overall dataset of extracted features contains 281 samples for
the DDE cells and 269 samples for the DDP cells. How-
ever, it is noted that not all cells have information for all co-
variates. The various cells have been cycled between differ-
ent voltage limits, and therefore have different subsets of the
voltage-based features. Other features suggested in the liter-
ature, include features from derivative curves and from prob-
ability density functions from time spent in different voltage
ranges, see e.g. Weng et al. (2013); Feng et al. (2013); Zheng
et al. (2018); Jiang et al. (2020); Ibraheem et al. (2023).
A number of rather simple statistical models are employed
in this study to predict the capacity of the battery cells based
on snapshot features, i.e., Linear regression (Linear), Linear
regression with missing covariates (Miss), Ridge regression
(Ridge), Least absolute shrinkage and selection operator re-
gression (Lasso), Multivariable fractional polynomial regres-
sion (MFP), Generalized additive models (GAM), Regression
tree (RT), Random forest (RF) and Support vector regression
(SVM), see Vanem et al. (2023). See also Hastie et al. (2009)
for full mathematical description of the various models.
As outlined in Vanem et al. (2022, 2023), this snapshot ap-
proach yields quite good results for some of the cells, but un-
fortunately not for all. Examples of model predictions com-
pared to observations are shown in Figure 11 for an arbitrary
cell. The prediction performance of this approach is eval-
uated by calculating the average RMSE from all model al-
ternatives for the individual cells. Results are illustrated in
Figure 12, which also indicate the test parameters for the var-
ious cells. The orange markers present the average RMSE for
each cell when the data from that cell is included in the train-
ing data and the red markers present the results when data
from that cell have been excluded from the training. The ver-
tical bars correspond to the voltage range the cells have been
cycled between (right axis), and the two colours of each ver-
Figure 10. Extracted charge and discharge curves from the
raw time series for an arbitrary DDE cell
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tical bar correspond to the C-rate (leftmost colour) and tem-
perature (rightmost color) of the different cells, respectively,
as indicated by the colour legends in the plots. Evaluations
of performance across predictive models are also presented
in Vanem et al. (2022, 2023), without any particular model
being consistently the best one.
The fact that the simple statistical models are able to yield
good results for some of the cells is encouraging, but results
need to be improved in order to be able to recommend such an
approach from a class perspective. Presumably, more relevant
training data would be needed in order to improve results, as
elaborated in more detail in Vanem et al. (2022, 2023).
3.2.2. Simple Linear Model Based on Coulomb Counting
Coulomb counting is based on a fundamental relationship be-
tween integrated current and change in state of charge (SOC),
than can be used to estimate total capacity of a battery. The
cumulative current-time that the battery can deliver from fully
charged to fully discharged state corresponds to the charge ca-
pacity of the battery (in terms of Ampere-hours (Ah)). This
relationship should also be preserved during partial cycling
and can be utilized in a simple linear model to estimate ca-
pacity and subsequently the state of health.
The relationship between the total capacity Qand state of
charge SOC of a battery at times t1and t2is described by
Figure 11. Example of data-driven predictions based on snap-
shot features from charge cycles only
Figure 12. Average RMSE and test parameters for each cell
the following equation:
SOC(t2) = S OC (t1) + 1
QZt2
t1
ηI(τ)dτ (5)
where I(τ)is the battery current at time τmeasured in am-
peres, which is defined as positive when charging and nega-
tive when discharging, and ηis a unitless Coulomb efficiency
factor. For simplification, η≈1may be assumed.
By can be rewritten as
Zt2
t1
ηI(τ)dτ =Q(SOC(t2)−S OC (t1)) (6)
which can be presented as a linear regression problem
Y=QX +ε, (7)
where Y=Rt2
t1ηI(τ)dτ and X=SOC(t2)−S OC (t1), as
suggested by Plett (2011). By collecting data for Yand Xthe
regression coefficient Q, representing total capacity, can be
estimated by different methods, such as ordinary least squares
(OLS) and total least squares (TLS). Note that the regression
model does not have an intercept; when there is no current, or
when the integrated current is zero, there should also not be
any change in SOC. Hence, in principle, one observation of
concurrent (X, Y )should be sufficient to give an estimate of
the regression coefficient. Different implementations of such
a simple linear model has been applied to both laboratory and
operational data, as outlined in the following.
First, a simple OLS version of this model is applied to the
Fraunhofer lab data for the three different types of cells. Af-
ter each capacity measurement, data are collected from the
first 25 cycles and the integrated current and the change in
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Figure 13. Applying the simple linear method to estimate SoH on one cell; Calculated X=change in SOC and Y=integrated
current for the full and partial cycles together with estimates regression lines
Figure 14. Estimated SOH based on full and partial cycles from the simple linear model. X-axis denote the check-ups.
SOC is calculated from the complete charge and discharge cy-
cles, as well as from partial cycles, where random segments
of the charge and discharge are extracted. Figure 13 shows
the extracted data for X= ∆SOC and Y=Rt2
t1I(τ)dτ
and estimated regression lines for an arbitrary cell and Figure
14 shows estimated SOH based on both full and partial cy-
cles. Overall, the results are satisfactory and indicate that this
approach can yield reasonable results for most of the cells.
However, for a few cells the estimate capacity deviate no-
tably from the measured capacity. This is most likely due to
inaccuracies in the calculated SOC values.
The same method was also tried on operational data from
ships in service. Different ways of filtering the data in order to
get comparable capacity estimates at various stages of the bat-
teries’ life were explored and compared with annual capacity
tests. Figure 15 shows estimates for four of the packs based
on daily, weekly and monthly data. As can be seen, despite an
overall decreasing trend, there is much variability and the un-
certainty increases as the time period for the data decreases.
Figure 16 shows estimated capacity based on yearly data for
eight different battery packs (from two arrays). For these es-
timates, all data from a whole year is combined to yield and
average annual capacity estimate. A decreasing trend is ob-
served, but with some outliers, most notably in the year 2018.
However, in practice one want to use this method as a snap-
shot method without the need to collect data from a whole
year. Hence, estimates based on shorter time intervals would
be preferred. Additional filtering based on C-rates, tempera-
tures and depth of discharge were investigated, and reference
is made to Kejvalova (2022a) for details.
The simple linear model can also be solved as a total least
squares (TLS) problem, where uncertainties in both the
change of state of charge (X) and integrated current (Y) can
be taken into account. These uncertainties can be due to mea-
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Figure 15. Daily, weekly and monthly estimates of total capacity based on simple linear model (from Kejvalova (2022a))
Figure 16. Yearly capacity estimates
surement error, and it is known that ignoring this in a linear
regression model will tend to a bias towards zero of the re-
gression coefficient – an attenuation bias (see Carroll et al.
(2006)). The total least squares method aims at accounting
for this by considering additive measurement errors in both
Xand Y. That is, given true values X?and Y?, the error-
prone Xand Yare observed,
X=X?+ ∆X
Y=Y?+ ∆Y.
The measurement errors ∆Xand ∆Ycan typically be as-
sumed to be normally distributed with mean 0and variances
σ2
∆Xand σ2
∆Y. Hence, the linear regression model of eq. (7)
can be rewritten as
Y?+ ∆Y=Q(X?+ ∆X) + ε(8)
Note that the measurement error in the dependent variable
can not be distinguished from the equation error εand will
not introduce a bias (only add to the variance), but the mea-
surement error in the explanatory variable Xwill lead to the
attenuation bias. Total least squares will seek to minimize the
squares of errors in both the dependent and independent vari-
ables and hence to correct for the attenuation bias of ordinary
least squares. Various TLS implementations proposed in Plett
(2011) have been applied to operational data from ships in
service, and details are presented in Kejvalova (2022b). The
sensitivity of sensor measurement error and the influence this
has on the uncertainties of Xand Yis highlighted in Kejval-
ova (2022b), and Figure 17 illustrates the difference between
OLS-estimates and TLS-estimates of total capacity based on
operational data from a battery pack. Results show differ-
ent results for the TLS model for different variance ratios,
φ=σ2
∆x
σ2
∆y
; when the ratio is small, indicating that the error
in Xis small compared to the error in Y, then the TLS esti-
mate is similar to the OLS estimate. However, the difference
increases as the error in Xgrows compared to the error in
Y, as expected. In all cases, the OLS estimate underestimate
the regression coefficient Q(total capacity), meaning that this
could be construed as a lower limit. Note that the variances
(or the variance ratio) need to be known in the TLS approach.
Figure 17. Difference between OLS and TLS estimates of ca-
pacity for different variance ratios (from Kejvalova (2022b))
The simple linear model in (6) has also been implemented
as a Bayesian linear regression model (BLR) and applied on
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operational data from a ship in service. Rather than fitting
the model to the data by OLS or TLS, a prior distribution
for the model parameters is introduced and the likelihood is
computed from the observed data to give the posterior of the
model parameters using Bayes’ theorem. Hence, predictive
distributions rather than point estimates can be obtained, see
Goldstein & Wooff (2007) for more details. This implemen-
tation of the model includes an intercept with a zero-mean
Gaussian prior with small variance. The prior for the slope is
based on the data in an empirical Bayes approach, see Gel-
man et al. (2014). An example of capacity estimates from the
Bayesian linear model over time for one vessel is shown in
Figure 18. It is observed that the estimated capacity initially
increases, before it stabilize and tend to decrease. Such be-
havior may seem counter-intuitive, and needs to be carefully
evaluated. However, it may also be explained by the fact that
total capacity is not a fixed quantity but rather a function of
the operating conditions, as discussed above. If the opera-
tional conditions change, e.g. a change in c-rate or temper-
ature, and estimated increase in total capacity might not be
unexpected.
Figure 18. BLR model prediction and uncertainty over time.
In summary, the simple linear model based on Coulomb
counting remains an intuitive and promising approach for
condition monitoring on maritime battery systems. Some of
its advantages are that there is no need for training data to
train the model and that it is a snapshot method that do not
rely on complete uninterrupted data-streams from the vessel.
Moreover, it may equally well be applied on pack level as on
cell lever, if pack SOC can be provided.
One challenge with this approach is that the total capacity of
a battery is not really a fixed quantity; it is a function of sev-
eral variables such as temperature, current, depth of discharge
and voltage. Hence, the capacity of a particular battery for a
particular time is not constant, but will vary according to how
it is operated. Hence, Q=Q(θ), where θmay be a num-
ber of variables influencing the capacity (Rozas et al., 2021).
It is not obvious how to account for such effects in the sim-
ple linear model. Additional covariates can be included, or
careful filtering of the data can be applied prior to analysis.
Another challenge with this method is that it relies heavily on
state of charge, which is a derived measure and not directly
observed. Ideally, the state of charge should reflect the tem-
perature and current variations but calculating this from real
data is not straightforward and there can be large uncertainties
in calculated SOC values.
3.2.3. Voltage-Deviation Method
The voltage deviation method is a method for estimating bat-
tery capacity/State of Health by exploiting the relationship
between decreasing capacity and increasing internal resis-
tance and impedance. It was promoted in Yamamoto et al.
(2022), where it was applied to LTO-types of batteries and
reportedly performed well. In this study it is tried out on the
NMC-type of batteries from the maritime battery system.
The voltage deviation method (VDM) needs to be trained in
order to establish the relationship between the voltage devi-
ation and the other features and the battery capacity/state of
health. Hence, in this study, the idea is to use the lab data
from the DDF-cells as training data and to apply them on op-
erational data from some of the vessels with similar battery
cells. However, it should be noted that only 6 DDF-cells have
been cycled in the lab, so the amount of training data is very
limited.
The voltage deviation method, is a rather simple linear regres-
sion model based on features related to the voltage deviation
at certain state of charge sections and the standard deviation
of charge and discharge power and mean temperature. The
overall prediction model is on the form
SOH =α1X1+α2,
αi=βi,1X2+βi,2X3+βi,3, i = 1,2,(9)
Here, X1denotes the voltage deviation feature (F V in Ya-
mamoto et al. (2022)), X2denotes the power deviation fea-
ture (P f v in Yamamoto et al. (2022)) and X3denote the av-
erage temperature (T f v in Yamamoto et al. (2022)). The dif-
ferent deviation features are calculated by first dividing the
data into small tiles of state of charge and calculate the stan-
dard deviation of the voltage and power, respectively, within
each tile. The voltage and power deviations are then the av-
erage standard deviations over all tiles within the entire range
of SoC used in the analysis. The perhaps most important fea-
ture in this model is the voltage deviation, and the idea is that
when the internal resistance and impedance of the battery in-
creases as the battery ages, the over- and underpotential oc-
curring during charging and discharging will increase. Hence
the model establishes a relationship between two effects of
aging: capacity fade and resistance increase.
A SoC range of 50% - 70% was chosen since this is a range
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that is frequently found in the operational data. The train-
ing data are obtained from the lab data by selecting the 25
first charge and discharge cycles after a check-up and then
extracting the features. An example of extracting the voltage
deviation feature is shown in Figure 19. The top figure shows
state of charge plotted against voltage. The different colors
correspond to data from different check-up periods (25 first
cycles after a check-up). It can be observed that as the battery
degrades, the charge-discharge curves tend to get somewhat
wider. In the bottom plot, the standard deviations of the volt-
age within SoC-tiles of 1% within the 50% - 70% SoC-range
are shown. The final feature to use in the data-driven model
is the average voltage standard deviation across all tiles. Vi-
sually, it is observed that the voltage deviation changes as the
battery degrades; it increases from 0.0366 just after the initial
check-up to 0.0551 for the last observation.
The linear regression model in eq. (9) is fitted to these data
and yields an adjusted R2-value of about 0.894. Then, fea-
tures are extracted in the same way from the operational data.
Snapshots of data from two-weeks periods are selected about
3 months apart for each cell and the VDM method is used to
estimate the state of health for these periods. Preliminary re-
sults obtained with this method estimates a sudden increase
on capacity after approximately one year, see Figure 20. This
seems counter-intuitive, and it can be observed that this sud-
den shift appear at the same time as these batteries start doing
fast-charging. Apparently, the models are not able to properly
adjust for this change in loading. It should be noted that these
results are based on only six or four cells used for training
data, and lack of sufficient relevant training data can possibly
explain this. Indeed, looking at the combined features from
the training and the test data, as shown in Figure 21, it is clear
that the power feature has a limited range in the training data
Figure 19. Extracting voltage deviation features from the
training data
Figure 20. Predictions from preliminary analysis of the VDM
method on actual field data
compared to the test data; the training data simply did not ex-
perience the same power deviation as the test data, most likely
due to the fast charging. Hence, the model is not trained to
account for this effect. Possibly, with an extended dataset,
results would be improved.
4. DISCUSSION
Several different approaches to data-driven estimation of bat-
tery capacity have been explored in this study, with the aim
of establishing a framework for monitoring state of health
for class compliance. Various data sources have been ex-
ploited, including results from laboratory experiments, oper-
ational data from ships in service and other publicly available
datasets. Several of the approaches yields promising results,
but accurate and reliable state of health estimation remains
a challenge. Some lessons learned from these investigations
are discussed in the following.
Both cumulative damage models and snapshot methods have
been explored, and these have different data requirements.
Although initial studies have indicated that cumulative mod-
els may yield reasonable capacity estimates, these approaches
are sensitive to missing data, something that must be expected
to occur occasionally for ships in operation. One solution to
this could be to utilize edge computing and process the data
locally onboard the ship. Further studies are needed in or-
der to investigate whether this is a feasible solution. More-
over, for very large battery systems, the amount of data be-
comes huge, and cumulative approaches that require all data
might not scale well. One of the case studies on a cumulative
method presented in this paper found that the data handling
and computational cost becomes prohibitively large even for
a subset of the data. Hence, snapshot methods that only need
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Figure 21. Pairwise scatterplots of the features for training
and test data
data from certain time-intervals would be much preferred
from a practical point of view.
Several snapshot approaches have been explored in this study,
some of which yields promising results. One important dis-
tinction between the snapshot methods in this study is that
whereas some of them require training data to train the data-
driven models, the simple linear model based on Coulomb
counting does not. This is believed to be a huge advantage,
especially since it has been found extremely challenging to
obtain sufficient relevant training data. For snapshot meth-
ods that rely on training data, carefully designed and time-
consuming experiments will probably be needed in order to
ensure that the trained models can predict any realistic oper-
ational condition. Hence, class requirements would need to
include strict criteria for the quality, amount and representa-
tiveness of the training data. Semi-supervised methods have
also been investigated in this study, with the purpose of la-
beling operational data for use as training data. Although
this is an interesting approach, representativeness is again a
challenge, and one would need to ensure that the operational
data used to train the models always come from the battery
systems that have experienced most degradation. This may
be difficult to guarantee in practice unless complete data his-
tories from several systems that have reached its end of life
are available. Fundamentally, data-driven models are better
for interpolating than extrapolating, and this will always be a
challenge for models trained on a finite amount of data.
Hence, it is believed that methods similar to the simple linear
model based on Coulomb counting are the most promising
candidates for data-driven state of health estimation of mar-
itime battery systems. They are snapshot methods and they
do not need to be trained prior to prediction. However, one
main challenge with this approach is that it relies on the state
of charge, which is not measured directly but need to derived
from other observed quantities. This gives rise to additional
uncertainty and the accuracy of SOC would need to be ver-
ified. There are different ways of estimating SOC from ob-
served time series of currents, voltages and temperatures, and
variations in SOC estimates may introduce bias in SOH pre-
dictions. Notwithstanding, it is believed that if reliable and
accurate SOC values are available, snapshot methods based
on this may be useful, and verification of SOC may be in-
cluded in class requirements if such approaches should be
recommended. Hence, the problem of verifying SOH, which
is challenging, may partly be shifted to verification of SOC,
which might be easier. Alternatively, similar approaches that
are based on voltage differences rather than state of charge
may be attractive and this will be investigated in future re-
search.
Different implementations of the linear model based on
Coulomb counting has been explored in this study, in addi-
tion to the standard OLS method. With a Bayesian imple-
mentation, one may get a full posterior predictive distribution
and one may use prior information in addition to the data if
available. Moreover, it is known that the OLS solution has an
attenuation bias that can be corrected by accounting for mea-
surement errors (Plett (2011); Kejvalova (2022b)). However,
in light of the other challenges and uncertainties involved, this
effect is not believed to be significant, and an OLS implemen-
tation would presumably suffice. Since the attenuation bias
yields a bias towards lower SOH, the OLS estimate will tend
to be conservative and this can be construed as an extra safety
factor rather than a serious problem.
Still, there are remaining challenges that needs to be resolved
in order to ensure reliable and accurate estimates from the
linear model between integrated current and state of charge.
One fundamental issue is the fact that the total capacity of
the battery is not a constant quantity, but will be a function
of cycling conditions such as temperature, current and volt-
age, and it will also be affected by stresses caused by preced-
ing conditions (it is not memoryless), see e.g. Rozas et al.
(2021). It is not obvious how to best account for this in the
modeling. One solution is to apply narrow filters to ensure
that only data from similar conditions are compared, at the
expense of significantly reduced datasets. Further research
will focus on this to find optimal ways of filtering operational
data. Another solution is to include additional covariates in
the simple linear model, although this means that the effect of
these would need to be learned from some training data. On
the other hand, since this method relies on the derived quan-
tity SOC, the effect of varying conditions may also be, at least
partly, accounted for by the SOC-algorithm, Further research
will focus on optimizing this approach for maritime battery
systems in actual operation.
The focus has been on purely data-driven approaches in this
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study, and physics based or hybrid modeling approaches have
not been investigated. There exist a large amount on literature
on such methods, exploiting various types of equivalent cir-
cuit models or electrochemical models (see e.g. the review in
Vanem, Bertinelli Salucci, et al. (2021)). It is noted that such
approaches might be useful, even though they have not been
investigated in this study.
Model evaluation and verification remains a big challenge
and makes it difficult to arrive at conclusive recommenda-
tions. Some approaches are found to work well on laboratory
data, but still fails to achieve the same accuracy and reliabil-
ity when applied to actual field data. Hence, it is questionable
whether lab data can be used to verify the models. Moreover,
the most relevant operational data only exist for relatively
new battery systems without a large extent of degradation.
Hence, it is difficult to verify how the models perform when
the batteries approach their end of life, when condition mon-
itoring really becomes important. Data from older battery
systems exist, but they are less relevant if the systems con-
tain different battery cells. Furthermore, it has been observed
that the quality and completeness of data from older systems
are less, due to less focus on data collection and storage in
the past. Hence, more robust verification of the various data-
driven approaches cannot be achieved until more data with
longer operational history are available from relevant battery
systems.
5. SUM MA RY AN D CONCLUSION
This paper summarizes case studies of several approaches to
data-driven estimation of state of health of lithium-ion batter-
ies, with a focus on the needs from the maritime industry and
ship classification. The various approaches, which include
cumulative and snapshot methods have different challenges
and advantages, and even though no conclusive recommen-
dations on the best approach have been formulated, some im-
portant lessons have been learned. From a practical point of
view, snapshot methods are much preferred over cumulative
models. Moreover, approaches that do not need prior training
would be much preferred over models that depend on training
data. Even with semi-supervised approaches it will be chal-
lenging to obtain sufficient high-quality, relevant and repre-
sentative data. Furthermore, laboratory experiments are both
time consuming and costly, and lab data may not be represen-
tative for data from actual operations onboard ships. Hence,
some variant of the simple linear model based on Coulomb
counting are believed to be the most promising candidates
for data-driven SOH verification of maritime battery systems.
Further work will focus on optimizing this approach with re-
gards to data handling and data requirements, including re-
quirements of the required input variable state of charge.
ACKNOWLEDGMENT
This work has partly been carried out within the DDD BAT-
MAN project, supported by MarTERA and the Research
Council of Norway (project no 311445). Parts of this study
have been performed in collaboration with the University of
Oslo within the BIG INSIGHT SFI, supported by the Re-
search Council of Norway (project no. 237718).
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