![Sorting results when clients have heterogeneous data access
a Sorting accuracy as a function of heterogeneity index. The results are averaged over 50 Monte Carlo runs (n=50\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=50$$\end{document}), with one standard deviation region (±1σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pm 1\sigma$$\end{document}) indicated by shaded color. b The data distribution when benchmarking the best majority voting (MV) performance. c Class-wise (upper part) and client-wise (lower part) sorting accuracy corresponds to our federated and independent machine learning (IL) methods. The Sanky chart (middle) presents the heterogeneous data distribution among clients. Source data are provided as a Source Data file.](https://www.researchgate.net/profile/Terence-Shengyu-Tao/publication/376207311/figure/fig4/AS:11431281209754635@1701834924757/Sorting-results-when-clients-have-heterogeneous-data-access-a-Sorting-accuracy-as-a_Q320.jpg)
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Article https://doi.org/10.1038/s41467-023-43883-y
Collaborative and privacy-preserving retired
battery sorting for profitable direct recycling
via federated machine learning
Shengyu Tao
1,6
, Haizhou Liu
1,6
, Chongbo Sun
1,6
,HaochengJi
1
, Guanjun Ji
1
,
Zhiyuan Han
1
, Runhua Gao
1
,JunMa
1
,RuifeiMa
1
,YuouChen
1
,ShiyiFu
2
,
Yu Wang
2
, Yaojie Sun
2
, Yu Rong
3
, Xuan Zhang
1
, Guangmin Zhou
1
&
Hongbin Sun
1,4,5
Unsorted retired batteries with varied cathode materials hinder the adoption
of direct recycling due to their cathode-specific nature. The surge in retired
batteries necessitates precise sorting for effective direct recycling, but chal-
lenges arise from varying operational histories, diverse manufacturers, and
data privacy concerns of recycling collaborators (data owners). Here we show,
from a unique dataset of 130 lithium-ion batteries spanning 5 cathode mate-
rials and 7 manufacturers, a federated machine learning approach can classify
these retired batteries without relying on past operational data, safeguarding
the data privacy of recycling collaborators. By utilizing the features extracted
from the end-of-life charge-discharge cycle, our model exhibits 1% and 3%
cathode sorting errors under homogeneous and heterogeneous battery
recycling settings respectively, attributed to our innovative Wasserstein-
distance voting strategy. Economically, the proposed method underscores the
value of precise battery sorting for a prosperous and sustainable recycling
industry. This study heralds a new paradigm of using privacy-sensitive data
from diverse sources, facilitating collaborative and privacy-respecting deci-
sion-making for distributed systems.
Lithium-ion batteries (LIBs), serving as energy storage devices, have
gained widespread utilization across various domains, from industry
production to daily life as an accepted technical route. Projections
suggest that the global production scale of LIBs will surpass1.3 TWh by
20301when the escalating demand for batteries will far outpace the
availability of vital metal resources like lithium and cobalt2,3. However,
the current average lifespan of LIB products stands at 5–8years,
leading to an imminent surge in retired batteries in many countries. If
not appropriately managed, retired batteries will result in unsustain-
able resource wastage and environmental harm. Given these
circumstances, the development of battery recycling technology
assumes crucial importance as we confront the impending tide of LIB
retirements4.
Recent advances in battery recycling research have been focused
on the pyrometallurgical, hydrometallurgical, and direct recycling
approaches5. In contrast to the pyrometallurgical and hydro-
metallurgical methods, direct recycling stands apart as a distinct
approach. This process does not inflict secondary damage on the
material structure, enabling more efficient structural repair and per-
formance restoration. Moreover, direct recycling exhibits higher
Received: 22 June 2023
Accepted: 22 November 2023
Check for updates
1
Tsinghua-Berkeley Shenzhen Institute, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen, China.
2
School of Information
Science and Technology, Fudan University, Shanghai, China.
3
Tencent AI Lab, Tencent, Shenzhen, China.
4
Department of Electrical Engineering, Tsinghua
University, Beijing, China.
5
College of Electrical and Power Engineering, Taiyuan University of Technology, Taiyuan, China.
6
These authors contributed equally:
Shengyu Tao, Haizhou Liu, Chongbo Sun. e-mail: xuanzhang@sz.tsinghua.edu.cn;guangminzhou@sz.tsinghua.edu.cn;shb@tsinghua.edu.cn
Nature Communications | (2023) 14:8032 1
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profitability, as it entails lower energy consumption, reduced green-
house gas emissions, and lighter environmental footprints6,7. In actual
production, however, battery recyclers frequently encounter LIBs
comprising unknown components or battery modules that consist of a
mixture of different cathode material types. Considering that direct
recycling can be heavily cathode-specific, such a complexity renders
the application of direct recycling infeasible for achieving value con-
version of the retired batteries8. It is crucial to emphasize that even if
the vital metals from mixed cathode material types can be extracted
using conventional recycling strategies, the interplay between differ-
ent cathode materials during the recycling process can adversely
impact product quality9. Therefore, understanding cathode material
type information on the recycling side markedly impacts the direct
recycling route choice and ultimately improves product quality,
profitability, and sustainability.
Human-assisted direct recycling has been proposed to identify
retired battery cathode material type information in the pre-treatment
link, which is still not financially viable when the recycling industry is
scaling up1. To effectively retrieve the retired battery cathode type
information, the scientific and industrial community has recently
initiated a battery lifetime tracing system10 and emerging concepts like
battery passport11 and battery data genome12. Although substantial
batteries have been utilized before those initiatives, there is a growing
consensus that battery information should be accessible throughout
the life chain to facilitate second-life decision-making13.Thisisnotably
the case for the battery recycling sector, the last station of the battery’s
second life, as the recycling route can be heavily cathode-specific.
However, battery lifetime tracing systems or battery passports are
enabled by electronic gadgets like bar codes and near-field commu-
nications, which could introduce intensive investment and could be
widely incompatible with different battery designers. Furthermore,
electronic gadgets remain challenging to consistently manage
throughout their lifespan, leading to worn-out devices and inaccessi-
bilityat the recyclingstage since the modern manufacturing process of
LIBs is still not production-to-recycling integrated14.Hence,more
breakthroughs are urgently needed to achieve an efficient battery
cathode type sorting only using easy-to-access field information15,16,
opposite to the historical data recorded or the human-assisted man-
ner, facilitating the adoption of direct recycling to improve the quality
and profitability of recycled products.
In the past few years, machine learning has emerged as a viable
tool to tackle open questions in all battery fields. In other battery-
related topics, machine learning has recently allowed us to auto-
matically discover complex battery mechanisms17–19, predict remaining
useful life20–24, evaluate the state of health19,25,26, optimize the cycling
profile27,28, approximate the failure distribution29,eventoguidethe
battery design30,31, and predictlife-long performance immediately after
manufacturing32. In the case of battery recycling, few works have
investigated machine learning regarding cathode materials33,34,which
blames the scarce battery data, especially for those cycled to the end-
of-life stage. The vast majority of published studies showcase very
limited sample sizes35 and are even more limited in battery cathode
diversity36. The scarcity is attributed to the intensive cost, the long
testing time37, and, most importantly, the data privacy due to com-
mercial or interest concerns. Consequently, the privacy issue rigidifies
the dilemma where the existing battery data, though substantial in
volume and diversity from multiple parties such as battery manu-
facturers, practical applications, academic institutions, and third-party
platforms, cannot be shared. Such a dilemma calls for studying the
cathode material sorting to optimize battery recycling route choice in
a collaborative while privacy-persevering fashion.
Federated machine learning, as a distributed and privacy-
preserving paradigm, has the potential to resolve both multi-party
collaboration (equivalently, the battery data volume and diversity) and
privacy issues through collaborative machine learning38–40.Ineach
training iteration, the distributed data owners perform local training
with their local computational power, encrypt the as-trained model
parameters/results, and upload them to a central coordinator for
aggregation. Facts that raw datasets never leave their respective data
owners and that transferred parameters/results are properly encryp-
ted to protect data privacy. Federated machine learning has been
extensively investigated in numerous applicative fields, including
public health41,42, clinical diagnosis43–45, e-commerce46,Internetof
Things47, mobile computing48, and smart grid49–51. This approach can
revolutionize the data-driven research paradigm in wide energy sec-
tors by enabling privacy-preserving collaboration, especially for those
with limited data access. Regarding the battery recycling sector, fed-
erated machine learning assumes promising possibilities for lever-
aging the giant amount of battery data that already exists but cannot
be shared due to privacy concerns. With such a collaborative while
privacy-preserving paradigm, retired battery sorting can be imple-
mented with high accuracy, efficiency, scalability, and generalization,
optimizing the quality and profitability of recycled products. To our
knowledge, federated machine learning studies focused on battery
recycling have never been reported.
In this study, we perform a cathode material sorting of the retired
batteries, leveraging the existing battery data from multiple colla-
borators, such as battery manufacturers, practical application opera-
tors, academic research institutions, and third-party platforms, in a
collaborative while privacy-preserving machine learning fashion as
illustrated in Fig. 1. Our federated machine learning model was trained
using only one cycle of field testing data via a standardized feature
extraction process, without any prior knowledge of the historical
operation conditions. We compare the predictive power of our fed-
erated machine learning model with that of independently learned
local models based on local data under both homogeneous and het-
erogeneous battery recycling circumstances. The heterogeneity issue
is resolved by our proposed Wasserstein-distance voting strategy. An
economic evaluation of retired battery recycling using our proposed
federated machine learning framework is conducted, highlighting the
relevance and necessity of accurate sorting of retired batteries. We
comprehensively discuss the model interpretability, battery recycling
implications, and broader prospects of the future battery recycling
practice integrated with federated machine learning.
Results
Data collection and standardization
The unique battery kinetics in different battery types are often high-
dimensional and hard to characterize due to divergent operating
cases, manufacturing variability, and historical usages52.Tofind a
solution to this dilemma, we collected and standardized 130 retired
batteries with 5 cathode material types from 7 manufacturers to con-
struct an out-of-distribution, equivalently heterogeneous dataset.
Given different historical usages, the capacities of the collected bat-
teries are below 90% of the nominal capacity. The battery cathode
materials are lithium cobalt oxide (LCO), nickel manganese cobalt
(NMC), lithium ferrophosphate (LFP), nickel-cobalt-aluminum oxide
(NCA), and NMC-LCO blended types, which are further grouped into 9
classes based on the manufacturers (Supplementary Table 1). We
intentionally include batteries with divergent historical usages, from
laboratory testing to electric vehicle driving profiles, to train a gen-
eralized model for the battery recycler independent of historical usa-
ges and battery types.
For standardization, all data required from the recycler are the
currently-probed (field-testing) cycle with one charging and dischar-
ging test, which is easy to implement in practical cases. The as-probed
data are first denoised by filling in missing values, replacing outliers,
and performing median filtering. Human-induced and cathode-
heterogeneity-induced noises are deliberately retained, though, to
make the model robust to imperfect inputs. The data are then linearly
Article https://doi.org/10.1038/s41467-023-43883-y
Nature Communications | (2023) 14:8032 2
Content courtesy of Springer Nature, terms of use apply. Rights reserved
interpolated for curve filling (Supplementary Fig. 1) and feature engi-
neered for dimensionality reduction, with a shared set of standardiza-
tion parameters (Supplementary Note 1). Features extracted from the
standardization pipeline are well interpretable, a concern of significant
commercial interest. To the best of our knowledge, it is the first time
that heterogeneous battery data from multiple sources and historical
usages are utilized to assist in the strategy design of battery recycling.
Figure 2a, b demonstrate the feature engineering process. We
focus on the charging and discharging curve of the retired batteries in
the last cycle, i.e., one charging and one discharging cycle (Supple-
mentary Figs. 2–5). In the charging cy cle, 15 features are extracted from
the voltage-capacity and dQ/dV curves, where V and Q refer to the
voltage and capacity values, respectively. The same set of features are
extracted for the discharging cycle. As a result, 30 features are
extracted in total, as indicated from F1 to F30. Refer to Supplementary
Table 2 and Supplementary Note 2 for a detailed explanation of the
features. Figure 2c showcases the absolute and relative feature values
of the selected batteries from each class. Most relative feature valuesin
different classes overlap in the −1 to 0 region (with the light green
color) and are indistinguishable, illustrating the difficulty in classifying
battery type using one cycle of battery data. The difficulty is expected
because the divergent historical operation conditions can influence
the charging-discharging kinetics of the batteries so that the extracted
features can be largely correlated despite the different battery types
(Supplementary Fig. 6). Rather than directly interpreting theextracted
features using expert knowledge, we employ an alternative data-driven
approach that automatically leverages the latent patterns across var-
ious battery types.
Retired battery sorting with homogeneous data access
We first consider a setting where the battery data are homogeneously
distributed across the collaborators (namely, the clients). The homo-
geneity means that each client offers to share the battery data across
all 9 classes, even though the specific number of batteries is not
restricted (Supplementary Table 3). We train our federated machine
learning model without requiring information on the historical use of
the retired batteries. In our work, the recycler and the clients only need
to test the retired batteries at the current (field-testing) cycle, speci-
fically, with a complete charging-discharging cycle for a standard fea-
ture engineering process initiated by the recycler. Local models are
trained based on features extracted from their private battery data.
The federated machine learningframework aggregates the local model
parameters, rather than the private battery data, for the recycler to
classify the retired batteries.
Figure 3shows the sorting results when clients contribute
homogeneous battery data. Figure 3a compares two federated
machine learning methods, i.e., the majority voting (MV) and our
proposed Wasserstein distance voting (WDV), with the independent
learning (IL) paradigm. It should be noted that the accuracy for theIL is
averaged over all clients in a non-federated manner. Compared with
the IL, the MV does not sacrifice sorting performance, with an average
accuracy of 95%, while being capable of protecting data privacy and
mitigating computational burden. However, 3 classes are missorted
using the MV. For instance, 3 batteries in NMC (SNL, class 8, 15 in total)
are missorted into NCA (SNL, class7), resulting in a sorting accuracy of
80%. The sorting accuracy for NCA (UL-PUR, class 9) is 81%, with 2
batteries missorted into NMC (MICH_Form, class 4) and 1 battery
missorted into NMC/LCO blended type (HNEI, class 2), respectively. In
contrast, the WDV outperforms the MV since it only missorted one
battery, resulting in a sorting accuracy of 99%. We also evaluate the
prediction probability of each class for the MV and WDV, respectively.
It turns out that the WDV makes a more confident sorting than the MV
since the prediction probabilities of the WDV are generally right-
skewed to a higher probability value. Therefore, our proposed WDV
produces higher sorting accuracies across allclasses, and the sorting is
of richer probability confidence margins.
Classified
batteries
Optimized
recycling
Battery
manufacture
Practical
application
Academic
research
Third party
platform
Privacy
Aggregation
Data source
General model
Data sharing Privacy preserving
Scalable collaborators
Feature extraction Local model Global model
Wasserstein distance
Model deployment
Our work
Retired
batteries
Federated
model
Federated learning framework for battery recycling classification
Traditional Data islanding Independent model
Voting
a
b
Fig. 1 | The federated machine learningframework of retiredbattery sortingfor
recycling. a Multiple data sources, such as battery manufacturers (Image courtesy
Addionics), practical application operators (battery pack in the floorpan of a Tesla.
Image courtesy ofTesla), academicresearch institutions, and third-partyplatforms,
can be data contributors. The battery data are neither exchanged between con-
tributors nor uploaded to the battery recycler. Instead, the data contributors train
local models and share model parameterswith the battery recyclerto build a global
model.The proposed Wasserstein-distancevoting technique fuses the localmodels
into the global model, which is robust to data imbalance and noise. Battery recy-
clers can usethe jointly-builtmodel for battery sorting, combined with the easy-to-
access field testing data. bOur federated machine learning framework encourages
collaborators to sharing the data while preserving data privacy as apposed to the
traditional data islanding paradigm.
Article https://doi.org/10.1038/s41467-023-43883-y
Nature Communications | (2023) 14:8032 3
Content courtesy of Springer Nature, terms of use apply. Rights reserved
We also evaluate the privacy budget (PB, “Methods”section),
considering that client data might be vulnerableto reverse engineering
by eavesdropping on private data53. In this regard, we add random
Gaussian noise to the client data with different intensities. The
intensity of the randomness is controlled by a noise-to-signal ratio
(NSR), ranging from 1% to 10%. Figure 3b shows the accuracy and
privacy budget comparison when using IL, MV, and WDV, respectively.
The sorting accuracy of the MV decreases from 95% to 82%, similar to
Charging data
Discharging data
a
b
Q1
Q2
F6
Q1 Q2 Q3
F3
F1
F2
F4
F5
Q3
F7 F8
F9
F10
F11
F12: Kurtosis Capacity
F13: Kurtosis Voltage
F14: Skewness Capacity
F15: Skewness Voltage
Q1
Q2
F21
Q1 Q2 Q3
Q3
Base distribution
Qk:25 × k% quantile
F23
F22
F25
F26
F24
F16
F18
F19
F20
F27: Kurtosis Capacity
F28: Kurtosis Voltage
F29: Skewness Capacity
F30: Skewness Voltage
Base distribution
-----
c
F17
39.8
-18.5
Absolute feature value
LCO (CACLE)
NMC/ LCO (HNEI)
NMC (MICH_Expa)
NMC (MICH_Form)
LCO (OX)
LFP (SNL)
NCA (SNL)
NMC (SNL)
NCA (UL-PUR)
Z-score (standard score of feature value)
F: Feature
Fig. 2 | The feature engineering result. a For the charging process, 15 features are
extracted from the voltage-capacity (left) and dQ/dV curve (right). bThe same set
of features are for the discharging process as F16 to F30. cFeatures are visualized
by classes, following the format CxBn, indicating the nth battery from class x. The
size of a circle maps the absolute feature value. Source data are provided as a
Source Data file.
Article https://doi.org/10.1038/s41467-023-43883-y
Nature Communications | (2023) 14:8032 4
Content courtesy of Springer Nature, terms of use apply. Rights reserved
Separable distance
Separable distance
bd
Accuracy
MV:95%
IL:95%
a
0 1 0 1
Prediction probability distribution Prediction probability distribution
cMV WDV
IL
Accuracy
WDV:99%
IL:95%
PB reference
46
10
PB
PB
PB
NSR(%)
PB reference
NSR(%)
5% 95%
25% 75%
50%
=10
=10
=1800
1Zoomed in view
mean
1
-1
mean
Neighbouring regions
Salient features
Non-salient features
Importance (arb. units)
Fig. 3 | Sorting results when clients have homogeneous data access. a The
confusion matrix for the majority voting (MV) and Wasserstein distance voting
(WDV) methods, respectively. We consider the prediction probability distribution
for each class. The sorting of independent learning (IL) is annotated. bSorting
accuracy distribution and privacy budget (PB) of the IL, MV, and WDV in the pre-
sence of random noise. The PB value is referenced at a 90% accuracy level.
cAverage F1-score of sorting results and PBs in each class using the IL, MV, and
WDV. The PB values are all referenced at a 0.9 F1-score level. Data are presented as
mean values±1 standard deviation. dFeature importance, in descending order.The
subplot shows the feature space spanned by the first two mostsalient features. Data
are presented as mean values+ 1standard deviation. Source data are provided as a
Source Data file.
Article https://doi.org/10.1038/s41467-023-43883-y
Nature Communications | (2023) 14:8032 5
Content courtesy of Springer Nature, terms of use apply. Rights reserved
that of the IL when the noise intensity increases from 1% to 10%. In this
noise range, the median sorting accuracy of the MV and IL is 92% and
86%, respectively. In contrast, the sorting accuracy of the WDV is still
above 90% in the presence of 10% noise, which is a stringent noise level
in practical cases. The WDV has a median sorting accuracy of over 95%
in the same noise range. Taking an average sorting accuracy of 90% as
an acceptable reference level, the PB values of IL, MV, and WDV are 4,
6, and 10, respectively. Therefore, applying federated machine learn-
ing produces a more privacy-secure sorting than IL, hence being cap-
able of preventing data eavesdropping. Furthermore, our proposed
WDV is more accurate and performs much better (with nearly doubled
PB values) in the privacy-accuracy trade-off than the MV. In addition,
the robustness to stringent noise when using the WDV also implies a
good tolerance of the ba ttery measurement requirement, reducing the
expensive battery testing disbursement.
Noticing that a high sorting accuracy does not necessarily imply
an acceptable sorting for a specific class, we also consider within-class
sorting performance s. Figure 3c shows the F1-score and privacy budget
of the IL, MV, and WDV in each predicted class; note that the privacy
setting is identical to that in Fig. 3b. The result shows that the IL has
smaller F1-scores than the federated machine learning manner in all
the classes, making poor sortings. Regarding federated machine
learning, WDV outperforms the MV in each predicted class by produ-
cing higher average F1 scores. The deviation range of the F1 scores for
WDV is smaller than that of the MV, indicating that the WDV is more
robust (Supplementary Fig. 7). Therefore, our proposed WDV not only
has a better overall sorting accuracy among all nine classes (Fig. 3b)
but also within each class, compared with the MV. Regarding the
privacy budget, the PB value when using the non-federated IL, refer-
enced at a 0.9 F1-score level, is significantly lower than the federated
way (Supplementary Table 4) across all classes. This indicates a more
severe risk of data leakage for IL compared with federated machine
learning. When further applying our proposed WDV, the private bud-
get can increase by 78% and 44% compared with the non-federated IL
and the federated MV, respectively (Supplementary Table 4). The
results demonstrate that the WDV successfully leverages the battery-
chemistry-related insights hidden in clients while effectively preser-
ving client data privacy.
We then interpret our federated machine learning model by
evaluating the most salient features correlated with battery cathode
chemistry. Figure 3d shows the importance of the features in des-
cending order. The error bar indicates the importance deviation.
Features F1 and F16 rank the top two features regarding out-of-bag
importance (“Methods”section). Interestingly, these two features have
a clear physical interpretation of the battery dynamics, which we will
further discussin later sections.Here, we rationalize these two features
by plotting the grouped battery samples in the feature space spanned
by features F1 and F16. The subplot of Fig. 3dshowsthatNMC/LCO
blended type (HNEI, class 2), NMC (MICH_Expa, class 3), and LFP (SNL,
class 6) (sharing the color with Fig. 3a) are clearly separable in the
spanned featurespace. For the remaining classes,the batteries are still
separable (see the zoomed-in view), though in relatively more minor
grains. On the contrary, the non-salient features have a relatively
weaker sorting ability due to the non-separable feature space spanned
(Supplementary Fig. 8). As a result, our federated machine learning
framework successfully discovered useful mechanism insights to
guarantee sorting accuracies. Such an insight could be further exten-
ded to simplify the model for light computation, hence less invest-
ment. Once the client models classify the batteries, the recycler can
aggregate the client results to make a finaldecisiononthebattery
cathode material types underpinned by the salient features.
Retired battery sorting with heterogeneous data access
We also consider an extreme, while a more actual situation where the
data can be exclusively scattered among clients, i.e., the data
distribution is heterogeneous. In this situation, the heterogeneity issue
poses more challenges to battery type sorting since the clients are
prone to train biased models and deteriorate global accuracy, which is
still an open question in federated machine learning. In this section, we
explore a more challenging situation rather than having homogeneous
data access among each client (Supplementary Note 3). We demon-
strate that our federated machine learning framework can still classify
retired batteries based on the standard feature engineering process at
the current (field-testing) cycle without any knowledge of the previous
operation conditions.
Figure 4shows the sorting results when clients have hetero-
geneous data access. We consider the heterogeneity index, defined as
the minimum number of battery classes for each client in each Monte
Carlo simulation run. A higher heterogeneity index indicates a less
heterogeneous battery data distribution. The heterogeneity index is
no smaller than two such that one client can train a local model for a
sorting task. Figure 4a shows average sorting accuracy when the het-
erogeneity index varies. The average accuracies are plotted with solid
lines, with the ± 1 standard deviation range indicated in the shaded
region. As the heterogeneity index decreases from 9 to 2, the perfor-
mance of the MV and the IL rapidly deteriorates at a sublinear rate. The
average sorting accuracy of the MV is 0.55, slightly better than the IL,
equivalent to a random guess when the heterogeneity level is two. This
observation shows that the MV can help little to aggregate the local
models under heterogeneous data access. In contrast, the WDV out-
performs its MV counterpart in all heterogeneity levels, successfully
mitigating the heterogeneous data distribution issue. Moreover, the
WDV shows an interesting asymptotic effect when the heterogeneity
index increases. This indicates that the WDV can potentially support
the optimal allocation/distribution of client battery data to reduce the
collaboration cost in practical battery recycling situations.
We select the best model using the MV when the heterogeneity
index equals two and compare it with the sorting result of our pro-
posed WDV under the same setting. The selected best model has an
average sorting accuracy of 71%, as shown in Fig. 4a.
The detailed battery data distribution setting of the best model
using MV is illustrated in Fig. 4b, which is heterogeneous (Supple-
mentary Table 5). For instance, client 2 contributes to all battery
classes except for NMC (MICH-Expa, class 3), while client 5 only con-
tributes to NMC/LCO blended type(HNEI, class 2) and NMC (SNL, class
8). Under the heterogeneous data distribution setting in Supplemen-
tary Table 5, we further compare the class-wise and client-wise sorting
performance of the MV and the WDV to the non-federated IL with two
considerations: (1) the significance of our federated machine learning
framework and (2) why our proposed WDV outperforms the MV. First,
we evaluate the client-wise sorting accuracy, shown in the lower side of
Fig. 4c. Client 5 achieves an average sorting accuracy of 25%, ranking
last among all clients. Meanwhile, client 2 achieves an average sorting
accuracy of 86%, ranking first among all clients. However, the average
sorting accuracy is only 55%, close to a random guess. Therefore, the
client performance using the non-federated IL depends heavily ondata
access (Supplementary Fig. 9). In fact, without our federated machine
learning framework, the battery recycler i s equivalent to a single client,
and the battery recycler can only make sortings on the battery types
stored in its local database. This non-federated paradigm could not
handle various types of retired batteries if the recycler did not build a
database covering all the battery types it would handle. With our
federated machine learning framework, the recycler can collaborate
with several clients, even if under heterogeneous data situations.
We turn to analyze how to collaborate with clients under het-
erogeneous data access settings. The upper part of Fig. 4cshowsthe
class-wise accuracy of the MV and WDV. It is noticed that the average
sorting accuracy after using the MV is better than the non-federated
way, which is 79%, as indicated in the lower side of Fig. 4c. It demon-
strates the success of applying the federated machine learning
Article https://doi.org/10.1038/s41467-023-43883-y
Nature Communications | (2023) 14:8032 6
Content courtesy of Springer Nature, terms of use apply. Rights reserved
framework to address the heterogeneous data distribution issue in this
case. However, the MV totally missorted LFP (SNL, class 6) and NMC
(SNL, class 8) with zero accuracy. The failure of the MV in specific
classes can be rationalized by its core idea of giving more weight to the
clients who contribute more battery samples while not guaranteeing
diversity in battery types. For instance, the contribution of client 7 will
be strengthened by the MV due to a large number of batteries (spe-
cifically, 195 augmented batteries, ranking second among clients),
despite only contributing four classes of batteries. As a result, the MV
will lead the aggregated model to be biased towards large client such
as client 7 (Supplementary Table 4). The biased phenomenon is evi-
denced bythe as-described zero sorting accuracy for LFP (SNL,class 6)
since the large client, such as client 7, never contributed any batteries
in class 6. Similarly, client 1, the largest client with 197 augmented
batteries, failed to contribute helpful information to the recycler
regarding classifying NMC (SNL, class 8), which is consistent with zero
accuracy in class 8. In contrast to the MV, our proposed WDV focuses
on the battery similarities between the recycler and each client by
measuring the pairwisedistance. We aim to assign fewer weightings to
the clients with biased data distributions (equivalently, higher het-
erogeneity),whose batteries are of higher similarities with the recycler,
such that the recycler can have generalized information from each
client. The results show that our proposed WDV successfully leverages
helpful information from heterogeneous data distribution among cli-
ents. The WDV achieves 100% and 89% sorting accuracy for the
otherwise missorted batteries in LFP (SNL, class6) and NMC (SNL,class
8), respectively. The overall sorting accuracy using the WDV is up to
97%, with only 5 batteries missorted out of 144 samples. In Supple-
mentary Fig. 10, we also notice that the missorted batteries are of
similar cathode materials. Specifically, 2 batteries with the NMC cath-
ode material were missorted into the NMC/LCO blended type; while 1
batterywith the NCA cathode material was correctin material type but
missorted into another manufacturer. On the contrary, the missorted
results produced by the MV can spread to either many irrelevant
a
c
71%
b
0.52
0.86
0.590.60
0.25
0.44
0.32
0.69
0.55 0.68
0.0
1.0
0.5
1.0
0.5
0.71
(Avg. MV)
0.97
(Avg. WDV) MV
WDV
0.55
(Avg. IL)
Prediction accuracy
Prediction accuracy
Federated
learning
Independent
learning
Task specific
General model
0.92
Accuracy by collaborator
(averaged among classes)
0.87 0.89
00
0.83
0.0
12345 678910 Collaborators(data owners)
Accuracy for recycler (by class)
Privacy
preserving
Retired batteries
WD-Voting
Aggregation
±1
=50
Insufficient data
00.4
Class distribuon
Fig. 4 | Sorting results when clients have heterogeneous data access. a Sorting
accuracy as a function of heterogeneity index. The results are averaged over 50
Monte Carlo runs (n=50), with one standard deviation region ( ± 1σ) indicated by
shaded color. bThe data distribution when benchmarking the best majority voting
(MV) performance. cClass-wise (upper part) and client-wise (lower part) sorting
accuracy corresponds to our federated and independent machine learning (IL)
methods. The Sanky chart (middle) presents the heterogeneous data distribution
among clients. Source data are provided as a Source Data file.
Article https://doi.org/10.1038/s41467-023-43883-y
Nature Communications | (2023) 14:8032 7
Content courtesy of Springer Nature, terms of use apply. Rights reserved
classes or manufacturers. Therefore, we conclude that the WDV can
aggregate helpful client insights by distinguishing inherited differ-
ences in cathode material types. Inspired by this, the WDV also sug-
gests that the clients are encouraged to contribute more battery data
in diversity rather thanmore data in some specificclasses.Therecycler
can optimize the benefit distribution based on helpful client infor-
mation provided. Ultimately, our federated machine learning frame-
work enables the recycler to know the battery cathode material type,
even if without their own data access to various battery data, while
preserving the data privacy of potential clients.
An economic evaluation of retired battery recycling
To help understand the relevance and necessity of battery sorting in
actual recycling practice, also to verify the significance of our pro-
posed WDV strategy, an economic evaluation is performed. Three
recycling methods (pyrometallurgy, hydrometallurgy, and direct
recycling), two battery cathode types (LFP-graphite and NMC-gra-
phite), two recycling modes (individual, hybrid), three sorting
accuracy levels (97%, 71%, 55%) induced by the federated and non-
federated machine learning methods (WDV, MV, IL) are included in the
evaluation. The notation of ML-direct in Fig. 5a denotes direct recy-
cling enabled by our federated machine learning framework. The
individual mode denotes that batteries have been previously sorted in
a human-aided manner (Fig. 5b–d), which is used to compare different
recycling methods given a known cathode type. The hybrid mode
denotes that batteries are collected with mixed cathode types
(Fig. 5e–g), which is used to analyze the significance of the battery
sorting toward recycling profits. The detailed calculation procedure
and numerical results can be found in Supplementary Note 4 and
Supplementary Tables 6–15, respectively.
Figure 5a shows a schematic diagram of three recycling methods,
including pyrometallurgy, hydrometallurgy, and ML-direct recycling.
The final product of pyrometallurgy is metalalloy. While final products
of hydrometallurgy are lithium salt and precursor, which should be
further processed to assemble batteries, as indicated by red and
blue arrows in Fig. 5a. Compared to the other two non-machine
Data
sharing Profit
Environment
protection
Privacy
Operation simplicity
Pyro- Hydro- ML-Direct
(¥)
NMC
LFP
NMC
LFP
NMC
LFP
ML-Direct
Pyro-
Hydro-
54%
18%
17%
524
74%
13% 8
21
2
Inner: LFP
Outer: NMC
Retired NMC and LFP batteries
Classification
Annealing
Assembly
Disassembly
Disassembly
separation
Acid/alkali
leaching
Extraction/
precipitation
Lithium salt +
precursor
Crushing
Metal alloy
Refine
Slags
Smelting
Hydro-
Pyro- ML-direct
New batteries
abc
de
LFP NMC LFP NMC LFP NMC
Hydro-
Pyro- ML-Direct
Cost (¥) Revenue (¥) Profit (¥)
Raw material Average labor Equipment depreciation
Reagent Electricity & Water Sewage treatment
fg
(k¥)
75
60
45
30
15
0WDV MV IL
1:2 1:1 2:1
LFP : NMC
(k¥)
75
60
45
30
15
0WDV MV IL WDV MV IL
ML-Direct Pyro- Hydro-
WDV MV IL WDV MV IL WDV MV IL
(k¥)
LFP : NMC 1:2 1:1 2:1
0
5
10
15
20
25
30
010 20 30 40
1
5
NMC: Nickel Manganese Cobalt Oxide
LFP: Lithium Iron Phosphate
ML: Machine Learning
Fig. 5 | An economic evaluation of retired batteryrecycling. a Comparison of the
Pyro- (pyrometallurgical), Hydro-(hydrometallurgical), and ML-direct (machine
learning aided direct) recycling methods. bCostanalysis of Lithium Iron Phosphate
(LFP) andNickel Manganese CobaltOxide (NMC) batteries usingdifferent recycling
methods in individual modes. cCost analysis of LFP and NMC batteries using ML-
direct recycling in individual mode. dCost, revenue, and profitcomparisonofthe
individual battery type using different recycling methods in individual mode.
eCost, revenue, and profit comparison using Wasserstein distance voting (WDV),
majority voting (MV), and independent learning (IL) methods in hybrid mode. The
ratio isthe amount of LFP batteryto that of NMC battery.fSensitivityanalysis of the
profit of WDV, MV, and IL methods in a hybrid model towards sorting accuracy in
hybrid mode. The ratio is the amount of LFP to that of the NMC battery.
gComprehensive comparison of different battery recycling technologies in hybrid
mode. Source data are provided asa Source Data file. The graphics in panel a were
created using icons from Flaticon.com.
Article https://doi.org/10.1038/s41467-023-43883-y
Nature Communications | (2023) 14:8032 8
Content courtesy of Springer Nature, terms of use apply. Rights reserved
learning-aided methods, ML-direct recycling has the shortest process
flow since the product is standard battery materials, which brings
about the largest possible convenience and the least possible envir-
onmental footprints. It should be stressed that such convenience is
enabled by accurate sorting, a vital link in pretreatment for actual
battery recycling practice, thanks to our federated machine learning
framework.
The cost analysis of LFP and NMC batteries using different recy-
clingmethodsisshowninFig.5b, including raw material, reagent,
average labor,electricity& water, equipment depreciation, and sewage
treatment. It can be observed that the raw material accounts for the
largest proportion of the cost. As a result, the cost of NMC is always
higher than LFP in any method owing to the large price difference
between NMC and LFP. Besides, for the same type of batteries, the cost
of ML-direct recycling is the largest while the pyrometallurgy is the
least, owing to the large expense of reagents. Considering the reagents
can be heavily cathode material specific, the profitability of ML-direct
recycling largely depends on the sorting accuracy of the mixed retired
batteries. Further analysis of the detailed proportion of cost structure
in ML-direct recycling is summarized in Fig. 5c. The outer and inner
annuluses stand for NMC and LFP batteries, respectively. Except for
raw material and reagent, the sum of the other costs is the same in
price (5620 ¥/t) but more than twice the difference in percentage
(NMC for 28%, LFP for 13%). The cost of raw materials for NMC (29900
¥/t, accounting for 74%) is nearly three times that of LFP (9687.5 ¥/t,
accounting for 54%), which again indicates the profit of ML-direct
recycling is sensitive to the sorting accuracies. Figure 5d lists the cost,
revenue, and profit of LFP and NMC batteries using different recycling
methods. For the largest profit option, NMC battery using ML-direct
recycling (29944.25 ¥/t) is 2.25 times the second largest profit option
(LFP batteries using ML-direct recycling, 13279.51 ¥/t). It can be sum-
marized that ML-direct recycling has the largest revenue and profit.
Moreover, it is also noticed that the profit of recycling NMC is always
larger than LFP, highlighti ng the significance of efficiently sorting high-
value recycling candidates from a bulk of mixed retired batteries.
In a practical scenario, collected retired batteries could be
expensive and even impossible to sort by human-aided pretreatment,
especially when the recycling is scaling up. On the contrary, ML-direct
recycling has the unique advantage of efficiently sorting the retired
batteries by leveraging existing data sources from multiple battery
recycling collaborators. An economic analysis using different machine
learning paradigms (independent learning, i.e., IL; and federated
machine learning, i.e., MV and WDV) is carried out in Fig. 5e, f. Due to
the high sorting accuracy of WDV, the two types of batteries (LFP and
NMC) can be completely sorted and the final product can be utili zed to
assemble new batteries directly. On the contrary, the MV and IL would
produce significant errors in distinguishing cathode materials, thus
leading to low-value products (impure materials) that are unable to be
directly utilized, requiring further refining. As a result, the profit
decreases asymptotically for MV and IL methods when sorting accu-
racy is lower than WDV, specifically 97%. NMC battery recycling using
WDV-based ML-direct recycling has a high profit of 24389.33, 21611.88,
and 18834.42 ¥/t for the LFP/NMC ratio of 1:2, 1:1 and 2:1, respectively,
which are higher than those of pyrometallurgy (4372.32, 3994.46, and
3616.61 ¥/t) and hydrometallurgy (9957.45, 10039.27, and 10121.09
¥/t). The profits of pyrometallurgy and hydrometallurgy are not sen-
sitive to sorting accuracy since these methods do not require stringent
retired battery cathode material information. Such a high profit from
ML-direct recycling not merely stems from the inherited advantage of
direct recycling but is enabled by our effective and accurate retired
battery sorting. Finally, a qualitative comparison of different battery
recycling technologies is illustrated in Fig. 5g. ML-direct recycling
performs noticeable advantages in environmental protection7,54,
operation simplicity, privacy, data sharing, and profit. Our ML-direct
recycling method has huge socioeconomic values and can quickly
accelerate the development of the battery recycling industry, espe-
cially when next-generation batteries are even more complex in cath-
ode material diversities.
Discussion
We have successfully demonstrated our federated machine learning
framework, especially our proposed WDV strategy, serving as a key to
profitable battery recycling from a practical perspective. Such success
is achieved by leveraging existing data sources to train a general data-
driven battery sorting model, rather than an expensive human-aided
sorting. Our model features a collaborative while privacy-preserving
fashion, enabling the direct recycling methodology, which is currently
heavily cathode-specific and sensitive to the recycling candidates. We
discuss the merit of our work from a multi-level perspective, including
the fundamental mechanism of battery sorting, the implication of
profitable recycling, and the advantage of the federated battery recy-
cling paradigm.
To realize the sorting of retired batteries, we extracted 30 features
based on the battery charging-discharging and dQ/dV curves in the
feature engineering process. In the previous sections, we have ratio-
nalized the salient features, i.e., F1 and F16, from the machine learning
perspective that the feature space spanned by F1 and F16 is separable
for different cathode material types, as shown in Fig. 3d. Here we aim
to rationalize the physical interpretation of these two salient features.
Features F1 and F16 are extracted from the dQ/dV curve, commonly
used to analyze phase reactions in electrochemistry, though agnostic
to the underlying mechanism. Regarding battery thermodynamics, the
number of dQ/dV peaks and the corresponding voltage values can be
used to analyze the reaction on electrodes and to judge the compo-
sition of the cathode material. Regarding battery kinetics, the shape of
the dQ/dV curve can help analyze the transport capacity of electrons
and ions inside the battery, from which the chemical properties of
battery materials can be deduced. Here, the Gibbs phase law can fur-
ther help the rationalization: F = C-P + n, where F represents the degree
of freedom, C represents the number of independent components, P
represents the number of phase states, and n represents external
factors. When studyingelectrode materials, constanttemperature and
pressure are assumed; thus, n = 0. The number of independent com-
ponentsonthecathodeisC=2.SincethedischargingprocessofLFPis
a phase change process, there are two phases, i.e., P= 2. Since LCO,
NCM, and NCA are solid solutions, only one phase exists during the
discharging process i.e., P = 1. Therefore, the degree of freedom of LFP
(F = 0) is lower than that of LCO, NCM, and NCA (F = 1). As a result, the
voltage of LFP does exhibit significant change during the reaction
process, consequently, there is a noticeable peak on the dQ/dV curve.
On the comparison, during the charging and discharging process of
LCO, NCM, and NCA (F = 1), the slope of the voltage change in the
plateau is more significant than that of LFP, which can be reflected on
the dQ/dV curve accordingly. Although LCO, NMC, and NCA (F = 1)
have similar structures, their components, and Li-ion mobility during
the charging-discharging process differ, resulting in different dQ/dV
peak values, which can be interpreted from F1 and F16. While other
features are possible to decipher battery kinetics, they demonstrate
less importance since more complicated expert knowledge is required
for further processing. However, we highlight the power of our
machine learning model by automatically utilizing the information
provided by F1 and F16, whichhave a clear physical interpretation and
underpin a general and high-accuracy model. Such good accuracies
are independent of historical usages and use only one cycle of end-of-
life charging and discharging data. Consequently, the battery recycling
collaborators realize good sorting accuracies with our proposed sali-
ent features aided by machine learning.
When the recycling collaborators successfully sort the retired
batteries from the recycler, a voting procedure is performed. Noting
that the data volume and data diversity of each recycling collaborator
Article https://doi.org/10.1038/s41467-023-43883-y
Nature Communications | (2023) 14:8032 9
Content courtesy of Springer Nature, terms of use apply. Rights reserved
may differ, the voting results could be biased to the specificcathode
depending on the data distribution. This still hinders the profitability
of battery recycling given low sorting accuracies, highlighting the
significance of our WDV strategy. The result shows using our WDV-
based federated machine learning framework, the battery recycling
industry has a high possibility of transforming from the current
human-aided battery sorting to an automatic, collaborative, and
privacy-preserving fashion, with high sorting accuracy. Such effective
retired battery sorting serves as a key to the battery recycling practice
using direct recycling, equivalently, our ML-direct recycling. Without
our method, the economic benefits of direct recycling could be greatly
reduced to a level lower than traditional pyrometallurgy and hydro-
metallurgy even with small errors in sorting accuracy. In next-
generation battery recycling, there could be various battery types
involving different chemical compositions, including Si anode, Na ion,
lithium-sulfur, and zinc-air batteries, etc.The data collection for model
training will be even more challenging due to data privacy and data
heterogeneity (battery diversity), calling for federated machine
learning to address such issues. In addition to battery type informa-
tion, direct recycling also requires sorting for the state of health (SOH)
since SOH directly determines the amount of reagents added to the
direct recycling process, accounting for the majority of the recycling
cost. Excessive or insufficient reagents will lead to a declined product
quality, which in turn leads to a decline in revenue and sustainability.
Different from the sorting problem, SOH estimation is more challen-
ging since it requires historical data toformulate a regressionproblem.
Moreover, the SOH can be heavily dependent onhistorical usage, while
such information is difficult to retrieve at the end-of-life stage due to
poor lifecycle management. Using only field-available information to
determine SOH remains a critical challenge. It should be noted that the
profit calculation assumes an 80% SOH forthe retired batteries. Future
work should consider SOH information to increase the profitability of
ML-direct recycling, which is a great commercial concern.
As mentioned above, the core idea of adopting federated machine
learning into battery recycling is leveraging the existing data infor-
mation in a collaborative while privacy-preserving manner, which is
intuitively consistent with the distributed nature of battery data. We
note that the cost of sorting through machine learning is not con-
sidered, which attributes to a lack of relevant industry data and con-
version standards. Under a federated machine learning setting, the
recycler only needs to process battery information, thus the machine
learning cost is not sensitive to the recycling scale. We, therefore,
assume that the once-for-all machine learning cost will be covered
when the battery recycling scale enlarges. Even though more in-depth
investigations on the accuracy-privacy-cost balance should be con-
ducted, we emphasize that the proposed federated machine learning
framework tackles the common concerns in collaborative learning,
including privacy, efficiency, and fairness, which can be addressed
consistently and elegantly. We begin by noticing that the data privacy
of the collaborating clients is fully protected, as neither the raw battery
data nor the extracted features are leaked out of their respective data
sources; even the as-trained local models are kept confidential to the
data sources themselves. The only information being transferred, the
local battery cathode sorting result, can be appropriately encrypted
before transferal to eliminate potential eavesdroppers, ensuring priv-
acy budget. Also, with the full support of parallelized localtraining and
only one round of result transfer, the proposed framework is highly
efficient in computation and communication, which remains a huge
challenge in commercialization in other fields. Specifically, the selec-
tion of random forests as the bottom-level machine learning algo-
rithm,instead of more advanced neural networkarchitectures, is made
with full consideration of the feature engineering settings and cost-
effectiveness requirements. Feature engineering, which prepares the
data for federated machine learning with expert-knowledge-based
information extraction, transforms the raw gigabyte-scale sequential
data into kilobyte-scale tabular data. Decision trees such as random
forests are more adept at learning from such low-dimensional data
with heterogeneous features, whether in terms of accuracy, efficiency,
or interpretability. Also, advanced neural network architectures such
as Convolutional Neural Networks (CNNs) require much higher com-
putational power from every collaborating manufacturer, with a sig-
nificantly lengthened training time and compromised model
interpretability, despite gaining a slight edge in accuracy (See Sup-
plementary Fig. 11). Thus, our proposed framework is light and scalable
without requiring intensive investment in the battery recycling sector,
which is of significant interest to industrial practice. The framework
further achieves fairness by assigning a local training task of the same
scale, though in different cathode types and sample sizes, to all clients
under the recycling collaboration. Even when compared with other
alternative federated machine learning frameworks, the proposed
framework is still better in terms of these metrics, as those alternative
frameworks would most likely require various rounds of model
updates with considerable parameter transferals, which would com-
promise efficiency and expose collaborators to an immense level of
privacy leakage. Currently, the framework is implemented under the
ideal assumption that all collaborators are fully cooperative, such that
the uploaded local results are assumed to be reliable. Supplementary
Figure 12 shows that, despite such an ideal assumption, the random
forest model, incorporated with the Wasserstein distance voting, is
naturally robust against random parameter transfer losses even if
parameters from a few collaborators end up missing. The sorting
accuracy only slightly degrades given the same heterogeneity setting.
In the case of a blockchain-like environment with numerous colla-
borators of unknown trustworthiness and reliabilities, our research
could be further extended in search of a proper incentivization
mechanism such that all recycling collaborators would fully contribute
to their respective local model instead of attempting to become total
free-riders. We prospect quantifying the helpful information that the
recycling collaborators provided to design a benefit distribution
strategy and a free-rider detection scheme to make the federated
battery recycling ecosystem economically feasible.
By exploring federated machine learning in the battery recycling
sector, the major concern on the profitability of recycled products can
be guaranteed. Our work highlights a general retired battery sorting
model only using one cycle of end-of-life battery data, enabling the
rational design of a direct recycling route for higher product quality
and profitability in practice. The privacy-preserving information-shar-
ing mechanism encourages extensive multi-party collaboration in
battery recycling practices, thanks to our proposed WDV strategy. Our
work enlightens using machine learning to facilitate an efficient and
profitable next-generation battery recycling industry in the future.
To conclude, federated machine learning is a promising route for
retired battery sorting and enables emerging battery recycling tech-
nologies, especially direct recycling, in their development, practical
application, and optimization. We create a retired battery sorting
model using only one cycle of end-of-life charging and discharging
data as opposed to any historical data while preserving the data priv-
acy budgets of multiple battery recycling collaborators. In the homo-
geneous setting, we obtain a 1% cathode material sorting error; in the
heterogeneous setting, we obtain a 3% cathode material sorting error,
thanks to our Wasserstein-distance voting strategy. Such a level of
accuracy is achieved by (1) automaticallyexploring theunique patterns
in the salient features without assuming any prior knowledge of his-
torical operation conditions and (2) using our proposed Wasserstein-
distance voting strategy to correct heterogeneous data distribution
among recycling collaborators. An economic evaluation showcases the
relevance and necessity of accurate retired battery sorting to the
profitable battery recycling industry using direct recycling. In general,
our approach can complement the existing first-principle-based recy-
cling route research paradigms on actual battery recycling practice,
Article https://doi.org/10.1038/s41467-023-43883-y
Nature Communications | (2023) 14:8032 10
Content courtesy of Springer Nature, terms of use apply. Rights reserved
where retired batteries arenecessary whilechallenging to sort. Broadly
speaking, our work enlightens the possibilities of leveraging existing
data from multiple data owners, rather than extra time-consuming and
expensive data generations, to develop and optimize complex
decision-making procedures suchas the battery recycling route design
in a collaborative while privacy-preserving fashion.
Methods
Privacy-informed data augmentation
We perform data augmentation with two considerations: (1) more
diversified data for training a generalized model and (2) protecting
data privacy by preventing adversarial reconstruction (reverse engi-
neering to eavesdrop on the private data).Given a feature matrix FN×M
and a class label vector CN×1=fcig,i=f1,2, ,9g,whereNand Mare
the numbers of measured batteries (known as “observations”)and
associated features, respectively. The data augmentation includes the
following three steps: First, we index the feature matrix Ffor a subset
Fiusing each unique class label ci. Second, we augment Fiinto Fi
Aug by
resampling with replacements using Bootstrapping. The resampling
size (or the number of bootstrapped observations) of Fi
Aug is set to
S= 200. For the class label of Fi
Aug,wehavefe
ci
Augg=fcig, which means
the augmented class labels fe
ci
Auggis identical to theoriginal class labels.
Third, we add random Gaussian noise to each observation of Fi
Aug to
evaluate the robustness and the privacy budget of the trained model,
then we have a noisy feature matrix subset e
Fi
Aug.Ahyperparameter
NSR, i.e., the noise-to-signal ratio in percentage, controls the noise
intensity, defined as the ratio of noise power to signal power. Intui-
tively, the model performance Acan be deteriorated by increasing
NSR, denoted by a function AðNSRÞ.Thedefinition of the privacy
budget (PB) is given:
PB= 100% × maxðNSRjAðNSRÞ≥AÞð1Þ
where Adenotes the lower bound of acceptable accuracy of the model,
depending on specific application requirements.
Finally, we stack the augmented data of each class to get the
augmented feature matrix e
F9S×M=fe
Fi
Auggand the class label vector
e
C9S×1 =fe
ci
Augg,wherei=f1,2, ,9g. We use 80% (the primary split) of
the augmented data to generate the client samples as the training set.
We use 40% (the secondary split) of the remaining augmented data as
the testing set. Both primary and secondary splits are in a stratified
manner to ensure samples required in each client are sampled. The
detailed data split setting here is for illustration and can be modified to
further investigate the minimum data sample requirement for
collaborators.
Client Simulation
The federated machine learning framework involves multiple colla-
borators, known as clients, to train a global model jointly. One client
serves as a data contributor for the battery type sorting task in our
setting. In this work, we simulate 10 clients, each possessing different
classes and different observations of battery data. To be specific, each
Clientkis defined over a triplet, i.e., Clientk≜ðlbk,ubk,NCkÞ,
k=f1,2, ,10g, where lbkand ubkare the minimum and maximum
number of observations in Clientk. The value of lbkand ubkare set to
100 and 200 for all clients, respectively. NCkstands for the minimum
number of classes in each Clientk, quantifying the level of client-wise
heterogeneity (namely, the heterogeneity index in the main manu-
script). Then, random observations are subsequentially drawn from
the augmented data fe
F,e
Cgfor the client based on the as-defined triplet.
Client model
The random forest is a decision-tree-based machine-learning algo-
rithm, with each tree defined over a collection of random variables.
Formally, for an m-dimensional feature vector X≜½x1,,xmT=e
F,
and a response vector Y≜e
C, the goal is to learn a prediction function
gðXÞfor predicting Y. The prediction function gðXÞis determined by
minimizing the expectation of the loss function L:
EXY LY,gXðÞðÞ
½ ð2Þ
where,thesubscriptsdenoteexpectationsonthejointdistributionof
Xand Y.
The j-thdecisiontree,orthej-th base learner, is denoted as
hjðX;ΘjÞ,whereΘjparameterizes a random collection of a set of ran-
dom variables of X. In the sorting, a class assignment rule to every
terminal (leaf) node tconsidering a zero-one loss function gives:
hjðX;ΘjÞ=argmax
y2e
C
pyjtðÞ ð3Þ
where, we pick the class with the maximum posterior probability.
The random forest constructs gby learning a series of base lear-
ners, h1ðX;Θ1Þ,,hJðX;ΘJÞ. These base learners are combined to give
an ensembled prediction function g, determined by the most fre-
quently predicted classes:
gXðÞ= argmax
y2e
CX
J
j=1
Iðy=hjðX;ΘjÞÞ ð4Þ
where, Iis the indicator function. Iðy=hjðX;ΘjÞÞ =1ify=hjðX;ΘjÞand 0
otherwise. The number of trees in each random forest is fixed at ten,
i.e., J= 10 for a balanced classification accuracy and computation cost
(Supplementary Figure 13). We deliberately let the collaborators (cli-
ents) learn the most suitable random forest structure, i.e., the model
parameters, by themselves, rather than fixing the parameters since
each collaborator could have very different battery numbers and
cathode material types. By only presetting the number of trees in the
random forest, the collaborators could have enough flexibility to train
the best model that suits their own data distribution. The bottom-level
random forest algorithm (client model) is implemented using readily
available MATLAB packages, more specifically, the TreeBagger func-
tion in the Statistics and Machine Learning Toolbox. The MATLAB
version is R2022a, and the code runs on a personal computer with Intel
(R) Core (TM) i5-10400 CPU @ 2.90 GHz RAM 8 GB.
Federated machine learning
In the proposed federated machine learning framework, local random
forests are first trained on each client with its own local data in a
parallel fashion. Then the local client models are aggregated into a
global model by means of a proper voting strategy from the local
sorting results.In our work, batteryclass distribution across clients can
be heterogeneous, which brings difficulty in aggregating the biased
client models. To this end, we propose a Wasserstein distance voting
method to aggregate the client models rather than the traditional
majority voting. Our model aggregation method is robust to hetero-
geneous class distributions across clients. The core idea of the Was-
serstein distance voting is to reduce the weightings of clients whose
observations are similar to ones in the global model. The Wasserstein
distance measure is defined as:
Wq,ðÞ=inf
γ2MP ZΩ1×Ω2
jx1x2jqdγðx1,x2Þ
!
1
q
ð5Þ
where γis a transport operator, referring to the transport of arbitrary
attributes pairs, i.e., ðx1,x2Þ, from the global feature space Ω1to the
client feature space Ω2. MP stands for a measurably preserved
transport.
Article https://doi.org/10.1038/s41467-023-43883-y
Nature Communications | (2023) 14:8032 11
Content courtesy of Springer Nature, terms of use apply. Rights reserved
The Wasserstein distance voting term ωis defined as:
ωk=αλð1MkðWqÞÞ ð6Þ
where, α>0andλ> 0 are voting hyperparameters. Mkis the average
operator on the pairwise Wasserstein distance between feature spaces
of Clientkand the global feature space, i.e., the recycler.
The aggregated global model GðxÞcan be obtained as:
GxðÞ= argmax
y2e
CX
K
k=1
ωkIy=gkxðÞ
ð7Þ
where, Kis the number of clients. Iis the indicator function.
Iðy=hjðX;ΘjÞÞ =1if y=hjðX;ΘjÞand 0 otherwise. Finally, to maximally
protect data privacy, the local votes are properly encrypted before
being uploaded to the recycler. Most encryption methods, e.g., secure
Hash Algorithms, shall suffice without compromising the sorting
accuracy. The high-level federated machine learning framework,
including the Wasserstein-distance voting and the transfer of
parameters, is implemented from scratch.
Feature importance
We use permutation importance to measure the feature importance in
the client model, i.e., the random forest algorithm. The core idea of the
permutation importance is to use out-of-bag data to examine the
effect of feature permutation using the trained random forest model.
In the first step, a prediction is made on several observations of the
out-of-bag data. In the second step, the feature θm,m=1, ,mis
randomly permutated for observations of out-of-bag data, then the
modified out-of-bag data is passed down each tree in the random
forest. In the first and second steps, two predictions are made by the
trained random forest model, i.e., ^
Cand ^
C*. The permutation feature
importance of θmis defined as:
Impm
n=1
JnX
j2In
Iðyn≠^
C*
n,jÞ 1
JnX
j2In
Iðyn≠^
Cn,jÞð8Þ
where, Inis the cardinality of the nout-of-bag observations, Jnis the
number of trees in the random forest considering nout-of-bag
observations. The feature importance of Impm
nis averaged over all
observations as a global importance in the client model. Similarly,
feature importance in the federated machine learning framework is
averaged over all clients.
Evaluation metric
We use a one-vs-all prediction strategy to predict a multi-class classi-
fication problem, such that the original problem is converted into
several binary classification problems. The accuracy of each binary
classification sub-problems is defined as follows:
accura cy = Number of correct predictions
Total number of predictions =TP + TN
TP+FN+FP+TN ð9Þ
where, TP,FP,FN,TN refer to the number of true positive, false positive,
false negative, and true negative predictions.
The prediction accuracy for the multi-class classification problem
gives:
Accuracy = 1
NC X
NC
i=1
accuracyið10Þ
where, iis the class label, NC is the number of battery classes.
The accuracy could not provide an adequate model evaluation
when classification samples are imbalanced, i.e., heterogeneous data
distribution. Thus, the F1-score is used, whose definition is as follows:
F1 = 2 × Precision × Reca ll
Precis ion + Recall ð11Þ
where, Precision = TP =ðTP + FPÞand Recall = TP=ðTP + FNÞ.
Reporting summary
Further information on research design is available in the Nature
Portfolio Reporting Summary linked to this article.
Data availability
The Center for Advanced Life Cycle Engineering (CALCE), Hawaii
Natural Energy Institute (HNEI), University of Michigan (MICH), Uni-
versity of Oxford (OX), the Sandia National Laboratories (SNL) and
Underwriters Laboratories–Purdue University (UL-PUR) datasets used
in this study are available at www.batteryarchive.org.Forthefull
details of the dataset and policies for data reuse, please refer to their
website, respectively. Source data are provided with this paper.
Code availability
Code for the modeling work is available from the corresponding
authors upon request.
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Acknowledgements
This work was supported by the Shenzhen Science and Technology
Program (Grant No. KQTD20170810150821146) [X.Z.], the Tsinghua
Shenzhen International Graduate School Interdisciplinary Innovative
Fund (JC2021006) [X.Z. and G.Z.], the Key Scientific Research Support
Project of Shanxi Energy Internet Research Institute (SXEI2023A002)
[X.Z.] and the Tsinghua Shenzhen International Graduate School-
Shenzhen Pengrui Young Faculty Program of Shenzhen Pengrui Foun-
dation(SZPR2023007) [G.Z.]. The first author would like to thank Xin Qin
from the University of Cambridge, Zihao Zhou from the University of
Oxford, Tsaijou Wu from Jinan University, Tingwei Cao, and Zixi Zhao
from Tsinghua University for their helpful discussions in preparing the
manuscript accessible to a broad readership. The authors would like to
thank Prof. Qiang Yang from WeBank, as well as Ms. Yaxin Wang,for their
constructive insights on federated learning. The authors would like to
thank Dr. Yuliya Preger, from Sandia National Laboratory, co-founder of
batteryarchive.org, for providing the first public-available repository for
easy comparison of lithium-ion battery degradation data across
institutions.
Article https://doi.org/10.1038/s41467-023-43883-y
Nature Communications | (2023) 14:8032 13
Content courtesy of Springer Nature, terms of use apply. Rights reserved
Author contributions
S.T. conceptualized, designed, and performed the numerical
experiments and prepared the first manuscript draft; H.L. discussed
the experiments and prepared the response letter to the reviewers;
C.S. contributed to the techno-environmental analysis by specifying
the details of battery recycling; H.J., G.J., Z.H., R.G., and J.M. con-
tributed to identifying the scientific issues of cathode sorting in bat-
tery recycling; R.M. and Y.C. reviewed and edited the first and revised
manuscript draft; S.F., Y.W., and Y.S. contributed to the data curation
and discussions; Y.R. contributed to machine learning experiment
design in the revised manuscript and discussions; X.Z., G.Z., and H.S.
conceptualized, reviewed, discussed, supervised this work and
retrieved fundings.
Competing interests
The authors declare no competing interests.
Additional information
Supplementary information The online version contains
supplementary material available at
https://doi.org/10.1038/s41467-023-43883-y.
Correspondence and requests for materials should be addressed to
Xuan Zhang, Guangmin Zhou or Hongbin Sun.
Peer review information Nature Communications thanks Zongguo
Wang, and the other, anonymous, reviewer(s) for their contribution to
the peer review of this work. A peer review file is available.
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