Papers
Papers
   Abstract— The large-scale application of lithium-ion batteries               and performance [3]. Nevertheless, due to the highly nonlinear
(LIBs) in electric vehicles (EVs) requires meticulous battery                   temperature characteristic of LIBs, it becomes difficult to
management to guarantee vehicular safety and performance.                       manage battery safety, performance, and lifetime in EVs.
Temperatures play a significant role in the safety, performance,                Specifically, high temperatures increase the risk of safety haz-
and lifetime of LIBs. Therefore, the state of temperature (SOT) of
batteries should be monitored timely by the battery management                  ards such as thermal runaways, which might cause catastrophic
system. Due to limited onboard temperature sensors in EVs, the                  loss [4]. Low temperatures undermine the energy and power
SOT of most batteries must be estimated through other measured                  capability of LIBs by causing sluggish electrochemistry inside
signals such as current and voltage. To this end, this article                  the cell [5]. Both low and high temperatures can contribute to
develops an accurate method to estimate the surface temperature                 accelerated battery degradation, with lithium plating triggered
of batteries by combining the physics-based thermal model                       by the former factor and the growth of solid electrolyte
with machine learning (ML). A lumped-mass thermal model is
applied to provide prior knowledge of battery temperatures for                  interphase (SEI) caused by the latter [6]. In this context, it is
ML. Temperature-related feature, such as internal resistance,                   of paramount importance to regulate the battery temperature to
is extracted in real time and fed into the ML framework as                      an optimal range through active thermal control [5], [7], during
supplementary inputs to enhance the accuracy of the estimation.                 which accurate monitoring of battery temperature serves a
An ML model, which combines a convolutional neural network                      fundamental role.
(CNN) with a long short-term memory (LSTM) neural network                          Typically, the temperature of LIBs can be measured directly
(NN), is sequentially integrated with the thermal model to
learn the mismatch between the model outputs and the real
                                                                                by the surface-mounted temperature sensors in the EV battery
temperature values. The proposed method has been verified                       pack. Nevertheless, it is impossible to install a temperature
against experimental results, with an accuracy improvement of                   sensor at the surface of each cell to monitor its temperature
79.37% and 86.24% compared to conventional pure thermal                         since this will inevitably increase the cost and hardware
model-based and pure data-driven approaches, respectively.                      complexity of the battery pack, especially when the pack
  Index Terms— Electric mobilities, lithium-ion batteries (LIBs),               consists of hundreds and even thousands of cells [8]. It has
machine learning (ML), temperature estimation, thermal models.                  been reported that the average temperature sensors-to-cell ratio
                                                                                in an EV battery pack is around 1/10, which means that the
                          I. I NTRODUCTION                                      temperature information of the majority of the cells cannot
                                                                                be obtained directly through measurements [8]. However,
T     RANSPORTATION electrification is one of the most
      promising ways to realize sustainable energy devel-
opment. As the predominant energy storage component in
                                                                                temperature abnormity might still occur in those cells without
                                                                                surface-mounted temperature sensors and such abnormity can
electric mobilities such as electric vehicles (EVs) and electric                hardly be detected by temperature sensors installed on nearby
aircraft, lithium-ion batteries (LIBs) exhibit superiority in                   cells. Therefore, tracking the state of temperature (SOT) of
energy and power density, cycle life, and charge/discharge                      those cells by taking advantage of nontemperature signals,
efficiency compared with previous generations of batter-                        such as current and voltage, is of paramount importance to
ies [1], [2]. The ever-increasing use of LIBs in transportation                 the safety and performance of the whole battery pack in
applications leads to higher requirements for battery safety                    EVs, which makes this work different from existing SOT
                                                                                estimation/prediction studies relying on a surface temperature
  Manuscript received 14 March 2023; revised 12 June 2023; accepted 28 June     sensor [9], [10], [11], [12].
2023. Date of publication 11 July 2023; date of current version 18 June 2024.      Generally, there are three main methods to achieve sen-
This work was supported in part by the Villum Foundation for Smart Battery
Project under Grant 222860 and in part by the National Natural Science          sorless SOT estimation in the existing literature, based
Foundation of China under Grant 52111530194. (Corresponding authors:            on battery impedance [13], [14], [15], battery thermal
Yunhong Che; Xiaosong Hu.)                                                      models [16], [17], [18], and machine learning (ML) algo-
  Yusheng Zheng, Yunhong Che, Xin Sui, and Remus Teodorescu are with
the Department of Energy, Aalborg University, Aalborg 9220, Denmark             rithms [19], [20], [21]. In impedance-based estimation, the
(e-mail: yzhe@energy.aau.dk; ych@energy.aau.dk; xin@energy.aau.dk;              relationship between battery temperature and impedance
ret@energy.aau.dk).                                                             parameters (e.g., real part, imaginary part, and phase) will
  Xiaosong Hu is with the College of Mechanical and Vehicle
Engineering, Chongqing University, Chongqing 400044, China (e-mail:
                                                                                be calibrated offline by selecting an optimal frequency under
xiaosonghu@ieee.org).                                                           which the impedance parameters are sensitive to battery tem-
  Digital Object Identifier 10.1109/TTE.2023.3294417                            perature while insensitive to the state of charge (SOC) and
                       2332-7782 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
                                     See https://www.ieee.org/publications/rights/index.html for more information.
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2644                                                              IEEE TRANSACTIONS ON TRANSPORTATION ELECTRIFICATION, VOL. 10, NO. 2, JUNE 2024
state of health (SOH) [22], [23]. Afterward, the parameterized                  LIBs, the online identification of the battery’s internal resis-
impedance-temperature relationship will be applied to estimate                  tance, and the CNN-LSTM will be introduced in detail. Then,
battery temperature according to the measured impedance                         the way of integrating physics with CNN-LSTM will be
online. As for thermal model-based estimation, various sim-                     elucidated.
plified thermal models can be developed to capture battery
thermal dynamics such as heat generation, heat accumula-
                                                                                A. Lumped-Mass Thermal Model
tion, and heat dissipation online [16], [17], [18]. Closed-loop
observers are designed based on simplified thermal models                          The lumped-mass thermal model is a simplified model
to estimate battery temperature through voltage or impedance                    used to capture the temperature response of the battery. This
feedback [17], [24]. Regarding data-driven estimations, mature                  model regards the battery cell as a single particle, and the
ML algorithms, such as artificial neural networks (ANNs),                       temperature gradient inside the cell is neglected so that the
can be applied to recognize the underlying data pattern                         thermal dynamics of the cell can be represented by its bulk
between measurements and battery temperatures by ignoring                       temperature. With this assumption, the governing equation for
the complicated thermal dynamics of LIBs [19], [20], [21].                      energy balance can be expressed as follows:
Nevertheless, the aforementioned three methods have limita-                                           dT                      
tions. For impedance-based estimations, the need for excitation                                  mC p     = Q − h A T − Tf                   (1)
                                                                                                      dt
equipment increases the hardware cost and complexity. Fur-
                                                                                where m, C p , and A are the mass, heat capacity, and surface
thermore, batteries need to be at a close-to-equilibrium state
                                                                                area of the battery cell, respectively, T is the time-varying
for precise impedance measurement, which requires sufficient
                                                                                temperature of the cell during operations (can be substituted
relaxation time before measurement and makes it difficult to
                                                                                with surface temperature Ts in this study), t is the time,
capture battery temperature timely [17]. For thermal model-
                                                                                Q is the total heat generation rate of the cell, h is the
based estimation, how to strike a balance between the model
                                                                                equivalent convective heat transfer coefficient from the battery
accuracy, complexity, and parameterization difficulty is a key
                                                                                cell to the coolant, and T f is the coolant temperature. Here,
issue. Simple thermal models are lightweight but may suffer
                                                                                the radiation heat dissipation is not considered since it is
from poor accuracy [25]. Complex thermal models can achieve                     negligible compared to convective heat dissipation, due to
high accuracy, yet will increase the computational burden and                   the low emissivity of the battery case, small geometric size,
parameterization difficulty [25]. For data-driven estimation,                   and relatively low operating temperature (from −30 ◦ C to
the generalization capability of the algorithm is always the                    60 ◦ C) [25].
biggest concern despite high accuracy. Moreover, data-driven                       The heat generation inside the cell consists of ohmic
methods are not able to achieve accurate estimation when prior                  heat, polarization heat, and various electrochemical reaction
knowledge of the battery temperature is lacking [10].
                                                                                heat [27]. The complete heat generation equation contains
   In recent years, physics-informed ML (PIML), as a way
                                                                                numerous electrochemical parameters that are onerous to be
of integrating physical information and ML techniques,
                                                                                obtained in real applications. Therefore, a simplified equation
exhibits great potential in addressing the aforementioned prob-
                                                                                can be used to capture the internal heat generation of the cell,
lems [26]. To this end, this article develops a sensorless
                                                                                which is expressed as [28]
surface temperature estimation method for LIBs by combining
physics-based models and ML algorithms to leverage their                                                                  ∂ Voc
                                                                                                     Q = I (Vt − Voc ) + I T                 (2)
respective strengths. In this way, both the estimation accuracy                                                            ∂T
and the generalization ability can be guaranteed. Specifically,                 where I , Voc , and Vt denote the current (positive for charging
a lumped-mass thermal model, with the advantages of being                       and negative for discharging), open-circuitvoltage (OCV), and
simple, physically identifiable, and less susceptible to overfit-               terminal voltage, respectively, and ∂ Voc ∂ T is the entropic
ting, is established to capture the thermal dynamics of LIBs                    heat coefficient corresponding to the entropy change during
and provide prior knowledge of battery temperature for the                      electrochemical reactions. The total heat generation consists
ML algorithms. Temperature-related features, such as internal                   of irreversible heat and reversible heat, denoted by the first
resistance, can be extracted timely and treated as inputs to                    and the second terms, respectively, at the right-hand side of
the ML algorithm to further increase the estimation accuracy.                   (2). Under high-rate operations, the reversible heat can be
Finally, a combined convolutional neural network (CNN)-long                     neglected due to its small contributions.
short-term memory (LSTM) neural network (NN) is leveraged                          Although the lumped-mass thermal model was pointed out
to learn the mismatch between the physics-based models and                      to have the lowest accuracy and may lead to unfavorable
the real battery temperature so that the estimation errors caused               oversimplification of the battery thermal dynamics [25], it is
by unmodeled thermal dynamics and parameterization errors                       simple enough with its parameters being easily identifiable and
can be further reduced.                                                         less prone to overfitting. Most importantly, despite rough accu-
   The remainder of this article is organized as follows.                       racy, the model can capture the trend of battery temperature
Section II introduces the proposed methodology for sensorless                   under various operating conditions since it is developed based
temperature estimation. Section III describes the datasets used                 on first principles. The estimated battery temperature and the
in this work. Next, the results and discussions are presented                   calculated heat generation by the thermal model can provide
in Section IV, followed by the main conclusion in Section V.                    some prior thermal information for the ML algorithm.
       II. F RAMEWORK FOR S ENSORLESS S URFACE
                T EMPERATURE E STIMATION                                        B. Online Internal Resistance Identification
  This section presents the framework for sensorless surface                      For the sensorless SOT estimation, only the current, voltage,
temperature estimation. The lumped-mass thermal model of                        and coolant temperature are measurable. Hence, it is important
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ZHENG et al.: SENSORLESS TEMPERATURE MONITORING OF LIBs BY INTEGRATING PHYSICS WITH ML                                                                  2645
to extract some temperature-related features that can reflect                  Fig. 2.     Structure of the proposed CNN-LSTM for surface temperature
                                                                               estimation.
the current battery SOT from these signals. By adding these
                                                                               in which d I (t) dt  and d Vt (t) dt are approximated
                                                                                                                  
features to the estimation loop, the estimation accuracy can                                                                                 by
be improved. According to [18], the internal resistance of the                 [I (t) − I (t − 1t)] 1t and [Vt (t) − Vt (t − 1t)] 1t, respec-
                                                                                                                                  
battery is more sensitive to temperature change than voltage,                  tively, and 1t is the sampling period.
and therefore, it can be used as a temperature-related feature.                   Since n(t) and its regressive values are unmeasurable, the
   Due to the complex electrical dynamics, a battery cell                      input 8(t) cannot be obtained directly from voltage and cur-
cannot be regarded as pure resistance. In this regard, the                     rent. In this context, the noise is estimated before identifying
internal resistance of the battery should be extracted based                   the parameters θ (t) at each time index. The regressive values
on an electrical model that captures the electrical behavior of                of the noise n(t − i) can be estimated through the residual of
the cell. The first-order equivalent circuit model (ECM), with                 the measured outputs and estimated outputs based on (5)
its parameters being easily identified, can be applied in this                                                             T
work. This model consists of an OCV, an ohmic resistor R0 ,                                 n̂(t − i) = y(t − i) − 8̂ (t − i)θ̂ (t − i)                  (7)
and a resistor–capacitor (RC) pair, as shown in Fig. 1.                        where i = 1, 2, . . . , n d . In this way, the input 8(t) can be
   Assuming the constant value of model parameters during a                    approximated by
sampling period, the terminal voltage of the battery Vt in the                                                                                      T
                                                                                                d I (t) d Vt (t)
                                                                                        
first-order ECM can be expressed as [29]                                         8̂(t) = I (t),          ,         , n̂(t − 1), . . . , n̂(t − n d ) .
                                                                                                  dt          dt
       Vt (t) = Voc (SOC) + (R0 + R1 )I (t)
                                                                                                                                                       (8)
                             d I (t)          d Vt (t)
                 + R0 R1 C 1         − R1 C 1          + w(t) (3)                 The initialization of the inputs and parameters can be set as
                               dt               dt
where V1 is the voltage across the RC pair, Voc varies with                                     8̂(1) = 8̂(2) = · · · = 8̂(n d ) = 80                    (9)
battery SOC and can be obtained through experiments, the                                           θ̂ (1) = θ̂ (2) = · · · = θ̂ (n d ) = θ 0            (10)
current I (t) is positive for charging and negative for discharg-
ing, and w(t) denotes the noise in the model represented by                    where the first three terms in 80 are initialized through the
some unmodeled battery dynamics and can be expressed as                        measured data and the estimated noises in 80 are initialized
                            nd
                                                                               as
                            X
                   w(t) =          ci (t)n(t − i) + n(t)                (4)                      n̂(1) = n̂(2) = · · · = n̂(n d ) = 0.                  (11)
                             i=1
                                                                                  According to [30], θ 0 should be sufficiently small and
in which n d is the order of the noise model, ci (t) is the                    therefore can be set as
coefficient, and n(t) is the white noise, which represents the
                                                                                               θ 0 = 10−6 , 10−6 , . . . , 10−6 .
                                                                                                                              
random error of the first-order ECM; n(t − 1), . . . , n(t − n d )                                                                    (12)
are its regressive values.                                                     After obtaining the inputs, the parameters of the model can be
   With the first-order ECM, the internal resistance of the                    identified timely through the following iterations:
battery can be extracted in real time through online identifica-                                                 h         T
                                                                                                                                         i
tion. In particular, this study adopts the method proposed by                      θ̂(t) = θ̂ (t − 1) + P(t)8̂(t) y(t) − 8̂ (t)θ̂ (t − 1)  (13)
Feng et al. [29] based on the recursive extended least squares
                                                                                                           P(t − 1)8̂(t)8̂T (t)P(t − 1)
                                                                                                                                        
                                                                                           1
(RELS) algorithm. To realize online identification, (3) can be                    P(t) =        P(t − 1) −                                 (14)
further expressed as a parametric model                                                    λ                 λ + 8̂T (t)P(t − 1)8̂(t)
                                                                               where P(t) is the gain factor and can be initialized as
                       y(t) = 8T (t)θ (t) + n(t)                        (5)
                                                                                                P(1) = P(2) = · · · = P(n d ) = p0 E                    (15)
where we have output y(t), parameters θ (t), and input 8(t)
                                                                                                                                     6
defined as follows:                                                            in which p0 is a large positive number (10 in this study), E
                                                                               is an identity matrix, and λ 0.95 < λ < 1 is a user-defined
   y(t) = Vt (t) − Voc
                                                                               forgetting factor and is set to be 0.99 in this work.
                                                         T
 θ (t) = θ1 (t), θ2 (t), θ3 (t), c1 (t), . . . , cn d (t)
         
                                                              T                  With the identified parameters, the total internal resistance
  = (R0 + R1 ), R0 R1 C1 , −R1 C1 , c1 (t), . . . , cn d (t)
     
                                                                               of the battery Rt at the time step t can be extracted as
                                                                    T
                  d I (t) d Vt (t)
          
                                                                                                        Rt = R0 + R1 = θ1 (t)
                                                                                                                                                        (16)
 8(t) = I (t),           ,          , n(t − 1), . . . , n(t − n d )
                     dt        dt
                                                                               where Rt is used as the temperature-related feature to indicate
                                                                       (6)     battery SOT for the ML model introduced in the following.
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2646                                                              IEEE TRANSACTIONS ON TRANSPORTATION ELECTRIFICATION, VOL. 10, NO. 2, JUNE 2024
where N is the number of samples in the training set and ŷ i                             III. D ESCRIPTION OF E XPERIMENTAL DATA
and yi are the output of the network and the truth value of the
ith sample, respectively.                                                          A publicly available experimental dataset has been used in
                                                                                this article to validate the proposed surface temperature esti-
                                                                                mation method. The dataset was collected from the University
D. Integration of Physics With ML                                               of Wisconsin–Madison [36] and the details of experiments
   To combine the advantages of physics-based models and                        were described in [37]. The test equipment includes a battery
ML algorithms, the CNN-LSTM network is integrated sequen-                       tester, a thermal chamber, and a host computer. A 2.9-Ah
tially with the lumped-mass thermal model to realize accurate                   Panasonic 18650PF cell with lithium nickel cobalt aluminum
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ZHENG et al.: SENSORLESS TEMPERATURE MONITORING OF LIBs BY INTEGRATING PHYSICS WITH ML                                                                  2647
Fig. 3. Framework of integrating physics with CNN-LSTM for surface temperature estimation.
                                 TABLE I
             S UMMARY OF THE E XPERIMENTAL DATASET [36]
oxide (NCA) chemistry was used for the test. The temperature
at the middle surface of the cell was measured by a ther-
mocouple and used as the surface temperature. The dataset
covers a series of tests under a wide ambient temperature
range (from −20 ◦ C to 25 ◦ C). At each test temperature,                      Fig. 4. Measured data during Cycle 1 under 10 ◦ C. (a) Current. (b) Voltage.
the cell was tested using different driving cycles from the                    (c) SOC. (d) Surface temperature.
fully charged state until the cell reached its cutoff voltage,
namely, 2.5 V. Standard driving cycles, such as Highway Fuel                   (Cycles 1 and 3), are used as the training data. The other
Economy Test (HWFET), Los Angeles 92 (LA92), Urban                             driving cycles are used to test the accuracy of the estimation
Dynamometer Driving Schedule (UDDS), and Supplemental                          method. It should be noted that the tested battery in this
Federal Test Procedure Driving Schedule (US06), were applied                   experimental dataset is placed in the thermal chamber with air
to the test. In addition, some synthesized cycles with the                     cooling, and therefore, the ambient temperature is used as the
random mix of US06, HWFET, UDDS, and LA92 were also                            coolant temperature when implementing the proposed method.
used to test the cell and these cycles include Cycle 1, Cycle                  In addition, since the RELS needs some time to converge, the
2, Cycle 3, Cycle 4, and NN. Apart from the tests at fixed                     data in the beginning 60 s of each driving cycle are not used
ambient temperatures, experiments were also conducted at                       as the input to the estimation framework to avoid the effect
varying ambient temperatures, which started from −20 ◦ C to                    of unreasonable Rt on estimation results. All the inputs to the
10 ◦ C and drifted upward in steps. The OCV of the battery was                 CNN-LSTM are normalized between [0, 1] to eliminate the
tested at 25 ◦ C by cycling the cell with a constant current (CC)              differences in the order of magnitude between input features.
of 1/20 C. All the tests of this battery cell, including different             To train the CNN-LSTM, the training epoch is set as 2000,
ambient temperatures and driving profiles, are summarized in                   and the learning rate is 0.001. The training process stops when
Table I.                                                                       there is no significant decrease in the loss function to avoid
   It should be noted that the original dataset was collected                  overfitting.
with a sampling frequency of 10 Hz. In this article, how-                         The accuracy of the estimation can be evaluated through
ever, the original data are preprocessed with a sampling                       root mean square error (RMSE), mean absolute error (MAE),
frequency of 1 Hz, which is close to the real-world scenarios.                 and maximum error (MAX), which are defined as follows:
Furthermore, to remove the noise in the temperature data,                                               v
                                                                                                        u     K
a Gaussian-weighted moving average filter with a window                                                 u1 X                       2
length of 40 is used and the filtered temperature is used as                                 RMSE = t             Ts (t) − T̂ s (t)        (19)
                                                                                                           K t=1
the true value. An illustration of the experimental data under
Cycle 1 at the fixed ambient of 10 ◦ C can be shown in Fig. 4.                                              1 X
                                                                                                               K
                                                                                                 MAE =            Ts (t) − T̂ s (t)                     (20)
                                                                                                            K t=1
                  IV. R ESULTS AND D ISCUSSION
                                                                                                MAX = Max Ts (t) − T̂ s (t)                             (21)
  To train the proposed hybrid model, half of the driving
cycles at different ambients, including two standard driv-                     where K is the length of data in a testing cycle. Smaller values
ing cycles (HWFET and LA92) and two synthesized cycles                         of these three metrics indicate better estimation accuracy.
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2648                                                                IEEE TRANSACTIONS ON TRANSPORTATION ELECTRIFICATION, VOL. 10, NO. 2, JUNE 2024
                            TABLE II
         PARAMETERS OF THE L UMPED -M ASS T HERMAL M ODEL
                                                                                   Fig. 6. Current, the identified resistance, the estimation result of the surface
                                                                                   temperature, and the estimation errors of Cycle 4 under fixed ambient of
                                                                                   10 ◦ C.
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ZHENG et al.: SENSORLESS TEMPERATURE MONITORING OF LIBs BY INTEGRATING PHYSICS WITH ML                                                                  2649
Fig. 7. Current, ambient temperature, the estimation result of the surface     Fig. 9. Comparison of different estimation methods under Cycle 2 driving
temperature, and the estimation errors of NN driving cycle under varying       cycle at −20 ◦ C.
ambient starting −20 ◦ C.
                                                                               Fig. 10. Comparison of the four estimation methods under different driving
                                                                               cycles and ambient conditions in terms of their estimation accuracy and
Fig. 8. Current, ambient temperature, the estimation result of the surface
                                                                               computation time.
temperature, and the estimation errors of UDDS driving cycle under varying
ambient starting 10 ◦ C.
                                                                               C. Comparison of Different Methods
                             TABLE III
E STIMATION R ESULTS W ITH THE P ROPOSED M ETHOD AT F IXED A MBIENT               In this section, the proposed surface temperature esti-
                                                                               mation method is compared with conventional approaches.
                                                                               Four methods, namely, the pure data-driven estimation, pure
                                                                               thermal model-based estimation, the hybrid method without
                                                                               temperature-related features in the input, and the hybrid
                                                                               method with temperature-related features in the input (i.e.,
                                                                               the proposed method), are compared in terms of their per-
                                                                               formance in surface temperature estimation. Fig. 9 shows
                                                                               the comparison results under Cycle 2 at a fixed ambient
                                                                               condition of −20 ◦ C as an example and the estimation errors
                                                                               of these four methods are summarized in Table V. As can
                                                                               be concluded from the results, the pure data-driven method
                                                                               using original measurements (i.e., [I , Vt , SOC, T f ]) as input
estimation errors are presented in the results. In the ambient                 has the worst accuracy among these four approaches. It is
where the temperature increases gradually, the internal heat                   hypothesized that there is a poor correlation between the 15-s
generation and the reduced heat dissipation contribute to a                    inputs and surface temperature. The same problem has also
remarkable battery temperature rise compared to that in the                    been identified by Ojo et al. [10], where the poor estimation
fixed ambient case. The results in Figs. 7 and 8 show that                     performance of a two-layer LSTM-RNN (with the same input
the estimation errors are basically within ±2 ◦ C and ±1 ◦ C,                  as the pure data-driven method in this article) was ascribed
for the battery operations starting from −20 ◦ C to 10 ◦ C.                    to the lack of prior knowledge of battery temperature. As a
More driving cycles under varying ambient temperatures are                     consequence, although the loss function can be reduced to a
applied to test the accuracy and generalization of the trained                 low level during the training process, the trained CNN-LSTM
model, and the estimation performance can be summarized in                     network still has poor estimation performance in the test-
Table IV, where in most cases, the RMSE and MAE can be                         ing dataset. As for the lumped-mass thermal model, due to
within 1 ◦ C and MAX can be within 2 ◦ C.                                      the uncertainties in thermal parameters and heat generation
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2650                                                              IEEE TRANSACTIONS ON TRANSPORTATION ELECTRIFICATION, VOL. 10, NO. 2, JUNE 2024
                                                                                                        V. C ONCLUSION
                                                                                   This article proposes a sensorless surface temperature esti-
                                                                                mation method for LIBs by combining a physics-based thermal
                                                                                model with ML algorithms. In this estimation framework,
                                                                                a lumped-mass thermal model is integrated sequentially with
                                                                                the CNN-LSTM network. The temperature calculated by the
                                                                                thermal model serves as the prior knowledge of battery tem-
                                                                                perature. With this prior information, the CNN-LSTM network
                                                                                can achieve an accurate estimation of surface temperature.
calculation, the temperature estimated by the thermal model                     Moreover, the internal resistance of the cell, which could be
will deviate from the real value. Specifically, the thermal                     used as a direct indicator of battery SOT, is identified from
parameters identified under one operating condition may not                     the current and voltage in a real-time manner and treated as
be able to capture battery thermal dynamics under other                         supplementary input to the network to improve the estimation
conditions and therefore lead to increased estimation errors.                   accuracy. The proposed method has been validated under
As for the hybrid estimation, since it receives prior knowledge                 various large current profiles and extreme ambient conditions,
of battery temperature from the thermal model, the estima-                      with RMSE less than 1 ◦ C and MAX less than 2 ◦ C in
tion error can be greatly reduced compared with the pure                        most cases, even under subzero ambient where the battery cell
data-driven and the pure model-based methods, with the                          has a significant temperature rise. A comparison of different
accuracy improvement of 86.24% and 79.37%, respectively.                        methodologies indicates that the proposed method outperforms
The CNN-LSTM network in the hybrid model can learn from                         pure data-driven and pure model-based estimations. By adding
the error between the thermal model output and the real surface                 the identified internal resistance and heat generation rate in the
temperature and then reduce this error. The supplementation                     CNN-LSTM inputs, the estimation accuracy can be further
of temperature-related features, such as internal resistance and                improved. The proposed method can be applied to real-time
heat generation, can further improve the estimation accuracy                    estimation and monitoring of the battery temperature without
by 37.35% in contrast to the hybrid method without these                        temperature sensors.
features.
   In order to compare the four methodologies comprehen-
sively, various driving cycles at different ambient conditions                                        VI. F UTURE W ORK
are used to examine these methods in terms of their compu-                         The methodology in this article is developed based on fresh
tational complexity and generalization capability. To this end,                 battery data without considering battery aging, which makes
the computation time and the MAE of these four methods are                      it challenging to achieve effective temperature monitoring in
recorded in different testing cycles. The result of the compari-                the long term. In particular, since the internal resistance of
son can be shown in Fig. 10. As can be seen from the results,                   the battery is not only dependent on operating conditions (i.e.,
the proposed hybrid method achieves significantly higher                        temperature and SOC) but also SOH, the rise of the internal
estimation accuracy compared to pure data-driven estimation                     resistance due to battery aging will increase the estimation
and pure thermal model-based estimation in all the testing                      error when applying the same algorithm to estimate battery
scenarios, indicating good generalization capability. Adding                    temperature. However, compared to the resistance change
temperature-related features can further improve the estimation                 caused by operating conditions, the internal resistance change
accuracy in most driving cycles. In terms of computation                        as a result of battery aging is a slow process and such change
complexity, the pure thermal model-based estimation has the                     can be negligible in dozens of cycles [39], [40]. In real-
least computation time due to its simple model structure.                       world applications, the CNN-LSTM network can be updated
The hybrid method without temperature-related features as                       periodically over time by taking advantage of the temperature
input has comparable computational complexity with pure                         data measured by the sparsely arranged temperature sensors
data-driven method since the computational cost added by the                    in the battery pack, to make the algorithm adaptive to battery
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ZHENG et al.: SENSORLESS TEMPERATURE MONITORING OF LIBs BY INTEGRATING PHYSICS WITH ML                                                                         2651
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2652                                                                IEEE TRANSACTIONS ON TRANSPORTATION ELECTRIFICATION, VOL. 10, NO. 2, JUNE 2024
[38] B. Shahriari, K. Swersky, Z. Wang, R. P. Adams, and N. de Freitas,                                      Xin Sui (Member, IEEE) received the B.Eng. degree
     “Taking the human out of the loop: A review of Bayesian opti-                                           in electrical engineering from Northeast Electric
     mization,” Proc. IEEE, vol. 104, no. 1, pp. 148–175, Jan. 2016, doi:                                    Power University, Jilin, China, in 2015, the M.Sc.
     10.1109/JPROC.2015.2494218.                                                                             degree in electrical engineering from the Institute
[39] J. Guo et al., “Unravelling and quantifying the aging processes of                                      of Electrical Engineering, Chinese Academy of Sci-
     commercial Li(Ni0.5 Co0.2 Mn0.3 )O2 /graphite lithium-ion batteries under                               ences, Beijing, China, in 2018, and the Ph.D. degree
     constant current cycling,” J. Mater. Chem. A, vol. 11, no. 1, pp. 41–52,                                in machine learning for battery state of health esti-
     2023, doi: 10.1039/D2TA05960F.                                                                          mation from Aalborg University, Aalborg, Denmark,
[40] S. Barcellona, S. Colnago, G. Dotelli, S. Latorrata, and L. Piegari,                                    in 2022.
     “Aging effect on the variation of Li-ion battery resistance as function of                                 She is currently a Post-Doctoral Researcher with
     temperature and state of charge,” J. Energy Storage, vol. 50, Jun. 2022,                                the Center for Research on Smart Battery (CROS-
     Art. no. 104658, doi: 10.1016/j.est.2022.104658.                             BAT), AAU Energy, Aalborg University. Her research interests include battery
                                                                                  state of health estimation, lifetime extension, feature engineering, and machine
                                                                                  learning.
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