Experimental investigation of the Time-Temperature difference (t-dT) defrosting control method in frost-free household refrigerators

Abstract

To improve the defrosting accuracy and the energy efficiency of frost-free household refrigerators, a novel Time-Temperature difference (t-dT) defrosting control method, based on experimental and theoretical studies, is proposed in this paper. Experimental frosting and defrosting results verify the feasibility and applicability of the t-dT defrosting control method. The experimental data comparing two refrigerators at three different ambient temperatures show that the refrigerator applying the t-dT method had a shorter defrosting period and a shorter interval than those of the Time-Temperature (t-T) defrosting control method. Furthermore, the experimental results simulated real-life processes prove that the t-dT defrosting method could save more energy. Under the standard testing condition, the average total energy consumption including defrosting in the refrigerator applying the t-dT defrosting method is from 1.04 kW⋅h to 1.06 kW⋅hwithin 24 hours, and the ratio of defrosting energy consumption to the whole energy consumption is under 5%. All the results indicate that the t-dT method being suitable for the frost-free refrigerator has a more competitive performance than the t-T method.

Full text

International Journal of Refrigeration 160 (2024) 182–196
Available online 25 January 2024
0140-7007/© 2024 Elsevier Ltd and IIR. All rights reserved.
Light Gradient Boosting Machine (LightGBM) to forecasting data and
assisting the defrosting strategy design of refrigerators
Machine de renforcement du gradient de lumi`
ere (LightGBM) pour pr´
edire les donn´
ees et
assister la conception de la strat´
egie de d´
egivrage des r´
efrig´
erateurs. ´
Etude exp´
erimentale et
mod´
elisation math´
ematique
Chenxi Ni
a
, Haihong Huang
a
,
*
, Peipei Cui
b
, Qingdi Ke
a
, Shiyao Tan
a
, Kim Tiow Ooi
c
,
Zhifeng Liu
a
a
Key Laboratory of Green Design and Manufacturing of Machinery Industry, Hefei University of Technology, Hefei, 230009, PR China
b
Changhong Meiling Company Limited, Hefei, 230009, PR China
c
School of Mechanical & Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore
ARTICLE INFO
Keywords:
Defrosting control strategy
LightGBM
Feature sets
Correlation analysis
Mots cl´
es:
Strat´
egie de r´
egulation du d´
egivrage
LightGBM
Fonctionnalit´
es
Analyse de corr´
elation
ABSTRACT
This study proposes using the Light Gradient Boosting Machine (LightGBM) to improve the defrosting control
strategy in frost-free refrigerators. By analyzing data and optimizing control parameters, the aim is to enhance
defrosting performance and reduce energy consumption using the time–temperature difference (t–dT) approach.
The research involves analyzing performance and reliability data for two control strategies (time–temperature
(t–T) and t–dT), creating three feature sets (FS1, FS2, and FS3) based on correlation analysis, and employing
LightGBM models to forecast datasets. The control parameter threshold (ΔT
op,s
) is optimized using the
LightGBM-based data. The key ndings indicate that the t–dT strategy with a xed threshold (7.8 ◦C) out-
performs the t–T method in efciency at an ambient temperature of 38 ◦C. At 10 ◦C, the performance tests show
no signicant difference, but the t–T method performs better in reliability tests. The FS1-based data from the
t–dT strategy in the reliability test at 10 ◦C are considered ideal input, and the LightGBM models generate FS2-
based and FS3-based data for evaluation. The optimized t–dT defrosting strategy achieves favorable refrigeration
conditions with minimal power consumption and optimal cooling capacity. The ideal ΔT
op,s
threshold, based on
data for the idealized frosting condition, is determined to be 8.3 ◦C.
1. Introduction
In China, frost-free refrigerators have led to a signicant increase in
household energy consumption. The accumulation of frost on the
evaporator due to frequent door opening and closing reduces the per-
formance of refrigerators and necessitates energy-intensive defrosting
processes. This frost formation occurs when the temperature of the heat
exchanger surface drops below the dew point, causing condensation and
the formation of frost droplets (Seker et al., 2004a, 2004b; Getu and
Bansal, 2006). As a result, the coefcient of performance (COP) de-
creases by 35–60 %, heat capacity decreases by 35–57 % (Jiang et al.,
2013), and energy consumption increases by 20 % (Xiao et al., 2009; Li
et al., 2017). Given that frosting can account for over 30 % of the
defrosting cycle’s duration, implementing frost-retarding measures is
crucial. Electric heater defrosting (EHD) is cost-effective and requires
minimal modication to the refrigeration system, making it suitable for
household frost-free refrigerators (Amer and Wang, 2017; Song et al.,
2018). However, the mismatch between full frost coverage and
bottom-up heat transfer prolongs the defrost duration. During defrost-
ing, the intrusion of warm air into freezer cabinets (FCs) results in
increased FC temperature rise and overall energy consumption (Zhao
et al., 2020). Researchers have proposed various methods to enhance the
defrost performance of frost-free refrigerators, focusing on redistribut-
ing frost, optimizing EHD cycles, and introducing novel defrosting
control methods. Melo et al. (2013) and Yoon et al. (2018) explored
* Correspondng author.
E-mail address: huanghaihong@hfut.edu.cn (H. Huang).
Contents lists available at ScienceDirect
International Journal of Refrigeration
journal homepage: www.elsevier.com/locate/ijrefrig
https://doi.org/10.1016/j.ijrefrig.2024.01.025
Received 18 June 2023; Received in revised form 16 December 2023; Accepted 24 January 2024

International Journal of Refrigeration 160 (2024) 182–196
183
power input modes for defrosting heaters in their optimization efforts.
Additionally, Maldonado et al. (2018) proposed a system control strat-
egy with a specic emphasis on fan operation. Furthermore, Ghadiri
Modarres et al. (2016) introduced an adaptive defrosting method that
includes extra cooling for compartments before initiating the defrost
cycle.
Efcient control methods for periodic defrosting can greatly improve
the operation of frost-free refrigerators. The traditional time-
–temperature (t–T) defrosting method controls the evaporating tem-
perature and compressor function time but may lead to excessive
defrosting due to door openings and the complex nature of frost accu-
mulation (Buick et al., 1978). One challenge is the issue of elevated
temperatures in cabinets during the defrost process, a phenomenon
noted by several researchers. In their study, Bansal et al. (2010) con-
ducted both experimental and numerical analyses to examine the heat
transfer pattern of the heater in a domestic freezer cabinet (FC). A
demand-based defrosting control strategy, on the other hand, initiates
defrosting operations only when the frost adversely affects the re-
frigerator’s performance, resulting in improved defrosting efciency by
up to 37 % (Li et al., 2017; Melo et al., 2013; Ni et al., 2019).
Adaptive defrosting control strategies incorporate parameters such
as door open time, compressor on time, previous defrost duration, and
actions of the compressor, fans, and heater before, during, and after
defrosting (Ghadiri Modarres et al., 2016). However, poorly designed
control parameters can compromise the reliability of these strategies. To
enhance long-term performance, machine learning algorithms trained
on temperature and humidity sensor data can be employed for current
forecasting to predict future temperatures (Diedrichs et al., 2018).
Machine learning algorithms have been widely utilized in medical
studies, energy prediction, and system fault forecasting (Ju et al., 2019;
Chen et al., 2019; Pu et al., 2019; Qiu et al., 2020). It is a branch of
articial intelligence to obtain and analyze rules from data. The typical
machine learning methods contain decision trees, articial neural net-
works (ANN), and so on. ANN is the most widely used algorithm in the
refrigeration eld. The comparison of results from the 3D computational
uid dynamics (CFD) model and ANN model shows that the method
based on the ANN with supervised learning performed using the genetic
algorithm performs better in transient airside temperature eld than the
simple Fluent code (Conceiç˜
ao Ant´
onio and Afonso, 2011). The trained
ANN model integrated with the CFD model of the airside ow allowing a
realistic transient response of the evaporator based on the instantaneous
thermal state of the cabin air is a better method to predict the transient
cool-down phenomena in the airside ow (Singh and Abbassi, 2018).
Owing to the accurate prediction of the airside ow temperature,
ANN-based algorithms have been used in the control through electronic
expansion valves (Cao et al., 2016; Chen et al., 2019), varying
compressor and supply fan speeds (Li et al., 2013), and some integrated
control methods (Moon, 2015; Moon et al., 2017) for some air condi-
tioners owing to the variable indoor and outdoor air uid eld. Con-
ventional rule-based control methods are still widely used for domestic
refrigerators due to the periodic variation of the internal temperature of
refrigerators and the stable ambient temperature. The complex frost
phenomena and rules on the evaporator in the refrigerator are still
worthy to be deeply studied by some machine learning methods (Zen-
dehboudi et al., 2017).
Traditional machine learning algorithms, such as neural networks,
support vector machines, and Bayesian belief networks, have mostly
been applied to fault diagnosis rather than control strategies (Guo et al.,
2017; Hao et al., 2019). Decision trees, particularly Gradient Boosting
Decision Trees (GBDT), are widely used due to their comprehensibility
and effectiveness in high-dimensional data analysis (Chen and Guestrin,
2016). GBDT, Recurrent Neural Networks (RNN), Gated Recurrent Unit
(GRU) networks, and Long Short-Term Memory (LSTM) networks are
commonly used for time series forecasting (Gao et al., 2022; Yang et al.,
2020). Among these, GBDT, including its implementation as eXtreme
Gradient Boosting (XGBoost), has been extensively employed in energy
consumption prediction for HVAC systems (Wang et al., 2019; Ahmad
and Chen, 2019). A newer contender, the Light Gradient Boosting
Nomenclature
A area (m
2
)
C constant
F “strong” tree model
F(X) regarding the “X” set calculation model
f “weak” base leaner
f(X) regarding the “X” set base leaner
h heat transfer coefcient (W/(m
2
⋅◦C))
L mean square loss
Q heat capacity (J)
q heat ow rate (W)
r correlation coefcient
T temperature (◦C)
t Time (s)
X feature set of “x” feature label
x value of “x” feature label
x average value of “x” feature label
y value mapped by “x”

Y predicted set mapped by X

y predicted value mapped by “x”
y average value of the sum of 
Y

y the rst-order gradient on L
z value of “z” feature label
z average value of “z” feature label
Greek
ΔT temperature difference between evaporating temperature
and FC temperature (◦C)
Δt time difference per unit (s)
δ thickness (m)
λ thermal conductivity (W/(m⋅◦C))
Σt accumulated time (s)
Subscripts
a air
am ambient
am-cab ow from ambient to cabinet
com compresser working state
coun time counter
ΔT temperature difference between evaporating temperature
and FC temperature
e evaporating status
ev evaporator
ev-fre ow from evaporator to freezer
cab cabinet
fr frost
fre freezer cabinet
h higher than 0 status
i i
th
component
m m
th
component
n n
th
component
op the state with the door is opened within 30 min
s setting
xz the correlation between x and z
C. Ni et al.

International Journal of Refrigeration 160 (2024) 182–196
184
Machine (LightGBM), has gained popularity for its data modeling ca-
pabilities based on GBDT (Ke et al., 2017). While LightGBM performs
exceptionally well with large datasets, its advantages may not be as
pronounced on smaller datasets, potentially being surpassed by simpler
models. Both XGBoost and LightGBM are potent algorithms, each with
distinct strengths. XGBoost (Mo et al., 2019) is versatile and widely
adopted, whereas LightGBM particularly excels in efciency, especially
with large datasets. The refrigerator test data examined in this paper
spans a considerable duration, encompasses a wide array of features,
and constitutes a substantial volume of information. Consequently, it is
particularly well-suited for making predictions using LightGBM.
2. Forecasting and optimizing methology
The proposed methodology focuses on defrosting control strategy,
Light Gradient Boosting Machine (LightGBM) method, and performance
evaluation. An innovative defrosting control strategy called the time-
–temperature difference (t–dT) approach is introduced, which in-
corporates a temperature difference threshold (ΔT
s
) between freezing
and evaporating temperatures to determine the frost condition. This
strategy improves upon conventional defrost timing by providing an
additional safeguard. In extreme circumstances, the refrigeration sys-
tem’s operation and frost condition can be negatively affected if the ΔT
s
value is inappropriate. Consequently, parameter adjustments must be
made through testing. This study addresses the issue of continuous
parameter tuning by utilizing correlation analysis and the LightGBM
method to predict and optimize control parameters. This approach saves
time and effort.
2.1. Schematic overview
Fig. 1 illustrates the schematic representation of the study. Initially,
two different defrost control strategies were implemented and their
reliability and performance were assessed using data acquired from the
Performance and Reliability Test Centre of Changhong Meiling Com-
pany Limited. Next, the data was analyzed to create a correlation heat
map of the feature parameters, which were then divided into three
feature sets. Subsequently, the optimal feature set was identied, and
LightGBM models were sequentially built using the three feature
parameter sets to obtain the forecasting data. Finally, a third LightGBM
model with "Power" as the output was trained using the optimal and
predicted data. The LightGBM-based data were analyzed to evaluate
energy consumption and temperature.
2.2. The t–dT control strategy
2.2.1. The principle of the t–dT control strategy
For indirect cooling refrigerators, ΔT between the T
e
and the T
fre, a
can directly indicate the thickness of the frost on the evaporator. ΔT is
the essential monitoring parameter for the t–dT defrosting start-time.
Frosting conditions cause the humid air inside the freezer cabinet
(FC) to transfer potential and sensible heat to the frost layer on the
evaporator. The Eq. (1) can be used to represent the heat transfer of
evaporators,
qev−fre =ha⋅Aev⋅Tfre,a−Te(1)
where q
ev-fre
is the heat ow rate between the evaporator and freezer,
A
ev
is the area of the evaporator. The air-side equivalent heat transfer
Fig. 1. The optimization owchart of the defrosting control strategy based on LightGBM.
C. Ni et al.

International Journal of Refrigeration 160 (2024) 182–196
185
coefcient (h
a
) under the frost condition is correlated more with the
thickness of frost (δ
fro
) but less with frost density inuencing thermal
conductivity (λ
fro
). At the preliminary stage of frosting, A
ev
increases at
rst and decreases then because δ
fro
keeps growing which covers the n
surface of the evaporator leading to the decline in A
ev
when the refrig-
erating procedure continues without defrosting. Owing to the air path
blocked by the frost layer, it causes the reduction in the air velocity
inuencing the heat transfer. Thus, h
a
and q
ev-fre
are respectively
decreasing as the increase of frost amount on the evaporator surface
increases. When the evaporator performance deteriorates due to frost
growth, T
fre, a
increases and T
e
decreases. Based on Eq. (1), the above
analysis means that as the frost thickness increases, the h
a
decreases and
ΔT increases.
Under high humidity conditions at an ambient temperature of 38 ◦C,
an experiment was conducted to verify the feasibility of a novel
defrosting control strategy for a refrigerator without a defrosting pro-
cess. The range of ambient relative humidity was controlled between 45
% and 85 %. In Fig. 2, the time range has been selected from stable
refrigerating time after the temperature uctuation to the time before
the sudden shut-up due to a machine fault. The variation trends of T
fre, a
,
T
e
, and ΔT are shown in Fig. 2. Technically, the temperature uctuation
of these variables has the same trend at other ambient temperatures (Ni
et al., 2019). The evaporating cabinet was briey opened three times
non-consecutively between 625 and 1000 min to observe the frost
condition, and twice at 120–1375 min to observe the frost state.
Combining the observations of Fig. 2 with theoretical analysis (Seker
et al., 2004a, 2004b; Getu and Bansal, 2006; Jiang et al., 2013; Xiao
et al., 2009; Li et al., 2017), it was discovered that early frosting helped
with cooling storage when the compressor was turned on, as well as
when ΔT was slightly elevated. The frost effect blocked the air ducts and
reduced cooling effectiveness when ΔT was raised excessively. It in-
dicates that ΔT would gradually vary with T
fre, a
and T
e
in the long term.
ΔT directly reects the heat transfer condition of the evaporator. These
experiments prove that ΔT is an appropriate parameter for defrosting.
2.2.2. The t–dT control strategy
The traditional t–T method for controlling refrigerator defrosting is
based on several factors, including door opening status, refrigerating
and freezer temperatures, evaporator surface temperature, and
compressor turn-on rate. To comprehensively reect the frosting status,
defrosting control parameters such as humidity inside the cabinet,
duration of damper opening, and compressor turn-on rate should also be
taken into consideration. Experimental results show that incorporating
these control parameters requires almost twice the number of experi-
ments compared to the t–T control strategy without them, especially in
the development of different types of refrigerators with different air duct
structures. However, the inuence of adding the temperature difference
control parameter is relatively small for different air duct structures.
Furthermore, this approach can accurately determine the frost condition
and requires relatively less effort to determine the thresholds. Therefore,
an optimized t–dT control strategy based on the traditional t–T control
strategy is proposed (Ni et al., 2019). The ΔT serves as a new criterion in
the t–dT defrosting control strategy, supplementing the conventional t–T
defrosting control strategy.
The whole process is shown in Fig. 3. After inputting the control
parameters, the defrosting judgment process formally starts. After the
last defrosting and strong cooling processes, the compressor working
timer (t
com
) starts. Σt
ΔT,h
is another timing duration used to specify the
time range for judgment rules of ‘ΔT >0’ and the time integration in-
terval for calculating the integral value. Before T
e
and ΔT are monitored,
the formal judging owchart starts. The rst step is to determine
whether the refrigerator door is opened frequently. There are two
identical logical processes for determining whether to open or close the
door. Both processes involve checking that the temperature difference,
integral accumulations of the temperature difference and surface tem-
perature, and compressor on-time meet the defrosting criteria. However,
the thresholds for each step are set differently depending on whether the
door is open or closed. Frequent door opening simulates extreme con-
ditions in reliability tests, while infrequent door opening simulates
normal use scenarios and performance tests for refrigerators. If one of
the doors is not opened in 30 min, the rst step is to determine whether
ΔT is higher than ΔT
s
in the last 90 min. If not satised, the stable
frosting condition is not formed. Thus, Σt
ΔT,h
should be restarted. If
satised, it should determine whether the integral of the temperature
difference exceeding the threshold (Σ(ΔT
h
−ΔT
s
)Δt) in the time area
(Σt
ΔT,h
) is greater than C
ΔT
ΔT
s
. If satised, the compressor is stopped,
and the timer is started (Σt
coun
). After 10 min, heating starts. If this is not
the case, then the integral evaporating temperature exceeding the
threshold (Σ(T
e,h
−T
e,s
) Δt) in the time area (Σt
ΔT,h
) should be compared.
If it is greater than C
T
T
e,s
, the compressor is stopped, and the defrosting
program is started. On the other hand, if Σ(T
e,h
−T
e,s
)Δt is less than C
T
T
e,
s
, the working time (Σt
com
) under the condition is compared with the set
compressor running time thresholds (t
s
). If these time thresholds are
reached, the defrosting program is started. If one of the doors is opened
in 30 min, all the above judgment statements will be executed again, but
the parameters above (ΔT
s
, T
e,s
, and t
s
) are replaced by ΔT
op,s
, T
op,e,s
,
and t
op,s
.
2.3. Optimization based on LightGBM
2.3.1. LightGBM method
LightGBM develops from Gradient Boosting Decision Tree (GBDT). It
is the supervised learning algorithm using decision tree learners to t
gradients. Decision tree regression is a machine learning algorithm used
for predicting numerical values based on input features. It also in-
tegrates predictions of the “weak” base learner (tree model) to achieve a
“strong” tree model via a serial training process. In the paper, the model
was used in regression for predicting data of different features. There are
two components of GBDT which are gradient boosting and decision tree.
The basic formulation in gradient boosting is shown as follows:
F(X) = M
m=0fm(X)(2)
In the model, f(X) is “base leaner”, and the decision tree is used in
GBDT. Boosting is a linear combination of many regression tree models,
and it is a stage-wise optimized algorithm. Gradient boosting is the
boosting algorithm by adjusting the current label to the current iteration
residual between the original label and predicting value as the tting
target based on the model. It is designed for decreasing training error
and loss in the process. The loss function is designed as the mean square
loss (L) shown as Eq. (5). The formulation is as follow:
L= (yi−Fm−1(xi))2(3)
Fig. 2. The temperature variation at 38
◦C ambient temperature under the
frosting condition without defrosting.
C. Ni et al.

International Journal of Refrigeration 160 (2024) 182–196
186
In gradient descent view, we want to minimize f
m
(X) in Eq. (8). The
greedy way is adopted in the model to let L(y, F
m
(X)) <L(y, F
m-1
(X))
shown as Eq. (6). F
m
(X) is treated as parameters and take derivatives to
learn f
m
(X) for tting 
Y by using square loss. The learning process for-
mulations are shown as follows:
Fm(X) = Fm−1(X) + fm(X)(4)
yi= −
∂
Fm−1(xi)L(Fm−1(xi),yi)(5)
fm(X) = argmin
f(X)n
i=1(f(xi) − yi)2(6)
In conclusion, GBDT is to t new models to residual which equals the
negative gradient. It means that F
m
(X) is updated based on gradient
descent. The important pseudo codes and data processing of LightGBM
were depicted in Fig. 4. The pseudo-code of the schematic diagram of
GBDT and depicts the improved principle of lightGBM.
LightGBM uses histogram-based algorithms which bucket contin-
uous feature values into discrete values (bins) to speed up the training
procedure and reduce memory usage. It converts the feature value to a
"bin" before training and uses the "bin" to index the histogram without
sorting. The diagrammatic sketch to nd the best split by histogram is
shown in Fig. 4. Binning features reduces the memory requirements,
making LightGBM more memory-efcient as compared to algorithms
that use exact splits. The histogram-based approach can be easily par-
allelized, allowing for faster training times on multi-core systems.
Most boosting decision tree learning algorithms grow long trees by
level (depth), but LightGBM uses the leaf-wise (best-rst) growth
strategy when growing the decision tree. It chooses the leaf with the
maximum delta loss to grow, and leaf-wise algorithms tend to achieve
lower loss than level-wise algorithms. This makes it a better choice for
large datasets of experimental data, and it is the only option available in
LightGBM. The diagrammatic sketch of the leaf-wise growing tree is
shown in Fig. 4 (Ke et al., 2017; Lee Rodgers and Nicewander, 1988; Shi,
2007).
2.3.2. Evaluation of LightGBM model
To evaluate the quality of the training model, three indices of per-
formance (root-mean-squared error (RMSE), mean absolute percentage
error (MAPE), and determination coefcient (R
2
)) were used. The
calculation of them are described in Eqs. (7)–(9):
RMSE =
1
n
n
i=1
(yi−yi)2
(7)
MAPE =100%
n
n
i=1
yi−yi
yi(8)
Fig. 3. The workow of the t–dT defrosting control strategy.
C. Ni et al.

International Journal of Refrigeration 160 (2024) 182–196
187
R2=1−
i
(yi−yi)2

i
(yi−yi)2(9)
In the above equations, "n" stands for the number of instances, "y" is
the average of the response variable, "y
i
" is the calculated amount of the
response variable for the i
th
instance, and "
yi" is the modeled amount of
the response variable for the i th instance.
3. Data preparation and anaylsis
3.1. Data preparation
Refrigerator performance tests were conducted at Changhong Meil-
ing Company Limited, where energy consumption, power, and other
pertinent data were collected according to the standards set by
‘Household refrigerator power consumption limit value and energy ef-
ciency level standards’ (GB 12021.2-2015) in China. This research
utilizes these data sets to analyse and forecast the refrigerator perfor-
mance data. The data were collected from the refrigerator with regularly
opening doors in different temperatures and high humidity to ensure the
defrosting stability based on the ‘corporate standard of Changhong
Meiling Company Limited’ (Q/MLK108-2019).
In accordance with the standards outlined in ’GB 12021.2-2015
′
, the
ambient temperatures were maintained at 32 ±0.7 ◦C and 16 ±0.7 ◦C
for energy consumption tests, with a relative humidity of 50 ±1 %. In
order to study the optimal ΔT
s
and ΔT
op,s
under extreme conditions,
performance tests were also conducted without opening the refrigerator
doors at 38 ±0.7 ◦C and 10 ±0.7 ◦C ambient temperatures. The hu-
midity levels were maintained at 50 ±1 % and 30 ±5 % respectively, as
it is difcult to maintain high humidity levels at low ambient temper-
atures. Fig. 5(a) and (b) respectively are the probably stable defrosting
period and unstable defrosting period may happen in test or real life in
’GB 12021.2-2015
′
. When the refrigerator door is closed, the power of
the air-cooled refrigerator’s refrigeration process with two gaps in the
defrosting process remains stable. Its corresponding temperature follows
a regular and periodic pattern, indicating a stable state shown in
following Fig. 5(a). However, while energy consumption tests offer some
insight into the advantages and disadvantages of defrosting policies,
they do not accurately replicate real-world refrigerator usage and may
not fully showcase the superiority of the defrosting control strategy.
Fig. 4. LightGBM decision tree formation process and GBDT formation pseudo code.
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International Journal of Refrigeration 160 (2024) 182–196
188
In reality, when the door is opened and closed, regardless of whether
the temperature inside the box changes regularly, there is a signicant
uctuation in power, indicating a non-stable state shown in Fig. 5(b). To
address this, we conducted an extreme usage simulation based on the
reliability test. To conrm the reliability of the refrigerator, the tests
were conducted in accordance with the ’Q/MLK108-2019
′
corporate
standard. The reliability tests were conducted at 10 ±0.7 ◦C ambient
temperatures with a relative humidity of 30 ±5 %, and at 38 ±0.7 ◦C
ambient temperatures with a relative humidity of 50 ±1 %.
The test benches, test prototypes, and other test equipment are
shown in Fig. 6. The assisted door-opening machine operates as follows:
1) The door of the refrigerating cabinet opens for 1 min every 30 min.
2) The door of the freezer cabinet opens for 1 min every 60 min.
Fig. 5. Schematic graphs of the periodically stable and non-stable defrosting processes.
Fig. 6. The device schematic of performance test and reliability test.
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International Journal of Refrigeration 160 (2024) 182–196
189
3) The opening is conducted for 12 h every 24 h.
Since cyclical unstable heat exchange is common under extreme
conditions, calculating stable heat exchange is not ideal for optimizing
control parameters in each temperature range. One notable improve-
ment of this study is the use of all data developed under particular
ambient temperatures (38 ◦C and 10 ◦C) to study ΔT and temperature
trends rather than relying on energy consumption at standard temper-
atures (32 ◦C and 16 ◦C).
3.2. Data analysis
Performance and reliability tests were conducted on two re-
frigerators using both t–dT and t–T defrosting control strategies. The
measured mean temperature of the freezer’s right side (Freezer2) was
used as T
fre,a
but not as the temperature control parameter for the freezer
cabinets due to the air duct’s unique structure. RefAverage, the average
temperature of RC, was calculated and collected. The measured evapo-
rator inlet temperature (EvaporatorIn) was assumed to be T
e
, and thus
ΔT was the temperature difference (EvapDiff) between Freezer2 and
EvaporatorIn.
3.2.1. Data analysis of performance tests
After running for a period of time, the refrigerators under the
traditional t–T control strategy and t–dT control strategy reached a
stable state of periodic cooling and defrosting cycles that meet the "GB
12,021.2–2015" standard. For the t–dT control strategy without the
door-opening status, the control parameter ΔT
op,s
was set to 7.8 ◦C for
any ambient temperature. To compare the performance at 38 ◦C, we
collected data from two units for 1800 min. Due to the long interval of
defrosting under the operating condition of 10 ◦C, it was difcult to
analyze data over a long period of time. Therefore, we selected 500 min
of data from two units for further comparison in detail.
Fig. 7(a) and (b) depict RefAverage, Freezer2, EvaporatorIn, and
EvapDiff at an ambient temperature of 38 ◦C for the traditional t–T
control strategy and t–dT control strategy refrigerators. The temperature
control range for the refrigerating cabinet was 3–8 ◦C, and for the freezer
cabinet, it was −17 to −22 ◦C. The data analysis for Fig. 7(a) show that
after the rst defrost, the normal cooling process lasted from 294 to
1248 min, comprising 16 periods with an average refrigeration cycle of
59.625 min. The average compressor running time was 31 min, and the
integrated value of the evaporator temperature did not meet the
requirement under this condition. The defrost was triggered by the
compressor running time reaching the threshold, and the ΔT of each
cycle remained between 0 and 10 ◦C, with the maximum temperature
difference reaching 10 ◦C. In contrast, the data analysis for Fig. 7(b)
indicates that, after the rst defrosting process, the normal cooling
process lasted from 302 to 1496 min, comprising 17 cycles with an
average refrigeration cycle of 70.235 min. The compressor’s average
operating time was 28 min, and the integrated value of the evaporator
temperature and temperature difference did not meet the requirement
under this condition. The defrosting process was triggered by the com-
pressor’s operating time reaching the threshold, and the ΔT of each
cycle remained below 7 ◦C. The unstable defrosting cycles triggered the
judgement rules about T
e
and ΔT, resulting in the subsequent frosting
environment before stable heat exchange was achieved. Therefore, the
compressor operating time triggering the defrosting process in both
prototypes still reects the overall frosting environment. Based on Eq.
(1) and Fig. 2, by comparing Fig. 7(a) and (b), we can draw the following
conclusions:
1) The smaller temperature difference in the t–dT strategy indicates a
better frost environment and better refrigeration performance can be
achieved with a smaller temperature difference in the system.
2) The longer defrosting interval in the t–dT strategy implies that fewer
defrosting processes started during a longer stable operating cycle,
resulting in lower energy consumption.
3) The evaporator inlet temperature is slightly higher in the t–dT
strategy compared to the t–T strategy, while the temperature of
Freezer2 in the t–dT strategy is slightly lower than that in the t–T
strategy. Therefore, based on the characteristics of the refrigeration
Fig. 7. The temperature variations in different defrosting control strategies in the performance tests at 38
◦C and 10 ◦C.
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cycle, the t–dT strategy shows higher heat transfer efciency under
this heat transfer condition.
Fig. 7(c) and (d) illustrate RefAverage, Freezer2, the observed
EvaporatorIn, and EvapDiff at an ambient temperature of 10 ◦C. The
temperature control range for the refrigerating cabinet is 3–5 ◦C, while
the temperature range for Freezer2 is slightly lower than the average
temperature, ranging from −15 to −20 ◦C. Data analysis from Fig. 7
reveals little difference in statistical data between the two methods
during the performance test experiment without opening the door. The
average cooling cycle lasts 111.2 min, with an average compressor
running time of 55.55 min. During the cooling process, the highest
temperature difference reached 10 ◦C in each cycle. However, the in-
tegral values of evaporator temperature and temperature difference did
not meet the requirements under this condition. The defrost was trig-
gered when the compressor run time exceeded the threshold. The un-
stable defrost cycle in the early stage still triggered the judgment rules
about T
e
and ΔT separately, leading to the formation of a stable defrost
process in a frosty environment.
3.2.2. Data analysis of reliability tests
In the reliability tests, both the traditional t–T control strategy and
the t–dT control strategy refrigerators reached a stable state of periodic
refrigeration and defrost cycles that met the ‘Q/MLK108–2019’ standard
after a period of operation. In the t–dT control strategy with periodic
door openings, the control parameter ΔT
s
was set to 10 ◦C at an ambient
temperature of 38 ◦C. In the reliability comparison experiment at an
ambient temperature of 38 ◦C, the experimental results of the t–T control
strategy showed a short-term periodicity for each defrost interval, while
the t–dT control strategy showed a regular periodicity for every two
defrost intervals. Therefore, we plotted the details of each group sepa-
rately with a shorter time length of 2000 min and a longer time length of
4000 min to observe the periodicity. For the reliability test at 10 ◦C
ambient temperature, the defrosting intervals were short. Therefore, we
compared the data from two machines with two defrost cycles for 1000
min under this condition.
In the reliability test at 38 ◦C, Fig. 8(a) shows that the defrosting
interval has reached 625 min and the temperature difference often ex-
ceeds 15 ◦C. During one cycle, the compressor run time limit was trig-
gered when the freezing temperature could not reach the target
temperature after defrosting. After defrosting, the harsh icing environ-
ment made it difcult for the evaporator temperature to drop during the
maximum power operation of the refrigeration system (strong cooling
process). Therefore, it could be concluded that the refrigerator with the
t–T defrosting control strategy in the 38 ◦C reliability test caused a poor
frosting environment, and even icing occurred, resulting in the refrig-
eration cycle and freezer temperature not being in the ideal state after
each defrost.
Fig. 8(b) shows that the refrigerator with the t–dT defrosting control
strategy completed one cycle every two defrosting intervals, and the
time of this cycle reached 1412 min. The average defrosting interval was
706 min, which was much higher than that of the t–T defrosting strategy
shown in Table 1. In the rst defrosting interval of a cycle, the strong
cooling phase continued until the compressor stopped for defrost after
reaching the run time limit. The second defrosting interval was after the
chilling and refrigeration temperatures could reach the standard after
the strong cooling, followed by the completion of a stable cooling cycle
process. Defrost still started after the compressor run time limit was
triggered. Compared to the t–T defrosting strategy, the t–dT defrosting
strategy could not only meet the cooling demand and target, but could
also extend the defrosting interval to achieve the goal of reducing energy
consumption shown in Table 1.
In the reliability comparison test at 10 ◦C, the t–dT defrost strategy
with a ΔT
s
of 7.8 ◦C was not initially stable in defrost, unlike the t–T
defrost strategy prototype. As shown in Fig. 9(a), during the unstable
state of the t–T defrosting strategy, the temperature difference in the
cooling stage did not reach the upper limit, continuing for 90 min in
some parts, invalidating the timer, and resulting in an invalid determi-
nation of the integral value. Defrosting only occurred when the
compressor operating time limit was triggered. It then gradually stabi-
lized, as shown in the blue box in Fig. 9(a). At an ambient temperature of
38 ◦C, the temperature control range of the two strategies was the same.
The temperature control range of the refrigerating cabinet was from 3 to
8 ◦C, and that of the freezer cabinet was −8 to 18 ◦C. However, the
freezer temperature could not drop below −18 ◦C in the t–T strategy.
Comparing Fig. 9(b) and (c), under the ambient condition of 10 ◦C,
the temperature range of the refrigeration cabinet setting under the t–T
strategy was from 3 to 5 ◦C, while the temperature setting range under
the t–dT strategy was from 4 to 7 ◦C to trigger the temperature difference
judgment and maintain a defrost cycle and energy consumption similar
to that of the t–T strategy. The temperature range of Freezer2 under the
t–dT strategy was from −20 to −17 ◦C, which is higher than that of the
t–T prototype.
The interior of the refrigerator in the t–dT method should have been
more susceptible to frost in a high humidity environment, but the t–T
control strategy showed even better cooling and frosting conditions in-
side the cabinet. In addition, the energy consumption of t–dT control
Fig. 8. The temperature variations in different defrosting control strategies in the reliability tests at 38
◦C ambient temperature.
Table 1
Comparison of the t–T control method and t–dT control method in reliability
tests.
Ambient
temperature (
◦C)
The t–T control method The t–dT control method
Defrosting
interval
(mins)
Energy
(kW⋅h/
2000mins)
Defrosting
interval
(mins)
Energy (kW⋅h
/2000mins)
38 625.0 3.89 706.0 3.48
10 623.5 0.88 687.0 0.93
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International Journal of Refrigeration 160 (2024) 182–196
191
strategy was more than that of t–T control strategy shown in Table 1.
Therefore, setting ΔT
s
at 7.8 ◦C and increasing the temperature control
range of the refrigerating cabinet is not a good strategy in the 10 ◦C
reliability test, and the defrosting control parameters need to be
redesigned.
4. Forecasting and anlysis
4.1. Correlation analysis for feature selection
4.1.1. Correlation analysis
The test data set consists of 26 inter-related variables. The correla-
tion coefcient is a measure of the level of correlation between two
variables, and is represented numerically by “r” in the samples. This
accurately reects the degree of linear correlation between the vari-
ables. The Pearson simple correlation coefcient (Lee Rodgers and
Nicewander, 1988) is a popular method for calculating correlation co-
efcient, which describes the degree of correlation between two interval
scale variables. The correlation coefcient between the two sets of data
is presented below:
rxz =n
i=1(xi−x)(zi−z)

n
i=1(xi−x)
 
n
i=1(zi−z)
(10)
where xi is the ith value of “x” feature label, and x is the average value of
“x” feature label. Similarly, zi and z respectively are the ith value and
average value of “z”. The meaning of different values of r
xz
is explained
as shown in Eq. (3):











|rxz| = 1.0,completely linear correlation
|rxz|>0.8,high correlation
0.5<|rxz|<0.8,moderate correlation
0.3<|rxz|<0.5,low correlation
|rxz|<0.3,uncorrelation
(11)
The 26 variables in the eld test account for the air temperature
distribution and cooling system operation state in the refrigerator. The
complex relationships between all of these variables cannot be expressed
by a simple relation. Redundant information and uncorrelated features
should be removed. Meanwhile, the features must be used as many times
as possible to predict the feature values required. In Fig. 1, the values of
the partial features were predicted using LightGBM based on partial
data. According to Eq. (3), |r
xz
| >0.8 indicates a high correlation be-
tween the two feature variables, which aids in splitting relatively in-
dependent coupling feature variables to predict the others.
4.1.2. Feature selection
The association rules method is a powerful data mining algorithm for
determining the relationship between attributes in a transaction data-
base. Fig. 10 presents the results of the correlation analysis for the 26
feature variables. It is a heatmap of correlations with a clustering
dendrogram.
In machine learning methods, a broader range of diverse features
typically leads to improved output results. However, our predictable
parameters are quite limited. Therefore, grouping the feature set into
distinct groups aids in providing ample diversity in the input data. The
selected features are grouped into three feature sets, which are con-
nected and serve as input and output for prediction. According to the
clustering dendrogram in Fig. 10, 26 features are selected for three
feature sets. Feature set 1 (FS1) includes environment temperature
(’TempEnv’) and ambient humidity (’Humidity’), which can be accu-
rately controlled by the same environment control equipment, operating
setting, and compressor setting in the two different systems. The cor-
relation coefcients among the variables in FS1 show that they can be
divided into three groups: the ambient control parameters, the param-
eters of the operating electric control, and the temperatures of the
freezer chamber. It is evident that the features of FS1 are more relevant
to the features of FS3 than the features of FS2 based on the heat map
correlation’s color depth. Note that the correlation coefcients among
the air temperatures in FS3 are all higher than 0.4. The features of FS3
are temperatures in the refrigerating cabinet and variable cabinet that
are highly relevant to each other. The features in FS2 include temper-
ature difference (’TempDiff’) and evaporator inlet and outlet tempera-
tures (’EvaporatorIn’ and ’EvaporatorOut’). These data in FS2 directly
reect the frosting condition and operational status of the refrigeration
system. FS2 also includes temperature difference setting
Fig. 9. The temperature variations in different defrosting control strategies in the reliability tests at 10
◦C ambient temperature.
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International Journal of Refrigeration 160 (2024) 182–196
192
(’TempDiffSet’), which is strongly correlated with ’Relation-
shipBetValues,’ which is the ’TempDiff’ divided by the ’TempDiffSet.’
’TempDiffSet’ is the key to determining when the system defrosts.
Therefore, the data in FS2 reect what we would prefer to observe than
FS3. Based on the optimization owchart in Fig. 1 and the analysis of the
feature selection in Fig. 10, we can use the test data of FS1 as the initial
input and output the test data of FS2, which can train the LightGBM
model for prediction. After using the initial test data of FS1 and the
predicted data of FS2 as input and outputting the test data of FS3, the
LightGBM model forecasting data of FS3 can be trained.
A LightGBM model was developed to predict power output using
reliability test data at an ambient temperature of 10 ◦C. All features,
except ’Power’, were used as input features, and ’Power’ was used as the
output feature. The visual results of variable importance in the
LightGBM model are shown in Fig. 11, which were used to verify the
rationality of the data generation method based on LightGBM. The
objective was to rank the importance order of the variables to verify the
feasibility and accuracy of the predicted data. In Fig. 11, it is observed
that ’Voltage’ and ’Electricity’ in FS1 have the strongest correlation with
’Power’, which aligns with the analysis of heat maps and correlations.
These variables are energy-related parameters of the refrigeration sys-
tem. Other variables that are highly relevant to performance are
’HeatUp’, ’EvaporatorIn’, ’EvaporatorOut’, and ’TempDiff’, all of which
are parameters in FS2 that reect the evaporator operation of the
refrigeration system. This demonstrates that the ndings from correla-
tion analysis and the LightGBM modeling are consistent. Predicting the
data of FS2 from the original data of FS1 is crucial, and appropriate
evaluation values had to be used for both the training and test sets.
Based on the correlation analysis, design factors signicantly affect the
process of producing fresh data for FS2, but they have little effect on the
nal ‘Power’ forecast.
4.2. Parameter optimization results and anlysis
4.2.1. Original data collection
To improve the adaptability of the LightGBM model in forecasting
the t–dT data of FS2, the training and test data were expanded to include
the data obtained from t–dT method reliability tests at 10 ◦C ambient
temperature. The total number of statistical samples used was 206,272,
collected during the period from August 19th to December 25th, 2022.
This large dataset is sufcient for training and testing to simulate a more
accurate model.
4.2.2. Data generation
Fig. 12(a) and (b) illustrate the test data for two prototypes without
opening the damper using the t–T and t–dT strategies, respectively.
These data were used for comparative analysis. The cooling time range
for the t–T defrosting strategy in one refrigeration period is 44–68 min,
and its energy consumption is 37.652 kJ. In contrast, the t–dT strategy
has a cooling time range of 44.5–68 min and an energy consumption of
38.051 kJ. We found that the t–dT defrosting strategy consumed more
energy and had a higher temperature range in the freezer. In the t–T
defrosting test data, the compressor shutdown period is 0–44 min in
Fig. 12(a). From 0 to 8 min of this process, the temperature of the
refrigerant inlet in the evaporator rises abruptly, and the freezer tem-
perature continues to drop steadily. However, from 8 to 44 min, the
temperature difference between the refrigerant inlet in the evaporator
Fig. 10. The results of correlation analysis for 26 feature variables.
Fig. 11. The variable importance in the nal LightGBM model.
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International Journal of Refrigeration 160 (2024) 182–196
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and the freezer remains relatively stable. This indicates that there is no
external transfer of electrical energy. To achieve quasi-static equilib-
rium, which results in a stable temperature change and allows the sys-
tem to reach a state of uniform temperature change, the heat ow from
the environment to the refrigerator is identical to the heat ow from the
evaporator to the freezer. Frosting did not make it difcult to raise the
evaporating temperature during the shutdown of the prototype in the
t–T strategy. However, in the prototypes of the t–dT strategy, the
evaporating temperature increased slowly during the shutdown, and
challenging frosting made it difcult to raise the temperature.
After analyzing Fig. 3, Σ(ΔT
h
−ΔT
op,s
)Δt in the time area (Σt
ΔT,h
) is
used to determine the timing of defrosting, which suggests that ΣΔT
h
Δt
in Σt
ΔT,h
reects the frosting situation. To make a fair comparison of the
relevant parameters, all data are averaged for a single refrigeration
period in combination with test data with the dampers opened during
the defrost interval. Under these conditions, the t–T strategy’s ΣΔT
h
Δt is
9168, while the t–dT strategy’s ΣΔT
h
Δt is 12,060. Based on Fig. 13,
which depicts the refrigerator including air as the subject of the study,
the cooling capacity calculation Eq. (13) and the heat ow balance Eq.
(12) can both be concluded. h
a
and A can be regarded as constant when
there are no signicant changes to the evaporator’s structure and no
layers of frost obstructing the ow paths. Therefore, the cooling capacity
can be determined directly by comparing the values of ΣΔT
h
Δt in the
time area (Σt
com
) for those two defrosting strategies. The ΣΔT
h
Δt in the
t–T cooling strategy and the t–dT cooling strategy for the cooling time
are 8673 and 9864, respectively. In summary, it can be concluded that
the t–dT strategy in this condition has a larger cooling capacity and a
thicker accumulated frost layer during a single cooling period, but the
cooling effect is worse.
qev−fre +qam−cab =qcab (12)
Qcooling =
tcom
qev−freΔt(13)
Based on the correlation analysis and the comparing reliability test
data for one refrigeration period at 10 ◦C ambient temperature, the t–T
mehod reliability test data of FS1 include temperatures in the Freezer
and humidity should be inpututed as an ideal dataset for optimization.
The t–T defrosting method at 10 ◦C ambient temperature can maintain a
good performance owing to the appropriate evaporator temperature
status with compressor off and stable energy consumption. In other
words, we want to predict the appropriate t–dT strategy control pa-
rameters from the temperature state under the t–T strategy.
To ensure the accuracy of the data used to build the model, we use
reliability test data for the t–dT strategy at 10 ◦C as training samples. The
original data is divided into FS1-based data, FS2-based data, and FS3-
based data according to feature sets. The original data is split into test
and training sets. The original data set with the t–dT method of FS1 at 10
◦C ambient temperature, considered as FS1-based data, is used as the
input to establish the rst LightGBM model for forecasting data of FS2.
Then, the original FS1-based data and forecasting FS2-based data are
used to simulate the FS3-based data by the second trained LightGBM
model. Finally, the third LightGBM model is obtained by using "Power"
as the output and other feature data, including original and forecasting
data, as input. The entire owchart is shown in Fig. 14. It is essential to
note that we used the original and forecasting data as inputs and the
original data as outputs to train and improve the accuracy of the models.
Table 2 displays the three performance indices for the training and test
sets of these models. The regression performance, accuracy, and t of
the three models are found to be satisfactory using Eqs. (7), (8), and (9).
Since the freezing data and the state of the refrigeration system for
the reliability test in the t–T strategy are considered ideal, we establish a
prediction model for the reliability test data based on FS1 of the t–T
strategy. We use the FS1-based data of the t–T strategy as input and
forecast the FS2-based data using the rst LightGBM model. The pre-
dicted FS2-based data and the original FS1-based data are then used as
input to the second LightGBM model to calculate the FS3 feature data.
Finally, the third LightGBM model is used to calculate ‘Power’ using the
raw and predicted data, except for ’Power’. Table 3 displays three per-
formance indices from this test.
After predicting FS2-based data from FS1-based data using Table 3, it
was found that the RMSE of the data predicted by the rst LightGBM
model met the requirement of being close to 0, indicating that the
regression effect on FS2-based data was better. The t–dT property was
demonstrated by the R
2
>0.5, indicating a good t effect. Although the
MAPE was within the normal range, it was not quite close to 0 %, sug-
gesting that the generation process reduced the t’s accuracy and caused
jagged data to appear, but the trend was still present. The evaluation of
forecasting ‘Power’ and the generation of FS3-based data both improved
to a higher level.
Fig. 12. Variations applied (a) t–T defrosting method and (b) t–dT defrosting method without optimization in one refrigeration period.
Fig. 13. Schematic diagram of the ow of heat through the refrigerator during
the refrigeration cycle and compressor shutdown state.
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International Journal of Refrigeration 160 (2024) 182–196
194
4.2.3. Data analysis and optimization
The data from the ideal t–T strategy were used to create Fig. 15. The
refrigeration temperature can also be controlled within the optimal
range of 2–5 ◦C, and the calculated temperature difference predictions
are almost identical to those of ’TempDiff’. The optimized t–dT strat-
egy’s evaporator inlet temperature seems to fall between that of the t–T
and t–dT initial strategies. The slope of the increase in evaporator inlet
temperature is steeper in the shutdown state compared to the initial t–dT
strategy, indicating less frosting. We collected the average data of the
optimized t–dT strategy and the average data in the t–T defrosting
strategy and the non-optimized t–dT defrosting strategy at the reliability
test at 10 ◦C ambient temperature in Table 4 for comparative analysis.
The optimized t–dT strategy has the smallest Σt
ΔT,h
ΔT
h
(8209) in the
cooling state than the other two strategy. What’s more, the energy
sonsumptiong in one cycle period is the lowest. This suggests that the
amount of frost layer simply improves the effectiveness of heat transfer
in achieving the same effect, allowing the t–T strategy to maintain the
same cooling effect at the lowest necessary cooling capacity. A higher
cooling capacity is needed for the open-damper cooling process because
the refrigerating cabinet in the LightGBM models based on the original
t–dT strategy is kept at a higher humidity level. The Σt
ΔT,h
ΔT
h
of it in
one cycle period is 13,552 which is the highest in comparing with other
two values in Table 4. Combing the analysis of Fig. 15, the three times
the damper opening in one defrost interval is greater than the original
opening the damper once, which causes the average Σt
ΔT,h
ΔT
h
of the
optimized t–dT strategy to rise, so the frost layer is not worse than that in
the original t–dT strategy. Compared to the original t–dT prototype
experimental data, the maximum temperature difference data at pre-
dicted cooling did not improve, but the average temperature difference
did. The t–dT strategy’s cooling process has a low temperature differ-
ence decline slope and a weak tendency to quickly counterbalance the
difference’s quick decline. The stable, long-lasting frost layer has some
advantages over the t–T strategy for total frost eradication because it
stores the cooling capacity. The refrigeration system of the optimized
system tends to be more stable in terms of heat exchange and the
condensing temperature does not rise as quickly, increasing the refrig-
eration system’s efciency ratio and lowering total power consumption.
Therefore, calculations based on the data for the idealized frost in Fig. 15
show that setting ΔT
op,s
at 8.3 ◦C is more logical in accordance with the
principle that C
T
cannot be changed.
5. Conclusions
This paper presents a methodology to optimize the defrost control
strategy of frost-free refrigerators utilizing the LightGBM algorithm. The
purpose of this study is to predict and adjust the control parameters by
data analysis, to improve the defrosting performance and reduce the
energy consumption of refrigerators. Main ndings and conclusions
from this study are listed as follows:
(1) In the comparison between the refrigerators under the t–T and
t–dT defrosting methods, the t–dT defrosting strategy with the
xed ΔT
s
/ ΔT
op,s
(7.5/7.8 ◦C) works efciently at 38 ◦C ambient
Fig. 14. The owchart of the simulation process based on LightGBM.
Table 2
The training and tested performance indices of the LightGBM models in the t–dT
defrosting control strategy based on original reliabity test.
Algorithm Training dataset Test dataset
RMSE MAPE R
2
RMSE MAPE R
2
1st
LightGBM
0.5049 7.0893 % 0.9969 2.6049 10.5571
%
0.9817
2nd
LightGBM
1.1151 9.9216 % 0.9941 2.8843 13.4254
%
0.9770
3rd
LightGBM
1.9453 13.9260
%
0.9979 4.7112 23.5675
%
0.9874
Table 3
The tested performance indices of the LightGBM models for optimization based
on FS1-based data in the t–T defrosting control strategy.
Algorithm Test dataset based on FS1-based data in the t–T defrosting control
strategy
RMSE MAPE R
2
1st LightGBM 7.2107 76.3970 % 0.6440
2nd LightGBM 0.1519 2.2859 % 0.9636
3rd LightGBM 2.8148 13.5284 % 0.9954
C. Ni et al.

International Journal of Refrigeration 160 (2024) 182–196
195
temperature in both performance and reliability tests. The energy
consumption in the t–dT method is less than that in the t–T
method in that condition. In the condition without frequently
opening the door, the compressor comsumes lower power of in
every refrigeration period. In the condition with frequently
opening the door, the defrosting interval in the t–dT method is
shorter while the freezer temperature cannot be reached in the
t–T method. For the performance tests at 10 ◦C ambient tem-
perature, it makes no difference between these methods. How-
ever, the t–dT method with ΔT
op,s
at 7.8 ◦C does not work better
in the realiabilty tests at 10 ◦C ambient temperature comparing to
t–T method.
(2) The t–dT strategy data of FS1-based features from the reliability
test at 10 ◦C ambient temperature are regarded as the ideal input
data. Then the FS2-based data to FS3-based data is outputted by
the t–dT LightGBM models. The requirements for the data-based
evaluations of the generated test datasets have been fullled.
(3) The average ΣΔT
h
Δt in Σt
ΔT,h
and Σt
com
show the frosting con-
dition and the cooling capacity respectively. The optimized t–dT
defrosting strategy has the ΣΔT
h
Δt in Σt
com
of 8209, the smallest
value among the two test data, with an energy consumption of
36.038 kJ, the lowest value among them. The ΣΔT
h
Δt in Σt
ΔT,h
of
the optimized t–dT strategy is 13,552 that is the highest value
among those three values. The predicted data for the optimized
t–dT strategy demonstrates that good refrigeration condition can
be maintained with the least amount of power, proper cooling
storage, and the least cooling capacity. The ideal ΔT
op,s
based on
the data for the idealized frosting condition is 8.3 ◦C.
This study showcases the capabilities of LightGBM as a robust tool for
time series prediction and optimization in refrigeration engineering.
However, it is important to note that this study does have certain limi-
tations. Firstly, tests were solely conducted under the extreme ambient
temperatures of both the highest and lowest values. Consequently, other
inuential factors, including but not limited to cooling capacity, hu-
midity in cabinets, wind speed, and door opening frequency, were not
taken into consideration, which could potentially affect refrigerator
performance and defrosting efciency. Hence, future comprehensive
studies will be conducted, encompassing the aforementioned parame-
ters, in order to provide a more holistic understanding of the subject
matter.
Declaration of competing interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inuence
the work reported in this paper.
Acknowledgments
This work was supported by the National Natural Science Foundation
of China (51722502). The authors would like to thank the sponsor of
Changhong Meiling Company Limited.
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