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3 to 30 GPa. Compared to other bio-metals, except TNTZ
alloys, which are similar to bone, bio-magnesium alloys
exhibit a modulus of elasticity closer to that of natural bone
[6, 7]. For the patient, treatment with biodegradable mate-
rial instead of permanent implants obviates the necessity for
major surgery, the costs associated with treatment, the risk
of osteomyelitis (bone and joint infection), and the concom-
itant negative impact on the patient’s comfort and psychol-
ogy [8–10].
Nevertheless, the material also exhibits disadvantages,
including poor wear resistance and a high corrosion rate
[11]. Therefore, researchers aim to enhance biodegradable
magnesium’s properties by manipulating its mechanics and
biodegradability. To this end, various metal particle rein-
forcements, alloying agents, and mechanical processes have
been incorporated into biodegradable magnesium, thereby
addressing the aforementioned issues and enhancing related
properties [12–15].
Several studies have examined the corrosion behavior of
zinc-containing biodegradable magnesium alloys in body
1 Introduction
Magnesium (Mg) and its light alloys are becoming increas-
ingly prevalent in healthcare, where they are being employed
as biodegradable metallic materials. Mg, an essential human
body component, contains several alloys, including copper
and zinc (Cu, Zn [1–3]. Moreover, it exhibits one of the
most analogous qualities to bone mechanics among biode-
gradable materials, which is paramount for bone health [3,
4]. The modulus of elasticity of bio-magnesium alloys is
approximately 45 GPa [5], comparable to the modulus of
elasticity of natural bone, which ranges from approximately
Bilge Demir
bdemir@karabuk.edu.tr
1 Eskipazar Vocational School, Karabuk University, Karabuk,
Türkiye
2 Department of Mechanical Engineering, Engineering Faculty,
Karabuk University, Karabuk, Türkiye
Abstract
Incorporating Cu and Zn into Mg as a biomaterial oers a unique opportunity to exploit their antibacterial performance
and biodegradability. The main challenge in this area is understanding the ratio and eects of these elements. To achieve
this, the present work, based on two separate studies, aims to develop a regression model and apply machine learning (ML)
to predict the wear behaviors using the eects of Cu and Zn elements doped into Mg matrix at low ratios on wear and
micro and nanostructure properties (Grain size, density, hardness, Crystallite Size, microstrain, dislocation density). The
wear behavior of the samples was investigated under 5–20 N loads at a constant sliding speed of 42 mm/s. Auto Sklearn
library was used to generate training models that accurately predict the wear loss, friction coecient, and specic wear
rate values. The model showed satisfactory explanatory power and reliability in predicting the volume loss target. It also
exhibited remarkable capability in predicting the friction coecient and specic wear rate targets. The results of sample
wear tests (MgZn2 under 15 N) conducted to generate data not included in the dataset showed a high degree of agree-
ment with the ML results. Sensitivity analyses conrmed that Load, Environment, Hardness, and Grain Size are the most
inuential factors in predicting wear behavior, further validating the model’s reliability and interpretability.
Keywords Powder metallurgy · Wear test · Biodegradable · Regression analysis · Machine learning
Received: 11 January 2025 / Accepted: 16 March 2025 / Published online: 24 March 2025
© The Author(s) 2025
The regression analysis of dry - wet wear outcomes and materials
properties of biodegradable MgCu and MgZn, made by P/M, using
machine learning models
RukiyeTekin Ünver1,2· CihanBayraktar1· BilgeDemir2
1 3
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R. Tekin Ünver et al.
uids, focusing on their potential for transient implantation
[8, 16–18] Adding zinc to magnesium results in a continu-
ous increase in yield strength (YS) with an increase in zinc
from 1 to 6 wt%. However, to obtain an optimal combina-
tion of mechanical properties and corrosion resistance, the
zinc content should be limited to 4 wt%, the requirement
mentioned above [19]. The mechanical properties exhibit
considerable variation according to the production method.
It is understood that grain renement and nano-grain forma-
tion, in particular, can be highly benecial [20, 21]. It has
been reported that for MgCu alloys not to have toxic eects,
Cu should not exceed 2% concerning daily release. Copper
is a trace element that plays an important role in the func-
tioning of the cytochrome oxidase enzyme. It is also vital
for cross-linking plastic bers and collagen in connective
tissue [22, 23].
Micro-movements at the interface between the implant
and bone cement have the potential to result in wear [11,
24, 25]. Complex cellular interactions can release media-
tors, such as cytokines, facilitating osseous tissue forma-
tion. However, despite the growing interest in magnesium
alloys, further research is required to fully understand their
wear and friction characteristics. In essence, wear is con-
nected to both chemical and physical characteristics. For
biodegradable materials, tuning and life tuning can enhance
these qualities. Wear, hardness, strength, and hardness are
closely related, as is well known [15, 20, 21].
Traditional regression models have been widely preferred
to understand the wear movements that occur in metallic
materials. Some of the conventional regression models are
as follows:
●Linear Regression Model: This regression model es-
tablishes linear relationships between output attributes
such as yield stress and elastic modulus using input pa-
rameters [26–28].
●Quadratic Regression Model: This model extends lin-
ear regression by including quadratic terms and allows
for a more exible data t by ignoring the interactions
between variables [26–29].
●Full Quadratic Regression Model: This model in-
cludes mixed and quadratic terms. It represents the
interactions between variables more comprehensively.
This is especially useful when the relationships between
dierent parameters are important [26].
●Moving Least Squares (MLS) Regression Model:
This nonparametric regression technique ts a subset of
a polynomial data point and allows for local t [26].
●Polynomial Regression Model: This multiple regres-
sion model relates a response variable to multiple pre-
dictor variables using polynomial Eqs. [28, 29].
●Penalized Spline Regression Model: This model can
be an alternative to the polynomial regression model,
especially in cases where outputs close enough to seem-
ingly complex data cannot be obtained in the second
stage. It provides more accurate results by applying
smoothing techniques to the data, especially when there
is noise or complex relationships [29].
Such models are eective when the relationships between
variables are well-dened and relatively simple. However,
machine-learning models show more advanced and success-
ful predictive capabilities in complex material structures
where interactions between multiple variables cause non-
linear dependencies.
Recent research has investigated the application of
machine learning (ML) techniques for predicting wear
behavior in magnesium alloys and composites. Several
machine learning models, including support vector regres-
sion, extreme learning machines, articial neural networks,
and random forests, have been employed to predict wear
loss and friction coecients [30–35]. These models have
demonstrated high accuracy in predicting wear proper-
ties, with R² values exceeding 0.96 in some cases [30, 34].
Researchers have investigated the eects of coating meth-
ods, reinforcement materials, and tribological factors on
wear behavior. Load was identied as the most inuential
parameter aecting the wear rate [31].
Aydın et al. [34] established ve machine learning algo-
rithms to evaluate their capacity to predict wear behavior
in restricted data subjected to diverse testing operations. To
ensure a fair comparison, the hyperparameter tuning phase
of the models was applied following the study’s method-
ology. The prediction results were also subjected to evalu-
ation according to a variety of statistical criteria. These
machine-learning approaches present a promising avenue
for optimizing the design and manufacturing of materials to
enhance wear resistance in magnesium alloys and compos-
ites. In the study by Pasha et al. [33], supervised machine
learning regression models were employed to predict the
wear rate and friction coecient. To guarantee a fair com-
parison, hyperparameter tuning was performed, hyperpa-
rameter tuning was conducted. The results were subjected
to statistical analysis using a range of metrics. Moreover, the
most ecacious model for precise wear behavior prediction
was identied.
Furthermore, the study demonstrates that nanocompos-
ites exhibit enhanced wear resistance and reduced friction
coecients compared to pure Mg. In a separate survey,
Macit et al. [35] reported that A hybrid GA-SVR (genetic
algorithm-support vector regression) was employed to
enhance the wear prediction of AZ91 magnesium alloy
matrix composites. A comparison of the results revealed
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The regression analysis of dry - wet wear outcomes and materials properties of biodegradable MgCu and…
a notable distinction in the prediction performance of the
hybrid GA-SVR model, with an accuracy of 98.79% and
optimized parameter values. Applying machine learning
techniques oers signicant simplications and important
analyses, enabling predicting the mechanical properties,
wear and corrosion characteristics, and tribological perfor-
mance of various materials, including magnesium and its
composites.
Even though bio-magnesium alloys are gaining popu-
larity, it is clear that a thorough analysis of their wear and
friction properties is necessary using enhanced experimen-
tal and metallurgical parameters as this study concept. It is
commonly known how a material’s physical and chemical
properties are aected by both dry and moist wear. These
characteristics can be changed and improved, giving biode-
gradable materials a longer lifespan [24, 36]. Furthermore,
the fabrication and wear behavior assessment processes are
associated with nancial and time constraints.
This study contributes to the existing literature by apply-
ing regression analysis to the results of two experimental
studies. These analyses oer new perspectives on using Cu
and Zn additions using P/M mechanical alloying, aiming to
improve material properties and reduce the complexity of
process parameters. The experimental studies that form the
basis of this study have not yet been published in separate
forms.
Consequently, machine learning methods have become
essential in forecasting the tribological performance, wear
characteristics, and mechanical attributes of various materi-
als, such as magnesium and its composites [33]. Therefore,
this study aims to integrate machine learning techniques
with experimental outcomes. In this study, regression analy-
ses of the wear test data obtained under dierent loads of
Mg composite materials with low addition of Mg and Cu
(0.2-2%wt) were performed with machine learning, as these
materials are of signicant interest as potential biomaterials.
To create training models that can successfully predict Vol-
ume Loss, Coecient of Friction, and Specic Wear Rate
values, the Auto Sklearn library was used to integrate the
experimental results of the current study with machine learn-
ing techniques. The objective is to create and predict ideal
experiments and results, optimizing material design and
production for superior wear performance. Following the
completion of the ML regression analyses, further wear tests
were conducted, utilizing data from the regressed set that
had not been incorporated into the ML. This supplementary
experimental outcome was then subjected to a comparative
analysis with the ML regression result. The results were
found to be in complete agreement with one another.
2 Experimental studies
2.1 Materials
The pure Zn, Cu, and Mg powders employed in this
research were provided by a company based in Türkiye.
The chemical compositions (%wt.) of these powder sam-
ples were determined by XRF analysis and are presented in
Table 1. Furthermore, the powders’ size distributions and
SEM images, along with the equivalent pure Zn, Mg, and
Cu powder size amounts obtained from image processing,
are illustrated in Fig. 1.
2.2 The fabrication of the samples via P/M with
mechanical alloying
The supplier rm provided the grain size of the pure pow-
ders as 120 μm for magnesium, 75 μm for zinc, and 75 μm
for copper. This research synthesized combined MgZn and
MgCu using a rigorous powder metallurgy (P/M) technique,
emphasizing accurate composition and robust microstruc-
tural properties for subsequent tribological analysis. To the
magnesium powders, zinc or copper (0.2%, 0.5%, 1%, and
2% by weight) powders were added in precise quantities
to form two primary alloy series, designated as MgZnX
and MgCuX, respectively. Furthermore, 2% zinc citrate
(C36H70O4Zn) was added as a lubricant to enhance pow-
der dispersion and minimize particle agglomeration during
mechanical alloying. Each powder batch was weighed with
high precision on an electronic balance with an accuracy of
± 0.001 g to ensure accurate addition rates.
The powder mixtures were subjected to mechanical
alloying with SAE 420 tool steel balls (4 mm in diameter)
in a 1:10 weight-to-powder weight ratio. The mechanical
alloying process was conducted by bidirectional rotation
at 200 rpm for 16 h, with 15-minute clockwise and coun-
terclockwise grinding intervals. This approach ensured the
attainment of homogeneous mixtures without excessive
temperature increases or material stress.
Table 1 The chemical composition of the samples
Samples base Materials Element (%wt.)
Mg Zn Si Fe PCu
Mg 99,3934 0,0749 0,2281 0,3036 - -
Cu - - 0,0620 - 0,0860 99,8520
Zn 99,9019 0,0587 0,0265 0,0129
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R. Tekin Ünver et al.
βT = βD + βε (1)
In this context, βT represents the total expansion, βD
denotes the expansion attributable to crystallite size, and βε
signies the expansion resulting from strain. As established
by the Scherrer equation [ ]:
D=Kλ / (βD cosθ)
(2)
βD =Kλ / (D cosθ)
(3)
In this context, βD represents the full width at half maxi-
mum (FWHM) in radians, with K = 0.9 denoting the shape
factor and λ = 0.15406 nm signifying the wavelength of the
X-ray source. D, on the other hand, refers to the crystallite
size, while θ denotes the peak in radians.
Similarly, the XRD peak broadening due to microstrain is
given by the following equation:
βε = 4ε tanθ (4)
In this context, β is the expansion due to strain, ε is the
strain, and θ is the peak in radians. By applying (Eq. 3) and
(Eq. 4) to (Eq. 1), we obtain the following equation:
βT = (Kλ / D cosθ) + 4ε tanθ (5)
Substituting tanθ = sinθ / cosθ into (Eq. 5), we obtain the
following expression:
βT = (Kλ / D cosθ) + 4ε (sinθ / cosθ) (6)
The equation is then multiplied on both sides by cosθ,
cosθ × βT = Kλ / D + 4ε sinθ (7)
Veya, βT cosθ = ε (4 sinθ) + Kλ / D (8)
2.2.1 P/M pressing, sintering, and density measurements
After mechanical alloying, the powder mixtures were sub-
jected to cold pressing at 500 MPa. Before processing, the
pressing steel molds were coated with a layer of ethanol-
based zinc stearate, which facilitated the removal of the
specimens and maintained their structural integrity. Sub-
sequently, the samples were subjected to sintering in an
argon atmosphere, which kept the purity of the metal and
prevented oxidation. The sintering process was conducted
at 500 °C for two hours to promote diusion bonding, mate-
rial densication, and attaining the desired microstructural
properties.
After the manufacturing process, the densities of the
samples were determined through the utilization of the
Archimedes principle, which enables the assessment of
porosity and the verication of bulk density following the
standards set forth by the ASTM B962. The mean of three
successful density measurements was calculated to obtain
the true density reading.
2.3 The assessment of XRD data (as microstrain,
dislocation density, and cristal size)
In X-ray diraction (XRD) analysis, crystal grain size,
microstrain, and dislocation density were calculated using
the Williamson-Hall (W-H) method and the Scherrer equa-
tion. These methods entail evaluating prole-broadening
data, which is particularly important in nanomaterials. The
W-H plot allows the eect of crystal size and strain to be
decomposed and an accurate analysis to be conducted.
The crystal grain sizes, microstrain, and dislocation den-
sity were calculated from the XRD data using the William-
son-Hall plotting method. The broadening of peaks (βT) in
XRD data can be attributed to the combined eect of crys-
tallite size (βD) and microstrain (βε). Namely
Fig. 1 The schematic represen-
tation of the P/M production
system as it was studied
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The regression analysis of dry - wet wear outcomes and materials properties of biodegradable MgCu and…
2.5 Materials characterization
To gain detailed insights into the microstructure, SEM
coupled with energy-dispersive X-ray spectroscopy (EDS)
was employed to assess the grain size, phase distribution,
and elemental composition. Furthermore, a Vickers hard-
ness test (Qness Q10 A instrument) with a load of 1 kg was
employed to assess the surface hardness in multiple areas of
each sample and to obtain a representative hardness prole.
2.6 Preprocessing of data analysis (ML)
This study employed the Auto Sklearn library to construct
training models that could accurately predict the target
variables: Volume Loss, Coecient of Friction, and Spe-
sic Wear Rate. That was achieved through the utilization
of regression analysis on the data. Auto-Sklearn is an auto-
mated machine learning (AutoML) system capable of auto-
matically selecting optimal data preprocessing methods,
machine learning algorithms, and hyperparameters, aiming
to create high-precision prediction models [39]. Automated
Machine Learning (AutoML) is a rapidly evolving eld
that aims to automate various stages of the machine learn-
ing process, from feature extraction to model design [40].
It encompasses several problem types, including Hyperpa-
rameter Optimization (HPO), Combined Algorithm Search
and Hyperparameter Optimization (CASH), and Machine
Learning Pipeline Creation (MLPC) [41]. AutoML serves
as a bridge between dierent levels of expertise, making
high-performance machine-learning techniques accessible
to a broader audience [42]. The eld has seen signicant
advancements recently, with various methodologies and
frameworks developed to address dierent requirements
[43]. Key components of AutoML systems include the
search space, search strategy, and performance evaluation
[42]. While AutoML oers numerous benets, such as
reducing external assistance and improving model devel-
opment eciency, challenges remain in unifying dierent
approaches and addressing diverse user needs [41]. Auto-
Sklearn, a library based on the Scikit-Learn framework, has
been developed to accelerate and facilitate machine learning
processes. It does this by determining the most appropri-
ate learning model and related hyperparameters. Like other
AutoML libraries, it provides a solution that performs best
by minimizing user intervention [44].
The conguration parameters required for performing
regression analysis with the Auto Sklearn library are illus-
trated in Fig. 2.
Equation (Eq. 6) represents a straight line, where ε is the
slope (slope) of the line and Kλ/D is the y-intercept. The
standard equation of a straight line is given by the follow-
ing: y = mx + c [6]. In this context, “m” represents the slope
of the line, while “c” denotes the y-intercept. A comparison
between equation (Eq. 5) and equation (Eq. 6) reveals that,
y=βT cosθ
(9)
A comparison of Eqs. [5] and [6] reveals the following:
m = ε (ii), x = 4 sinθ (iii), and c = Kλ / D (iv).
y=βT cosθ (i)
(10)
2.4 Dry and wet (in SBF) wear test
Dry and simulated body uid (SBF) environments evalu-
ated tribological performance, mimicking conditions perti-
nent to biomedical applications. A reciprocating tribometer
was employed to conduct wear testing on the specimens
at a constant sliding speed of 42 mm/s over 250 m. The
counter material was an AISI 420 stainless ball, and the
test loads were 5 N, 10 N, and 20 N. The wear tests were
conducted in a 7 mm stroke setup at 3 Hz in both condi-
tions. The test parameters comprised a temperature of 21 °C
with 35% humidity for the dry condition and 37.5 °C at
the same humidity level in SBF. The worn surfaces, wear
scars, debris, and other features were analyzed by scanning
electron microscopy with energy-dispersive spectroscopy
(SEM-EDS). The study yielded signicant insights into the
predominant wear mechanisms, including abrasion, adhe-
sion, and oxidative wear.
A virtual bodily uid with properties resembling those of
blood plasma was created as a simulated body uid (SBF).
The chemicals listed in Table 2. and 900 milliliters of deion-
ized water were used to develop the solution [16, 37, 38].
Table 2 Lists the components of SBF along with their amounts
Reagent-grade
chemicals
Amount Reagent-grade
chemicals
Amount
Distilled Water 8300 ml K2HPO40,231 g
NaCl 0,035 g MgCl2. 6H2O0,311 g
NaHCO30,335 g HCl 39 ml
KCl 0,225 g CaCl20,292 g
K2HPO40,231 g Na2SO40,072 g
Fig. 2 Illustrates the settings
required to install the Auto
Sklearn Library for regression
analysis
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R. Tekin Ünver et al.
automatically evaluated a series of models and selected the
one with the optimal performance.
The preprocessing steps on the data set before the analy-
sis were also conducted using the Auto Sklearn library. The
preprocessing steps for the optimal models developed for
the target variables are presented in Tables 3 and 4 and 5.
The Auto Sklearn model has been developed to solve
regression problems for the data set used in the study. The
ensemble selection structure was selected as the optimal
structure for the model. The objective is to enhance the pre-
dictive performance by employing a combination of models.
The model has been designed to facilitate parallel process-
ing. This approach ensures that all available processor cores
are utilized. The maximum time limit for each model was
set at 60 s to promote more expeditious optimization. To
enhance the model’s overall performance and circumvent
the issue of overlearning, the 10-fold cross-validation
method was selected as the optimal approach for the test
processes. In conclusion, the total time limit for the entire
AutoML process was 600 s. During this period, the system
Table 3 The preprocessing processes for an ensemble model for the volume loss target variable
Model ID Numerical Values
Impute
Scaling Numeric
Values
Text Encoding Text Reduction
Component
Count
Processing Features Regression Model
0 Mean MinMax TF-IDF (word) 8856 Extra Trees Gaussian Process
1 Median Robust Scaler TF-IDF (char) 700 Feature Agglomeration AdaBoost
2 Mean Quantile
Transformer
TF-IDF (char) 100 None Gaussian Process
3 Median None TF-IDF (char) 100 Polynomial (Degree 2) Gradient Boosting
4 Most Frequen None TF-IDF (char) 2 Select Rates (fpr,
f_regression)
Gradient Boosting
5 Mean MinMax TF-IDF (char) 100 Fast ICA (Exp) LibSVM SVR
6 Mean None TF-IDF (char) 1 Feature Agglomeration Gaussian Process
Table 4 The ensemble model, created for the coecient of friction target variable, underwent a series of preprocessing procedures
Model ID Numeric Val-
ues Impute
Numeric Values
Scaling
Text Encoding Text Reduction
Componet Count
Feature Preprocessing Regression Model
0 Mean Robust Scaler TF-IDF (char) 4 None Gradient Boosting
1 Median None TF-IDF (char) 9 None Gradient Boosting
2 Median None TF-IDF (char) 11 None Gradient Boosting
3 Mean MinMax TF-IDF (char) 100 Fast ICA (Exp) LibSVM SVR
4 Mean MinMax TF-IDF (char) 9690 Extra Trees MLP
5 Mean None TF-IDF (char) 69 Feature Agglomeration Gradient Boosting
6 Median MinMax TF-IDF (char) 100 Polynomial (Degree 2) Gaussian Process
7 Mean Standardized TF-IDF (char) 100 Extra Trees Gradient Boosting
Table 5 The ensemble model, created for the specic target variable of the specic wear rate, underwent a series of preprocessing procedures
Model ID Numeric Values
Impute
Numeric Values
Scaling
Text Encoding Text Reduction
Component
Count
Feature Preprocessing Regression Model
0 Mean Robust Scaler TF-IDF (char) 4995 Select Rates (for, f_regression) Gradient Boosting
1 Most Frequent Robust Scaler TF-IDF (char) 10 Select Rates (fpr, f_regression) Gradient Boosting
2 Mean Robust Scaler TF-IDF (char) 100 Feature Agglomeration Extra Trees
3 Most Frequent Robust Scaler TF-IDF (char) 12 Select Rates (fpr, f_regression) Gradient Boosting
4 Mean Quantile
Transformer
TF-IDF (char) 100 None Gaussian Process
5 Most Frequent Robust Scaler TF-IDF (char) 12 Select Rates (fpr, f_regression) Gradient Boosting
6 Most Frequent Robust Scaler TF-IDF (char) 16 Select Rates (fpr, f_regression) Gradient Boosting
7 Mean None TF-IDF (char) 78 Extra Trees AdaBoost
8 Mean Robust Scaler TF-IDF (char) 76 Select Rates (fpr, f_regression) Gradient Boosting
9 Mean Robust Scaler TF-IDF (char) 76 Select Rates (fpr, f_regression) Gradient Boosting
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The regression analysis of dry - wet wear outcomes and materials properties of biodegradable MgCu and…
increases with the addition of Zn, up to a maximum of 6%
[16, 18, 51] The experimental density values of MgZn com-
posites are also close to the theoretical values; however,
precise alignment cannot be attained due to porosity. The
relative density value obtained in the experimental density
of MgZn alloys oscillates between 94% and 99%. Notably,
alloys with 4% Zn content exhibit a homogeneous structure
with elevated density and minimal porosity [17, 52, 53].
The sintering conditions and pressure application inu-
ence the formation and density of the pores. In MgZn alloys
produced by P/M, the sintering temperature and time are
optimized to achieve high-density values [19]. As men-
tioned earlier, the mechanism forms a more compact and
homogeneous structure in Zn alloys, which in turn enhances
their mechanical strength and corrosion resistance [15, 54].
As illustrated in Table 6, the incorporation of Cu and
Zn markedly enhances the hardness values of pure Mg, as
evidenced by the results of the hardness tests (HV1). The
hardness of pure Mg increased by 35.13% to 59.48 HV by
mechanical alloying, whereas it increased by 64.63% with
the addition of 1% Cu, reaching the highest hardness value
(70.11 HV) [19, 55]. However, a slight decrease in hardness
was observed when the Cu content increased to 2%, indicat-
ing that a high Cu content may have a detrimental eect on
the material’s hardness [24, 55].
Incorporating Cu and Zn into magnesium metal as rein-
forcement elements enhances their hardness and, conse-
quently, their strength, rendering them suitable for use in
biomedical applications [23, 56–58]. This improvement in
hardness is linked to the formation of a ne grain structure
resulting from mechanical alloying and powder metallurgy
processes, which in turn contributes to the mechanical sta-
bility of the material.
X-ray diraction (XRD) analyses furnish crucial data
for investigating microstructural alterations in MgCu and
MgZn alloys. Figure 3. illustrates the XRD patterns of
pure Mg and Zn-doped Mg samples. During the mechani-
cal alloying process, the formation of a solid solution in the
Mg-Zn binary system was observed when the Zn content
was increased between 0.2 and 2%. Nevertheless, the for-
mation of equilibrium phases (MgZn) was not observed.
Incorporating Zn atoms into the Mg crystal structure results
in a linear increase in the lattice parameters, which causes
strain in the crystal structure. That is evidenced by a slight
shift of XRD peaks and an increase in density [59, 60].
In MgZn alloys, substituting Zn atoms for Mg atoms
changes the symmetry and density of the crystal lattice,
thereby providing a more homogeneous crystal structure.
As the concentration of Zn doping increases, the degree
of crystallinity rises while the prevalence of microstruc-
tural defects declines. These changes result in an observ-
able shift in the position and intensity of XRD peaks [61].
3 Experimental and ML results and
discussions
3.1 Experimental data based on machine learning
The density of MgCu and MgZn alloys produced by the
P/M method varies according to the quantity of Cu and Zn
incorporated into the alloy.
In MgCu alloys, an increase in the concentration of Cu
results in an elevated theoretical density due to the higher
atomic weight of Cu compared to Mg. To illustrate, the
theoretical density of pure Mg is 1.738 g/cm³, whereas a
MgCu alloy containing 2% Cu exhibits a theoretical den-
sity of 1.8824 g/cm³ [45, 46]. Nevertheless, although the
experimental densities of these alloys produced by the P/M
method are close to the theoretical values, they do not align
precisely. This discrepancy may be attributed to porosity
resulting from the manufacturing process [34, 47]. In meth-
ods such as P/M and casting, the formation of pores is a
common occurrence, which presents a challenge in achiev-
ing full density during sintering [47].
Relative density is the ratio of the experimental density to
the theoretical density, expressed as a percentage. In MgCu
alloys, the relative density is as high as 99.01%, particularly
in the alloy containing 1% Cu. This elevated relative den-
sity suggests that the production quality is superior and that
the alloy exhibits a more compact structure. However, at a
Cu content of 2%, the relative density decreases to 97.73%,
indicating the potential for further pore formation or embrit-
tlement of the material [48]. These pores can adversely
aect the mechanical strength of the material [36]. High-
density values indicate that the oxide layer is broken with
sucient pressure and temperature during sintering and that
metal-to-metal contact is ensured for sintering [18, 49, 50].
In MgZn alloys, an increase in the concentration of Zn
has a corresponding eect on the theoretical density. The
theoretical density obtained by adding Zn indicates that
the MgZn alloy has a denser and more compact structure.
The theoretical density of pure Mg is 1.738 g/cm³, which
Table 6 The value of relative density, hardness, and metallurgical
grain size
Materials Relative Density
(%)
Hardness (HV
1)
Grain
Size
(µm)
Pure Mg 94,93 59.48 42,54239
MgCu0,2 94,98 60.63 26,93097
MgCu0,5 94,39 61.63 25,38713
MgCu1 99,09 72.47 17,63357
MgCu2 97,54 65.31 19,77616
MgZn0,2 97,22 64,29 29,00941
MgZn0,5 99,32 68,19 20,01587
MgZn1 99,33 68,7 11,43308
MgZn2 99,19 70,11 10,56875
1 3
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R. Tekin Ünver et al.
∆
V=
2
3∗
Ww
∗
Wd
∗
S (11)
ΔV represents the volume loss (mm3), Wd is the wear depth
(µm), Ww is the wear width (mm), and S is the sliding dis-
tance (mm). An electronic caliper measured the sliding dis-
tance and wear width. The frictional forces measurement
process is given to the wear evaluation setup via the load
cell. Ff and Fn represent the friction force of the load cells
and the applied normal force to the wear sample, respec-
tively. Finally, the wear tracks’ in-depth characteristics,
microstructure, and chemical composition were evaluated
by SEM elemental analysis. The COF, which is examined
using (Eq. 12) may be aected by structural, topological,
and chemical changes during sliding contact.
µ=
Ff
Fn
(12)
The database data generated and obtained via the systematic
methodology described above and used as the basis for the
ML regressions are presented in Table 8.
3.2 Data analysis
As evidenced by Table 9, 10 and 11, the Auto Sklearn
library employs ensemble modeling techniques to construct
optimal learning models capable of accurately predicting
the three target variables. Ensemble models in machine
learning integrate multiple models to achieve enhanced pre-
diction performance compared to individual models [65].
This approach employs a variety of classiers intending to
reduce individual biases and improve overall accuracy [66].
The key techniques employed include bagging, boosting,
and stacking, which integrate multiple models intending
Furthermore, microstrain, crystallite size, and dislocation
density were determined through XRD analysis. It was
found that Zn doping resulted in a reduction in dislocation
density and an increase in crystal size [62, 63].
Hashemi and Clark [64] observed reduced dislocation
density and microstrain values in MgCu after sintering. The
incorporation of Cu increases the strength of the Mg struc-
ture and provides microstructural relief despite the increase
in hardness. In addition, the results indicate that dislocation
density aects corrosion resistance, with high dislocation
density regions potentially acting as anodes, thereby accel-
erating corrosion.
The X-ray diraction (XRD) assessment of the samples
can be categorized according to the following parameters:
crystallite size (µm), dislocation density (mm/mm³), and
microstrain (mε/mm). These data are presented in Table 7.
The data were subjected to an ML regression analysis with
the independent variables.
During the wear testing, the volüme loss (ΔV) is
assessed as a crucial tribological parameter with the help of
(Eq. 11):12) may be aected by structural, topological, and
chemical changes during sliding contact.
Table 7 XRD assessment of samples group as the value of crystallite
size, dislocation density, microstrain
Materials Crystallite Size
(µm)
Dislocation Density
(mm/mm3)
Microstrain
(mε/mm)
Pure Mg 19,02744 127,21 1,34148
MgCu0,2 22,81504 88,28621 1,01355
MgCu0,5 22,76024 93,61909 1,05046
MgCu1 23,23857 88,67133 1,02343
MgCu2 24,4971 82,7518 0,9399
MgZn0,2 21,07945 112,4036 1,23519
MgZn0,5 16,47282 134,0698 1,50978
MgZn1 21,96371 109,1619 1,15938
MgZn2 18,314 124,2616 1,30691
Fig. 3 Weight and Cost Distribu-
tion of Models for Volume Loss
Target
1 3
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The regression analysis of dry - wet wear outcomes and materials properties of biodegradable MgCu and…
variance and data representation [65]. The superiority of
ensemble methods in terms of prediction accuracy and their
ability to address complex challenges in dierent domains is
supported by experimental evidence [69]. The tables below
illustrate the distribution of the eects of the algorithms
used in the ensemble models created by the Auto Sklearn
to enhance the quality of predictions [65]. The objective of
ensemble methods is to construct capable yet complemen-
tary models whereby errors made by one member can be
rectied by another [67]. The ecacy of ensemble learning
is exemplied by popular algorithms such as AdaBoost and
bagging, demonstrating its eectiveness in various appli-
cations [68]. The ecacy of ensemble learning is contin-
gent upon the models’ diversity, encompassing algorithmic
Table 8 The database data, generated and obtained via the systematic methodology described above, serves as the basis for the ML regressions
Sample Type Wear
Rate
Load Volume
Loss
Fric.
Cof.
Specic
Wear Rate
Sample
Type
Wear
Envirement
Load Volume
Loss
Fric.
Cof.
Spe-
sic
Wear
Rate
Pure Mg Dry 5 N 14,040 0,497 10,900 0,2 Zn Dry 5 N 6,258 0,505 2,393
Dry 10 N 19,580 0,453 9,100 Dry 10 N 4,398 0,438 2,046
Dry 20 N 24,604 0,439 7,300 Dry 20 N 4,403 0,436 1,170
Wet 5 N 7,224 0,378 5,779 We t 5 N 7,224 0,350 5,529
Wet 10 N 10,771 0,257 3,367 We t 10 N 8,416 0,237 3,082
Wet 20 N 13,905 0,230 2,610 We t 20 N 13,048 0,224 2,183
0,2 Cu Dry 5 N 14,457 0,588 10,366 0,5 Zn Dry 5 N 3,841 0,516 2,386
Dry 10 N 19,143 0,490 8,957 Dry 10 N 5,285 0,438 1,882
Dry 20 N 23,268 0,460 6,954 Dry 20 N 6,197 0,436 1,152
Wet 5 N 6,175 0,333 3,340 We t 5 N 6,939 0,304 5,551
Wet 10 N 9,659 0,269 2,056 Wet 10 N 7,553 0,220 3,021
Wet 20 N 13,477 0,263 1,742 We t 20 N 10,040 0,226 2,008
0,5 Cu Dry 5 N 13,467 0,606 9,973 1 Zn Dry 5 N 4,991 0,528 2,315
Dry 10 N 18,294 0,584 8,517 Dry 10 N 5,031 0,436 1,570
Dry 20 N 22,314 0,505 6,663 Dry 20 N 4,041 0,438 1,056
Wet 5 N 5,602 0,337 3,802 We t 5 N 6,293 0,311 5,034
Wet 10 N 9,042 0,291 3,864 Wet 10 N 6,739 0,214 2,695
Wet 20 N 12,756 0,277 2,097 We t 20 N 9,009 0,212 1,802
1 Cu Dry 5 N 8,805 0,714 7,844 2 Zn Dry 5 N 3,542 0,537 1,697
Dry 10 N 16,795 0,682 6,218 Dry 10 N 3,005 0,466 1,451
Dry 20 N 19,144 0,598 5,529 Dry 20 N 6,811 0,465 0,895
Wet 5 N 1,540 0,482 2,115 We t 5 N 5,747 0,291 4,598
Wet 10 N 5,140 0,482 4,308 Wet 10 N 6,270 0,202 2,508
Wet 20 N 8,709 0,401 2,351 Wet 20 N 6,939 0,202 1,388
2 Cu Dry 5 N 10,675 0,699 10,140
Dry 10 N 17,697 0,653 6,979
Dry 20 N 19,991 0,529 5,958
Wet 5 N 2,644 0,475 1,232
Wet 10 N 6,842 0,414 2,337
Wet 20 N 10,485 0,317 2,695
Table 9 Ensemble model for volume loss target
Rank Model
ID
Ensemble
Weight
Model Type Cost Dura-
tion
(s)
1 146 0.02 Gaussian Process 0.038116 06.67
2 31 0.28 Gaussian Process 0.057315 06.86
3 9 0.16 Gradient Boosting 0.059279 60.53
4 66 0.26 AdaBoost 0.061753 11.54
5 23 0.22 Gaussian Process 0.067433 16.76
6 26 0.02 LibSVM SVR 0.111264 11.87
7 58 0.04 Gradient Boosting 0.129408 09.88
Table 10 Ensemble model for coecient of friction target
Rank Model
ID
Ensemble
Weight
Model Type Cost Dura-
tion
(s)
1110 0.30 Gradient Boosting 0.015179 13.16
2115 0.22 Gradient Boosting 0.016215 14.65
3 103 0.06 Gradient Boosting 0.019046 10.88
4 82 0.18 Gradient Boosting 0.023459 14.66
5 26 0.10 LibSVM SVR 0.046663 11.38
6 20 0.02 Gaussian Process 0.048423 56.35
7117 0.10 MLP 0.052416 15.80
8 54 0.02 Gradient Boosting 0.201315 14.98
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R. Tekin Ünver et al.
ratio of 0.30. Furthermore, the model with the identier 110
represents the least expensive learning model within the
ensemble structure, with a cost value of 0.015.
The results are presented in Table 11 and Fig. 5. dem-
onstrate the ensemble model structure’s predictive ecacy
in accurately forecasting the Spresic Ware Rate target
variable. In this structure, an ensemble model comprises
10 dierent learning models, each generated by a machine
learning algorithm. Upon closer examination of the struc-
ture, it becomes evident that while it does not possess the
lowest cost value, model 54 has the most signicant impact
on the result prediction, with a weight ratio of 0.26. It can
also be stated that model 94 ID, with a weight ratio of 0.22,
and model 18 ID, with a weight ratio of 0.20, have a notable
impact on the prediction result.
The results are presented in Table 11 and Fig. 5. dem-
onstrate the ensemble model structure’s predictive ecacy
in accurately forecasting the Spresic Ware Rate target
variable. In this structure, an ensemble model comprises
10 dierent learning models, each generated by a machine
learning algorithm. Upon closer examination of the struc-
ture, it becomes evident that while it does not possess the
lowest cost value, model 54 has the most signicant impact
on the result prediction, with a weight ratio of 0.26. It can
also be stated that model 94 ID, with a weight ratio of 0.22,
and model 18 ID, with a weight ratio of 0.20, have a notable
impact on the prediction result.
A series of metric values must be calculated to elucidate
the performance levels of the ensemble models yielded by
the regression analysis conducted on the data set. These
metrics are as follows:
●Mean Absolute Error (MAE): It is a frequently em-
ployed metric for evaluating the precision of a model,
library for the three target variables in the data set on the
prediction performance of the regression analysis.
As illustrated in Table 9 and Fig. 3., seven distinct train-
ing models were employed to construct the ensemble model
to target the Volum Loss variable. To illustrate, while mod-
els 146, 31, and 23 utilize the identical machine learning
algorithm, they encompass disparate hyperparameter opti-
mizations, thereby engendering divergent results concern-
ing the predictions. An examination of the results in the
table reveals that the model with the identication number
31 exerts the greatest inuence on the prediction perfor-
mance of the ensemble model created for the Volume Loss
variable, with a weight ratio of 0.28.
The Auto Sklearn library was employed to construct dis-
tinct ensemble models for each target variable. Eight dis-
tinct learning models generated through machine learning
algorithms were used in the ensemble model created for
the coecient of friction target variable. As evidenced in
Table 10 and Fig. 4, model 110 demonstrates the most sig-
nicant impact on prediction performance, with a weight
Table 11 Ensemble model for specic ware rate target
Rank Model
ID
Ensemble
Weight
Model Type Cost Dura-
tion
(s)
1 108 0.06 Gradient Boosting 0.047370 26.73
2 89 0.02 Gradient Boosting 0.056276 23.74
3 104 0.02 Gradient Boosting 0.056349 25.51
4 54 0.26 Gradient Boosting 0.063653 12.84
5 102 0.06 Gradient Boosting 0.064307 26.33
6 94 0.22 Gradient Boosting 0.068101 25.89
7 65 0.02 AdaBoost 0.076333 10.24
8 18 0.20 Extra Trees 0.081593 27.67
9 23 0.06 Gaussian Process 0.123272 23.32
10 106 0.08 Gradient Boosting 0.137790 16.75
Fig. 4 Weight and Cost Distribu-
tion of Models for Coecient of
Friction Target
1 3
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The regression analysis of dry - wet wear outcomes and materials properties of biodegradable MgCu and…
ecacy of the estimation process, these values should be as
minimal as possible, approaching zero, thereby indicating
that the model can produce successful estimates. Further-
more, the optimal value for the R2 metric is 1. The closer
the value obtained in the analysis results is to 1, the more
successful the model can make the estimates. The results
of the regression analysis conducted within the scope of
the study, about the three target variables, are presented in
Table 12.
Upon examination of the results presented in Table 12, it
becomes evident that the ensemble learning models devel-
oped through the regression analysis conducted using the
Auto Sklearn library on the dataset can attain the perfor-
mance necessary to produce successful predictions for all
three target variables. Upon examination of the metrics indi-
cating the error rates between the projections and the actual
values, it becomes evident that the models exhibit minimal
discrepancies in their predictions.
The R2 metric values of 0.998 and 0.999 for the targets
demonstrate that the projections are made with high preci-
sion, closely aligning with the actual values. The results
indicate that the constructed learning models are highly
eective in predicting the Volume Loss, Coecient of Frac-
ture, and Specic Wear Rate targets associated with the
materials examined within the scope of the study. Further-
more, the graphs in Figs. 6 and 7, and 8 provide additional
evidence to support this success.
Upon examination of the graphs visualizing the pre-
dictions made by the models, it becomes evident that the
signifying the mean absolute discrepancy between the
projected and actual values [70].
●Mean Squared Error (MSE): A fundamental metric in
statistics and machine learning, dened as the expected
value of the squared dierence between an estimator
and the true parameter [71].
●R Squared Score (R2): It indicates the extent to which
the variance observed in data sets can be attributed to
the explanatory power of learning models. It is frequent-
ly employed as a metric that highly indicates the predic-
tive ecacy of the model in question [72].
●Root Means Squared Error (RMSE): The square root
of the squared dierences between the actual value and
the predicted value is calculated, with the resulting val-
ue being used in a more accurate interpretation of errors
in regression analysis [72].
●Mean Log Square Error (MLSE): It is expressed as
the ratio between the values predicted by the model and
the actual values, which allows for a comparison be-
tween the two [72].
●Median Absolute Error (MEDAE): It is the preferred
unit of measurement for regression analysis in model-
ing forecasts. The median of the absolute errors between
predictions and actual values is employed as the mea-
sure [73].
The metrics mentioned earlier, namely MAE, MSE, RMSE,
MLSE, and MEDAE, demonstrate the discrepancy between
the estimated and actual values. In terms of establishing the
Table 12 Results of regression analysis
Target MAE MSE RMSE MLSE MEDAE R2
Volume Loss 0.216 0.086 0.294 0.001 0.181 0.998
Coecient of Friction 0.003 1.942e-05 0.004 8.754e-06 0.002 0.999
Spesic Ware Rate 0.075 0.010 0.099 0.001 0.060 0.999
Fig. 5 Weight and Cost Distribu-
tion of Models for Specic Wear
Rate Target
1 3
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R. Tekin Ünver et al.
The model demonstrated consistent performance regard-
ing the Volume Loss target and exhibited an excellent capac-
ity to explain the data, with all error metrics exhibiting a low
error and high variance value. Concerning the Coecient
of Friction target, the model exhibited minimal prediction
error and a high degree of success in predicting this target.
Furthermore, the model produced low error rates concern-
ing the Specic Ware Rate target and exhibited a high level
of explained variance. A conclusion may be drawn based on
the data obtained.
After successfully analyzing the model with the provided
data sets, the model was tested with real-time values. Exper-
iments were conducted on the 2Zn sample in a laboratory
setting with a 15 N load in a dry environment to acquire data
not included in the existing dataset. Subsequently, the iden-
tical data characteristics were incorporated into the learning
models generated with the Auto Sklearn library, ensuring
that predictions were made for all three target variables
(Table 13.).
Upon examination of the results presented in Table 10,
it was observed that the 2Zn sample exhibited a deviation
of 0.085 in the results obtained for the Volume Loss tar-
get variable when subjected to 15 N load testing in a dry
environment. A comparison of this deviation with the error
rates provided by the model in its predictions reveals that
the model’s performance is within an acceptable range, with
the predicted value exhibiting a close alignment with the
actual value. A discrepancy of 0.021 was observed in the
Coecient of Friction target variable. Once more, when
predicted outcomes for the three targets in question are
close to the ideal line. Consequently, the graphs corroborate
the data presented in the table to a considerable extent.
The results of the analysis allow us to make the following
observations regarding the learning models that have been
created:
Fig. 8 Distribution of Real and Predicted Values for Specic Ware
Rate Target
Fig. 7 Distribution of Real and Predicted Values for Coecient of
Friction Target
Fig. 6 Distribution of Real and Predicted Values for Volume Loss
Target
1 3
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The regression analysis of dry - wet wear outcomes and materials properties of biodegradable MgCu and…
with Ensemble Models created using Auto Sklearn. Espe-
cially the extremely low error values and R² value of 0.9990
for the Friction Coecient estimation demonstrate the
accuracy and power of our model. Similarly, the R² value
(0.9980) and low error metrics obtained for the Volume
Loss estimation show that the model also provides high per-
formance for this target variable.
In light of the results obtained, it can be said that the use
of Automatic Machine Learning (AutoML) libraries such as
Auto Sklearn in machine learning regression applications
applied to estimate the physical change rates revealed by
the tests performed on material samples enables the creation
of learning models that have much lower error rates and can
explain the real values at a much better level.
3.3 Sensitivity analysis of ML models
Sensitivity Analysis is a method to understand how changes
in a learning model’s input values aect the output value. It
aims to reveal which input values have the greatest eect on
the result. These results are an important process to clarify
the reliability and robustness of the predictions made by the
model on the data set. This analysis is a preferred method
for researchers to understand which independent variables
are the most critical to the model’s predictive ability and
which variables do not signicantly aect the result when
changed [74–76].
To further determine the eect of input attributes on the
prediction results of the regression models we created with
Auto-Sklearn, we applied Shapley Additive Explanations
(SHAP) and Global Sensitivity Analysis (GSA) using the
Sobol method. SHAP is a method to interpret the predic-
tion performances of learning models created with machine
learning algorithms by assigning a signicance value to
each input attribute [77]. GSA uses a broad approach that
makes many examples to understand the eect of input attri-
butes on the predicted output value across the entire param-
eter space [74].
the deviation rates obtained from the model’s error metrics
are considered, it becomes evident that the deviation value
for this data is somewhat elevated. Nevertheless, given that
the model typically exhibits minimal error, this discrepancy
can be regarded as acceptable. The deviation value obtained
for the specic ware rate target variable was 0.034. Upon
examination of the error metrics determined by the model
for the relevant target, it can be stated that predictions are
created that are near the actual values and that the deviation
amount is within an acceptable range in model performance.
The comparison of this study with results from similar
literature is given in Table 14. According to Table 14, the
best results obtained in the studies on estimating Volume
Loss and Coecient of Friction ratios on magnesium-based
samples prepared by Pasha et al. and Aydın et al. [27] using
machine learning methods and the results obtained in this
study are given in Table X.
Firstly, in the study of Pasha et al. [26], the R² value for
Wear Rate estimation using the Random Forest model was
reported as 0.9679. However, the MAE, MSE, and RMSE
values obtained in the same study show higher error rates
than those obtained for Specic Wear Rate estimation using
the Auto Sklearn library in our research. This situation
reveals that the model used in our study provides higher
accuracy. In addition, while the R² value for Coecient of
Friction estimation with Articial Neural Networks was cal-
culated as 0.9108 in the study [26], the R² value obtained
for the same target variable in our research is 0.9990. That
shows that the model in our study is much more successful
than previous studies.
In the study Aydın et al. [27], the Decision Tree model
was used to estimate the Wear Rate, and the R² value was
reported as 0.8580. However, the MAE, MSE, and RMSE
values obtained in this study are quite high compared to the
error metrics of the models in our research. That proves that
the model in our study provides high accuracy with lower
error rates compared to the methods used in other studies.
Compared to other studies, our study has achieved very
low error rates and high R² values for all target variables
Table 13 Real-Time data test results
Sample Environment Load Value Volume Loss Coecient of Friction Specic Ware Rate
2Zn Dry 15 N Real 4.4726 0.4409 1.3439
Predicted 4.5578 0.4622 1.3781
Table 14 Comparison of results with other similar studies
The compared Studies Analyse Type Model MAE MSE RMSE R2
[26], That ref. ‘s result Wear Rate Random Forest 0.0775 0.0101 0.1003 0.9679
Coecient of Friction Articial Neural Network 0.0192 0.0005 0.0238 0.9108
[27], That ref. ‘s result Wear Rate Decision Tree 0.2691 0.1332 0.3447 0.8580
This Study’s results Volume Loss Ensemble Model 0.216 0.086 0.294 0.9980
Coecient of Friction Ensemble Model 0.003 1.942e-05 0.004 0.9990
Specic Wear Rate Ensemble Model 0.075 0.010 0.099 0.9990
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R. Tekin Ünver et al.
and ST = 0.004 of the strain variable especially suggests that
this variable does not signicantly aect the model output.
According to SHAP analysis (Fig. 10.), the variables that
aect the model output the most are Environment, Load(N),
and Grain Size, respectively. In terms of mean SHAP value
(mean|SHAP value|), the Environment variable has the high-
est eect and contributes signicantly to model estimates.
SHAP summary graph shows in detail how variables aect
model output. It is observed that variables with high values
especially have signicant eects on increasing or decreas-
ing estimates. For example, it is seen that high values of
Grain Size and Load(N) variables are generally associated
with higher Volume Loss estimates.
3.3.1 Results of sensitivity analysis for volume loss target
According to the Sobol sensitivity analysis results (Fig. 9.),
Grain Size and Dislocation variables have the highest sensi-
tivity indices and have a signicant eect on determining the
model output. First-order sensitivity (S1) values show that
the Grain Size variable is 0.249 and the Dislocation vari-
able is 0.214. Total-order sensitivity (ST) values are 0.327
and 0.341, respectively, indicating that these variables have
very strong direct and indirect eects on model estimates.
On the other hand, the very low sensitivity indices of strain
and material type variables indicate that they are relatively
less eective in model estimates. The fact that S1 = 0.007
Fig. 10 SHAP summary plot
illustrating the contribution of
input features to the model’s pre-
dictions for Volume Loss Target
Fig. 9 Sobol sensitivity indices
showing the impact of dierent
variables on model outputs for
Volume Loss Target
1 3
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The regression analysis of dry - wet wear outcomes and materials properties of biodegradable MgCu and…
SHAP and GSA analyses. Although the eect of other vari-
ables is lower, the combination of material properties and
environmental factors plays an important role in estimating
the coecient of friction.
3.3.3 Results of sensitivity analysis for specic wear rate
target
According to the Sobol sensitivity analysis results (Fig. 13.),
Hardness and Environment variables have the highest sensi-
tivity indices and have a signicant eect on determining the
model output. First-order sensitivity (S1) values show that
the Hardness variable is 0.343 and the Environment vari-
able is 0.079. Total-order sensitivity (ST) values are 0.545
and 0.378, respectively, indicating that these variables have
very strong direct and indirect eects on model estimates.
Although the First-Order Sensitivity value seems relatively
low when the Environment is not, the high Total-Order Sen-
sitivity value signicantly aects the estimation result. On
the other hand, the very low sensitivity indices of grain size
and material type variables indicate that they are relatively
less eective in model estimates. This suggests that the rel-
evant variables do not signicantly aect the model output.
According to the SHAP analysis of the Specic Wear
Rate variable (Fig. 14.), the variables that aect the model
output the most are Environment, Load(N), Hardness, and
Intensity. Regarding the average SHAP value, the Environ-
ment variable has the highest eect on the Specic Wear
Rate variable and contributes greatly to the model estimates.
The results of the sensitivity analyses using SHAP and
GSA methods are largely consistent, Sensitivity analysis
shows that Load(M), Environment, Hardness, and Intensity
are the most important factors in estimating the Specic
Wear Rate variable. These variables greatly impact SHAP
The ndings obtained with two dierent sensitivity
analysis methods are largely consistent. Grain Size and
Load(N) variables are critical for the model in both meth-
ods. However, while SHAP analysis emphasizes the direct
eect of variables on the estimation process of the model,
Sobol analysis provides a comprehensive sensitivity assess-
ment by also taking into account the interactions between
variables.
3.3.2 Results of sensitivity analysis for coecient of
friction target
According to the Sobol sensitivity analysis results (Fig. 11.),
Crystal Grain Size and Hardness variables have the highest
sensitivity indices and have a signicant eect on determin-
ing the model output. First-order sensitivity (S1) values
show that the Crystal Grain Size variable is 0.333 and the
Hardness variable is 0.273. Total-order sensitivity (ST) val-
ues are 0.352 and 0.295, respectively, indicating that these
variables have very strong direct and indirect eects on
model estimates. On the other hand, the very low sensitiv-
ity indices of grain size and material type variables indicate
that they are relatively less eective in model estimates.
This suggests that the relevant variables do not signicantly
aect the model output.
According to SHAP analysis (Fig. 12.), the variables
most aecting the model output are Environment, Load(N),
and Crystal Grain Size. Regarding the mean SHAP value,
the environmental variable has the highest impact and con-
tributes greatly to the model predictions.
Sensitivity analyses show that Hardness, Load(N), Envi-
ronment, and Crystal Grain Size variables are the most
important factors in estimating the Coecient of Friction
variable. These variables have high impact values in both
Fig. 11 Sobol sensitivity indices
showing the impact of dierent
variables on model outputs for
the Coecient of Friction Target
1 3
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R. Tekin Ünver et al.
4 Conclusions
●The high R² values (0.998–0.999) obtained for all target
variables in the models produced within the scope of the
study demonstrate that the model can eectively explain
the variations in the target variables and is, in general,
successful.
●Additionally, the error rates exhibited by the models
were notably low, indicating that the models can make
highly accurate predictions.
●In the real-time wear test data (15 N load in a dry en-
vironment for the 2Zn sample) conducted for compari-
son with the model, the predictions for volume loss and
and GSA analyses and signicantly aect the model output.
Although the contribution of other variables is relatively
lower, the interaction of material properties and environ-
mental factors is critical in accurately estimating the wear
rate.
highlighting Load(N), Environment, Hardness, and Grain
Size as key factors across dierent target variables. While
SHAP analysis emphasizes the direct inuence of these
variables on model predictions, Sobol analysis provides a
broader perspective by accounting for variable interactions.
Additionally, the interplay between material properties and
environmental factors emerges as a crucial element in accu-
rately estimating model outputs.
Fig. 13 Sobol sensitivity indices
showing the impact of dierent
variables on model outputs for
Specic Wear Rate Target
Fig. 12 SHAP summary plot
illustrating the contribution of
input features to the model’s
predictions for the Coecient of
Friction Target
1 3
311 Page 16 of 19
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The regression analysis of dry - wet wear outcomes and materials properties of biodegradable MgCu and…
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Author contributions Rukiye Tekin: conception, experimental design,
and application, carrying out measurements, writing the article. Cihan
Bayraktar: Machine Learning application and discussions, manuscript
composition, writing the article. Bilge Demir: Conception, experimen-
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