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Manufacturers have faced an increasing need for the development of predictive models that predict mechanical failures and the remaining useful life (RUL) of manufacturing systems or components. Classical model-based or physics-based prognostics often require an in-depth physical understanding of the system of interest to develop closed-form mathematical models. However, prior knowledge of system behavior is not always available, especially for complex manufacturing systems and processes. To complement model-based prognostics, data-driven methods have been increasingly applied to machinery prognostics and maintenance management, transforming legacy manufacturing systems into smart manufacturing systems with artificial intelligence. While previous research has demonstrated the effectiveness of data-driven methods, most of these prognostic methods are based on classical machine learning techniques, such as artificial neural networks (ANNs) and support vector regression (SVR). With the rapid advancement in artificial intelligence, various machine learning algorithms have been developed and widely applied in many engineering fields. The objective of this research is to introduce a random forests (RFs)-based prognostic method for tool wear prediction as well as compare the performance of RFs with feed-forward back propagation (FFBP) ANNs and SVR. Specifically, the performance of FFBP ANNs, SVR, and RFs are compared using an experimental data collected from 315 milling tests. Experimental results have shown that RFs can generate more accurate predictions than FFBP ANNs with a single hidden layer and SVR.
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Dazhong Wu
1
Department of Industrial and
Manufacturing Engineering,
National Science Foundation
Center for e-Design,
Pennsylvania State University,
University Park, PA 16802
e-mail: dxw279@psu.edu
Connor Jennings
Department of Industrial and
Manufacturing Engineering,
National Science Foundation
Center for e-Design,
Pennsylvania State University,
University Park, PA 16802
e-mail: connor@psu.edu
Janis Terpenny
Department of Industrial and
Manufacturing Engineering,
National Science Foundation
Center for e-Design,
Pennsylvania State University,
University Park, PA 16802
e-mail: jpt5311@psu.edu
Robert X. Gao
Department of Mechanical and
Aerospace Engineering,
Case Western Reserve University,
Cleveland, OH 44106
e-mail: robert.gao@case.edu
Soundar Kumara
Department of Industrial and
Manufacturing Engineering,
Pennsylvania State University,
University Park, PA 16802
e-mail: skumara@psu.edu
A Comparative Study on
Machine Learning Algorithms
for Smart Manufacturing: Tool
Wear Prediction Using
Random Forests
Manufacturers have faced an increasing need for the development of predictive models
that predict mechanical failures and the remaining useful life (RUL) of manufacturing
systems or components. Classical model-based or physics-based prognostics often
require an in-depth physical understanding of the system of interest to develop closed-
form mathematical models. However, prior knowledge of system behavior is not always
available, especially for complex manufacturing systems and processes. To complement
model-based prognostics, data-driven methods have been increasingly applied to machin-
ery prognostics and maintenance management, transforming legacy manufacturing sys-
tems into smart manufacturing systems with artificial intelligence. While previous
research has demonstrated the effectiveness of data-driven methods, most of these prog-
nostic methods are based on classical machine learning techniques, such as artificial
neural networks (ANNs) and support vector regression (SVR). With the rapid advance-
ment in artificial intelligence, various machine learning algorithms have been developed
and widely applied in many engineering fields. The objective of this research is to intro-
duce a random forests (RFs)-based prognostic method for tool wear prediction as well as
compare the performance of RFs with feed-forward back propagation (FFBP) ANNs and
SVR. Specifically, the performance of FFBP ANNs, SVR, and RFs are compared using an
experimental data collected from 315 milling tests. Experimental results have shown that
RFs can generate more accurate predictions than FFBP ANNs with a single hidden layer
and SVR. [DOI: 10.1115/1.4036350]
Keywords: tool wear prediction, predictive modeling, machine learning, random forests
(RFs), support vector machines (SVMs), artificial neural networks (ANNs), prognostics
and health management (PHM)
1 Introduction
Smart manufacturing aims to integrate big data, advanced ana-
lytics, high-performance computing, and Industrial Internet of
Things (IIoT) into traditional manufacturing systems and proc-
esses to create highly customizable products with higher quality at
lower costs. As opposed to traditional factories, a smart factory
utilizes interoperable information and communications technolo-
gies (ICT), intelligent automation systems, and sensor networks to
monitor machinery conditions, diagnose the root cause of failures,
and predict the remaining useful life (RUL) of mechanical sys-
tems or components. For example, almost all engineering systems
(e.g., aerospace systems, nuclear power plants, and machine tools)
are subject to mechanical failures resulting from deterioration
with usage and age or abnormal operating conditions [13].
Some of the typical failure modes include excessive load, over-
heating, deflection, fracture, fatigue, corrosion, and wear. The
degradation and failures of engineering systems or components
will often incur higher costs and lower productivity due to unex-
pected machine downtime. In order to increase manufacturing
productivity while reducing maintenance costs, it is crucial to
develop and implement an intelligent maintenance strategy that
allows manufacturers to determine the condition of in-service sys-
tems in order to predict when maintenance should be performed.
Conventional maintenance strategies include reactive, preven-
tive, and proactive maintenance [46]. The most basic approach
to maintenance is reactive, also known as run-to-failure mainte-
nance planning. In the reactive maintenance strategy, assets are
deliberately allowed to operate until failures actually occur. The
assets are maintained on an as-needed basis. One of the disadvan-
tages of reactive maintenance is that it is difficult to anticipate the
maintenance resources (e.g., manpower, tools, and replacement
parts) that will be required for repairs. Preventive maintenance is
often referred to as use-based maintenance. In preventive mainte-
nance, maintenance activities are performed after a specified
period of time or amount of use based on the estimated probability
that the systems or components will fail in the specified time inter-
val. Although preventive maintenance allows for more consistent
and predictable maintenance schedules, more maintenance activ-
ities are needed as opposed to reactive maintenance. To improve
1
Corresponding author.
Manuscript received October 25, 2016; final manuscript received March 13,
2017; published online April 18, 2017. Assoc. Editor: Laine Mears.
Journal of Manufacturing Science and Engineering JULY 2017, Vol. 139 / 071018-1
Copyright V
C2017 by ASME
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the efficiency and effectiveness of preventive maintenance, pre-
dictive maintenance is an alternative strategy in which mainte-
nance actions are scheduled based on equipment performance or
conditions instead of time. The objective of proactive mainte-
nance is to determine the condition of in-service equipment and
ultimately to predict the time at which a system or a component
will no longer meet desired functional requirements.
The discipline that predicts health condition and remaining use-
ful life (RUL) based on previous and current operating conditions
is often referred to as prognostics and health management (PHM).
Prognostic approaches fall into two categories: model-based and
data-driven prognostics [712]. Model-based prognostics refer to
approaches based on mathematical models of system behavior
derived from physical laws or probability distribution. For exam-
ple, model-based prognostics include methods based on Wiener
and Gamma processes [13], hidden Markov models (HMMs) [14],
Kalman filters [15,16], and particle filters [1720]. One of the
limitations of model-based prognostics is that an in-depth under-
standing of the underlying physical processes that lead to system
failures is required. Another limitation is that it is assumed that
underlying processes follow certain probability distributions, such
as gamma or normal distributions. While probability density func-
tions enable uncertainty quantification, distributional assumptions
may not hold true in practice.
To complement model-based prognostics, data-driven prognos-
tics refer to approaches that build predictive models using learn-
ing algorithms and large volumes of training data. For example,
classical data-driven prognostics are based on autoregressive
(AR) models, multivariate adaptive regression, fuzzy set theory,
ANNs, and SVR. The unique benefit of data-driven methods is
that an in-depth understanding of system physical behaviors is not
a prerequisite. In addition, data-driven methods do not assume
any underlying probability distributions which may not be practi-
cal for real-world applications. While ANNs and SVR have been
applied in the area of data-driven prognostics, little research has
been conducted to evaluate the performance of other machine
learning algorithms [21]. Because RFs have the potential to han-
dle a large number of input variables without variable selection
and they do not overfit [2224], we investigate the ability of RFs
for the prediction of tool wear using an experimental dataset.
Further, the performance of RFs is compared with that of FFBP
ANNs and SVR using accuracy and training time.
The main contributions of this paper include the followings:
Tool wear in milling operations is predicted using RFs along
with cutting force, vibration, and acoustic emission (AE) sig-
nals. Experimental results have shown that the predictive
model trained by RFs is very accurate. The mean squared
error (MSE) on the test tool wear data is up to 7.67. The
coefficient of determination (R
2
) on the test tool wear data is
up to 0.992. To the best of our knowledge, the random forest
algorithm is applied to predict tool wear for the first time.
The performances of ANNs, support vector machines
(SVMs), and RFs are compared using an experimental data-
set with respect to the accuracy of regression (e.g., MSE and
R
2
) and training time. While the training time for RFs is lon-
ger than that of ANNs and SVMs, the predictive model built
by RFs is the most accurate for the application example.
The remainder of the paper is organized as follows: Section 2
reviews the related literature on data-driven methods for tool wear pre-
diction. Section 3presents the methodology for tool wear prediction
using ANNs, SVMs, and RFs. Section 4presents an experimental
setup and the experimental dataset acquired from different types of
sensors (e.g., cutting force sensor, vibration sensor, acoustic emis-
sion sensor) on a computer numerical control (CNC) milling
machine. Section 5presents experimental results, demonstrates the
effectiveness of the three machine learning algorithms, and com-
pares the performance of each. Section 6provides conclusions that
include a discussion of research contribution and future work.
2 Data-Driven Methods for Tool Wear Prediction
Tool wear is the most commonly observed and unavoidable
phenomenon in manufacturing processes, such as drilling, milling,
and turning [2527]. The rate of tool wear is typically affected by
process parameters (e.g., cutting speed and feed rate), cutting tool
geometry, and properties of workpiece and tool materials. Tay-
lor’s equation for tool life expectancy [28] provides an approxi-
mation of tool wear. However, with the rapid advancement of
sensing technology and increasing number of sensors equipped on
modern CNC machines, it is possible to predict tool wear more
accurately using various measurement data. This section presents
a review of data-driven methods for tool wear prediction.
Schwabacher and Goebel [29] conducted a review of data-
driven methods for prognostics. The most popular data-driven
approaches to prognostics include ANNs, decision trees, and
SVMs in the context of systems health management. ANNs are a
family of computational models based on biological neural net-
works which are used to estimate complex relationships between
inputs and outputs. Bukkapatnam et al. [3032] developed effec-
tive tool wear monitoring techniques using ANNs based on fea-
tures extracted from the principles of nonlinear dynamics.
Ozel
and Karpat [33] presented a predictive modeling approach for sur-
face roughness and tool wear for hard turning processes using
ANNs. The inputs of the ANN model include workpiece hardness,
cutting speed, feed rate, axial cutting length, and mean values of
three force components. Experimental results have shown that the
model trained by ANNs provides accurate predictions of surface
roughness and tool flank wear. Palanisamy et al. [34] developed a
predictive model for predicting tool flank wear in end milling
operations using feed-forward back propagation (FFBP) ANNs.
Experimental results have shown that the predictive model based
on ANNs can make accurate predictions of tool flank wear using
cutting speeds, feed rates, and depth of cut. Sanjay et al. [35]
developed a model for predicting tool flank wear in drilling using
ANNs. The feed rates, spindle speeds, torques, machining times,
and thrust forces are used to train the ANN model. The experi-
mental results have demonstrated that ANNs can predict tool wear
accurately. Chungchoo and Saini [36] developed an online fuzzy
neural network (FNN) algorithm that estimates the average width
of flank wear and maximum depth of crater wear. A modified
least-square backpropagation neural network was built to estimate
flank and crater wear based on cutting force and acoustic emission
signals. Chen and Chen [37] developed an in-process tool wear
prediction system using ANNs for milling operations. A total of
100 experimental data were used for training the ANN model.
The input variables include feed rate, depth of cut, and average
peak cutting forces. The ANN model can predict tool wear with
an error of 0.037 mm on average. Paul and Varadarajan [38] intro-
duced a multisensor fusion model to predict tool wear in turning
processes using ANNs. A regression model and an ANN were
developed to fuse the cutting force, cutting temperature, and
vibration signals. Experimental results showed that the coefficient
of determination was 0.956 for the regression model trained by
the ANN. Karayel [39] presented a neural network approach
for the prediction of surface roughness in turning operations. A
feed-forward back-propagation multilayer neural network was
developed to train a predictive model using the data collected
from 49 cutting tests. Experimental results showed that the predic-
tive model has an average absolute error of 2.29%.
Cho et al. [40] developed an intelligent tool breakage detection
system with the SVM algorithm by monitoring cutting forces and
power consumption in end milling processes. Linear and polyno-
mial kernel functions were applied in the SVM algorithm. It has
been demonstrated that the predictive model built by SVMs can
recognize process abnormalities in milling. Benkedjouh et al. [41]
presented a method for tool wear assessment and remaining useful
life prediction using SVMs. The features were extracted from
cutting force, vibration, and acoustic emission signals. The experi-
mental results have shown that SVMs can be used to estimate the
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wear progression and predict RUL of cutting tools effectively. Shi
and Gindy [42] introduced a predictive modeling method by com-
bining least squares SVMs and principal component analysis
(PCA). PCA was used to extract statistical features from multiple
sensor signals acquired from broaching processes. Experimental
results showed that the predictive model trained by SVMs was
effective to predict tool wear using the features extracted by PCA.
Another data-driven method for prognostics is based on deci-
sion trees. Decision trees are a nonparametric supervised learning
method used for classification and regression. The goal of deci-
sion tree learning is to create a model that predicts the value of a
target variable by learning decision rules inferred from data fea-
tures. A decision tree is a flowchart-like structure in which each
internal node denotes a test on an attribute, each branch represents
the outcome of a test, and each leaf node holds a class label. Jiaa
and Dornfeld [43] proposed a decision tree-based method for the
prediction of tool flank wear in a turning operation using acoustic
emission and cutting force signals. The features characterizing the
AE root-mean-square and cutting force signals were extracted from
both time and frequency domains. The decision tree approach was
demonstrated to be able to make reliable inferences and decisions
on tool wear classification. Elangovan et al. [44] developed a deci-
sion tree-based algorithm for tool wear prediction using vibration
signals. Ten-fold cross-validation was used to evaluate the accuracy
of the predictive model created by the decision tree algorithm. The
maximum classification accuracy was 87.5%. Arisoy and
Ozel [45]
investigated the effects of machining parameters on surface micro-
hardness and microstructure such as grain size and fractions using a
random forests-based predictive modeling method along with
finite element simulations. Predicted microhardness profiles and
grain sizes were used to understand the effects of cutting speed,
tool coating, and edge radius on the surface integrity.
In summary, the related work presented in this section builds
on previous research to explore how the conditions of tool wear
can be monitored as well as how tool wear can be predicted using
predictive modeling. While earlier work focused on prediction of
tool wear using ANNs, SVMs, and decision trees, this paper
explores the potential of a new method, random forests, for tool
wear prediction. Further, the performance of RFs is compared
with that of ANNs and SVMs. Because RFs are an extension of
decision trees, the performance of RFs is not compared with that
of decision trees.
3 Methodology
This section presents the methodology for data-driven prognos-
tics for tool wear prediction using ANNs, SVR, and RFs. The
input of ANNs, SVR, and RFs is the following labeled training
data:
D¼ðxi;yiÞ
where xi¼ðFX;FY;FZ;VX;VY;VZ;AEÞ,yi2R. The description
of these input data can be found in Table 1.
3.1 Tool Wear Prediction Using ANNs. ANNs are a family
of models inspired by biological neural networks. An ANN is
defined by three types of parameters: (1) the interconnection pat-
tern between different layers of neurons, (2) the learning process
for updating the weights of the interconnections, and (3) the acti-
vation function that converts a neuron’s weighted input to its out-
put activation. Among many types of ANNs, the feed-forward
neural network is the first and the most popular ANN. Back-
propagation is a learning algorithm for training ANNs in conjunc-
tion with an optimization method such as gradient descent.
Figure 1illustrates the architecture of the FFBP ANN with a
single hidden layer. In this research, the ANN has three layers,
including input layer i, hidden layer j, and output layer k. Each
layer consists of one or more neurons or units, represented by
the circles. The flow of information is represented by the lines
between the units. The first layer has input neurons which act as
buffers for distributing the extracted features (i.e., Fi) from the
input data (i.e., xi). The number of the neurons in the input layer
is the same as that of extracted features from input variables.
Each value from the input layer is duplicated and sent to all
neurons in the hidden layer. The hidden layer is used to process
and connect the information from the input layer to the output
layer in a forward direction. Specifically, these values entering a
neuron in the hidden layer are multiplied by weights wij . Initial
weights are randomly selected between 0 and 1. A neuron in the
hidden layer sums up the weighted inputs and generates a single
output. This value is the input of an activation function (sigmoid
function) in the hidden layer fhthat converts the weighted input
to the output of the neuron. Similarly, the outputs of all the neu-
rons in the hidden layer are multiplied by weights wjk . A neural
in the output layer sums up the weighted inputs and generates a
single value. An activation function in the output layer focon-
verts the weighted input to the predicted output ykof the ANN,
which is the predicted flank wear VB. The output layer has only
one neuron because there is only one response variable. The per-
formance of ANNs depends on the topology or architecture of
ANNs (i.e., the number of layers) and the number of neurons in
each layer. However, there are no standard or well-accepted
methods or rules for determining the number of hidden layers
and neurons in each hidden layer. In this research, the single-
hidden-layer ANNs with 2, 4, 8, 16, and 32 neurons in the hid-
den layer are selected. The termination criterion of the training
algorithm is that training stops if the fit criterion (i.e., least
squares) falls below 1.0 10
4
.
Table 1 Signal channel and data description
Signal channel Data description
Channel 1 FX: force (N) in Xdimension
Channel 2 FY:force (N) in Ydimension
Channel 3 FZ: force (N) in Zdimension
Channel 4 VX: vibration (g) in Xdimension
Channel 5 VY: vibration (g) in Ydimension
Channel 6 VZ: vibration (g) in Zdimension
Channel 7 AE: acoustic emission (V)
Fig. 1 Tool wear prediction using a feed-forward back-
propagation (FFBP) ANN
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3.2 Tool Wear Prediction Using SVR. The original SVM
for regression was developed by Vapnik and coworkers [46,47]. A
SVM constructs a hyperplane or set of hyperplanes in a high- or
infinite-dimensional space, which can be used for classification
and regression.
The framework of SVR for linear cases is illustrated in Fig. 2.
Formally, SVR can be formulated as a convex optimization
problem
Minimize 1
2kxk2þCX
i¼1
niþn
i

Subject to
yihx;xiibeþni
hx;xibyieþn
i
ni;n
i0
8
>
<
>
:
(3.1)
where x2v;C¼1, e¼0:1, and ni;n
i¼0:001. bcan be com-
puted as follows:
b¼yihx;xiiefor ai0;C
b¼yihx;xiefor a
i0;C(3.2)
For nonlinear SVR, the training patterns xican be preprocessed
by a nonlinear kernel function kðx;x0Þ:¼hUðxÞ;UðxÞi0, where
UðxÞis a transformation that maps xto a high-dimensional space.
These kernel functions need to satisfy the Mercer’s theorem.
Many kernels have been developed for various applications. The
most popular kernels include polynomial, Gaussian radial basis
function (RBF), and sigmoid. In many applications, a nonlinear
kernel function provides better accuracy. According to the litera-
ture [32,33], the Gaussian RBF kernel is one of the most effective
kernel functions used in tool wear prediction. In this research, the
Gaussian RBF kernel is used to transform the input dataset
D¼ðxi;yiÞ, where xiis the input vector and yiis the response
variable (i.e., flank wear) into a new dataset in a high-dimensional
space. The new dataset is linearly separable by a hyperplane in a
higher-dimensional Euclidean space as illustrated in Fig. 2. The
slack variables niand n
iare introduced in the instances where the
constraints are infeasible. The slack variables denote the deviation
from predicted values with the error of e¼0:1. The RBF kernel is
kðxi;xjÞ¼exp ðððkxixjk2Þ=2r2ÞÞ, where r2¼0:5. At the
optimal solution, we obtain
x¼X
i¼1
ðaia
iÞUðxÞand fðxÞ¼X
i¼1
ðaia
iÞkðxi;xjÞþb
(3.3)
3.3 Tool Wear Prediction Using RFs. The random forest
algorithm, developed by Breiman [22,48], is an ensemble learning
method that constructs a forest of decision trees from bootstrap
samples of a training dataset. Each decision tree produces a
response, given a set of predictor values. In a decision tree, each
internal node represents a test on an attribute, each branch repre-
sents the outcome of the test, and each leaf node represents a class
label for classification or a response for regression. A decision
tree in which the response is continuous is also referred to as a
regression tree. In the context of tool wear prediction, each indi-
vidual decision tree in a random forest is a regression tree because
tool wear describes the gradual failure of cutting tools. A compre-
hensive tutorial on RFs can be found in Refs. [22,48,49]. Some of
the important concepts related to RFs, including bootstrap aggre-
gating or bagging, slipping, and stopping criterion, are introduced
in Secs. 3.3.13.3.4.
3.3.1 Bootstrap Aggregating or Bagging. Given a training
dataset D¼fðx1;y1Þ;ðx2;y2Þ;;ðxN;yNÞg, bootstrap aggregating
or bagging generates Bnew training datasets Diof size Nby sam-
pling from the original training dataset Dwith replacement. Diis
referred to as a bootstrap sample. By sampling with replacement
or bootstrapping, some observations may be repeated in each Di.
Bagging helps reduce variance and avoid overfitting. The number
of regression trees Bis a parameter specified by users. Typically,
a few hundred to several thousand trees are used in the random
forest algorithm.
3.3.2 Choosing Variables to Split On. For each of the boot-
strap samples, grow an un-pruned regression tree with the follow-
ing procedure: At each node, randomly sample mvariables and
choose the best split among those variables rather than choosing
the best split among all predictors. This process is sometimes
called “feature bagging.” The reason why a random subset of the
predictors or features is selected is because the correlation of the
trees in an ordinary bootstrap sample can be reduced. For regres-
sion, the default m¼p=3.
3.3.3 Splitting Criterion. Suppose that a partition is divided
into Mregions R1,R2,…, Rm. The response is modeled as a con-
stant cmin each region
fðxÞ¼X
M
m¼1
cmIðxRmÞ(3.4)
The splitting criterion at each node is to minimize the sum of
squares. Therefore, the best c
cmis the average of yiin region Rm
c
cm¼aveðyijxiRmÞ(3.5)
Consider a splitting variable jand split point s, and define the
pair of half-planes
R1ðj;sÞ¼fXjXjsgand R2ðj;sÞ¼fXjXjsg(3.6)
The splitting variable jand split point sshould satisfy
min
j;smin
c1X
xi2R1ðj;sÞ
ðyic1Þ2þmin
c2X
xi2R2ðj;sÞ
ðyic2Þ2

(3.7)
For any jand s, the inner minimization is solved by
b
c1¼aveðyijxiR1ðj;sÞÞ and b
c2¼aveðyijxiR2ðj;sÞÞ (3.8)
Having found the best split, the dataset is partitioned into two
resulting regions and repeat the splitting process on each of the
two regions. This splitting process is repeated until a predefined
stopping criterion is satisfied.
3.3.4 Stopping Criterion. Tree size is a tuning parameter gov-
erning the complexity of a model. The stopping criterion is that
the splitting process proceeds until the number of records in Di
falls below a threshold, and five is used as the threshold.
Fig. 2 Tool wear prediction using SVR
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After Bsuch trees fTbgB
1are constructed, a prediction at a new
point xcan be made by averaging the predictions from all the indi-
vidual Bregression trees on x
b
fB
rf x
ðÞ
¼1
BX
B
b¼1
Tbx
ðÞ (3.9)
The random forest algorithm [48,49] for regression is as follows:
(1) Draw a bootstrap sample Zof size Nfrom the training data.
(2) For each bootstrap sample, construct a regression tree by
splitting a node into two children nodes until the stopping
criterion is satisfied.
(3) Output the ensemble of trees fTbgB
1.
(4) Make a prediction at a new point xby aggregating the pre-
dictions of the Btrees.
The framework of predicting flank wear using an RF is illus-
trated in Fig. 3. In this research, a random forest is constructed
using B¼500 regression trees. Given the labeled training dataset
D¼ðxi;yiÞ, a bootstrap sample of size N¼630 is drawn from
the training dataset. For each regression tree, m¼9ðm¼ðp=3Þ;
p¼28Þvariables are selected at random from the 28 variables/
features. The best variable/split-point is selected among the nine
variables. A regression tree progressively splits the training data-
set into two child nodes: left node (with samples <z) and right
node (with samples z). A splitting variable and split point are
selected by solving Eqs. (3.7) and (3.8). The process is applied
recursively on the dataset in each child node. The splitting process
stops if the number of records in a node is less than 5. An
individual regression tree is built by starting at the root node of
the tree, performing a sequence of tests about the predictors, and
organizing the tests in a hierarchical binary tree structure as
shown in Fig. 4. After 500 regression trees are constructed, a pre-
diction at a new point can be made by averaging the predictions
from all the individual binary regression trees on this point.
4 Experimental Setup
The data used in this paper were obtained from Li et al. [50].
Some details of the experiment are presented in this section. The
experimental setup is shown in Fig. 5.
The cutter material and workpiece material used in the experi-
ment are high-speed steel and stainless steel, respectively. The
detailed description of the operating conditions in the dry milling
operation can be found in Table 2. The spindle speed of the cutter
was 10,400 RPM. The feed rate was 1555 mm/min. The Ydepth
of cut (radial) was 0.125 mm. The Zdepth of cut (axial) was
0.2 mm.
315 cutting tests were conducted on a three-axis high-speed
CNC machine (R
oders Tech RFM 760). During each cutting test,
seven signal channels, including cutting force, vibration, and
acoustic emission data, were monitored in real-time. The sampling
rate was 50 kHz/channel. Each cutting test took about 15 s. A sta-
tionary dynamometer, mounted on the table of the CNC machine,
was used to measure cutting forces in three, mutually perpendicu-
lar axes (x,y, and zdimensions). Three piezo accelerometers,
mounted on the workpiece, were used to measure vibration in
three, mutually perpendicular axes (x,y, and zdimensions). An
acoustic emission (AE) sensor, mounted on the workpiece, was
Fig. 3 Tool wear prediction using an RF
Fig. 4 Binary regression tree growing process
Fig. 5 Experimental setup
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used to monitor a high-frequency oscillation that occurs spontane-
ously within metals due to crack formation or plastic deformation.
Acoustic emission is caused by the release of strain energy as the
microstructure of the material is rearranged. After each cutting
test, the value of tool wear was measured off-line using a micro-
scope (Leica MZ12). The total size of the condition monitoring
data is about 8.67 GB.
5 Results and Discussion
In machine learning, feature extraction is an essential prepro-
cessing step in which raw data collected from various signal chan-
nels are converted into a set of statistical features in a format
supported by machine learning algorithms. The statistical features
are then given as an input to a machine learning algorithm. In this
experiment, the condition monitoring data were collected from (1)
cutting force, (2) vibration, and (3) acoustic emission signal chan-
nels. A set of statistical features (28 features) was extracted from
these signals, including maximum, median, mean, and standard
deviation as listed in Table 3.
Three predictive models were developed using ANNs, SVR,
and RFs, respectively. Two-thirds (2/3) of the input data (i.e.,
three datasets) were selected at random for model development
(training). The remainder (1/3) of the input data was used for
model validation (testing). Figures 68show the predicted against
observed tool wear values with the test dataset using ANNs, SVR,
and RFs, respectively. Figure 9shows the tool wear against time
with RFs.
In addition, the performance of the three algorithms was
evaluated on the test dataset using accuracy and training time.
Accuracy is measured using the R2statistic, also referred to as
the coefficient of determination, and mean squared error (MSE).
In statistics, the coefficient of determination is defined as
R2¼1ðSSE=SSTÞ, where SSE is the sum of the squares of
Table 2 Operating conditions
Parameter Value
Spindle speed 10,400 RPM
Feed rate 1555 mm/min
Ydepth of cut 0.125 mm
Zdepth of cut 0.2 mm
Sampling rate 50 kHz/channel
Material Stainless steel
Table 3 List of extracted features
Cutting force
(X,Y,Zdimensions)
Vibration
(X,Y,Zdimensions)
Acoustic
emission
Max Max Max
Median Median Median
Mean Mean Mean
Standard deviation Standard deviation Standard deviation
Fig. 6 Comparison of observed and predicted tool wear using
an ANN with 16 neurons in the hidden layer (termination crite-
rion: tolerance is equal to 1.0 310
24
)
Fig. 7 Comparison of observed and predicted tool wear using
SVR (termination criterion: slack variable or tolerance nis equal
to 0.001)
Fig. 8 Comparison of observed and predicted tool wear using
RFs (termination criterion: minimum number of samples in
each node is equal to 5)
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residuals, SST is the total sum of squares. The coefficient of deter-
mination is a measure that indicates the percentage of the response
variable variation that is explained by a regression model. A
higher R-squared indicates that more variability is explained by
the regression model. For example, an R2of 100% indicates that
the regression model explains all the variability of the response
data around its mean. In general, the higher the R-squared, the
better the regression model fits the data. The MSE of an estimator
measures the average of the squares of the errors. The MSE is
defined as MSE ¼ð1=nÞPn
i¼1ðb
yiyiÞ2, where b
yiis a predicted
value, yiis an observed value, and nis the sample size. The ANN,
SVR, and RF algorithms use between 50% and 90% of the input
data for model development (training) and use the remainder for
model validation (testing). Because the performance of ANNs
depends on the hidden layer configuration, five ANNs with a sin-
gle hidden layer but different number of neurons were tested on
the training dataset. Tables 48list the MSE, R-squared, and train-
ing time for the ANNs with 2, 4, 8, 16, and 32 neurons. With
respect to the performance of the ANN, the training time increases
as the number of neurons increases. However, the increased in
training time are not significant as shown in Fig. 10. In addition,
while the prediction accuracy increases as the number of neurons
increases, the performance is not significantly improved by adding
more than eight neurons in the hidden layer as shown in Figs. 11
and 12. Tables 9and 10 list the MSE, R-squared, and training
time for SVR and RFs. While the training time for RFs is longer
than that of ANNs and SVR, the predictive model built by RFs is
the most accurate as shown in Figs. 1012.
Table 5 Accuracy on the test data and training time for the
FFBP ANN with four neurons in the hidden layer
ANN (number of neurons ¼4)
Training size (%) MSE R
2
Training time (s)
50 43.428 0.958 0.122
60 51.001 0.951 0.084
70 43.645 0.958 0.093
80 45.661 0.955 0.103
90 45.058 0.958 0.118
Table 6 Accuracy on the test data and training time for the
FFBP ANN with eight neurons in the hidden layer
ANN (number of neurons ¼8)
Training size (%) MSE R
2
Training time (s)
50 36.810 0.964 0.167
60 34.168 0.968 0.186
70 39.795 0.961 0.202
80 44.175 0.957 0.197
90 46.634 0.954 0.234
Table 7 Accuracy on the test data and training time for the
FFBP ANN with 16 neurons in the hidden layer
ANN (number of neurons ¼16)
Training size (%) MSE R
2
Training time (s)
50 36.337 0.964 0.394
60 41.420 0.959 0.412
70 40.138 0.960 0.468
80 42.486 0.957 0.506
90 44.056 0.957 0.566
Fig. 9 Tool wear against time (cut) using RFs
Table 4 Accuracy on the test data and training time for the
FFBP ANN with two neurons in the hidden layer
ANN (number of neurons ¼2)
Training size (%) MSE R
2
Training time (s)
50 49.790 0.951 0.049
60 45.072 0.955 0.054
70 45.626 0.956 0.055
80 47.966 0.953 0.062
90 48.743 0.955 0.056
Table 8 Accuracy on the test data and training time for the
FFBP ANN with 32 neurons in the hidden layer
ANN (number of neurons ¼32)
Training size (%) MSE R
2
Training time (s)
50 35.305 0.965 1.165
60 38.612 0.963 1.301
70 38.824 0.963 1.498
80 42.469 0.959 1.496
90 48.138 0.953 1.633
Fig. 10 Comparison of training times
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6 Conclusions and Future Work
In this paper, the prediction of tool wear in milling operations
was conducted using three popular machine learning algorithms,
including ANNs, SVR, and RFs. The performance of these
algorithms was evaluated on the dataset collected from 315 mill-
ing tests. The performance measures include mean squared error,
R-squared, and training time. A set of statistical features was
extracted from cutting forces, vibrations, and acoustic emissions.
The experimental results have shown that while the training time
on the particular dataset using RFs is longer than the FFBP ANNs
with a single hidden layer and SVR, RFs generate more accurate
predictions than the FFBP ANNs with a single hidden layer and
SVR. The main contribution of this paper is twofold: (1) we dem-
onstrated that the predictive model trained by RFs can predict tool
wear in milling processes very accurately for the first time to the
best of our knowledge and (2) we compared the performance of
RFs with that of FFBP ANNs and SVR, as well as observed
that RFs outperform FFBP ANNs and SVR for this particular
application example.
In the future, a comparison of the performance of SVR and RFs
with that of other types of ANNs, such as recurrent neural networks
and dynamic neural networks, will be conducted. In addition, our
future work will focus on designing the parallel implementation of
machine learning algorithms that can be applied to large-scale and
real-time prognosis.
Acknowledgment
The research reported in this paper is partially supported by
NSF under Grant Nos. IIP-1238335 and DMDII-15-14-01. Any
opinions, findings, and conclusions or recommendations expressed
in this paper are those of the authors and do not necessarily reflect
the views of the National Science Foundation and the Digital Man-
ufacturing and Design Innovation Institute.
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