sensors
Article
Use of Machine Learning and Wearable Sensors to
Predict Energetics and Kinematics of
Cutting Maneuvers
Matteo Zago 1,2,3,*, Chiarella Sforza 4
, Claudia Dolci 4, Marco Tarabini 3,5
and
Manuela Galli 1,3
1
Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, 20133 Milano, Italy
2
Fondazione Istituto Farmacologico Filippo Serpero, 20159 Milano, Italy
3
E4Sport Lab, Politecnico di Milano, 20133 Milano, Italy
4
Dipartimento di Scienze Biomediche per la Salute, Università degli Studi di Milano, 20133 Milano, Italy
5
Dipartimento di Meccanica, Politecnico di Milano, 20129 Milano, Italy
*
Correspondence: matteo2.zago@polimi.it; Tel.: +39-02-2399-3351
Received: 14 June 2019; Accepted: 9 July 2019; Published: 12 July 2019


Abstract: Changes of directions and cutting maneuvers, including 180-degree turns, are common
locomotor actions in team sports, implying high mechanical load.
While the mechanics and
neurophysiology of turns have been extensively studied in laboratory conditions, modern inertial
measurement units allow us to monitor athletes directly on the ﬁeld. In this study, we applied
four supervised machine learning techniques (linear regression, support vector regression/machine,
boosted decision trees and artiﬁcial neural networks) to predict turn direction, speed (before/after
turn) and the related positive/negative mechanical work. Reference values were computed using an
optical motion capture system. We collected data from 13 elite female soccer players performing a
shuttle run test, wearing a six-axes inertial sensor at the pelvis level. A set of 18 features (predictors)
were obtained from accelerometers, gyroscopes and barometer readings. Turn direction classiﬁcation
returned good results (accuracy > 98.4%) with all methods. Support vector regression and neural
networks obtained the best performance in the estimation of positive/negative mechanical work
(coeﬃcient of determination R2 = 0.42–0.43, mean absolute error = 1.14–1.41 J) and running speed
before/after the turns (R2 = 0.66–0.69, mean absolute error = 0.15–018 m/s). Although models can
be extended to diﬀerent angles, we showed that meaningful information on turn kinematics and
energetics can be obtained from inertial units with a data-driven approach.
Keywords: supervised learning; changes of direction; IMU; mechanical work
1. Introduction
Changes of direction (CoD) and cutting maneuvers are basic locomotor actions in team sports,
implying high physiological and mechanical load [1–3]. High-intensity and abrupt sidestepping is
the most frequent cause for non-contact ligamentous injuries at the knee level, involving primarily
anterior cruciate ligament lesions, and secondarily meniscal or medial collateral ligament strains [4].
The amount of deceleration required in sidestep cutting is related to the angle and speed of approach
and has been associated to the likelihood of knee injuries [5,6]. CoDs also have a high associated
metabolic cost, impacting on the energetic requirements of exercise [7,8].
The mechanics and neurophysiology of CoDs have been accurately described primarily in
laboratory conditions, unveiling joint kinematics and loads as a function of the running angle
and technique [1,9–11], foot-landing strategies [12], muscular activations [3,13], and response to
Sensors 2019, 19, 3094; doi:10.3390/s19143094
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fatigue [14,15]. In addition, we recently proposed an algorithm to estimate the energy cost of running
with repeated 180 degree-CoDs [16]: the external mechanical energy associated to the trajectory of a
body’s center of mass was combined with the knee ﬂexion angle and ground contacts to provide an
estimation of the positive (concentric) and negative (eccentric) muscular work.
Although promising, this method was limited by the obtainment of full-body kinematics with
optical motion capture systems, being therefore conﬁned to laboratory conditions. Rather, gathering
reliable information on the side, speed and energetics of 180-degree sidestep CoDs in realistic
on-the-ﬁeld conditions would better help in monitoring the energetic, physiological and mechanical
load, as well as to prevent overuse injuries.
An emerging trend, quantifying sport actions with body-worn inertial measurements units (IMU),
enables the assessment of athletes in ecologic conditions [17,18]. The metrological issues related to
the use of wearable sensors for sport performance assessments have been the focal point of diﬀerent
research works: even though magneto-inertial technology allows monitoring the performance of
athletes of all levels, especially when complemented with a sensor fusion network, there is a need
for further research on the ease of use and error compensation to provide coaches and practitioners
with informative and concise metrics [19–22]. The use of inertial units also raises technical issues
to extract meaningful data from a broad class of signals (acceleration, angular velocity, magnetic
ﬁeld orientation, etc.) which are often prone to noise, non-linearities, and measurement inaccuracies.
These characteristics might practically limit the usability of results in speciﬁc conditions. In the case of
changes of direction, obtaining running speed analytically from one inertial unit and then applying
linear equations to estimate the related energy cost in [8] appears practically unfeasible due to inherent
biases and drifts.
A way to overcome these limitations is to apply machine learning techniques to IMU data.
Supervised machine learning algorithms take a known set of input data (called predictors) and know
responses and train a model to generate predictions from new data [23]. These techniques have been
applied in team sports to quantify movement patterns during training and competition, like physical
output and tackling impacts in rugby and Australian football [18,24], player load [25] or deceleration
before turns in soccer [26]. However, the estimation of the energetics associated with 180-degree cutting
actions in team sports has not been investigated. This study intends to introduce the application of
machine learning models to detect direction, speed and external mechanical work associated with
180-degree CoDs, by using only data coming from a single inertial unit. We hypothesize that a unique
sensor placed close to the core (pelvis) could capture the key information on athletes’ actions during
these tasks. Our complementary aim is to show that the combination of regression analysis technique
and easily available sensors can provide coaches and practitioners with a wealth of information about
such crucial game actions.
2. Materials and Methods
2.1. Experimental Procedures and Equipment
All tests were performed in the morning within two weeks after the end of the regular season.
The experimental setting was a full motion capture laboratory equipped with an eight-camera system
(sampling frequency: 100 Hz; Smart-Dx, BTS Bioengineering, Milano, Italy). A set of 14 reﬂective
markers (diameter: 15 mm) were positioned on the skin in the following anatomical landmarks:
tragi, acromia, olecranons; radius styloid processes; greater trochanters; femoral lateral epicondyles;
and lateral malleoli (additional markers were added for further biomechanical investigations, but they
were not considered in the current study). A six-axes IMU (GaitUp Physilog 5, Lausanne, Switzerland)
was ﬁxed to the shorts with a plastic clip close to the sacrum marker. Inertial sensor settings were:
sampling frequency 512 Hz, measurement range ±2000 degrees/s (gyroscope) and ±16 g (accelerometer).
The x-axis of the sensor reference frame pointed backwards, the y-axis upwards and the z-axis to the
subjects’ left. The unit also included a barometer with a sampling frequency of 64 Hz.
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Ambient temperature was 22–24 ◦C. Participants wore minimal sports clothing and running shoes.
They were ﬁrst acquainted with the experimental procedures; after a 10 min warm up supervised by a
professional strength and conditioning coach, participants completed a 5 m shuttle-run test (Figure 1)
at the average speed of 70% of their maximal aerobic speed, as detailed in [7]. Maximal aerobic speed
is the lowest running speed at which the maximum oxygen uptake occurs, and it was estimated with
aerobic power tests (Yo-Yo intermittent recovery test [27]) throughout the season. Average running
speed was 2.5 ± 0.2 m/s. Athletes had to keep running to exhaustion, i.e., when they could not reach
the end lane by the acoustic signal—pacing the shuttle rhythm—for two consecutive times.
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run test (Figure 1) at the average speed of 70% of their maximal aerobic speed, as detailed in [7]. 
Maximal aerobic speed is the lowest running speed at which the maximum oxygen uptake occurs, 
and it was estimated with aerobic power tests (Yo-Yo intermittent recovery test [27]) throughout the 
season. Average running speed was 2.5 ± 0.2 m/s. Athletes had to keep running to exhaustion, i.e., 
when they could not reach the end lane by the acoustic signal—pacing the shuttle rhythm—for two 
consecutive times. 
 
Figure 1. Experimental setting and turn (180-degree change of direction) action. In the right picture, 
the orientation of the sensor reference frame is displayed. 
2.2. Study Design and Participants 
This observational case-series study involved 13 female soccer players (age 23.6 ± 3.3 years, body 
mass: 59.0 ± 7.3 kg, height: 1.66 ± 0.05 m, body mass index: 21.2 ± 1.9 kg/m2), playing for elite clubs 
competing in the first and second Italian league. All participants were judged by a medical doctor 
not to have any restriction to sports practice, had no injuries in the 12 months preceding the test, and 
signed a written informed consent after a detailed explanation of the aims, benefits and risks of this 
study. The study was approved by the Institutional Ethics Committee (n. 1/2016) and was conducted 
according to the Declaration of Helsinki. 
2.3. Data Processing and Features Engineering 
Custom routines were developed within Matlab (v. 2018b, The Mathworks Inc., Natick MA, USA). 
The three-dimensional coordinates of body center of mass (CoM) were obtained using the segmental 
centroid method, specifically validated for sports applications [28–30], after applying a low-pass, zero-
lag second order Butterworth filter (cut-off frequency: 15 Hz) to the raw marker trajectories. CoD events 
were easily identified with the peaks of the CoM position in the running direction (CoMx). Mass-specific 
CoM external energy was computed according to classical physiology texts [31]: 
𝐸௘௫௧ = 1
2 𝒗஼௢ெ
ଶ
+ 𝑔ℎ஼௢ெ 
(1) 
where vCoM is the norm of instantaneous CoM speed, and hCoM is its vertical height. Positive (negative) 
mechanical work (W+/−) was then obtained as the sum of positive (negative) changes of Eext [31] in the 
two second window across the turn. Also, for each turn, we computed CoM approach speed (1 s before 
the turn, vbefore), and CoM speed during acceleration (1 s after the turn, vafter). These four variables, 
alongside the side of the pivoting limb (right or left), constitute the set of known targets (responses). 
Their distribution is illustrated in Figure 2: as negative external work is required to decelerate the CoM 
before the turn, and positive work is needed to accelerate it back in the new direction, W− was 
represented relative to vbefore, and W+ to vafter. 
Figure 1. Experimental setting and turn (180-degree change of direction) action. In the right picture,
the orientation of the sensor reference frame is displayed.
2.2. Study Design and Participants
This observational case-series study involved 13 female soccer players (age 23.6 ± 3.3 years,
body mass: 59.0 ± 7.3 kg, height: 1.66 ± 0.05 m, body mass index: 21.2 ± 1.9 kg/m2), playing for elite
clubs competing in the ﬁrst and second Italian league. All participants were judged by a medical
doctor not to have any restriction to sports practice, had no injuries in the 12 months preceding the
test, and signed a written informed consent after a detailed explanation of the aims, beneﬁts and risks
of this study. The study was approved by the Institutional Ethics Committee (n. 1/2016) and was
conducted according to the Declaration of Helsinki.
2.3. Data Processing and Features Engineering
Custom routines were developed within Matlab (v. 2018b, The Mathworks Inc., Natick, MA, USA).
The three-dimensional coordinates of body center of mass (CoM) were obtained using the segmental
centroid method, speciﬁcally validated for sports applications [28–30], after applying a low-pass,
zero-lag second order Butterworth ﬁlter (cut-oﬀ frequency: 15 Hz) to the raw marker trajectories.
CoD events were easily identiﬁed with the peaks of the CoM position in the running direction (CoMx).
Mass-speciﬁc CoM external energy was computed according to classical physiology texts [31]:
Eext = 1
2v2
CoM + ghCoM
(1)
where vCoM is the norm of instantaneous CoM speed, and hCoM is its vertical height. Positive (negative)
mechanical work (W+/−) was then obtained as the sum of positive (negative) changes of Eext [31] in the
two second window across the turn. Also, for each turn, we computed CoM approach speed (1 s before
the turn, vbefore), and CoM speed during acceleration (1 s after the turn, vafter). These four variables,
alongside the side of the pivoting limb (right or left), constitute the set of known targets (responses).
Their distribution is illustrated in Figure 2: as negative external work is required to decelerate the
CoM before the turn, and positive work is needed to accelerate it back in the new direction, W− was
represented relative to vbefore, and W+ to vafter.
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Sensors 2019, 19, x FOR PEER REVIEW 
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Figure 2. Negative (left) and positive (right) external mechanical energy computed in the two second 
window across the turn as a function of running speed before (left) and after (right) the turn. The 
distribution of the variables is also displayed on the edges. 
Eighteen features (predictors) were extracted from IMU data. We first had to detect the same 
CoD events in the IMU readings: smoothed (Butterworth, zero-lag low-pass filter, fcut = 0.5 Hz) 
angular velocity around the y (vertical) axis was particularly suitable for this, as it showed clear peaks 
in correspondence to turns (Figure 3). Matching between events timing was obtained by computing 
the cross-correlation between the resampled and rectified gyroscope and CoM trajectory and shifting 
them in time by an offset equal to the lag corresponding to maximum cross-correlation (Figure 3). 
The average CoD events detection error was 0.001 ± 0.102 s. Likewise for optical data, a two second 
window across this event was considered for the following computations. Static biases on each 
channel of the inertial sensors were obtained with a 30 min test with the unit kept still. We then 
subtracted these values from the accelerometer and gyroscope readings, which were additionally 
filtered with a fourth order Butterwort filter (cut-off frequency: 128 Hz). 
 
Figure 3. Events detection, based on center of mass (CoM) horizontal position (red curve, referred to 
the origin of the laboratory global reference system) and raw/filtered gyroscope rotation around the 
vertical axis (gray and blue, respectively). The autocorrelation function between the two allowed us 
to synchronize the two measurement systems. 
Figure 2.
Negative (left) and positive (right) external mechanical energy computed in the two
second window across the turn as a function of running speed before (left) and after (right) the turn.
The distribution of the variables is also displayed on the edges.
Eighteen features (predictors) were extracted from IMU data. We ﬁrst had to detect the same CoD
events in the IMU readings: smoothed (Butterworth, zero-lag low-pass ﬁlter, fcut = 0.5 Hz) angular
velocity around the y (vertical) axis was particularly suitable for this, as it showed clear peaks in
correspondence to turns (Figure 3). Matching between events timing was obtained by computing
the cross-correlation between the resampled and rectiﬁed gyroscope and CoM trajectory and shifting
them in time by an oﬀset equal to the lag corresponding to maximum cross-correlation (Figure 3).
The average CoD events detection error was 0.001 ± 0.102 s. Likewise for optical data, a two second
window across this event was considered for the following computations. Static biases on each channel
of the inertial sensors were obtained with a 30 min test with the unit kept still. We then subtracted
these values from the accelerometer and gyroscope readings, which were additionally ﬁltered with a
fourth order Butterwort ﬁlter (cut-oﬀ frequency: 128 Hz).
Sensors 2019, 19, x FOR PEER REVIEW 
4 of 11 
 
 
Figure 2. Negative (left) and positive (right) external mechanical energy computed in the two second 
window across the turn as a function of running speed before (left) and after (right) the turn. The 
distribution of the variables is also displayed on the edges. 
Eighteen features (predictors) were extracted from IMU data. We first had to detect the same 
CoD events in the IMU readings: smoothed (Butterworth, zero-lag low-pass filter, fcut = 0.5 Hz) 
angular velocity around the y (vertical) axis was particularly suitable for this, as it showed clear peaks 
in correspondence to turns (Figure 3). Matching between events timing was obtained by computing 
the cross-correlation between the resampled and rectified gyroscope and CoM trajectory and shifting 
them in time by an offset equal to the lag corresponding to maximum cross-correlation (Figure 3). 
The average CoD events detection error was 0.001 ± 0.102 s. Likewise for optical data, a two second 
window across this event was considered for the following computations. Static biases on each 
channel of the inertial sensors were obtained with a 30 min test with the unit kept still. We then 
subtracted these values from the accelerometer and gyroscope readings, which were additionally 
filtered with a fourth order Butterwort filter (cut-off frequency: 128 Hz). 
 
Figure 3. Events detection, based on center of mass (CoM) horizontal position (red curve, referred to 
the origin of the laboratory global reference system) and raw/filtered gyroscope rotation around the 
vertical axis (gray and blue, respectively). The autocorrelation function between the two allowed us 
to synchronize the two measurement systems. 
Figure 3. Events detection, based on center of mass (CoM) horizontal position (red curve, referred to
the origin of the laboratory global reference system) and raw/ﬁltered gyroscope rotation around the
vertical axis (gray and blue, respectively). The autocorrelation function between the two allowed us to
synchronize the two measurement systems.
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The ﬁrst feature F1 was the sum of the root mean square of changes in acceleration and deceleration
per second, also known as ’player load’, a metric commonly used to calculate the load or activity level
of athletes in team sports [25]:
player load =
1023
X
t=1
r
(ax,t+1 − ax,t)2 +

ay,t+1 − ay,t
2 + (az,t+1 − az,t)2
(2)
Other accelerometer features were the trapezoidal numerical integral of each axes positive and
negative acceleration (F2−7). Features F8−10 were the integral of each gyroscope axis. Features F11−13
and F14−16 were the root mean square, the skewness and the kurtosis of the norm of the accelerometer
and gyroscope readings during the two second turn window. Skewness describes the symmetry of the
acceleration and angular velocity signal distributions and is given by:
skewness = E(x − x)3
σ3
(3)
The kurtosis quantiﬁes the extent to which the acceleration and angular velocity signals are peaked
or ﬂat with respect to a normal distribution:
kurtosis = E(x − x)4
σ4
(4)
In Equations (3) and (4), E is the expected value, x is the mean and σ is the standard deviation of
the signal in the two second window [32]. These two features quantify the degree of distortion with
respect to a normal distribution of acceleration or angular velocity data series: for instance, an abrupt
braking action would contain more negative than positive acceleration values, and so it would be
highly skewed.
The last two features F17 and F18 were obtained from the ﬁltered barometer output (low-pass
tenth order Butterworth ﬁlter, cut-oﬀ frequency: 1 Hz) and were the diﬀerence between the mean sea
level altitude (computed from ambient pressure) at the CoD event and one second before or after the
CoD, respectively. Table 1 provides an overview of features and responses. Before further processing,
outliers were removed when examples were outside the variable’s mean ± 3 standard deviations,
and the coeﬃcient of variation (CV) was computed for each variable.
2.4. Regression and Classiﬁcation Models
For the prediction of W+, W−, vbefore and vafter, we applied four supervised machine learning
regression techniques:
1.
Multiple linear regression, modeling the linear relationship between predictors and the response
(dependent) variables.
2.
Support vector regression (SVR): this technique is based on support vector machines (SVM),
which in turn construct hyperplanes to deﬁne decision boundaries in a multi-dimensional space.
SVR computes the parameter of a function f(x), where x is the matrix of predictors, ﬁtting the
input data with the most ε-deviation from the target y (response). As SVR is particularly suited to
handle non-linear tasks, in this study we chose a Gaussian kernel.
3.
Boosted trees (BT): classiﬁcation or regression models are in the form of a tree structure, which
is built top-down from a root node, and involves partitioning data into subsets that contain
common features based on the level of information gain, i.e., a decrease in entropy after a dataset
is separated [33]. Boosted trees are an extension of decision trees that aggregate an ensemble
of decision trees into a unique result, which reduces the chance of overﬁtting. The number of
learners (trees) set in this study was 40.
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4.
Artiﬁcial neural networks (ANN): a feedforward network consisting of an input, a hidden and an
output layer was designed. Neurons (n = 40) in the hidden layer process the input features in
accordance to hyperbolic tangent sigmoid functions. The output layer is a single neuron which
returns the estimated (predicted) response. The back-propagation learning algorithm was used
to update the weights and biases of the ANN. Input data was split into three subsets: 70% for
training, 15% for testing and 15% for validation.
Classiﬁcation models to determine turn direction (right or left) matched the previous techniques
and included: (1) linear discriminant analysis, (2) SVM, (3) BT, (4) ANN.
Table 1. Overview of the ﬁve responses (Ri, where R5 is a categorical variable) and of the 18 features
(Fi) used to train the models.
Variable
Description
Unit
Mean
SD
CV
Min
Max
R1
Positive work
J/kg
8.49
2.35
0.28
1.18
18.44
R2
Negative work
J/kg
8.17
2.73
0.33
1.02
18.91
R3
Speed before turn
m/s
2.60
0.38
0.15
1.49
3.69
R4
Speed after turn
m/s
2.59
0.33
0.13
1.57
3.44
R5
Turn side
cat.
-
-
-
F1
Player load
A.U.
190.6
62.6
0.33
67.3
407.4
F2
Positive accx integral
m/s
325.8
86.0
0.26
125.7
584.0
F3
Positive accy integral
m/s
528.00
96.1
0.18
267.4
846.3
F4
Positive accz integral
m/s
238.7
67.6
0.28
82.0
435.1
F5
Negative accx integral
m/s
−328.7
89.4
0.27
−587.1
−107.8
F6
Negative accy integral
m/s
−508.8
89.2
0.18
−810.1
−263.4
F6
Negative accz integral
m/s
−251.7
79.0
0.31
−504.5
−93.4
F7
Norm acc RMS
m/s2
7.59
3.57
0.47
1.19
21.04
F8
Acceleration skewness
-
4.95
1.35
0.27
2.08
9.00
F9
Acceleration kurtosis
-
35.8
18.5
0.52
7.6
98.4
F10
Gyroscopex integral
rad
9.9·103
1.4·104
1.44
−2.9·104
4.7·104
F11
Gyroscopey integral
rad
0.9·103
6.7·104
n.a.
−8.5·104
8.6·104
F12
Gyroscopez integral
rad
−45.3
3.8·104
n.a.
−6.0·104
6.1·104
F13
Gyroscope norm RMS
rad/s
2.4·103
1.7·103
0.69
0.3·103
7.9·103
F14
Gyroscope skewness
-
4.64
1.61
0.35
0.41
9.31
F15
Gyroscope kurtosis
-
32.8
20.1
0.61
2.41
104.0
F17
∆baro, before
m
−0.39
0.26
0.65
−1.08
0.36
F18
∆baro, after
m
0.41
0.26
0.62
−0.35
1.12
∆baro: altitude diﬀerence between before/after 1 s. acc: acceleration; A.U. arbitrary units; cat.: categorical variable.
CV: coeﬃcient of variation; RMS: root mean square; SD: standard deviation; n.a.: not applicable (bimodal variable,
CV > 50).
2.5. Validation
To evaluate the predictive accuracy, models 1–3 underwent a standard 10-fold cross-validation
procedure: data were randomly partitioned into two sets, the ﬁrst was used for training, while the
second was used for validation. This process was repeated 10 times, by randomly selecting the training
and validation portions [34]. The means of the 10 classiﬁcation accuracy rates were taken as an unbiased
estimate of the model for the complete dataset. Root mean square error (RMSE), mean absolute error
and coeﬃcient of determination (R2) were computed as performance metrics for regression models.
Classiﬁcation models were evaluated in terms of accuracy, sensitivity, speciﬁcity and area under the
receiver operating characteristic curve (AUC).
3. Results
Th shuttle run test duration was on average 158.4 ± 65.1 s, with 72 ± 30 turns per participant.
Overall, we collected 937 cutting maneuvers. Outlier removal led us to exclude 32 of them. Feature
means, standard deviations and ranges are shown in Table 1: while the variability of speed was below
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15%, that of positive/negative mechanical work reached 33%; the highest variability in predictors was
contained by gyroscope integrals and RMS, the lowest in the acceleration integrals.
Turn direction was detected with good accuracy (98.4%, Table 2) by linear discriminant analysis
(sensitivity = 97.3%, speciﬁcity = 99.6%, AUC = 1.00), while with the other methods (boosted trees,
SVM and ANN), we obtained perfect classiﬁcation (accuracy = 100%, AUC = 1.00).
The best performance in predicting the mechanical work in decelerations and accelerations was
achieved by SVR models, with a moderate R2 and an error of about 15% (Table 2). ANNs best
predicted incoming and sprint speed with a moderate to substantial R2, and an error lower than 10%
(0.15–0.18 m/s). Feature importance for BT is reported in Figure 4.
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The best performance in predicting the mechanical work in decelerations and accelerations was 
achieved by SVR models, with a moderate R2 and an error of about 15% (Table 2). ANNs best 
predicted incoming and sprint speed with a moderate to substantial R2, and an error lower than 10% 
(0.15–0.18 m/s). Feature importance for BT is reported in Figure 4. 
 
Figure 4. Feature importance returned by boosted trees models when predicting positive/negative 
mechanical work (Wp and Wn, top), and approach/sprint running speed (vbefore and vafter, bottom). 
Refer to Table 1 for the description of features Fi. 
4. Discussion 
The combination of accelerometer-, gyroscope- and barometer-based features and relatively 
simple machine learning models enabled us to estimate key kinematic and energetic characteristics 
of 180-degree turns with an error of about 15%. Features were obtained from a single pelvis-mounted 
unit, and no prior calibration procedure was required. In addition, we limited signal processing to a 
few basic steps, with only standard low-pass filtering being applied to sensor readings: this 
potentially increases the generalizability to different units and vendors. 
Table 2. Performance of regression models. In bold, the best model for each response, in terms of root 
mean square error (RMSE). 
Response 
Regression Model 
R2 
RMSE 
MAE 
Positive work (J) 
Multilinear regression 
0.36 
1.96 
1.30 
 
Support vector regression 
0.43 
1.85 
1.14 
 
Boosted trees 
0.39 
1.91 
1.22 
 
Artificial neural network 
0.39 
2.40 
1.80 
 
 
 
 
 
Figure 4. Feature importance returned by boosted trees models when predicting positive/negative
mechanical work (Wp and Wn, top), and approach/sprint running speed (vbefore and vafter, bottom).
Refer to Table 1 for the description of features Fi.
4. Discussion
The combination of accelerometer-, gyroscope- and barometer-based features and relatively
simple machine learning models enabled us to estimate key kinematic and energetic characteristics of
180-degree turns with an error of about 15%. Features were obtained from a single pelvis-mounted
unit, and no prior calibration procedure was required. In addition, we limited signal processing to a
few basic steps, with only standard low-pass ﬁltering being applied to sensor readings: this potentially
increases the generalizability to diﬀerent units and vendors.
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Table 2. Performance of regression models. In bold, the best model for each response, in terms of root
mean square error (RMSE).
Response
Regression Model
R2
RMSE
MAE
Positive work (J)
Multilinear regression
0.36
1.96
1.30
Support vector regression
0.43
1.85
1.14
Boosted trees
0.39
1.91
1.22
Artiﬁcial neural network
0.39
2.40
1.80
Negative work (J)
Multilinear regression
0.35
2.27
1.66
Support vector regression
0.42
2.14
1.41
Boosted trees
0.41
2.16
1.49
Artiﬁcial neural network
0.44
2.34
1.84
Speed before (m/s)
Multilinear regression
0.53
0.26
0.21
Support vector regression
0.65
0.23
0.17
Boosted trees
0.60
0.24
0.19
Artiﬁcial neural network
0.66
0.23
0.18
Speed after (m/s)
Multilinear regression
0.47
0.25
0.20
Support vector regression
0.65
0.20
0.15
Boosted trees
0.62
0.21
0.16
Artiﬁcial neural network
0.69
0.19
0.15
MAE: mean absolute error; R2: coeﬃcient of determination.
4.1. Turn Direction
As CoDs and sidestepping maneuvers impose a high muscular and mechanical load on lower limb
structures, knowing the intensity and direction of these actions might help in preventing unilateral
overloading and in turn potential injuries [2,35]. Turn side (direction) was satisfactorily estimated even
with linear discriminant analysis, which makes the adoption of BT, SVM and ANNs redundant for this
speciﬁc task.
In fact, the combination of gyroscope features F11 (integral of the angular velocity around the pelvic
anteroposterior axis) and most importantly F12 (integral around the pelvic mediolateral axis) returned
almost perfect classiﬁcations. In other words, pelvis rotation captures the most relevant information
about turning direction and could be easily implemented in existing global positioning system (GPS)
activity trackers [36]. This sensor location allows for the implementation of smart apparel, that unlike
smartwatches or wristbands, can be worn during games. A potential improvement to this model could
be the classiﬁcation among multiple classes of directional changes, i.e., 45–90 degree, 90–120 degree
and 120–180 degree CoDs. Further, it is likely that the classiﬁcation performance would decrease when
positioning the sensor on other less favorable—limited to turn direction classiﬁcation—segments such
as feet or shanks.
4.2. Turn Speed and Mechanical Energy
Turning speed is related to the energy dissipated during the deceleration (braking) phase, and thus
impacts on the risk of ligamentous lesions, especially at the knee level [37]. Once a directional change
was detected, the proposed models were successfully able to estimate turn speed with an error below
0.2 m/s, which is comparable to 10 Hz GPS error in common sports applications [38,39]. However, rapid
directional changes usually degrade GPS accuracy [38]: obtaining speed during CoDs still represents a
challenge for such systems [40], whose weaknesses can be mitigated by adding or integrating data
from inertial sensors [36,41].
The best prediction performance of ANNs showed that a linear relationship between predictors
and response (i.e., multiple linear regression) was outperformed by non-linear models: ANNs can detect
complex nonlinear interactions between inputs and targets [42]. However, the lack of transparency in
the mathematical models of ANNs hinders the interpretation of their output. Decision trees showed
slightly lower performance, but the model structure of the entire procedure can be followed and
Sensors 2019, 19, 3094
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interpreted: in BT models, prediction appeared highly dependent on positive mediolateral acceleration
(F4) for sprinting speed, and acceleration skewness for approach speed (Figure 4).
A similar reasoning applies to Wp and Wn, which were better predicted by SVR with Gaussian
kernel. Mechanical energy during a CoD is an indirect measure of its associated metabolic cost.
Computed positive/negative external CoM work was in line with previous investigations from diﬀerent
groups [8,16], which ensures the predictions were constructed on a solid basis. The prediction error
(1.1–1.4 J) can be considered acceptable as it allows us to get a realistic measure of the amount of energy
involved in the braking/propulsive actions, which is highly dependent on running speed.
4.3. Limitations and Perspectives
Turning event detection was particularly easy in the featured experimental protocol,
which involved repeated 180-degree turns with just few running steps in between: further developments
should include various angles of approach, and potentially a less homogeneous sample to increase the
model’s generalizability. Compared to the reference optical system, CoD events were determined with
a variability of about 0.1 s, which is of the same order of magnitude of the stance phase of the pivoting
limb (~0.3 s [14]). However, we chose to compute features over a two second span; thus, any overlaps
should be in the range of 5% of the whole window. Although data were processed oﬀ-line, once a
turn is detected it would be relatively straightforward to apply the regression algorithms to moving
windows containing updated data streams.
More complex features could be also added to exploit the IMU three-dimensional orientation
(i.e., quaternions): however, (i) accurate long-term orientation tracking based on a unique inertial
sensor is not trivial and (ii) we intentionally limited feature processing to variables that could be easily
computed on a portable device. In addition, the proposed models did not rely on anthropometric
information (height, weight, BMI, etc.), that were purposefully excluded from predictions.
Even if a more general scope should be adopted for practical on-the-ﬁeld implementations,
this paper showed that the extraction of meaningful information on turn kinematics and energetics
is highly viable with a data-driven approach using commercially-available units and established
regression and classiﬁcation techniques. The current study represents a further step towards the
accurate, ecological quantiﬁcation of the key features of changes of direction in team sports.
Author Contributions: Conceptualization, M.Z. and C.S.; methodology, M.G. and M.T.; formal analysis, M.Z.;
data curation, M.Z.; resources, C.D., C.S. and M.T.; supervision, M.G. and C.S.; project administration, C.D.;
writing—original draft preparation, M.Z.; writing—review and editing, M.G., C.S. and M.T.
Funding: University of Milan (Piano di sostegno alla ricerca 2015–17).
Acknowledgments: The Authors are grateful to Filippo Bertozzi and Francesca Salaorni for the precious
collaboration and the recruitment of participants, respectively.
Conﬂicts of Interest: The authors declare no conﬂict of interest.
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Use of Machine Learning and Wearable Sensors to Predict Energetics and Kinematics of Cutting Maneuvers.
Zago, Matteo,Sforza, Chiarella,Dolci, Claudia,Tarabini, Marco,Galli, Manuela