# Can a Tesla Turbine be Utilised as a Non-Magnetic Actuator for MRI-Guided
Robotic Interventions?

David Navarro-Alarcon, Luiza Labazanova, Man Kiu Chow, Kwun Wang Ng and Derek
Kwok D. Navarro-Alarcon, L. Labazanova and M. Chow are with The Hong Kong
Polytechnic University, KLN, Hong Kong.K. W. Ng is with the Chinese University
of Hong Kong, Shatin, Hong Kong.D. Kwok is with Time Medical Ltd, Shatin, Hong
Kong.

###### Abstract

This paper introduces a new type of non-magnetic actuator for MRI
interventions. Ultrasonic and piezoelectric motors are one the most commonly
used actuators in MRI applications. However, most of these actuators are only
MRI-safe, which means they cannot be operated while imaging as they cause
significant visual artifacts. To cope with this issue, we developed a new
pneumatic rotary servo-motor (based on the Tesla turbine) that can be
effectively used during continuous MR imaging. We thoroughly tested the
performance and magnetic properties of our MRI-compatible actuator with
several experiments, both inside and outside an MRI scanner. The reported
results confirm the feasibility to use this motor for MRI-guided robotic
interventions.

##  I Introduction

Magnetic resonance imaging (MRI) is a medical imaging technique that creates
detailed anatomical pictures of internal structures of the body. A common
application of MRI scanners is for guiding of needles during biopsy
interventions (where sample tissues are extracted from an area of interest).
Compared to other medical imaging modalities, MRI offers several advantages
when performing interventional procedures, amongst them are: MRI does not
expose the patient to harmful radiation (e.g. as with x-ray machines), it
offers excellent soft tissue contrast for locating lesions, it produces
detailed spatial information of tissues in 3D, to name a few [1]. With the aim
of improving the precision and dexterity of these interventions, robotic
technologies have been recently introduced to the MRI room. However, since the
operation principle of MRI is based on strong magnetic fields, traditional
actuation technologies (e.g. standard electric servo-motors) cannot be used to
drive the motion of an interventional robot; conventional electronic and
signal transmission systems used in the actuator’s controls severely affect
the imaging process. Furthermore, the high magnetic field also imposes strict
requirements to the types of materials that can be used in an actuator
operating nearby the magnetic bore; ferromagnetic metals should be avoided as
they cause image artifacts.

To understand the extent to which devices (including actuators and sensors)
can operate within an MRI bore, we must first introduce two definitions. A
device is considered to be _MRI-safe_ if it does not present any potential
risk to patients or others, but may introduce noise into the images. A device
is considered to be _MRI-compatible_ if it is MRI-safe and does not
significantly affect the imaging quality and the operation of the scanner [2]
(clearly, MRI-safe actuators may only be applicable to procedures that can be
conducted/guided with off-line scans). In the past two decades, many
researchers that have developed both MRI-safe and MRI-compatible actuation
systems for various types of interventions [3]. Based on their operation
principle, these actuators can be classified into three main categories: (1)
piezoelectric/ultrasonic motors, (2) hydraulic actuators, and (3) pneumatic
actuators.

Piezoelectric/ultrasonic motors are frequently found in the MRI robotics
literature. These types of actuators produce motion based on the non-magnetic
piezoelectric effect, that allows them to safely be brought inside the bore.
Some examples of these systems are given in [4], where a thermo-therapy robot
for liver tumors is proposed, and [5], where a haptic interface controlled by
an ultrasonic motor is developed). In order to generate motion, this type of
motors are activated with high frequently signals that may affect the signal-
to-noise ratio (SNR) and cause severe degradation to the images. Many authors
stress that these actuators should not be operated while performing MRI scans,
see [6, 7]. Piezoelectric/ultrasonic are only MRI-safe.

Hydraulic actuators use controllable liquid flows to generate driving forces.
Examples of this technique are given in [8], which describes a master-slave
interface for studying motor control, and [9] which presents robot for a
neurosurgery application. Hydraulic actuation provides high driving forces
(thanks to the incompressibility of liquids), can be accurately controlled,
and is MRI-compatible. However, hydraulic devices and installations tend to
create bulky setups and, most importantly, suffer from fluid leakage that
might contaminate the MRI room.

Pneumatic actuation is a cleaner and easier to maintain option that relies on
compressed air to power a system. Pneumatics is MRI-compatible, and according
to some studies (see e.g. [10]) it presents the best performance for
continuous imaging applications. An early application is given [11], where a
robotic needle driver for radiological interventions is reported. The authors
in [12, 13] developed a pneumatic stepping rotary motor (based on a planetary
mechanism) that has an angular step of 3.33 degrees and output torques of
several hundred of N-mm. Another stepping motor was developed in [14]; this
system uses two air cylinders to form a crank-link mechanism that outputs
rotary motions. Recently, the authors in [15] developed new kind of stepping
robot (using laser cutting technology) for needle positioning applications.
These types of stepping systems are characterised by moving through discrete
motions. Note that resonances might arise when rotating around the system’s
natural frequency; accelerations are also difficult to control.

To cope with the above-mentioned issues, we have developed a new MRI-
compatible pneumatic actuator that allows to effectively generate continuous
smooth rotary motions. The basic mechanical structure of this new system is
based on the Tesla turbine. To guarantee that it can operate under continuous
MR imaging, it is fabricated using 3D printing technology, and its angular
position is measured using fibre optics. Experiments are conducted to verify
the motor’s MRI-compatibility and performance.

The rest of this paper is organised as follows: Section II describes the
design of the new actuator; Section III presents the conducted experimental
study; Section IV gives final conclusions.

##  II Methods

###  II-A Mechanics of the Tesla Motor

In this section we present the development of the pneumatically actuated
motor, whose motion principle is based on the Tesla turbine, which was
developed by Nicola Tesla in 1905 as a hydroelectric power generator [16]
(along this paper, we shall refer to the application of this system as the
_Tesla motor_). The proposed motor is a blade-less turbine that operates based
on the boundary layer effect of the driving fluid. It consists of a set of
several smooth disks separated by a small gap, and that are fixed together to
central rotating shaft. Each disk is provided with four exhaust holes that are
placed near to the disk’s centre. When compressed air flows into the motor
through the inlet nozzle, it spirals around the shaft and moves towards the
exhaust ports creating a vortex. The fluid vortex induces a drag force over
the disks’ surface, that results in rotational motion of the motor shaft. The
proposed motor is equipped with two independent inlet ports that enable bi-
directional rotations (Figure 1 shows the schematic drawing).

Figure 1: Working principle of a pneumatic actuator

We mathematically model the motor’s driving torque by analysing its fluid-
structure interactions. Consider the velocity profile $v$ of the fluid
(assumed to be parabolic) that moves along the tangential direction relative
to the disks’ surface. This tangential flow between two consecutive disks
generates a shear stress that is proportional to the fluid’s friction
coefficient $\mu$. The total driving torque $\tau$ that is generated by a
motor with $n$ disk gaps satisfies the following relation [17]:

$\tau=n\mu\int_{r_{1}}^{r_{2}}\frac{\partial v}{\partial y}\,dr$ (1)

where $r_{1}$ and $r_{2}$ are the radius of the outlet at the centre of the
disk and the outer radius of the disk, respectively, and $y$ denotes the
normal direction to the disk’s surface (see Figure 1 bottom). The velocity $v$
is proportional to the pressure of the driving compressed air system, and its
monotonic (yet nonlinear) relation can be used for controlling the motion of
the motor (and it will be shown later).

###  II-B Motor Prototyping

Our objective is to develop an MRI-compatible actuator that can operate within
the magnetic bore. Therefore, in the design and fabrication of the motor it is
important to select non-magnetic materials for its components. The motor’s
structure was 3D printed with PLA (polylactic acid) using a standard 3-axis
printer in our laboratory; only the disks and spacers were printed by resin
using SLA (stereo-lithography) printing. The disks were fabricated with this
latter method since it produces a much smoother surface that helps to create
stable airflow for driving the motor. The disks printed with PLA have a much
rougher surface, even when using the smallest layer achievable by our 3D
printer ($0.06$ mm in our case); if this method used to build the motor, the
rough finishing causes unsteady airflow that affects the motor’s performance.
It is important to remark that since the disks are fabricated with plastics,
they have less rigidity and strength compared to metal-based disks (they may
be susceptible to bending when the compressed air first strikes the disk next
the inlet port). For our MRI robotics application, we use non-magnetic metals
(viz. brass and aluminium) only for a few essential support and driving
components. By using this type of metals, we aim to reduce the overall
magnetic susceptibility of the actuator.

The basic design of a Tesla motor is characterised for generating a high
rotational speed with a low driving torque. In laboratory tests, sensor
feedback shows that the developed motor can achieve a rotational speed of
around 13000 RPM when driven by compressed air of 4 Bar. To use this motor in
a robotic mechanism, we must first modify its speed and torque properties. For
that, we developed an custom-made MRI-compatible gearbox with a 1:60 gear
reduction (some of the components of this gearbox are fabricated with brass
and not plastics so as to improve its strength). The gearbox is built with
worm gears for the following reasons: (1) it provides high gear ratio that
effectively increases torque and reduces the output speed; (2) it provides a
self-locking feature (i.e. it is non back-drivable) that improves stiffness
and prevents undesired motions when disturbances arise; (3) it has a compact
structure with fewer components than e.g. planetary gears with the same
reduction ratio. Figure 2 shows the fabricated prototype with its different
components.

Figure 2: (Left) Schematic drawing of Tesla motor: (a) disks assembly, (b)
worm gears, (c) output shaft, (d) inlets ports, (e) silencer, (f) optical
fibre, (g) rotary encoder (h) encoder disc. (Right) Prototype of Tesla motor
Figure 3: (Left) Details of the proposed rotary encoder, where: (a) optical
fibre; (b) encoder disk; (c) output shaft. (Right) The developed prototype for
the MRI-compatible sensor.

The use of electrical signals in a sensor operating inside the magnetic bore
can potentially create noise in the image when performing scans. Therefore, we
developed a custom-made rotary encoder that uses optical fibres (from
Keynece®) to measure/estimate the angular position and velocity of the motor.
Since the rotational speed of the turbine’s shaft is very high at its nominal
operation, there might be many missed counted pulses if the rotary encoder is
installed on it. Therefore, the rotary encoder is instead installed at the
shaft but of the gearbox, which has a much smaller rotational speed due to its
1:60 gear reduction ratio (e.g. if we use a nominal 4 Bar driving pressure,
the gearbox has a speed of around 200 RPM, which is much easier to detect with
simple electronic board). The input-output speed relation of the gearbox is
expressed as follows:

$\omega_{out}=\frac{1}{60}\omega_{turbine}$ (2)

###  II-C Application to MRI-Guided Interventions

We developed a test set-up to evaluate the performance and magnetic
compatibility of the Tesla motor. This test system has a 1-DOF linear joint
mechanism that uses a non-magnetic slide (Del-Tron®), an aluminium power screw
(Abssac®), and a nylon nut. The purpose of the mechanism is to transform the
rotary motions of the actuator into controllable linear motions of a
biopsy/coaxial needle (hence, simulating in a simple MRI-guided intervention).
The use of the power screw further reduces the speed of the insertion motions.
Figure 4 shows the developed pneumatically-powered needle insertion mechanism.

Compactness is an important concern for MRI robotics as there is limited space
inside the scanner. To guarantee that the motor can be used in an
interventional robotic system, it is necessary to build it with a moderate
size but at the same time it should be able to provide sufficient torque. In
the developed insertion mechanism, the motor is fabricated with a diameter of
${\diameter}60$ mm and a length of $130$ mm. Six ${\diameter}55$ mm disks with
$2$ mm thick spacers are utilised to generate the driving torque. We selected
this configuration based on the observed performance of previous test
prototypes. For a motor with fewer disks, the rotary assembly will have a
smaller mass that generates less output torque. For a motor with many disks
and heavier rotary assembly, the generated (nominal) torque is certainly
larger, yet, it requires a higher starting torque to begin the motion.

Figure 4: Test set-up for needle insertions: (1) Tesla motor, (2) aluminium
power screw, (3) coaxial needle, (4) compression grid, (5) silicon breast
phantom.

###  II-D Motion Control System

The control system that commands the motion of the Tesla motor is composed of
various parts: a real-time control PC with analogue boards to program the
algorithms and output the control actions, a data acquisition system to
process the optical sensor feedback, and pneumatic servo valves to regulate
the air flow and pressure inside the actuator. Figure 5 shows a schematic
diagram of the developed motion controller. This diagram shows that to servo-
control the motor, only light signals and compressed air need to be passed
inside the MRI room; all electrical signals are processed outside the room,
therefore, eliminating possible sources of noise.

The Tesla motor is controlled by the action of two pneumatic valves: a flow
proportional valve from Festo® (MPYE-5-1/8-LF-010-B) that regulates the
volumetric flow rate that is sent to the motor, and a solenoid valve from SMC®
that directs the flow towards either of the two inlet ports (which determine
the directions of rotation). These pneumatic valves are controlled by an
embedded analogue output board from Phidgets®, that is programmed in a Linux
PC with standard C++ language. Since all the pneumatic devices and controller
are placed outside the shielding room, the solenoid valve must be connected to
the motor using two $5$ metre-long plastic tubes (which are passed through the
scanner’s waveguide). The motor’s rotations are measured by counting the
optical pulses from the encoder; these are first processed by the sensor’s
transceiver, and then acquired into the control PC via the Phidgets board.

In general, to control the motion of pneumatically-driven actuators, one must
regulate either the air pressure or the air flow rate. For our Tesla motor,
the input flow rate $\phi$ is used to indirectly specify the generated output
torque [18]. With this flow-proportional servo-valve, the flow $\phi=\kappa u$
can be accurately set by a commanded analogue voltage $u$, for $\kappa$ as a
known parameter of the valve. We locally approximate the relation (around the
nominal operation speed) between $\phi$ and the driving torque $\tau$ with the
following expression:

$\tau\approx i\rho h(\phi)=i\rho h(\kappa u)$ (3)

where the scalar $i=\pm 1$ models the positive/negative direction of rotation
(as determined by the solenoid valve), $\rho$ denotes a positive
proportionality constant, and $h(\cdot)$ represents a monotonically increasing
function of the flow (both $\rho$ and $h(\cdot)$ can be experimentally
estimated with standard calibration methods). From equation (3), it is clear
that the driving torque can be (approximately) adjusted via the analogue
voltage that is commanded to the flow valve. Note that this local model is
only valid for a motor under continuous rotations, and does not account for
the highly nonlinear static starting torque properties.

The second-order dynamic equations of motion of the Tesla motor are given by:

$\ddot{q}=\frac{1}{J}(-b\dot{q}-c\operatorname{sgn}(\dot{q})+\tau_{L}+\tau(u))$
(4)

where $J$ denotes the inertia of rotor, $b$ and $c$ are the viscous and the
Coulomb friction coefficients, respectively, $\tau_{L}$ represents the torque
due to external loads. In our system, the motion controller is designed
considering the command voltage $u$. We implemented a standard PID regulator
with the following form:

$u=-K_{P}\left(q-q_{d}\right)+K_{I}\int\left(q-q_{d}\right)\mathop{}\\!\mathrm{d}t-K_{D}\dot{q}$
(5)

for $K_{p}$, $K_{i}$, and $K_{d}$ as the proportional, integral and derivative
gains, which were experimentally tuned by trial and error, and $q_{d}$ as the
target position.

Figure 5: Schematic diagram of the control system

##  III Results

We carried out two types of experimental studies to test the new actuator: (1)
in-the-lab experiments, and (2) in-bore experiments. The former were conducted
(outside MRI scan room) to evaluate the motor’s positioning error, maximum
force, and speed-pressure response. The latter were conducted inside the
magnetic bore with the aim of testing the MRI-compatibility, signal-to-noise
ratio (SNR), percent integral uniformity (PIU), and homogeneity.

###  III-A In-the-Lab Experiments

We evaluated the resulting rotational speed of the motor under various air
pressure inputs. This type of test is particularly important for our system
since some of the 3D printed parts of the rotary disk assembly might melt at
high speeds. Figure 6 shows the obtained speed-pressure curve. From these
tests, we observed that the motor shaft starts to deform for speeds higher
than 13000 RPM, and that a minimum pressure of around 0.5 Bar must be used in
order to overcome the motor’s static friction. It is important to identify
these values so as to set both upper and lower pressure limits for achieving a
normal operation with the motor.

Figure 6: Experimental speed-pressure curve

Next, we evaluated the positioning accuracy of the pneumatic motor. For that,
we used the setup shown in Figure 4, where the task is to introduce the
coaxial needle into different targets inside the silicon breast phantom
tissue. The resulting position profiles for a step response of $32$ mm are
shown in Figure 7 top where the labels A and B denote motions with and without
the phantom tissue, respectively. From these results we can see that the
joint’s motion is slowed down by the opposing forces that result from the
interaction with the phantom. Figure 7 middle depicts the motor’s positioning
performance when multiple (smaller) $10$ mm targets are given. Due to the
continuous air injection, the actuator will accumulate considerable kinetic
energy for “large” target positions (i.e. for greater than $50$ mm). In this
situation, it will exhibit substantial overshoot during the positioning motion
(therefore, it is recommended to command motions through small incremental
targets or ramp targets). Figure 7 bottom depicts the measured position errors
$e=q-q_{d}$ for several experiments conducted with the target located inside
the phantom tissue.

Figure 7: (Top) Positioning curves obtained without (A) and with (B) phantom;.
(Middle) Positioning curves for multiple $10$ mm step increments. (Bottom)
Position errors for various targets inside the phantom tissue. Figure 8: The
set-up to test the pressure-force relations.

The forces that the Tesla motor can generate were also tested. This experiment
is particularly important as we must determine whether the actuator has
sufficient power to penetrate human tissues and even tumours. To conduct these
experiments, we use the setup shown in Figure 8 which has a 6 axis
force/moment transducer (ATI Mini40) to measure the generated forces. The
obtained pressure-force relations are given in Table I; these data shows that
the coupling of the rotary actuator with the linear power screw can generate
forces larger that $10$ N. It has been reported in previous studies (see e.g.
[19, 20]) that an insertion force of around $2$ N is required to introduce a
biopsy needle into animal and human breast tissues. In [21], it is reported
that a maximum $4$ N axial force is required to penetrate a tumour. These data
suggests that the developed Tesla motor can provide enough force to perform a
biopsy procedure.

TABLE I: The measured pressure-force relations. Pressure (Bar) |  Force (N)
---|---
1.5 |  11.49
2.0 |  22.05
2.5 |  29.38
3.0 |  36.01

###  III-B In-Bore Experiments

The magnetic properties and compatibility of the actuator was tested with MRI
scanners from Time Medical Systems®. We first evaluated the performance of the
one degree-of-freedom needle driving mechanism using a $0.2$ T Mona scanner,
see Figure 9. In this experiment, the motor drives the coaxial needle into a
silicon phantom tissue while performing continuous MR imaging. Figure 10
(left) shows the MR image before the needle was introduced into the phantom;
Figure 10 (middle) and (right) show the MR image when the needle is inserted
at a distance of $13$ mm and $30.2$ mm, respectively, into silicon tissue.
These results show that the operation of the Tesla motor did not induce any
image artifacts during continuous imaging.

Figure 9: Needle driving mechanism inside the 0.2 T scanner® Figure 10: Needle
insertion under continuous MRI

The following experiments were all conducted with a high intensity system; we
used a $1.5$ T Venus® scanner from Time Medical, see Figure 11. In these
experiments, the Tesla motor was placed at the centre of the scanner’s
magnetic bore; the motor was operated while performing continuous MR imaging.
We evaluated the motor’s magnetic compatibility by comparing the computed MR
images, signal-to-noise ratio (SNR), homogeneity, and percent integral
uniformity (PIU). These comparison values were obtained from three cases: (1)
with only the phantom tissue placed inside the scanner; (2) with the Tesla
motor and the phantom placed inside the scanner; (3) with a piezoelectric
motor (model GTUSM60, from Glittering Orient Ultrasonic Motor Co®) and the
phantom placed inside the scanner. Image subtraction was performed to detect
geometric changes between the images obtained from cases (1) and (2), and
between the images from cases (1) and (3).

Figure 11: A 1-DOF linear joint inside the 1.5T MRI®

SNR can be used to show whether the imaging process is affected by the
operation of the actuator or its mechanical structure. We computed the SNR for
the above-mentioned three cases: the SNR obtained with only the phantom inside
the scanner was $454.0$, with both Tesla motor and phantom inside the scanner
was $440.0$, and with the piezo-motor and phantom inside the scanner was
$409.82$. These data shows that the SNR drops $3$% by operating the Tesla
actuator, whereas the piezo-motor makes it drop by almost $10$%. Magnetic
homogeneity (a value describing the uniformity of the magnetic field) was also
computed to evaluate the actuator. This value is important as it directly
related to the image quality and geometric artifacts. For this value, the
further the robot is placed away from the magnetic field centre, the less it
affects the field strength. In this experiment, both the Tesla motor and
piezoelectric motor were placed at the centre of the field centre, in order to
compare their properties. The computed homogeneity value with only the phantom
placed inside the scanner was $5.56$, with the Tesla motor and phantom was
$5.433$, and with the piezo-motor and phantom was $12.982$. By comparing these
results, it can be seen that the homogeneity value is not considerably
affected by the operation of the Tesla motor within the scanner. However, the
results show that the homogeneity value increases more than double after the
piezoelectric motor is introduced to the scanner.

The PIU values are useful to quantify geometric distortions of the MR image..
It is the percentage difference between the high and low signal values of the
water-only regions in the phantom. This PIU value was computed for the three
cases under consideration, however, no significant difference was detected
amongst the cases. Finally, we performed a qualitative evaluation of the
induced geometric distortions. This test was conducted by visually inspecting
the straightness and lengths of a test calibration device. Figure 12 (left)
shows the computed MR scan with the phantom only. Figure 12 (middle) and
(right) show the same phantom scans obtained with the Tesla motor and the
piezoelectric motor, respectively. By comparing these figures, it can be
clearly seen that the presence and operation of our Tesla motor does not cause
geometric distortions to the image. The relative distortions caused by these
two actuators can be appreciated by inspecting the subtraction images shown in
Figure 13. These results prove the feasibility of using our pneumatic rotary
actuator to conduct MRI-guided interventions with continuous imaging.

Figure 12: MRI scans of a calibration device placed along the: (left) phantom
tissue, (middle) phantom and Tesla motor, (right) phantom and piezoelectric
motor. Figure 13: Subtraction images of (left) Tesla motor, and (right)
piezoelectric motor

##  IV Conclusions

In this paper, we present a new pneumatic rotary motor that can be used as a
robot actuator for continuous MR imaging. The proposed mechanism is inspired
and further modified based on the Tesla turbine: it consists of a blade-less
turbine system that exploits the boundary layer effect of the fluid to
generate motion (this mechanism enables the generation of continuous rotations
in a controllable manner). To measure the motor’s position, we developed a new
rotary sensor that counts the pulses of an encoder using optical fibre.
Several experiments were conducted to evaluate the mechanical, control, and
magnetic compatibility properties of the system. The obtained results show
that our new actuator can be operated during continuous MRI scans without
affecting the scanner.

The motor’s design philosophy is to have all the required electronic devices
and signals outside the scanning room to prevent interference with MR imaging
process. Since the motor is driven by pneumatic power and its angular position
measured with fibre optics, only light and air signals need to be passed to
the MRI room through the waveguides (this feature effectively eliminates
crucial possible sources of noise and image artifacts). Compared to other
existing pneumatic motors for MRI, the proposed system does not rely on
discrete stepping motions; due to its particular mechanical properties, this
actuator has the potential to be used as a type of “servo-motor” for MRI. As
future work, we would like to improve the dynamic performance of the actuator.
Note that for the current system, we only use a simple PID controller for
regulating the position via flow control (this method is susceptible to large
overshoot for large targets). Also, we are currently planning the development
of a 3-DOF interventional robot that is completely driven by our new Tesla
motor.

TABLE II: Summary of the compatibility experiments with the $1.5$ T scanner MRI Indices |  Phantom only |  Tesla motor & phantom |  Piezo & phantom
---|---|---|---
SNR |  454.0 |  440.0 |  409.82
PIU (%) |  84.88 |  85.46 |  82.82
Homogeneity |  5.56 |  5.433 |  12.982
Geom. distortion |  |  Pass |  Fail

## References

  * [1] C. H. Lee, D. D. David, D. Kopans, P. Evans, B. Monsees, D. Monticciolo, B. R. James, L. Bassett, W. Berg, and S. Feig, “Breast cancer screening with imaging: recommendations from the society of breast imaging and the acr on the use of mammography, breast mri, breast ultrasound, and other technologies for the detection of clinically occult breast cancer,” _Journal of the American college of radiology_ , vol. 7, no. 1, p. 18–27, 2010.
  * [2] N. Tsekos, A. Khanicheh, E. Christoforou, and C. Mavroidis, “Magnetic resonance-compatible robotic and mechatronics systems for image-guided interventions and rehabilitation: a review study.” _Annual review of biomedical engineering_ , vol. 9, p. 351, 2007.
  * [3] H. Elhawary, Z. Tse, H. Tsz, A. Hamed, M. Rea, B. L. Davies, and M. U. Lamperth, “The case for mr-compatible robotics: a review of the state of the art,” _Int. J. Med. Rob. Compt. Ass. Surgery_ , vol. 4, no. 2, p. 105–113, 2008.
  * [4] _Needle guiding robot for MR-guided microwave thermotherapy of liver tumor using motorized remote-center-of-motion constraint_ , 2005.
  * [5] _fMRI compatible haptic interface actuated with traveling wave ultrasonic motor_ , vol. 3, 2005.
  * [6] K. Masamune, E. Kobayashi, Y. Masutani, M. Suzuki, T. Dohi, H. Iseki, and K. Takakura, “Development of an mri-compatible needle insertion manipulator for stereotactic neurosurgery,” _J. Image Guid. Surg._ , vol. 1, no. 4, pp. 242–248, 1995.
  * [7] P. C. Mozer, A. W. Partin, and D. Stoianovici, “Robotic image-guided needle interventions of the prostate,” _Reviews in Urology_ , vol. 11, no. 1, pp. 1–15, 2009.
  * [8] _An MR compatible robot technology_ , vol. 1, 2003.
  * [9] _A new Hydraulically/Pneumatically actuated MR-Compatible robot for MRI-Guided neurosurgery_ , 2008.
  * [10] G. S. Fischer, A. Krieger, I. Iordachita, C. Csoma, L. Whitcomb, and G. Fichtinger, “Mri compatibility of robot actuation techniques: A comparative study,” _Med Image Comput Comput Assist Interv._ , vol. 11, no. 2, pp. 509–517, 2008.
  * [11] E. Hempel, H. Fischer, L. Gumb, T. Hoehn, H. Krause, U. Voges, H. Breitwieser, B. Gutmann, J. Durke, M. Bock, and A. Melzer, “An mri-compatible surgical robot for precise radiological interventions.” _Computer aided surgery : official journal of the International Society for Computer Aided Surgery_ , vol. 8 4, pp. 180–91, 2003.
  * [12] D. Stoianovici, A. Patriciu, D. Petrisor, D. Mazilu, and L. Kavoussi, “A new type of motor: pneumatic step motor,” _IEEE/ASME Transactions On Mechatronics_ , vol. 12, no. 1, p. 98–106, 2007.
  * [13] M. Muntener, A. Patriciu, D. Petrisor, M. Sch’́ar, D. Ursu, D. Y. Song, and D. Stoianovici, “Transperineal prostate intervention: Robot for fully automated mr imaging—system description and proof of principle in a canine model,” _Radiology_ , vol. 247, no. 2, pp. 543–549, 2008.
  * [14] Y. Chen, K.-W. Kwok, and Z. T. H. Tse, “A mr-conditional high-torque pneumatic stepper motor for mri-guided and robot-assisted intervention,” _Annals of biomedical engineering_ , vol. 42, no. 9, p. 1823, 2014.
  * [15] V. Groenhuis and S. Stramigioli, “Laser-cutting pneumatics,” _IEEE/ASME transactions on mechatronics_ , vol. 21, no. 3, p. 1604–1611, 2016.
  * [16] S. Šarboh, “The patents of nikola tesla,” _World Patent Information_ , vol. 32, no. 4, p. 335–339, 2010.
  * [17] A. Guha and S. Sengupta, “The fluid dynamics of the rotating flow in a tesla disc turbine,” _European J. of Mechanics-B/Fluids_ , vol. 37, p. 112–123, 2013.
  * [18] B. P. Ho-Yan, “Tesla turbine for pico hydro applications,” _Guelph Engineering Journal_ , vol. 4, p. 1–8, 2011.
  * [19] _Experimental study on needle insertion force for breast_. Springer, 2013.
  * [20] Y. Kobayashi, M. Suzuki, A. Kato, M. Hatano, K. Konishi, M. Hashizume, and M. G. Fujie, “Enhanced targeting in breast tissue using a robotic tissue preloading-based needle insertion system,” _IEEE Transactions on Robotics_ , vol. 28, no. 3, p. 710–722, 2012.
  * [21] R. Kokes, K. Lister, R. Gullapalli, B. Zhang, A. MacMillan, H. Richard, and J. P. Desai, “Towards a teleoperated needle driver robot with haptic feedback for rfa of breast tumors under continuous mri,” _Medical image analysis_ , vol. 13, no. 3, p. 445–455, 2009.


Eun Jung Yeo*1††thanks: * Equal contribution., Kwanghee Choi*2, Sunhee Kim1,
Minhwa Chung1

# Speech Intelligibility Assessment of Dysarthric Speech
by using Goodness of Pronunciation with Uncertainty Quantification

###### Abstract

This paper proposes an improved Goodness of Pronunciation (GoP) that utilizes
Uncertainty Quantification (UQ) for automatic speech intelligibility
assessment for dysarthric speech. Current GoP methods rely heavily on neural
network-driven overconfident predictions, which is unsuitable for assessing
dysarthric speech due to its significant acoustic differences from healthy
speech. To alleviate the problem, UQ techniques were used on GoP by 1)
normalizing the phoneme prediction (entropy, margin, maxlogit, logit-margin)
and 2) modifying the scoring function (scaling, prior normalization). As a
result, prior-normalized maxlogit GoP achieves the best performance, with a
relative increase of 5.66%, 3.91%, and 23.65% compared to the baseline GoP for
English, Korean, and Tamil, respectively. Furthermore, phoneme analysis is
conducted to identify which phoneme scores significantly correlate with
intelligibility scores in each language.

Index Terms: dysarthric speech, speech intelligibility, automatic assessment,
goodness of pronunciation, uncertainty quantification

##  1 Introduction

Dysarthria is a motor speech disorder caused by weakness or paralysis of the
articulators [1]. People with dysarthria often suffer from degraded speech
intelligibility, repeated communication failures, and ultimately low quality
of life. Accordingly, dysarthric speech assessments regarding speech
intelligibility are conducted to check the patient's status and track the
effectiveness of treatments [2]. While the common way of dysarthric speech
assessment is perceptual evaluation, the method is often subjective and
laborious. Therefore, automatic speech assessment with objective and rapid
results can assist clinicians in diagnosis and treatment planning.

There are two main approaches to automatic assessment of dysarthric speech.
The first approach is to propose a list of hand-crafted features that are
expected to capture the characteristics of dysarthric speech. Explored feature
sets include voice quality features [3], prosody features [4], articulation or
pronunciation features [5, 6], and their combinations [7, 8]. This approach
has the benefit of having medical implications, as it provides a transparent
understanding of the features employed for automatic assessment. Nevertheless,
this approach has the drawback that features that could be valuable in the
assessment could be discarded during feature extraction. The second approach
involves leveraging the capabilities of neural networks (NNs), which can
achieve better results by using raw inputs. [9, 10]. However, due to the
black-box nature of NNs, the approach limits interpretability, which
clinicians often crave for.

Figure 1:  Example of GoP scores for each phone within an utterance. Higher
values indicate greater deviation from the correct pronunciation. GoP scores
allow easy identification of mispronounced phonemes.

Recent studies have attempted to integrate the benefits of both approaches, by
enforcing the neural networks to learn the intermediate labels used for
perceptual assessment, such as voice quality, articulation precision,
nasality, and prosody [11, 12]. Furthermore, certain studies focused on
decoding misarticulation characteristics, which are the prominent aspect of
dysarthric speech across languages [8] and a significant factor that
influences speech intelligibility [13]. For instance, the framework that
measures the level of phonetic impairment was proposed by utilizing the
activations of the hidden neuron [14, 15]. While the method could provide
overall phonetic characteristics of utterances, it is unable to provide
assessments at the level of individual phonemes, which can help clinicians to
pinpoint specific phonemes that require pronunciation training.

A common approach of phoneme-level speech assessment is to use the parallel NN
that employs parallel datasets. The NN was trained using the same set of
utterances recorded by both healthy speakers and patients to learn how to
distinguish whether each phone in the utterances was from healthy or
disordered speech [16, 17]. However, obtaining parallel datasets is a
challenging task, especially for disordered speech. Moreover, this approach
often constrains the analysis to pre-defined speech materials, which may not
capture the natural speech patterns utilized in everyday communication.

Figure 2: Overview of the improved GoP with UQ methods.

Another conventional approach of phoneme-level pronunciation evaluation is
Goodness of Pronunciation (GoP) [18]. GoP, which is defined as the degree of
similarity between produced and correct pronunciation of phonemes, has two
advantages in automatic speech assessments. First, it provides detailed
information on which phonemes are mispronounced and to what extent each
phoneme is atypical. Second, it does not necessitate a parallel dataset for
model training. While GoP is often applied to non-native (L2) speech
pronunciation assessment, some studies have also verified its potential use in
assessing speech disorders as well [19, 20].

With the development of NNs, variants of GoP which employ probabilities from
the state-of-the-art neural networks have been suggested [21, 22, 12].
However, using these probabilities without taking into account the modern NNs'
tendency towards overconfidence can result in inaccurate conclusions: NNs
often generate probabilities close to $1.0$ even when their predictions are
incorrect [23]. Since GoP relies heavily on probabilities, this can be
especially problematic. The issue is compounded when the model encounters out-
of-distribution (OOD) inputs, which are data that differ significantly from
the training data's distribution [24], such as dysarthric speech for healthy
speech. To alleviate such issues, UQ techniques, techniques to combat OOD
problem [23, 24], can be applied.

This paper proposes improved GoP for automatic speech intelligibility
assessment for dysarthric speech by employing Uncertainty Quantification (UQ)
methods in two ways: (1) normalizing the phoneme prediction and (2) modifying
the scoring function. As pathological speech greatly differs in acoustics from
healthy speech [25], dysarthric speech can be also understood as OOD input.
Therefore, we employ conventional UQ methods to improve GoP calculations for
dysarthric speech assessment. To assess the effectiveness of the improved GoP
with UQ techniques, three dysarthric datasets, namely, UASpeech English, QoLT
Korean, and SSNCE Tamil dataset, are utilized. To summarize, this paper
redefines the current versions of GoP from a UQ standpoint and evaluates the
effectiveness of UQ methods in improving GoPs.

##  2 Proposed approach

The study applies various conventional UQ methods to calculate GoP scores,
which are demonstrated in Figure 2. We release the source code of all the
experiments.111https://github.com/juice500ml/dysarthria-gop

###  2.1 Prerequisite: Goodness of Pronunciation (GoP)

In this subsection, we provide a succinct summary of the existing GoP-based
methods from the uncertainty quantification perspective. Starting from GMM-
GoP, Equation 1 presents the definition of the corresponding method: Given a
phone $p$ during frames $f\in F$ with frame-wise phone probability and its
logits as $P^{f}(p|f)$ and $L^{f}(p|f)$, and the total phone set as $Q$, GMM-
GoP [18] is defined as an averaged log probability across the phone duration,
$\mathbb{E}_{F}[\log P^{f}(p|f)]$:

$s_{\text{GMM-GoP}}(p)=\frac{1}{|F|}\sum_{f\in
F}\log\frac{e^{L^{f}(p|f)}}{\sum_{q\in Q}e^{L^{f}(q|f)}}.$ (1)

Averaging the log probabilities can be seen as a form of temporal ensembling
[26], which is a well-known UQ method, as it combines the predictions from
multiple frames into a single estimate. Further, directly using the
probability output is often used as a baseline for OOD [24].

Another popular baseline is NN-GoP [21], which improved GMM-GoP by leveraging
the development of deep neural networks and modifying the score function:

$\displaystyle\bar{P}(p|F)=\mathbb{E}_{F}[P^{f}(p|f)]=\frac{1}{|F|}\sum_{f\in
F}P^{f}(p|f),$ (2) $\displaystyle s_{\text{NN-
GoP}}(p)=\log\bar{P}(p|F)-\max_{q\in Q}\log\bar{P}(q|F).$ (3)

Finally, DNN-GoP [21] normalizes the phone probability with the phone prior
[27]:

$\displaystyle s_{\text{DNN-GoP}}(p)=\bar{P}(p|F)/P(p).$ (4)

###  2.2 Normalizing the phoneme predictions

There are two commonly used ways to calibrate the posterior prediction
$P(p|F)$ by modifying its logit $L(p|F)$. One is to normalize by removing the
influence of the prior $P(p)$ [27, 21] (Prior), and the other is to reduce the
peakiness by temperature scaling [23] Scale:

$\displaystyle L^{f}(p,f)$ $\displaystyle=L^{f}(p|f)-\log P(p),$ (5)
$\displaystyle L^{f}_{T}(p|f)$ $\displaystyle=L^{f}(p|f)/T,$ (6)

where $T$ is the hyperparameter and the modified predictions are the softmax
function's output of the corresponding logits.

Normalizing via the prior is the same with the idea of DNN-GoP, where it is
commonly applied to disentangle the training distribution of the phone
recognizer, where majority classes are often overconfident than minority
classes [27]. Temperature scaling is also commonly used as a baseline for UQ,
as it avoids the peaky distribution of posterior probabilities.

###  2.3 Modifying the scoring function

We first employ one of the most common methods to measure the data
uncertainty: Entropy $H$ and Margin $M$. Entropy measures the uncertainty
associated with a set of possible outcomes:

$\displaystyle s_{\text{H}}(p)=-\sum_{q\in Q}\bar{P}(q|F)\log\bar{P}(p|F).$
(7)

Specifically, the entropy represents the average amount of information needed
to specify which outcome was actually observed. Entropy does not require
ground truth labels, so it is often used when obtaining the labels is
expensive.

Margin refers to the difference between the true class and the highest class
probabilities for a given prediction:

$\displaystyle s_{\text{M}}(p)=\bar{P}(p|F)-\max_{q\in
Q-\\{p\\}}\bar{P}(q|F).$ (8)

Note that the equation is strikingly similar to that of NN-GoP except the
above definition excludes the true phone as $Q-\\{p\\}$.

On the other hand, the MaxLogit [28] and LogitMargin involves directly
utilizing the logits. Softmax function is often known to squash the useful
information inside logits, so that it can normalize the sum into one. Hence,
one can apply the idea of both GMM-GoP (directly using the probability) and
NN-GoP (using the Margin):

$\displaystyle s_{\text{MaxLogit}}(p)$ $\displaystyle=\frac{1}{|F|}\sum_{f\in
F}L^{f}(p|f)=\bar{L}(p|F),$ (9) $\displaystyle s_{\text{LogitMargin}}(p)$
$\displaystyle=\bar{L}(p|F)-\max_{q\in Q-\\{p\\}}\bar{L}(p|F).$ (10)

##  3 Experimental setting

###  3.1 Datasets

To train the acoustic model to learn the distribution of healthy phonemes, we
use the Common Phone dataset [29] and the L2-ARCTIC dataset [30]. To evaluate
the efficacy of our proposed approach, three dysarthric datasets are utilized:
UASpeech English dataset [31], QoLT Korean dataset [32], and SSNCE Tamil
dataset [33]. All three datasets contain dysarthric speech from speakers
suffering from Cerebral Palsy. We focus the analysis on sentences from QoLT
and SSNCE dysarthric datasets, since the Common Phone and L2-ARCTIC datasets
solely consist of sentences. Word materials are analyzed for the UASpeech
dataset, since the dataset contains words only.

####  3.1.1 Common Phone dataset and L2-ARCTIC dataset

The acoustic model is trained on healthy speech using the Common Phone dataset
and the L2-ARCTIC dataset, which were selected for their extensive phoneme
coverage and phonetic annotations. These datasets are expected to cover most
of the phonemes used in English, Korean, and Tamil. Common Phone dataset [29]
is a gender-balanced, multilingual corpus with six languages. Comprised of
more than 11,000 speakers, the dataset includes around 116 hours of speech.
L2-ARCTIC dataset [30] is a speech corpus often used for detecting
mispronunciations in non-native English speakers. It includes recordings from
24 speakers with a balanced distribution of gender and first language,
representing six different countries. On average, each speaker has around 67.7
minutes of speech, which has a total duration of approximately 27.1 hours.

####  3.1.2 UASpeech English dysarthric datasat

UASpeech dataset [31] is a publicly-available English dysarthric speech
dataset, which contains 15 dysarthria speakers (11 males, 4 females) and 13
aged-matched healthy speakers (9 males, 4 females). Speakers were classified
based on the scores on the Frenchay Dysarthria Assessment (FDA) [34]: 5 mild
speakers (score 1), 3 moderate-to-severe speakers (score 2), 3 moderate-to-
severe speakers (score 3), and 4 severe speakers (score 4). Montreal Forced
Aligner (MFA) [35] is employed to extract phoneme-level alignments.

####  3.1.3 QoLT Korean dysarthric dataset

Quality of Life Technology (QoLT) dataset [32] is a privately held dataset of
Korean dysarthric speech. The corpus consists of 70 dysarthric speakers (45
males, 25 females) and 10 healthy speakers (5 males, 5 females). Each speaker
recorded five phonetically balanced sentences twice. Five speech pathologists
were asked to determine the intelligibility levels of the speakers on a
5-point Likert scale. With a score of 0 considered healthy, the dataset holds
25 mild (score 1), 26 mild-to-moderate (score 2), 12 moderate-to-severe (score
3), and 7 severe (score 4) intelligibility level speakers. Accordingly, 100
healthy utterances and 700 dysarthric utterances are used for the experiment.
After using MFA to align the phonemes, two speech pathologists further fixed
the automated alignment for better quality.

####  3.1.4 SSNCE Tamil dysarthric dataset

SSNCE dataset [33] is a Tamil dysarthric speech corpus available by request.
The dataset includes recordings from 20 dysarthric speakers (13 males and 7
females) and 10 healthy speakers (5 males and 5 females). The dataset groups
dysarthric speakers based on their speech intelligibility scores, which were
marked by two speech pathologists on a 7-point Likert scale. A score of 0
considered healthy, score 1 and 2 are grouped into mild (score 1), score 3 and
4 into moderate (score 2), and score 5 and 6 into severe (score 3). There were
different numbers of speakers in each score category: 7 with mild, 10 with
moderate, and 3 with severe. For the experiment, we used a total of 5,200
utterances from the dysarthric speakers and 2,600 utterances from the healthy
speakers, with 260 unique sentences recorded from each speaker. For forced
alignments, we use the time-aligned phonetic transcriptions provided by the
dataset.

###  3.2 Experimental details

In this study, we evaluated GoP performance by following the approach of the
previous study [20]. Concretely, rather than evaluating the models based on
their accuracy in mispronunciation detection, our objective was to calculate
the average GoP score for each utterance and compare their correlation with
the intelligibility scores.

####  3.2.1 Phoneme Prediction

To fairly compare the performances between various GoP scoring functions, we
extract the posterior probabilities from the common cross-lingual Wav2Vec 2.0
XLS-R model [36] instead of using the acoustic model from Kaldi, following
recent literature [12]. We slightly modify the architecture by attaching the
linear phone prediction head to the convolutional layer, not the transformer
layer, to avoid extensive computational overhead and preserve the phonetic
characteristics in convolutional features [37]. Also, the loss function is
simplified by removing the adaptive pooling, where we observed that the final
performance difference was negligible. AdamW optimizer [38] is used with the
default learning rate of $0.001$ for three epochs. As we only trained the
linear prediction head, the final performance was not sensitive to other
hyperparameters. Refer to [12] and our source code1 for more details.

####  3.2.2 Baselines

We conducted three baseline experiments: GMM-GoP [18], NN-GoP [21], and DNN-
GoP. We compare the baselines with the UQ methods introduced in Section 2.3
and Section 2.2 by using the same phoneme probabilities. As we aim to see the
correlations between GoP scores (continuous) and intelligibility scores
(ordinal), we utilize the Kendall Rank Coefficient $\tau$ to compare the
performances. Kendall's $\tau$ measures the strength of the relationships,
with a higher absolute coefficient indicating higher correlations between the
two variables.

Table 1:  Kendall's rank coefficient between GoP & intelligibility severity
levels. A higher absolute value indicates a stronger correlation between the
two variables.

Method | Norm. | Scoring Func. | English | Korean | Tamil
---|---|---|---|---|---
Baseline | None | GMM [18, 39] | -0.2049 | -0.5237 | -0.3571
None | NN [21] | -0.1536 | -0.4687 | -0.4003
Prior | DNN-GoP [21] | -0.1836 | -0.4237 | -0.4681
Proposed | None | Entropy | -0.1831 | -0.2643 | -0.3251
Margin | -0.1628 | -0.4434 | -0.4445
MaxLogit | -0.2164 | -0.5440 | -0.5786
LogitMargin | -0.1732 | -0.4753 | -0.5158
Scale | Entropy | -0.1755 | -0.1974 | -0.2263
Margin | -0.1260 | -0.4444 | -0.4210
MaxLogit | -0.2164 | -0.5440 | -0.5786
LogitMargin | -0.1732 | -0.4753 | -0.5158
Prior | Entropy | -0.1833 | -0.2645 | -0.3254
Margin | -0.1630 | -0.4432 | -0.4447
MaxLogit | -0.2165 | -0.5442 | -0.5788
LogitMargin | -0.1733 | -0.4753 | -0.5160

##  4 Experimental results

###  4.1 Correlation between GoPs and intelligilbity scores

Table 1 demonstrates the performances of both baseline and proposed
experiments, with the best performance indicated in bold. GoP with prior
normalized MaxLogit performed the best on all the languages among the
baselines and the UQ methods, achieving $-21.65\%$, $-54.42\%$, $-57.88\%$
correlation, for English, Korean, and Tamil, respectively.

The results of the baseline experiments show that GMM-GoP has the highest
correlation for English and Korean at $-20.49\%$ and $-52.37\%$, respectively,
while DNN-GoP performs best for Tamil with a correlation of $-46.81\%$. For
the proposed experiments, GoP without normalization generally shows lower
performance than the baseline, except for MaxLogit-based GoP. Additionally,
while scaling normalization has minimal impact, prior normalization has a
positive effect on GoP performance for all languages. Furthermore, when
entropy-based, probability-based (Margin), and logit-based (MaxLogit,
LogitMargin) GoP variants are compared, the logit-based GoPs show the highest
correlations to the intelligibility scores. Additionally, performances on
English are notably lower than that of Tamil and Korean. We suspect that
automatically generated alignment causes the degradation to occur [40], for
the severe cases where alignment becomes much more challenging. We aim to
mitigate this issue in our future work.

###  4.2 Analysis on phonemes

Figure 3 illustrates the GoP distribution between two Korean phonemes /i/ and
/m/. While the distribution of /i/ differs significantly, the distribution of
/m/ is similar across all severity levels. This finding suggests that certain
phonemes have more impact power for severity levels based on speech
intelligibility, which is consistent with previous findings [17].

(a) Korean phoneme /i/. (b) Korean phoneme /m/.

Figure 3:  Kendall's $\tau$ distributions for two phonemes by severity.
0:healthy, 1:mild, 2:mild-to-mod., 3:mod.-to-sev., 4:severe.

Identifying which phoneme pronunciation scores highly correlate to speech
intelligibility can be useful in the clinical scenario, such as diagnosis and
treatment. For example, as demonstrated in Figure 1, one can pinpoint the
mispronounced phonemes within a single utterance.

Further, we conduct a quantitative analysis on which phoneme scores highly
correlate to speech intelligibility by languages. Kendall's $\tau$ is
calculated for each phoneme between our best-performing Prior+MaxLogit GoP
score and the intelligibility scores. The top-5 phonemes based on correlation
are as follows- English: /a/,//,/a/,/z/,//; Korean:/i/,/s/,/n/,/a/,//;
Tamil://,/h/,//,/z/,/a/. In summary, fricative sounds (/s/,//,//,/z/) strongly
correlates to speech intelligibility across languages, consistent with the
previous results [41]. Affricates (//,//) and diphthongs (/a/,/a/) were shared
as the top-5 phoneme list for English and Tamil. This can be explained by the
complexity in the articulation of affricates and diphthongs leading to
difficulties in correct pronunciation for speakers with lower speech
intelligibility. On the other hand, Korean showed higher correlations for
nasal (/n/) and monophthongs (/a/,/i/,//). This may be again related to the
movement of the articulators, such as the tongue, velum, and jaw. We
additionally provide the correlation scores of all the phonemes in our
repository.1

##  5 Conclusion

This paper proposes an improved GoP for dysarthria speech intelligibility
assessment by using UQ methods. Expected to alleviate the problem of modern
NN's overconfidence, especially for disordered speech, tested UQ methods
include (1) normalization of phoneme prediction and (2) modification of the
scoring function. The experiments were carried out on dysarthric speech
datasets in English, Korean, and Tamil. According to the experimental results,
the prior normalized MaxLogit GoP shows the best performance, outperforming
both the traditional GoPs and other proposed GoP variants. Furthermore, to
verify the usefulness of our proposed method, an analysis of which phoneme
pronunciation scores highly correlate to speech intelligibility is conducted.

##  6 Acknowledgements

This work was supported by Institute of Information & communications
Technology Planning & Evaluation (IITP) grant funded by the Korea government
(MSIT) (No.2022-0-00223, Development of digital therapeutics to improve
communication ability of autism spectrum disorder patients).

## References

  * [1] F. L. Darley, J. R. Brown, and N. P. Goldstein, ``Dysarthria in multiple sclerosis,'' _Journal of Speech and Hearing research_ , vol. 15, no. 2, pp. 229–245, 1972.
  * [2] R. D. Kent, G. Weismer, J. F. Kent, and J. C. Rosenbek, ``Toward phonetic intelligibility testing in dysarthria,'' _Journal of Speech and Hearing Disorders_ , vol. 54, no. 4, pp. 482–499, 1989.
  * [3] N. Narendra and P. Alku, ``Automatic assessment of intelligibility in speakers with dysarthria from coded telephone speech using glottal features,'' _Computer Speech & Language_, vol. 65, p. 101117, 2021.
  * [4] A. Hernandez, S. Kim, and M. Chung, ``Prosody-based measures for automatic severity assessment of dysarthric speech,'' _Applied Sciences_ , vol. 10, no. 19, p. 6999, 2020.
  * [5] M. J. Kim and H. Kim, ``Automatic assessment of dysarthric speech intelligibility based on selected phonetic quality features,'' in _ICCHP_. Springer, 2012, pp. 447–450.
  * [6] Y. Liu, N. Penttilä, T. Ihalainen, J. Lintula, R. Convey, and O. Räsänen, ``Language-independent approach for automatic computation of vowel articulation features in dysarthric speech assessment,'' _TASLP_ , vol. 29, pp. 2228–2243, 2021.
  * [7] J. C. Vásquez-Correa, J. Orozco-Arroyave, T. Bocklet, and E. Nöth, ``Towards an automatic evaluation of the dysarthria level of patients with parkinson's disease,'' _Journal of communication disorders_ , vol. 76, pp. 21–36, 2018.
  * [8] E. J. Yeo, S. Kim, and M. Chung, ``Multilingual analysis of intelligibility classification using english, korean, and tamil dysarthric speech datasets,'' in _Oriental-COCOSDA_ , 2022, pp. 1–6.
  * [9] E. J. Yeo, K. Choi, S. Kim, and M. Chung, ``Automatic severity assessment of dysarthric speech by using self-supervised model with multi-task learning,'' in _ICASSP_ , 2023.
  * [10] A. A. Joshy and R. Rajan, ``Dysarthria severity classification using multi-head attention and multi-task learning,'' _Speech Communication_ , vol. 147, pp. 1–11, 2023.
  * [11] M. Tu, V. Berisha, and J. Liss, ``Interpretable objective assessment of dysarthric speech based on deep neural networks.'' in _Interspeech_ , 2017, pp. 1849–1853.
  * [12] X. Xu, Y. Kang, S. Cao, B. Lin, and L. Ma, ``Explore wav2vec 2.0 for mispronunciation detection.'' in _Interspeech_ , 2021, pp. 4428–4432.
  * [13] M. S. De Bodt, M. E. H.-D. Huici, and P. H. Van De Heyning, ``Intelligibility as a linear combination of dimensions in dysarthric speech,'' _Journal of communication disorders_ , vol. 35, no. 3, pp. 283–292, 2002.
  * [14] S. Abderrazek, C. Fredouille, A. Ghio, M. Lalain, C. Meunier, and V. Woisard, ``Interpreting deep representations of phonetic features via neuro-based concept detector: Application to speech disorders due to head and neck cancer,'' _TASLP_ , vol. 31, pp. 200–214, 2022.
  * [15] ——, ``Validation of the neuro-concept detector framework for the characterization of speech disorders: A comparative study including dysarthria and dysphonia,'' in _Interspeech_ , 2022.
  * [16] G. F. Miller, J. C. Vásquez-Correa, and E. Nöth, ``Assessing the dysarthria level of parkinson’s disease patients with gmm-ubm supervectors using phonological posteriors and diadochokinetic exercises,'' in _TSD_ , 2020, pp. 356–365.
  * [17] S. Quintas, J. Mauclair, V. Woisard, and J. Pinquier, ``Automatic assessment of speech intelligibility using consonant similarity for head and neck cancer,'' in _Interspeech_ , 2022.
  * [18] S. M. Witt and S. J. Young, ``Phone-level pronunciation scoring and assessment for interactive language learning,'' _Speech communication_ , vol. 30, no. 2-3, pp. 95–108, 2000.
  * [19] T. Pellegrini, L. Fontan, J. Mauclair, J. Farinas, and M. Robert, ``The goodness of pronunciation algorithm applied to disordered speech,'' in _Fifteenth Annual Conference of the International Speech Communication Association_ , 2014.
  * [20] L. Fontan, T. Pellegrini, J. Olcoz, and A. Abad, ``Predicting disordered speech comprehensibility from goodness of pronunciation scores,'' in _SLPAT@Interspeech_ , 2015.
  * [21] W. Hu, Y. Qian, F. K. Soong, and Y. Wang, ``Improved mispronunciation detection with deep neural network trained acoustic models and transfer learning based logistic regression classifiers,'' _Speech Communication_ , vol. 67, pp. 154–166, 2015.
  * [22] S. Cheng, Z. Liu, L. Li, Z. Tang, D. Wang, and T. F. Zheng, ``Asr-free pronunciation assessment,'' in _Interspeech_ , 2020.
  * [23] C. Guo, G. Pleiss, Y. Sun, and K. Q. Weinberger, ``On calibration of modern neural networks,'' in _ICML_ , 2017, pp. 1321–1330.
  * [24] D. Hendrycks and K. Gimpel, ``A baseline for detecting misclassified and out-of-distribution examples in neural networks,'' in _ICLR_ , 2017.
  * [25] J. Wilson, Bronagh Blaney, ``Acoustic variability in dysarthria and computer speech recognition,'' _Clinical Linguistics & Phonetics_, vol. 14, no. 4, pp. 307–327, 2000.
  * [26] S. Laine and T. Aila, ``Temporal ensembling for semi-supervised learning,'' in _ICLR_ , 2017.
  * [27] Y. Hong, S. Han, K. Choi, S. Seo, B. Kim, and B. Chang, ``Disentangling label distribution for long-tailed visual recognition,'' in _CVPR_ , 2021, pp. 6626–6636.
  * [28] D. Hendrycks, S. Basart, M. Mazeika, A. Zou, J. Kwon, M. Mostajabi, J. Steinhardt, and D. Song, ``Scaling out-of-distribution detection for real-world settings,'' in _ICML_. PMLR, 2022, pp. 8759–8773.
  * [29] P. Klumpp, T. Arias-Vergara, P. A. Pérez-Toro, E. Nöth, and J. R. Orozco-Arroyave, ``Common phone: A multilingual dataset for robust acoustic modelling,'' _arXiv preprint arXiv:2201.05912_ , 2022.
  * [30] G. Zhao, S. Sonsaat, A. Silpachai, I. Lucic, E. Chukharev-Hudilainen, J. Levis, and R. Gutierrez-Osuna, ``L2-arctic: A non-native english speech corpus.'' in _Interspeech_ , 2018.
  * [31] H. Kim, M. Hasegawa-Johnson, A. Perlman, J. Gunderson, T. S. Huang, K. Watkin, and S. Frame, ``Dysarthric speech database for universal access research,'' in _Ninth Annual Conference of the International Speech Communication Association_ , 2008.
  * [32] D.-L. Choi, B.-W. Kim, Y.-W. Kim, Y.-J. Lee, Y. Um, and M. Chung, ``Dysarthric speech database for development of qolt software technology.'' in _LREC_ , 2012, pp. 3378–3381.
  * [33] M. TA, T. Nagarajan, and P. Vijayalakshmi, ``Dysarthric speech corpus in tamil for rehabilitation research,'' in _Region TENCON_. IEEE, 2016, pp. 2610–2613.
  * [34] P. Enderby, ``Frenchay dysarthria assessment,'' _British Journal of Disorders of Communication_ , 1980.
  * [35] M. McAuliffe, M. Socolof, S. Mihuc, M. Wagner, and M. Sonderegger, ``Montreal forced aligner: Trainable text-speech alignment using kaldi.'' in _Interspeech_ , 2017, pp. 498–502.
  * [36] A. Babu, C. Wang, A. Tjandra, K. Lakhotia, Q. Xu, N. Goyal, K. Singh, P. von Platen, Y. Saraf, J. Pino, A. Baevski, A. Conneau, and M. Auli, ``XLS-R: self-supervised cross-lingual speech representation learning at scale,'' in _Interspeech_ , 2022.
  * [37] K. Choi and E. J. Yeo, ``Opening the black box of wav2vec feature encoder,'' _arXiv preprint arXiv:2210.15386_ , 2022.
  * [38] I. Loshchilov and F. Hutter, ``Decoupled weight decay regularization,'' in _ICLR_ , 2019.
  * [39] J. Zhang, ``Gmm-based gop (goodness of pronunciation) using kaldi.'' https://github.com/jimbozhang/kaldi-gop, 2020.
  * [40] V. C. Mathad, T. J. Mahr, N. Scherer, K. Chapman, K. C. Hustad, J. Liss, and V. Berisha, ``The impact of forced-alignment errors on automatic pronunciation evaluation.'' in _Interspeech_ , 2021, pp. 1922–1926.
  * [41] A. Hernandez, H.-y. Lee, and M. Chung, ``Acoustic analysis of fricatives in dysarthric speakers with cerebral palsy,'' _Phonetics and Speech Sciences_ , vol. 11, no. 3, pp. 23–29, 2019.