# Mechanism Design Optimization through CAD-Based Bayesian Optimization and
Quantified Constraints

Abdelmajid Ben Yahya  Santiago Ramos Garces  Nick Van Oosterwyck  Annie Cuyt
Stijn Derammelaere

###### Abstract

This study addresses the challenge of mechanism design optimization,
particularly focusing on the energy efficiency and design space of
reciprocating mechanisms. The research question centers on how to effectively
utilize Computer-Aided Design (CAD) simulations alongside Bayesian
Optimization (BO) and a constrained design space to streamline the design
optimization process, overcoming the limitations of traditional kinematic and
dynamic analysis methods. The objective was to investigate and develop a novel
optimization framework that integrates CAD-based simulations with a BO
approach. To achieve this, the study employed a methodological approach. At
first, the feasibility of a chosen mechanism design is evaluated through a
sequence of CAD-motion simulations to quantify the (in)feasibility of this
design. When this design appears to be feasible a CAD-based design evaluation
method is started, in which the objective value is extracted by a sequence of
CAD-motion simulations. In this paper, we advocate the use of non-parametric
Gaussian processes to build a surrogate model of the objective function and
the feasible design space constrained by static and dynamic constraints. The
main research results demonstrated that the proposed CAD-based Bayesian
Optimization framework could effectively identify optimal design parameters
that minimize the root mean square (RMS) torque while adhering to specified
static and dynamic constraints. This optimization approach significantly
reduces the complexity associated with analytic methods, making it scalable to
more complex mechanisms and implementable by machine builders. In conclusion,
the study successfully developed a novel optimization framework that leverages
CAD-based simulations and Bayesian Optimization to streamline the design
process of mechanisms. The results of an emergency ventilator case study with
three design parameters show a reduction of the RMS torque with 71% after 255
CAD-based design evaluations. Moreover, the results illustrate the
effectiveness of incorporating constraints into the design optimization
process and the potential of this approach for achieving global optimal design
in a computationally efficient manner.

###### keywords:

Dimensional synthesis , Mechanical systems , Motion control , Bayesian
optimization

††journal: Mechatronics

[1]organization=Department of Electromechanics, CoSys-Lab, University of
Antwerp,city=Antwerp, postcode=2020, country=Belgium

[2]organization=AnSyMo/Cosys, Flanders Make, the strategic research centre for
the manufacturing industry, country=Belgium

[3]organization=Department of Mathematics and Computer Science, University of
Antwerp,city=Antwerp, postcode=2020, country=Belgium

[4]organization=Department of Computing Science and Mathematics, University of
Stirling,city=Stirling, postcode=FK9 4LA, country=Scotland

##  1 Introduction

Mechatronic systems account for about 70 % of industrial energy consumption,
contributing to 40-45 % of global energy usage [1]. This underscores the need
for energy-saving strategies in industrial machinery, particularly through
reducing losses in electric motors, which, as [2] notes, are predominantly
stator losses (55-60 %). This paper presents an optimization method to
decrease energy consumption in industrial mechanisms by optimizing link
lengths $|OA|$, $|AB|$, and $|BC|$, as illustrated in Figure 1.

The paper demonstrates the proposed method’s real-world applicability and
potential through a use case, emphasizing that only the CAD model of the
mechanism is needed. The use case involves an emergency ventilator, shown in
Figure 1, developed by a non-profit organization [3] during the initial wave
of the COVID-19 pandemic. The mechanism depicted in Figure 1 operates by
pressing an indentor into a bag, facilitating airflow towards the patient.
Figure 1 showcases the CAD model of the emergency ventilator, highlighting how
the red beam, attached to the indentor (the end-effector), moves by rotating
the input link OA around point O over an angle $\theta(t)$, which is driven by
an electric motor. This ventilator was specifically designed for low- and
middle-income countries, where consistent access to electricity is not
guaranteed. The ventilator’s design, particularly the link lengths $|OA|$,
$|AB|$, and $|BC|$, is optimized for minimal energy consumption to facilitate
the use of batteries.

Figure 1: The use case within this research is an emergency ventilator
developed by Gear Up Medical VZW [3]. Figure 2: The mechanism shown in its
ending $\delta_{e}$ (left) and starting position $\delta_{i}$ (right) of its
point-to-point movement.

The ventilator’s primary function, compressing a bag via motor-driven movement
$\theta(t)$, is detailed in Figure 2. The angle of $\delta_{i}$ and
$\delta_{e}$ determine the mechanism’s motion requirement, which represents
the starting and ending positions of the indentor. Altering the link lengths
$|OA|$, $|AB|$, and $|BC|$, while adhering to the motion requirements, impacts
the motor’s torque profiles $T_{m}(t)$, as shown in Figure 3. These link
lengths $|OA|$, $|AB|$, and $|BC|$ are thus key design parameters (DPs) in the
optimization process. Prior research [4] has shown that such design
optimization significantly reduces electric motor energy consumption by
minimizing the Root Mean Square (RMS) motor torque $T_{RMS}$, which in turn
reduces stator losses in the motor [5]. The significance of machine
components’ geometry in energy efficiency has gained increasing recognition in
recent studies [6, 7, 8].

Figure 3: The emergency ventilator performs the same task, being the end-
effector movement $\delta(t)$ (right), for different combinations of design
parameters (DPs) $|OA|$, $|AB|$, and $|BC|$ (left). Resulting in a difference
in the motor torque profile $T_{m}(t)$ (right).

This paper focuses on dimensional synthesis, specifically targeting the
optimization of linkage dimensions ($|OA|$, $|AB|$, and $|BC|$) for predefined
end-effector movements ($\delta_{i}$ to $\delta_{e}$), as discussed in [9].
Dimensional synthesis, especially for determining precise end-effector
movements in mechanisms like slider-crank and four-bar mechanisms, is
extensively studied [10, 11, 12, 13]. Traditional methods involve analytic
kinematic derivations, with studies like [8, 14] deriving dynamics for simple
mechanisms and seeking optimal dimensions to minimize torque fluctuations.
Methods for deriving the dynamics of mechanisms, such as Lagrangian dynamics
and the principle of virtual work, are utilized for sensitivity analysis of
dynamical systems, as discussed in [15, 16, 17]. Furthermore, principles
including virtual work, vector mechanics, and Lami’s theorem [18], along with
Hamilton’s principle and Lagrange multipliers [19, 20, 21], are employed in
the dynamics derivation of toggle clamping mechanisms. [22] demonstrates the
use of analytic dynamics derivation in conjunction with genetic algorithms to
optimize toggle clamping mechanism designs for enhanced mold clamping forces.

However, these analytic methods are complex, time-consuming, and prone to
errors [23]. Their complexity increases with the mechanism’s complexity and
requires detailed component information, such as the center of gravity and
mass, which change with design modifications. For example, [24] demonstrates
the complexity in deriving dynamics for a mono-actuated industrial planar
mechanism using the method of kinetic energy. This complexity limits the
practicality of design optimization for machine builders and restricts the
scalability of these dynamic equations to different or more complex
mechanisms.

Recent research [25, 26] has shifted towards using CAD models to ascertain the
dynamics of mechanisms, rather than relying on analytical derivation of the
system’s dynamics. This paper introduces a novel Computer-Aided Design
(CAD)-based method for optimizing the design of industrial mechanisms.
Computer-Aided Design (CAD) software, a fundamental tool for mechanical
engineers [27], is leveraged for conceptualizing mechanisms, highlighting the
proposed method’s industrial relevance. Unlike studies focused on Finite
Element Modelling (FEM) like [28], which typically require a single CAD
simulation per evaluation, this study emphasizes sequential CAD motion
simulations.

This study adopts a CAD-based approach for simulating the dynamics of
mechanisms, incorporating key elements like volume, mass, friction, damping,
and joints. It focuses on motion simulations to evaluate various design
parameter configurations $|OA|$, $|AB|$, and $|BC|$ (as shown in Figure 3).
This method bypasses the intricate kinematic and dynamic analyses that often
challenge machine builders. In a prior study by the authors [4], the
optimization in CAD employs heuristic and gradient-based optimizers, common in
state-of-the-art techniques [13]. However, these algorithms do not guarantee
finding the global optimum. Addressing a constrained-global optimization
problem effectively requires defining the feasible design space. Researchers
like [8, 14, 15] often do not specify the design space, potentially leading to
infeasible designs or defects in mechanism synthesis, as highlighted in [10].
In contrast, our earlier study [29] established the feasible design space
using kinematic analysis to facilitate the search for the global optimum.

This paper proposes a CAD-based methodology to evaluate the feasibility of
design parameter combinations ($|OA|$, $|AB|$, and $|BC|$), eliminating the
need for any analytic analysis. The CAD-based feasibility evaluation allows
for the modeling of the feasible design space without necessitating a detailed
analysis of the mechanism. This method can handle increased mechanism
complexity by utilizing CAD simulations and avoiding analytical analysis,
enhancing its applicability.

Incorporating CAD simulation into the optimization loop, as done in this
study, inevitably increases the computational time required for solving the
design problem. To address this, Bayesian optimization is employed. This
stochastic process involves fitting an objective function or a surrogate model
to the collected data. A critical aspect of using response surfaces for global
optimization, as highlighted by [30], is the balance between exploiting the
area around the currently identified minimum objective value and exploring
other areas where the fitting error might be higher. Bayesian optimization can
efficiently navigate towards the global optimum. Moreover, Bayesian
optimization is particularly valuable as it offers a more comprehensive
understanding of the optimal design, factoring in potential uncertainties.
This approach allows for a more informed conclusion, suggesting that the
identified optimum is likely the expected global optimum.

Bayesian optimization has seen significant advancements in recent years.
Traditionally, optimization problems involving computationally intensive
models or lacking gradient information have often relied on heuristic
optimizers like evolutionary algorithms. These algorithms primarily depend on
function evaluations, as discussed in [31]. However, a limitation of these
heuristic algorithms is their inability to confirm whether the identified
minimum is global, and they typically require a large number of function
evaluations. The review by [32] illustrates that recent developments in
Bayesian optimization have resulted in a variety of new techniques. For
instance, [33] employed Bayesian optimization to refine the shape of a turbine
for enhanced power output, utilizing Computational Fluid Dynamics (CFD)
software to gather data for Gaussian processes. This approach was chosen
because gradient-based algorithms often become trapped in local minima, and
evolutionary algorithms demand numerous computationally expensive function
evaluations to approach a minimum. Bayesian optimization, with its ability to
efficiently navigate the design space and provide insights into the global
optimality of solutions, presents a more effective alternative for complex
optimization tasks.

The methodology presented in this paper effectively harnesses the capabilities
of CAD tools and Bayesian optimization to establish a more versatile and
efficient framework for optimizing the design of mechanisms, particularly
complex ones. This approach is especially beneficial for achieving energy-
efficient designs due to several key factors:

  * 1.

Avoiding Analytics: The use of only a CAD model for mechanism design
optimization greatly simplifies the process by removing the necessity to model
the mechanism’s kinematics or dynamics, which are typically complex and error-
prone.

  * 2.

CAD-Based Constraint Quantification: This paper introduces a new method for
assessing the feasibility of designs through CAD simulations, improving the
accuracy and reliability of the design process. The CAD simulation produces a
measurable value that reflects the feasibility or infeasibility of a design.
This quantification enables the use of a surrogate model to estimate the
constraint design space effectively.

  * 3.

Global Optimum Search with Bayesian Optimization: The adoption of Bayesian
optimization for the search of the global optimum is a strategic choice. This
stochastic algorithm identifies the optimum design and provides valuable
insights into the uncertainty associated with this optimum.

This paper introduces a novel approach in design optimization, applying
Bayesian optimization for energy-efficient mechanism design. The methodology
involves three key steps: enhancing the objective function’s sampling process
based on [4] for better robustness and efficiency (section 2); a CAD-based
method to assess the feasibility of design parameters ($|OA|$, $|AB|$, $|BC|$)
(section 3); and using Bayesian optimization to determine the global optimum,
shifting from traditional methods mentioned in [4] (section 4). The
effectiveness of these methods is demonstrated in section 5 through the design
optimization of an emergency ventilator. The paper concludes in section 6,
summarizing the findings.

##  2 CAD-Based Design Evaluation

This section of the paper focuses on the methodology that calculates the RMS
motor torque $T_{RMS}$ through a series of CAD simulations. Multiple
simulations are necessary as changes in these design parameters affect the
motor’s start and end angles $\theta(t)$, given the pre-defined end-effector
movement $\delta_{i}$ to $\delta_{e}$, as can be seen in Figure 3. The motion
requirement of the mechanism during operation is defined by setting the end-
effector to two specific angles: $\delta_{e}$, where it positions to touch the
bag, and $\delta_{i}$, corresponding to the position for maximal compression
of the bag. A kinematic transformation then determines the required motion
profile $\theta(t)$. Subsequently, this profile is used in the dynamic
analysis of the mechanism to retrieve the required motor torque $T_{m}(t)$ and
corresponding $T_{RMS}$.

Figure 4: Three essential motion simulations and measurements are required to
determine the driving torque for a specific design.

The kinematic transformation mentioned is executed through kinematic
simulations 1a and 1b, followed by a dynamic analysis conducted in the dynamic
simulation, as depicted in Figure 4. Crucially, assessing the feasibility of
the design parameter combination ($|OA|$, $|AB|$, and $|BC|$) is essential
before initiating these simulations. The methodology for assessing the
feasibility of design parameter combinations is comprehensively described in
section 3.

The forthcoming subsections, 2.1 and 2.2, are dedicated to providing a
detailed description of the kinematic transformation and dynamic analysis.

###  2.1 Kinematic Transformation

The initial motion simulation is designed to conduct kinematic calculations,
translating the predefined end-effector movement from $\delta_{i}$ to
$\delta_{e}$ into the required motor profile $\theta$. This process is divided
into two simulations: ”kinematic simulation 1a” and ”kinematic simulation 1b,”
as shown in Figure 4. Each simulation begins with positioning the end-effector
at the midpoint of its movement ($\delta_{mid}$). From there, one simulation
moves the end-effector (driven from point C) to its end position
($\delta_{e}$), and the other to its starting position ($\delta_{i}$).
Splitting this kinematic transformation into two simulations tackles issues
where specific designs could erroneously appear unsolvable when transitioning
from $\delta_{e}$ to $\delta_{i}$. The issue is not with the design parameters
($|OA|$, $|AB|$, and $|BC|$) themselves but with the setup of the motion
simulation. In designs where bars OA and AB are extended, forming a straight
line between point B and the fixed point O, a singularity occurs within the
motion simulation. This singularity makes it impossible to lower the end-
effector by rotating the red beam at point C, as shown in Figure 5. It is
important to recognize that the aforementioned issue does not occur when the
specific design is actuated from the motor, as in real-life operation.
Consequently, such a design cannot be considered infeasible based on this
aspect. Therefore, starting the movement from $\delta_{mid}$ ensures that this
problem does not affect feasible designs.

This approach is novel compared to the previous study by the authors [4],
where the kinematic transformation was conducted within a single simulation.
In that single simulation, moving the end-effector from $\delta_{e}$ to
$\delta_{i}$ could erroneously be perceived as unsolvable in scenarios like
those depicted in Figure 5.

Figure 5: Choosing design parameters lengths ($|OA|$, $|AB|$, and $|BC|$) that
cause bars OA and AB to align in a straight line from point B to O creates an
unsolvable simulation when driving the end-effector from point C.

###  2.2 Dynamic Analysis

As depicted in Figure 4, the final simulation ”Dynamic simulation” is key to
determining the necessary driving motor torque $T_{m}(t)$ for a given set of
design parameters $|OA|$, $|AB|$, and $|BC|$.

The CAD software calculates the inertial properties of the mechanism
components using their material properties. The motion simulation then
formulates the equations of motion based on these inertial properties and
kinematic relations, which include actual positions and their derivatives,
speed, and acceleration of the individual mechanism components. Providing the
motor profile $\theta(t)$ to the simulation would necessitate differentiating
the measured signal to acquire both speed $\dot{\theta}(t)$ and acceleration
$\ddot{\theta}(t)$. However, differentiating a signal measured within a
simulation tends to amplify the inherent noise present in the numerical
results. In contrast, by inputting the acceleration profile $\ddot{\theta}(t)$
into the simulation, the speed $\dot{\theta}(t)$ and motor position profile
$\theta(t)$ can be obtained through integration, a process less prone to
amplifying numerical simulation noise.

Hence, the kinematic transformation extracts the motor’s acceleration profile
$\ddot{\theta}(t)$ at point O from the outcomes of the two preceding
simulations: Kinematic simulation 1a and Kinematic simulation 1b. This method
is a departure from the previous study [4], which focused on the motor profile
$\theta(t)$.

The CAD software employs a numerical solver to resolve the equations of motion
and determine the necessary motor torque $T_{m}(t)$. This eliminates the need
for manual dynamic analysis by the machine builder. The dynamic simulation
enables the extraction of the required motor torque $T_{m}(t)$ for driving the
mechanism according to the predefined end-effector movement ($\delta_{i}$ to
$\delta_{e}$) in kinematic simulations 1a and 1b. This facilitates calculating
the $T_{RMS}$ objective value for each design, based on its specific motor
torque profile $T_{m}(t)$.

##  3 CAD-Based Feasible Design Space Quantification

The selection of design parameter combinations ($|OA|$, $|AB|$, and $|BC|$) in
the methodology is determined by the optimization algorithm. Specifically, the
Bayesian optimization algorithm selects new designs based on its model of the
objective function. To enhance the efficiency of the optimization algorithm,
it is beneficial to define the feasible design region.

Moreover, since the objective function model tends to be lower at the
boundaries of the design space, there’s a likelihood that the model may
continue to decrease even outside the feasible region. Without objective
values from infeasible regions, the algorithm fails to learn and may persist
in evaluating designs that appear to have a low objective value according to
the model, yet being in fact infeasible.

To address this, it’s essential to model the constraint design space for the
optimization process. A basic approach might involve checking whether a
simulation solves or not, but this provides limited information about the
degree of infeasibility of a point, hindering the algorithm’s learning about
its proximity to the border of the feasible space.

Therefore, this paper introduces a method to evaluate the feasibility of a
design and quantify its infeasibility. Prioritizing industrial applicability,
this method relies entirely on the CAD model, extracting infeasibility
quantification through CAD motion simulations.

This method marks a significant improvement over the authors’ earlier approach
in [4], which used one of the simulations solely for a binary feasibility
check of the design parameters, offering limited insight. The new method
advances beyond this binary evaluation by quantitatively assessing a design’s
feasibility, thereby providing more information on a design choice.

###  3.1 Static constraints

The initial step in determining feasible designs involves examining static
constraints, focusing on whether a design can be assembled at the points where
the end-effector is closest ($\delta_{i}$) and farthest ($\delta_{e}$) from
the driver joint O. Static constraints essentially assess the assemblability
of the mechanism in these critical positions [29]. An example of a design that
fails to meet these criteria is depicted in Figure 6, where the chosen values
for the design parameters $|OA|$, $|AB|$, and $|BC|$ result in a configuration
where the link OA’ cannot connect with the link A”B.

Figure 6: The combination of design parameters $|OA|$, $|AB|$, and $|BC|$
result in an infeasible design that cannot be assembled in $\delta_{e}$.

This paper introduces a CAD-based methodology that quantifies the degree of
constraint violation in an infeasible design using motion simulation.

This approach begins with a baseline design that is assemblable throughout the
entire range of the end-effector movement, from $\delta_{i}$ to $\delta_{e}$.
From this starting point, the relative positions of the mechanism’s bars are
maintained by fixing the angles between them. For instance, in Figure 7, the
angles $\alpha$ and $\beta$ are constrained to remain constant at their
original values, corresponding to those in the baseline design when the end-
effector is at position $\delta_{e}$.

Figure 7: The relative positions between the bars are fixed through the angles
$\alpha$ and $\beta$.

Once the baseline design is established with fixed angles $\alpha$ and $\beta$
between the bars, directly modifying $|OA|$, $|AB|$, and $|BC|$ is impossible
due to the overconstrained nature of the CAD model—with fixed angles and all
joints attached. To circumvent this, the authors suggest detaching one joint,
specifically the joint at point O. This detachment allows for changes in the
lengths of the bars.

As depicted in Figure 8 (left), detaching the joint at point O creates a gap
between points O and O’, resulting from the alteration of the design
parameters $|OA|$, $|AB|$, and $|BC|$ from the baseline design. With fixed
angles $\alpha$ and $\beta$, only the baseline design will align points O and
O’. To assess the assemblability of a new combination of design parameters
($|OA|$, $|AB|$, and $|BC|$), a simulation is conducted to attempt closing the
gap between O and O’, as illustrated in Figure 8 (right). Before starting the
simulation, constraints on $\alpha$ and $\beta$ are removed, while the end-
effector position is fixed at $\delta_{e}$. The simulation moves point O’
along a straight line towards O. This simulation process is repeated with the
mechanism at its starting position $\delta_{i}$. By conducting these
simulations for both $\delta_{i}$ and $\delta_{e}$, which represent the end-
effector’s farthest and closest positions to the motor, the assemblability of
the design parameters $|OA|$, $|AB|$, and $|BC|$ is assessed at the
mechanism’s extreme positions. Thus, the mechanism is considered assemblable
across its entire range from $\delta_{i}$ to $\delta_{e}$ [29].

Figure 8: A combination of design parameters ($|OA|$, $|AB|$, and $|BC|$)
results in a gap between points O and O’ when the end-effector is in position
$\delta_{e}$ (left). To close the gap, a motion simulation is configured to
move point O’ towards point O, following the straight line through these two
points.

At this stage, the feasibility of a design can be initially assessed by
checking if the motion simulation successfully aligns points O and O’. If
point O’ cannot align with point O the design is infeasible. However, this
approach does not yet quantify the degree of infeasibility.

To address this, the authors utilize the motion simulation to track the
distance between points O and O’ throughout the simulation. The distance
measurement’s final data point, captured just before the simulation stops,
provides an indication of the design’s feasibility. Furthermore, the
methodology extends beyond merely measuring infeasibility; it also quantifies
feasibility by determining how far point O’ can move past point O along the
straight line connecting them. The authors have set a maximum allowable
movement of point O’ to be 20 mm past point O, as can be seen in Figure 8
(right).

As depicted in Figure 9, the last data point of the distance measurement
varies depending on the specific combination of design parameters ($|OA|$,
$|AB|$, and $|BC|$) chosen. The relative distance of point O’ to O is
calculated as the projected length of the vector $\mathbf{OO^{\prime}}$ onto
the vector $\mathbf{OO^{\prime}}_{init}$, as detailed in Equation (1). This
approach not only identifies infeasible designs but also provides a
quantitative measure of how close a design is to being feasible in both
$\delta_{i}$ and $\delta_{e}$ end-effector positions.

$|OO^{\prime}|\Big{|}_{\delta=\delta_{i},\delta_{e}}=\frac{\mathbf{OO^{\prime}}_{init,\delta}\cdot(\mathbf{O}-\mathbf{O^{\prime}}_{\delta})}{\sqrt{(\mathbf{O}-\mathbf{O^{\prime}}_{init,\delta})_{X}^{2}+(\mathbf{O}-\mathbf{O^{\prime}}_{init,\delta})_{Y}^{2}}},$
(1)

where, $\textbf{OO'}_{init,\delta}$ represents the vector between points O and
O’ at the beginning of the simulation, with the end-effector configured in
either position $\delta_{i}$ or $\delta_{e}$. The vector O indicates the fixed
position of point O in the XY plane, which does not change during the
simulation. $\textbf{O'}_{init,\delta}$ refers to the initial position of
point O’, corresponding to the end-effector in $\delta_{i}$ or $\delta_{e}$.
The vector $\textbf{O'}_{\delta}$ tracks the changing position of point O’
throughout the simulation, while the end-effector remains in either
$\delta_{i}$ or $\delta_{e}$. The denominator in Equation (1) is used to
compute the length of $\textbf{OO'}_{init,\delta}$.

Figure 9 illustrates that the feasibility quantification method produces three
possible values: positive, zero, or negative. As per Equation (1), a positive
value denotes an infeasible design, where points O and O’ fail to align at the
simulation’s end, indicating alignment impossibility. A zero value implies
that point O’ aligns with point O but cannot proceed further along their
connecting line, placing the design at the feasibility boundary. Conversely, a
negative value indicates a feasible design where not only points O and O’ can
be aligned, but point O’ can also move beyond this alignment, up to a maximum
of 20 mm. This additional movement beyond the alignment point is incorporated
to gather information about the designs on both sides of the constraint line.
Consequently, this approach allows for the quantification of not only
infeasible designs but also feasible designs that are near the constraint
boundary, enhancing the precision of the design optimization process.

Figure 9: The final data point in the distance measurement serves as a
quantifier of a design’s feasibility. This value can be positive (indicated in
red), signifying an infeasible design; zero (shown in purple), denoting a
design that is just feasible; or negative, up to a minimum of -20 mm
(represented in blue and green), indicating that the design is feasible.

In each design evaluation, the information obtained from the constraint
quantification is utilized to construct a non-parametric surrogate model using
Gaussian processes. This surrogate model serves as an approximation of the
feasible design space, bounded by the static constraints, and aids in guiding
the optimization process towards designs that satisfy these constraints.

###  3.2 Dynamic constraints

The static constraints outlined in chapter 3.1 are not entirely adequate for
ruling out all infeasible designs. So far, they only ensure that the mechanism
can be assembled and moved from $\delta_{i}$ to $\delta_{e}$. However, it’s
also crucial to consider defects that may arise during the mechanism’s
movement. The three types of defects that can occur are order, branch, and
circuit defects. The comprehensive review in [34] highlights the importance of
research on avoiding these defects in linkage synthesis.

As outlined in [29], each defect type has specific characteristics. Order
defects are not relevant in this study, as only reciprocal mechanisms, which
move continuously back and forth between $\delta_{i}$ and $\delta_{e}$, are
considered. Branch defects occur when the transmission angle, denoted as
$\beta$ in Figure 7, crosses 0 or $\pi$. This crossing results in a reversal
of the motor displacement profile $\theta(t)$. Circuit defects arise when it’s
necessary to disassemble the linkage and reassemble it in another circuit to
complete its motion. This also involves the transmission angle $\beta$ passing
through 0 or $\pi$, leading to a reversal in $\theta(t)$. Such reversals are
problematic in this context, as the movement is driven by a single joint at
point O. A direction change in the motor displacement profile $\theta(t)$
indicates that the mechanism passes a transmission angle of 0 or $\pi$, a
situation where connected links become collinear. This collinearity can cause
excessively high torques, hindering movement from $\delta_{i}$ to
$\delta_{e}$.

In summary, ensuring that the motor displacement profile $\theta(t)$ remains
monotonic throughout the end-effector’s movement from $\delta_{i}$ to
$\delta_{e}$ is crucial to eliminate potential circuit and branch defects.

The evaluation of dynamic constraints relies on the availability of the motor
displacement profile $\theta(t)$. This motor profile, necessary for moving the
designed mechanism from $\delta_{i}$ to $\delta_{e}$, can only be obtained
after completing kinematic simulations 1a and 1b. These simulations provide
the required $\theta(t)$ profile. Additionally, the motor speed profile
$\dot{\theta}(t)$, which is also essential for this analysis, can be extracted
following these simulations.

As detailed in Algorithm 1, the motor speed profile $\dot{\theta}(t)$ is
crucial for identifying changes in the direction of the motor displacement
profile $\theta(t)$. A reversal in the direction of $\theta(t)$ is signaled by
a sign change in $\dot{\theta}(t)$. When such a sign change is detected, the
dynamic constraint is assigned a nonzero value. This value specifically
represents the extent of motor displacement during the interval where the
mechanism violates the constraint.

Figure 10 demonstrates an instance of dynamic constraint violation, showcasing
the corresponding motor displacement ($\theta$) and speed ($\dot{\theta}$)
profiles. In Figure 10, the occurrence of a sign change in the speed profile,
detected in line 3 in Algorithm 1, indicates a violation of the dynamic
constraint. Quantifying the dynamic constraint’s violation is done by the
range of motor displacement during which the speed profile $\dot{\theta}(t)$
deviates in sign from a predetermined reference.

Figure 10: Design parameters ($|OA|$, $|AB|$, and $|BC|$) lead to the left
design, assemblable in $\delta_{e}$ and $\delta_{i}$ but with a speed profile
sign change. Dynamic constraints assess the complete movement, quantifying
infeasibility by the $\theta$ range with speed sign change, shown between
purple vertical lines on the right. Algorithm 1 Dynamic Constraint Calculation

1:if all($\dot{\theta}\geq 0$) or all($\dot{\theta}\leq 0$) then

2: $dynamic\\_constraint\leftarrow 0$

3:else if all($\dot{\theta}_{bot}\geq 0$) or all($\dot{\theta}_{top}\leq 0$)
then

4: $dynamic\\_constraint\leftarrow\textbf{range}(\theta(\dot{\theta}<0))$

5:else

6: $dynamic\\_constraint\leftarrow\textbf{range}(\theta(\dot{\theta}>0))$

7:end if

For each design evaluation, a specific value is assigned to the dynamic
constraint, corresponding to the design being assessed. This value is then
utilized to develop a non-parametric surrogate model using Gaussian processes.
This surrogate model of the dynamic constraint provides an approximation of
the design space that is limited by the dynamic constraint.

Figure 11 (a) illustrates the surrogate model that approximates the feasible
design space based on two design parameters ($|OA|$ and $|AB|$) for
demonstration purposes. The red surface indicates a design’s degree of
violation by a value between -1 and 1, mapping out the feasible design space.
Designs with violation values exceeding 0 (above the green plane) are likely
infeasible, whereas those less than 0 (below the green plane) are likely
feasible. In Figure 11 (b), the surrogate constraint model is overlaid with
the design space’s analytically derived static and dynamic constraints, as
detailed in [29]. This combination, shown in a 2D overlay, confirms that
regions enclosed by the analytically derived static (dashed blue lines) and
dynamic (purple lines) constraints match the feasible (green) areas identified
by the surrogate model. The comparison reveals that the surrogate model
closely approximates the analytic constraints within the design space,
demonstrating its effectiveness.

Figure 11: The surrogate model in (a) delineates the feasible design space for
two parameters, $|OA|$ and $|AB|$, with a red surface indicating feasible
areas (below the green plane) and probable infeasible zones (above the green
plane). In (b), the model incorporates overlays of analytically derived static
(dashed blue lines) and dynamic (purple lines) constraints, identifying the
same design space’s feasible regions in green.

The model of the design space as shown in Figure 11 (a), constrained by both
dynamic and static constraints, aids the optimization process. The approach
guides the selection of new combinations of design parameters ($|OA|$, $|AB|$,
and $|BC|$) towards a better resulting objective value and a design with a
high probability of feasibility for evaluation.

##  4 Optimization Approach

In this work, the design optimization problem, as stated in Equation (2), is
to find the optimal design (being lengths $|OA|$, $|AB|$, and $|BC|$) leading
to a minimal $T_{RMS}$ for this mechanism.

$\begin{array}[]{ll}\min:&T_{RMS}(\textbf{x})\\\ \text{ subject to:
}&\text{Static constraint({x}) $\leq$ 0}\\\ &\text{Dynamic constraint({x}) $=$
0}\\\ &x_{i}\in\left[x_{i\min},x_{i\max}\right];\quad
x_{i}\in\textbf{x}\end{array}$ (2)

where

$\begin{array}[]{ll}&T_{RMS}\ \text{is the objective function,}\\\ &\text{The
Static and Dynamic constraint evaluates the feasibility}\\\ &\text{of a
certain design,}\\\ &\textbf{x}\ \text{is a vector, which contains the
independent}\\\ &\text{design parameters}\ |OA|,|AB|\ \text{and}\ |BC|,\\\
&x_{i\min}\ \text{and}\ x_{i\max}\text{define the limits of each design
variable}\ x_{i}.\end{array}$

In a previous study [4], the authors addressed the optimization problem using
two prevalent algorithms in design optimization [10], Sequential Quadratic
Programming (SQP) and Genetic Algorithm (GA). The findings from [4] reveal
that while the GA minimizes the likelihood of getting stuck in a local
minimum, it does not guarantee to find the global optimum [35]. Moreover, GA
is computationally expensive due to the high number of design evaluations
required to identify an optimal solution. Conversely, the outcome of the SQP
algorithm is heavily dependent on the chosen initial point. Starting from an
initial design, SQP progresses along the steepest negative gradient towards a
minimum, leading to quicker convergence. Thus, this method significantly
increases the risk of getting stuck in a local optimum.

To tackle the challenge of uncertainty in reaching the global optimum and to
decrease the extensive number of design evaluations, the authors adopt
Bayesian Optimization (BO) as an approach. Bayesian optimization employs a
stochastic surrogate model to approximate an expensive objective function and
its constraints based on a limited set of observed function values. This
model, trained using the observed function value points, results in a
surrogate model with a posterior mean ($\mu$) and a posterior standard
deviation ($\sigma$) representing uncertainty, as depicted in 1D for
illustration at the top of Figure 12.

Figure 12: A trained Gaussian Process by observed function value points
(blue), resulting in a function model with a posterior mean ($\mu$) depicted
in red and a posterior standard deviation ($\sigma$) shown in purple. Below
the surrogate model, the acquisition function utilized by BO is constructed,
highlighting the new expected and feasible optimum $\textbf{x}_{n+1}$,
identified as the x-value with the highest acquisition function value.

These surrogate models are constructed using Gaussian Processes (GP), which
extend Gaussian distributions to function spaces [36]. A GP is a distribution
over functions completely defined by its mean function $\mu$ and covariance
function (or kernel) $k$, as stated in Equation (3).

$f(\textbf{x})\sim\mathcal{N}(\mu,\,k(\textbf{x,x'}))$ (3)

Here, $\mathcal{N}$ denotes the normal distribution, and $k(\textbf{x,x'})$ is
calculated using the squared-exponential covariance function, as indicated in
Equation (4):

$k(\textbf{x,x'})=\sigma^{2}\exp(-\frac{(\textbf{x}-\textbf{x}^{\prime})^{2}}{2\textbf{l}^{2}}).$
(4)

The covariance function provides the correlation between points x and x’ in
the design space, parameterized by the amplitude parameter $\sigma$ and the
length scale l, known as hyperparameters. Note that the length scale l is a
diagonal matrix with a dimension corresponding to the number of design
parameters. Given $n$ observations of the objective function
$T_{RMS}(\textbf{x})$ at points $\textbf{x}_{i}$, the complete
covariance/kernel matrix is computed as in Equation (5).

$\mathbf{K}=\left[\begin{array}[]{ccc}k\left(\mathbf{x}_{1},\mathbf{x}_{1}\right)&\ldots&k\left(\mathbf{x}_{1},\mathbf{x}_{n}\right)\\\
\vdots&\ddots&\vdots\\\
k\left(\mathbf{x}_{n},\mathbf{x}_{1}\right)&\ldots&k\left(\mathbf{x}_{n},\mathbf{x}_{n}\right)\end{array}\right]$
(5)

As outlined by [37], Bayesian Optimization (BO) comprises two primary
components. The first is the probabilistic surrogate models for the objective
and constraint models, which mimic the behavior of, computationally expensive,
functions as shown at the top of Figure 12. The second involves using an
acquisition function based on these probabilistic models, guiding the
selection of the next optimal evaluation point. This acquisition function
calculates a value at any unobserved point $\textbf{x}{n+1}$, based on the
posterior distribution that provides a posterior mean ($\mu$) and standard
deviation ($\sigma$) at $\textbf{x}{n+1}$ [36], leveraging the Gaussian
Process (GP) properties. In this study, we employ the Expected Improvement
(EI) method, an improvement-based acquisition function introduced by [30]. The
EI acquisition function assesses the surrogate model’s predicted mean against
the present optimal minimum objective value, incorporating the standard
deviation to quantify the anticipated improvement at any point within the
design space. Additionally, this paper advocates to incorporate the static and
dynamic constraints, discussed in Section 3, by a constraint surrogate model
to predict the probability of feasibility at any point in the design space.
This probability is integrated into the expected improvement, leading to the
use of the constrained expected improvement (cEI) as the acquisition function.
The acquisition function, depicted at the bottom of Figure 12, identifies the
new expected and feasible optimum $\textbf{x}_{n+1}$ as the x-value with the
highest ordinate. Each iteration assesses the computationally costly objective
function at this new optimum $\textbf{x}_{n+1}$. BO employs cEI to navigate
within the design space, ensuring that not only a certain area is exploited
but also that exploration of the design space is performed to avoid sub-
optimal results and aim for the global optimum.

Figure 13 presents the complete optimization process. Initially, a point of
interest is selected in the design space, for which the objective
$T_{RMS}(\textbf{x})$, Static constraint(x), and Dynamic constraint(x) value
are determined. The constraint values are established using the CAD-based
constraint quantification method detailed in Section 3, while the objective
value is derived from the CAD-based design evaluation approach described in
Section 2. These values for the objective and constraint functions serve as
training data for the Gaussian Process models of the objective and constraint
functions. The constrained bayesian optimization process employs the posterior
distribution to obtain a posterior mean ($\mu$) as the predicted objective and
constrained value and a posterior standard deviation ($\sigma$), from these
surrogate models. These posterior parameters are used to formulate the
acquisition function as in [38], which then guides the selection of an
unobserved point as the expected and feasible optimum. This BO approach
provides insights into the uncertainty associated with the obtained optimum.
This aspect of uncertainty is pivotal, as it allows for the establishment of a
threshold. Users can set this threshold to determine that any further
improvements in the optimum will not exceed the predefined threshold, thereby
suggesting that the attained optimum is, within a certain level of uncertainty
and across all evaluated points, likely the global optimum.

Figure 13: The entire optimization workflow, integrating Gaussian Process (GP)
models for both objective and constraint functions. Utilizing these surrogate
models, the workflow initiates constrained Bayesian optimization, which
establishes the acquisition function and selects an unobserved point
$\textbf{x}_{n+1}$ as the expected and feasible optimum. At this point in the
design space, the constraint and objective values are ascertained through CAD
motion simulations, the results of which are fed back into the GP model to
further refine the surrogate model.

##  5 Results & Discussion

In this section, the authors discuss the effectiveness of Bayesian
Optimization (BO) in the design optimization of an emergency ventilator. The
results of the BO method, labeled as BOCon1 and BOCon2, are presented in Table
1. This is compared with the outcome from the Sequential Quadratic Programming
(SQP) optimization, which incorporates design feasibility as a nonlinear
inequality constraint and is listed in the same table as SQPCon1 and SQPCon2.
The study also contrasts these findings with previous research outcomes.
Specifically, in [4], both SQP and Genetic Algorithm (GA) were utilized
without the integration of CAD-based constraint quantification or insights
into the feasible design space, relying solely on simulations for a binary
feasibility assessment of design parameters. These earlier results are
presented in Table 1 under the labels SQP and GA.

In contrast, [29] adopted an analytical method to define the feasible design
space, facilitating the use of the sparse interpolation method. This approach
involved modeling the objective function with the fewest possible samples and
then determining the optimal objective value within the convex hull of the
feasible design space using a brute-force method. The result is displayed in
Table 1 under the label SI. The limitation of this SI method is that it
guarantees finding the global optimum only within the convex hull that spans
the larger part of the feasible design space, thereby excluding smaller
regions that might contain the global optimum.

Table 1: Saving potential achieved by design optimization.

Design |  $|OA|$ ($\mathrm{mm}$) |  $|AB|$ ($\mathrm{mm}$) |  $|BC|$ ($\mathrm{mm}$) |  $T_{\text{rms}}$ ($\mathrm{N}\text{\,}\mathrm{m}$) |  $T_{\text{max}}$ ($\mathrm{N}\text{\,}\mathrm{m}$) |  $T_{\text{rms}}$ savings (%) |  $T_{\text{max}}$ savings (%) |  Number of evaluations
---|---|---|---|---|---|---|---|---
Original | $53$ | $65$ | $282$ | $7.9$ | $13.3$ | - | - | -
GA [4] | $82.68$ | $141.25$ | $281.8$ | $3.1$ | $5.4$ | $60$ | $59$ | $399$
SQP [4] | $30$ | $76.22$ | $271.75$ | $3.4$ | $5.2$ | $57$ | $61$ | $39$
SI [29] | $33.2$ | $79.4$ | $266.1$ | $2.6$ | $4.4$ | $67$ | $67$ | $618$
SQPCon1 | $30.02$ | $79.2$ | $269.39$ | $2.3$ | $4.1$ | $71$ | $69$ | $64$
SQPCon2 | $35.84$ | $106$ | $295.59$ | $2.7$ | $4.7$ | $66$ | $65$ | $107$
BOCon1 | $30.21$ | $72.36$ | $258.4$ | $2.3$ | $4.1$ | $71$ | $69$ | $255$
BOCon2 | $30.43$ | $80.38$ | $270.55$ | $2.3$ | $4.1$ | $71$ | $69$ | $363$

The data in Table 1 generally indicates that incorporating constraints into
the design optimization process improves the quality of the obtained optimum.
The SQP algorithm, enhanced by the inclusion of the constraint quantification
method and a well-defined finite difference step size, achieved an optimum of
2.3 Nm after 64 iterations (SQPCon1).This point of optimum is defined by the
criterion that the objective value does not decrease by more than 0.001 Nm
over 3 consecutive objective value reductions. Furthermore, initiating the SQP
algorithm with constraints from a different initial point ($|OA|$=95,
$|AB|$=60, $|BC|$=265) led to an optimum of 2.7 Nm after 107 iterations, as
indicated by SQPCon2, adhering to the same minimal objective value decrease
criterion and identical algorithmic settings. This variation in results based
on the starting point reinforces the understanding that outcomes of gradient-
based optimization are highly sensitive to initial conditions.

Regarding Bayesian Optimization, both results showed an objective value of 2.3
Nm, equating to 71% savings in the objective $T_{RMS}$. However, the
iterations varied: BOCon1 reached the optimum in 255 iterations, while BOCon2,
starting from the same initial conditions as SQPCon2, required 363 iterations.
The number of iterations is determined based on the stopping criterion, as set
for the SQP algorithm, that the objective value cannot improve more than 0.001
Nm over 3 consecutive iterations. Moreover, as Gaussian processes provide
insights into the uncertainty associated with the obtained optimum, one can
calculate this uncertainty based on the attained objective function surrogate
model at iteration 255 and 363 while using a 95% standard deviation. Given
both Gaussian processes models we’ve developed from different starting points
with respectively 255 and 363 iterations, we consider all points in our design
space, marked by a granularity of 1 mm, for which the constraint model is 95%
sure that it is feasible. For each of these points, the obtained objective
function model holds 95% confidence that the function value cannot be
decreased. Based on this model’s insights, we’re led to believe that the
optimum we’ve identified stands as the global optimum.

##  6 Conclusion

This paper presents a comprehensive study on the design optimization of an
emergency ventilator, emphasizing energy efficiency through the use of
Computer-Aided Design (CAD) and Bayesian Optimization (BO). The ventilator,
initially developed for low- and middle-income countries during the COVID-19
pandemic, required optimization to minimize electric energy consumption. The
study optimizes geometric design parameters ($|OA|$, $|AB|$, and $|BC|$)
towards a minimal Root Mean Square (RMS) motor torque, directly linked to
energy consumption.

The authors propose a novel approach that utilizes CAD motion simulations to
simplify the optimization process, avoiding the complexities of traditional
kinematic and dynamic analyses, which are generally less general and more
cumbersome. The method described in this paper evaluates different design
parameter combinations ($|OA|$, $|AB|$, and $|BC|$) and quantifies the
feasibility, facilitating the optimization process. By employing CAD-based
feasibility evaluation, the method facilitates delineating the feasible design
space without needing the detailed mechanism analysis typically found in the
literature, which is cumbersome and demands user expertise. This optimization
approach can handle increased mechanism complexity by utilizing CAD
simulations and avoiding analytical analysis, enhancing its applicability.

Bayesian Optimization is introduced to overcome the impracticality of brute-
force approaches in seeking global optimum designs. BO employs probabilistic
surrogate models based on Gaussian Processes, efficiently navigating the
design space and balancing exploration and exploitation. This approach also
provides insights into the uncertainty of the optimum, enhancing confidence in
the attained optimum being the global optimum.

The study contrasts the Bayesian Optimization (BO) method, achieving a root
mean square torque ($T_{RMS}$) of 2.3 Nm in 255 or 363 iterations, against the
traditional Sequential Quadratic Programming (SQP) method under constraints,
which attains the same objective value of 2.3 Nm in 64 iterations or 2.7 Nm in
107 iterations, varying by the algorithm’s starting position. Additionally, it
presents comparison results with a binary feasibility check of the design
parameters, where SQP reaches an objective value of 3.4 Nm in 39 iterations,
and the Genetic Algorithm (GA) achieves 3.1 Nm after 399 iterations. These
outcomes underscore the initial condition sensitivity of gradient-based
optimizations and the GA’s computational intensity. Besides that, the findings
suggest that integrating constraints overall enhances the optimization’s
effectiveness. The study concludes that the BO method, with its ability to
predict the objective value at new points and assess the feasibility,
effectively reduces the evaluation of infeasible designs, leading to a more
efficient optimization process and potentially achieving the global optimum.

## CRediT authorship contribution statement

Abdelmajid Ben Yahya: Conceptualization, methodology, software, formal
analysis, investigation, data curation, writing—original draft, visualization.
Santiago Ramos: Conceptualization, methodology, writing—review and editing.
Nick Van Oosterwyck: Conceptualization, methodology, writing—review and
editing. Annie Cuyt: Conceptualization, writing—review and editing,
supervision. Stijn Derammelaere: Conceptualization, methodology,
writing—review and editing, supervision.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or
personal relationships that could have appeared to influence the work reported
in this paper.

## Acknowledgment

This research received no external funding.

## Data availability

The data presented in this study are available on request from the
corresponding author.

## Declaration of Generative AI and AI-assisted technologies in the writing
process

During the preparation of this work the authors used ChatGPT-4 in order to
suggest structure for individual sentences and paragraphs. After using this
tool/service, the authors reviewed and edited the content thoroughly and take
full responsibility for the content of the publication.

## References

  * [1] P. Waide, C. U. Brunner, Energy-Efficiency Policy Opportunities for Electric Motor-Driven Systems, Tech. rep., IEA, Paris (2011).
  * [2] R. Saidur, A review on electrical motors energy use and energy savings, Renewable and Sustainable Energy Reviews 14 (3) (2010) 877–898.  doi:10.1016/j.rser.2009.10.018.
  * [3] S. Herregodts, H. J., Gear up medical vzw, https://www.gearupmedical.be/, accessed: 2023-11-14 (2019).
  * [4] A. Ben Yahya, N. Van Oosterwyck, J. Herregodts, S. Herregodts, S. Houwen, B. Vanwalleghem, S. Derammelaere, An Industrial Applicable Approach towards Design Optimization of a Reciprocating Mechanism: an emergency ventilator case study, in: 2023 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), 2023, pp. 1020–1026, iSSN: 2159-6255.  doi:10.1109/AIM46323.2023.10196204.
  * [5] N. Van Oosterwyck, F. Vanbecelaere, F. Knaepkens, M. Monte, K. Stockman, A. Cuyt, S. Derammelaere, Energy optimal point-to-point motion profile optimization, Mechanics Based Design of Structures and Machines (2022) 1–18doi:10.1080/15397734.2022.2106241.
  * [6] P. Sheppard, S. Rahimifard, Improving energy efficiency in manufacturing using peer benchmarking to influence machine design innovation, Clean Technologies and Environmental Policy 21 (6) (2019) 1213–1235.  doi:10.1007/s10098-019-01701-4.
  * [7] G. Carabin, E. Wehrle, R. Vidoni, A Review on Energy-Saving Optimization Methods for Robotic and Automatic Systems, Robotics 6 (4) (2017) 39.  doi:10.3390/robotics6040039.
  * [8] B. EL-Kribi, A. Houidi, Z. Affi, L. Romdhane, Application of multi-objective genetic algorithms to the mechatronic design of a four bar system with continuous and discrete variables, Mechanism and Machine Theory 61 (2013) 68–83.  doi:10.1016/j.mechmachtheory.2012.11.002.
  * [9] W.-T. Lee, K. Russell, Developments in quantitative dimensional synthesis (1970-present): four-bar motion generation, Inverse Problems in Science and Engineering 26 (1) (2018) 133–148.  doi:10.1080/17415977.2017.1310858.
  * [10] A. Hernández, A. Muñoyerro, M. Urízar, E. Amezua, Comprehensive approach for the dimensional synthesis of a four-bar linkage based on path assessment and reformulating the error function, Mechanism and Machine Theory 156 (2021) 104126.  doi:10.1016/j.mechmachtheory.2020.104126.
  * [11] J. A. Cabrera, A. Simon, M. Prado, Optimal synthesis of mechanisms with genetic algorithms, Mechanism and Machine Theory 37 (10) (2002) 1165–1177.  doi:10.1016/S0094-114X(02)00051-4.
  * [12] G. R. Gogate, S. B. Matekar, Optimum synthesis of motion generating four-bar mechanisms using alternate error functions, Mechanism and Machine Theory 54 (2012) 41–61.  doi:10.1016/j.mechmachtheory.2012.03.007.
  * [13] A. Hernández, A. Muñoyerro, M. Urízar, E. Amezua, Hybrid Optimization Based Mathematical Procedure for Dimensional Synthesis of Slider-Crank Linkage, Mathematics 9 (13) (2021) 1581.  doi:10.3390/math9131581.
  * [14] Z. Affi, B. EL-Kribi, L. Romdhane, Advanced mechatronic design using a multi-objective genetic algorithm optimization of a motor-driven four-bar system, Mechatronics 17 (9) (2007) 489–500.  doi:10.1016/j.mechatronics.2007.06.003.
  * [15] R. Rayner, M. Sahinkaya, B. Hicks, Combining Inverse Dynamics With Traditional Mechanism Synthesis to Improve the Performance of High Speed Machinery, Proc. ASME 2008 Dynamic Systems and Control Conference (DSCC2008) (Jan. 2008).  doi:10.1115/DSCC2008-2186.
  * [16] D. Dopico, Y. Zhu, A. Sandu, C. Sandu, Direct and adjoint sensitivity analysis of ordinary differential equation multibody formulations, Journal of Computational and Nonlinear Dynamics 10 (2014) 011012.  doi:10.1115/1.4026492.
  * [17] D. Dopico, A. Sandu, C. Sandu, Adjoint sensitivity index-3 augmented lagrangian formulation with projections, Mechanics Based Design of Structures and Machines 50 (1) (2022) 48–78.  doi:10.1080/15397734.2021.1890614.
  * [18] S. H. Gawande, S. A. Bhojane, Numerical and Experimental Design Optimization of Toggle Clamping Mechanism, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering 43 (4) (2019) 763–779.  doi:10.1007/s40997-018-0237-y.
  * [19] M.-S. Huang, K.-Y. Chen, R.-F. Fung, Numerical and experimental identifications of a motor-toggle mechanism, Applied Mathematical Modelling 33 (5) (2009) 2502–2517.  doi:10.1016/j.apm.2008.07.021.
  * [20] Y.-L. Hsu, M.-S. Huang, R.-F. Fung, Energy-saving trajectory planning for a toggle mechanism driven by a PMSM, Mechatronics 24 (1) (2014) 23–31.  doi:10.1016/j.mechatronics.2013.11.004.
  * [21] Y.-L. Hsu, M.-S. Huang, R.-F. Fung, Adaptive Tracking Control of a PMSM-Toggle System with a Clamping Effect, International Journal of Mechanical Engineering and Applications 4 (1) (2016) 1–10.  doi:10.11648/j.ijmea.20160401.11.
  * [22] M.-S. Huang, T.-Y. Lin, R.-F. Fung, Key design parameters and optimal design of a five-point double-toggle clamping mechanism, Applied Mathematical Modelling 35 (9) (2011) 4304–4320.  doi:10.1016/j.apm.2011.03.001.
  * [23] G. Berselli, F. Balugani, M. Pellicciari, M. Gadaleta, Energy-optimal motions for Servo-Systems: A comparison of spline interpolants and performance indexes using a CAD-based approach, Robotics and Computer-Integrated Manufacturing 40 (2016) 55–65.  doi:10.1016/j.rcim.2016.01.003.
  * [24] F. Vanbecelaere, S. Derammelaere, N. Nevaranta, J. De Viaene, F. Verbelen, K. Stockman, M. Monte, Online Tracking of Varying Inertia using a SDFT Approach, Mechatronics 68 (2020) 102361.  doi:10.1016/j.mechatronics.2020.102361.
  * [25] N. Van Oosterwyck, F. Vanbecelaere, M. Haemers, D. Ceulemans, K. Stockman, S. Derammelaere, CAD Enabled Trajectory optimization and Accurate Motion Control for Repetitive Tasks, in: 2019 IEEE 15th International Conference on Control and Automation (ICCA), 2019, pp. 387–392, iSSN: 1948-3457.  doi:10.1109/ICCA.2019.8899728.
  * [26] N. Van Oosterwyck, A. Ben Yahya, A. Cuyt, S. Derammelaere, CAD Based Trajectory optimization of PTP Motions using Chebyshev Polynomials, in: 2020 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), 2020, pp. 403–408, iSSN: 2159-6255.  doi:10.1109/AIM43001.2020.9158893.
  * [27] A. Schulz, J. Xu, B. Zhu, C. Zheng, E. Grinspun, W. Matusik, Interactive design space exploration and optimization for CAD models, ACM Transactions on Graphics 36 (4) (2017) 157:1–157:14.  doi:10.1145/3072959.3073688.
  * [28] V.-D. Le, V.-T. Hoang, Q.-B. Tao, L. Benabou, N.-H. Tran, D.-B. Luu, J. M. Park, Computational study on the clamping mechanism in the injection molding machine, The International Journal of Advanced Manufacturing Technology 121 (11) (2022) 7247–7261.  doi:10.1007/s00170-022-09817-6.
  * [29] A. Ben Yahya, N. Van Oosterwyck, F. Knaepkens, S. Houwen, S. Herregodts, J. Herregodts, B. Vanwalleghem, A. Cuyt, S. Derammelaere, CAD-Based Design Optimization of Four-Bar Mechanisms: An Emergency Ventilator Case Study, Designs 7 (2) (2023) 38.  doi:10.3390/designs7020038.
  * [30] D. R. Jones, M. Schonlau, W. J. Welch, Efficient Global Optimization of Expensive Black-Box Functions, Journal of Global Optimization 13 (4) (1998) 455–492.  doi:10.1023/A:1008306431147.
  * [31] X. Wang, Y. Jin, S. Schmitt, M. Olhofer, Recent Advances in Bayesian Optimization, ACM Computing Surveys 55 (13s) (2023) 287:1–287:36.  doi:10.1145/3582078.
  * [32] S. Greenhill, S. Rana, S. Gupta, P. Vellanki, S. Venkatesh, Bayesian Optimization for Adaptive Experimental Design: A Review, IEEE Access 8 (2020) 13937–13948.  doi:10.1109/ACCESS.2020.2966228.
  * [33] H. M. Sheikh, T. A. Callan, K. J. Hennessy, P. S. Marcus, Optimization of the shape of a hydrokinetic turbine’s draft tube and hub assembly using Design-by-Morphing with Bayesian optimization, Computer Methods in Applied Mechanics and Engineering 401 (2022) 115654.  doi:10.1016/j.cma.2022.115654.
  * [34] S. S. Balli, S. Chand, Defects in link mechanisms and solution rectification, Mechanism and Machine Theory 37 (9) (2002) 851–876.  doi:10.1016/S0094-114X(02)00035-6.
  * [35] U. Bodenhofer, Genetic Algorithms: Theory and Applications, Tech. rep., Johannes Kepler Universitat (Jan. 1999).
  * [36] C. E. Rasmussen, C. K. I. Williams, Gaussian processes for machine learning., Adaptive computation and machine learning, MIT Press, 2006.
  * [37] S. Shende, A. Gillman, D. Yoo, P. Buskohl, K. Vemaganti, Bayesian topology optimization for efficient design of origami folding structures, Structural and Multidisciplinary Optimization 63 (4) (2021) 1907–1926.  doi:10.1007/s00158-020-02787-x.
  * [38] M. A. Gelbart, J. Snoek, R. P. Adams, Bayesian optimization with unknown constraints, in: Proceedings of the Thirtieth Conference on Uncertainty in Artificial Intelligence, UAI’14, AUAI Press, Arlington, Virginia, USA, 2014, pp. 250–259.

## Short Biography of Authors

Abdelmajid Ben yahya, born in 1996 in Antwerp, Belgium, is an engineer and
researcher. In 2019, he received his Master of Science degree in
Electromechanical Engineering Technology from the University of Antwerp, where
he graduated summa cum laude. Following his graduation, he was employed as a
Project Engineer at the University of Antwerp, working on technology transfer
to small and medium-sized enterprises in Flanders. Currently, Ben Yahya is a
PhD student at the University of Antwerp, starting from 2021 in the Cosys-Lab
research group, researching the optimization of design for reciprocating
mechatronic systems.

Santiago Ramoswas born in 1992 in Popayan, Colombia. He earned a Joint
Master’s in Mechatronic Engineering (EU4M) in 2020 from the University of
Oviedo. After graduation, he became a researcher in motion control at the
University of Antwerp. Since 2022, Santiago has been a PhD researcher at the
University of Antwerp in the Cosys-Lab research group, collaborating with the
Belgian Nuclear Research Center (SCK-CEN). His research focuses on optimizing
and controlling the Isotope Separator OnLine technique (ISOL).

Nick Van Oosterwyck was born in 1996 in Antwerp, Belgium. He received his MSc
degree (magna cum laude) in Electromechanical Engineering Technology from the
University of Antwerp in 2018 after which he started as a Ph.D. researcher at
the Cosys-Lab research group. In 2019, he received additional funding from the
FWO for his PhD project on energy-optimal motion profile optimization, which
he successfully defended in 2023. Since then, he has been working as a
teaching assistant within the Department of Electromechanics at the University
of Antwerp where he is responsible for various seminars and lab sessions
focused on Motion Control and Electrical Engineering, as well as integrating
the research findings into the educational curriculum. His research interests
include CAD motion simulations, motion profile optimization and optimization
algorithms in general.

Annie Cuyt is an emerita full professor at the University of Antwerp’s Faculty
of Science. She received her Doctor Scientiae degree in 1982 summa cum laude
and with the felicitations of the jury. She was a research fellow with the
Alexander von Humboldt Foundation and honored with a Masuda Research Grant.
Cuyt is a lifetime member of the Royal Flemish Academy of Belgium for Sciences
and Arts and author of over 220 peer-reviewed publications, books, and
organizer of international events. Her research focus is in numerical
approximation theory and its applications in scientific computing, computer
science, engineering, and bio-informatics, specifically rational approximation
and its relation to sparse interpolation and exponential analysis. Cuyt has
served on several national and international science foundation boards and
prestigious international award juries. In 2005, she helped establish a HPC
center for Flanders which has grown into a successful ongoing project.

Stijn Derammelaere, born in Kortrijk, Belgium, in 1984, earned his Master’s in
automation in 2006 from the Technical University College of West-Flanders,
Belgium. He completed his PhD in 2013 at Ghent University, Belgium, focusing
on control engineering and mechatronic systems co-design. Since 2017, he
continues this research at the University of Antwerp, now serving as an
associate professor in mechatronics. His expertise includes co-design, motion
control, and optimization of mechatronic systems. He is the associate editor
of Discover Mechanical Engineering Springer journal and teaches control
engineering and motion optimization at the faculty of applied engineering.


# Improving Performance And Inference On Audio Classification Tasks Using
Capsule Networks

###### Abstract

Classification of audio samples is an important part of many auditory systems.
Deep learning models based on the Convolutional and the Recurrent layers are
state-of-the-art in many such tasks. In this paper, we approach audio
classification tasks using capsule networks trained by recently proposed
dynamic routing-by-agreement mechanism. We propose an architecture for capsule
networks fit for audio classification tasks and study the impact of various
parameters on classification accuracy. Further, we suggest modifications for
regularization and multi-label classification. We also develop insights into
the data using capsule outputs and show the utility of the learned network for
transfer learning. We perform experiments on 7 datasets of different domains
and sizes and show significant improvements in performance compared to strong
baseline models. To the best of our knowledge, this is the first detailed
study about the application of capsule networks in the audio domain.

Index Terms—  Capsule Networks, Deep Learning, Audio Classification, Insights,
Transfer Learning

##  1 Introduction

Audio Classification tasks are important as part of the complex auditory
systems or as the end goal itself. Noise and music event detection is an
important pre-processing step for many downstream systems. The performance of
speech recognition systems can be improved by supplementing it with a
hierarchical gender identification classifier [1]. Detecting depression [2]
and emotion [3] from audio recordings has been getting plenty of attention in
recent years due to applications in medical and conversational AI systems.

Deep Learning models have shown significant improvement over traditional
machine learning algorithms in audio classification systems. Convolutional and
Recurrent Neural Networks are used for many audio classification tasks [4]
[5]. Addition of Attention Layer to recurrent networks to focus on the most
salient parts of an input via weighting has been very successful in numerous
applications, including machine translation [6] and image captioning [7] and
sound event detection [8] [9].

The notion of a capsule was first introduced in [10] and very recently
revisited in [11] with the addition of a routing-by-agreement mechanism. The
authors of [11] found that routing-by-agreement with capsules performed better
than the state-of-the-art for digit recognition from images.

In this paper, we propose a capsule network architecture (CapsNet) fit for
audio classification tasks and compare it with other deep learning models. We
experimentally analyze the impact of various parameters on performance and
introduce changes to loss function and network architecture for adding
regularization and multi-label classification. We also present insights into
the data using the output of the capsules and show utility of the trained
network for transfer learning.

Fig. 1: Capsule Network Architecture

##  2 Background Work

Deep learning approaches are becoming popular for modelling emotion-specific
information from speech signals [12]. Adding attention mechanism to
Bidirectional LSTM models improves the performance significantly [3]. [13]
obtained good results on gender and age identification tasks using deep
learning approaches. [14] showed superior performance of deep convolutional
networks on sound event detection task.

While these approaches have worked well, they have some major drawbacks. CNNs
have ability to deal with translation, but for the other dimensions of an
affine transformation we have to choose between replicating feature detectors
on a grid that grows exponentially with the number of dimensions, or
increasing the size of the labelled training set [11]. RNNs/LSTMs, apart from
being much slower than CNNs, are highly dependent on the temporal position of
entities. Hence, low variability on the temporal scale in training data can
deteriorate the generalizability of the models. We intend to overcome these
drawbacks using capsule network architecture and dynamic routing-by-agreement
mechanism.

A capsule is a group of neurons whose output vector represents the
instantiation parameters of a specific type of entity such as an object. The
length of the output vector represents the probability that the entity exists
and its direction represents the orientation of the entity. Active capsules
predict the instantiation parameters of higher-level capsules, via
transformation matrices. Routing-by-agreement mechanism enables a lower-level
capsule to send its output to higher level capsules whose activity vectors
have a big scalar product with the prediction advancing from the lower-level
capsule. The motivation for capsule routing is that it implicitly learns
global coherence by enforcing part-whole relationships to be learned. Capsule
Networks and routing-by-agreement mechanism is described in detail in [11].

In recent times, capsule networks have been applied to a variety of image
classification problems like brain tumour detection [15], traffic sign
detection [16]. [17] have used capsule networks for Sound Event Detection
task.

##  3 Datasets

For our experiments, we use datasets across different domains and sizes to
capture the applicability of proposed system for general use. We now describe
the datasets in detail.

  * •

IEMOCAP : The IEMOCAP dataset proposed in [18] is a multi-modal emotion
recognition dataset containing improvised and scripted scenarios designed to
elicit specific types of emotions. We use audio data of 4 emotion categories
as per existing research [3].

  * •

RAVDESS : The RAVDESS dataset proposed in [19] is a multi-modal database of
emotional speech and song. We use speech data representing calm, happy, sad,
angry, fearful, and neutral expressions.

  * •

VCTK : The VCTK corpus [20] contains utterances by 109 speakers. We use this
dataset for gender identification from sound. The dataset has 47 male speakers
and 61 female speakers and 1 unspecified speaker.

  * •

Urban8K : Urban8K corpus [21] contains 8732 labelled sound excerpts of urban
sounds from 10 classes like air_conditioner, car_horn, children_playing etc

  * •

FSDD : FSDD is a small dataset [22] containing spoken utterances of 10 digits
by three speakers out of which one speaker is used only for testing. We
calculate the classification accuracy for 10 classes for the speaker not used
in training.

  * •

Multi-VCTK : We create an augmented dataset (Multi-VCTK) from VCTK corpus
which contains the concatenation of male(M) and female(F) speakers thereby
creating four categories of M-M, M-F, F-M and F-F.

  * •

Multi-MUSAN : The MUSAN corpus [23] contains utterances of music, speech, and
noise. We create ”Multi-Musan” corpus by augmenting some of the speech files
with noise files with SNR 5. The resultant dataset contains three categories
of speech, noise and speech-noise.

Datasets | CNN | LSTM | ATT | CAPS | 1 | 3 | 5 | No Regularization | Regularization
---|---|---|---|---|---|---|---|---|---
VCTK | 0.797 | 0.895 | 0.894 | 0.905 | 0.925 | 0.902 | 0.900 | 0.925 | 0.902
IEMOCAP | 0.512 | 0.530 | 0.566 | 0.583 | 0.586 | 0.586 | 0.587 | 0.579 | 0.582
Urban8K | 0.518 | 0.585 | 0.595 | 0.662 | 0.695 | 0.669 | 0.684 | 0.636 | 0.650
FSDD | 0.728 | 0.673 | 0.689 | 0.692 | 0.760 | 0.695 | 0.651 | 0.648 | 0.730
Table 1: Model Accuracy

##  4 Model

We use series of MFCC features as input to the model. For MFCC features, the
scale of different features varies considerably over an input, this leads to
longer time for convergence and numerical instability. We add a batch
normalization layer to counter the large variability in scale of inputs.
Experimentally we’ve found, for audio data, adding LSTM layer before the
capsule layer is much more beneficial than convolutional layers. Hence, we add
two Bidirectional LSTM layers. The outputs of each cell of LSTM is passed to
the next layer. To improve generalization we add a Dropout Layer. The output
of this layer is treated as a series of vectors which is passed to capsule
layer. We use capsules of dimension 16. Then we add Length layer which
calculates the length of the activity vector of capsule layer which denotes
the probability of the class being present. This model is depicted in figure
1. The architecture of the model is inspired by [11], however, unlike [11] we
don’t add decoder network except in experiments where we test the utility of
regularization. This is done to ensure a fair comparison with other models. We
use margin-loss as described in [11] as the loss function.

$L_{k}=T_{k}max(0,m^{+}-||v_{k}||)^{2}+\lambda(1-T_{k})max(0,||v_{k}||-m^{-})^{2}$
(1)

where $T_{k}$ = 1 if class k is present and $m^{+}$ = 0.9 and $m^{-}$ = 0.1.
The $\lambda$ down-weighting of the loss for absent classes stops the initial
learning from shrinking the lengths of the activity vectors of all the
capsules. We use $\lambda$ = 0.5.

Apart from Capsule Network, we use Deep Convolutional Networks (CNN),
Bidirectional LSTM networks (LSTM) and Bidirectional LSTMs with attention
mechanism (ATT) as baselines in our experiments.

##  5 Experiments

We experiment with model architectures presented in the previous section. The
effect of the dimensionality of capsule output, number of routings in the
routing-by-agreement mechanism and regularization on the performance of
capsule networks are analyzed. Thereafter, we evaluate the models under multi-
label setting. For our experiments, we use the standard MFCC features of 40ms
frame length and 10ms hop length. For each frame, we calculate 19 leading
coefficients along with delta and delta-delta derivatives and energies.
Although adding other features such as zero-crossing rate (ZCR), root mean
square (RMS) energy, pitch etc. can give better results than using MFCCs
alone. We refrain from including them as they are task specific and the goal
is to compare different models and parameter values in general setting rather
than getting the best results on some particular task. All the datasets are
approximately balanced, hence we choose accuracy as our performance metric.

###  5.1 Model Comparison

As shown in Table 1, we observe significant improvement in performance with
capsule networks when compared with other deep learning models, except for
FSDD dataset. The capsule network consistently out-performs Attention LSTM
network which is considered state-of-the-art for many audio classification
tasks. The improvement is especially prominent in the Urban8K dataset where
accuracy improved from 59.5% to 66.2%. This experiment shows the advantage of
using the capsule network with dynamic routing-by-agreement compared to other
models.

###  5.2 Effect of Routings

We experiment with three values of routings 1,3 and 5. Like [11], we found
that higher values of routings tend to overfit the dataset. In Table 1, we can
see that this is especially noticeable for a small dataset like FSDD.

Fig. 2: Dimension of Capsule vs Accuracy

###  5.3 Effect of Dimensionality of Capsules

We vary the dimension of capsules from 2 to 32 and measure the accuracy on the
test set. From figure 2, we observe a trend in accuracy that it first
increases with dimension and then decreases. One plausible explanation of this
behaviour is that, at lower dimensions, CapsNet doesn’t have the capacity to
learn and it underfits the data, while at higher dimension it becomes easier
to overfit the training data. Thus, the model capacity acts as a regularizer.
One more supporting evidence is that datasets with lesser data (VCTK) are more
affected by increasing the dimension.

###  5.4 Regularization

Inspired by [11], we increase regularization by adding a decoder network of
fully connected layers after the capsule layer to reconstruct the MFCCs. To
reconstruct the inputs, the capsules have to encode the instantiation
parameters of the input signal. As the scale of the data varies across
features, we first scale the data using min-max scaling to prevent few
features dominating the loss. Total loss for the model is the weighted sum of
margin loss and Mean Absolute Error for reconstruction. As seen in Table 1,
adding regularization is generally beneficial especially when training data is
not very large like FSDD.

| ATT | CAPS
---|---|---
Multi-VCTK | 0.877 | 0.90
Multi-MUSAN | 0.721 | 0.737
Table 2: Multi-label Accuracy

###  5.5 Multi-label Setting

In this setting, we compare Bidirectional LSTM with Attention model, trained
using binary cross-entropy loss, with Capsule Networks. We use Multi-VCTK and
Multi-Musan datasets described in section 3. Weighted accuracy is used for
comparing the models. We change the weighing down parameter, $\lambda$, from
equation 1 to 1 to increase the effect of false positives. Results in Table 2
suggest that routing-by-agreement allows each capsule to pick inputs which are
consistent with its current output by increasing their weights and decreasing
the weight of others. This reduces interference of other classes, leading to
better results.

##  6 Inference & Transfer Learning

Fig. 3: Scatter Plot of Amplitude Variations Fig. 4: Scatter Plot of Speed
Variations

###  6.1 Amplitude & Speed Variation

In [11], the authors infer the effect of coefficients of the capsule’s
activity vector by perturbing the vector by a small amount and observing the
reconstructed output. MFCCs lose a lot of information about voicing/pitch and
thus it is not possible to generate good quality audio back from MFCCs. Hence,
unlike images, observing the effect by perception is not the ideal solution.
Instead, we alter the input signal slightly and observe the changes in capsule
output.

We vary the amplitude by adding and reducing constant signals. The CapsNet
model is trained on this augmented data. We then pass the same audio with
different values of the added signal and observe the capsule activity vectors
by applying PCA on the output of the relevant capsule. This is plotted in
figure 3. The label denotes the fixed signal used for augmentation. We perform
a similar experiment with augmented data generated by reducing and increasing
speed. The result is in figure 4, where the label signifies the factor by
which the signal was sped up. In both figures, we observe that the signals
with increased amplitude/speed are clearly separated from those with decreased
amplitude/speed. Moreover, two components are able to explain majority of
variance in data. This implies that output vector stores information about the
orientation(pose) of the input signal and it only requires few dimension in
PCA space to store the majority of information about a particular aspect of
orientation.

###  6.2 Transfer Learning

Transfer learning applies knowledge gained on the source domain to a related
target domain. Capsule Network offers a direct way of applying transfer
learning as we can use the activity vectors of capsules as supplementary
features. To verify this, we use the model trained on Iemocap dataset and use
the output of the capsule layer as additional input along with MFCCs on
Ravdess dataset, where the emotion classes and settings are different but
related. The six class classification accuracy jumped from 41% to 50% with
transfer learning signifying that activity vectors of capsule contain
information about presence and orientation of corresponding entity which can
be translated to a related domain.

##  7 Conclusion

In this paper, we have proposed a novel capsule network architecture and
regularization technique fit for the audio domain. We showed that our approach
works better than other deep learning approaches under similar conditions.
Regularization, along with varying the number of routings and dimension of
capsule, can significantly improve the results. We also demonstrated that
outputs of capsules can be used for getting insights into the data and for
transfer learning on a related dataset.

## References

  * [1] Sreedhar Bhukya,  “Effect of gender on improving speech recognition system,”  2018\.
  * [2] Alexandros Roniotis and Manolis Tsiknakis,  “Detecting depression using voice signal extracted by chatbots: A feasibility study,”  in Interactivity, Game Creation, Design, Learning, and Innovation, Anthony L. Brooks, Eva Brooks, and Nikolas Vidakis, Eds., Cham, 2018, pp. 386–392, Springer International Publishing.
  * [3] Mousmita Sarma, Pegah Ghahremani, Daniel Povey, Nagendra Goel, Kandarpa Sarma, and Najim Dehak,  “Emotion identification from raw speech signals using dnns,”  pp. 3097–3101, 09 2018.
  * [4] Emre Çakir, Giambattista Parascandolo, Toni Heittola, Heikki Huttunen, and Tuomas Virtanen,  “Convolutional recurrent neural networks for polyphonic sound event detection,”  CoRR, vol. abs/1702.06286, 2017.
  * [5] Jinkyu Lee and Ivan Tashev,  “High-level feature representation using recurrent neural network for speech emotion recognition,”  in Interspeech 2015. September 2015, ISCA - International Speech Communication Association.
  * [6] Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio,  “Neural machine translation by jointly learning to align and translate,”  CoRR, vol. abs/1409.0473, 2014.
  * [7] Kelvin Xu, Jimmy Ba, Ryan Kiros, Kyunghyun Cho, Aaron C. Courville, Ruslan Salakhutdinov, Richard S. Zemel, and Yoshua Bengio,  “Show, attend and tell: Neural image caption generation with visual attention,”  CoRR, vol. abs/1502.03044, 2015.
  * [8] Yong Xu, Qiuqiang Kong, Qiang Huang, Wenwu Wang, and Mark D. Plumbley,  “Attention and localization based on a deep convolutional recurrent model for weakly supervised audio tagging,”  CoRR, vol. abs/1703.06052, 2017.
  * [9] Yong Xu, Qiuqiang Kong, Wenwu Wang, and Mark D. Plumbley,  “Large-scale weakly supervised audio classification using gated convolutional neural network,”  CoRR, vol. abs/1710.00343, 2017.
  * [10] Geoffrey E. Hinton, Alex Krizhevsky, and Sida D. Wang,  “Transforming auto-encoders,”  in Artificial Neural Networks and Machine Learning – ICANN 2011, Timo Honkela, Włodzisław Duch, Mark Girolami, and Samuel Kaski, Eds., Berlin, Heidelberg, 2011, pp. 44–51, Springer Berlin Heidelberg.
  * [11] Sara Sabour, Nicholas Frosst, and Geoffrey E. Hinton,  “Dynamic routing between capsules,”  CoRR, vol. abs/1710.09829, 2017.
  * [12] Kun Han, Dong Yu, and Ivan Tashev,  “Speech emotion recognition using deep neural network and extreme learning machine,”  September 2014.
  * [13] Zakariya Qawaqneh, Arafat Abu Mallouh, and Buket D. Barkana,  “Deep neural network framework and transformed mfccs for speaker’s age and gender classification,”  Knowledge-Based Systems, vol. 115, pp. 5 – 14, 2017.
  * [14] Justin Salamon and Juan Pablo Bello,  “Deep convolutional neural networks and data augmentation for environmental sound classification,”  CoRR, vol. abs/1608.04363, 2016.
  * [15] Parnian Afshar, Arash Mohammadi, and Konstantinos N. Plataniotis,  “Brain tumor type classification via capsule networks,”  in ICIP, 2018.
  * [16] Amara Dinesh Kumar,  “Novel deep learning model for traffic sign detection using capsule networks,”  CoRR, vol. abs/1805.04424, 2018.
  * [17] Turab Iqbal, Yong Xu, Qiuqiang Kong, and Wenwu Wang,  “Capsule routing for sound event detection,”  CoRR, vol. abs/1806.04699, 2018.
  * [18] Carlos Busso, Murtaza Bulut, Chi-Chun Lee, Abe Kazemzadeh, Emily Mower Provost, Samuel Kim, Jeannette N. Chang, Sungbok Lee, and Shrikanth Narayanan,  “Iemocap: interactive emotional dyadic motion capture database,”  Language Resources and Evaluation, vol. 42, pp. 335–359, 2008.
  * [19] Steven R. Livingstone and Frank A. Russo,  “The ryerson audio-visual database of emotional speech and song (ravdess): A dynamic, multimodal set of facial and vocal expressions in north american english,”  PLOS ONE, vol. 13, no. 5, pp. 1–35, 05 2018.
  * [20] Kirsten MacDonald et al. Christophe Veaux, Junichi Yamagishi,  “Cstr vctk corpus: English multi-speaker corpus for cstr voice cloning toolkit,”  2017\.
  * [21] J. Salamon, C. Jacoby, and J. P. Bello,  “A dataset and taxonomy for urban sound research,”  in 22nd ACM International Conference on Multimedia (ACM-MM’14), Orlando, FL, USA, Nov. 2014, pp. 1041–1044.
  * [22] Zohar Jackson, César Souza, Jason Flaks, Yuxin Pan, Hereman Nicolas, and Adhish Thite,  “Jakobovski/free-spoken-digit-dataset: v1.0.8,” Aug. 2018.
  * [23] David Snyder, Guoguo Chen, and Daniel Povey,  “MUSAN: A music, speech, and noise corpus,”  CoRR, vol. abs/1510.08484, 2015.