This chapter presents an overview on the experimental setup and the methodology for performing the test series and acquiring the data.\\
The shaking table in VKI laboratories was used for performing the test cases of interest, It has 3 degree of freedom with hydraulic piston type actuators and a well lubricated mechanism that performs independent motion in sway, surge and heave. ALFRED model had been designed by VKI team in the past years and was properly mounted on the shaking table for the PASCAL project purposes (Chapter \ref{parag:PASCAL_project}). The model consists of a 1:18.4 scaled reproduction in plexiglass of the very hot plenum of ALFRED reactor demonstrator, based on equivalence related to Froude's number because waves amplitude depend on the acceleration of external excitation and gravitational acceleration. The model represents properly the internal structure of the nuclear reactor demonstrator in according to the similarities studies, which are based on the assumptions described in Chapter \ref{parag:similarity}.\\
A combination of two different types of accelerometer has been mounted on the table. The primary acceleration measurements system is a proper configuration of six digital accelerometers developed in VKI, and based on the MMA8451Q digital sensor. The secondary acceleration measurements system is a ceramic shear high sensitivity sensor, a PCB Piezotronics 356B18.\\
The 1D elevation of the free surface of water has been captured by two capacitance probes provided by Artelia. These sensors measure the capacitance of a copper wire in function of its immersed height in the water. Three capacitance probes were supposed to work, but one of them revealed faulting for reasons still unknown by the time of the first experimental campaign. Calibration of them has been performed twice, one at the beginning and one at the ending of the test, as good practice suggests. According to ASME Performance Test Code 19.1 (2018) \cite{ASMEptc191}, a Monte Carlo method has been used to extract uncertainty from probes measurements. In particular, for the capacitance probes this method has been repeated on 50,000 random points from the probability density function calculated on the calibration test. At the end of the first campaign, the calibration results were each other consistent for the two working probes, while it shows some issues on the uncertainty values for the faulting sensor.\\
An Arduino at 200 Hz interface is used to drive the six accelerometers and acquire the measurements, while the PCB accelerometers and the capacitance probes are connected to a NI DAQ 9215 at 2048 Hz with their own cards to acquire the data. The whole system is connected to a PC by USB ports, so the collective data are summed up in one \texttt{.tdms} file compiled properly by the LabView program. In post-processing phase, the acceleration from PCB and the amplitude of free surface was resampled at 200 Hz, according to the acceleration taken from the Arduino.\\
In addition to the essential experimental setup, for the first test campaign a high-speed camera \textit{Dantec - SpeedSense M310} camera was positioned at a proper distance from the shaking table for catching the free surface motion of this special case study. The acquisition resolution was set to 768 pixels*576 pixels and the frame rate was of 50 frame per second. The camera was not fitted for capturing quantitative amplitude of the free surface motion, but only for identifying the sloshing resonance modes and capturing non-linear phenomenon. Behind the ALFRED model is collocated a large sheet of translucent paper, which filtrates the light of a square white LED device for providing a uniform illumination.\\
In the following paragraphs, a deeper look on the setup is furnished. ALFRED model is described for giving the reader a glimpse of the complexity and distinctiveness of it. Besides, it aims to give the reader an explanation on why this structural configuration should be congenial to the sloshing problem. Shaking table is described in order to learn how to treat the acquired data from the test in terms of instrumentation limits, so the uncertainty budgets on the results. Capacitance probes are analysed in details and a deeper look in Monte Carlo code is provided for a correct interpretation of the calibration laws output. Finally, a final and complete overview of the shaking table facility is provided, highlighting issues and practical procedures that have been followed to perform the test campaign.
%=====================================================================================
\section{Shaking table - SHAKESPEARE facility}
Here, a small overview about the shaking table facility is provided. SHAKESPEARE stands for SHaking Apparatus for Kinetic Experiments of Sloshing Projects with EArthquake REproduction. This facility has been designed for testing the MYRRHA reactor's mockup, which is the ALFRED "brother" and it's managed by the \textit{Belgian} \textit{Centre} \textit{for} \textit{Nuclear} \textit{Research}, \textit{SCK} \textit{CEN}.\\
SHAKESPEARE is a three axis shaking table used for simulating the seismic events on a prototype of the ALFRED reactor. It allows a maximum acceleration of 1.1 g for a maximum mass of 500 kg load, according to \cite{Democritos_sloshing_phase_4_report}. SHAKESPEARE shaking table is dimensioned considering that the larger model scale cannot be bigger 1/10 of the prototype. This is a crucial point because the geometric similarity must be respected. The dimensions of the table are the product of a tradeoff: closer the model dimension are to the prototype and more all the non-dimensional number are easily respected; by the other hand, large model are expensive.\\
In order to provide the forces for reaching the required accelerations in the three directions of the geometrical space, this shaking table is installed with one hydraulic cylinder piston type actuator, as it's shown in Figure \ref{fig:shakespeare_1}. This system assures high frequency response, for reaching a more realistic seismic simulation from up to 10-15 Hz. The energy that the actuator needs is provided by a hydraulic system collocated outside the laboratory, while it's controlled by a control unit shown in Figure \ref{fig:shakespeare_2}.
\begin{figure}[h]
     \centering
     \begin{subfigure}[b]{0.45\textwidth}
         \centering
         \includegraphics[scale=0.45]{immagini/setup/Shakespeare_placement_VKI.png}
         \caption{Shaking table placement}
     \label{fig:shakespeare_1_a}
     \end{subfigure}
     \begin{subfigure}[b]{0.45\textwidth}
         \centering
    \includegraphics[scale=0.30]{immagini/setup/Shakespeare_working_concept.png}
         \caption{}
         \label{fig:shakespeare_1_b}
     \end{subfigure}
        \caption{SHAKESPEARE shaking table (\cite{Democritos_sloshing_phase_4_report}): (a) shaking table placement; (b) shaking table concept}
        \label{fig:shakespeare_1}
\end{figure}
\begin{figure}[h]
     \centering
     \begin{subfigure}[b]{0.45\textwidth}
         \centering
         \includegraphics[scale=0.50]{immagini/setup/Shakespeare_control_unit.png}
         \caption{}
     \label{fig:shakespeare_2_a}
     \end{subfigure}
     \begin{subfigure}[b]{0.45\textwidth}
         \centering
    \includegraphics[scale=0.55]{immagini/setup/Shakespeare_pumps.png}
         \caption{}
         \label{fig:shakespeare_2_b}
     \end{subfigure}
        \caption{SHAKESPEARE shaking table (\cite{Democritos_sloshing_phase_4_report}): (a) shaking table control unit; (b) external hydraulic pumps that provide the hydraulic power for the shaking table facility}
        \label{fig:shakespeare_2}
\end{figure}
A concrete base attaches the whole shaking table to the floor, added by a floating base that supports the shaking table during the excitations. Each one of them are divided by an anti-vibration zone, specifically design for protecting the building by vibrations of the table. The supporting frame is installed upon the floating base, and it's composed by three share-shaped frames: the first one, on the top of it, provides movement along X-axis; the second one provides movement along Y-axis; the third one provides movement along Z-axis, supports the total weight of the table and its guides are fixed on the supporting frame. The movement of each frame is independent because of the guides amid them. The modular design can ensure that the motion on each degree of freedom is independent and enough well controlled. The lack of a feedback loop on the module's position doesn't give so much confidence as on the frequency actuation. For more information about table uncertainties on displacements and frequencies, Simonini provides an example of demonstration of that in \cite{Sloshing_dynamics_investigation_by_means_of_non-intrusive_measurement_techniques}.
%================================================================================
\section{ALFRED model}
\begin{wrapfigure}{r}{0.30\textwidth}
    \centering
    \includegraphics[scale=0.3]{immagini/setup/Alfred0.png}
    \caption{\textit{Advanced Lead Fast Reactor European Demonstrator} \cite{Alfred_ansaldo_nucleare}}
    \label{fig:ALFRED_primary_system}
\end{wrapfigure}
ALFRED demonstrator reactor sketch is shown in Figure \ref{fig:ALFRED_primary_system}, taken from the technical report in \cite{Alfred}. The model consists of a 1:18.4 scaled reproduction in plexiglass of the very hot plenum of the demonstrator, based on equivalence related to Froude's number because waves amplitude depend on the acceleration of external excitation and the gravitational one. The model is in plexiglass, and it's contained in a plexiglass cubic container for protecting the model from the outside agents, minimizing optical distortion when an external camera is used, besides an easy way to install it on the shaking table.\\
Entering the real demonstrator, the central core is in the very centre of the internal structure, and it's surrounded by an annulus filled with molten lead (chemical element \textit{Pb}). According to the similarities studied previously and conducted by VKI, the model is filled with distilled water.
\subsection{Similarity}\label{parag:similarity}
The study case's container can be seen as an excited annular tank partially filled with liquid at a certain height, $h$. The fluid is considered incompressible, $\nabla\rho=0$ and no heat transfer is considered during the sloshing processes. Bond number is considered negligible, so in the current case study the surface tension doesn't affect the sloshing processes.\\
The similarity within the actual demonstrator and the model is to ALFRED scaled is presented in the technical report \cite{ALFRED_Mockup}. Starting from the momentum conservation equation, the Navier-Stokes equation for momentum is made dimensionless and the manipulated in order to make appear the following characteristic numbers:
\begin{itemize}
    \item \textit{Froude number} $Fr=\frac{U^2}{gL}$, which represents the relation within inertial load and gravitational forces.
    \item \textit{Strouhal number} $St=\frac{L}{U\tau}$, which represents the relation within characteristic time of the phenomenon and the one of the liquid on exam;
    \item \textit{Reynolds number} $Re=\frac{UL}{\nu}=\frac{UL\rho}{\mu}$, which represents the relation within inertial load and viscous force.
\end{itemize}
Appendix \ref{appendix:dimensionless_analysis} presents some critical considerations made during this fundamental dimensionless analysis.\\
%If a sinusoidal excitation along \textit{x-axis} side is considered, as displacement $X=Asin(\omega t)$, and the velocity $U$ is equal to excitation velocity $U=\frac{\partial X}{\partial t}\sim A\omega$, so the characteristic numbers in function of the very specific case study are the following:
%$$
%    St=\frac{L}{U\tau}=\frac{R}{A}
%$$
%$$
%    Re=\frac{AR\omega}{\nu}
%$$
%$$
%    Fr=\frac{A^2}{R}\frac{\omega^2}{g}
%$$
%where $L$ indicates the hydraulic diameter of the tank which corresponds to the external radius of the tank $R$, $\tau$ the characteristic time of sloshing phenomenon equal to the invers of the forcing pulsation $\tau=\omega^{-1}$ and $A$ is the forcing amplitude.\\
The sloshing processes in the ALFRED's model involve gravitational dependent waves, so the fundamental similarity with the actual demonstrator is in relation to the Froude number. Other condition that has been imposed in \cite{ALFRED_Mockup} are about the Strouhal number and the ratio between water depth and external radius $h/R$. From the technical report, it's known the result:
\begin{equation}\label{eq:similary_with_ALFRED}
    \begin{cases}
    (Fr)_{ALFRED}=(Fr)_{Model}\\
    (St)_{ALFRED}=(St)_{Model}\\
    (h/R)_{ALFRED}=(h/R)_{Model}
    \end{cases}
    \to 
    \begin{cases}
        A_{Model}=0.054\times A_{ALFRED}\\
        f_{Model}=4.29\times f_{ALFRED}\\
        h_{Model}=8.84\,\mathrm{cm}
    \end{cases}
\end{equation}
where $A$ and $f$ are the amplitude and frequency of the external excitation to the pool, and $h_{model}$ is the computed water depth for a well fitted geometrical analogy.\\
Figure \ref{fig:ALFRED_geometry_2} presents the  model geometry in the CAD file with design dimensions for the plexyglass model's elements. Table \ref{tab:geometric_values_similarity} sums up the effective dimension before and after the application of the similarity studies within the demonstrator and the model.
\begin{figure}[H]
    \centering
    \includegraphics[scale=0.95]{immagini/setup/CAD_model_1.png}
    \caption{CAD drawing of ALFRED's model \cite{ALFRED_Mockup}: it's clear in the drawing that the membrane has six holes in the annulus surface, for suiting the SGs and the Pumps of the three triplets}
    \label{fig:ALFRED_geometry_2}
\end{figure}
\begin{table}[H]
\centering
\begin{tabular}{|llll|}
\hline
\multicolumn{1}{|c|}{} & \multicolumn{1}{c|}{ALFRED} & \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}ALFRED's \\ model\end{tabular}} & Model scaling \\ \hline
\multicolumn{1}{|l|}{Internal Diameter d {[}m{]}}       & \multicolumn{1}{l|}{3.500} & \multicolumn{1}{l|}{0.1900} & 1:18.4 \\ \hline
\multicolumn{1}{|l|}{External Diameter D {[}m{]}}       & \multicolumn{1}{l|}{7.3000}  & \multicolumn{1}{l|}{0.3960} & 1:18.4  \\ \hline
\multicolumn{1}{|l|}{Water depth h {[}m{]}}        & \multicolumn{1}{l|}{1.6300}  & \multicolumn{1}{l|}{0.0884} & 1:18.4  \\ \hline
\multicolumn{1}{|l|}{h/R ratio}                         & \multicolumn{1}{l|}{0.4465}  & \multicolumn{1}{l|}{0.4465} & 1:1     \\ \hline
\end{tabular}
\caption{Geometric parameters that affect the similarity studies; $h/R$ ratio is correctly equal to 1, where $h$ refers to the water depth up to the diaphragm}
\label{tab:geometric_values_similarity}
\end{table}
%---------------------------------------------------------------------------------
\subsection{Internal structure}
The model has been designed taking in account the following design expedients:
\begin{itemize}
    \item the pool below the hot plenum is full of the same liquid used for the top one, and it's not considered for the specific sloshing problem; so, the free surface is located in the hot plenum, while the bottom part of the reactor is full of liquid;
    \item upper pool and bottom pool are separated by a non-elastic diaphragm orthogonal to the longitudinal axe of the tank, creating a key-element discontinuity;
    \item the Steam Generator (SG) and the pumps are connected to the bottom part with a certain porosity, which could be changed depending on the initial condition of performed test; instead, the Decay Heat Removal (DHR), which in the actual demonstrator is dedicated to the cooling of the remaining heat due to decay after the showdown of the reactor, is represented as a plain tube not connected to the diaphragm.
\end{itemize}
The discontinuity membrane is the key-element because from it the water depth of reference starts. Since the geometry similarity is specifically built to preserve the hot plenum to radius ratio $(h/R)$ equal to 1, it's easy to understand its importance.\\
The external annulus it's provided with 9 cylindrical seats, which are suitable for the entering of 9 cylindrical piston structures. The 9 plain tubes are organized in 3 triplets of elements distributed evenly at 40 degrees intervals.\\
The DHR are represented as close transparent plexiglass tubes fixed on the top of the model (Figure \ref{fig:ALFRED_geometry_2}). With a diameter of $49.5$ mm and height of $223$ mm, they cannot go through the diaphragm.\\
The three Steam Generators are 3D-printed cylinders because their main function is damping the motion of the liquid. The external diameter is equal to $d_{SG}=60$ mm while its height is equal to $239$ mm. In reality, they are a complex composition of very small tubes, one near the others, that create damping in the motion from a dynamic point of view of the system. In theory, the porosity is a level of the motion damping imposed by design and can be changed as preferred only by means of a new 3D-manufactured piece. This kind of variability is an add-on useful if one wants to simulate an internal accident in the reactor. In the following test, something like that will be reproduced but removing entirely the three steam generators, because the lack of time have not allowed to wait for new 3D-printed pieces.\\
In this model, the pumps are seated to suit the capacitance probes to measure the water height in the hot plenum part. They are in aluminium and on their top are drilled in order to successfully complete the probe installation. The outer diameter is equal to $50.1$ mm and the height of the cylindrical corp is equal to $235$ mm. As it's shown in Figure \ref{fig:ALFRED_geometry_3}, the pumps present a drilled bottom floor, and the number of holes gives the \textit{pressure drop} $\xi$ aimed. In the real demonstrator, $17.4$ tonne/s are flowing through the pumps so each of them bleed $5.8$ tonne/s, and a pressure drop of $\Delta P=1kPa$ can be considered. The singular pressure losses are equal to $\xi=\frac{\Delta P}{1/2\rho w_0^2}=23.8$, where $\rho=10570$ $\mathrm{kg/m^2}$ is the density of \textit{Pb}. In Table \ref{tab:plain_tube_dimension} there's an overview on the plain tube dimensions in the model.\\
It's not a matter in this work explaining the reasons of this choice as all the other parameters, such as the porosity for example. It's important, instead, highlighting that the pressure drop represents a consistent element in the liquid's dynamic in the model, if it has to be representative of reality. Parameters such as the pressure drop are not going to be changed during the test performed.
\begin{table}[H]
\centering
{\fontsize{10}{13}\selectfont
\begin{tabular}{|lllll|}
\hline
\multicolumn{5}{|l|}{\textbf{Dimensions of cylindrical tubes}}                                                           \\ \hline
\multicolumn{1}{|l|}{} &
  \multicolumn{1}{l|}{Diameter {[}mm{]}} &
  \multicolumn{1}{l|}{Height {[}mm{]}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}Number on \\ the mockup\end{tabular}} &
  \begin{tabular}[c]{@{}l@{}}Goes across\\ diaphragm?\end{tabular} \\ \hline
\multicolumn{1}{|l|}{SG}   & \multicolumn{1}{l|}{60.0} & \multicolumn{1}{l|}{239} & \multicolumn{1}{l|}{3} & Yes \\ \hline
\multicolumn{1}{|l|}{DHR}  & \multicolumn{1}{l|}{49.5} & \multicolumn{1}{l|}{223} & \multicolumn{1}{l|}{3} & No  \\ \hline
\multicolumn{1}{|l|}{Pump} & \multicolumn{1}{l|}{50.1} & \multicolumn{1}{l|}{235} & \multicolumn{1}{l|}{3} & Yes \\ \hline
\end{tabular}}
\caption{Main dimensions of the elements of the three triplets: SG, DHR and Pumps; it's highlighted which tube goes across the diaphragm \cite{ALFRED_Mockup}}
\label{tab:plain_tube_dimension}
\end{table}
\begin{figure}[H]
    \centering
    \includegraphics[scale=0.80]{immagini/setup/CAD_model_2.png}
    \caption{CAD drawing of hot plenum of ALFRED's model \cite{ALFRED_Mockup}: it's clear in the drawing that the membrane has six holes in the annulus surface, for suiting the SGs and the Pumps of the three triplets}
    \label{fig:ALFRED_geometry_3}
\end{figure}
\begin{figure}[h]
    \centering
    \includegraphics[scale=0.9]{immagini/setup/Geometry3.png}
    \caption{Some photos of the DHR, SG and pump used for completing the ALFRED's model \cite{ALFRED_Mockup}); the Figure includes also a CAD model of the Pump to highlight the holes-configuration at the bottom of the tube}
    \label{fig:ALFRED_tubes}
\end{figure}
%=================================================================================
%\clearpage
\section{Accelerometers applied on the shaking table}\label{parag:accelerometers_on_table}
A combination of two different types of accelerometers has been mounted on the shaking table. The primary acceleration measurements system is a proper configuration of six digital accelerometers developed in VKI, and base on the MMA8451Q digital sensor. The accelerometers are applied in a configuration shown in Figure \ref{fig:accelerometers_1} to average the acceleration all around the table, and avoiding great interference noise because the table resonance at 12-14 Hz. Before fastening the six small boxes, the surfaces have been cleaned and approximately polished for assuring planar contact. Besides, they must be positioned accordingly to the three axis of the shaking table, which are underlined in Figure \ref{fig:drawing_mockup_a}.\\
The "Octopus" of six accelerometers is connected to the \texttt{LabView} interface through an Arduino card by means of a USB port and provides measurement of acceleration. The frequency of data acquisition of the "Octopus" Arduino card is equal to 200 Hz.\\
The secondary acceleration measurements system is a ceramic shear high sensitivity sensor, a \textit{PCB Piezotronics 356B18}. The PCB Piezotronics 356B18 analogic accelerometer is installed on the top surface of the shaking table. The sensor is connected to a NI DAQ 9215, which is the same used for the capacitance probes data acquisition (\ref{parag:capacitance_probes}). The reference system of the acceleration recorded by the PCB sensor is rotated of an $\alpha=37^{\circ}35'$ angle with respect to $\{x,y,z\}$ reference system of the table. In Table \ref{tab:chapter_setup_PCB_acceleration} are reported the effective sensitivity along the $\{x,y,z\}$ directions of the PCB accelerometer. The PCB acquires data at a very high frequency of above 2000 Hz, so a post-processing consideration has been done to resolve the contradiction by the means of a resampling of the signals at the lowest acquisition frequency of 200 Hz.
\begin{table}[H]
\centering
\begin{tabular}{|l|l|}
\hline
\multicolumn{1}{|c|}{Axis} & \multicolumn{1}{c|}{Sensitivity $e_i${[}mV/g{]}} \\ \hline
x                          & 1037                                        \\ \hline
y                          & 1088                                        \\ \hline
z                          & 1033                                        \\ \hline
\end{tabular}
\caption{Accelerometer sensitivity \cite{PCB_Piezotronics}: common sensitivity used in the \texttt{LabView} program is equal to $e=1000$ mV/g, so it's necessary to multiply the acquired acceleration in each direction by a factor equal to $e_i/1000$}
\label{tab:chapter_setup_PCB_acceleration}
\end{table}
\begin{figure}[H]
     \centering
     \begin{subfigure}[b]{0.45\textwidth}
         \centering
         \includegraphics[scale=0.75]{immagini//setup/accelerometers_photo.png}
         \caption{}
     \label{fig:accelerometers_1_a}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.45\textwidth}
         \centering
         \includegraphics[scale=0.85]{immagini/setup/accelerometers_positioning.png}
         \caption{}
         \label{fig:accelerometers_1_b}
     \end{subfigure}
        \caption{Accelerometers on the table: $A$ stands for the MMA8451Q digital sensor \cite{MMA8451Q_data_sheet} in the \textit{octopus configuration}; $B$ stands for the PCB}
\label{fig:accelerometers_1}
\end{figure}
%===================================================================
\section{Capacitance probes}\label{parag:capacitance_probes}
The amplitude of the liquid free surface motion were supposed to be measured with three capacitance probes, which are provided by Artelia group. Each of them is constituted of a single wire of copper attached to a spring at the top of the particular structure of the pump tubes, providing so the preload mechanically, as it can be seen in Figure \ref{fig:capacitance_probes}. The conductive surface of the wire will start working as a capacitor by the proximity of the water in the hot plenum pool. A simplified scheme is reported in Figure \ref{fig:capacitance_probes}, while the respective dimensions are reported in Table \ref{tab:plain_tube_dimension} and Table \ref{tab:chapter_setup_probe_placement_2}.
\begin{figure}[H]
     \centering
     \begin{subfigure}[b]{0.30\textwidth}
         \centering
         \includegraphics[scale=0.35]{immagini/setup/Capacitance_probes_drawing_1.png}
         \caption{}
     \label{fig:capacitance_probes_a}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.30\textwidth}
         \centering
        \includegraphics[scale=0.35]{immagini/setup/Capacitance_probes_drawing_2.png}
         \caption{}
         \label{fig:capacitance_probes_b}
     \end{subfigure}
     \begin{subfigure}[b]{0.30\textwidth}
         \centering
        \includegraphics[scale=0.45]{immagini/setup/Capacitance_probes_drawing_3.png}
         \caption{}
         \label{fig:capacitance_probes_c}
     \end{subfigure}
        \caption{Simplified scheme of the capacitance probes: (a) overview on the pump tube structure, in which the copper wire is mechanically keeps in position by means of a spring; (b) scheme of the copper wire around the pump rigid supports; (c) section of the copper wire}
        \label{fig:capacitance_probes}
\end{figure}
\begin{table}[H]
\centering
\begin{tabular}{|l|l|l|l|}
\hline
\multicolumn{1}{|c|}{} & \multicolumn{1}{c|}{Probe 0} & \multicolumn{1}{c|}{Probe 1} & Probe 2 \\ \hline
w {[}mm{]} & 9    & 9    & 9    \\ \hline
l {[}mm{]} & 3    & 2.25 & 1    \\ \hline
d {[}mm{]} & 13.4 & 11.9 & 13.6 \\ \hline
\end{tabular}
\caption{Probe placement and position uncertainty on the measurement referring to Figure \ref{fig:capacitance_probes_c}}
\label{tab:chapter_setup_probe_placement_2}
\end{table}
The measurement principle is that the output capacitance is proportional to the part immersed in water of the probe. As it's written in \cite{Capacitance_probes}, each part of the capacitance probe immersed in water create infinite capacitors in parallel connection. So, the final capacitance is:
\begin{equation}
    C(h)\simeq\frac{2 \pi\epsilon_r\epsilon_0}{ln(d2/d1)}\sum h_i
\end{equation}
where $h_i$ is the length of probes dived in water; $\epsilon_r$ is the relative permittivity of the water in this case; $\epsilon_0=8.8542\times10^{-12}$ F/m is the permittivity of vacuum; $d_1$ and $d_2$ are the diameters of the metal probe and the insulating coating of the cable, respectively. A certain approximation must be kept into account to consider the uncertainty on the measurements of the probes.\\
A composition of oscillator/integrator connected by BNC permits to measure the evolution of height of the free surface. As the height of the water level increase, the capacitance increase with an increasing of the voltage of the capacitor probes. For technical reasons, it's preferred that the voltage variation don't exceed the range from -10 V to 10 V. Besides, the DAQ acquires data from the probes at a frequency above 2000 Hz. These sensors are connected to the NI DAQ 9215 to acquire data, also used for the PCB accelerometer.\\
For each of the three probes, the voltage measurements of the level of water in time is a mean within the two filaments. Table \ref{tab:chapter_setup_probe_placement_1} provides the location in the $X-Y$ plane of each of the three probes, and it refers to Figure \ref{fig:drawing_mockup_a}.
\begin{figure}[H]
    \centering
    \includegraphics[scale=0.65]{immagini/setup/drawing_mockup_1.png}
    \caption{Simplified sketch for the probes placement.}
    \label{fig:drawing_mockup_a}
\end{figure}
\begin{table}[H]
\centering
\begin{tabular}{|l|l|l|l|}
\hline
                             & P0                           & P1                           & P2    \\ \hline
{\color[HTML]{242021} x {[}mm{]}} & {\color[HTML]{242021} -154} & {\color[HTML]{242021} +69.0} & +104 \\ \hline
{\color[HTML]{242021} y {[}mm{]}} & {\color[HTML]{242021} -19.0} & {\color[HTML]{242021} +154} & -84.0 \\ \hline
\end{tabular}
\caption{Probe placement on the $X-Y$ plane, referring to the Cartesian reference frame in Figure \ref{fig:drawing_mockup_a}}
\label{tab:chapter_setup_probe_placement_1}
\end{table}
Other measurements techniques could be applied and used for monitoring the free surface of the liquid in the tank, as was done in the previous years (\cite{Sloshing_dynamics_investigation_by_means_of_non-intrusive_measurement_techniques} and \cite{Experimental_investigation_sloshing}). The detection of the free surface motion can be recorded by means of no-intrusive ways, such as by Level Detection and Recording (LeDaR) in 2D or by Reference Image Topography (RIT) in 3D.
%======================================================================
\section{Uncertainty on the probes' measurement}
\subsection{Calibration of the capacitance probes}\label{subsection:calib_capacitance_probes}
The three probes were calibrated by filling up the empty tank with the distilled water. In particular, the lower part of the ALFRED model until the porosity section has been filled faster than the last part of it. On the contrary, the upper part that includes the nine cylinder seats and the inner cylinder has been filled very carefully, because the probes has been measured an increasing level of water starting from zero values. Each 5mm as been taken a series of measurement from the three probes until the top of the model; then, the water has been drawn in the same way as before, so taking also the measurements each 5 mm. This process has been stopped until the desired level height has been reached. The level depends on which initial condition of water depth is requested, taking in account also that the plain tubes occupy volumes in the hot plenum representation, as they are basically dumping elements. The measures for each level has been taken with a \texttt{LabView} code that read the voltage for some seconds from the probes. In Figure \ref{fig:calibration_input_file} can be seen that there’s a measurement in voltage for each of the time step in a time range from 0 seconds to 4 seconds. Starting from this picture, it’s clear that something it’s not working properly with the P0 sensor.\\
It’s fundamental to notice that all the height used for compiling the calibration filenames are taken from a regular ruler attached to the model. The reference system in this case is from the top to the bottom of the hot plenum pool, so the raw data in voltage of each of the file are referred to a height measure that has to be properly post processed.\\
Those files and their contents are then post processed by means of a code written, created by Jean Muller, in \texttt{Python} environment. The code applies a Monte Carlo method to estimate the uncertainty on the height measurements of water depth, using 50000 points on the \textit{Probability Density Function} extracted from the raw data.
\begin{figure}[H]
    \centering 
    \includegraphics[scale=0.5]{immagini/setup/csv_calibration_file.png}
    \caption{Calibration file \textit{.csv} architecture: is outlined the time step of acquisition data, the column relative to the raw data measured from the three probes P0, P1 and P2; the final time step is equal to 4 seconds}
    \label{fig:calibration_input_file}
\end{figure}
\subsection{Initial uncertainty budget}
Calibration is normally taken as a systematic error source, and knowing that the uncertainty propagates from direct measurement (in voltage V from the probes measurements) to the derived quantities (in mm), a Monte Carlo method has been chosen to compute this propagation. The calibration is completed to find the best fit for a linear fit of the output, given in Voltage V by the probes, in function of the height. The standard that has been taken as a reference is the \textit{ASME PTC 19.1, 2018} \cite{ASMEptc191}.\\
The MCM allows taking to account correlated uncertainty sources automatically, without providing a simplified formulation for the propagation of the errors. For example, if compared to a Taylor series expansion the MCM makes no assumption on input and output \textit{Power Density Function} and, above all, doesn't require linearization, while the first above-mentioned method assumes Gaussian output PDF and requires linearization of the measurement system. Using 50000 repetition in the Monte Carlo should allow having a good fit for the calibration law.\\
The code used for the application of the MCM has been written by Jean Muller and properly modified to ask in output the calibration law linear fit. An overview of the code is provided in the Appendix \ref{appendix:MC}. The code performs 50000 repetition of the Monte Carlo method on the Probability Density Function extracted form the \textit{csv} file previously indicated.\\
For each probe a mean value for the slope $m_i$ of the curve, its intercept $q_i$ and their standard deviation $\delta m_i$ and $\delta q_i$ has been found. The law for each $i-probe$ is the following,
\begin{equation}
    h_i=m_i\times V_i+q_i
\end{equation}
with $h_i$ the free surface height (mm), $V_i$ the output voltage (V) and $m_i$ and $q_i$ the fitting couple.\\
The uncertainty is computed as follows,
\begin{equation}
    u_{h_i}=max(\sqrt{A^2+B^2+C^2})
\end{equation}
with
\begin{equation}
    \begin{cases}
        A=V\times\delta m\\
        B=\delta q\\
        C=m\times\delta V
    \end{cases}
\end{equation}
$\delta m$ and $\delta q$ go out from the Monte Carlo, V is considered within ${[}-10,10{]}$ V and $\delta V$ is the smallest measurable value of voltage, equal to $20/2^{16}$ for the NI DAQ 9215.\\
In Table \ref{tab:probes_calib_10_10_2023} and \ref{tab:probes_calib_06_11_2023} there are the results for the first and the last calibration concerning the first experimental campaign. It was necessary to confirm the consistency of the data from the probes after the P0 sensor revealed to faulting and some of the BNC cables have been changed on October 30, so the first fitting law is used for the test series until that date.
\begin{table}[H]
\centering
\begin{tabular}{|l|l|l|l|l|l|}
\hline
Probe & $m${[}mm/V{]} & $q${[}mm{]} & $\delta m$ & $\delta q$ & $u_{h_i}${[}mm{]} \\ \hline
0     & -18.3406      & 78.7737     & 0.0321     & 0.1609     & 0.3592            \\ \hline
1     & -18.2275      & 104.4165    & 0.0282     & 0.0893     & 0.2957            \\ \hline
2     & -18.6136      & 1048.1397   & 0.0293     & 0.0894     & 0.3066            \\ \hline
\end{tabular}
\caption{Calibration table for linear fitting of the 1D height measurement of the capacitance probes-results from the October 10, 2023}
\label{tab:probes_calib_10_10_2023}
\end{table}
\begin{table}[H]
\centering
\begin{tabular}{|l|l|l|l|l|l|}
\hline
Probe & $m${[}mm/V{]} & $q${[}mm{]} & $\delta m$ & $\delta q$ & $u_{h_i}${[}mm{]} \\ \hline
0     & -17.2128      & 86.3444     & 0.4398     & 1.7984     & 4.7518            \\ \hline
1     & -18.9240      & 109.5946    & 0.0284     & 0.0828     & 0.2962            \\ \hline
2     & -19.2108      & 109.4787    & 0.0297     & 0.0873     & 0.3092           \\ \hline
\end{tabular}
\caption{Calibration table for linear fitting of the 1D height measurement of the capacitance probes-results from the November 6, 2023}
\label{tab:probes_calib_06_11_2023}
\end{table}
In spite of the computed intercepts for the linear fit, what really matter are the slope coefficient because the sloshing problem of the free surface motion will be studied by means of non-dimensional amplitude $\zeta=\frac{h_i-(still\:water\:depth)}{non\:dimensional\:parameter}$. Besides, the reference system for height measurement used in the Monte Carlo method it's not the same used for studying the dynamic system; in particular, that intercept and that slope refers to a coordinate system from the top to the bottom of the tank, so indicates minor $h_i$ when the water level increases. In Figure \ref{fig:calibration_fitting_curve} a post-processed representation of the calibration fitting law is proposed.
\begin{figure}[H]
     \centering
     \begin{subfigure}[b]{0.45\textwidth}
         \centering
         \includegraphics[width=\textwidth]{immagini/setup/fitting_curve_first.png}
         \caption{}
         \label{fig:calibration_fitting_curve_a}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.45\textwidth}
         \centering
         \includegraphics[width=\textwidth]{immagini/setup/fitting_curve_second.png}
         \caption{}
         \label{fig:calibration_fitting_curve_b}
     \end{subfigure}
        \caption{(a) Fitting curve for the calibration results of October 10, 2023, used in test until; (b) Fitting curve for the calibration results of November 06, 2023}
        \label{fig:calibration_fitting_curve}
\end{figure}
\subsection{Total uncertainty budget}\label{parag:total_uncertainty}
The total uncertainty budget is computed summing up the initial uncertainty budget from the Monte Carlo method and an experimentally uncertainty related to the shake table. Repeatability test has been consisted of six test series, equal to each other for the sinusoidal input signal at 0.71 Hz, and a level of confidence of $95\%$ from a two-sides Student's t-distribution is considered. Table \ref{tab:total_uncertainty} the total uncertainty budget is presented for the probes P1 and P2.
\begin{table}[H]
\centering
\begin{tabular}{|llll|}
\hline
\multicolumn{4}{|l|}{Calibration of October 10, 2023}                                                                                 \\ \hline
\multicolumn{1}{|l|}{Probe} & \multicolumn{1}{l|}{$u_{i-MC}[\mathrm{mm}]$ initial budget} & \multicolumn{1}{l|}{$u_{i-TABLE}[\mathrm{mm}]$} & $u_i[\mathrm{mm}]$ \\ \hline
\multicolumn{1}{|l|}{P1}    & \multicolumn{1}{l|}{0.296}                         & \multicolumn{1}{l|}{1.056}             & 1.352     \\ \hline
\multicolumn{1}{|l|}{P2}    & \multicolumn{1}{l|}{0.307}                         & \multicolumn{1}{l|}{0.993}             & 1.300     \\ \hline
\multicolumn{4}{|l|}{Calibration of November 6, 2023}                                                                                 \\ \hline
\multicolumn{1}{|l|}{Probe} & \multicolumn{1}{l|}{$u_{i-MC}[\mathrm{mm}]$ initial budget} & \multicolumn{1}{l|}{$u_{i-TABLE}[\mathrm{mm}]$} & $u_i[\mathrm{mm}]$ \\ \hline
\multicolumn{1}{|l|}{P1}    & \multicolumn{1}{l|}{0.296}                         & \multicolumn{1}{l|}{1.056}             & 1.352     \\ \hline
\multicolumn{1}{|l|}{P2}    & \multicolumn{1}{l|}{0.309}                         & \multicolumn{1}{l|}{0.993}             & 1.302     \\ \hline
\end{tabular}
\caption{Total uncertainty on the probes measurements: $u_{i-TOTAL}=u_{i-MC}+u_{i-TABLE}$}\label{tab:total_uncertainty}
\end{table}
%=======================================================================
\section{Complete setup}
In Figure \ref{fig:ALFRED_topview} is shown the top view. The darker cylinders are the steam generators in 3D-printed material, removable or replaceable if a changed of porosity is wanted to be performed. Also in Figure \ref{fig:ALFRED_topview} can be seen the capacitance probes, while the remaining three seats can be suited for the addition of strain gauge sensors. In confirmation of what has already been written, the order in the position of three triplets, counting the 3D-printed ones, the capacitance probes and the possible seats for strain gauge it's respected in accordance to the CAD model (Figure \ref{fig:ALFRED_geometry_2} and Figure \ref{fig:ALFRED_geometry_3}).\\
In figure \ref{fig:ALFRED_complet_setup_frontview} an oversight of the complete operating facility is shown. A high-speed camera \textit{Dantec - SpeedSense M310} camera was positioned at a proper distance from the shaking table for catching the free surface motion of this special case study. The acquisition resolution was set to 768 pixels*576 pixels and the frame rate was of 50 frame per second. The camera was not fitted for capturing quantitative amplitude of the free surface motion, but only for identifying the sloshing resonance modes and capturing non-linear phenomenon. Behind the ALFRED mockup is collocated a large sheet of translucent paper, which filtrates the light of a square white LED device for providing a uniform illumination.\\
The central PC is connected with a special interface to the shaking table, providing a specific Control Bench Unit of the facility. From the interface, the proper status of the facility can be checked and managed if needed. Besides, all the input file are loaded there, with all the limitation that the software imposes for a correct test performance. It's noticed that all the signal used to catch significant results respect those limitations, otherwise the confidence of the results became really unacceptable. For example, one of the major issue has been creating proper input signals that don't abruptly stop the movements of the shaking table's plates or give a shock to the dynamic system with unexpected high accelerations. It has been really challenging the setting up of the sampling frequency of the input file and the correct correlation with the table's reading frequency of the input signal.
\begin{figure}[h]
     \centering
     \begin{subfigure}[b]{0.45\textwidth}
         \centering
         \includegraphics[width=\textwidth]{immagini/setup/Alfred5.png}
         \caption{}
         \label{fig:ALFRED_a}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.45\textwidth}
         \centering
         \includegraphics[width=\textwidth]{immagini/setup/Alfred4.png}
         \caption{}
         \label{fig:ALFRED_b}
     \end{subfigure}
        \caption{ALFRED model mounted on the shaking table: (a) mockup with the 3 SG installed; The model is provided with a ruler on the side to measure the water depth each time that it needs to be changed. (b) mockup without the 3 SG for simulating a changing porosity of the internal structure due to an accident simulation}
        \label{fig:ALFRED}
\end{figure}
\begin{figure}[h]
     \centering
     \begin{subfigure}[b]{0.45\textwidth}
         \centering \includegraphics[scale=0.80]{immagini/setup/Alfred3.png}
    \caption{}
    \label{fig:ALFRED_topview}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.45\textwidth}
         \centering \includegraphics[scale=0.075]{immagini/setup/Alfred6.jpg}
    \caption{}
    \label{fig:ALFRED_complet_setup_frontview}
     \end{subfigure}
        \caption{ALFRED model mounted on the shaking table: (a) top view. (b) a front view of the lab facility}
        \label{fig:ALFRED_abcde}
\end{figure}
\clearpage
\section{Creation of the input signal}
\subsection{Horizontal base excitation input signal}\label{parag:creation_input_signal}
Horizontal input harmonic signal has been created in such a way that the maximum amplitude of the free-liquid surface is captured from the P1 sensor alongside Y-direction of the Cartesian reference frame in Figure \ref{fig:drawing_mockup_a}.\\
Harmonic base excitation in one DoF input signal has been created with the code in \ref{appendix:harmonic_base_excitation_generation}. The harmonic excitation selected has the following form:
\begin{equation}\label{eq:harmonic_base_excitation_1DoF}
    a(t)=a_y\sin(\omega_y t)
\end{equation}
where $a_y$ is the amplitude of the external excitation and $\omega_y=2\pi f_y$ where $f_y$ is the forcing pulsation.\\ 
Three types of 1 DoF signal for the harmonic base excitation have been created for the following forcing amplitude:
\begin{itemize}
    \item $a_y=5$ mm;
    \item $a_y=15$ mm;
    \item $a_y=30$ mm.
\end{itemize}
Forcing frequencies $f_y$ are selected near/at and away from the first natural frequency of the free-liquid surface of ALFRED a CFD model \cite{ALFRED_Mockup} predicted:
\begin{equation}\label{eq:CFD_natural_frequency}
    f_{1}=0.89\,\mathrm{Hz}
\end{equation}
The internal structure adds damping to the motion and makes impossible to compare ALFRED's model to one of the nearest theoretical configuration of the problem, exposed in the Eq. \ref{eq:natural_frequency}.
The harmonic base excitation in the form of Eq. \ref{eq:harmonic_base_excitation_1DoF} leads to the following definition of the horizontal acceleration:
\begin{equation}
    a(t)=a_y\sin(\omega_y t)\implies \Ddot{a}_y(t)=a_y(t)\cdot\omega_y^2
\end{equation}
Maximum acceleration occurs when $\sin(\omega_y t)=1$. The shaking table mechanics limitations, which are mostly due to the type of hydraulic actuators, have required some precaution about the acceleration imposed to each of the three moving plates in X-Y-Z direction (Figure \ref{fig:shakespeare_1_b}). The input signal is created with initial and ending ramps whom duration is equal both of 10 seconds. The most interesting central part of the signal lasts 60 s and it represents the full-regime oscillation of the input signal. Figure \ref{fig:input_signal_1DoF_recap} represents the input signals provided to the table in terms of position $a(t)$ in function of the time array varying the forcing amplitude. The time array was constructed using a constant step size of $dt=\frac{1}{f_{SAMPLING}}=\frac{1}{200Hz}=0.005$ s.
\begin{figure}[H]
    \centering
    \includegraphics[width=\textwidth]{immagini/harmonic_base_excitation_1DoF/harmonic_recap.png}
    \caption{Input signal in 1 DoF alongside $Y$ direction for forcing amplitude equal to $a_y=5,15,30$ mm and $f_y=0.94$ Hz; the sampling frequency is equal to the reading frequency from the shaking table, $f_{SAMPLING}=200$ Hz; the physical signal is within the time range [10,70] s.}
    \label{fig:input_signal_1DoF_recap}
\end{figure}
\subsection{Norm base earthquake signals}\label{parag:creation_input_signal_seismic}
Earthquake simulations' input signal have been taken from the norm IEC 60068-3-3, which have been modified by the research engineer Jean Muller at the time of the test. The required response spectrum is in Figure \ref{fig:required_response_spectrum} and the input signal is scaled to respect the soil and seismic characterization of Mioveni (Romania), where the reactor is gonna be built. The zero period acceleration is equal to 
\begin{equation}
    a_t=a_g \times K \times D \times D \times \alpha \times G 
\end{equation}
where the following choices weren't made by the author but are the results of agreements within VKI in the PASCAL framework:
\begin{itemize}
    \item wave factor $\alpha=1$;
    \item geometric factor $G=1$;
    \item superelevation factor $K=1$ because the reactor is mounted on rigid fixation;
    \item direction factor $D=1$;
    \item ground acceleration $a_g=1\,\mathrm{m/s^2}$.
\end{itemize}
The ground acceleration $a_g$ was selected knowing that the region of interest is a zone 1  for seismic activities. The damping ratio in the response spectra is chosen equal to $5\%$ to have a maximum value of the acceleration equal to three times $a_t$ and a frequency range within $f_1=1$ Hz and $f_2=35$ Hz. In Figure \ref{fig:required_response_spectrum} the required response spectra is plotted: the entire acceleration is developed within $f_1$ and $f_2$, while the plateau at the maximum value is within $2f_1=2$Hz and $\scriptstyle\frac{1}{3}$$f_2=11.7$ Hz.\\
From the similarity studies (\S \ref{parag:similarity}) a frequency scaling should be necessary to fulfil the dynamic similarities, but this would mean input signal in terms of position that impose too higher acceleration on the shake table and, at the same time, frequency of no interest for the sloshing investigation. Existing \texttt{MATLAB} codes generates the accelerogram from the non-scaled power spectral density of the norm, then a Newmark baseline correction (\texttt{MATLAB} code manual) is applied because an unrealistic mean shift occurs at the end of the input signal between 15 seconds and 20 seconds.\\
The input signal is in figure \ref{fig:input_signal_1DoF_norm}. The nominal one presents a displacement within 0.4 mm and -0.7 mm, but to see interesting sloshing dynamics a more energetic case is considered multiplying the amplitude by five times and ten times.
\begin{figure}[H]
    \centering
    \includegraphics[width=0.60\textwidth]{immagini/setup/required_response_spectrum.png}
    \caption{Required response spectrum in generalized form taken from IEC 60068-2-57 for vibration test, time-history and sine-beat method. Curve at damping ratio $\xi=5\%$ is selected for having three times the zero period acceleration $a_t$.}
    \label{fig:required_response_spectrum}
\end{figure}
\begin{figure}[H]
    \centering
    \includegraphics[scale=0.65]{immagini/setup/Norm_scaled_x10_x_only.png}
    \caption{Norm base signal after the baseline correction. The Figure presents the varying amplitude multiplied by one, five and ten, which is the most energetic case.}
    \label{fig:input_signal_1DoF_norm}
\end{figure}
An additional shifting in frequency is applied because the previous signal excites the free-liquid surface motion at higher frequencies than the estimated numerical equal to $0.89$ Hz \cite{ALFRED_Mockup}: the entire acceleration is developed within $f_1$ and $f_2$, while the plateau at the maximum value is within $2f_1=0.89$ Hz and $\scriptstyle\frac{1}{3}$$f_2=11.4$ Hz. Figure \ref{fig:PSA_acceleration_shifting} presents the shifting to 0.89Hz of the norm signal and Figure \ref{fig:input_signal_1DoF_shifted_norm} presents the actual input signal following the same procedure indicated for the non-shifted case.
\begin{figure}[H]
    \centering
    \includegraphics[width=0.80\textwidth]{immagini/setup/psa_acceleration_shift.png}
    \caption{Pseudo spectral acceleration from the norm following a scaling due to model similarities and a frequency shifting due to experimental necessity to study sloshing dynamics in ALFRED's model.}
    \label{fig:PSA_acceleration_shifting}
\end{figure}
\begin{figure}[H]
    \centering
    \includegraphics[scale=0.65]{immagini/setup/Norm_scaled_shifted_x10_x_only.png}
    \caption{Norm base signal after the baseline correction and PSA acceleration shifting close to $f=0.89$ Hz. The Figure presents the varying amplitude multiplied by one, five and ten, which is the most energetic case and intense sloshing.}
    \label{fig:input_signal_1DoF_shifted_norm}
\end{figure}
%==============================================================
\clearpage
\section{Matrix of performed test series}\label{parag:test_matrix}
In the current section the test matrix is presented.
\begin{table}[H]
\centering
{\fontsize{10}{13}\selectfont
  \begin{tabular}{|lllll|}
\hline
\multicolumn{5}{|l|}{Horizontal harmonic base excitation} \\ \hline
\multicolumn{1}{|l|}{DoF} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}Forcing \\ frequency\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}Forcing \\ amplitude\end{tabular}} &
  \multicolumn{1}{l|}{Internal structure} &
  Water depth \\ \hline
\multicolumn{1}{|l|}{1 DoF in y} &
  \multicolumn{1}{l|}{$f_y=0.68$Hz} &
  \multicolumn{1}{l|}{$a_y=5,15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{1 DoF in y} &
  \multicolumn{1}{l|}{$f_y=0.78$Hz} &
  \multicolumn{1}{l|}{$a_y=5,15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{1 DoF in y} &
  \multicolumn{1}{l|}{$f_y=0.82$Hz} &
  \multicolumn{1}{l|}{$a_y=5,15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{1 DoF in y} &
  \multicolumn{1}{l|}{$f_y=0.84$Hz} &
  \multicolumn{1}{l|}{$a_y=5,15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{1 DoF in y} &
  \multicolumn{1}{l|}{$f_y=0.845$Hz} &
  \multicolumn{1}{l|}{$a_y=5,15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{1 DoF in y} &
  \multicolumn{1}{l|}{$f_y=0.85$Hz} &
  \multicolumn{1}{l|}{$a_y=5,15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{1 DoF in y} &
  \multicolumn{1}{l|}{$f_y=0.86$Hz} &
  \multicolumn{1}{l|}{$a_y=5,15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{1 DoF in y} &
  \multicolumn{1}{l|}{$f_y=0.68$Hz} &
  \multicolumn{1}{l|}{$a_y=5,15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{1 DoF in y} &
  \multicolumn{1}{l|}{$f_y=0.90$Hz} &
  \multicolumn{1}{l|}{$a_y=5,15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{1 DoF in y} &
  \multicolumn{1}{l|}{$f_y=0.94$Hz} &
  \multicolumn{1}{l|}{$a_y=5,15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config.\\ no 3SG config.\end{tabular}} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{1 DoF in y} &
  \multicolumn{1}{l|}{$f_y=0.98$Hz} &
  \multicolumn{1}{l|}{$a_y=5,15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{1 DoF in y} &
  \multicolumn{1}{l|}{$f_y=1.04$Hz} &
  \multicolumn{1}{l|}{$a_y=5,15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{1 DoF in y} &
  \multicolumn{1}{l|}{$f_y=1.08$Hz} &
  \multicolumn{1}{l|}{$a_y=5,15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{1 DoF in y} &
  \multicolumn{1}{l|}{$f_y=1.12$Hz} &
  \multicolumn{1}{l|}{$a_y=5,15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{1 DoF in y} &
  \multicolumn{1}{l|}{$f_y=1.20$Hz} &
  \multicolumn{1}{l|}{$a_y=5,15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{1 DoF in y} &
  \multicolumn{1}{l|}{$f_y=1.38$Hz} &
  \multicolumn{1}{l|}{$a_y=5,15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{1 DoF in y} &
  \multicolumn{1}{l|}{$f_y=1.54$Hz} &
  \multicolumn{1}{l|}{$a_y=5,15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\end{tabular}}
\caption{Horizontal harmonic base excitation in 1 DoF test matrix; nineteen forcing frequencies around near/at and away $f=0.89$ Hz are selected; forcing amplitude tested $a_y=5,15,30$ mm; internal structure with and without the 3SG; water depths tested $h=5.00,6.50,7.84,8.84,9.90$ cm.}\label{tab:horizontal_harmonic_base_excitation}
\end{table}
\begin{table}[H]
\centering
{\fontsize{10}{13}\selectfont
  \begin{tabular}{|lllll|}
\hline
\multicolumn{5}{|l|}{Harmonic base excitation in sway and pitch} \\ \hline
\multicolumn{1}{|l|}{DoF} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}Forcing \\ frequency\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}Forcing \\ amplitude\end{tabular}} &
  \multicolumn{1}{l|}{Internal structure} &
  Water depth \\ \hline
\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}2 DoF in y\\ and z\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}$f_y=0.68$Hz \\ $f_z=2.23$Hz\end{tabular}} &
  \multicolumn{1}{l|}{$a_y=15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}2 DoF in y \\ and z\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}$f_y=0.78$Hz  \\ $f_z=2.23$Hz\end{tabular}} &
  \multicolumn{1}{l|}{$a_y=15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}2 DoF in y \\ and z\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}$f_y=0.82$Hz  \\ $f_z=2.23$Hz\end{tabular}} &
  \multicolumn{1}{l|}{$a_y=15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}2 DoF in y \\ and z\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}$f_y=0.84$Hz  \\ $f_z=2.23$Hz\end{tabular}} &
  \multicolumn{1}{l|}{$a_y=15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}2 DoF in y \\ and z\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}$f_y=0.845$Hz  \\ $f_z=2.23$Hz\end{tabular}} &
  \multicolumn{1}{l|}{$a_y=15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}2 DoF in y \\ and z\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}$f_y=0.85$Hz  \\ $f_z=2.23$Hz\end{tabular}} &
  \multicolumn{1}{l|}{$a_y=15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}2 DoF in y \\ and z\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}$f_y=0.86$Hz  \\ $f_z=2.23$Hz\end{tabular}} &
  \multicolumn{1}{l|}{$a_y=15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}2 DoF in y \\ and z\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}$f_y=0.68$Hz  \\ $f_z=2.23$Hz\end{tabular}} &
  \multicolumn{1}{l|}{$a_y=15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}2 DoF in y \\ and z\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}$f_y=0.90$Hz  \\ $f_z=2.23$Hz\end{tabular}} &
  \multicolumn{1}{l|}{$a_y=15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}2 DoF in y \\ and z\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}$f_y=0.94$Hz  \\ $f_z=2.23$Hz\end{tabular}} &
  \multicolumn{1}{l|}{$a_y=15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config.\\ no 3SG config.\end{tabular}} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}2 DoF in y \\ and z\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}$f_y=0.98$Hz  \\ $f_z=2.23$Hz\end{tabular}} &
  \multicolumn{1}{l|}{$a_y=15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}2 DoF in y \\ and z\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}$f_y=1.04$Hz  \\ $f_z=2.23$Hz\end{tabular}} &
  \multicolumn{1}{l|}{$a_y=15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}2 DoF in y \\ and z\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}$f_y=1.08$Hz  \\ $f_z=2.23$Hz\end{tabular}} &
  \multicolumn{1}{l|}{$a_y=15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}2 DoF in y \\ and z\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}$f_y=1.12$Hz  \\ $f_z=2.23$Hz\end{tabular}} &
  \multicolumn{1}{l|}{$a_y=15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}2 DoF in y \\ and z\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}$f_y=1.20$Hz  \\ $f_z=2.23$Hz\end{tabular}} &
  \multicolumn{1}{l|}{$a_y=15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}2 DoF in y \\ and z\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}$f_y=1.38$Hz  \\ $f_z=2.23$Hz\end{tabular}} &
  \multicolumn{1}{l|}{$a_y=15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}2 DoF in y \\ and z\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}$f_y=1.54$Hz  \\ $f_z=2.23$Hz\end{tabular}} &
  \multicolumn{1}{l|}{$a_y=15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  h=8.84cm \\ \hline
\end{tabular}}
\caption{Combined harmonic base excitation in 2 DoF test matrix; nineteen forcing frequencies around near/at and away $f=0.89$ Hz are selected; forcing amplitude tested $a_y=15,30$ mm; internal structure with and without the 3SG; water depths tested $h=8.84$ cm.}
\end{table}
\begin{table}[H]
\centering
{\fontsize{10}{13}\selectfont
  \begin{tabular}{|lllll|}
\hline
\multicolumn{5}{|l|}{Earthquake test series} \\ \hline
\multicolumn{1}{|l|}{DoF} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}Forcing \\ frequency\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}Forcing \\ amplitude\end{tabular}} &
  \multicolumn{1}{l|}{Internal structure} &
  Water depth \\ \hline
\multicolumn{1}{|l|}{1 DoF in x} &
  \multicolumn{1}{l|}{Around f natural} &
  \multicolumn{1}{l|}{$\times 5$} &
  \multicolumn{1}{l|}{3SG config.} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{1 DoF in x} &
  \multicolumn{1}{l|}{Around f natural} &
  \multicolumn{1}{l|}{$\times 10$} &
  \multicolumn{1}{l|}{3SG config.} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{1 DoF in x} &
  \multicolumn{1}{l|}{Norm scaled} &
  \multicolumn{1}{l|}{$\times 1$} &
  \multicolumn{1}{l|}{3SG config.} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{1 DoF in x} &
  \multicolumn{1}{l|}{Norm scaled} &
  \multicolumn{1}{l|}{$\times 5$} &
  \multicolumn{1}{l|}{3SG config.} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{1 DoF in x} &
  \multicolumn{1}{l|}{Norm scaled} &
  \multicolumn{1}{l|}{$\times 10$} &
  \multicolumn{1}{l|}{3SG config.} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{All 3 DoF} &
  \multicolumn{1}{l|}{Norm scaled shifted} &
  \multicolumn{1}{l|}{$\times 1$} &
  \multicolumn{1}{l|}{3SG config.} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{All 3 DoF} &
  \multicolumn{1}{l|}{Norm scaled shifted} &
  \multicolumn{1}{l|}{$\times 5$} &
  \multicolumn{1}{l|}{3SG config.} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{All 3 DoF} &
  \multicolumn{1}{l|}{Norm scaled shifted} &
  \multicolumn{1}{l|}{$\times 10$} &
  \multicolumn{1}{l|}{3SG config.} &
  \begin{tabular}[c]{@{}l@{}}h=5.00,6.50,7.84,\\ 8.84,9.90cm\end{tabular} \\ \hline
\multicolumn{1}{|l|}{1 DoF in x} &
  \multicolumn{1}{l|}{Norm scaled} &
  \multicolumn{1}{l|}{$\times 1$} &
  \multicolumn{1}{l|}{no 3SG config.} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{1 DoF in x} &
  \multicolumn{1}{l|}{Norm scaled} &
  \multicolumn{1}{l|}{$\times 5$} &
  \multicolumn{1}{l|}{no 3SG config.} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{1 DoF in x} &
  \multicolumn{1}{l|}{Norm scaled} &
  \multicolumn{1}{l|}{$\times 10$} &
  \multicolumn{1}{l|}{no 3SG config.} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{All 3 DoF} &
  \multicolumn{1}{l|}{Norm scaled shifted} &
  \multicolumn{1}{l|}{$\times 1$} &
  \multicolumn{1}{l|}{no 3SG config.} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{All 3 DoF} &
  \multicolumn{1}{l|}{Norm scaled shifted} &
  \multicolumn{1}{l|}{$\times 5$} &
  \multicolumn{1}{l|}{no 3SG config.} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{All 3 DoF} &
  \multicolumn{1}{l|}{Norm scaled shifted} &
  \multicolumn{1}{l|}{$\times 10$} &
  \multicolumn{1}{l|}{no 3SG config.} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}2 DoF in y \\ and z\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}$f_y=1.20$Hz  \\ $f_z=2.23$Hz\end{tabular}} &
  \multicolumn{1}{l|}{$a_y=15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}2 DoF in y \\ and z\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}$f_y=1.38$Hz  \\ $f_z=2.23$Hz\end{tabular}} &
  \multicolumn{1}{l|}{$a_y=15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  h=8.84cm \\ \hline
\multicolumn{1}{|l|}{\begin{tabular}[c]{@{}l@{}}2 DoF in y \\ and z\end{tabular}} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}$f_y=1.54$Hz  \\ $f_z=2.23$Hz\end{tabular}} &
  \multicolumn{1}{l|}{$a_y=15,30$mm} &
  \multicolumn{1}{l|}{\begin{tabular}[c]{@{}l@{}}3SG config. \\ no 3SG config.\end{tabular}} &
  h=8.84cm \\ \hline
\end{tabular}}
\caption{PASCAL sloshing framework input signals, taken from the norm; 1 DoF and 3 DoF signals with the amplitude multiplied by 1, 5 and 10 times the scaled signal; changing water has been tested only in the 3SG configuration; no 3SG configuration has been tested only for water depth $h=8.84$ cm.}
\end{table}