DOI: 10.5281/zenodo.16578372
title: Sloshing-Height Estimation for Liquid-filled Containers under Four-Dimensional Motions Including Spatial Translation and Rotation about a Fixed Direction: Modelling and Experimental Validation

description: DESCRIPTION:

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This repository provides the essential data and files for reproducing and visualizing the results presented in the paper entitled 

'Sloshing-Height Estimation for Liquid-filled Containers under Four-Dimensional Motions Including Spatial Translation and Rotation about a Fixed Direction: Modelling and Experimental Validation'.

 

CSV FILES:

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In the "Trajectories" folder, the files named with <trajectory>.csv (where <trajectory> can refer to the Se, Sc, Sg, Te, Tc and Tg motions described in the paper), contain the trajectory imposed to the liquid-filled container.

In particular, in every .csv file the data are organized as follows.

 

   Columns:

   [1] Time [s]

   [2] x_c container position along x [m]

   [3] y_c container position along y [m]

   [4] z_c container position along z [m]

   [5] \dot{x}_c container velocity along x [m/s]

   [6] \dot{y}_c container velocity along y [m/s]

   [7] \dot{z}_c container velocity along z [m/s]

   [8] \ddot{x}_c container acceleration along x [m/s²]

   [9] \ddot{y}_c container acceleration along y [m/s²]

   [10]\ddot{z}_c container acceleration along z [m/s²]

   [11] qx container orientation 

   [12] qy container orientation 

   [13] qz container orientation 

   [14] qw container orientation 

   [15] ω_cx container angular velocity about x [rad/s]

   [16] ω_cy container angular velocity about y [rad/s]

   [17] ω_cz container angular velocity about z [rad/s]

   [18] \dot{ω}_cx container angular acceleration about x [rad/s²]

   [19] \dot{ω}_cy container angular acceleration about y [rad/s²]

   [20] \dot{ω}_cz container angular acceleration about z [rad/s²]

 

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In the "Sloshing Height" folder, the files named <trajectory>_h<filling height>_exp.csv, <trajectory>_h<filling height>_PMD.csv, <trajectory>_h<filling height>_PEN.csv contain the data regarding the experimental sloshing height, the PMD-model sloshing height 

and the PEN-tan sloshing height for the motions indicated with <trajectory> (where <trajectory> can refer to the Se, Sc, Sg, Te, Tc and Tg motions described in the paper) and for the tested filling heights (h = 30, 49, 78mm).

In each .csv file the data are organized as follows.

 

   Columns:

   [1] Time [s]

   [2] Sloshing height η [mm]

   

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In the "PMSD Sloshing Height" folder, the files named <trajectory>_w<X>_N<Y>_h<filling height>.csv contain the data regarding the sloshing-height time histories from the PMSD model for multiple values of \alpha,

w and N, considering the motions indicated with <trajectory> (where <trajectory> can refer to the Se, Sc, Sg, Te, Tc and Tg motions described in the paper) and the three tested filling heights (h = 30, 49, 78mm).

The variables <X> (referred to the power of the nonlinear spring) and <Y> (indicating the number of sloshing masses) can take values 1, 2 and 3

In each .csv file the data are organized as follows.

 

   Rows:

   [1] Time [s]

   [2-end] Sloshing height η [mm] in correspondence of different values of \alpha

   

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In the 'Indices' folder, the files named eps_w<X>_N<Y>_h<filling height>.csv and lambda_w<X>_N<Y>_h<filling height>.csv refer to the trends of the indices \epsilon and \lambda defined in Eqs. (63) and (64), as function of \alpha, for all the motions (Se, Sc, Sg, Te, Tc and Tg)

described in the paper. The variables <X> (referred to the power of the nonlinear spring) and <Y> (indicating the number of sloshing masses) can take values 1, 2 and 3, whereas <filling height> can take values 30, 49 and 78. 

In each eps_w<X>_N<Y>_h<filling height>.csv file the data are organized as follows.

 

Columns:

   [1] \alpha 

   [2] \epsilon trend for the Se motion

   [3] \epsilon trend for the Sc motion

   [4] \epsilon trend for the Sg motion

   [5] \epsilon trend for the Te motion

   [6] \epsilon trend for the Tc motion

   [7] \epsilon trend for the Tg motion

   

In each lambda_w<X>_N<Y>_h<filling height>.csv file the data are organized as follows.

 

Columns:

   [1] \alpha 

   [2] \lambda trend for the Se motion

   [3] \lambda trend for the Sc motion

   [4] \lambda trend for the Sg motion

   [5] \lambda trend for the Te motion

   [6] \lambda trend for the Tc motion

   [7] \lambda trend for the Tg motion

 

 

CORRESPONDENCE WITH PAPER FIGURES:

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The folder "Sloshing Height" also contains also a brief Matlab script "plotSloshingHeight.m" that allows to generate the plots in Figs. 15, A3 and A4.

 

The folder "PMSD Sloshing Height" also contains also a brief Matlab script "plotPMSDSloshingHeight.m" that allows to generate the plots depicting the time history of the sloshing height from the PMSD model for multiple values of \alpha,

w and N.

 

In addition, the Matlab script "plotIndex" in the "Indices" folder allows the reproduction of plots illustrated in Fig. 13, A1 and A2. 

 

VIDEOS:

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The "Video" directory contains two subfolders, "GoPro Right" and "GoPro Left", each housing the videos recorded by the GoPro cameras mounted on the experimental setup (Fig. 8). Additionally, 

both camera folders include auxiliary videos of Aruco Markers, which were utilized to identify the relative pose between the two cameras.

 

The videos corresponding to the recorded container motions are named with <trajectory>_h<filling height>.MP4 (where <trajectory> can refer to the Se, Sc, Sg, Te, Tc and Tg motions described in the paper <filling height> can take values 30, 49 and 78).

 

Due to the nature of the experimental setup and the various recording sessions, multiple camera localization runs were necessary. For this reason four videos for the marker identification are present for each camera folder.

Specifically:

 

- `marker_h30.mp4`  

  This file corresponds to localization for videos:  

  - `Se_h30` 

  - `Sc_h30`

  - `Sg_h30`

  - `Te_h30`

  - `Tc_h30`  

  - `Tg_h30`

  

- `marker_h49.mp4`  

  This file corresponds to localization for videos:  

  - `Se_h49` 

  - `Sc_h49`

  - `Sg_h49`

  - `Te_h49`

  - `Tc_h49`  

  - `Tg_h49`

  

- `marker_h78_1.mp4`  

  This file contains camera localization data for videos with the following filenames:  

  - `Se_h78`  

  - `Te_h78`  

  - `Sg_h78`  

  - `Tg_h78`

 

- `marker_h78_2.mp4`  

  This file corresponds to localization for videos:  

  - `Sc_h78`  

  - `Tc_h78`

  

 

The "Video" directory also contains the subfolder "Robot Videos", in which the recordings of the robot motions (Se, Sc, Sg, Te, Tc and Tg) are available.