esa-sceva/satcom-chunk-collection huggingface dataset:
# The Influence of Feature Representation of Text on the Performance of Document Classification
## 4 Results
### AUROC Performance and Rankings
It reconfirms previous observations about the superior performance of the (blue colored) doc2 vec document representation model, both in terms of ranks on individual data sets and averaged ranks. Note also that the average rankings were consistent with the rankings on the majority of the document classification tasks. Two notable exceptions were Reuters8 and 20 News, where the TFIDF variant of the BOW model outperformed the equally ranked doc2 vec and word2 vec models. Two other exceptions included WebKD, where BOW, word2 vec and the low-dimensional variants of doc2 vec were top-ranked, and Brown10, where bow-TF was among the top-ranked models. Note that three out of four exceptions corresponded to the tasks with a moderate number of class labels. Other data set properties did not seem to be related to the AUROC performance. \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **Brown2** & **Brown4** & **Brown10** & **[PERSON]** & **Reuters8** & **WebKB** & **20 News** & **Avg. Rank** \\ \hline bow-TF & 8 & 5 & **3.5** & 9 & 4 & **5** & 11.5 & 6.57 \\ bow-TFIDF & 5 & 12 & 11.5 & 9 & **1** & 5 & **1** & 6.36 \\ \hline word2 vec-25 & 12 & 12 & 11.5 & 9 & 8 & **5** & 8 & 9.36 \\ word2 vec-50 & 7 & 12 & 11.5 & 9 & 4 & **5** & 4 & 7.50 \\ word2 vec-75 & 6 & 12 & 11.5 & 9 & 4 & **5** & 4 & 7.36 \\ word2 vec-100 & 10.5 & 12 & 11.5 & 9 & 4 & **5** & 4 & 8.00 \\ \hline doc2 vec-25 & 4 & 5 & **3.5** & 9 & 4 & **5** & 4 & 4.93 \\ doc2 vec-50 & **1** & **1.5** & **3.5** & **1** & 8 & **5** & 4 & **3.43** \\ doc2 vec-75 & 2 & **1.5** & **3.5** & 9 & 4 & **5** & 8 & 4.71 \\ doc2 vec-100 & 9 & 5 & **3.5** & 9 & 11.5 & 10.5 & 8 & 8.07 \\ doc2 vec-200 & 4 & 5 & **3.5** & 9 & 11.5 & 12.5 & 11.5 & 8.14 \\ doc2 vec-500 & 14 & 12 & 11.5 & 9 & 11.5 & 12.5 & 11.5 & 11.71 \\ doc2 vec-1000 & 10.5 & 12 & 11.5 & 9 & 8 & 10.5 & 11.5 & 10.43 \\ \hline gow-avg & 13 & 5 & 11.5 & 9 & 16 & 15 & 15 & 12.07 \\ gow-qrt & 15 & 12 & 11.5 & 9 & 14.5 & 15 & 15 & 13.14 \\ gow-hist & 16 & 12 & 11.5 & 9 & 14.5 & 15 & 15 & 13.29 \\ \hline \end{tabular}
\end{table} 
Table 5: Multi-objective ranking of the 16 variants of the three document representation models by the document classification task with respect to AUROC. The last column reports the average rankings over the seven tasks. The top-ranked models in each column are shown in bold. Figure 2: Average ranks of the four top-performing variants of the document representation models in each of the four groups with respect to the macro-averaged AUROC. In sum, according to AUROC, the doc2 vec variants with low-dimensional embedding vectors (\(\leq\)75) outperformed other document representation models. For tasks with a moderate number of class labels, one can also consider the bag-of-word model, although the decision for BOW calls for the careful selection of one of its two variants.
# Ice Thickness Detection of Transmission Lines Based on Cross-Guide-UNet
## 1 Introduction
The experimental results for the ice cover dataset show that the network can achieve an edge detection accuracy (ODS) of 0.934 and an edge recognition accuracy (OIS) of 0.938, with a thickness detection error controlled within 7.2%.
## 3 Attitude Controller Design
### Constrained Virtual Control Solution  
For the predicted control inputs \(\mathbf{u}_{[k+i]}\) where \(i=1\), \(2\), \(\ldots\), \(N_{\mathsf{P}}\), there are upper and lower boundary constraints:  
\[\mathbf{u}_{\min}\leq\mathbf{u}_{[k+i]}\leq\mathbf{u}_{\max}. \tag{27}\]  
Utilizing the feedback linearization control law from (15), it follows that:  
\[\mathbf{u}_{\min}\leq\mathbf{M}_{[k+i-1]}^{-1}(\mathbf{v}_{[k+i]}-\mathbf{N}_{[k+i-1]})\leq \mathbf{u}_{\max}. \tag{28}\]  
Therefore, the inequality constraints for the predicted virtual control input \(\mathbf{v}_{[k+i]}\) at step \(k\) are:  
\[\begin{pmatrix}\mathbf{I}_{3\times 3}\\ -\mathbf{I}_{3\times 3}\end{pmatrix}\mathbf{v}_{[k+i]}\leq\begin{pmatrix}\mathbf{M}_{[k+i-1]} \mathbf{u}_{\max}+\mathbf{N}_{[k+i-1]}\\ -(\mathbf{M}_{[k+i-1]}\mathbf{u}_{\min}+\mathbf{N}_{[k+i-1]})\end{pmatrix}. \tag{29}\]  
Given that \(\mathbf{v}_{[k+i]}=\mathbf{v}_{[k+i-1]}+\delta\mathbf{v}_{[k+i]}\), it can be concluded that:  
\[\begin{pmatrix}\mathbf{I}_{3\times 3}\\ -\mathbf{I}_{3\times 3}\end{pmatrix}\delta\mathbf{v}_{[k+i]}\leq\begin{pmatrix}\mathbf{M}_{[k+i- 1]}\mathbf{u}_{\max}+\mathbf{N}_{[k+i-1]}-\mathbf{v}_{[k+i-1]}\\ -(\mathbf{M}_{[k+i-1]}\mathbf{u}_{\min}+\mathbf{N}_{[k+i-1]}-\mathbf{v}_{[k+i-1]})\end{pmatrix}. \tag{30}\]  
Similarly, the upper and lower constraint vectors for the predicted angular rate \(\mathbf{\omega}_{[k+i]}\) at step \(k\) are denoted as \(\mathbf{\omega}_{\max}\) and \(\mathbf{\omega}_{\min}\). And from (4), the inequality constraints for \(\hat{\mathbf{\Omega}}_{[k+i]}\) can be expressed as:  
\[\begin{pmatrix}\mathbf{I}_{3\times 3}\\ -\mathbf{I}_{3\times 3}\end{pmatrix}\hat{\mathbf{\Omega}}_{[k+i]}\leq\begin{pmatrix} \mathbf{M}_{[k+i-1]}\mathbf{\omega}_{\max}\\ -\mathbf{M}_{[k+i-1]}\mathbf{\omega}_{\min}\end{pmatrix}. \tag{31}\]  
According to the theory of constrained model predictive control, the simulation tool \"quadprog\" can be utilized to obtain a set of optimal predicted control increment vectors for incremental control law (22), subject to the constraints (30) and (31), as well as the quadratic performance criterion (26). The first element of the predicted control increment vector, as shown in (32), corresponds to the virtual control input vector base on model predictive control theory [31,32]. This predictive control process is repeated to achieve MPC receding horizon control theory.  
\[\mathbf{v}_{[k]}=\begin{bmatrix}\mathbf{I}_{3\times 3}&\mathbf{0}_{3\times 3}&\cdots&\mathbf{0}_{3 \times 3}\end{bmatrix}\delta\mathbf{V}_{[k]}^{\ast}+\mathbf{v}_{[k-1]} \tag{32}\]  
Based on the design principles outlined above, the attitude control of the quadrotor UAV is achieved through feedback linearization model predictive control, with the control law computation given by (15).
# Underwater SLAM Meets Deep Learning: Challenges, Multi-Sensor Integration, and Future Directions
## 8 Underwater SLAM Systems Evaluation and Comparison
### Comparison of Underwater SLAM Methods
#### 8.3.2 DL-Based Methods  
DL-based methods, such as _RU-SLAM_ and _pose estimation with CNN and LSTM_, generally outperform traditional methods on the Aqualoc dataset. For example, _pose estimation with CNN and LSTM_ achieves the lowest localization error (0.0519 m), demonstrating the effectiveness of deep learning techniques in feature extraction and pose estimation. However, _RU-SLAM_ shows a slightly higher error (0.110 m) compared to some traditional methods, indicating that the performance of DL-based methods can vary depending on the specific architecture and training approach.
# Surface Discharge Mechanism on Epoxy Resin in Electronegative Gases and Its Application
###### Abstract  
This study presents the surface discharge characteristics of insulating gases, including sulfur hexafluoride (SF\({}_{6}\)), dry air, and N\({}_{2}\), under a non-uniform field. Surface discharge experiments were conducted, with the gas pressure ranging from 0.1 to 0.6 MPa, on samples of epoxy dielectrics under an AC voltage. The experimental results showed that the surface insulation performance significantly improved in insulating gases possessing electronegative gases, such as SF\({}_{6}\) and dry air. Surface flashover voltages of SF\({}_{6}\) were saturated with an increasing pressure, compared to dry air and N\({}_{2}\). The surface discharge mechanism is proposed to explain the improvement and saturation of dielectric characteristics of the electronegative gas in complex dielectric insulations, as well as its influence on the surface flashover voltage. As an application, an insulation design method is discussed with regards to replacing SF\({}_{6}\) gas in high-voltage power equipment based on the knowledge of the physics behind gas discharge.  
surface discharge; epoxy resin; electronegative gas; high-voltage power equipment +
Footnote †: journal: Applied Physics Letters
## 2 Materials and Methods
### Study Coding and Data Extraction  
Two reviewers ([PERSON] and [PERSON]) independently collected the data of studies finally included using standardized forms in Microsoft Excel. Specifically, the following information was extracted from each study: identification information (authors and year of publication), sample characteristics (size, sex, and initial relative strength ratio (1 RM/Body mass, RSR)), configuration of the RT program (VL programmed and actually incurred, total volume, training velocity, load used, exercises trained, duration, and frequency), dependent variables of interest (strength and athletic outcomes), and the evaluation methodologies (e.g., 1 RM, sprint, or countermovement jump). For the quantitative analyses (meta-analysis), the group size, mean pre-post differences, and standard deviations (SD) of the dependent variables of interest were collected. The corresponding author was contacted to provide missing data when necessary. Considering the definition of the VL term (progressive decline of barbell velocity across repetitions within the set [13]), only data from those experimental groups that incurred a VL equal to or higher than 1% (i.e., performing at least two repetitions per set) were analyzed. To achieve a minimum of five comparators for each outcome [25] in the between- and within-group analyses, individual VL thresholds (e.g., 10%, 15%, or 20%) from included studies were categorized as low-moderate VL (Low-ModvL, \(\leq\)25% VL) and moderate-high VL (Mod-HighvL, >25% VL). Previous investigations on the topic found that a 25% VL corresponds to completing about half of the total number of repetitions that could be performed in the training set during both upper- and lower-limb resistance exercises [14; 26].
# Modelling and Assessment of a New Triple-Frequency IF1213 PPP with BDS/GPS
## 3 Results and Discussion  
### Data Processing Strategies  
This study used 60 stations provided by the MGEX of the IGS organization and the observation data with a 30 s sample interval for a week-long period of day of the year (DOY) 121-127, 2022. Figure 1 shows the geographical distribution of the selected stations. Table 2 shows the GPS and BDS satellites that can broadcast triple-frequency observations, including some GPS satellites and all BDS satellites, except for the experimental satellites.  
Table 3 provides an in-depth summary of the processing strategy of IF1213 PPP models, including the DF PPP model. In static PPP, if the east (E) and north (N) directions are less than 5 cm and the upwards (U) direction is less than 10 cm at the current epoch and the following 20 epochs, the positioning error satisfies convergence. In the kinematic PPP, the E and N directions are less than 10 cm, and the U direction is less than 20 cm. The time taken to reach the first epoch that satisfies the convergence condition is defined as the convergence time.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**System** & **PRN** & **Orbit Type** \\ \hline GPS & G01, G03, G04, G06, G08, G09, G10, G14, G18, G23, & Medium Earth Orbit (MEO) \\ & G24, G25, G26, G27, G30, G32. & \\ \hline  & C01, C02, C03, C04, C05; & Geostationary Earth Orbit (GEO) \\ \cline{2-3} BDS-2 & C06, C07, C08, C09, C10, C13, C16; & Inclined Geo-Synchronous Orbit (IGSO) \\ \cline{2-3}  & C11, C12, C14; & MEO \\ \hline  & C19, C20, C21, C22, C23, C24, C25, C26, C27, C28, & \\ BDS-3 & C29, C30, C32, C33, C34, C35, C36, C37, C41, C42, & MEO \\ & C43, C44, C45, C46; & \\ \cline{2-3}  & C38, C39, C40. & IGSO \\ \hline \end{tabular}
\end{table}
Table 2: BDS/GPS satellites transmitting triple frequency signals.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Items** & **Strategy** \\ \hline Model & DF, TF-C, TF-F, TF-CF, TF-FP(GPS) \\ Satellite elevation mask & 15\({}^{\circ}\) \\ Estimator & Kalman filter \\ Weighting scheme & Elevation-dependent weight; 0.003 m and 0.3 m for raw phase and code, respectively \\ PCO/PCV & igs14\_2196.atx according to [PERSON] et al. [37] \\ Phase windup & Corrected [38] \\ Satellite DCB corrections & Corrected with MGEX DCB products except TF-C model \\ Satellite orbit and clock & Products from WUM \\ Tropospheric delay & Zenith Hydrostatic Delays (ZHD) are corrected using the Saastamoinen model, and \\  & Zenith Wet Delays (ZWD) are estimated using random walk [39] \\ Tide effect & Solid Earth, pole and ocean tide [40] \\ Relativistic effect & Corrected [41] \\ Station coordinates & Static: estimated using constants; kinematic: estimated using white noise process \\ Receiver clock & Estimated using white noises \\ Receiver inter-frequency bias & Estimated using random walk \\ Inter-frequency clock bias & Estimated using random walk \\ Ambiguity & Estimated using a constant \\ \hline \hline \end{tabular}
\end{table}
Table 3: Data-processing strategies.
# FedOpt: Towards Communication Efficiency and Privacy Preservation in Federated Learning
## 4 Federated Optimisation (FedOpt)
### Efficiency and Privacy in FedOpt
#### 4.3.2 Encryption Phase  
In this phase, all the users jointly choose the same level of privacy budget \(\epsilon\) in order to maintain the differential privacy. Specifically, in each epoch, the set of users \(\Pi\) derives their initial parameters \(\varpi\) and obtains their local gradients \(G_{\Pi}\) through their individual datasets. Afterwards, the set of users \(\Pi\) utilise a privacy measure by randomly choosing the noises from the Laplace distribution \(Lap(\frac{\Delta f_{\Pi}}{\epsilon})\) and adds it to the local gradients.  
\[\begin{array}{l}G_{\Pi,j}\equiv(G_{\Pi}+Lap(\frac{\Delta f_{\Pi}}{\epsilon} ))\mod j\\ G_{\Pi,k}\equiv(G_{\Pi}+Lap(\frac{\Delta f_{\Pi}}{\epsilon}))\mod k\end{array} \tag{8}\]  
In the equation above, both the privacy budget \(\epsilon\) and the sensitivity \(\Delta f_{\Pi}\) of Laplace distribution play important roles in differential privacy. Meanwhile, \(\Delta f_{\Pi}\) can be set to 1 and each gradient is assumed to set at \(0\leq G_{\Pi}\leq 1\) by utilising the min-max normalisation [21].  
Subsequently, the users encrypt their local gradients using the secret key \(\delta\) from \(j\), \(k\) as given below:  
\[E_{\rm II}=j^{-1}jG_{\rm II,k}^{k}+k^{-1}kG_{\rm II,j}^{j}\mod M \tag{9}\]  
where, \(M\) is the public parameter \(M=jk\) and \(j^{-1}\), \(k^{-1}\) denote the inverses of \(j\), \(k\) respectively. In the end, these encrypted local gradients \(E_{\rm II}\) from all the users are sent to the cloud server.
# Thurstonian Scaling for Sensory Discrimination Methods
## 4 Discussion
### Application of Sensory Discrimination Methods  
Sensory evaluation is typically used alongside microbiological and analytical instrumental laboratory testing for a more comprehensive assessment of food safety. Below is how sensory discrimination methods play an important role for monitoring food safety.  
1. Identification of subtle differences before becoming easily perceptible that might indicate spoilage (unpleasant smells, visual changes, taste off-flavors and unexpected texture changes) or foreign substances (chemical residues, cleaning agents, etc.) or contaminants from processing or packaging (metals, dirt, plastics, etc.);
2. Threshold testing to estimate the minimum level detectable to provide a measurable threshold when a product should be considered changed or unsafe;
3. For shelf life, quality control, and monitoring quality, an example being rancidity that can develop in fats and oils with age;
4. Detection of mold odors indicating potential mycotoxins or presence of fermentation or yeast activity in foods;
5. Contamination from off-flavors during processing due to improper equipment cleaning or cross-contact with other foods;
6. Determination if consumers can reliably differentiate standard (control) vs. contaminated or adulterated foods or changes in processing environment and the perceived associated consumer risk--how the perception of the sensory difference affects consumer acceptance to align safety margins with consumer expectations for safety and high quality;
7. For assessor training to increase reliability; and
8. Development of rapid sensory-based screening tools like electronic noses or tongues by quantifying how these devices mimic human sensory evaluations; Thurstonian models can validate instrumental data accuracy in detecting subtle contamination levels that might not yet be harmful but that could lead to consumer rejection.
## 3 System Model
### PDR Review
#### 3.5.3 Heading  
The heading section primarily updates the pedestrian's orientation and direction using angular velocity information captured by the gyroscope. The quaternion approach is used to update the angle increment. The quaternion vector at the \((k+1)\)-th epoch is expressed as follows.  
\[q_{k+1}=\left[I\text{-}cos\frac{\Delta\theta_{k}}{2}+\Delta\Theta\frac{sin \frac{\Delta\theta_{k}}{2}}{\Delta\theta_{k}}\right]\cdot q_{k} \tag{13}\]  
where \(q_{k+1}\) is the state vector at the \((k+1)\)-th epoch, \(\Delta\theta_{k}\) represents the angular increment at the \(k\)-th epoch, \(I\) is the identity matrix of the same dimension as \(q_{k}\), and \(\Delta\Theta\) is a matrix representing the angular increments in the \(x\)-, \(y\)-, and \(z\)-axes at the \(k\)-th epoch.  
The following formula converts a quaternion into a direction cosine matrix (DCM). The DCM \(C_{b}^{n}\) is used to describe the rotation relationship from one coordinate system (body coordinate system b) to another coordinate system (navigation coordinate system n).  
\[C_{b}^{n}=\left[\begin{matrix}q_{1}^{2}-q_{2}^{2}-q_{3}^{2}+q_{4}^{2}&2q_{1}q_ {2}-2q_{3}q_{4}&2q_{1}q_{3}+2q_{2}q_{4}\\ 2q_{1}q_{2}+2q_{3}q_{4}&-q_{1}^{2}+q_{2}^{2}-q_{3}^{2}+q_{4}^{2}&2q_{2}q_{3}-2 q_{1}q_{4}\\ 2q_{1}q_{3}-2q_{2}q_{4}&2q_{2}q_{3}+2q_{1}q_{4}&-q_{1}^{2}-q_{2}^{2}+q_{3}^{2} +q_{4}^{2}\end{matrix}\right] \tag{14}\]  
The three following formulas are used to calculate the attitude angles: pitch, roll, and yaw. These angles are derived from specific elements of the direction cosine matrix \(C_{b}^{n}\).  
\[\vartheta=arctan\frac{-C_{b}^{n}(3,1)}{\sqrt{\left(C_{b}^{n}(3,1)\right)^{2}}} \tag{15}\]  
\[\mathcal{O}=arctan\frac{C_{b}^{n}(3,2)}{C_{b}^{n}(3,3)} \tag{16}\]  
Figure 7: Step length diagram: Green mark indicates direction, red and blue marks explain the elements in Formula 12.  
\[\varphi=arctan\frac{C_{b}^{n}(2,1)}{C_{b}^{n}(1,1)} \tag{17}\]  
where \(\vartheta\) denotes pitch, \(\emptyset\) represents roll, and \(\varphi\) is the yaw.
# An Efficient Causal Group Communication Protocol for Free Scale Peer-to-Peer Networks
## 2 Materials and Methods
### Background and Definitions
#### 2.2.1 The Immediate Dependency Relation (IDR)  
The Immediate Dependency Relation [14] is the propagation threshold of the control information, regarding the messages sent in the causal past which must be transmitted to ensure a causal delivery. IDR is denoted as \"\(\downarrow\)\" and its formal definition is as follows.  
Figure 1: Internal and external groups of a free scale P2P (peer-to-peer) network.  
**Definition 2**.: _Two messages \(m\) and \(m^{\prime}\) form an IDR \(m\bot m^{\prime}\) if and only if \(m\to m^{\prime}\) and \(m^{\prime\prime}\) does not exist, such that \(m\to m^{\prime\prime}\) and \(m^{\prime\prime}\to m^{\prime}\)._  
Thus, a message \(m\) directly precedes a message \(m^{\prime}\), if and only if no other message \(m^{\prime\prime}\) exists in a system, such that \(m^{\prime\prime}\) belongs at the same time to the causal future of \(m\), and to the causal past of \(m^{\prime}\).  
This relation is important since if the delivery of messages respects the order of their diffusion for all pairs of messages in IDR, then the delivery will respect the causal delivery for all messages.  
Causal information that includes the messages immediately preceding a given message is sufficient to ensure a causal delivery of such message [14].
However, the main weaknesses of the current research on liquid sloshing are that most researchers used simplified ship tanks instead of the real ship tanks to simulate liquid sloshing, and do not consider the effect of real ship motion under actual loading conditions. For complicated surface shapes, like structure of arc and slope, equally spaced particle distribution with nearly constant thickness is not readily found [35]. Thus, the initialization of boundary particles in complex tanks is more cumbersome than that in simplified tanks. Furthermore, the solid boundary shape is represented by a finite number of particles, and the representation of the complete details of the geometric information will be more complicated. Although sloshing simulations in real ships are complex, it is necessary for a realistic investigation of sloshing-inducing force. Meanwhile, the excitation period adopted in previous works came from the natural frequencies of gravity waves in an upright resting cylindrical tank [56]. However, this period is different from the rolling period of real ships in most cases. Therefore, the sloshing-induced force in ship tanks under more realistic conditions needs to be further investigated. This paper aims to compute the dynamic force acting on the bulkhead caused by more realistic excitation in real ship tanks. The efficiency of MPS is generally better than that of WCSPH, but similar to ISPH [57]. From the discrepancies of the kernel function between SPH and MPS methods, the MPS method is more suitable for simulating incompressible fluids than the SPH method. Thus, this paper uses the MPS method to calculate the sloshing-induced force in ship tanks. First, the MPS method used in this paper is verified via numerical simulations of liquid sloshing in a rectangular tank. After that, numerical simulations of liquid sloshing in a real ship tank are carried out. Finally, the sloshing-induced force is computed and analyzed. The rest of this paper is organized as follows: Section 2 introduces the basic theories of the MPS method. Section 3 verifies the MPS method used in this paper via liquid sloshing simulations. Section 4 gives the numerical results of the liquid sloshing in a real ship tank under different ship rolling motions. Section 5 draws conclusions.
# A Pseudo-3D Model for Electromagnetic Acoustic Transducers (EMATs)
## 3 Horizontal Surface Plane Modelling--Directivity Analysis of Rayleigh Waves
### Linking EMAT-EM and EMAT-US Models  
On the surface plane of the material, the combination between the EMAT-EM model and the EMAT-US model is described in Figure 12. The calculated \(\mathbf{F}\) values, acting as the excitation source, are imported to each surface layer at various depths. The Rayleigh waves' distribution is the addition of the Rayleigh waves generated by each point source. Table 1 illustrates the parameters used for the EMAT-US model.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Description** & **Symbol** & **Value** \\ \hline Length of the aluminium plate & \(Y\) & 600 mm \\ Width of the aluminium plate & \(X\) & 600 mm \\ Field spatial step & \(\Delta x_{f}\) & 1 mm \\ Length of the meander-line-coil & \(L\) & 50 mm \\ Source spatial step for each wire & \(\Delta x_{s}\) & 0.2 mm \\ Density of the aluminium plate & \(\rho\) & 2700 kg/m\({}^{3}\) \\ Frequency & \(f\) & 483 kHz \\ Longitudinal waves’ velocity & \(C_{l}\) & 6.375 mm/\(\mu\)s \\ Shear waves’ velocity & \(C_{s}\) & 3.14 mm/\(\mu\)s \\ Rayleigh waves’ velocity & \(C_{r}\) & 2.93 mm/\(\mu\)s \\ \hline \hline \end{tabular}
\end{table}
Table 1: Detailed parameters used for the EMAT-US modelling.  
Figure 11: The model used to simulate Rayleigh waves. Reproduced with permission from [18], Elsevier, 2017.  
Figure 12: On the surface plane of the material, the transformation between the EM and US models. Reproduced with permission from [18], Elsevier, 2017.