esa-sceva/satcom-chunk-collection huggingface dataset:
# Firmware Updates over the Air via LoRa: Unicast and Broadcast Combination for Boosting Update Speed
## 5 Simulation Tests and Results
### Comparison between the Update Methods Using Single-Run Simulations  
#### 5.2.1 Only Unicast Method  
The results obtained in a scenario with a radius of 400 m are presented in Figure 8: the timestamp and the RSSI of the reception of each firmware chunk by the node are shown in (a), and the timestamp and the RSSI of the reception of each ACK by the gateway in (b). The red line represents the sensitivity of the receptor, i.e., the frames below that line are lost and retransmission is required.  
As can be observed, in this case, almost all the frames are received correctly (the RSSI is above the sensitivity), so there are hardly any retransmissions. Consequently, the time for the update of each of the nodes is roughly the same. Another remark is that the difference between Figure 8a,b is minimal, which could be expected, considering that the channel is symmetrical and that a frame is always followed by an ACK.  
Figure 8: _Only unicast_ firmware update of 10 peers with a maximum radius of 400 m: (**a**) RSSI of the frames received by each node, containing the firmware chunks; and (**b**) RSSI of the ACK frames received by the gateway. The red line corresponds to the sensitivity of the receiver.  
The total update time of the project is 176,725 s, i.e., roughly 49 h, equivalent to less than 5 h per node. This time is significant, and is mainly imposed by the 1% duty cycle, which means that the air usage is slightly higher than 29 min.  
Figure 9 reports the results of a scenario with a maximum radius of 2 km. As can be observed, some nodes (#4, #5, and #8, note that numbering starts with #0) are very close to the gateway, so they receive most of the frames upon the first attempt and their update times are shorter than those of other nodes such as, e.g., #2, #3, #6, and #9, which require many retransmissions. The time difference can be quite significant: from 35,664 s for node #6 to 21,258 s for node #8.  
In this case, the total update time of the project is 294,613 s, i.e., 81.8 h (air usage of 49 min). The higher distance results in an increase of 66% in the update time with respect to the 400 m case.
# An Algorithm for Painting Large Objects Based on a Nine-Axis UR5 Robotic Manipulator
## 2 Construction of a Point Cloud Model of the Target Object
### Determining the Normal Vector of a Target Point on the Painting Trajectory  
In order to ensure that the painting area is uniform during the painting process, it is necessary to ensure that the axis of the end of the spray gun coincides with the normal vector of the target point on the painting trajectory. Thus, the normal vectors of the target model must be obtained. As is shown in Figure 3, the target points on the painting trajectory can be divided into two types, which include the trajectory points obtained through the filling algorithm and the vertices of the original triangle.  
The points obtained by filling are still coplanar with the original triangles. The normal vectors of the points obtained by filling can be determined with the normal vector of the plane. The normal vectors of the triangles can be directly extracted from the STL file. However, for the normal vectors of the vertices of the original triangle, there is a common vertex of multiple triangles. Ergo, the normal phase of the plane cannot be employed  
Figure 4: (**a**) The triangle filling results; (**b**) the improved triangle filling results.  
instead of the normal phase of the points. In this paper, local plane fitting and principle component analysis (PCA) estimation methods were harnessed to create the normal vectors of the target points [19; 20; 21]. In order to acquire the target point field conveniently, the k-d tree algorithm was harnessed to store the coordinates of the target points [22]. The step-by-step algorithm is shown in Figures 5 and 6.  
In the actual processing procedure, the normal vector of the target model should take its external normal phase, and the external normal vector of the model can be determined by Equation (4), where \(\mathbf{p}\) is the center of all target points, and \(\left|\left|x\right|\right|_{2}\) is the second norm of the vector \(\mathbf{x}\).  
\[\mathbf{n}=\left\{\begin{array}{l}\mathbf{n}\left|\left|\left(\mathbf{p}+ \mathbf{n}\right)-\overline{\mathbf{p}}\right|\right|_{2}\geq\left|\left( \mathbf{p}-\mathbf{n}\right)-\overline{\mathbf{p}}\right|\right|_{2}\\ -\mathbf{n}\left|\left|\left(\mathbf{p}+\mathbf{n}\right)-\overline{\mathbf{p }}\right|\right|_{2}<\left|\left(\mathbf{p}-\mathbf{n}\right)-\overline{ \mathbf{p}}\right|_{2}\end{array}\right. \tag{4}\]
## 5 Conclusions and Future Work  
### Conclusions  
In this work, we consider selection bias in dynamic scenarios and the impact of sentiment factors on bias. On the basis of the bias caused by sentiment factors, we built the SCS for processing, which solves the problem of sentiment bias between reviews and ratings by filtering bad reviews through a screening layer and then deriving the sentiment score matrix through a training layer. Moreover, we apply a debiased recommendation method based on time-dynamic scenarios to process the enhanced rating matrix obtained from the previous optimization of the sentiment score module to mitigate the influence of selection bias. Our model correctly captures and removes the sentiment bias between user ratings and reviews to improve recommendation performance, which is not considered by other selection bias models. In addition, our model takes into account the dynamic drift of user preferences as well as the dynamic change in selection bias and builds a dynamic debiasing layer to enhance robustness in the presence of highly sparse user data. Experimental results on the Yelp and Jingdong datasets show that our model (1) outperforms the state-of-the-art baseline model in terms of debiasing effect, (2) is more robust than the baseline model in the case of sparse data, (3) removes users' latent emotional bias between ratings and reviews for fairer recommendations, (4) fully takes into account dynamically biased user preferences, and (5) can better perceive real-world scenarios, which is of great research importance in today's era of ever-changing user preferences.
## 7 Risk Analysis
### Camera
#### 7.7.4 Repudiation  
1. **Component** _Security risk_: Repudiation threats against ACN camera systems are a critical concern as they enable malicious users to deny their involvement in recorded incidents, leading to legal and accountability issues. This jeopardizes the reliability of accident data, emergency response efforts, and insurance claims, undermining the trustworthiness of ACN systems. _Security measure_: Implementing digital signatures for all captured crash data and maintaining comprehensive audit logs can counter repudiation attempts. Digital signatures provide a unique and verifiable identifier for each piece of data, ensuring its authenticity and origin. Audit logs record all interactions and changes made to the system, creating a trail of evidence that can be used to confirm the legitimacy of the actions taken. These measures collectively deter users from denying their involvement in modifying or deleting crash data.
# Revalorization of _Posidonia oceanica_ Waste for the Thermochemical Production of Biochar
## 3 Results and Discussion
### Biochar Characterization
However, only two peaks were observed in the results obtained for the biochar produced at 400 \({}^{\circ}\)C (Figure 2c,d). They corresponded to cellulose (435 \({}^{\circ}\)C) and lignin (663 \({}^{\circ}\)C) decomposition. It was not possible to observe the cellulose decomposition as it is likely to have taken place during the production of the biochar. \begin{table}
\begin{tabular}{c c c c} \hline  & **Biochar 300 \({}^{\circ}\)C** & **Biochar 400 \({}^{\circ}\)C** & **Biochar 500 \({}^{\circ}\)C** \\ \hline Nitrogen (wt\%) & 0.93 & 0.61 & 0.56 \\ Carbon (wt\%) & 41.07 & 28.31 & 26.60 \\ C (inorganic) (wt\%) & 2.74 & 3.52 & 4.21 \\ C (organic) (wt\%) & 38.32 & 24.79 & 22.40 \\ Hydrogen (wt\%) & 2.50 & 1.17 & 0.65 \\ H/C organic & 0.07 & 0.05 & 0.03 \\ Ashes (wt\%) & 44.46 & 66.42 & 57.02 \\ Oxygen (by difference) & 11.04 & 3.50 & 15.16 \\ CaCO\({}_{3}\) (wt\%) & 22.86 & 29.36 & 35.06 \\ Conductivity (dS/m) & 3.19 & 3.31 & 3.08 \\ Salt content (mg KCl/L) & 1682.56 & 1745.92 & 1624.83 \\ pH & 8.02 & 10.32 & 10.38 \\ Bulk density (kg/m\({}^{3}\)) & 258.31 & 256.26 & 245.80 \\ \% yield of biochar & 75 & 67 & 57 \\ \hline \multicolumn{4}{c}{Fluorescence analysis-semiquantitative analysis} \\ \hline Na (wt\%) & 0.65 & 0.77 & 0.96 \\ Mg (wt\%) & 1.61 & 2.01 & 2.49 \\ Ca (wt\%) & 21.6 & 21.9 & 25.5 \\ K (wt\%) & 0.25 & 0.24 & 0.27 \\ Fe (wt\%) & 1.48 & 1.67 & 1.57 \\ Sr (wt\%) & 0.18 & 0.2 & 0.19 \\ Si (wt\%) & 2.36 & 2.18 & 2.84 \\ P (wt\%) & 0.08 & 0.09 & 0.11 \\ S (wt\%) & 1.30 & 1.40 & 1.50 \\ Ni (wt\%) & 0.01 & 0.01 & 0.01 \\ \hline \end{tabular}
\end{table} 
Table 4: Characteristics of the different biochars obtained from washed _Posidonia oceanica_ leaves.
## 3 IEEE 802.15.6: The Key-Enabling Standard for WBANs
### A Brief History of IEEE 802.15.6 Standard  
In November 2007, the IEEE 802.15 Task Group 6 (also known as IEEE 802.15.6) was formed in order to standardize Wireless Body Area Networks (WBANs), which were not covered by any existing communication standard by then and later in 2012, the final version of the standard has been released as presented in [9]. The standard defined Physical (PHY) and Medium Access Control (MAC) layers optimized for short-range transmissions in, on, or around the human body. The purpose is to support a low complexity, low cost, ultra-low power, and high reliable wireless communication for use in close proximity to, or inside, a human body (but not limited to humans) to serve a variety of applications  
Figure 5: Power and Data Rate Requirements for the IEEE 802.15.6 WBAN Standard [9].  
both in the medical/healthcare and in the non-medical fields. In the following sections, we will explore more details of the standard and its important features.
# Versatile High-Throughput Platform for Focused Ultrasound In Vitro Application
## 2 Materials and Methods
### Simulation of Different Platform Configurations
#### 2.2.1 Low Intensity Focused Ultrasound (LIFU) Platform  
The main requirement for the LIFU platform was the ability to sonicate all 96 wells of the multi-well plate in parallel, using a single transducer for each well. Accordingly, the pitch of the well applicator was given by one of the multi-well plates (9 mm), and the size of the individual transducers was determined by the individual well diameter (6.58 mm). The remaining design choices were associated with the thickness and the material (PZT or piezo composite) of the piezoceramic layer. For the design of the piezo composite, different configurations with varying rod sizes (lateral) and kerfs were initially simulated in PZFlex V. 1.25.3.0 (Onscale, ANSYS, Inc., Redwood City, CA, USA) and compared with the behavior of bulk PZT. The simulations were limited to individual transducers because there was no overlap of the pressure fields in the final set-up design, with air-filled walls separating different wells.  
The simulations shown in Figure 1 were performed in a free field and, therefore, only partially represent the final setup with wells filled to a defined target level. Nevertheless, they confirmed that the lateral spread of the sound field (relative to the aperture, which corresponded to the placement of the well) did not exceed the well diameter, indicating that most of the acoustic energy was applied to the well. However, it was evident in the simulations that with this small aperture diameter, the sound field maxima at the different operating frequencies were at different depths. According to the simulations, only the 0.5 and 1 MHz versions showed axial focus positions within a well depth of 10.9 mm.
## 2 Thermo-Coupled \(J_{2}\)-Flow Model with Evolving Elastic Potential
### Thermo-Elastic Rate Equation with Evolving Potential  
The thermo-elastic behavior is characterized by a strain energy function, also known as elastic potential. Usually, this potential keeps unchanged under the assumption that any process of inelastic deformations has no effects on the elastic behavior. As a departure from usual treatment, here an evolving elastic potential is introduced. This idea will prove essential in simulating the stress softening behavior at unloading, as has been shown in a previous study [40].  
For our purpose, a complementary elastic potential characterizing thermo-elastic behavior of SMPs is introduced as follows:  
\[\hat{W}=\overline{W}(\tilde{\mathbf{\tau}},\tilde{\kappa},T)+\left(\text{tr}\mathbf{ \tau}\right)\Theta(T)\,, \tag{2}\]  
where the \(T\) is the absolute temperature and the \(\tilde{\kappa}\) is the effective plastic work and will be given slightly later by Equation (11). In the above, the second term represents the volumetric expansion effect arising from temperature change, while the first term implies the incompressibility effect in the isothermal case. Note here that the thermal expansion parameter \(\Theta(T)\) is usually very small, but becomes appreciable in a thermal process through the glass transition.  
Then, the elastic part \(\mathbf{D}^{e}\) is determined by an objective Eulerian rate equation below [40]:  
\[\mathbf{D}^{e}=\frac{\partial^{2}\overline{W}}{\partial\tilde{\mathbf{\tau}}^{2}}\cdot \overset{\circ}{\tilde{\mathbf{\tau}}}\log+\frac{\partial^{2}\overline{W}}{ \partial\tilde{\mathbf{\tau}}\partial\kappa}\dot{\kappa}+\frac{\partial^{2} \overline{W}}{\partial\tilde{\mathbf{\tau}}\partial T}\dot{T}+\Theta^{\prime}(T) \dot{T}\mathbf{I}\,, \tag{3}\]  
where \(\mathbf{I}\) is the 2 nd-order identity tensor and \(\overset{\circ}{\tilde{\mathbf{\tau}}}\log\) is the logarithmic rate of the deviatoric Kirchhoff stress \(\tilde{\mathbf{\tau}}\). Here and henceforth, the notation \(\dot{A}\) designates the material time rate of the time-varying quantity \(A\).  
Following the procedures in [43], it may be demonstrated that, prior to the initial yielding with \(\mathbf{D}^{e}=\mathbf{D}\), the elastic rate Equation (3) is exactly integrable to deliver a finite hyperelastic relation, namely,  
\[\mathbf{h}=\frac{\partial\overline{W}}{\partial\mathbf{\tau}}\,. \tag{4}\]  
This explains the meaning of the complementary elastic potential \(\overline{W}\). Since the latter evolves with the effective plastic work \(\kappa\) (cf., Equation (11) below), it may be clear that the elastic behavior will be different for different cases of unloading.
## 2 Materials and Methods
### Statistical Analysis  
Descriptive statistics were used to calculate and compare different variables in our study (\(n=160\)). Additionally, a multivariate analysis of variance (MANOVA) was carried out using SPSS software (version 23.0, IBM Corporation, Armonk, NY, USA). Data were previously inspected for univariate and multivariate normality using the Mahalanobis distance regression test with an alpha level of 0.001 [36]. Ten of the data were discarded; two were outliers and did not fit the conditions for normal distribution, and the other eight values were considered as being missing from the sensory analysis, since the relevant participants were not present at one of the appointments. For the rest of the data (\(n=150\)), the statistical processing was based on the differences and interactions between the relevant independent variables, i.e., transport distance (TD), animal weight (AW), and muscle position (MP), and their effects on meat quality traits. Transport distances were divided into three groups: (i) short distance (TD \(<\) 34.5 km); (ii) medium distance (34.5 km \(<\) TD\(<\) 59.1 km); and (iii) long distance (TD \(>\) 59.1 km). Animal weight was also split between light (AW \(<\) 445 kg) and heavy animals (AW \(>\) 445 kg). Muscle position was determined either as shoulder clad (SC) or silverside (SS).  
The dependent variables in the MANOVA model were the meat color scores (\(L^{*}\), \(a^{*}\), \(b^{*}\), \(h_{ab}\), and C\({}^{*}\)), pH\({}_{48}\), the WBSF values obtained from the instrumental texture determination, and the sensory quality traits (odor, taste, and hardness) obtained from the sensory analysis. Medias between treatments were compared using a Tukey post-hoc test at a significance level of 0.05. Additionally, a Pillay's Trace test was used to find correlations between the different factors that may affect meat quality, at a significance level of 0.01.
## 5 Simulation Results
Thus, the error combinations are limited and therefore the BER values tend to be discrete. In Figure 5(a), 256 samples were substituted by others at the receiver for four levels of data sparseness (0.5%, 1%, 2%, or 4% of the data bits that are input to the transmitter are non-zero). The BER floor ranges between 0.005 (for 0.5% data sparseness) and 0.06 (for 4% sparseness). In Figure 5(b), 128 samples were substituted and the error floor tends to be \(10^{-6}\) for 0.5% sparseness when the channel SNR is adequately high. Nevertheless, there is no significant improvement when the sparseness is 2% or 4%. In Figure 5(c), 86 samples were substituted and there is one case where the input is fully reconstructed (when the sparseness is 0.5%) while the error floors at the other cases are significantly improved. Finally, when 64 samples were replaced (Figure 5(d)), the input can be fully reconstructed when the sparseness degree is 0.5% or 1% and the channel SNR is about 18 dB. In Figure 7, a different view is given by comparing, in the same figure, the cases where different number of samples is replaced and RS decoding is used. Using RS decoder the full input signal reconstruction is possible when the data sparseness is 4% and 32 or 48 samples are substituted (see  
Figure 6: Cont. Figure 7a). The full signal reconstruction requires an SNR that is 2 or 4 dB higher than the optimal case where no samples are replaced. In Figure 7b, the sparseness is 2% and again the full reconstruction takes place when 32 or 48 samples are substituted but this occurs at the same SNR with the optimal case. The error floor at the other cases is improved compared to the case of 4% sparseness degree. In Figure 7c, 1% sparseness degree is tested but now the substitution of 64 samples does not lead to full reconstruction, as in the case of Figure 6d. Taking into consideration the exact values of the error floors in all the sparseness cases it can be stated that Viterbi decoding is more efficient than RS for the proposed undersampling scheme. Figure 7: BER _vs._ SNR when RS decoder is used and the data sparseness is (**a**) 4%; (**b**) 2%; (**c**) 1%.
## 5 Conclusions
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c c} \hline  & \multicolumn{3}{c}{PRECISION} & \multicolumn{3}{c}{PRC-AUC} & \multicolumn{3}{c}{RECALL} & \multicolumn{3}{c}{ROC-AUC} & \multicolumn{3}{c}{F1} & \multicolumn{3}{c}{CM} \\ \hline
**Method** & **Macro \(\uparrow\)** & **3\(\uparrow\)** & **4\(\uparrow\)** & **3\(\uparrow\)** & **4\(\uparrow\)** & **Macro \(\uparrow\)** & **3\(\uparrow\)** & **4\(\uparrow\)** & **3\(\uparrow\)** & **4\(\uparrow\)** & **Macro \(\uparrow\)** & **3\(\uparrow\)** & **4\(\uparrow\)** & **3\(\uparrow\)** & **4\(\uparrow\)** \\ \hline CE-None & 0.71 & 0.78 & 0.74 & 0.74 & 0.58 & 0.79 & 0.95 & 0.77 & 0.97 & 0.88 & 0.74 & 0.86 & 0.76 & 21 & 17 \\ CE-RW & 0.68 & 0.68 & 0.66 & 0.65 & 0.57 & 0.80 & 0.95 & 0.86 & 0.97 & 0.92 & 0.71 & 0.79 & 0.75 & 21 & 19 \\ CE-DRW & 0.72 & 0.84 & 0.60 & 0.80 & 0.50 & 0.81 & 0.95 & 0.82 & 0.97 & 0.90 & 0.75 & 0.89 & 0.69 & 21 & 18 \\ CE-RLPr & 0.70 & 0.72 & 0.66 & 0.69 & 0.57 & 0.81 & 0.95 & 0.86 & 0.97 & 0.92 & 0.73 & 0.82 & 0.75 & 21 & 19 \\ \hline Focal-None & 0.72 & 0.75 & 0.74 & 0.72 & 0.58 & 0.79 & 0.95 & 0.77 & 0.97 & 0.88 & 0.74 & 0.84 & 0.76 & 21 & 17 \\ Focal-RW & 0.69 & 0.72 & 0.73 & 0.69 & 0.64 & 0.81 & 0.95 & 0.86 & 0.97 & 0.93 & 0.72 & 0.82 & 0.79 & 21 & 19 \\ Focal-DRW & 0.69 & 0.78 & 0.59 & 0.74 & 0.52 & 0.81 & 0.95 & 0.86 & 0.97 & 0.92 & 0.73 & 0.86 & 0.70 & 21 & 19 \\ Focal-RLPr & 0.68 & 0.75 & 0.53 & 0.72 & 0.48 & 0.78 & 0.95 & 0.91 & 0.97 & 0.94 & 0.72 & 0.84 & 0.67 & 21 & 20 \\ \hline LDAM-None & 0.63 & 0.86 & 0.0 & 0.75 & 0.40 & 0.68 & 0.86 & 0.0 & 0.93 & 0.50 & 0.65 & 0.86 & 0.0 & 19 & 0 \\ LDAM-RW & 0.68 & 0.70 & 0.66 & 0.67 & 0.57 & 0.80 & 0.95 & 0.86 & 0.97 & 0.92 & 0.71 & 0.81 & 0.75 & 21 & 19 \\ LDAM-DRW & 0.69 & 0.77 & 0.54 & 0.70 & 0.47 & 0.79 & 0.91 & 0.86 & 0.95 & 0.92 & 0.73 & 0.83 & 0.67 & 20 & 19 \\ LDAM-RLPr & 0.63 & 0.64 & 0.48 & 0.61 & 0.44 & 0.79 & 0.95 & 0.91 & 0.97 & 0.93 & 0.67 & 0.76 & 0.62 & 21 & 20 \\ \hline DLWP-None-None & 0.75 & 0.84 & 0.86 & 0.80 & 0.71 & 0.80 & 0.95 & 0.82 & 0.97 & 0.91 & 0.77 & 0.89 & 0.84 & 21 & 18 \\ DLWP-None-ENPr & 0.77 & 0.83 & 0.95 & 0.76 & 0.83 & 0.80 & 0.91 & 0.86 & 0.95 & 0.93 & 0.78 & 0.87 & 0.90 & 20 & 19 \\ DLWP-None-DENPr & 0.79 & 0.91 & 0.82 & 0.83 & 0.68 & 0.79 & 0.91 & 0.82 & 0.95 & 0.91 & 0.79 & 0.91 & 0.82 & 20 & 18 \\ DLWP-None-RLPr & 0.79 & 0.91 & 0.85 & 0.83 & 0.67 & 0.79 & 0.91 & 0.77 & 0.95 & 0.88 & 0.79 & 0.91 & 0.81 & 20 & 17 \\ \hline DLWP-RW-None & 0.70 & 0.72 & 0.73 & 0.69 & 0.64 & 0.81 & 0.95 & 0.86 & 0.97 & 0.93 & 0.73 & 0.82 & 0.79 & 21 & 19 \\ DLWP-RW-ENPr & 0.70 & 0.72 & 0.59 & 0.69 & 0.52 & 0.81 & 0.95 & 0.86 & 0.97 & 0.92 & 0.73 & 0.82 & 0.70 & 21 & 19 \\ DLWP-RW-ENPr & 0.71 & 0.72 & 0.74 & 0.69 & 0.68 & 0.81 & 0.95 & 0.91 & 0.97 & 0.95 & 0.75 & 0.82 & 0.82 & 21 & 20 \\ DL
## 4 Reynolds Number Effect on VIV Characteristics and the Underlying Mechanism
### Time-Frequency Characteristics of Dynamic Aerodynamic Forces
#### 4.2.3 Dominant Frequency of Fluctuating Pressure  
The surface pressure fluctuation spectrum of the main beam reflects the frequency characteristics of the pressure, with the dominant frequency representing the main frequency of the pressure. By comparing the dominant pressure fluctuation frequency at individual measurement points with the dominant vibration frequency of the model, the relationship between local pressure fluctuations and overall vibration can be assessed [37; 38; 39]. Figure 11 shows a comparison of the distribution characteristics of the dominant frequencies in the pressure fluctuation spectrum at different measurement points on the surface of the main beam during VIV for four different Reynolds number tests.  
As shown in Figure 11a, when \(Re=3.2\times 10^{4}\) and \(4.7\times 10^{4}\), the dominant frequencies of the fluctuating pressure at all of the measurement points are nearly the same, matching the vertical VIV frequencies of 1.90 Hz and 2.97 Hz, respectively. However, when \(Re=7.1\times 10^{4}\) and \(8.3\times 10^{4}\), the dominant frequencies at the measurement points differ. At these two Reynolds numbers, the dominant frequencies at most measurement points are 4.53 Hz and 5.27 Hz, respectively, which are consistent with the vibration frequencies observed in the VIV tests of the corresponding Reynolds numbers. However, the dominant frequencies at the measurement points in the upper surface regions of \(D_{\rm d}=0.12\)-0.15 and \(D_{\rm d}=0.35\)-0.55 deviate from the VIV frequencies.  
As shown in Figure 11b, the dominant frequency of the fluctuating pressure at each measurement point is consistent with the VIV frequency only when \(Re=3.2\times 10^{4}\). For the  
Figure 11: Distribution characteristics of the dominant frequencies of pressure at different Reynolds numbers at each measurement point. (**a**) Upper surface. (**b**) Lower surface.  
other Reynolds number tests, the dominant frequencies at most measurement points do not match the VIV frequency.  
Overall, the spatial distribution characteristics of the dominant frequencies of fluctuating pressure at each measurement point on the main beam surface differ at different Reynolds numbers. As the Reynolds number increases, the frequencies become more dispersed. This could be a significant reason for the decrease in the VIV amplitude with increasing Reynolds numbers, which is consistent with the conclusion drawn by [PERSON] et al. [40].