esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Modelling
### A Unified Thermal Conductivity and Water Retention Model
At last, Equation (13) may be rewritten in a simplified form as:  
\[\langle p_{c}\rangle=\varphi_{0}+P_{0}[\exp(\alpha S_{w})-\exp(\beta(1-S_{w}))] \tag{14}\]  
where \(\varphi_{0}\), \(P_{0}\), \(\alpha\), and \(\beta\) are four redefined parameters related to the pore structure and the nature of all the material phases involved. Equation (12) describes the state of the coexisting water and vapour phases in unsaturated soils in terms of their interaction with the solid phase at the interface. The derived Equation (14) has been successfully used to describe the water retention characteristic of unsaturated soils and building materials [42; 44; 45]. It has been demonstrated that Equation (14) is able to represent the water distribution and the pore size distribution in porous media. Considering that the thermal conductivity of unsaturated soils is influenced by both the heat transfer at the interface between the soil particles and the fluids retained in pores, which relates to the water distribution in the pore system, and with the noticed resemblances between the variation of thermal conductivity against water content and water retention characteristic curves, this paper applies Equation (14) for thermal conductivity modelling. To avoid confusion, Equation (14) is rewritten in the following form given by Equation (15) as  
\[K_{eff}=\lambda_{0}+K_{0}[\exp(\alpha S_{w})-\exp(\beta(1-S_{w}))] \tag{15}\]  
where \(K_{eff}\) is called the effective thermal conductivity, \(\lambda_{0}\), \(K_{0}\), \(\alpha\), and \(\beta\) are four redefined parameters depending on the pore structure and the material nature of all phases. Figure 11 compares the modelling results using Equations (4) and (15) for the reported experiment data of this paper, respectively. It can be seen that Equation (15) gives impressively close agreement to the experiment data in comparison to Equation (4) in all of the four cases of different porosities. Table 3 lists out the values of the four parameters defined in Equation (15). This suggests that Equation (15) can be used as a unified model for both the thermal conductivity and water retention characteristics of unsaturated soils. However, a deeper understanding the underlying mechanisms of the model working for the two constitutive soil properties and verification on a large experimental data of different soils still need to be studied, and represent continuing research.
## 3 Image Processing Procedure
### Image Restoration and Enhancement  
Image restoration mainly deals with the de-noising issues while image enhancement is used for adjusting the image contrast. For de-noising, several image filters can be applied, e.g., Average filter, Midian filter, and Gaussian filter, dedicated to a presumed noise scenario. In this paper, a Wiener filter is used because it can adapt to the noise scenario in an image and usually outperforms the other filters mentioned in different applications. Image enhancement can be accomplished with histogram equalisation or direct contrast mapping through a linear or nonlinear function, which can stretch the image contrast between the background and foreground pixels and highlight specific detailed. At the moment, image enhancement operation is not applied after image filtering since no significant improvement can be achieved but it may be used in the future.  
Figure 4: Flow diagram of image processing.
# Planar Delaunay Mesh Smoothing Method Based on Angle and a Deep Q-Network
## 2 Smoothing Method Based on Angle and Deep Q-Network
### Construction of the Inner Polygon  
The inner polygon is constructed based on the angle-based smoothing method proposed by [PERSON] and [PERSON] [14]. As shown in Figure 3a, \(N_{i}\) is the central node of the polygon, and \(N_{j}\) is the adjacent point of the polygon. N\({}_{j}^{\rightarrow}\)\(N_{i}\) denotes \(V_{j}\), N\({}_{j}^{\rightarrow}\)\(N_{i+1}\) denotes \(V_{j+1}\), and N\({}_{j}^{\rightarrow}\)\(N_{j-1}\) denotes \(V_{j-1}\). \(\alpha_{1}\) is the angle formed by \(V_{j}\), and \(V_{j-1}\), and \(\alpha_{2}\) are the angles formed by \(V_{j}\) and \(V_{j+1}\). With \(N_{j}\) as the center and \(\overline{N_{i}N_{j}}\) as the radius, \(V_{j}\) is rotated until the included angle formed by \(V_{j}\) and \(V_{j-1}\) equals to that formed by \(V_{j}\) and \(V_{j+1}\). The angle to be rotated is \(\beta_{j}\), and the updated central node is shown in Figure 3b. The central node has a total of \(k\) adjacent points, so when the same operation is performed \(k\) times, \(k\) central nodes are generated inside the polygon after one round of the operation, as shown in Figure 3c.  
Ref. [14] used the mean coordinate value of the updated \(k\) central nodes as the new central node. When the updated central node is moved out of the polygon, such nodes will impact the location of the central node, resulting in a reduction in the quality of the element. The updated center point will be referred to as a scatter point in the following text.  
In this paper, the updated k scatter points are further processed. First, when the shape of the polygon is too complex or the central node is too close to the boundary, the updated scatter point may fall outside the polygon. Suppose the number of scatter points falling outside the polygon is \(m_{1}\) and the number of scatter points inside the polygon is \(m_{2}\). Then, \(m_{2}=k-m_{1}\), and these \(m_{1}\) scatter points need to be deleted when constructing the inner polygon. After that, the convex hull algorithm [28] connects \(m_{2}\) scatter points inside the polygon to form an inner polygon. As shown in Figure 3d, suppose the number of points on the convex packet is \(v_{2}\), and the number of points inside the polygon and not on the  
Figure 2: Impact of the central node moving position on node quality. (**a**) Case 1, where the central node moves near the polygon boundary; (**b**) Case 1, where the central node moves near the polygon boundary; (**c**) Case 2, where the central node moves near the center of the polygon; (**d**) Case 2, where the central node moves near the center of the polygon.  
convex packet is \(v_{1}\). Then, \(v_{1}=m_{2}-v_{2}\). Finally, the generated inner polygon is shown in Figure 3e.
## 2 Numerical Approach  
### Estimation Method of Turbulence Intensity  
Turbulence intensity (\(Tu\)) is a physical quantity to measure the degree of irregular motion of fluid element. Turbulence intensity is defined as the ratio of the rms of fluctuating velocity \(u^{\prime}\) to average velocity \(\overline{U}\)(Equation (1))  
\[Tu=\frac{\sqrt{{u^{\prime}}^{2}}}{\overline{U}} \tag{1}\]  
In turbulent flow, the mean values of velocity and pressure are easy to observe, while the fluctuating velocity can be measured by precise hot wire anemometer, laser velocimeter and particle image velocimetry. The turbulence energy is mainly concentrated in the large-scale eddy structure, which is related to the turbulence length scale \(l\). The characteristic length of turbulence depends on the geometric length and has a decisive influence on the development of turbulence. If the flow at the entrance is restricted by the wall and has a turbulent boundary layer, the turbulent length scale can be calculated by \(l=0.4\delta_{99\%}\), where the \(\delta_{99\%}\) is the thickness of boundary layer. As for the flow affected by the inlet grid, the turbulence length scale is approximately equal to the grid aperture, namely \(l\approx d\). [6; 21].  
\(R_{T}\) is the ratio of turbulence viscosity to laminar viscosity, which is directly proportional to the turbulent Reynolds number. In the high-Reynolds-number boundary layer, shear layer and fully developed pipe flow, the turbulence viscosity ratio is large, about 100-1000. However, in most free flow boundary layers, the turbulence viscosity ratio is quite small, usually 1-10.  
It is observed in a relative static wind tunnel that the turbulent flow behind the grid of the wind tunnel is steady, and its intensity is continuously attenuated along the flow direction from the inlet of the experimental section. According to the reference [29], the relationship between the turbulence attenuation and the increase of flow direction distance can be described as follows:  
\[Tu=Tu_{inlet}\bigg{(}1+Re_{x}1.5\beta\frac{Tu_{inlet}}{R_{T,inlet}}\bigg{)}^{ -\beta^{\prime}/2\beta} \tag{2}\]In the numerical simulation, the attenuation of turbulence intensity can be more directly reflected by the turbulent dissipation rate \(\varepsilon\) (Equation (3)).  
\[\varepsilon=\beta^{*3/4}\frac{k^{3/2}}{l} \tag{3}\]  
where \(k\) is turbulent kinetic energy, \(\beta\) and \(\beta^{*}\) are the empirical constants in the turbulence model. The values are \(\beta=0.0828\), \(\beta^{*}=0.09\).
# Omnidirectional Haptic Guidance for the Hearing Impaired to Track Sound Sources
## 3 System Configuration and Procedure  
### System Configuration  
The configuration and appearance of the hearing assist system are shown in Figures 7 and 8, respectively. The acoustic signal detected by the ear microphone (MDR-EX3 IBN, Sony) is amplified by the microphone amplifier and input to the FPGA module (myRIO-1900, N.I.) through the LPF. The LPF is used to remove aliasing noise. The sound played back through the loudspeakers in this study was a motorcycle engine. The principal components in this sound are distributed in a frequency range of 1 to 5 kHz. In order to detect the sound generated by a vehicle on the road from a distance, the cutoff frequency was set at 6.07 kHz because sound with a relatively low frequency that can easily propagate far is the target of detection. The sampling frequency was set at 15.4 kHz. To shorten the processing time, the distance to the sound source and the direction of the sound source were estimated by separate FPGA modules; then, the vibrators on both shoulders were activated. The two FPGA modules were synchronized in operation. An isolation amplifier was provided to prevent the output signal to the vibrators from interfering with the input signal. The analog signal output of the module was amplified by a class D amplifier and input to the vibrator. The gain of the class D amplifier is adjustable, in case the subject feels pain or cannot perceive the vibration. Therefore, the subject perceives changes in the intensity of the vibration rather than the absolute value of the intensity. The subject's  
Figure 6: Directional characteristics of mean standard deviation. Radial axis represents mean value of standard deviation (in degrees). It can be seen that this value is relatively low when the sound source is located either directly in front (180\({}^{\circ}\)) or directly behind (0\({}^{\circ}\)) and becomes higher as the sound source locates to the side. ©(2021) IEEE, Reprinted, with permission.  
appearance is shown in Figure 8. The subject was a 21-year-old man with normal hearing, who wore earplugs in both ears and an ear microphone. The sound level was turned down until he could no longer hear it. To avoid visual effects, he wore an eye mask. He was instructed to turn his face in the direction where the vibration intensity of the vibrators on both shoulders was equal.
# A Narrow-Down Approach Based on Machine Learning for Indoor Localization
## 3 System Design  
Wi-Fi RSSI-based indoor localization is a two-stage process [13]. In the first stage, the localization area of interest is composed of reference points (RPs) and test points (TPs) [30]. A database containing offline FPs is created where each entry (RSS vector/FP) is associated with a reference point (RP). A localization algorithm like DNN, RF, or SVM is trained on the offline database. In the second stage, the already-trained localization algorithm tries to find the user's location by matching online FPs with the database. Distinct from the traditional ML approaches, we process the dataset by using a three-step SDR-scheme sub-area overlapping technique and also utilize lightweight neural networks that are trained on each sub-area independently. The architecture of the proposed model is illustrated in Figure 1, which mainly consists of five components: area division and overlapping, training data selection for classification and regression, source domain refinement (SDR) scheme, coarse positioning phase, and accurate positioning phase. The proposed scheme consists of two phases: coarse and accurate positioning. For the coarse positioning phase, specific points are selected as reference points (RPs). A three-step domain source refinement (DSR) scheme is applied to these RPs to obtain a refined dataset and a classifier is trained on this refined dataset to find the relevant sub-area where the user can reside in. For the accurate positioning phase, the training dataset is divided into several sub-areas to train a deep neural network (DNN) on each sub-area independently. We will explain the aforementioned components in the following sections.
# Stable Evaluation of 3D Zernike Moments for Surface Meshes
## Appendix B A Recurrence for \(S^{k}_{nl}(r)\)  
We start from the recurrence over the \(R_{nl}(r)\) (Equation (20) in the main body of the text)  
\[R_{nl}(r)=K_{1}(n,l)r^{2}R_{n-2,l}(r)+K_{2}(n,l)R_{n-2,l}(r)+K_{3}(n,l)R_{n-4, l}(r), \tag{103}\]  
where \(K_{1}\), \(K_{2}\), and \(K_{3}\) were defined in Equation (21) in the main text. Let \(k\) be a non negative integer. After multiplication with \(r^{k}\), we get  
\[r^{k}R_{nl}(r)=K_{1}(n,l)r^{k+2}R_{n-2,l}(r)+r^{k}K_{2}(n,l)R_{n-2,l}(r)+r^{k} K_{3}(n,l)R_{n-4,l}(r), \tag{104}\]  
which we integrate over \([0,r_{0}]\)  
\[S^{k}_{nl}(r_{0})=K_{1}(n,l)S^{k+2}_{n-2,l}(r_{0})+K_{2}(n,l)S^{k}_{n-2,l}(r_{ 0})+K_{3}(n,l)S^{k}_{n-4,l}(r_{0}). \tag{105}\]  
Shifting \(n\to n+2\), we get  
\[S^{k}_{n+2,l}(r_{0}) = K_{1}(n+2,l)S^{k+2}_{nl}(r_{0})+K_{2}(n+2,l)S^{k}_{nl}(r_{0})+K_ {3}(n+2,l)S^{k}_{n-2,l}(r_{0}). \tag{106}\]  
This then yields Equation (27).  
Starting with \(S^{0}_{nl}(r)\), repeated use of Equation (106) allows us to compute all \(S^{k}_{nl}(r)\) for \(k\) even, while this is enough for recurrence required in this paper, for sake of completeness, we show how the same integrals can be evaluated for \(k\) odd.  
The recurrence on \(R_{nl}\) expressed in Equation (20) has a coefficient with \(r\) to the power 2, leading to the even recurrence. [PERSON] in their work on generalized Zernike Functions ([57]) derived a different recurrence on \(R_{nl}\) (his Equation (80)):  
\[R_{n+l,l}(r)=\frac{2n+3}{2n+2}r\bigg{(}\frac{2l+2}{2l+1}R_{n,l+1}(r)+\frac{2l }{2l+1}R_{n,l-1}(r)\bigg{)}-\frac{n+2}{n+1}R_{n-1,l}(r). \tag{107}\]  
Note that applications of this recurrence require the initialization \(R_{00}(r)=1\), and setting \(R_{nl}\equiv 0\) when \(n<l\). After integration over \([0,r_{0}]\), we get  
\[S^{0}_{n+l,l}(r_{0})=\frac{2n+3}{2n+2}\bigg{(}\frac{2l+2}{2l+1}S^{1}_{n,l+1}(r _{0})+\frac{2l}{2l+1}S^{1}_{n,l-1}(r_{0})\bigg{)}-\frac{n+2}{n+1}S^{0}_{n-1,l} (r), \tag{108}\]which we rewrite as  
\[S^{1}_{n,l-1}(r_{0})=-\frac{l+1}{l}S^{1}_{n,l+1}(r_{0})+\frac{(2n+2 )(2l+1)}{(2n+3)(2l)}S^{0}_{n+1,l}(r_{0})\\ +\frac{(2n+4)(2l+1)}{(2n+3)(2l)}S^{0}_{n-1,l}(r_{0}). \tag{100}\]  
Equation (100) provides a recurrence for computing \(S^{1}_{nl}(r_{0})\) from \(S^{0}_{nl}(r_{0})\). Integrals \(S^{k}_{nl}(r_{0})\) with \(k\) odd, \(k>1\) can then be derived by repeated use of Equation (101), starting with \(S^{1}_{nl}(r_{0})\).
## 3 Regulatory Barriers to Implementing an EU-Wide Grid Digital Twin
### Policy and Legal Mandates  
In the absence of formal mandates, adoption can lag. Some experts argue that achieving a true EU-wide digital twin might eventually require legislative action from the European Union, similar to how the rollout of smart meters or the implementation of common grid codes was mandated [37]. Until now, the approach has been voluntary and based on incentives. If this proves insufficient, the European Commission could consider proposing requirements in future energy legislation, for example, as part of the next revision of the Electricity Regulation, for TSOs and large DSOs to participate in collective digital twin frameworks and to share the necessary data [4]. The challenge is to design such mandates in a way that avoids over-prescription, especially given the varying levels of readiness among stakeholders. In addition, aligning cybersecurity regulations with the digital twin initiative is crucial. The digital twin will likely be classified as critical infrastructure because it will play a central role in grid operations. The upcoming NIS2 Directive and other cybersecurity regulations will impose strict requirements on its operators, such as the implementation of security measures and incident reporting. Policymakers must ensure that these requirements are both proportionate and harmonized to achieve high levels of security without imposing excessive burdens [29].
# Detection of Rock Mass Defects Using Seismic Tomography
## 3 Synthetic Experiment  
Following the workflow illustrated in Figure 2 for identifying rock mass anomalies and their boundaries using seismic tomography at the experimental scale, we carried out wave velocity inversions on a small scale with the purpose of imaging the wave structure and demarcating the boundaries according to the wave velocity difference. Each synthetic test described below was completed in the following six stages:  
1. Prepare the original model, including setting the velocity corresponding to each node in the normal and abnormal zones, arranging the sensor array, and generating random acoustic emission events.
2. Calculate the arrival times for each AE event source and active ultrasonic source to each sensor using the forward method described in Section 2.1.
3. Prepare the prior model for the inversion.
4. Configure the constraints for inversion, including the grid refinement factor; the standard deviation of survey picks and event picks; the maximum number of iterations; residual tolerance to ceasing iteration; the quasi-Newton step size; the standard deviation \(\sigma_{V}\) of \(\ln(V_{h})\); the standard deviation \(\sigma_{E}\) of \(E\); the correlation length \(\lambda\); the standard deviations \(\sigma_{x}\), \(\sigma_{y}\), and \(\sigma_{z}\) of the source positions; and the standard deviation \(\sigma_{t_{0}}\) of the original time \(t_{0}\) of the sources.
5. Apply the method described in Section 2.3 for the tomography inversion.
6. Evaluate the accuracy of the velocity images and identify the boundaries of the abnormal area according to the tomography results. The area defects (e.g., sectional defects in different shapes) and structure defects (e.g., linear defects with different widths) will be tested separately.
## 3 Simulation Studies
### Simulation Study 1
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Run** & \(x_{1}\) & \(x_{2}\) & \(\underline{y}\) & \(\underline{s}\) & \(\underline{s}^{2}\) \\ \hline
11 & \(0.00\) & \(1.00\) & \(91.7450\) & \(4.2200\) & \(17.8060\) \\
12 & \(-1.00\) & \(0.00\) & \(99.7800\) & \(3.7970\) & \(14.4200\) \\
13 & \(1.00\) & \(1.00\) & \(100.3540\) & \(5.0330\) & \(25.3290\) \\
14 & \(-0.50\) & \(0.50\) & \(66.1700\) & \(3.4490\) & \(11.8960\) \\
15 & \(0.00\) & \(-0.50\) & \(158.7880\) & \(4.8550\) & \(23.5740\) \\
16 & \(-0.50\) & \(-1.00\) & \(104.5000\) & \(5.0920\) & \(25.9290\) \\
17 & \(-0.50\) & \(-0.50\) & \(127.9310\) & \(5.3540\) & \(28.6630\) \\
18 & \(0.50\) & \(1.00\) & \(96.5800\) & \(4.4950\) & \(20.2080\) \\
19 & \(-1.00\) & \(-1.00\) & \(100.8770\) & \(4.3940\) & \(19.3060\) \\
20 & \(0.00\) & \(-1.00\) & \(113.8910\) & \(5.2110\) & \(27.1530\) \\
21 & \(0.00\) & \(0.50\) & \(54.8070\) & \(4.0020\) & \(16.0170\) \\
22 & \(1.00\) & \(0.50\) & \(95.8950\) & \(5.4510\) & \(29.7140\) \\
23 & \(-0.50\) & \(0.00\) & \(100.8800\) & \(4.0340\) & \(16.2710\) \\
24 & \(-0.50\) & \(1.00\) & \(91.2050\) & \(3.4390\) & \(11.8270\) \\
25 & \(0.50\) & \(-0.50\) & \(144.5120\) & \(5.3620\) & \(28.7530\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Model** & **Transfer Function** & **Training Function** & **Architecture** & **\#Epoch** \\ \hline \multirow{2}{*}{FFNN} & Mean & Tansig-Purelin & Trainlm & 2-17-1 & 3 \\  & Standard deviation & Tansig-Purelin & Trainrp & 2-6-1 & 44 \\ \hline \multirow{2}{*}{CFNN} & Mean & Tansig-Purelin & Trainlm & 2-17-1 & 5 \\  & Standard deviation & Tansig-Purelin & Trainrp & 2-5-1 & 28 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of multilayer feed-forward NN information for simulation \(1\). Figure 8: Response plots created using the proposed FFNN-based modeling method in simulation study 1: (**a**) Mean (R2 = 89.96%), (**b**) Standard deviation (R2 = 89.28%). Figure 7: Response plots created using the conventional LSM-based RSM in simulation study 1: (**a**) Mean (R2 = 29.54%), (**b**) Standard deviation (R2 = 86.61%). Figure 9: Response plots created using the proposed CFNN-based modeling method in simulation study 1: (**a**) Mean (R2 = 83.22%), (**b**) Standard deviation (R2 = 86.68%).
## 2 Optimal Lane Change Path Planning Based on the NSGA-II and TOPSIS Algorithms
### Lane Change Trajectory Based on Polynomials
#### 2.1.1 Lane Change Trajectory Constraints  
In the cluster of unconstrained lane changing trajectories, some cannot meet the feasibility requirements. Considering the dynamic constraints of the ego vehicle and the requirements of riding comfort, the constraint conditions of lane changing trajectories considered in this paper are as follows [32; 33]:  
1. Lateral displacement constraint: \(0<y(t)<width\).
2. Security constraints: During the lane changing process, the ego vehicle does not collide with the surrounding traffic vehicle; that is, the collision avoidance algorithm in Section 2.2 is satisfied.
3. Minimum lane change time constraint: \[t_{\min}=2.745-2.997\mu+0.01093v+1.138\mu^{2}+0.0004618\mu v-3.107\times 10^{-5}v^{2}\] (4)  
Figure 1: Schematic diagram of vehicle lane change.  
Figure 2: Unconstrained lane changing trajectory cluster.  
where \(t_{\text{min}}\) is the shortest time for the ego vehicle to change lanes smoothly, \(\mu\) is the road adhesion coefficient, and \(v\) is the speed of the ego vehicle. In this study, all the vehicles are assumed to be driving on an asphalt road, and the reference value of \(\mu\) is 0.85.
4. Limited by the constraints between the tire and the road, the maximum lateral acceleration is \(a_{y,\text{max}}=\mu g\).