esa-sceva/satcom-chunk-collection huggingface dataset:
## 5 Numerical Applications
### RBDO of the Cantilever Beam under the Displacement Constraint  
The beam consists of three segments, each of length \(L\). The cross-section of each segment has a hollow square form, as shown in Figure 7. The thickness of the section is \(t\) for all segments, and the length of the side of the square is \(d_{i}\) for segment \(i\) = 1,2,3. The objective of this RBDO problem is to minimize the volume of the beam under the constraint that the displacement, \(\Delta_{\text{tip}}\), at the tip is less than a prescribed value \(\Delta_{0}\). The design variables are the cross-sectional sizes, \(\mathbf{d}\) = (\(d_{1}\),\(d_{2}\), \(d_{3}\))\({}^{\text{T}}\), and the random variables are the modulus of elasticity, magnitude of force, and thickness of the cross-section, as \(\mathbf{x}\) = (\(E\),\(F\),\(\mu\))\({}^{\text{T}}\). The assumed distributions and second moments of the random variables are presented in Table 6. Based on the beam theory, the vertical displacement and its corresponding limit-state function are defined as:  
\[g(\mathbf{d},\mathbf{x})=\Delta_{0}-\Delta_{\text{tip}}(\mathbf{d},\mathbf{x} )=\Delta_{0}-\frac{3 FL}{2 Et}\cdot\sum_{i=1}^{3}\biggl{(}i^{2}-i+\frac{1}{3} \biggr{)}\frac{1}{d_{i}^{3}} \tag{31}\]  
The RBDO problem of the cantilever beam can be formulated as:  
\[\begin{split}\min_{\mathbf{d},\mu_{\mathbf{x}}}f(\mathbf{d}, \mu_{\mathbf{x}})&=4L\cdot\sum_{i=1}^{3}\left(d_{i}t-t^{2} \right)\\ \text{s.t.}& P[g(\mathbf{d},\mathbf{x})\leq 0]\leq P _{f}^{\text{t}}\\ &\mathbf{d}^{\text{t}}\leq\mathbf{d}\leq\mathbf{d}^{\text{u}} \end{split} \tag{32}\]  
The target failure probability and parameters used in structural analysis and optimization are summarized in Table 7. Figure 8 shows the convergence history of the objective function, design variables, and failure probability obtained using the proposed RBDO/CS with the SORM-i approach. The proposed approach can promptly identify a feasible solution, satisfying the probabilistic constraint within eight iterations, and can continuously find the optimal design by minimizing the objective function until the convergence criteria  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Random Variables** & **Marginal Distribution** & **Mean** & **c.o.v** & **Correlation** \\ \hline \(E\), ksi & Weibull & 29,000 & 0.2 & Independent \\ \(F\), kips & Gamma & 2000 & 0.2 & Independent \\ \(t\), m & Normal & 0.5 & 0.2 & Independent \\ \hline \hline \end{tabular}
\end{table}
Table 6: Description of the random variables for the cantilever beam problem.  
Figure 7: (**a**) Cantilever beam consisting of three segments, (**b**) hollow square cross-section, (**c**) deformation under a vertical force.  
are met. The results of the RBDO/CS using the SORM and SORM-i summarized in Table 8 demonstrate that the two approaches achieve similar results for the cantilever beam problem. Moreover, the optimization result indicates that strengthening the segment close to the fixed support is the most efficient approach to reduce the tip deflection.
## 4 Problem Formulation
### Stable Moment between Two Neighbor UAVs  
From [44], the model of free space attenuation, the strength of the single received \(P_{ij}\) of hello packet in the current UAV \(i\) transmitted from its neighbor UAV \(j\) in a distance \(d\) is:  
\[P_{ij}=P_{t}G_{t}G_{r}\bigg{(}\frac{\lambda}{4\pi d}\bigg{)}^{2} \tag{2}\]  
Here, \(G_{t}\) represents the transmitting antenna, \(G_{r}\) represents the receiving antenna, and \(\lambda\) shows the length of the radio wave, where \(P_{t}\) stands for the transmitting power of hello packet from the neighbor UAV. The covering range of the antenna is a circular region with radius \(R\), as shown in Figure 6. Then, the threshold value of received signal strength from the neighboring UAV is:  
\[\mathbf{P_{threshold}}=\mathbf{P_{t}G_{t}G_{r}}\bigg{(}\frac{\lambda}{4\pi\mathbf{R}} \bigg{)}^{2} \tag{3}\]  
Based on the known information of the current UAV and with hello packet information received from the neighboring UAV, the threshold value can be calculated. Using the real-time signal strength and the threshold value of the received single strength, we have:  
\[X_{ij}(t_{k})=\begin{cases}\quad 0,\ P_{ij}\leq P_{threshold}\\ 1-\frac{P_{threshold}}{P_{ij}},\ P_{ij}\geq P_{threshold}\end{cases} \tag{4}\]  
The Bienayme-Chebyshev inequality [31] is as follows:  
\[P\{|X-E\left(X\right)|<\varepsilon\}\geq 1-\frac{var(X)}{\varepsilon^{2}} \tag{5}\]  
where \(X\) is a discrete variable, \(E(X)\) is the expectation value of \(X\), \(var(X)\) is the variance of \(X\), \(\varepsilon\) is a positive arbitrary number. Here, if \(var(X)\) is equal to 0, then \(P\{|X-E(X)|<\varepsilon\}\) is equal to 1, which means the variable \(X\) is equal to its expected value, which shows that the smaller the variance of \(X\) is, the closer \(X\) will be its expected value. With multiple measurements of \(X\), the variance of \(var(X)\) is:  
\[var(X)=\bigg{(}\sum_{k}\frac{X_{k}^{2}}{n}\bigg{)}-\bigg{(}\sum_{k}\frac{X_{k} }{n}\bigg{)}^{2} \tag{6}\]  
Figure 6: Antenna coverage.  
For obtaining the variation of the received signal strength of packet hello in a live UAV, transmitted from neighbor UAV b, we take the different values of \(X_{ij}\) (\(t_{k}\)) at different moments and substitute these values into Equation (6). We can judge the current UAV \(i\) and UAV \(j\) moment condition. The moment stability between two neighboring UAVs \(NS_{ij}\) is calculated as follows:  
\[var\big{(}X_{ij}\big{)}=\left(\sum_{k}\frac{X_{ij}\left(t_{k}\right)^{2}}{n} \right)-\left(\sum_{k}\frac{X_{ij}\left(t_{k}\right)}{n}\right)^{2} \tag{7}\]  
\[NS_{ij}=1-var\big{(}X_{ij}\big{)} \tag{8}\]  
The higher the value of \(NS_{ij}\), the better the movement stability will be between two neighboring UAVs.
# The Traffic Adaptive Data Dissemination (TrAD) Protocol for both Urban and Highway Scenarios
## 3 Traffic Adaptive Data Dissemination  
The TrAD protocol is based on two main components. The first component adopts the broadcast suppression technique for well-connected networks, and the second one adopts a store-carry-forward mechanism for disconnected networks. Figure 1 presents the two running modes of the TrAD protocol according to the network scenarios: connected or disconnected network.  
Figure 1: Illustration of the TrAD protocol.  
For a better understanding of this protocol, we define several concepts for TrAD. These concepts will be used throughout the paper:  
* _Directional Cluster_\(C_{d}\): The directional cluster is a group of vehicles in the one-hop neighborhood of a sender \(S\). Moreover, these vehicles are travelling in a similar direction with respect to the sender \(S\). In an ideal situation, \(S\) can accurately classify its neighbors into different directional clusters that match the different road topologies around it. For instance, \(S\) classifies its neighbors \(N1,\ N2\) into \(C_{1}\) and \(N3,\ N4\) into \(C_{2}\) as illustrated in Figure 1. The two directional clusters are exactly on the roads in two directions.
* _Coordinator_: This concept was firstly defined in the Greedy Perimeter Coordinator Routing (GPCR) protocol [24]. The _coordinator_ is the vehicle located at an intersection (e.g., the transmitter \(S\) in the Figure 1).
* _Breaker_: In a well-connected network, the _breaker_ is not only the furthest vehicle in the forwarding direction but also moves towards the outside of the vehicular network (e.g., the green vehicle V0 in the Figure 1).
* _SCF-agent_: The role of a SCF-agent vehicle is to be responsible for storing and carrying the data messages until it meets opportunities to forward (broadcast) the stored data messages to uninformed vehicles that come from other VANETs.
* _Beacon and Beaconing_: A beacon is defined as a periodic message that is responsible for exchanging the up-to-date status of nodes in the one-hop neighborhood. This periodic exchanging process is called beaconing. The beacon format is defined as following: \(<\)_Beacon ID_, _Sender ID_, _Global GPS Position_, _Heading_, _Number of Neighbors_, _Channel Busy Ratio_, _Message List_\(>\).  
Figure 2: The operation of TrAD protocol flowchart.  
In this section, the principle of operation for the TrAD protocol is presented as shown in Figure 2. TrAD requires that every vehicle send beacons to exchange their up-to-date status in the one-hop neighborhood. The period of beaconing \(P_{b}\) is set to 1 s and the tolerance of beacon equals to 1.5 \(P_{b}\) for a rapid reaction to the change of neighbors. The beaconing is another critical research field for safety applications, which includes several congestion control mechanisms, such as transmit power control, transmission rate control and encoding [25; 26; 27; 28]. However, the adaptive beaconing is beyond the scope of this paper, we focus on the multi-directional and multi-hop data dissemination protocol. Therefore, we set a fixed beaconing interval for TrAD.
## 2 Sample Environment Components
### Temperature Control  
Precise and reproducible temperature control is an important issue when working with soft matter samples, due to the influence on molecular interactions and the sample structure. Therefore, the sample holder constructed for this instrument is characterized regarding the temperature control capabilities. The sample environment's temperature can be controlled with various fluids, allowing a temperature range from 253.15 K to 393.15 K, depending on the chosen fluid.  
An example of the temperature control characteristics is shown in Figure 2. Here, the set-point temperature, the bath temperature and the temperatures in three different cuvettes filled with water in one magazine (see Figure 1) are plotted against the time. It can be seen that the cuvette temperatures follow the bath temperature rapidly. The cuvette temperatures reach 1 K of their equilibrium temperatures after 1 min and 0.1 K of the equilibrium temperature within 3 min after the bath reached the setpoint temperature even for large temperature steps (50 K). The thermostat takes ca. 30 min to reach the setpoint for cooling 50 K from 333.1 K to 283.1 K. Heating from 283.1 K to 333.1 K takes 23 min. However, smaller temperature steps, from 283.1 K to 288.1 K only take 3 min. These times are dependent on the thermostat used and are only valid for the thermostat (FP50-HL, Julabo, Seelbach, Germany) applied here.  
The sample temperature can be measured using a PT-100 thermometer inside three cuvettes for each magazine. Figure 2 shows that all three cuvette temperatures are nearly identical. This indicates a homogeneous temperature distribution for all samples in one magazine. However, to correct even for these slight deviations, the sample temperature for all other cuvettes can be interpolated from the three measured temperatures in each magazine.
# Performance Analysis of Ambient Backscatter NOMA Systems
## 1 Introduction
In [28], the authors researched the adoption of frequency division multiplexed signals as carriers on AmBC systems, and analyzed the effect of receiving antenna count on system performance. The previous works have caused significant delays to BDs, due to the short time it takes for a BD to transmit information. To reduce system latency and improve system performance gains, collaboration between the AmBC and NOMA technologies was studied in [29; 30; 31]. In [29], the authors derived the OP expressions in the AmBC-assisted NOMA systems, and the asymptotic OP expressions of the system were further obtained. In addition, the authors of [30] analyzed the effective throughput of two downlink NOMA users and a BD. The sum rate of the system maximization algorithm of AmBC-NOMA was surveyed in [31], with the consideration of both the transmitting power and the reflecting coefficients. In [32], the authors investigated the performance analysis of combined NOMA and AmBC, which improved the spectral efficiency and EE of the systems. The authors of [33] studied two transceiver design approaches to achieving different trade-offs in performance gain and complexity for AmBC-NOMA systems. To facilitate efficient sharing of backscattered carrier spectrum resources, the authors in [34] proposed a hierarchical multiple access plan that allowed multiple access between groups, based on the spatial division of beamforming. In [35], the authors introduced the transmission scheme of the AmBC-NOMA system, which enabled simultaneous energy and spectrum cooperation between uplink and downlink users. Additionally, the authors of [36] evaluated the outage of the AmBC systems, by taking into account the in-phase and uneven quadrature phase characteristics.
## 3 Experimental Facilities and Procedures
### Evaluation Methods  
To characterize the erosion crushing performance of the SPWJ on granite, the erosion crushing area, erosion depth, erosion spalling quality, and erosion crushing rate of the rock mass were quantitatively analyzed. As shown in Figure 11a, the erosion area was measured using computer-aided design (CAD) software [44]. Specifically, a ruler or vernier caliper was used to measure rock mass samples, calibrated along the whole bit size of the vernier caliper, as shown in Figure 11. It can be observed from the images that the curve contains dual attributes, namely, the true length \(L_{c}\) of the calibration line and the CAD length \(L_{d}\) of the calibration curve. In addition, the envelope of the erosion and crushing area is drawn, the CAD area of the erosion and crushing area can be read as \(A_{d}\) by the software, and the actual area of the crushing area is expressed as \(A_{c}\). The following relationship exists:  
\[\frac{{L_{c}}^{2}}{{L_{d}}^{2}}=\frac{{A_{c}}}{{A_{d}}} \tag{4}\]  
The actual surface area of the envelope of the broken area is as follows:  
\[A_{c}=A_{d}\frac{{L_{c}}^{2}}{{L_{d}}^{2}} \tag{5}\]  
The depth measurements of the erosion and fracture areas of the rock samples are shown in Figure 11b,c. Due to the irregular distribution and tortuosity of erosion pits at the bottom of the granite after being destroyed by water jet erosion, the conventional vernier caliper measurement method was unable to accurately measure their depth. Therefore, the granite specimen damaged by water jet erosion was scanned using computed tomography (CT) technology. The point source data of the fracture pit was obtained, and the fracture pit depth, \(\Delta\)h was determined by 3D reconstruction using Solidworks. The rock erosion intensity was determined based on the volume loss of the sample evaluation, \(\Delta V\), and the volume measurement method was consistent with the depth measurement method. In addition, the erosion was evaluated by the curve slope of the cumulative volume loss changing with time. The granite erosion per unit input pressure level is used to evaluate the erosion performance of water jets.  
\[\Delta V_{ps}=\frac{\Delta V}{p_{si}} \tag{6}\]  
\[\Delta V_{pc}=\frac{\Delta V}{p_{ci}} \tag{7}\]  
Figure 11: Analysis method of fracture characteristics of granite erosion pit: (**a**) the apparent characteristics of erosion pits; (**b**) CT scan of erosion pits; (**c**) 3D reconstruction of erosion pits.
# Power System Voltage Correction Scheme Based on Adaptive Horizon Model Predictive Control
## 3 Adaptive Horizon Parameters
### Determination of the Horizon Parameters  
Based on the voltage regulation ability evaluation, an applicability judgment index for control horizon parameter settings is proposed:  
\[I_{\rm s(i)m}=\frac{DB}{2}+\frac{V_{\rm r}-\hat{V}^{*}_{(i)}(t_{n}+t_{\rm pn} )}{\left|V_{\rm r}-\hat{V}^{*}_{(i)}(t_{n}+t_{\rm pn})\right|}(V_{\rm a(i)m}- V_{\rm r}) \tag{17}\]  
where \(I_{\rm s(i)m}\) is the applicability judgment index of the \(i\)-th evaluation target when the control horizon is set to \(mt_{\rm s}\). It should be noted that the proposed scheme will not be triggered if \(V_{\rm r}=\hat{V}^{*}_{(i)}(t_{n}+t_{\rm pn})\).  
When the predicted voltage without control is lower than its reference value (\(V_{\rm r}>\hat{V}^{*}_{(i)}(t_{n}+t_{\rm pn})\)), Equation (13) can be written as:  
\[I_{\rm s(i)m}=V_{\rm a(i)m}-(V_{\rm r}-\frac{DB}{2})=V_{\rm a(i)m}-V_{\rm min} \tag{18}\]  
Similarly, when \(V_{\rm r}<\hat{V}^{*}_{(i)}(t_{n}+t_{\rm pn})\), Equation (13) can be written as:  
\[I_{\rm s(i)m}=(V_{\rm r}+\frac{DB}{2})-V_{\rm a(i)m}=V_{\rm max}-V_{\rm a(i)m} \tag{19}\]  
If \(I_{\rm s(i)m}>0\), it indicates that the controller is able to bring the voltage magnitude of bus \(i\) back to its desired range with the current horizon parameter settings. Let \(I_{\rm sm}\) be a vector that consists the applicability judgment index of all the evaluation targets, \(I_{\rm sm}=(I_{\rm s(1)m},I_{\rm s(2)m},\...\...\,I_{\rm s(N)m})\). The initial value of \(m\) is set to 1. If \(\forall I_{\rm s(i)m}\leq 0\) in vector \(I_{\rm sm}\), the proposed algorithm will keep increasing \(m\) until all the elements in \(I_{\rm sm}\) meet \(I_{\rm s(i)m}>0\), then \(mt_{\rm s}\) is determined as the control horizon of the \(n\)-th optimization and the prediction horizon of the \((n+1)\)-th optimization, \(mt_{\rm s}=t_{\rm cm}=t_{\rm p(n+1)}\).  
If it is evaluated that the candidate control variables cannot achieve \(\forall I_{S(l)m}>0\) according to Equations (13)-(16), \(m\) will be reset to 1, and control actions with high cost such as load shedding will be added to the candidate control actions. In this paper, it is assumed that the power system is equipped with adequate reactive power compensation and voltage regulation devices for a voltage correction scenario.  
As is presented in Figure 3, the length of the control horizon and prediction horizon are adaptively adjusted during the receding-horizon optimization process.
## 3 Proposed CNN-Based Power Allocation Method
### CNN Model Architecture and Feature Definition  
The proposed CNN maps input network features to hierarchical power allocation outputs as follows:  
\[[P_{\text{CPU-AP}},P_{\text{AP-UE}}]=f_{\theta}(\mathbf{X}) \tag{11}\]  
where \(\mathbf{X}\in\mathbb{R}^{C\times M\times K}\) is the input tensor, \(\theta\) denotes the CNN parameters, \(P_{\text{CPU-AP}}\in\mathbb{R}^{M}\) is the CPU-to-AP power vector, and \(P_{\text{AP-UE}}\in\mathbb{R}^{M\times K}\) is the AP-to-UE power matrix. The input tensor \(\mathbf{X}\) consists of \(C=4\) feature channels, capturing spatial and contextual characteristics of the wireless environment. Each channel corresponds to a specific feature describing the AP-UE relationship, including the channel gain \(|h_{i,j}|^{2}\), distance \(d_{i,j}\), estimated interference at each link, and initial SINR estimated under uniform power allocation. These four feature maps are stacked into a three-dimensional tensor of size \(4\times M\times K\), enabling the CNN to process spatially correlated patterns across all AP-UE pairs. By feeding this structured input to the network, the model is able to capture both local channel conditions and global interference characteristics, which are essential for making informed power allocation decisions.  
The CNN architecture consists of three convolutional layers, each with 32 filters and a kernel size of \(3\times 3\), followed by ReLU activation and batch normalization. This configuration was selected in order to balance computational efficiency and representation capacity. The \(3\times 3\) kernel size enables the model to capture fine-grained spatial features while maintaining a low parameter count, and 32 filters provides a practical baseline that offers sufficient expressiveness without incurring excessive complexity [20; 21]. Pooling layers are omitted to preserve the spatial resolution of the AP-UE grid, which is critical for fine-grained link-specific power control. The final convolutional output is flattened and passed through two separate fully-connected branches; one branch generates the CPU-to-AP power vector while the other produces the AP-to-UE power matrix, both of which are reshaped to match their target dimensions. This dual-head architecture allows the model to jointly learn global and local power control strategies within a single end-to-end framework. A detailed description of the CNN model architecture and training procedure is provided in Appendix A to support reproducibility (Figure 3).  
For comparison, a separate CNN was also trained using a stage-wise configuration in which the CPU-to-AP power is fixed equally across all APs and only the AP-to-UE allocation is learned. While this approach permits partial adaptability, it fails to account for heterogeneous AP conditions and spatial variations in user demand. In contrast, the proposed integrated CNN learns both allocation layers jointly, enabling globally optimized and context-aware power assignment tailored to dynamic network environments.
## 5 Simulation Results and Analysis
### Deformation and Stress Analysis
#### 5.2.1 Total Deformation  
The THM coupling simulations are carried out for the gas pressure regulator with nine openings to analyze the total deformation at each opening. Figure 5 illustrates the result for the regulator at 50% opening. Figure 5a shows a larger deformation at the sleeve, valve bore, and outlet valve seat wall for the regulator. Figure 6 shows the deformation at the three regulator locations under the nine openings.  
Figure 6 shows that the maximum deformation of the regulator sleeve, valve hole, and outlet seat wall appears at the 20% opening. At the same time, with the increase in the opening, the wall deformation at the valve hole and outlet seat is gradually reduced, and the sleeve deformation has a fluctuating downward trend. The deformation is relatively small at the 10% opening due to the smaller opening's structural stiffness. Compared to other parts, although the largest deformation occurs at the sleeve, valve bore, and outlet valve seat wall, from an overall perspective, the total deformation is still at a low level, and thus, the normal operation of the regulator is less affected.
# Extraction of Periodic Terms in Satellite Clock Bias Based on Fourier Basis Pursuit Bandpass Filter
Section 4 uses simulated data to compare the differences between the FBP spectrum and the WFT and to analyze the feasibility of the FBPBPF in terms of reconstructing the periodic term while comparing its accuracy with the LSM, FIR, and IIR methods. The effectiveness of the proposed method is then verified using precise clock bias data from the BeiDou Navigation Satellite System (BDS) provided by the GNSS Research Center of Wuhan University (WHU). Section 5 concludes the paper.