esa-sceva/satcom-chunk-collection huggingface dataset:
# Prediction of Vibration-Mode-Induced Noise of Structure-Acoustic Coupled Systems
## 2 Induction Characteristics of Acoustic Modes
### Structure-Acoustic Coupling System
 \tag{7}\]  
For the coupling matrix \(\gamma\) in Equation (5), \(g_{s}=g_{a}\) owing to the characteristics of the transposed matrix; however, a different subscript is used to distinguish the mode being applied. By substituting Equation (7) into Equation (6), the motion equation of the two coupled modes can be expressed as follows:  
\[ \begin{split}\ddot{\eta}+2\xi_{s}\omega_{s}\dot{\eta}+\omega_{s} ^{2}\eta+g_{s}q=\Phi_{i}^{T}\mathcal{E}\delta(t)\\ -\rho_{a}g_{a}\ddot{\eta}+\ddot{q}+2\xi_{a}\omega_{a}\dot{q}+ \omega_{a}^{2}q=0\end{split}  \tag{8}\]  
By applying the Laplace transformation to Equation (8), the vibration (acceleration) and acoustic modes can be expressed as follows:  
\[ \begin{split}\ddot{\eta}(s)&=\frac{s^{2}F_{a}(s)}{ F_{s}(s)F_{a}(s)+\rho_{a}g_{s}g_{a}s^{2}}X(s)\\ q(s)&=\frac{\rho_{a}g_{a}s^{2}}{F_{s}(s)F_{a}(s)+ \rho_{a}g_{s}g_{a}s^{2}}X(s)\end{split}  \tag{9}\]  
where  
\[ \begin{split} F_{s}(s)&=s^{2}+2\xi_{s}\omega_{s}s+ \omega_{s}^{2}\\ F_{s}(s)&=s^{2}+2\xi_{a}\omega_{a}s+\omega_{a}^{2} \end{split} \]  
Note that \(s\), which is not a subscript, denotes the Laplace variable, and _X(s)_ represents the Laplace transformation of the modal impact load (\(\Phi_{i}^{T}\mathcal{E}\delta(t)\)). Equation (9) shows the transfer function from the impact load to the vibration (acceleration) and acoustic mode (sound pressure). According to the equations, the vibration-acoustic coupling effect is influenced by the \(g_{s}\) and \(g_{a}\) values in the denominator. In the denominator in Equation (9), the two modes are combined owing to the coupling effect, and these modes can be decomposed into two single degree-of-freedom modes. Specifically, the denominator in Equation (9) can be decomposed into two independent forms:  
\[F_{s}(s)F_{a}(s)+\rho_{a}g_{s}g_{a}s^{2}=(s^{2}+2\xi_{1}\omega_{1}s+\omega_{1}^{2 })(s^{2}+2\xi_{2}\omega_{2}s+\omega_{2}^{2}) \tag{10}\]  
In this case, the original vibration and acoustic modes have two natural frequencies (\(\omega_{1},\omega_{2}\)) and damping ratios (\(\xi_{1},\xi_{2}\)), which are altered by the coupling effect. If \(g_{s}\) and \(g_{a}\) are large, the natural frequencies and damping ratios of the original vibration and acoustic modes will differ from the new frequencies and damping ratios owing to the coupling effect.
## 2 Dynamic Contact Model of SNBSP
### Calculation of the Frictional Force of SNBSP and Other Related Parameters
#### 2.3.3 Calculation of the Contact Pairs Slip Angle  
The slip angle of the contact pairs reflects the direction of the slip velocity at the contact point in the \(\text{CSO}^{\prime\prime}_{\varsigma}x^{\prime\prime}_{\varsigma}y^{\prime}_{ \varsigma}z^{\prime\prime}_{\varsigma}\), as shown in Figure 7; it can be expressed as [4]:  
\[\psi_{\varsigma}=\tan^{-1}\!\left(\frac{V_{y^{\prime\prime}}z}{V_{x^{\prime \prime}\varsigma}}\right)+\pi \tag{39}\]  
where \(V_{x^{\prime\prime}\varsigma}\) and \(V_{y^{\prime\prime}\varsigma}\) denote the component of the relative slip speed between the contact pair in the direction of the \(x^{\prime\prime}_{\varsigma}\) axis and \(y^{\prime\prime}_{\varsigma}\) axis, respectively. The relationship between the two parameters is as follows [5]:Relative slip velocity component of the ball screw contact pair:  
\[\frac{V_{y^{\prime\prime}}\mathrm{S}}{V_{x^{\prime\prime}}\mathrm{S}}=\frac{d( \omega_{m}-\omega)-r_{\mathrm{B}}[(\omega_{b}-\omega\cos\lambda)\cos\alpha_{ \mathrm{S}}-\omega_{n}\sin\alpha_{\mathrm{S}}]}{r_{\mathrm{B}}(\omega_{t}- \omega\sin\lambda)}\] (40a) Relative slip velocity component of the ball nut contact pair: \[\frac{V_{y^{\prime\prime}}\mathrm{N}}{V_{x^{\prime\prime}}\mathrm{N}}=\frac{d \omega_{m}+r_{\mathrm{B}}(\omega_{b}\cos\alpha_{\mathrm{N}}-\omega_{n}\sin \alpha_{\mathrm{N}})}{-r_{\mathrm{B}}\omega_{t}}\] (40b) where \[\omega_{t},\omega_{\mathrm{n}}\] and \[\omega_{b}\] denote the component of the angular velocity of the ball rolling in the direction of the t-, n- and b- axis in \[CSO^{\prime}\tau nb\], respectively. The calculation process of \[\omega_{t},\omega_{\mathrm{n}},\omega_{b}\] and \[\omega_{m}\] can be obtained in reference [7], so there is no repeat on it. The direction of each velocity is shown in Figure 2.
## 4 Analytical Prediction of Short- and Long-Term Strengths under Conventional Triaxial Compression
### Short-Term Strength  
As a popular loading path, the conventional triaxial compression loading path is conducted here. The plastic strain can be measured from the accumulated multiplier because the flow direction is unchanged in the whole loading process. In this case, the following analytical form is given of the flow direction \(\mathbf{D}\):  
\[\mathbf{D}=-\frac{1}{\sqrt{6}}\text{diag}(2,-1,-1)+\frac{1}{3}\eta\text{diag}(1,1,1) \tag{18}\]  
Then the accumulated multiplier can be expressed as the following form:  
\[\varLambda^{p}=\int\lambda^{p} \tag{19}\]  
from which the plastic strain can be rewritten as:  
\[\mathbf{\epsilon}^{p}=\varLambda^{p}\mathbf{D} \tag{20}\]  
Following the well-established equations, the yield criterion and damage evolution can be reformulated in coincidence with the conventional triaxial compression loading path:  
\[\left\{\begin{array}{l}f=\|\mathbf{s}\|+\eta\sigma-\frac{\varLambda^{p}}{d} \varchi=0\\ f_{d}=\frac{1}{2}\Big{(}\frac{\varLambda^{p}}{d}\Big{)}^{2}\chi-R_{d}=0\end{array}\right. \tag{21}\]  
with \(\chi=\frac{\kappa^{n}\eta^{2}}{\kappa_{1}}+\frac{2\eta^{n}}{\kappa_{2}}\). By combining these two criteria, we derive the following strength criterion in function of the stresses and damage.  
\[f=\|\mathbf{s}\|+\eta\sigma-\sqrt{2R_{d}\varchi}=0 \tag{22}\]  
When the loading path of conventional triaxial compression is concerned in particular, the maximum principal stress \(\sigma_{1}\) can be expressed in the terms of the confining pressure \(\sigma_{3}\) and internal damage variable \(d\).  
\[\sigma_{1}=\frac{\sqrt{6}+2\eta}{\sqrt{6}-\eta}\sigma_{3}+\frac{3\sqrt{2R_{d} \varchi}}{\sqrt{6}-\eta} \tag{23}\]  
In addition, by combining Equation (5) with Equation (20), the macroscopic strain can be expressed in terms of the macro stress \(\mathbf{\sigma}\) and the accumulated plastic multiplier \(\varLambda^{p}\).  
\[\mathbf{\epsilon}=\mathbb{S}^{m}:\mathbf{\sigma}+\varLambda^{p}\mathbf{D} \tag{24}\]  
where \(\mathbb{S}^{m}=(\mathbb{C}^{m})^{-1}\) is the compliance tensor of the solid matrix phase. With the relation \(\varLambda^{p}=d\sqrt{\frac{2R_{d}}{\varchi}}\), the following analytical solution of the short-term strength can be derived [39]:  
\[\begin{array}{l}\varepsilon_{1}=\frac{1}{\mathbf{\varepsilon}^{m}}\sigma_{1}- \frac{2\
u^{m}}{\mathbf{\varepsilon}^{m}}\sigma_{3}-\Big{(}\frac{2}{\sqrt{6}}- \frac{\eta}{3}\Big{)}d\sqrt{\frac{2R_{d}}{\varchi}}\\ \varepsilon_{2}=\varepsilon_{3}=\frac{1-\
u^{m}}{\mathbf{\varepsilon}^{m}}\sigma_{ 3}-\frac{\
u^{m}}{\mathbf{\varepsilon}^{m}}\sigma_{1}+\Big{(}\frac{\eta}{\sqrt{6} }+\frac{\eta}{3}\Big{)}d\sqrt{\frac{2R_{d}}{\varchi}}\end{array} \tag{25}\]
# A Study of Multi-Step Sparse Vessel Trajectory Restoration Based on Feature Correlation
## 3 Trajectory Data Sparsity and Anomaly Detection
### Sparse and Abnormal Trajectory Points Detection
#### 3.2.3 Detection Method Based on Location Elements  
The original AIS data often contain drift and error points, which in turn lead to abnormal vessel trajectories. To obtain accurate vessel trajectories, it is necessary to screen and repair abnormal position trajectory points. According to Equation (2), to determine whether the trajectory points are located in the study area if the trajectory points are beyond the study area, they are regarded as abnormal data and excluded. Then, according to the maximum SOC, to calculate the maximum sailing theoretical distance between neighboring trajectory points and compare with the actual distance, if the actual distance is greater than  
Figure 3: Map of SOC distribution.  
Figure 2: Map of time intervals of AIS trajectory data.  
the theoretical distance, the point is judged as abnormal and marked trajectory restoration points, and vice versa for normal points, which is calculated as in Equation (3).  
\[\begin{cases}-84.0\leq\text{lon}_{i}\leq-79.5\\ 23.0\leq\text{lat}_{i}\leq 24.5\end{cases} \tag{2}\]  
\[\begin{cases}D_{\text{act}}=2\text{arcsin}\sqrt{\sin^{2}\Bigl{(}\frac{\text{ lat}_{i}-\text{lat}_{i+1}}{2}\Bigr{)}+\cos(\text{lat}_{i})\cos(\text{lat}_{i+1}) \sin^{2}\Bigl{(}\frac{\text{lon}_{i}-\text{lon}_{i+1}}{2}\Bigr{)}}\\ D_{\text{theory}}=V_{\text{max}}\times|t_{i}-t_{i+1}|\\ V_{\text{max}}=1.852\times\text{SOG}_{\text{max}}\end{cases} \tag{3}\]  
where \(D_{\text{act}}\) is the actual distance, \(D_{\text{theory}}\) is the maximum sailing theoretical distance, \(r\) is the radius of the Earth, \(V_{\text{max}}\) is the maximum velocity, \(\text{SOG}_{\text{max}}\) is the SOG threshold, and \(t\) is the trajectory point timestamp.  
Based on the above three types of detection methods, sparse and anomaly detection is carried out on the trajectory data and the number and location of trajectory restoration points are accurately identified and marked, which provides the necessary support for the next step of preliminary trajectory restoration work.
# Research on O2O Takeout Delivery Route Optimization Problem Based on Improved Genetic Algorithm
## 5 Experimental Results and Analysis
### Design and Analysis of Experiments
#### 5.3.5 Comparative Experiment on the Number of Riders  
With the lower bound of average customer satisfaction fixed at 80% and the weights of platform costs (\(\omega_{1}\)) and average rider earnings (\(\omega_{2}\)) each set to 0.5, comparative experiments were conducted with the number of riders set to 6, 8, 10, and 12, respectively. The experimental results are shown in Table 4. From the results, it can be observed that, as the number of riders increases, the platform cost, average rider earnings, and average customer satisfaction all increase. Specifically, the platform costs increase by 13.40%, 10.78%, and 12.30%, respectively; the average rider earnings increase by 5.35%, 6.47%, and 0.46%, respectively; the average customer satisfaction increases by 4.76%, 5.68%, and 2.15%, respectively. When the number of riders increases from 10 to 12, the average rider earnings and average customer satisfaction increase less while the platform costs increase significantly. Therefore, for decision-makers, the configuration with 10 riders in this case better achieves a balance between platform costs, average rider earnings, and average customer satisfaction.
# GPU Adding-Doubling Algorithm for Analysis of Optical Spectral Images
## 2 Materials and Methods
### Preliminaries of Adding Doubling (AD) Algorithm
#### 2.1.3 Calculating Scattering Phase Function  
Two matrices are constructed, one for forward scattering, denoted as \(\mathbf{P^{+}}\), and one for backward scattering, denoted as \(\mathbf{P^{-}}\). The elements of scattering matrix \(P_{ij}\) determine the fraction of light scattered from an incident cone with angle \(v_{i}\) into a cone with angle \(v_{j}\) and are calculated by averaging the phase function \(p(v_{i},v_{j})\) over all possible azimuthal angles for fixed angles \(\
u_{i}\) and \(\
u_{j}\):  
\[P_{i,j}=\frac{1}{2\pi}\int_{0}^{2\pi}p\left(v_{i}v_{j}+\sqrt{1-{v_{i}}^{2}} \sqrt{1-{v_{j}}^{2}}\cos(\phi)\right)\,\mathrm{d}\phi \tag{11}\]  
The choice between obtaining the forward scattering matrix \(\mathbf{P^{+}}\) or the backward scattering matrix \(\mathbf{P^{-}}\) depends on the signs of angles \(\
u_{i}\) and \(v_{j}\). If both angles are either positive or negative, the forward scattering matrix \(\mathbf{P^{+}}\Matrices \(\mathbf{P^{+}}\) and \(\mathbf{P^{-}}\) can be calculated analytically if we utilize the Hanyey-Greenstein scattering phase function (SPF), which is defined as:  
\[p(\
u,g)=\frac{1}{2}\frac{1-g^{2}}{\left(1+g^{2}+2g\
u\right)^{\frac{3}{2}}} \tag{13}\]  
where \(-1<g<1\) is known as the asymmetry factor. The scattering matrix can be calculated from the following expression:  
\[\begin{split} p(\
u,g)=\frac{1-g^{2}}{\pi w_{-}\sqrt{w_{+}}}E_{0 }\left(\frac{4 gB}{w_{+}}\right)\\ w_{\pm}=1+g^{2}-2g(A\pm B)\end{split} \tag{14}\]  
where \(A=v_{i}\ v_{j}\) and \(B=\sqrt{1-{v_{i}}^{2}}\sqrt{1-{v_{j}}^{2}}\). and \(E_{0}\ (x)\) denotes an elliptic integral of the second kind.  
Alternatively, matrices \(\mathbf{P^{+}}\) and \(\mathbf{P^{-}}\) can be calculated through numerical integration:  
\[{P_{i,j}}^{\pm}=\frac{1}{2\pi}\int_{0}^{2\pi}p(A+B\ \cos(z))\,\mathrm{d}z \tag{15}\]  
with \(A\) and \(B\) as defined above. In this case, we employ the Gegenbauer scattering phase function (SPF), given by:  
\[p(\
u,g,\alpha)=2\alpha g\,\frac{\left(1-g^{2}\right)^{2\alpha}}{\left(1+g \right)^{2\alpha}-\left(1-g\right)^{2\alpha}}\frac{1}{\left(1+g^{2}-2g\
u \right)^{1+\alpha}} \tag{16}\]  
It has been demonstrated by [PERSON] [20] that when using the trapezoidal rule for numerical integration, an exponential convergence to the accurate scattering matrix elements can be achieved.
## 3 SDMob Architecture
### Enhanced SDMob
#### 3.2.3 New Route Projection Packet Format  
The packet format of the controller has some impact on the handoff process, mainly through notifying the previous parents. It is important to stop the previous parent from serving the MN immediately after switching to a new parent otherwise two parents will forward the data packets. This may be useful if the number of redundant parents does not increase in a way that too many replicas of the same packet congest the network. In some of the related works, uninstalling root-initiated routes is performed using timers, meaning that the routes are active for a specific time set by the controller. In our previous work, the controller sent the IP address of the MN's preferred parent to all potential parents. Taking these two approaches limits the flexibility in network management, but with low additional overhead due to the SET/UNSET commands in the current work, parents are managed independently.  
In Figure 3, a timeline demonstration of the SDMob's handoff process is illustrated. The handoff process is carried out in 4 steps, as described below:  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Feature** & **Basic SDMob** & **Enhanced SDMob** \\ \hline Control Window & ✓ & ✓ \\ RPL Aware Leaf & ✓ & ✓ \\ Downward routing & ✓ & ✓ \\ Integration with OF & ✓ & ✓ \\ Multi-instance filter & \(\times\) & ✓ \\ Multiple buffers & \(\times\) & ✓ \\ Buffer Timer & \(\times\) & ✓ \\ Congestion Timer & \(\times\) & ✓ \\ SET/UNSET commands & \(\times\) & ✓ \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparing main features of basic SDMob and enhanced SDMob.  
* Step 1: MN embeds its velocity in a control beacon and broadcasts it (during the Control Window).
* Step 2: All SNs in the vicinity of MN receive the beacons, append the measured RSSI values and transmit the beacon to the border router. Contention for the wireless channel towards the root node may overwhelm the network. To deal with this problem, we define a random congestion timer that randomly delays forwarding the RSSI values between 5 to 20 milliseconds. The SNs only relay the control beacon after the congestion timer expires.
* Step 3: Another challenge is deciding the amount of time that the border router waits for the RSSI values. We define a second timer called the buffer timer in a deterministic manner that specifies how long the border router waits for control packets. This timer can be tuned based on the distance from the mobile node to the controller and is set to 500 milliseconds by default. Once the buffer timer expires, the border router sends the accumulated buffer over the serial line to the controller for processing, and meanwhile, it assigns each RSSI measurement to its associated buffer.
* Step 4: Controller executes the particle filter, and selects the new best parent. Next, the new and old best parent get notified by a downstream packet containing a SET and UNSET command respectively. The new parent will continue serving the MN's data packets (during the data window) until it receives an UNSET command.
# Robust Fuzzy Adaptive Sliding Mode Stabilization for Fractional-Order Chaos
## 2 Preliminaries
### Implementation of Fractional Operator  
Generally, industrial control processes are sampled, so a numerical approximation of the applied fractional operator is indispensable. There exists several approximation approaches; some are temporal, while others are in frequency domain. In the literature, one of the current used approaches in frequency domain is the one of [PERSON] (2007, 2010). In temporal domain, there is a lot of work about the numerical solution of the fractional differentials equations. [PERSON] has proposed an efficient method based on the predictor-corrector Adams Algorithm ([PERSON], 2009). Definitions cited above also have numerical approximations:  
Grunwald-Leitnikov (G-L) Approximation  
For numerical computation of fractional order integrals and derivatives, we may use the Grunwald-Letnikov (G-L) definitions and Equations (5) and (6), respectively. Thus, for a causal function \(f(t)\), and for \(t=kh\) where \(h\) is a fixed sampling time period, the fractional order derivative is given as follows ([PERSON], 2009):  
\[D^{\mu}f(kh)=\frac{d^{\mu}}{dt^{\mu}}f(t)\cong h^{-\mu}\sum_{j=0}^{k}\omega_{j} ^{(\mu)}f(kh-jh) \tag{9}\]where the coefficients \(\omega_{j}^{(\mu)}\) are computed by using the following recursive formula:  
For \(j=1,2,...,k\):  
\[\omega_{0}^{(\mu)}=1\]  
and  
\[\omega_{j}^{(\mu)}=\left(1-\frac{1+\mu}{j}\right)\omega_{j-1}^{(\mu)} \tag{10}\]
# Gibbs Sampling Detection for Large MIMO and MTC Uplinks with Adaptive Modulation
## 7 Assessment of the Proposed GS for Large MIMO and AM-MIMO
The simulations are for \(n=32\), with a 16-QAM constellation (the system analysed in Figure 9, now with \(R=10\)). Finally, a comparative study is conducted between ML detection (using SD) and the T-MGS method for AM-MIMO systems employing \(M=4\) terminals and \(N=4\) antennas at the BS. The number of iterations \(t_{\text{max}}\) was set to 600, whereas the number of restarts was only \(R=5\). The BER performance for four distinct sets of constellations is shown in Figure 12. It should be noted that, given the low-complexity and power limitations of MTC devices, these terminals are expected to transmit using low-order modulation in the uplink. Millimeter-waves (mmWaves) systems are on the rise, but those also tend to use low-order modulation due to both the high attenuation channels (that would imply larger transmit powers to keep the SNR) and the challenges posed to the analogue-to-digital converters (ADCs) when using wideband signaling. For these reasons, constellations larger than 16-QAM are uncommon in 5G mmWave systems [35]. Even so, the AM-MIMO system considered users with 4-QAM, 64-QAM, and 256-QAM. Once again, it can be verified the quasi-optimal performance of our algorithm, proving itself as a viable alternative over SD-based AM-MIMO detectors. Figure 11: BER performance as a function of the SNR for the proposed triple mixed Gibbs sampling (T-MGS) algorithm with multiple restarts for \(N_{R}=N_{T}=32\) and a 16-QAM constellation. The simulated performance of the LRA benchmark is also plotted.
# Policy-Based Composition and Embedding of Extended Virtual Networks and SFCs for IIoT
## 5 Results
### Evaluation of the Chain Embedding Using a Random Topology
#### Acceptance Ratio with Increasing FG Length  
In this scenario, we evaluate how the acceptance ratio changes when the number of nodes in the FG increases. The SN size is fixed to 100 nodes and 100 EVNs are to be embedded. The FG length varies in the range 1-12. The resources and demands are highly relaxed, such that rejection is not because of resources, but due to the VNF mapping strategy. The results are shown in Figure 11 and they show that the acceptance ratio of the LightChain solution highly decreases with increasing FG length and fixed SN size. These rejections are met when the paths are shorter than the FG. Our chain embedding algorithm keeps a 100% acceptance ratio since it is adaptive to FG length.  
Figure 11: Acceptance ratio for increased FG size.  
Figure 10: Runtime for increased number of EVNs.  
Average Path Utilization with Increasing FG length  
With the same experiment parameters, Figure 12 shows the average path utilization with increasing FG length. The value for the LightChain approach is constantly zero, since the embedding strategy does not allow to place multiple VNFs of a FG on the same SNo. This is different from our proactive approach, where the utilization of SNos increases for longer chains.  
Acceptance Ratio for Increasing CPU Capacity  
Comparing the acceptance ratio for scenarios where resources are limited is also important. Therefore, in this scenario, we measure the acceptance ratio with increasing CPU resources, while the bandwidth is highly relaxed. The SN includes 100 SNos and the number of EVNs is 100. Based on the results in Figure 11, when each FG has five nodes, both of the algorithms can reach high acceptance ratio when the resources are highly relaxed. The CPU demand of each VNF is fixed to one. As depicted in Figure 13, the acceptance ratio for the proactive chain embedding approach is rapidly increasing and it reaches 100% acceptance for 15 CPU capacity. For the LightChain approach, the acceptance ratio is also increasing, but at a lower rate. The results clearly depict that occupying multiple SNos on a path results in a much higher acceptance ratio.