esa-sceva/satcom-chunk-collection huggingface dataset:
# Deadline-Aware Scheduling for Transmitted RSU Packets in Cooperative Vehicle-Infrastructure Systems
## 4 Lyapunov Optimization Model  
Lyapunov optimization refers to the optimal control of a dynamic system using the Lyapunov function. The Lyapunov function is widely used in control theory to ensure system stability. Multidimensional vectors usually describe a system's state at specific times. The Lyapunov function is a non-negative scalar measure of this multidimensional state. According to Lyapunov optimization technology, network stability is achieved by initiating the control action that causes Lyapunov drift from negative to zero. Moreover, the weighted (positive) network utility term is subtracted from the Lyapunov drift and minimizes the sum. As a result, the drift plus penalty algorithm for joint network stability and utility maximization is produced. It is necessary to transform the optimization model and reduce computational complexity because of the large state space of the problem and the high complexity of online optimization. We set the vector matrix \(G(t)=\left[Q_{n}^{H}(t)\,,\,Q_{n}^{L}(t)\right]\). The Lyapunov function is defined by this matrix:  
\[L(G(t))=\frac{1}{2}\sum\limits_{n=1}^{N}\left[Q_{n}^{H}(t)^{2}+Q_{n}^{L}(t)^{ 2}\right] \tag{28}\]  
According to Formula (28), the data queue length is positively correlated with the value of \(L(G(t))\). Data queue dynamics can be described using the Lyapunov function for differences between adjacent time slots, that is, the Lyapunov drift \(\Delta(G(t))\), which is expressed as follows:  
\[\Delta(G(t))=E\{L(G(t+1))-L(G(t))|G(t)\} \tag{29}\]  
System optimization aims to keep the RSU's data queue length low while minimizing end-to-end average delays. Therefore, the end-to-end average delay becomes the drift component in Formula (29), which can be rewritten as  
\[\Delta(G(t))+VE\{\Gamma(t)|G(t)\} \tag{30}\]  
\(V\) is the tradeoff parameter between data queue length and end-to-end average delays. If the \(V\) value increases, the weight of the end-to-end average delay in the Lyapunov drift parameter increases. In turn, the drift effect on the system increases. It makes the system focus on reducing the end-to-end average delay, but the length of the data queue increases accordingly. Therefore, the system can be optimized by adjusting the value of \(V\). System optimization is possible by minimizing the upper bound of the Lyapunov drift. According to the theorem, \(\{\max[(a-b+c),0]\}^{2}\leq(a-b+c)^{2}\) is true for \(\forall a,b,c>0\); therefore, the following inequality is derived from Formula (13). \[\frac{1}{2}Q_{n}^{H}(t+1)^{2}\leq\frac{1}{2}Q_{n}^{H}(t)^{2}+\frac{1}{2}\left( h_{n}^{H}(t)-B_{n}^{H}(t)\right)^{2}+Q_{n}^{H}(t)\Big{(}h_{n}^{H}(t)-B_{n}^{H}(t) \Big{)} \tag{31}\]  
It can be obtained in the same way:  
\[\frac{1}{2}Q_{n}^{L}(t+1)^{2}\leq\frac{1}{2}Q_{n}^{L}(t)^{2}+\frac{1}{2}\Big{(} h_{n}^{L}(t)-B_{n}^{L}(t)\Big{)}^{2}+Q_{n}^{L}(t)\Big{(}h_{n}^{L}(t)-B_{n}^{L}(t) \Big{)} \tag{32}\]  
According to Formula (28), the following relational expression can be derived:  
\[
## 3 Database of Water Content and Hyperspectral Information  
### Data Acquisition Method  
The goal of this study is to convert hyperspectral information, acquired at road construction sites where compaction processes are performed, into water content. To achieve this, actual water content and hyperspectral information at the same location are required, and a database for this must be secured. With a large amount of data, unnecessary data can be deleted and the accuracy of the predicted equation of water content using hyperspectral information can be improved. The data acquisition process was carried out as shown in Figure 2. At this time, 100 pieces of actual water content and hyperspectral information were acquired per drone flight. Drone flights were conducted a total of 10 times at intervals of 2 to 3 days, considering the influence of weather, among other things.
###### Abstract  
Power grid infrastructures, essential to modern societies for electricity distribution, are prone to vulnerabilities due to their numerous sensitive components, necessitating a comprehensive risk assessment. Uncertainty in historical failure data often compromises accurate risk quantification, leading to the integration of expert elicitation as a solution. This study develops a Bayesian network (BN) risk assessment model integrated with fuzzy set theory (FST), referred to as the fuzzy Bayesian network (FBN). By incorporating expert insights, this model quantifies internal and external risk variables more comprehensively. Crisp probabilities (CPr), derived from regional transmission operator (RTO) failure incident data, are complemented by fuzzy probabilities (FPr) from expert elicitation. The findings indicate that equipment conditions, specifically transmission lines and circuit breakers, are critical threats to power grids. Environmental factors, particularly storms, emerge as vulnerability risks. A comparison of results using both CPr plus FPr versus FPr alone underscores the utility of expert elicitation in risk assessment. This research demonstrates the effectiveness of FBNs through expert elicitation, providing a comprehensive and accurate framework for power grid risk assessment. To improve risk evaluation in critical infrastructure, integrated data collection techniques are recommended.  
Keywords:external and internal risk factors; fuzzy set theory; environmental factors; equipment conditions; critical infrastructure; crisp probabilities; fuzzy probabilities +
Footnote †: journal: _Algorithms_
# Dynamic Reconfiguration of Active Distribution Network Based on Improved Equilibrium Optimizer
## 4 Optimization Algorithms
### Feasible Solution Determination
#### 4.2.1 Network Coding Based on Basic Ring Matrix  
Power networks typically use two distinct types of switching structures: sectionalizing switches (S.S.s) and tie switches (T.S.s). During the reconfiguration process, T.S.s are normally open, while S.S.s are normally closed. Following the reconfiguration, certain switches may change their positions based on the optimization results.  
Distribution network design considers the loop formed by each T.S. and several S.S.s as the basic ring. For instance, in the IEEE 33-bus distribution network, five interconnection switches correspond to five basic loops. In this study, the basic loop matrix is defined as \(\mathbf{H}\), based on the decimal encoding of all branches within the distribution network loop.  
\[\mathbf{H}=(H_{\rm{Ik}})_{L\times K} \tag{25}\]  
where \(L\) is the number of basic loops, which is the same as the number of contact switches, \(K\) is the maximum value of the number of branches contained in all basic loops, and the rows with the number of segmented switches less than \(K\) are completed with zeros. In this paper, we utilize the natural number encoding to represent the branch \(H_{\rm{Ik}}\); \(H_{\rm{Ik}}\) is a non-zero integer, which represents the number of the branch where the kth switch of the 1 th basic ring is located; the matrix \(H_{0}\) represents the initial network topology before reconfiguration.  
Taking the IEEE 33-bus distribution network as an example, its basic ring matrix \(\mathbf{H}\) is presented in Equation (26), and the correspondence between its basic rings and branches is displayed in Table 1. The topology of the IEEE 33-bus distribution system [14] is shown in Figure 2.  
\[\mathbf{H}=\begin{pmatrix}2&3&4&5&6&7&20&19&18&0&0&0&0&0&0&0&0&0&0\\ 9&10&11&12&13&14&0&0&0&0&0&0&0&0&0&0&0&0&0\\ 2&3&4&5&6&7&8&9&10&11&21&20&19&18&0&0&0&0&0&0\\ 6&7&8&9&10&11&12&13&14&15&16&17&32&31&30&29&28&27&26&25\\ 3&4&5&25&26&27&28&24&23&22&0&0&0&0&0&0&0&0&0&0\end{pmatrix} \tag{26}\]  
\begin{table}
\begin{tabular}{c c c} \hline
**Basic Ring** & **Branches** & **T.S. Number** \\ \hline
1 & s2, s3, s4, s5, s6, s7, s20, s19, s18 & s33 & 1\textasci{}10 \\
2 & s9, s10, s11, s12, s13, s14 & s34 & 1\textasci{}7 \\
3 & s2, s3, s4, s5, s6, s7, s8, s9, s10, s11, s21, s20, s19, s18 & s35 & 1\textasci{}15 \\
4 & s6, s7, s8, s9, s10, s11, s12, s13, s14, s15, s16, s17, s32, s31, s30, s29, s28, s27, s26, s25 & s36 & 1\textasci{}21 \\
5 & s3, s4, s5, s25, s26, s27, s28, s24, s23, s22 & s37 & 1\textasci{}11 \\ \hline \end{tabular}
\end{table}
Table 1: The correspondence between basic loops and switches.  
Figure 2: The topology of the IEEE 33-bus distribution system.
## 3 Case Study
### Equivalent Dynamic Model of the Mast  
In general, a ship must structure is often susceptible to vibrations due to its significant slenderness. This study models the ship mast structure, depicted in Figure 2, as a cantilever beam, following the same procedure as in [PERSON] et al. (2020):  
The material of the mast and deck house is steel, assuming elastic behavior (Table 2).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Description** & **Value** \\ \hline Scantling length, \(L\) & 28 m \\ Breadth, \(B\) & 8.5 m \\ Depth to the main deck, \(D\) & 4.5 m \\ Scantling draught, \(T\) & 3.75 m \\ Service speed, \(V\) & 12 knots \\ \hline \hline \end{tabular}
\end{table}
Table 1: Main particulars of the tugboat.  
Figure 1: General arrangement. (**a**) Profile view, (**b**) front view.  
Figure 2: Mast on bridge top structural drawing. (**a**) 3D view, (**b**) equivalent dynamic model.  
The mass has a constant tubular section with an outer radius of 200 mm and a thickness of 10 mm, a height of 10.55 m, and a total weight of one ton. The location of the center of gravity is assumed in the midpoint of the mast.
## 4 The Experiment and Discussion
### The Noise Resistance Analysis  
Noise resistance refers to the anti-interference ability of image processing methods in different interference environments, and whether excellent processing methods can still show superior effects under interference environments is related to the robustness evaluation results of the system. In order to verify the anti-noise performance of the proposed method, Gaussian noise distribution \(\gamma\) in the range of 10-50 is added to the  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Extraction Methods** & \begin{tabular}{c} **The Grayscale Centers** \\ **of Gravity Method** \\ \end{tabular} & \
\begin{tabular}{c} **The Curve** \\ **Fitting Method** \\ \end{tabular} &
\begin{tabular}{c} **The Proposed Method** \\ **in This Paper** \\ \end{tabular} \\ \hline Standard errors & 0.0273 & 0.0175 & **0.0051** \\ \hline \hline \end{tabular}
\end{table}
Table 4: The standard deviations of different centerline extraction methods.  
Figure 15: The centerline extraction deviation chart.  
original image to simulate the interference scene, and the image containing Gaussian noise is carried out in the above experiment. The results of adding different \(\gamma\) are shown in Figure 16.  
The grayscale center of gravity method compares the actual effect of the image containing Gaussian noise, the curve fitting method, and the method proposed in this paper. Figure 17 is the partial enlargement of the laser center line extracted by the above method, where \(\gamma\) was 50.  
It can be seen that lines extracted by the grayscale center of gravity method fluctuated more, while those extracted by the curve fitting method and the method proposed in this work were less affected. The reason for this result is that the Gaussian noise changes the gray value near the laser line, and the grayscale center of gravity method is most affected by the gray value, so the fluctuation is more obvious. In order to quantify the evaluation indicators, the standard deviation mentioned above was used for comparison; the extraction results are shown in Figure 18.  
Figure 16: The laser lines under different noise.  
Figure 17: The partial enlargements of three methods (\(\gamma\) = 50).  
According to Figure 18, the improved grayscale center of gravity method has higher noise resistance and lower sensitivity to the image gray value noise compared with the traditional grayscale center of gravity method. At the same time, the accuracy is higher than that of the curve fitting method, because the curve of the curve fitting method is too smooth to show the characteristics reflected by the gray value. To sum up, the method proposed in this paper not only reflects the characteristics of gray changes but also has relatively smooth curves with higher accuracy and noise resistance. Therefore, the method proposed in this paper has strong robustness, good noise resistance, and higher precision.
# Solution of Orifice Hollow Cathode Plasma Model Equations by Means of Particle Swarm Optimization
## 3 Particle Swarm Optimization Methodology
### PSO-Code Based Solver  
It has been assessed that the developed PSO-code base solver can be used both to support the preliminary design of new hollow cathodes and for the rebuilding of plasma properties if the electrical characteristics are known.  
To design a new cathode, primarily the cathode geometry (i.e., insert, orifice and keeper diameters, orifice and keeper-orificeengths), the propellant mass flow rate, the insert material and the current value have to be set. Secondly, a reasonable exploration domain must be defined. Then PSO code can be run. It will give the evaluation of all the unknowns within a confidence bounds.  
It has been verified (this becomes clear in the application example of Section 4) that the trend of the emitter wall temperature as a function of mass flow rate can be better reproduced if a target total discharge voltage \(V_{target}\) is defined, which is calculated as the ratio of the absorbed power to the discharge current \(I_{d}\).  
Thus, it is necessary to modify the formulation of the cost function \(J\) since it has to consider a new parameter, i.e., \(V_{tot}\), as in Equation (36). In fact, in this case, the optimization process has to minimize also the difference between the total voltage \(V_{tot}\) and the target value \(V_{target}\).  
\[J_{z}^{q}=\|\epsilon_{I}\|+\|\epsilon_{Pow,\epsilon}\|+\|\epsilon_{ign,\epsilon }\|+\|\epsilon_{press,\epsilon}\|+\|\epsilon_{Pow,\rho}\|+\|\epsilon_{ion, \rho}\|+\|\epsilon_{press,\rho}\|+\|V_{tot}-V_{target}\| \tag{36}\]  
It is clear that thisast approach can be used also for the rebuilding of plasma properties in an existing hollow cathode when the experimental electrical characteristics are known.
## 2 Chaos Oscillators
### Vilnius Chaos Oscillator  
The Vilnius chaos oscillator is a simple and robust nonlinear system for generating chaotic signals. It is widely recognized for its simplicity and effectiveness, making it suitable for research and educational applications in nonlinear dynamics. The circuit, shown in Figure 2, consists of a noninverting operational amplifier, an LCR resonance circuit in a positive feedback loop, an additional capacitor, and a diode functioning as the nonlinear element. This configuration ensures chaotic dynamics with minimal components while facilitating experimental implementation and analysis.  
The behavior of the Vilnius chaotic oscillator is characterized by three state variables: \(v_{\text{CI}}\), the voltage across the capacitor \(C_{1}\); \(i_{L}\), the current through inductor \(L_{1}\); and \(v_{\text{C2}}\), the voltage across the supplementary capacitor \(C_{2}\). The system is defined by an array of differential equations derived using [PERSON]'s circuit laws:  
\[\begin{cases}C_{1}\dfrac{\text{d}v_{\text{C1}}}{\text{d}t}=i_{L}\\ C_{2}\dfrac{\text{d}v_{\text{C2}}}{\text{d}t}=i_{0}+i_{L}-i_{D}\\ L_{1}\dfrac{\text{d}i_{L}}{\text{d}t}=(k-1)\cdot R_{1}\cdot i_{L}-v_{C_{1}}-v_ {C_{2}}\end{cases}, \tag{4}\]  
where \(i_{D}\) is the current of the diode \(D_{1}\), \(i_{0}\) is the current of the resistor \(R_{0}\), and \(k\) is the gain of the operational amplifier.  
The oscillator's nonlinear behavior is defined by the diode's current-voltage characteristic, represented by the subsequent equation:  
\[i_{D}=i_{S}\cdot\left(\mathrm{e}^{\frac{v_{D}}{v_{T}}}-1\right), \tag{5}\]  
where \(v_{D}\) is the voltage across the diode and due to parallel connection \(v_{D}=v_{C2}\), \(i_{S}\) is the saturation current of the diode, and \(v_{T}\) is the thermal voltage.  
This nonlinear characteristic, combined with the circuit design, facilitates the onset of chaotic oscillations. The system exhibits a universal period-doubling route to chaos, as demonstrated through bifurcation diagrams and positive Lyapunov exponents, confirming its chaotic nature under suitable parameter conditions [41].
# Enhancing Vibration Isolation Performance by Exploiting Novel Spring-Bar Mechanism
## 2 Mathematical Modelling
### Frequency Response Function
The figure shows a shift of the resonance peak, which is due to the corresponding changes in the linearized natural frequency from \(0.4\) to \(0.6\) to \(0.8\) and then to \(1.2\). It can be seen that the resonance peak reduces with the natural frequency. In the low-frequency range, a lower natural frequency leads to a larger response amplitude. In contrast, for a large excitation frequency \(\Omega\), the response amplitude \(r\) is the almost same, and the curves tend to coincide with each other. The parameters set in Region III of Figure 5 yield systems of double-well potentials. This kind of system can exhibit chaotic motion, as seen by the bifurcation diagrams in Figure 7 when \(\xi=0.02,\alpha=-0.55,\beta=2,F_{0}=0.05\). Figure 7a,b presents low-to-high and high-to-low frequency sweepings of the displacement, respectively. The steady-state non-dimensional displacement \(X_{s}(T_{s})\) of the mass at sampling time \(T_{s}=T_{i}+2(n-1)\pi/\Omega\) is recorded, where \(T_{i}\) is the pre-iteration time. Note that for a periodic response, there will only be finite points shown in the bifurcation diagram at the particular frequency. For the current system with the prescribed parameters, the corresponding pattern of the bifurcation diagram is similar to that of the Duffing oscillator with double-well potential. Figure 7b indicates that the system can exhibit possible chaotic motion when \(\Omega\) is lower than \(0.28\) as well as when \(\Omega\) is located in the range between \(0.60\) and \(0.87\). In terms of vibration isolation, chaotic motion is generally considered undesirable. As there are infinite frequency signals in the chaotic response, the traditional force transmissibility is not suitable to reflect the vibration isolation effectiveness. Vibration power flow provides a good indicator of vibration isolation by effectively quantifying the amount of energy input, transmission, and dissipation associated with both periodic and non-periodic chaotic responses [29].
## 4 Experimental Results and Discussion
### Practical Experiments and Analysis  
Furthermore, to demonstrate the effectiveness of the proposed CPIMM-NAUKF method for real applications, two practical experiments were conducted. An unmanned aerial vehicle (UAV) was loaded with an Inertial Navigation System (INS)/Global Positioning System (GPS) integrated navigation system for its navigation and positioning, and equipped with an SAR tracking system to track the maneuvering targets.
# Gear Integrated Error Determination Using the Gaussian Template Convolution-Facet Method
## 5 Experiment and Discussion
### Comparative Experiment between GVMS and P26
#### 5.3.4 Measurement Speed Comparison  
The average speed of measuring one gear using the method described in this article is about 0.35 s/piece. However, classic gear integrated error measurement methods use contact measurement, which is much slower. [PERSON] [21] mentioned that measuring the one product gear with 28 teeth takes about 20 s, and the actual measurement also includes the clamping time, which takes even longer. Therefore, using the method described in this article to measure the gear integrated error has increased the measurement speed compared to classic methods, as shown in Figure 24.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Tooth Number** & **Tooth Flank** & **GVMS** & **P26** & **Error** \\ \hline \multirow{2}{*}{1} & left & \(-0.3\) & \(-3.1\) & \(2.8\) \\  & right & \(-2.2\) & \(-3.6\) & \(1.4\) \\ \hline \multirow{2}{*}{6} & left & \(3.8\) & \(-5.8\) & \(2.0\) \\  & right & \(-3.4\) & \(-7.6\) & \(3.2\) \\ \hline \multirow{2}{*}{10} & left & \(-1.2\) & \(-3.9\) & \(2.7\) \\  & right & \(-2.1\) & \(-6.0\) & \(3.9\) \\ \hline \multirow{2}{*}{14} & left & \(-3.2\) & \(-2.1\) & \(-1.1\) \\  & right & \(2.5\) & \(-0.4\) & \(2.9\) \\ \hline \end{tabular}
\end{table}
Table 6: Comparison of profile slope deviation \(f_{Ha}\) (four teeth).  
Figure 23: Profile deviation (four teeth, P26 measurement result).  
Figure 22: Profile deviation. (four teeth, GVMS measurement results).
# Computational Aspects of \(L_{0}\) Linking in the Rasch Model
## 4 Simulation Study
### Results
Following the suggestion of a reviewer, bias and RMSE were regressed onto the simulation factors using a two-way analysis of variance (ANOVA). The factors included sample size \(N\), number of items \(I\), the size of the DIF effect \(\kappa\), the type of loss function (i.e., ratio vs. Gaussian function), and the chosen \(\varepsilon\) value in the loss function \(\rho_{\varepsilon}\). All simulation factors were treated as categorical factors in the ANOVA. The same item numbers \(I\) (e.g., \(I=10,20,40\)) and \(\varepsilon\) values (i.e., \(\varepsilon=0.01,0.05,0.10,0.25\)) as reported in Tables 2 and 3 were used. The main focus of the analysis was the proportion of variance explained by the main effects and two-way interactions of the factors in the ANOVA. In the two-way ANOVA with bias as the dependent variable, 96.0% of the variance was explained by the main factors and their two-way interactions. The largest proportion was attributed to sample size \(N\) (39.8%), followed by \(\kappa\) (24.8%) and \(\varepsilon\) (24.8%). The number of items \(I\) (0.1%) and the type of loss function (0.2%) contributed minimally to the variability in bias. Among the two-way interactions, only the interaction between \(N\) and \(\kappa\) (\(N\times\kappa\), 2.3%) and \(N\times\varepsilon\) (1.7%) accounted for non-negligible proportions of variance. In the two-way ANOVA with RMSE as the dependent variable, 99.3% of the variance was explained by the simulation factors and their two-way interactions. As expected,sample size \(N\) accounted for the largest proportion of explained variance (89.9%), followed by number of items \(I\) (3.2%), \(\kappa\) (1.0%), \(\varepsilon\) (0.5%), and the type of loss function (0.0%). Among the two-way interactions, \(N\times I\) (1.3%), \(N\times\kappa\) (1.0%), and \(N\times\varepsilon\) (2.1%) contributed with non-negligible amounts to the variance. Figure 3: Simulation Study: Absolute bias, standard deviation (SD), and root mean square error (RMSE) of the estimated mean \(\hat{\mu}\) using the ratio loss function for \(I=20\) items as a function of sample size \(N\) and DIF effect size \(\kappa\). The minimum RMSE values are depicted with a triangle. Figure 4: Simulation Study: Relative root mean square error (RMSE) of the estimated mean \(\hat{\mu}\) using the ratio loss function based on \(\varepsilon=\varepsilon_{y}\) determined through \(\rho_{\varepsilon_{y}}(\sqrt{\hat{V}})=y\) as a function of sample size \(N\), the number of items \(I\), and DIF effect size \(\kappa\). The minimum relative RMSE values are depicted with a triangle. The ratio loss function with \(\varepsilon=0.01\) was chosen as the reference method when computing the relative RMSE.