esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Related Works  
### Multidimensional Index Methods  
Multidimensional data indexes can be divided into two categories according to different construction methods: indexes based on spatial partitioning and data-driven indexes.  
For indexes based on spatial partitioning, the internal nodes of the structure represent the spatial division area, and the child nodes correspond to the smallest unit in the space division, including the actual space object. The inclusion relationships of the spatial areas are represented by the tree node pointing relationships. The KD-tree [3] is a typical example of this category. This structure can design node-splitting rules according to data distribution to balance the data volume within the node and achieve more efficient query efficiency.  
Data-driven indexes, on the other hand, are data structures that dynamically adapt to data distribution, represented by R-tree and their variants [2; 13; 14; 15]. The key concept of the R-tree is to store a set of minimum bounding rectangles (MBRs) in each node, which are the smallest rectangles that contain all the child nodes of that node. The core idea of the R-tree search algorithm is to decide whether to search a subtree based on the search range, allowing most of the nodes in the tree to be skipped during the search. The R-tree can dynamically adapt to the insertion and deletion of data. When new data are inserted or old data are deleted, the R-tree will adjust accordingly to ensure the balance of the tree and efficient query. However, there is a drawback of MBR overlap during the construction process, leading to repeated retrieval of overlapping areas.  
Many scholars have proposed efficient index structures for three-dimensional spatiotemporal data, with common methods including TRindex [16] and DSTree [17]. Space-filling curves are widely used in spatiotemporal data processing and analysis because they can better maintain the spatiotemporal proximity of data, such as GeoMesa [18], TrajMesa [19] and HGST [20]. Traditional space-filling curves do not learn from data distribution and usually store a fixed number of data points in a page. LMSFC [21] designs a learnable monotonic space-filling curve to achieve optimal or suboptimal storage of data in pages. Piecewise SFCs [22] divide the data space into different subspaces and use different mapping modes in different data subspaces to achieve the best distribution in the entire data space.
### Evolution and Integration of Solar Power  
Initially conceptualized for military purposes, UAVs have evolved to become versatile tools in civilian and commercial domains [18]. Early UAV technology focused on military reconnaissance and target practice, but advancements in electronics, navigation, and materials science have enabled broader applications. The quest to extend the operational capabilities of UAVs led to the exploration of solar power as an additional energy source. Solar-powered UAVs emerged as a solution to the endurance limitations posed by onboard battery systems, marking a significant milestone with the integration of photovoltaic (PV) cells into UAV designs. High-altitude, long-endurance (HALE) UAVs, designed to operate at altitudes with intense and consistent solar radiation, have significantly extended mission durations [16; 17; 18; 20; 26; 27; 28].
## 3 Equation Fitting
### Fitting Results
For a clear description on Equation (3), the above sub-equations are illustrated together in Table 2.  
Figure 2: (**a–e**) The fitting results for Equation (3), and (**f**) all fitting results of 791 abundance records. The 45\({}^{\circ}\) diagonal line with lines deviating by \(\pm\)0.2 indicates the geochemical background value with its error range. In summary, the fitted equation includes five sub-equations sequentially as Equations (3a)-(3e) and was fitted on the 791 records on the respective different conditions (Figure 2f). The fitted results indicate that the residual errors of 42 records in the 791 records fall outside of the logarithmic difference of \(\pm\)0.2. The residual errors of the other 749 records are within a logarithmic deviation of \(\pm\)0.2, which constitutes ca. 95% of the 791 records. Additionally, the fitted r-values of the five sub-equations are all greater than 0.9, demonstrating significant fitting levels. According to these results, the logarithmic difference of \(\pm\)0.2 between the calculated and analyzed concentrations was suggested to discriminate a sample within or outside of its geochemical background area. Specifically, a sample within the logarithmic difference of \(\pm\)0.2 can be viewed as a normal geological material. In contrast, a sample without the logarithmic difference of \(\pm\)0.2 can be regarded as an anomalous sample or an outlier.
## 4 The Deformation Detection Experiment and Results
### Error Analysis  
From the experimental results presented above, it can be observed that CBSs, as a GB-SAR systems, are capable of effectively performing ground deformation detection tasks. However, certain errors remain evident in the detection results. Analyzing the data processing flow, it can be inferred that these errors may arise from three primary sources.  
First, processing errors introduced during the imaging process. According to the description of the BPA in Section 3.2, the coordinates of the array elements relative to the target are required to calculate the slant range. However, deviations in the actual positions of the array elements are inevitable, leading to inaccuracies in the calculated slant range and consequently introducing phase errors in the SAR images. While the impact of this error on deformation detection is relatively minor, it cannot be completely eliminated and can only be mitigated through improved production precision.  
Second, errors introduced by environmental change during interferometric processing. During multiple observations, the differential interferometric phase is affected by atmospheric variations, leading to atmospheric phase noise (as described in Section 3.4). Additionally, the CBS equipment may experience shifts due to factors such as wind, resulting in positional deviations during each observation that also introduce phase errors. These errors can significantly affect the accuracy of deformation detection and require the incorporation of external data sources for calibration.  
Lastly, phase errors caused by low transmission power. Due to the relatively low transmission power of individual array elements, the SNR of the obtained SAR images tends to be low, resulting in larger errors in deformation detection. However, the CBS's high temporal sampling rate ensures a high coherence between adjacent images, allowing for the enhancement of SNR through multi-look processing of time-series SAR image samples (refer to the analysis in Section 3.3), thereby improving the accuracy of deformation detection.
# Sea Level Estimation Based on GNSS Dual-Frequency Carrier Phase Linear Combinations and SNR
## 2 Methods
### Fundamentals of the GNSS-R Altimetry Using the Multipath Effect  
Scattered GNSS signals from the ocean surface in the vicinity of the GNSS antenna will interfere with the direct signal, thus contributing to the measured phase, power and amplitude [(35)]. According to [(27; 36)], when only the specular reflection path is considered, the sum of the direct and reflected signals is given by  
\[s(t)=A\sin\widetilde{\psi}(t) \tag{1}\]  
Figure 1: Simplified schematic diagram of the ground-based global navigation satellite system reflectometry (GNSS-R) altimetry system with one antenna and the multi-path effect of direct and reflected signals. Definitions: ARP, antenna reference point; GPS, global positioning system. TGZ: tide gauge zero.  
where  
\[A=\sqrt{A_{d}^{2}+A_{m}^{2}+2A_{d}A_{m}\cos\delta\varphi(t)} \tag{2}\]  
\[\widetilde{\psi}(t)=\psi(t)+\beta(t) \tag{3}\]  
\[\beta(t)=\tan^{-1}\frac{(\frac{A_{m}}{A_{d}})\sin\delta\varphi(t)}{1+(\frac{A_{ m}}{A_{d}})\cos\delta\varphi(t)} \tag{4}\]  
\[\delta\varphi(t)=\frac{4\pi h}{\lambda}\sin\theta(t) \tag{5}\]  
where \(A_{d}\) and \(A_{m}\) are the amplitudes of the direct and reflected signals, respectively, and \(\delta\varphi(t)\) is the phase caused by the excess range of the reflected signal compared with the direct one. The factors \(A\) and \(\widetilde{\psi}(t)\) represent the amplitude and phase of the composite signals received by the antenna, and \(\psi(t)\) represents the phase of the direct signal. The factor \(\beta(t)\) is the composite excess phase with respect to the direct phase, \(h\) is the vertical height between the antenna and the sea surface, \(\theta\) is the satellite elevation angle and \(\lambda\) is the electromagnetic wave length of the GNSS signal.
## 4 Experimental Results
### Effect Analysis of Generating Samples by Cycle GAN Network  
In order to verify the sample generation effect of the Cycle GAN network used in this paper, this paper uses the original GAN network and the Cycle GAN network to generate the three-phase stator current data of the inter-turn short-circuit fault PMSM. We carried out a correlation analysis with the collected current data, respectively. Taking the 2% inter-turn short-circuit fault of motor one as an example, Figure 13 shows three stator currents collected by motor one under three different operating conditions.  
Figure 12: PMSM inter-turn fault data acquisition experimental platform.  
Three motors operate under three working conditions and use different generative networks to generate their three-phase stator currents. They also analyze the correlation between the generated and the collected three-phase stator currents. The same motor has five different degrees of inter-turn short-circuit fault conditions under the same working condition, and the average value is taken after correlation analysis. The x-axis coordinates in Figure 16 represent three different working conditions, and the y-axis coordinates represent the motor number and different generative networks (a is the Cycle GAN network used in this paper, and b is the original GAN network). Due to the complex working condition of the motor in the actual operation and the normal fluctuation of the power supply, the three-phase stator current will inevitably generate noise signals. Therefore, even if the same experimental platform collects the PMSM three-phase stator current under the same working condition and fault degree, the same waveform will not appear. The similarity analysis shown in Figure 16 is consistent with the actual situation.  
Figure 17 shows the local comparison between the collected and the generated phase A current. The current samples generated by Cycle GAN are more consistent with the collected current samples in amplitude, waveform, and fluctuation. The current samples generated by the original GAN are limited in ability, lacking in detail generation and authenticity, thus failing to improve the fault diagnosis network.
# A Traffic Equilibrium Model for Multi-Modal Networks with Uncertain Demands
## 5 Solution Algorithm  
The method of successive averages (MSA) has been widely used for solving traffic equilibrium problems ([PERSON] and [PERSON] (2009) [22]). In this study, interval mathematics are applied to the algorithm to obtain the results in the form of interval variables, and similarity formulation is proposed to calculate the equilibrium coefficient \(E\). Considering the interval variables \(A=[a^{-},a^{+}]\) and \(b=[b^{-},b^{+}]\), according to interval mathematics, under the conditions \(P(A\geq B)=0.5\) and \(P(A\leq B)=0.5\), the interval variable A is regarded as equivalent to B. Therefore, the interval variable similarity formulation is expressed as follows:  
\[E=\sqrt{(P(A\geq B)-P(A\leq B))^{2}}(P(A\leq B))^{-1} \tag{41}\]  
Therefore, an MSA algorithm based on interval mathematics is proposed to solve the multi-mode traffic equilibrium problems under interval demands. The detailed steps for the solution are as follows.  
1. Initialization. Find all viable hyperpaths between OD pairs using a graph traversal algorithm; based on the free-flow route travel cost, perform an initial loading procedure according to Equations (27) and (28) to obtain link flows \(v_{l}^{(1)}\) and then set \(n=1\).
2. Update. Use the interval link flows \(v_{l}^{(n)}\) to calculate the route interval travel cost \(c_{w}^{p,(n)}\) and the route ETC \(c_{w}^{p,(n)}\) using interval mathematics.
3. Direction. Apply the loading process according to Equations (27) and (28) using \(\xi_{w}^{p,(n)}\) to obtain an auxiliary link flow pattern \(y_{l}^{(n)}\).
4. Move. Calculate the new link flow using an MSA scheme: \[v_{l}^{(n+1)}=v_{l}^{(n)}+\chi^{(n)}\Big{(}y_{l}^{(n)}-v_{l}^{(n)}\Big{)}\] (42)  
\[\chi^{(n)}=\frac{n^{d}}{1^{d}+2^{d}+3^{d}+\cdots+n^{d}}(d=1) \tag{43}\]
5. Convergence criterion. Set an acceptable convergence level \(e\), and calculate the equilibrium coefficient \(E\). If  
\[E=\sqrt{\sum\limits_{l}\Big{(}P\Big{(}v_{l}^{(n+1)}>v_{l}^{(n)}\Big{)}-P\Big{(} v_{l}^{(n+1)}<v_{l}^{(n)}\Big{)}\Big{)}^{2}}\Bigg{(}\sum\limits_{l}P\Big{(}v_{l}^{ (n+1)}<v_{l}^{(n)}\Big{)}\Bigg{)}^{-1}\leq e \tag{44}\]stop; otherwise, set \(n=n+1\), and return to Step 2.
## 3 Analytical Expressions
### Low-Frequency Amplifiers
#### 3.5.2 BJT-Based Amplifier Circuit  
The bipolar transistor can be operated in three basic circuits: common emitter, common collector, or common base configuration. Because of its high voltage gain and high input impedance, the common emitter circuit was selected for a single-stage amplifier, as shown in Figure 11, where the BJT transistor is named as \(Q_{1}\).  
Typically, the amplifier based on BJT requires a specific operation point. These operation points can be highly influenced by temperature changes and component tolerances. These problems can be solved by connecting \(R_{\text{B}}\) parallel to collector and base. This creates the stable operating point, but limits the output voltage span, due to \(V_{\text{CE}}\approx 0.7\,\mathrm{V}\).  
A small-signal analysis according to [45] was made in order to investigate the voltage amplification. Figure 12 shows the small-signal circuit of the amplifier. Equation (12) shows the result of the small-signal analysis with \(r_{\text{BE}},r_{\text{CE}}\), and \(\beta\) the small-signal parameters. Further approximations were made in order to simplify the formula. The resulting approx  
Figure 10: Schematic of the TIA amplifier.  
imation is only dependent on supply voltage \(V_{\text{S}}\), thermal voltage \(V_{\text{T}}\), load resistance \(R_{\text{L}}\), and collector resistor \(R_{\text{C}}\).  
\[G=\frac{r_{\text{CE}}||R_{\text{C}}||R_{\text{L}}}{r_{\text{BE}}}\cdot\frac{r_{ \text{BE}}-\beta\cdot R_{\text{B}}}{R_{\text{B}}+(r_{\text{CE}}||R_{\text{C}}|| R_{\text{L}})}\approx-\frac{V_{\text{S}}}{V_{\text{T}}}\cdot\frac{R_{\text{L}}}{R_{ \text{C}}+R_{\text{L}}} \tag{12}\]  
Practically, for WuRx, the \(R_{\text{L}}\) is the equivalent model of input resistance of AS3933.
# Optimal Lyapunov-Based Sliding Mode Control for Slotless-Self Bearing Motor System
## 1 Introduction
The provided stabilities in these papers are aimed to force the state and disturbance to the predefined value in the fast time and fixed-time, respectively. In this paper, an OLB-SMC method was proposed for SSBM system with the verification of the practical study. The novelty of this paper is that a new stability condition was intelligently proposed based on pole placement method. The aim of the proposed method is that to softening the calculation of stability analysis. The proposed stability condition can be expanded for many stability condition of disturbance and state observers. Motivations of the work are came from the works of [3; 4; 9], the perturbations factors were ignored. Second, in the paper [9] proposed the PID controller without considering the disturbance and uncertainty effects. Third, to reject the unexpected factors so a new disturbance rejection technique was discussed in [6], but it just verified via the simulation. Therefore, this paper applied an optimal SMC method to increase the power of system. The performance of the proposed control method was completed by the practice system and was compared with our previous paper [9]. Otherwise, the main effort of this work is to provide the new Finally, the prime contributions of this work are listed by  
1. The mathematical model of SSBM was slightly rewritten with considerations of perturbations. These unexpected factors were rejected by the optimal control algorithm, which were evaluated by experimental test. 2. The OLB-SMC method was discussed for the control of movements rotation of SSBM motor with the consideration of the uncertain and disturbance effects. 3. The stability of the proposed theory was analyzed by using the Lyapunov condition and experimentally validated via the practical system. 4. This research was completed by the support of the dSPACE DS1104 controller board with the linking of MATLAB software. The originality of the paper is that the proposed stability is newly proposed via the Lyapunov based with the poles placement method for softening the movement of stability analysis. The paper is constructed by. Second, the mathematical model with the consideration of disturbance and uncertain for the SSBM is slightly represented. Third, the design of the OLB-SMC was given, and the stability was proved via the Lyapunov theory. Finally, the practice tests will be performed to prove the performance of the OLB-SMC controller.
# Stress-Strain Model for Freezing Silty Clay under Frost Heave Based on Modified [PERSON]'s Equation
## 6 Discussion  
The frost heaving process of silty clay is a complex problem. The amount of moisture transfer in the soil is directly related to the frost heave increment on the specimen's surface. Firstly, a set of one-dimensional freezing experiments were carried out to research the fundamental law of frost heaving of saturated clay. Temperature and load are the main factors that determine the frost heaving characteristics of the soil. In order to reveal the development law and mechanism of soil frost heaving, it is necessary to deeply analyze the internal relationship between soil frost heaving characteristics and temperature distribution during soil freezing.  
[PERSON]'s equation was generalized so as to play a significant role in this research. It has been widely used as based on Japanese Geotechnical Society (JGS) regulations and is valuable for engineering purposes. According to Equation (5), if \(\sigma_{\
u}\) is infinitesimally small, \(\varepsilon\) will have an infinitely large value. Therefore, [PERSON]'s model is limited to cases with overburden stress larger than 98 kPa and smaller than 1470 kPa. It can be seen that the model does not take the influencing factors of the frost heave rate into account adequately. Necessary modifications should be carried out in order to operate in wider application conditions.  
In [PERSON]'s equation, the freezing rate and effective constraining stress in the freezing direction are the factors dominating frost heave prediction. As shown in Figures 6 and 13, the \(U_{i}\) is directly related to the \(\
abla T_{i}\). Thus, the \(T_{\text{fre,ci}}\) and \(\
abla T_{i}\) were introduced into the [PERSON] model, as shown in Equation (6). Then, [PERSON]'s equation can be used in cases with low \(\sigma_{\
u}\), even without overburden pressure.  
On the other hand, the analysis of soil deformation induced by frost heaving is another important target in the study. For this, the method of determining the compression modulus of freezing soil is given and a nonlinear elastic mechanical model is developed to map the stress-strain relationship of the freezing soil.  
In future studies, the stress-strain of freezing soil must be researched in action conditions, such as in freezing-thawing cycles. Then, a more realistic stress-strain model that includes elaborate factors could be developed.
# Monitoring of Reinforced Concrete Corrosion: Active and Passive Bars Exposed to Climate
## 1 Introduction
Among the electrochemical techniques, only polarization resistance (\(R_{p}\)) measurements can quantify the corrosion rate (\(I_{corr}\)) [26]. Through [PERSON]'s law, the corrosion rate can be transformed into a loss of reinforcement cross-section. In order to calculate this accurately, it is necessary to have sufficient measurements over time. Consequently, the monitoring of structures represents the optimal method for acquiring precise knowledge of their state and carrying out analyses.
## 1 Introduction
In this paper, we investigate splitters with variable splitting ratios by adjusting the asymmetry of the two side waveguides of the three-waveguide structure for PON applications with wavelengths between 1.53 and 1.57 \(\upmu\)m. It was found that when the two side waveguides of the original symmetric three-waveguides structure begin to become asymmetrical, the splitting ratios of the two output ports change accordingly. As the structural asymmetry increases, the difference in splitting ratio between the two output ports also increases. By using the BPM, it is demonstrated that the splitter with variable splitting ratio has excellent performances including excess loss, crosstalk, polarization sensitivity, and wavelength dependence.
## 2 Materials and Methods
### Machine Learning Algorithms
#### 2.5.1 Logistic Regression (LR)  
Logistic Regression is a statistical model that applies a logistic function to represent a binary dependent variable, making it suitable for binary classification tasks [37]. It is a type of generalized linear model (GLM) used for predicting the probability of a categorically dependent variable. The LR framework is predicated on the logistic function, which manifests an S-shaped curve capable of mapping any real-valued input to a value within the range of 0 to 1. The logistic function is defined as follows [38].  
\[f(x)=\frac{1}{1+e^{-x}} \tag{1}\]  
Within the context of LR, the log odds (the logarithm of the odds) corresponding to the outcome labeled \"1\" is expressed as a linear combination of one or more independent variables (\"predictors\"). The mathematical representation of the model is articulated as follows.  
\[\ln\left(\frac{p}{1-p}\right)=\beta_{0}+\beta_{1}X_{1}+\ldots+\beta_{k}X_{k} \tag{2}\]  
where \(p\) is the probability of the positive class, \(X\) is the input (or feature), and \(\beta\) values are the parameters of the model, which are learned from the data.
## 4 Experiments
### Experiment Results
#### 4.3.1 Experiments between Images Collected by Satellites and UAVs
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **B \(\rightarrow\) C** & **C \(\rightarrow\) B** & **A \(\rightarrow\) C** & **C \(\rightarrow\) A** & **Average** \\ \hline F-RCNN & 0.43 & 0.76 & 61.49 & 4.56 & 16.81 \\ (source) & 61.64 & 36.45 & 60.95 & 69.25 & 57.07 \\  Strong Weak & & & & & \\ Faster & 18.79 & 10.30 & 62.40 & 28.31 & 28.95 \\  R-CNN & & & & & \\ CROPTD & 37.80 & 20.82 & 64.81 & 48.38 & 42.94 \\  SW ICR-CCR & 67.41 & 25.80 & 61.60 & 71.54 & 56.59 \\  CAS-DA + & & & & & \\ filtering & **69.48** & **51.24** & **68.01** & **87.06** & **68.95** \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The F1-scores of different methods on four transfer tasks. our method obtained the highest F1-score in two different adaptation scenarios. which demonstrates the importance and effectiveness of improving the detection performance on the source domain to enhance the DA detector. Moreover, it is worth noting that our method brought a greater improvement for the adaptation with a large domain shift.