esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Optimal Layout for Shear Connectors
### Effect of Shear Connector Distribution on Deflection  
As described in Section 3, the deflection of composite beams decreases with the decrease in interface slip. From Section 4.2, we can get that the interface slip is decreased by using different redistributions of shear connectors. The corresponding maximum deflections along the beam under different stepped rectangle distributions of shear connectors (as shown in Figure 9) are shown in Table 5. As shown in Table 5, the 2-stepped rectangle distribution method can reduce the maximum deflection along the beam by 3.18% for the four kinds of load. Meanwhile, the 3-stepped rectangle distribution method is able to reduce the maximum deflection by 4.88%, and the 5-stepped rectangle distribution method is able to reduce the maximum deflection by 6.35%. However, it is not necessary to increase the total number of shear connectors. In other words, the proposed connector layout method can enlarge the service space without increasing the construction cost; furthermore, it can decrease the interface slip and deflection of composite beams, and increase the composite effect and stiffness of composite beams.  
Figure 10: Comparison of interface slip under four different types of load. (**a**) point load at mid-span; (**b**) uniformly distributed load at mid-span; (**c**) uniformly distributed load; (**d**) two-point load  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Load Types** & **I** & **II** & **III** & **IV** \\ \hline Uniformly deflection \(w_{1}\) (mm) & \(-31.35\) & \(-36.54\) & \(-38.75\) & \(-41.75\) \\
2-stepped rectangles deflection \(w_{2}\) (mm) & \(-30.56\) & \(-35.84\) & \(-37.51\) & \(-40.67\) \\
3-stepped rectangles deflection \(w_{3}\) (mm) & \(-30.17\) & \(-35.10\) & \(-36.92\) & \(-39.71\) \\
5-stepped rectangles deflection \(w_{4}\) (mm) & \(-29.87\) & \(-34.66\) & \(-36.43\) & \(-39.10\) \\ \((w_{1}-w_{2})/w_{1}\) (\%) & 2.51 & 1.93 & 3.18 & 2.57 \\ \((w_{1}-w_{3})/w_{1}\) (\%) & 3.75 & 3.95 & 4.72 & 4.88 \\ \hline \end{tabular}
\end{table}
Table 5: Comparison of maximum deflection under four load cases.
## 2 Materials and Methods
### Machine Learning Algorithms Used in the Study
#### 2.4.7 Symbolic Regression  
Symbolic regression (SR) is a machine learning algorithm that searches for mathematical equations or formulas that best describe and fit data relationships. It allows for the modeling of complex relationships and the creation of predictive equations without making any assumptions about the underlying mathematical form. In capturing complex nonlinear relationships, symbolic regression outperforms multiple linear regression (MLR), which is limited to linear relationships between variables [98]. The symbolic regression algorithm is used in this study to determine the equation of \(q_{u}\) and \(E_{t}\). In this study, EUREQA 1.24.0 software is used for this purpose. EUREQA begins the symbolic regression process by configuring algorithm parameters and establishing the equation space, as shown in Figure 11. It begins with a small set of equations. These equations are subjected to a fitness evaluation, which determines how well they correspond to the given dataset. The algorithm grows and refines this set by including and excluding equations dynamically based on their fitness and relevance. Equations with high fitness are subject to adaptive evolutionary mechanisms, allowing the algorithm to iteratively explore and refine equations. EUREQA adjusts its equation population, concentrating computational resources on promising equations. Iterations of this dynamic evolution continue until convergence or the fulfillment of predetermined termination criteria. In the end, EUREQA chooses the best-fit equation or equations to analyze and validate their correctness in capturing the underlying patterns in the dataset.
# Exploring Image Decolorization: Methods, Implementations, and Performance Assessment
## 6 Results
### Summary of the Results  
The analysis highlights that the GD and DL methods perform best according to the RMS measure, especially for high-contrast images like Image 6, while artificially generated images with low saturation, such as Image 18, yield the poorest results. For the NRMS measure, the CDF and Rec. 601 methods give good results, even for images dominated by white or pastel colors. FSIM shows inconsistencies, with Rec. 2020 and Rec. 601 performing well but diverging from other metrics, particularly struggling with artificially generated images. The GD and DL decolorization methods are the most suitable for edge detection, while low-contrast images yield the worst results. Metrics such as RMS and GRR for edge detection, and NRMS for object segmentation, proved suitable, whereas FSIM was found unsuitable for evaluating decolorization in these tasks.  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Test Image** & **CDF** & **DL** & **GD** & **LAB** & **Rec. 601** & **Rec. 709** & **Rec. 2020** & \begin{tabular}{c} **Image Mean** \\ \(\pm\) **SD** \\ \end{tabular} \\ \hline gray\_surface\_fully\_saturated & 46.872 & 5.000 & 3.606 & **2.828** & 80.000 & 3.000 & 3.000 & 20.615 \(\pm\) 30.784 \\ \hline white\_surface\_fully\_saturated & **3.000** & 4.123 & 3.606 & 101.518 & **3.000** & 101.518 & 101.518 & 45.469 \(\pm\) 52.430 \\ \hline black\_surface\_fully\_saturated & **3.000** & 3.162 & 5.000 & **3.000** & **3.000** & 43.000 & 43.000 & 14.737 \(\pm\) 19.320 \\ \hline gray\_surface\_not\_saturated & 3.000 & 3.606 & **2.828** & 101.518 & 101.518 & 101.980 & 101.518 & 59.424 \(\pm\) 52.645 \\ \hline white\_surface\_not\_saturated & **3.000** & 4.472 & 5.000 & **3.000** & **3.000** & **3.000** & **3.000** & 3.496 \(\pm\) 0.861 \\ \hline black\_surface\_not\_saturated & 3.000 & 3.000 & 3.606 & **2.236** & 43.000 & 43.000 & 43.000 & 20.120 \(\pm\) 21.406 \\ \hline Method mean \(\pm\) SD & \begin{tabular}{c} 10.312 \\ \(\pm\) 17.911 \\ \end{tabular} & \begin{tabular}{c} **3.894** \\ \(\pm\) 0.778 \\ \end{tabular} & \begin{tabular}{c} 3.941 \\ \(\pm\) 0.874 \\ \end{tabular} & \begin{tabular}{c} 35.683 \\ \(\pm\) 50.996 \\ \end{tabular} & \begin{tabular}{c} 38.920 \\ \(\pm\) 43.574 \\ \end{tabular} & \
\begin{tabular}{c} 49.250 \\ \(\pm\) 44.427 \\ \end{tabular} &
\begin{tabular}{c} 49.173 \\ \(\pm\) 44.317 \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 16: Hausdorff distance for different test images and different decolorization methods. The best results are shown in bold.
## 2 Materials and Methods  
The experimental fatigue tests were carried out on notched steel samples reinforced by adhesively bonded CFRP stripes (Figure 1). The core of each sample was made of low-alloy and normalized S355J2+N low-carbon manganese structural steel (ArcelorMittal Poland S.A. Oddzial w Krakowie, Krakow, Poland) with chemical composition as follows (in weight %): C, 0.15; Si, 0.13; Mn, 1.33; Al, 0.04; Cu, 0.02; P, 0.01; S, 0.04; Fe, res. The tested steel exhibited the following mechanical properties: Young's modulus, 210 GPa; Yield strength \(Y\)e, 427 MPa (\(\pm\)11 MPa) and ultimate tensile strength, 528 MPa (\(\pm\)10 MPa); elongation at failure (A\({}_{5}\)), min 22%. Its tensile curve is characterized by a typical stress-strain curve for mild steels including the yield plateau (plastic flow), strain hardening and necking [10]. The notch in the form of a square hole with rounded corners (radius R2) in the core was cut by using laser cutting technology. The CFRP stripes were made of prefabricated S&P C-laminate 150/2000 (S&P Reinforcement Poland, Malbork, Poland)with a main elastic modulus of 165 GPa, ultimate tensile strength of 2800 MPa, fiber volume content not less than 68%, density 1.6 g/cm\({}^{3}\) and elongation at break not less than 16% [42]. The thickness of the single strip was equal to 1.4 mm. The strips were glued on the steel core so that the fibers were arranged parallel to the direction of the tensile force (parallel to direction of x-axis in Figure 1b). Such strips were attached by means of an adhesive joint.  
Finally, the experimental fatigue tests have been performed for notched steel samples reinforced with the use of three different adhesives (Figure 1):  
* Solvent-free, thixotropic, two-component epoxy resin adhesive S&P Resin 220 (S&P Reinforcement Poland, Malbork, Poland)--4 samples tested;
* Two-component polyurethane-based structural adhesive 3M Scotch-Weld DP 6310 NS (3M Poland Sp. z o.o., Kajetany, Poland) --3 samples tested;
* Two-component structural hybrid Cyanoacrylate/Acrylic Hybrid Loctite HY 4080 GY (Henkel Polska Sp. z o.o., Warszawa, Poland)--3 samples tested.  
Figure 1: Exemplary notched steel samples reinforced by CFRP strips bonded by different adhesives: (**a**) photographs of exemplary specimens; (**b**) geometry and dimensions of the specimen and position of the paths (red and blue lines) used for validation of FEM models.  
The principal properties of the adhesives are given in Table 1. Before the bonding procedure, the steps suggested by the glue manufacturer have been carried out. The steel adherents were grounded in order to remove surface defects and oxide layers. In the next step after that, the sample surface was cleaned with extracted gasoline, sanded and, again, cleaned before bonding the CFRP overlays. A more detailed description of the sample preparation and the results of the fatigue tests are given in Ref. [10]. For each of the adhesives, at least three fatigue tests were carried out. The samples were subjected to tensile load with stress ratio \(R=0.1\) and with the maximal force \(Fmax=47.5\) kN, which is equal to 0.93 \(\gamma c\).
## 2 Materials and Methods
### Electromagnetic Model for Evaluating the Radiated Emission  
A main goal of this paper is the evaluation of the direct radiated emission from an IC in the far-field zone, assuming to know the currents flowing from the IC into the package. These currents are  
Figure 3: The proposed circuital model to describe the subparts package + PCB in Figure 1. Here the route from two generic I/O pins to the final load is shown, passing through the package and the PCB.  
indeed the output of the circuit model developed in Section 2.1, hence, the electromagnetic problem is cast in terms of the emission of known currents in the far-field zone. This field may be computed at a distance \(r\) by superimposing the contribution of each current loop in the package (see Figure 4a), if the following conditions hold [23]:  
\[r_{c}<\frac{\lambda_{min}}{6\pi},r\gg r_{c}, \tag{4}\]  
being \(r_{c}\) the average value of the loop radius. For typical package dimensions of today's ICs (of the order of mm \(\times\) mm), Equation (4) is fulfilled for frequencies up to the order of GHz. In the same assumption, a very good approximation of a small loop is the infinitesimal loop (or the infinitesimal magnetic dipole), whose far fields (see Figure 4b) are given in the frequency domain by [23]:  
\[E_{\theta}(r,f)=I(f)\cdot\eta\beta^{2}A\frac{e^{-j\beta r}}{4\pi r}\sin\theta, H_{\theta}(r,f)=-\frac{E_{\theta}(r,f)}{\eta} \tag{5}\]  
where \(I(f)\) is the spectrum of the loop current, \(\eta=377\)\(\Omega\) is the intrinsic impedance, \(\beta\) is the wavenumber, and \(A\) is the loop area. Note that the presence of a grounded metallic layer at the opposite side of the board where the package will be mounted can be taken into account by applying the image theorem, thus, by taking into account the contribution coming from image currents located by symmetry at opposite sides of the ground plane. In principle, vertical tracts of the package-to-board interconnects should be also taken into account if the area of the corresponding loop currents is comparable to that of the horizontal loops in Figure 4a. However, this is not the case for the application studied in this paper, where the vertical tracts of the interconnects to the pins are much smaller in length with respect to the horizontal ones.
## 3 Current Harmonics according to Winding Patterns
### Electromagnetic Loss  
Table 3 shows the electromagnetic loss analysis results owing to current harmonics. Both winding methods have higher losses than conventional methods (sinusoidal current) when considering the current harmonics. Figure 8 shows the loss distribution according to the current waveforms. Among them, the distributed winding model showed the largest increase of 34% in the core loss case, and 35% for the eddy current loss. Accordingly, the more detailed analysis of the electromagnetic losses generated owing to the current harmonics was performed. The Steinmetz Equation for calculating the core loss is as the following Equation (13).  
\[P_{core}=P_{h}+P_{e}+P_{a}=k_{h}f_{e}B^{nt}+k_{e}f_{c}{}^{2}B^{2}+k_{a}f_{c}{} ^{1.5}B_{c}{}^{1.5} \tag{13}\]  
Figure 6: Dynamic simulation block diagram.  
Figure 7: (**a**) Phase current waveforms and (**b**) harmonic components according to currents.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Loss** & **Current** & **Concentrated Winding** & **Distributed Winding** & **Unit** \\ \hline \multirow{2}{*}{Core Loss} & Sinusoidal & 392.46 & 390.75 & W \\  & Harmonics & 514.5 & 524.4 & W \\ \multirow{2}{*}{Eddy Current} & Sinusoidal & 210.06 & 208.82 & W \\  & Harmonics & 275 & 282.2 & W \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of electromagnetic losses obtained using FEM analysis.  
Here, \(P_{hr}\), \(P_{e}\), and \(P_{a}\) are the hysteresis loss, eddy current loss, and the anomalous loss in the iron core, respectively; and \(k_{h}\), \(k_{e}\), and \(k_{a}\) are the core loss coefficients from the core loss data for steel to calculate the core loss in a stator core, of the frequency functions. \(n_{st}\) is the Steinmetz constant. \(f_{c}\) and \(B\) are the frequency of the external magnetic field and flux density in the core, respectively, and the eddy current loss was expressed as in Equation (14) [12].  
\[W_{mag}=\sum_{n}\int\frac{J_{n}}{2\sigma}dv \tag{14}\]  
Here, \(W_{mag}\) is the eddy current loss, \(J_{n}\) is the time harmonic current density of the nth harmonic, and \(\sigma\) is the conductivity. The loss Equations (12) and (13) prove that the current harmonics can cause additional electromagnetic losses when the harmonic order \(n\) increases as a result of comparing the electromagnetic characteristics considering the space harmonics of MMF and time harmonics of current according to the winding patterns, which confirmed that the concentrated winding method is more efficient in this model.
## 2 Problem Description  
In this proposed model, it is assumed that there are several facilities at different levels in the region under study. Given that the existing facilities have been established over a long period spanning several years and considering that changes have occurred in the level and concentration of demand for services by customers during these years, it is necessary to comprehensively evaluate all existing hubs. In this section, initially, the existing hubs in the region for transporting network equipment are classified into three levels, and then the demand coverage by these facilities is examined. If there is a justifiable change in the capacity or location of the facilities in terms of cost, these changes are made in the location and capacity of the existing facilities. Finally, a new structure of hub location is proposed in which the location and capacity of some hubs have changed, but in return, the demand coverage for telecom services has increased. Improving demand coverage is not only performed by examining the capacity level of existing hubs and adjusting their locations. In this article, three levels of capacity are also considered for the hubs, and if necessary, a hub is upgraded to a higher capacity level, or a new hub is located. To improve the quality of demand coverage for customers, the coverage radius is also considered for each hub. The coverage radius helps us allocate demand to hubs in such a way that the distance from the demand point to the hub is optimized and acceptable. In this article, the coverage radius is considered as a variable. Since the level of demand coverage is directly related to the distance from the demand point to the hub and the variable coverage cost, efforts are made to minimize the coverage radius of each hub. In improving the current situation, only changes to existing hubs are not addressed, and if there is a need for locating a new hub, a new hub is established. In this problem, we aim to examine the efficiency of existing hubs in terms of coverage capacity and locate new hubs with the goal of reaching a higher level of demand coverage, reducing costs, and maximizing the level of greenness in hub locations. To this end, in our analysis, we consider the economic feasibility of the following actions: establishing new hubs, removing previous or existing hubs, and increasing or decreasing the capacity of hubs.  
In this proposed model, the necessity of evaluating existing BTS hubs is emphasized to ensure that they meet current and future demand efficiently. The study incorporates dynamic demand patterns, which reflect the evolving telecommunication needs of urban and rural areas. By introducing a hierarchical hub structure, the model allows for flexibility in upgrading, downgrading, or relocating facilities based on economic feasibility and service coverage requirements. Additionally, environmental sustainability factors such as minimizing carbon emissions and reducing the ecological footprint of BTS hubs have been integrated into the evaluation criteria.
## 2 System Model
### Model of OFDM Multi-Carrier Signal  
Upon the serial-to-parallel conversion of the symbol stream representing the original information, \(N\) parallel symbol streams are generated. These streams are modulated by different subcarriers and then transmitted using OFDM through inverse Fourier transform to the designated radio frequency signal. The signal is then transmitted through the transmitter. Let \(X_{k}[l]\) denote the \(k\)-th OFDM transmission symbol on the \(l\)-th subcarrier. The total length of an OFDM symbol is denoted by \(G\), where \(G=N+D\). \(N\) represents the length of the useful symbols (sample points) and \(D\) denotes the length of the cyclic prefix (sample points). Due to serial-to-parallel conversion, the transmission time of \(G\) symbols is expanded to \(GT_{s}\), where \(T_{s}\) represents the period of symbol \(X[l]\), and \(GT_{s}\) is the duration of a single OFDM symbol, i.e., \(T_{sym}=GT_{s}\). Let \(\psi_{k,l}(t)\) represent the \(k\)-th OFDM signal on the \(l\)-th subcarrier.  
\[\psi_{k,l}(t)=\begin{cases}e^{j2\pi f_{l}(t-kT_{sym})},&0<t\leq T_{sym},\\ 0,&other.\end{cases} \tag{1}\]  
The expression for the baseband time-continuous OFDM signal is presented as  
\[x_{k}(t)=\sum_{i=0}^{k-1}\sum_{l=0}^{G-1}X_{l}(l)\psi_{k,l}(t). \tag{2}\]  
The baseband signal of OFDM, as represented by Equation (2), is sampled with the sampling time \(t=kT_{sym}+nT_{s}\), where \(T_{s}=\frac{T_{sym}}{G}\) and \(f_{l}=\frac{l}{T_{sym}}\). This results in the discrete-time expression for the OFDM symbol as  
\[x_{k}(n)=\sum_{i=0}^{k-1}\sum_{l=0}^{G-1}X_{k}(l)e^{j2\pi ln/G},n=0,1,\cdots,N -1. \tag{3}\]  
The baseband OFDM receive symbol expression can be readily obtained as  
\[s_{k}(t)=\sum_{k=0}^{k-1}\sum_{l=0}^{G-1}X_{k}(l)e^{2\pi f_{l}(t-kT_{sym})}, kT_{sym}<t<kT_{sym}+nT_{s}. \tag{4}\]  
Considering the bandlimited nature of the channel, the baseband OFDM receive symbol can be expressed as \(X_{k}(l)=a_{k,l}g_{a}(t-kT_{s})\), where \(a_{k,l}\) represents the corresponding level value and \(g_{a}(t-kT_{s})\) represents the pulse shape of the signal.  
The time-domain expression for the l-th sample of the k-th OFDM symbol with a cyclic prefix equals:  
\[c_{k,l}=\frac{1}{\sqrt{N}}\sum_{n=0}^{G-1}a_{k,n}e^{(j2\pi(1-D)n/N)},l=0,1, \cdots,G-1. \tag{5}\]  
Hence, under the condition of additive Gaussian white noise, the multicarrier OFDM signal receive model expression is \[r(t)=s_{k}(t)+n(t). \tag{6}\]  
In the expression, \(n(t)\) denotes a zero-mean Gaussian white noise, \(n(t)\sim CN(0,2\sigma^{2})\), where \(2\sigma^{2}\) signifies the power of the noise.
## 2 Materials and Methods
### Characterization
#### 2.3.2 Electrical Conductivity  
Electrical conductivity tests were carried out for the 3D printed circuits by obtaining the electrical resistance, \(R\), from the V-I (Voltage-Intensity) slope using a voltage range from 0 to 50 V with a Keithley 2410 source-meter unit, supplied by Keithley Instruments. Then, the electrical conductivity was obtained based on the geometry of the specimens by the following expression (1), where \(L\) is distance between electrodes and \(A\) the cross-sectional area of the specimen.  
\[\text{Electrical conductivity}=\frac{L}{A\cdot R} \tag{1}\]  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Layer height (mm) & 0.34 \\ Number of skirt loops & 2 \\ Printing speed (mm/s) & 7 \\ Travel speed (mm/s) & 25 \\ Extrusion multiplier & 0.6 \\ Nozzle diameter (mm) & 0.4 \\ Retraction (mm) & 0.5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Experimental parameters of 3D printing.  
Figure 2: 3D printed circuit.  
The two main objectives of the electrical conductivity tests were to evaluate the electrical conductivity of the circuits as a function of the number of printed layers (1 to 4 layers) and, on the other hand, to study the influence of the interface between printed layers on the electrical conductivity. Regarding the last objective above mentioned, the electrical conductivity was measured for the ribbons with 2 to 4 layers by comparing two different electrode configurations, as shown in Figure 3. Figure 3a shows an electrode configuration within the same printed layer, while Figure 3b shows an electrode configuration with the electrodes placed in the first and the last printed layers, to evaluate the effect of the interface between printed layers on the electrical conductivity. A minimum of three measurements were carried out for each test in order to determine the mean value and the standard deviation between measurements.