esa-sceva/satcom-chunk-collection huggingface dataset:
# Insights into Bending Stiffness Modeling of Elementary Flexure Hinges
## 5 Domain of Application of the Linear Model  
All the models presented so far are based on the assumption that the flexure hinge behaves like a beam. Therefore, it must be ensured that this assumption is admissible.  
It is certainly known that a three-dimensional solid behaves like a beam when one of its dimensions is about ten times larger than the other two. The flexure hinge under study has two constant dimensions (length and depth), whereas the height is variable.  
Since the flexure hinge has to be compliant with rotations about the z-axis, its depth has to result from a compromise between transversal compliance and bending stiffness.  
With reference to Figure 5 and Equation (18), the length and the mean height of the flexure hinge from \(-x\) to \(x\) are equal to:  
\[\begin{split} L(x)=2x\\ \overline{H}(x)=\frac{1}{2x}\int_{-x}^{x}2y(\tau)d\tau.\end{split} \tag{48}\]  
From the previous two relations, the ratio between the length and the mean height is given by:  
\[r(x)=\frac{4x^{2}}{\int_{-x}^{x}2y(\tau)d\tau} \tag{49}\]  
Because the formula for \(y(\widetilde{x})\) has a complex nonlinear expression, a Taylor series expansion is used for expression in Equation (49), up to a fourth-order truncation error, in order to be precise enough but at the same time have a simple resulting expression. It follows:  
\[r_{T}(x)=\frac{\rho}{\beta_{y}}\frac{x}{a_{x}}-\frac{\rho}{6\beta_{y}^{2}} \left(\frac{x}{a_{x}}\right)^{3} \tag{50}\]  
Imposing the derivative of Equation (50) equal to zero and solving the resulting equation, the position along the axis of the flexure hinge where the ratio \(r_{T}(x)\) is maximum can be found. In particular, it is:  
\[\begin{split} x_{r}=\pm a_{x}\sqrt{2\beta_{y}}\\ r_{T,x_{r}}=\frac{2\sqrt{2}}{3}\frac{\rho}{\sqrt{\beta_{y}}} \end{split}\quad. \tag{51}\]  
Assuming the condition \(r_{T,x_{r}}\geq 10\), the following condition must apply:  
\[\rho\geq 15\sqrt{\frac{\beta_{y}}{2}} \tag{52}\]From Equations (39) and (46), it is possible to evaluate the stress in \(x_{r}\). Assuming \(\alpha_{M}=1\) and \(\alpha_{Q}=0\), it follows:  
\[|\sigma_{\widetilde{x}_{r}}|=\frac{\beta_{y}^{2}}{2+\beta_{y}^{2}-2\sqrt{1-2 \beta_{y}}(1+\beta_{y})}\sigma_{st} \tag{53}\]  
where \(\widetilde{x}_{r}=\frac{x}{\alpha_{x}}\).  
A limit for \(\beta_{y}\) is obtained from the previous relation, in particular \(\beta_{y}\in\left]0;\frac{1}{2}\right]\). Evaluating the mean absolute value of the stress in Equation (53) in the range mentioned for \(\beta_{y}\), a value of about \(0.2\sigma_{sm}\) is obtained.  
It follows that the area of the flexure hinge with length equal to \(2a_{x}\sqrt{2\beta_{y}}\), namely \(2|x_{r}|\), is the most stressed. Therefore, it is correct to consider it as the reference hinge length to evaluate the depth to be assigned to the joint, not the whole length of the flexure hinge.  
Assuming \(\frac{2|x_{r}|}{l}=r_{T,x_{r}}\) and that condition Equation (52) is verified, then it follows:  
\[l\leq\frac{\sqrt{2}}{5}\sqrt{\beta_{y}}\;a_{x} \tag{54}\]
## 2 Data Analysis Methodology
### Data Visualization Using Activity Data Plotter  
The activity data plotter takes the input data and plots them automatically using MATLAB script, performing data visualization for a sensor dataset that includes data obtained from the accelerometer, the gyroscope, and the orientation sensor (expressed as quaternions). The script computes the vector magnitude (VM) and Euler's angles.  
* The vector magnitude (VM) is the size of the vector with accelerations as components: \[VM=\sqrt{x^{2}+y^{2}+z^{2}}\] (1)
* Euler's angles (\(\varphi\), \(\theta\), and \(\mu\)) refers to a set of three angles that are used for describing the orientation or movement of a rigid body (in the current research, that of the user) in a three-dimensional space. These three angles (pitch, roll, and yaw) are determined using the quaternion components of the orientation sensor: \[\begin{bmatrix}\varphi\\ \theta\\ \mu\end{bmatrix}=\left[\begin{array}{c}\arctan\frac{2(qq_{1}+q_{2}q_{3})}{1-2 (q_{1}+q_{2}^{2})}\\ \arcsin(2(qq_{2}-q_{3}q_{1}))\\ \arctan\frac{2(qq_{3}+q_{1}q_{2})}{1-2(q_{2}^{2}+q_{3}^{2})}\end{array}\right]\] (2)  
The script provides a comprehensive visualization of loaded data in both 2D and 3D spaces, separated for each activity type.
## 5 Performance Evaluation  
There are several criteria to evaluate binary classification methods, including accuracy, precision, recall, F-measure, and area under ROC curve (AUC). All these criteria are affected by a cut-off value on the predicted probability of the student performance except the AUC criteria. In general, the devalue cut-off value is 0.5, which may not be a suitable value while examining the performance of a classifier [90]. As a result, the AUC measure is not related to the cut-off value, which makes it a more suitable criterion to evaluate binary classification methods [91; 92].  
Moreover, ROC curves are not affected by any changes in class distributions. The AUC value is determined based on the relation between True Positive (TP) rate vs. False Positive (FP) rate. A confusion matrix is used to evaluate the final AUC value, as shown in Table 3.  
\[Sensitivity=TP_{rate}=\frac{TP}{P} \tag{20}\]  
\[Specificity=TN_{rate}=\frac{TN}{N} \tag{21}\]  
where \(P\) and \(N\) are variables present the actual positive and negative samples, respectively. Finally, AUC criteria helps researchers to generalize the obtained results [93].  
\begin{table}
\begin{tabular}{l r r r r r r} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**\#Features**} & \multirow{2}{*}{**\#Instances**} & \multicolumn{4}{c}{**Class**} \\ \cline{3-6}  & & & **Target** & **Binary Values** & **Minority Class** & **\%Minority** \\ \hline Data1 & 32 & 1044 & G3 & 0: pass, 1: fail & 1: fail & 0.22 \\ Data2 & 32 & 5820 & repeat & 1, 0: \textgreater{} 1 & repeat \textgreater{} 1 & 0.156 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Details of student evaluation datasets.  
Figure 12: Visualization of distribution of the target class based on the first two principal components of the features in the dataset.
## 5 Evaluation
### Methodology  
The two most obvious evaluation criteria are _what proportion of the suggested tags is appropriate for the image_ and _what proportion of the possible tags for an image was suggested_. These can be likened to the standard criteria of information retrieval, namely _precision_ and _recall_. In this case _precision_ assesses the number of correct tags found, while _recall_ determines the proportion of total tags identified. Formally, for a set of suggested tags \(S\) and ground-truth valid tags \(G\), they are defined as follows:  
\[Precision=\frac{|S\cap G|}{|S|}\]  
\[Recall=\frac{|S\cap G|}{|G|}\]  
One limitation of precision and recall in this scenario is that neither reflects the rank of the retrieved tags, _i.e._ a correct tag last in the suggestions list scores just as highly as a correct tag in first place. This is in direct conflict with the project's use scenario, as users tend to only have a limited amount of time and attention span, meaning that they are more likely to only look at the start of the list. This evaluation utilizes average precision, a variant of precision adapted from the information retrieval domain that places emphasis on retrieving correct tags early [30]. Essentially, it is an average of precisions calculated after each tag is suggested:  
\[Average\ Precision=\sum_{i=1}^{N}\left(\frac{1}{i}\sum_{j=1}^{i}R(t_{j})\right)\]  
\[With\ R(t)=\begin{cases}1,&\text{if tag t is relevant to the image, contained in G}\\ 0,&\text{if tag t is not relevant to the image, not contained in G}\end{cases}\]  
An overview of an algorithm's general performance may be obtained by calculating the _Mean Average Precision_ (MAP), _i.e._ the average of the average precision calculated for individual photos.  
Generally speaking, MAP was calculated for suggestions for each single start tag available in the data set. The result MAP values were averaged to give an indication of algorithm performance. The algorithm under test was required to suggest a certain number of tags for each photo belonging to the given start tag, with average precision being calculated using the user assigned tags as ground-truth valid tags. In the case of the NCP model, the algorithm was able to utilize information from all photos belonging to the start tag with the exception of the one being tagged. This is commonly referred to as _leave-one-out cross-validation_, a special case of _k-fold cross-validation_[31]. Furthermore, each photo under test was required to have at least C tags.
## 4 Numerical Results and Discussion
### Magnetic Flux Control and Power Flow Analysis  
For a wind turbine system, the induced output torque is influenced by the magnetic flux of the rotor. In particular, in low winds, the input power will fail to produce enough output torque to drive the generator. In this study, the synchronous generator is capable of controlling the magnetic flux, which can be expressed in terms of a preset operating speed.  
\[\phi=0.03+0.03a \tag{18}\]  
where \(\phi\) is the magnetic flux (\(Wb\)). The parameter \(a\) is  
\[a=\left(\dot{\theta}_{11}-\dot{\theta}_{op}\right)/\dot{\theta}_{op} \tag{19}\]  
where \(\dot{\theta}_{11}\) and \(\dot{\theta}_{op}\) are respectively the actual angular speed and the preset operating speed for the output shaft. In this study, the allowable variation range of the magnetic flux is \(\pm 20\%\) of 0.3. Figure 9 shows the variation of the magnetic flux vs. The angular speed \(\theta_{11}\).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Terms** & \multicolumn{6}{c}{**Values**} \\ \hline \hline \begin{tabular}{c} Gear Number \\ Number of teeth \\ \end{tabular} & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \begin{tabular}{c} Gear Number \\ Number of teeth \\ \end{tabular} & 60 & 80 & 90 & 20 & 30 & 30 & 20 \\ \hline \
\begin{tabular}{c} Gear Number \\ Number of teeth \\ \end{tabular} & 8 & 9 & 10 & 11 & 12 & 13 & 14 \\
\begin{tabular}{c} Gear Number of teeth \\ \end{tabular} & 20 & 30 & 30 & 20 & 70 & 70 & 75 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Gear number.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Gear** & **m (mm)** & **F (mm)** & **Gear** & **m (mm)** & **F (mm)** \\ \hline \hline
1 & 5 & 20 & 8 & 6 & 60 \\
2 & 5 & 20 & 9 & 6 & 60 \\
3 & 5 & 20 & 10 & 6 & 60 \\
4 & 6 & 60 & 11 & 6 & 60 \\
5 & 6 & 60 & 12 & 5 & 20 \\
6 & 6 & 60 & 13 & 5 & 20 \\
7 & 6 & 60 & 14 & 5 & 20 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Gear module and face width.  
Figure 8: Steps form for the wind speed simulation.  
Figure 15 shows the power flow for a wind speed of 9.5 m/s. In the case, two input powers of the proposed mechanism have the same value of 3.02 kW. At Input 1, the power splits as two branches of 2.01 kW and 1.01 kW for the upper and lower planetary gear trains, respectively. At the lower planetary gear train, a sub-total power of 4.03 kW flows into the upper planetary gear train, which gives the total output power of 6.04 kW. It is found that the dual inputs of wind power can be easily integrated for a single output by a feasible mechanical mechanism design, as the proposed system does.  
Figure 14: Torque variation for the input shaft.  
Figure 12: Torque variation for the output shaft.  
Figure 13: Rotational variation for the input shaft.
## 3 Mountain-Based Test Results
### Comparison of Closed-Loop Tracking and Open-Loop Tracking
or \(B\), the way to evaluate the capture capability of the OL/closed loop tracking, and the effect of OL tracking are:  
\[E^{A}_{o,c}=\sum_{j\text{ {\em ecc. rising events}}}(\alpha_{e}-\alpha_{i})+\sum_{j \text{ {\em ecc. setting events}}}(\alpha_{i}-\alpha_{e}) \tag{10}\]  
\[E^{B}_{o,c}=\sum_{j\text{ {\em ecc. rising events}}}(0-\alpha_{i})+\sum_{j \text{ {\em ecc. setting events}}}(0-\alpha_{e}) \tag{11}\]  
\[A=\frac{E^{A}_{o}-E^{A}_{c}}{E^{A}_{c}},B=\frac{E^{B}_{o}-E^{B}_{c}}{E^{B}_{c}} \tag{12}\]  
in which \(\alpha_{i}\), \(\alpha_{e}\) are the initial pitch angle and end pitch angle, respectively; \(E^{A}_{o,c^{\prime}}\), \(E^{B}_{o,c}\) are values to evaluate the capture capability of the OL/closed-loop tracking with strategy \(A\) or \(B\); and \(A\), \(B\) are the effects of OL tracking evaluated with strategy \(A\) or \(B\). According to observations from Table 1, the result of accumulating the seven-day data are:  
\[A=19.35\%,\,B=88.54\%. \tag{13}\]  
The results show that in the case of counting all angles, the OL improves the capture angle range of data volume by nearly 20%, and when only the negative angle is calculated, the OL improves the capture angle value by nearly 89%. The mountain-based situation is different from the onboard situation. We will continue to verify the actual capture effect in the future. However, there is no doubt that the fully OL capture method greatly improves the capture effect. We make the difference between the OL angle and the closed-loop angle (only the negative angle is counted), and the result is shown in Figure 12. There is no specific coupling relationship between OL tracking and closed-loop tracking, but the overall effect is better than closed-loop. The reason why there is no specific coupling relationship is due to the difference between the two capture methods. The angle difference is mainly concentrated between \(1^{\circ}\) and \(1.2^{\circ}\).
# Damage Assessment of Shear Wall Structures in an Earthquake-Blast Disaster Chain
## 4 Results and Discussions
### The Maximum Story Drift Ratio  
Figure 14 shows the maximum story drift ratio (DRmax) of the shear wall structure, which was used to assess the response of the shear wall structure under earthquake-explosion chain disasters. As shown in Figure 14, the \(DR_{max}\) of cases 1-3 did not exceed the elastic story drift limit (0.001 [30]), but at the onset of the blast loads, the \(DR_{max}\) of all cases exceeded the elastic story limit. Using earthquake-induced damage as a baseline for comparison, an explosion in the corner room of the first floor increased the \(DR_{max}\) by 20 times, and an explosion in the middle room of the first floor increased the \(DR_{max}\) by 22 times. The explosion in the middle room caused more damage. This is because the middle location likely allowed the blast wave to spread over a larger area than in the cases where the explosions were confined to the corner. The story drift ratios of the shear wall structure on the top three floors were equivalent to the case in which only an earthquake occurred. This lack of blast damage was expected, as the earthquake and explosion were independent events. Thus, since the seismic load did not cause plastic deformation and the blast load did not reach the top floors, the post-earthquake explosion did not cause any plastic deformation in the top three floors.  
Figure 14 also shows that an explosion on the sixth floor propagated to more areas of the structure and resulted in much more damage than when the explosion occurred in the first floor. In this case, when the explosion occurred in the corner of the sixth floor, the \(DR_{max}\) increased by 21 times, and an explosion in the middle caused an increase by 29 times. However, while the story drift ratio of the sixth floor was not significantly affected, the drift ratios of the fifth and seventh floors increased appreciably. Finally, as anticipated, the blast damage was most severe at the sixth floor. Table 9 lists the \(DR_{max}\) of 15 medium earthquake-blast disaster chains.  
Figure 14: Comparison of the maximum story drift ratio: (**a**) Hector Mine–blast on the first floor; (**b**) San Fernando–blast on the first floor; (**c**) Imperial Valley–blast on the first floor; (**d**) Hector Mine–blast on the sixth floor; (**e**) San Fernando–blast on the sixth floor; and (**f**) Imperial Valley–blast on the sixth floor.  
In summary, the time-history analysis demonstrated the severity of the potential damage that can result from an earthquake-explosion chain. Even though the probability of the occurrence of such a disaster chain is low, the proximity of the blast loads to fragile and critical elements of an earthquake-weakened shear wall structure that is not designed to resist blast loads can greatly increase the chances of structural failure.
## 4 WASPAS Multi-Objective Assessment
### Weight Calculation Using Entropy Method  
When confronted with multi-criteria decision-making, or MCDM, the entropy approach can be used to determine the relative weight of each criterion. It is a mathematical technique that uses the concept of entropy from the theory of information to objectively and effectively designate weights to various criteria. In MCDM situations, decision-makers must consider a number of factors prior to making a final choice. By determining the relative significance of various criteria, the entropy technique facilitates the process of designating weights to various criteria. The technique attempts to reduce the uncertainty associated with each criterion by balancing the weights [41].  
The entropy method is superior to other approaches because it is objective, straightforward, and time efficient. This method can process both quantitative and qualitative data, and it does not require any prior assumptions or restrictions regarding the criteria's relationship [42].  
Step 1: It is necessary to normalize arrays of decision matrix (performance indices) in order to acquire the project's final outcome via Equation (6):  
\[P_{ij}=\frac{x_{ij}}{\sum_{i=1}^{m}x_{ij}} \tag{6}\]  
Here, \(P_{ij}\) is the value from the matrix whose desired weights are calculated.  
Step 2: The formula for determining entropy as a measure of the result of the project is calculated using Equations (7) and (8):  
\[E_{ij}=-k\sum_{i=1}^{m}P_{ij}\ln P_{ij} \tag{7}\]  
In which, \(k=\frac{1}{\ln(m)}\) (8)  
Step 3: Determining the objective weight using the concept of entropy via Equation (9).  
\[W_{j}=\frac{(1-E_{ij})}{\sum_{i=1}^{n}(1-E_{ij})} \tag{9}\]
## 2 Optimization Strategies  
### What is Optimization?  
Optimization is a term that covers almost all sectors of human life and work; from scheduling of airline routes to business and finance, and from wireless routing to engineering design. In fact, almost all research activities in computer science and engineering involve a certain amount of modeling, data analysis, computer simulations, and optimization [15]. In a word, it is an applied science that tries to obtain the related parameter values which facilitate an objective function to produce some minimum or maximum value [2]. In the real world, resources are limited, time and money are always less than required, so optimization is far more important in practice [16, 17, 18].  
A typical optimization process consists of three components: model, optimizer and simulator (see Figure 1). The representation of the physical problem is done by using mathematical equations which can be converted into a numerical model. The formulation of a simple optimization problem can be done in many ways [15].  
For instance, the most popular way to do the formulation is to write a nonlinear optimization problem as:  
\[\text{minimize}\,f_{i}(x),(i=1,2,...,M), \tag{1}\]  
subject to the constraints:  
\[h_{j}(x),\qquad(j=1,2,...,J), \tag{2}\] \[g_{k}(x),<\ 0(k=1,2,...,K), \tag{3}\]  
where \(f_{i}\), \(h_{j}\) and \(g_{k}\) are nonlinear functions. Here the design vector \(x=(x_{1}\), \(x_{2}\),...) can be continuous, discrete or mixed in n-dimension [15]. The function \(f_{i}\) is called objective function (cost function). Here when \(M\) is 1, it is a single objective function. But when \(M>1\), the optimization is multi objective [19]. It is possible to combine different objectives into a single objective and in some cases it is a useful approach. It can be noted that the problem we formulated here is a minimization problem. The maximization problem can be written by simply substituting \(f_{i}(x)\) by \(\
eg f_{i}(x)\).  
Figure 1: A simple optimization process.  
When \(K=0\), the optimization turns out to be an equality constrained problem, as we have only the equality constraints left. Equality \(h(x)=0\) can be expressed as two inequalities: \(h(x)\leq 0\) and \(-h(x)\leq 0\). It is important to mention that a number of formulations in the optimization literature use constraints with only inequalities.  
We are dealing with nonlinear constrained problems when all the functions are nonlinear. In some particular circumstances when \(f_{i}\), \(h_{j}\), and \(g_{k}\) are linear, the problem itself becomes linear. In this case we can apply the broadly used linear programming methods. If the problem is of mixed type, meaning some design variables take discrete values, while other variables take real continuous values, it is often complicated to solve them, especially when the optimization problem is large-scale.
## 5 Applications of Thermal Images to Future Space Missions
### Optical Navigation for Approaching the Asteroid  
Thermal imaging is applicable to the optical navigation for approaching the target body during rendezvous or fly-by operations. After extracting dark frame images, the target asteroid Ryugu was a one pixel-sized body that was taken during the first light event of Ryugu on 6 June 2018 at a distance of \(2.5\times 10^{3}\) km, and it became larger and brighter until the arrival at the home position. It was predicted that the asteroid was able to be detected by the TIR at a distance within \(1.5\times 10^{4}\) km, comparing the relationship of thermal radiation intensity to distance for Earth-Moon observations in 2015 [23]. Thermal images have an advantage in optical navigation compared with optical images by ONC, since there are no other bright spots in the images such as background bright stars, bad pixels, or irradiation of solar wind particles or galactic rays, and there is no need to change the exposure time to avoid overexposure when the target is seen from a single pixel until a numerous pixel-sized body. Onboard functions of dark frame subtraction and binarization implemented in TIR allow optical navigation by data delivery to the guidance and navigation control system of the spacecraft.
###### Abstract  
The power flows in the unified power flow controller (UPFC) embedded system is mainly regulated by the two variables containing the magnitude and the phase angle of the output series inserted voltage (OSIV) of UPFC. Different value combinations of the two variables can form multiple regulation modes of OSIV, and the regulation principles and efficiencies for power flows are distinct by different regulation modes. This paper dedicates to research the regulation principles of active and reactive power flow gradients (PFG) to multiple characteristic independent variables (CIVs) at several selected critical points (SCP) of the system in different operation conditions. The CIVs contains the magnitude of OSIV, the phase angle of OSIV, and the phase difference of the system. First, multiple power flow regulation modes of OSIV are designed, the mathematical models of the PFG to each CIV at each SCP are established, and the theoretical principles for the PFG to each CIV at each SCP are analyzed and compared. Next, four typical operation conditions of the system and four regulation scenarios are assumed and case studies for the PFG to each CIV at different SCP are carried out. The test results at each SCP are analyzed both in the two-dimensional planes and three-dimensional spaces. The regulation principles and efficiencies of PFG to each CIV at different SCP are compared with each other and summarized, which can offer useful references for practical engineering and applications of UPFC.  
unified power flow controller (UPFC); output series inserted voltage (OSIV); power flow gradients (PFG); characteristic independent variables (CIVs); selected critical points (SCP); different operation conditions