esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Applications to Center-Based Clustering
### Robustness of Generalized Kullback-Leibler Centroids
```
input :A finite set \(\mathcal{P}=\{p_{1},\ldots,p_{n}\}\) of \(n\) points, the number of cluster representatives \(k\geq 1\), and an arbitrary divergence \(D(\cdot:\cdot)\) Output : Set of initial cluster centers \(\mathcal{C}=\{c_{1},\ldots,c_{k}\}\)  Choose \(c_{1}\gets p_{i}\) with uniform probability and \(\mathcal{C}=\{c_{1}\}\); for\(i\gets 2\) to \(k\)do  Pick at random \(c_{i}=p_{j}\in\mathcal{P}\) with probability \[\pi(p_{j})=\frac{D(p_{j}:\mathcal{C})}{\sum_{p\in\mathcal{P}}D(p:\mathcal{C})}\]  where \(D(p:\mathcal{C}):=\min_{c\in\mathcal{C}}D(p:c)\); \(\mathcal{C}\leftarrow\mathcal{C}\cup\{c_{i}\}\);  end for return\(\mathcal{C}\);
```  
**Algorithm 1** Generic seeding of \(k\)-means with divergence-based \(k\)-means++. The advantage of using a conformal Bregman divergence such as a total Bregman divergence [33] or \(I_{1}^{f,g}\) is to potentially ensure robustness to outliers (e.g., see Theorem III.2 of [33]). Robustness property of these novel \(I_{1}^{f,g}\) divergences can also be studied for statistical inference tasks based on minimum divergence methods [4,76].
## 3 Results and Discussion
### Classification and Validation
A previous study found that discriminant analysis (DA) can detect grass and broadleaf weed species with 70 to 100% accuracy [26]. The differences in the classification between weeds and sorghum in 2013 and 2014 were insignificant. The statistical analysis showed that most of the classification was at 100% for both years. Additionally, the different growth stages between week two and week four were not prominent. Weed discrimination with other species was investigated during pre-planting and found the overall accuracy above 95% [25]. It is of excellent significance to increase weed identification accuracy for pre-planting applications. The differences in results seen here were influenced by the growth stages and locations of the plants, as well as abiotic and biotic parameters [27]. Additionally, the spectral reflectance of plants depends on the weather conditions and the amount of sunlight received, due to the atmospheric conditions and azimuth [28]. The plants' morphology also affects their spectral reflectance, such as the shape and color of the leaves. These similar findings suggest that the environmental factors, microclimates, plant leaves, solar angles, and changing morphological and spectral properties are different at every growth stage, which will influence weed detection [29]. Humans are unable to differentiate between these plants features using the naked eye; thus, by using spectral signatures, the plants can be differentiated and classified using statistical analysis and machine learning [30; 31; 32]. A previous study showed that linear discriminant analysis (LDA) is more accurate compared to principal component analysis (PCA) in classifying _Sesbania herbacea (Mill.) [PERSON]_ (hempsebsania), _Ipomoea wrightiti_ (palm leaf morning glory), _Ipomoea lacunosa_ (pitted morning glory), _Sida spinoas_ (prickly sida), _Senna obtsifolia_ (sicklepod), and _Jacquemotita tamnifolia_ (small flower morning glory) species in soybeans [33]. A similar study found that weeds and wheat were successfully classified with 100% accuracy using partial least squares (PLS) analysis and linear discriminant analysis (LDA) [34]. The short-wave infrared (SWIR) wavelengths between 1445 and 2135 nm were used in the previous study. Compared to our study, wavelengths of up to 1000 nm were used; thus, in the future, it is recommended to use SWIR wavelengths for weed classification. In a study in New Zealand, hyperspectral imaging was used to detect weeds using machine learning (ML). This method was another way of detecting weeds quickly and accurately using the multi-layer perceptron method at 89% accuracy [26]; thus, hyperspectral imaging can be used in weed detection using ML as compared to object-based image analysis.
## Appendix A  
We demonstrate that within a proportionality factor the optimum value of the weights appearing in Equation (7) is \(w_{j}=\frac{a_{j}}{\sigma_{j}^{2}}\); all three quantities \(a_{j},\sigma_{j},w_{j}\) are assumed positive; note that we use \(j\) to indicate a specific index, and tacitly replace it with \(k\) whenever it becomes a dummy index in a sum. We wish to maximize  
\[\frac{\left(\sum_{k}w_{k}a_{k}\right)^{2}}{\sum_{k}w_{k}^{2}\sigma_{k}^{2}}- \lambda\left(1-\sum_{k}w_{k}\right) \tag{11}\]  
where \(\lambda\) is a Lagrange multiplier. The condition of zero partial derivatives with respect to each of the \(w_{j}\) and of \(\lambda\) yields:  
\[2a_{j}\left(\sum_{k}w_{k}\alpha_{k}\right)\left(\sum_{k}w_{k}^{2 }\sigma_{k}^{2}\right)-2w_{j}\sigma_{j}^{2}\left(\sum_{k}w_{k}\alpha_{k} \right)^{2}+\lambda\left(\sum_{k}w_{k}^{2}\sigma_{k}^{2}\right)^{2} = 0 \tag{12}\] \[\sum_{k}w_{k} = 1 \tag{13}\]  
Multiplying (12) by \(w_{j}\) and summing over \(j\), one has:  
\[2\left(\sum_{k}w_{k}\alpha_{k}\right)^{2}\left(\sum_{k}w_{k}^{2}\sigma_{k}^{2} \right)-2\left(\sum_{k}w_{k}^{2}\sigma_{k}^{2}\right)\left(\sum_{k}w_{k} \alpha_{k}\right)^{2}+\lambda\left(\sum_{k}w_{k}\right)\left(\sum_{k}w_{k}^{2 }\sigma_{k}^{2}\right)^{2}=0 \tag{14}\]  
hence \(\lambda=0\); and Equation (12), divided by \(2\sigma_{j}^{2}\
eq 0\), simplifies to  
\[\frac{a_{j}}{\sigma_{j}^{2}}\left(\sum_{k}w_{k}^{2}\sigma_{k}^{2}\right)-w_{j }\left(\sum_{k}w_{k}\alpha_{k}\right)=0 \tag{15}\]  
Summing over \(j\), and using Equation (13) yields  
\[\sum_{k}w_{k}\alpha_{k}=\left(\sum_{k}\frac{a_{k}}{\sigma_{k}^{2}}\right) \left(\sum_{k}w_{k}^{2}\sigma_{k}^{2}\right) \tag{16}\]  
which replaced in Equation (15) finally gives  
\[w_{j}=\frac{a_{j}/\sigma_{j}^{2}}{\sum_{k}a_{k}/\sigma_{k}^{2}} \tag{17}\]Note that in the special case when \(\alpha_{k}\) is the same for all \(k\), one has the familiar result that the minimum variance of an average is the one with \(w_{j}=\sigma_{j}^{-2}/\sum_{k}\sigma_{k}^{-2}\)[11].
# Identifying Earthquakes in Low-Cost Sensor Signals Contaminated with Vehicular Noise
## 4 Experimental Evaluation
### Experiment 2
However, it significantly outperforms the latter by achieving a precision score exceeding 30%, underscoring its capacity to accurately identify positive instances (true positives) while mitigating the occurrence of false positive errors. Moreover, our model attains a substantially improved F1 score, sur \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Accuracy** & **Precision** & **Recall** & **F1 Score** & **AUC Curve** \\ \hline
78\% & 78\% & 100\% & 88\% & 51\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance metrics for experiment 2. Figure 10: AUC for the proposed model. model by more than 20%. This superior F1 score attests to our model's ability to strike an optimal balance between precision and recall, making it a promising choice for various real-world scenarios. As shown in Figure 12, we can see how our model performed in real-world scenarios. The red color presents the space between the first point predicted as the earthquake to the last point predicted as the earthquake. The two vertical lines show the actual start and end of the earthquake (ground truth). When it comes to the start of the event, our model classifies the starting point exactly at the onset. As we can also observe, the model classifies the whole earthquake event, not only the starting point. The ending part of an earthquake is always a complex task so the model performs decently (regarding classification) on that as well. When comparing these results with the stochastic methodology (Section 4.4), we can see a big improvement in finding the earthquake events, not only on the metrics, but also in the actual usage of a model like this, which detects an earthquake event. While our cost-effective system, built on open hardware and software, offers an attractive alternative to pricier traditional seismographs, it comes with inherent limitations in the sampling rate, bit precision, and amplification. Our dataset, a combination of high-quality and low-cost recordings, presents an imbalance issue due to the significantly smaller proportion of low-cost data. This imbalance affects our model's outcomes. Additionally, the constraints tied to our DNN's architecture were expected, given its off-the-shelf nature. However, this architecture can be enhanced through increased parameterization. Figure 11: Comparison of metric scores. Figure 12: _Cont._
## 2 Configuration of the Remote Center Compliance (RCC) Mechanism
### Compliance Modeling
\right]= \left[ \begin{array}{ccc}\cos\theta&0&-\sin\theta\\ 0&1&0\\ \sin\theta&0&\cos\theta\end{array} \right] \tag{4}\]  
where \(\theta\) is also equal to the geometric parameter of initial inclined angle of the beam flexure, as shown in Figure 5. \(\mathbf{C}(\overrightarrow{OO_{1}})\) is the skew symmetric matrix corresponding to the position vector \(\overrightarrow{OO_{1}}=\left[ \begin{array}{cc}r_{x}&r_{y}&r_{z}\end{array} \right]\) expressed in \(O-XYZ\), and can be written as  
\[\mathbf{C}(\overrightarrow{OO_{1}})=\left[ \begin{array}{ccc}0&-r_{z}&r_{y} \\ r_{z}&0&-r_{x}\\ -r_{y}&r_{x}&0\end{array} \right]. \tag{5}\]  
According to the displacement vector \(\Delta\mathbf{q}\) at Point \(O\) and the stiffness matrix of the beam flexure, the \(6\times 1\) force vector \(\mathbf{F}_{1}\) applied to \(O_{1}\) can be denoted as  
\[\mathbf{F}_{1}=\mathbf{K}^{0}\Delta\mathbf{q}_{1}=\mathbf{K}^{0}\mathbf{J}_{1} ^{\mathrm{T}}\Delta\mathbf{q} \tag{6}\]  
Transforming the force vector \(\mathbf{F}_{1}\) from \(O_{1}-XYZ\) to \(O-XYZ\) yields the equivalent force vector \(\mathbf{F}_{10}\) applied to \(O\), which can be represented as  
\[\mathbf{F}_{10}=\mathbf{J}_{1}\mathbf{F}_{1}=\mathbf{J}_{1}\mathbf{K}^{0} \mathbf{J}_{1}^{\mathrm{T}}\Delta\mathbf{q} \tag{7}\]  
Figure 5: Coordinate system of the RCC mechanism. There are four beam flexures connecting to the end-effector with a radius of \(|OO_{1}|\) and an interval angle of \(\pi/2\). Hence, the relationship of the force and displacement with respect to the \(O-XYZ\) is derived as [17]  
\[\mathbf{F}=\sum\limits_{i=1}^{4}\mathbf{J}_{i}\mathbf{K}^{0}\mathbf{J}_{i}^{ \mathrm{T}}\Delta\mathbf{q} \tag{8}\]  
where  
\[ \begin{array}{l}\mathbf{J}_{2}=diag(\mathbf{R}_{z}(90^{\circ}),\mathbf{R}_{ z}(90^{\circ}))\mathbf{J}_{1},\\ \mathbf{J}_{3}=diag(\mathbf{R}_{z}(180^{\circ}),\mathbf{R}_{z}(180^{\circ})) \mathbf{J}_{1},\\ \mathbf{J}_{4}=diag(\mathbf{R}_{z}(-90^{\circ}),\mathbf{R}_{z}(-90^{\circ})) \mathbf{J}_{1}.\end{array}  \tag{9}\]  
\(R_{z}(\theta_{z})\) is the the rotation matrix around the \(Z\) axis of \(O-XYZ\), which is written as  
\[\mathbf{R}_{z}(\theta_{z})=\left[ \begin{array}{ccc}\cos\theta_{z}&-\sin \theta_{z}&0\\ \sin\theta_{z}&\cos\theta_{z}&0\\ 0&0&1.\end{array} \right]. \tag{10}\]  
The symmetric compliance matrix \(\mathbf{C}\) of the RCC mechanism is derived as  
\[ \begin{array}{l}\mathbf{C}=\left(\sum\limits_{i=1}^{4}\mathbf{J}_{i}\mathbf{ K}^{0}\mathbf{J}_{i}^{\mathrm{T}}\right)^{-1}\\ =\left[\begin{array}{cccccc}C_{X_{i}}&F_{X}&0&0&0&C_{X_{i}\,M_{Y}}&0\\ 0&C_{Y_{i}}&0&C_{Y_{i}\,M_{X}}&0&0\\ 0&0&C_{Z_{i}\,F_{Z}}&0&0&0\\ 0&C_{\theta_{X_{i}}\,F_{Y}}&0&C_{\theta_{X_{i}}\,M_{X}}&0&0\\ C_{\theta_{Y_{i}}\,F_{X}}&0&0&0&C_{\theta_{Y_{i}}\,M_{Y}}&0\\ 0&0&0&0&0&C_{\theta_{Z_{i}}\,M_{Z}}\end{array}\right]\.\end{array}  \tag{11}\]  
The first subscript in the compliance factors of Equation (11) indicates the deformation about a particular degree of freedom, while the second one points out the load producing the corresponding deformation [22].
# Ride Comfort Prediction on Urban Road Using Discrete
## 4 Results
### Correlations between DRI and MTVV
#### 4.2.1 Vehicle Speed  
Research revealed that ride comfort was strongly related to vehicle speed [16]. Passengers suffer from more discomfort at a higher speed. For urban roads, vehicle speed has a wide range due to complex traffic conditions; hence, four different speeds are discussed in this study: 40, 60, 80, and 100 km/h.
# On-Chip Reconstructive Spectrometer Based on Parallel Cascaded Micro-Ring Resonators
## 2 Principle and Design
When \(M\) is less than \(N\), the problem described by Equation (3) is underdetermined. Reconstruction algorithms such as compressed sensing and convex optimization can be applied to solve this underdetermined problem and recover a high-resolution incident light spectrum [21; 27]. In our work, we designed an ANN model based on residual blocks, referring to the algorithm in the literature [28], to complete the task of reconstructing the incident light spectrum. Additionally, we have modified the model architecture to reduce computational complexity and resource requirements. Specifically, we have replaced the multiple convolutional layers with a single fully connected layer while retaining residual connections. This modification streamlines the model architecture, making it more efficient and less resource-intensive, without compromising its performance in reconstructing the incident spectrum from the sampled signals. Compared to traditional methods, the spectrum reconstruction algorithm based on deep learning does not rely on prior knowledge of the incident spectrum and offers faster solving speed [20]. After obtaining the intensity vector \(I_{M\times 1}\) from Equation (3), we transform it by multiplying it with the pseudo-inverse matrix of the sampling matrix \(T_{M\times N}\) to obtain \(\widetilde{\Phi}\in\mathbb{R}^{N\times 1}\). This transformed vector is then used as the input for the ANN. Through training, the network learns the nonlinear mapping between \(\widetilde{\Phi}\) and the true spectrum \(\Phi\), resulting in the reconstructed spectrum \(\hat{\Phi}\in\mathbb{R}^{N\times 1}\). The ANN model we employed includes two fully connected layers and a residual connection from the input to the output. After the fully connected layer, a Gaussian Error Linear Unit (GeLU) is used as the activation function. Dropout follows the layer to reduce the overfitting of the model. The output of the last fully connected layer is added to the network's input and then fed into the regression output layer. The number of units in each fully connected layer is depicted in Figure 3. The output layer consists of 2001 nodes, representing the reconstructed spectral intensity. These nodes correspond to wavelengths ranging from 1450 nm to 1650 nm, with a uniform spacing of 0.1 nm between each wavelength point. During the training of the network, we employ the Mean Squared Error (MSE) as the loss function.
## 3 Results
### Accuracy and RMSE  
The mean percentage of accuracy values for IMU measurements showed varying degrees of agreement with MoCap data: flexion 72.1% (SD: 12.7%), extension 64.1% (SD: 23.5%), lateral bending 61.4% (SD: 16.8%), and rotation 92.4% (SD: 7.61%). These findings highlight that accuracy ranges from moderate levels for lateral bending to good or optimal  
\begin{table}
\begin{tabular}{c c} \hline Gender N (M/F) & 27 (11/16) \\ \hline Age (years) & 31.1 (11.0) \\ \hline Body mass (kg) & 64.9 (9.68) \\ \hline Height (cm) & 171 (8.46) \\ \hline BMI (kg/m\({}^{2}\)) & 22.1 (2.16) \\ \hline \end{tabular} Data are expressed in mean and standard deviation ().  
\end{table}
Table 1: Summary of descriptive statistics for demographic and anthropometric variables of interest expressed as mean (standard deviation).  
Figure 4: ROM distribution by movement and measurement system (MoCap and IMU).  
levels for rotation. RMSE values highlighted discrepancies across movements, with the largest error in flexion: 3.01\({}^{\circ}\) (SD: 1.32\({}^{\circ}\)), and the smallest in rotation: 1.09\({}^{\circ}\) (SD: 1.01\({}^{\circ}\)). The results indicate that the agreement between the two measurement systems ranged from acceptable (flexion) to negligible (other tasks) error across all analyzed movements. Data are summarized in Table 2.
## 4 Dynamics and Isolation Performance of the Vibration Isolator
### Vibration Isolation Performance under Different Excitations
#### 4.4.3 Vibration Isolation Performance under Random Excitation  
Using the displacement signal provided by the road surface to moving vehicles as the input excitation, the vibration isolation performance of the QZS vibration isolator under a random base excitation is analyzed. By virtue of the standard stated in [31], the power spectral density (PSD) function of road roughness \(G_{\text{q}}(n)\) can be given as:  
\[G_{\text{q}}(n)=G_{\text{q}}(n_{0})(\frac{n}{n_{0}})^{-W} \tag{29}\]  
where \(n\) is the spatial frequency; \(n_{0}\) is the reference spatial frequency taken as \(n_{0}=0.1\) m\({}^{-1}\), and \(W\) is the frequency index taken as \(W=2\). \(G_{\text{q}}(n_{0})\) is the road roughness coefficient, and \(G_{\text{q}}(n_{0})=64\times 10^{-6}\) m\({}^{3}\) when the B-class road profile is used.  
Since the road roughness is a stationary Gaussian random process with mean value of zero and traversal of various states, the target random process can be described by discrete spectrum. After non-dimensional processing, the simulated excitation signal \(\overline{Z}_{\tau}\) of the road roughness in time domain can be obtained as the curve shown in Figure 17a. Then, the time history curves of the displacement response of the QZS vibration isolator and its equivalent linear isolator are compared in Figure 17b when \(\overline{a}=0.45\), \(r=1\) and \(\xi=0.10\). The QZS isolator has good performance in isolating a random excitation, and the overall vibration of the system is significantly reduced. The equivalent linear vibration isolator only isolates the vibrations in high-frequency band, but the vibration peak value after isolation even exceeds the maximum value of the excitation.  
Figure 16: Effects of coefficient \(\varepsilon\) on root mean square (RMS) of displacement.  
Figure 17: Time history under random excitation. (**a**) Displacement excitation; (**b**) displacement responses of QZS and equivalent linear isolators.  
Figure 18 shows the PSD of the displacement responses of the vibration isolator before and after the NSC is introduced. It can be observed in the figure that the trend of the PSD curves changing with the response frequency is consistent. Except for the weak vibration isolation at \(\overline{f}\) =0.04, the QZS vibration isolators can successfully decrease vibrations over the frequency range. However, for the equivalent linear vibration isolator, the vibration deteriorates when \(0.11<\overline{f}<0.23\), and its vibration isolation capability will not achieve that of the QZS isolator until \(\overline{f}\) is higher than 1. Besides, as shown in Figure 19, adding the NSC to the linear vibration isolation system makes the RMS of the displacement response decrease from 0.161 to 0.079. These demonstrate that the proposed QZS vibration isolator can also obtain better performance under random excitations.
# Numerical Simulation of the Hydrodynamic Performance and Self-Propulsion of a UUV near the Seabed
## 3 Numerical Methods  
To evaluate the hydrodynamic performance of the bare UUV and the self-propelled UUV, as well as the self-propulsion performance near subsea, the ANSYS FLUENT 17.0 was used to solve the governing equations. The Moving Reference Frame (MRF) model and \(SST-kw\) turbulence model are used. The governing equations are discretized by the finite-volume method, where convective and diffusive terms in the equations are discretized with second-order-upwind differential format, central differential format, respectively. To speed up the convergence, the Couple method is used to solve the discrete equations.
## 4 Results and Discussion
### Roof Displacement Trajectory Analysis  
To investigate the roof motion of the WGC, the displacement trajectory of the roof during the monitoring period is presented in this section on the basis of the horizontal displacement time series of the roof in the north-south and east-west directions obtained in the previous section, and the results are shown in Figure 10. As shown in Figure 10, the color bar on the right represents the time change, the negative value on the vertical axis denotes the westward movement, and the negative value on the horizontal axis indicates the northward movement. As illustrated in Figure 10, during the monitoring period, the general direction of roof movement was first toward the northwest for approximately 3 h, then moved toward the southeast to the maximum value, and subsequently moved along the northwest to the maximum value, and finally moved along the southeast to approximate the initial position (approximately a few millimeters deviation with respect to the initial position). The oscillation magnitude of the roof is basically less than 20 mm. To analyze the oscillation rule of the roof for a whole day, Figure 11 shows the displacement trajectory of the roof from 00:00 to 24:00 on 6 July 2017. Figure 11 intuitively reflects the diurnal oscillation rule of the roof, and the displacement trajectory is accompanied by slight fluctuation when it moves with time, which may be caused by the combined influences of construction vibration, wind load, and other factors.  
Figure 9: IBIS-S-derived horizontal displacement time series in east–west **(a)** and north–south **(b)** directions at 300 m height of the WGC. The red line indicates the displacement time series without denoising, and the black line denotes the displacement time series after denoising.