esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Volterra Integro-Differential Operators of Convolution Type  
In the previous two sections, we assume that inverse linear operator \(V^{-1}\) is known a priori. However, finding the inverse of a Volterra integro-differential operator is not always an easy task. In this section, we look at the special case where \(X=C[0,b]\), the Volterra integral operator in (6) is of convolution type, namely,  
\[Ku=\sum_{i=0}^{n}\int_{0}^{x}k_{i}(x-t)u^{(n-l)}(t)dt,\]  
and the vector of functionals \(\Phi(u)\) in (11) is as follows:  
\[\Phi(u)=\text{col}(\Phi_{1}(u),\Phi_{2}(u),\ldots,\Phi_{n}(u))=\text{col}\Big{(} u(0),u^{\prime}(0),\ldots,u^{(n-1)}(0)\Big{)}. \tag{23}\]  
In this case, the inverse operator \(V^{-1}\) of the linear Volterra integro-differential operator  
\[ \begin{array}{rcl}Vu&=&Au-Ku,\\ \mathcal{D}(V)&=&\{u:u\in C^{n}[0,b],\ \Phi(u)-\mathbf{N}\Theta(u)=\mathbf{0}\} \end{array}  \tag{24}\]  
can be constructed analytically using the Laplace transform for certain classes of functions as it is shown below. First, we recall the following definitions and properties about the Laplace transform: For a function \(f(x)\in C[0,\infty)\) of exponential order, that is, there exist real constants \(\gamma\) and \(M\) such that \(|f(x)|\leq Me^{\gamma x}\) for all \(x\geq 0\), the Laplace transform of \(f\) defined by  
\[F(s)=\mathcal{L}\{f\}=\int_{0}^{\infty}e^{-sx}f(x)dx,\]  
exists for all \(s>\gamma\). Laplace transform operator \(\mathcal{L}\) is linear and injective. For any two functions \(f(x)\) and \(g(x)\) of exponential order and any real constants \(a\) and \(b\),  
\[\mathcal{L}\{af+bg\}=a\mathcal{L}\{f\}+b\mathcal{L}\{g\},\]  
and  
\[f(x)=\mathcal{L}^{-1}\{F\}.\]  
The convolution of \(f\) and \(g\) is defined as  
\[(f*g)(x)=\int_{0}^{x}f(x-t)g(t)dt,\]  
and holds  
\[\mathcal{L}\{f*g\}=\mathcal{L}\{f\}\mathcal{L}\{g\}).\]  
For a function \(f(x)\in C^{n}[0,\infty)\) and its derivatives \(f^{(i)}(x)\in C[0,\infty)\), \(i=1,2,\ldots,n\), of exponential order, the Laplace transform of the \(n\)th derivative \(f^{n}(x)\) exists and is given by  
\[\mathcal{L}\{f^{(n)}\}=s^{n}\mathcal{L}\{f\}-\sum_{\ell=1}^{n}s^{n-\ell}f^{( \ell-1)}(0), \tag{25}\]  
see, for example, [36] and some new developments in [37]. We prove the following lemma. Lemma 1: _Let \(u^{(i)}(x)\), \(k_{i}(x)\), \(i=0,1,\ldots,n\), and \(f(x)\) be continuous functions of exponential order. Then, the equation_  
\[Au-Ku=f, \tag{26}\]  
_is equivalent to_\[u=\hat{p}\Phi(u)+\hat{f}, \tag{27}\]  
_where \(\Phi(u)\) is the functional defined in (23), and_  
\[F(s) = \mathcal{L}\{f\},\quad K_{i}(s)=\mathcal{L}\{k_{i}\},\,i=0,1,\ldots,n,\] \[Q(s) = \frac{1}{\sum_{i=0}^{n}(a_{i}-K_{i}(s))s^{n-i}},\] \[\mathcal{L}\{af+bg\}=a\mathcal{L}\{f\}+b\mathcal{L}\{g\},\]0 \[\mathcal{L}\{af+bg\}=a\mathcal{L}\{f\}+b\mathcal{L}\{g\},\]1 \[\hat{p} = \big{(} \begin{array}{cccc}\hat{p}_{1}&\hat{p}_{2}&\cdots&\hat{p }_{n}\end{array} \big{)},\quad\hat{p}_{\ell}=\mathcal{L}^{-1}\{Q(s)P_{\ell}(s) \},\quad\ell=1,2,\ldots,n. \tag{28}\]  
Proof.
# Nanomaterials in Photocatalysis: An In-Depth Analysis of Their Role in Enhancing Indoor Air Quality
###### Abstract  
Since people spend most of their time in indoor environments, they are continuously exposed to various contaminants that threaten human health. The air quality in these settings is therefore a crucial factor in maintaining health safety. In order to reduce the concentration of indoor air pollutants and improve air quality, photocatalytic oxidation has drawn the attention of researchers. This study aims to provide a comprehensive view of the nanomaterials used in the photocatalytic oxidation of the most common pollutants in indoor environments. The effects of various parameters like humidity, airflow, deposition time, and light intensity were also evaluated, as they can significantly influence photocatalytic reactions. The most common nanomaterials used in photocatalysis are TiO\({}_{2}\)-based and, in this study, they were classified and examined based on their morphology. TiO\({}_{2}\) doping with metals and non-metals has demonstrated an enhancement of its adsorption properties and photocatalytic efficiency for the removal of several pollutants. The role of carbon-based nanomaterials in photocatalysis was also evaluated due to their adsorption capabilities towards various pollutants. In addition, other less common photocatalysts such as ZnO, MnO\({}_{2}\), WO\({}_{3}\), CeO\({}_{2}\), and CdS also exhibited high photocatalytic activity for pollutant degradation. Applications of these photocatalysts in air purifiers, paints, and building materials e.g., concrete, glass, and wallpapers, lead to efficient reduction of pollutants in indoor settings.  
photocatalysis; nanomaterials; indoor air quality (AIQ); titanium dioxide (TiO\({}_{2}\)); volatile organic compounds (VOCs); photocatalytic oxidation; doping techniques; reactive oxygen species (ROS); environmental remediation; semiconductor photocatalysis +
Footnote †: journal: Applied sciences
# A Hybrid Data-Fusion System by Integrating CFD and PNN for Structural Damage Identification
## 2 Novel Hybrid Data-Fusion System
### Single PNN Damage Detection Model
#### 2.2.2 G-P Algorithm of Correlation Dimension  
There are different kinds of approaches to define FD (Fractal Dimension) in fractal geometry; the most recognized is Hausdorff's dimension. Correlation fractal dimension was used as the feature parameter in this paper for damage detection.  
For an \(N\)-point time series \(\{x_{1},x_{2},\dots,x_{N}\}\), the method of delays reconstructs the attractor dynamics by using delay coordinates to form multiple state-space vectors, \(Y_{i}:\)  
\[Y_{i}=[x_{1},x_{i+\tau},\cdots,x_{i+(m-1)\tau}]^{T},i=1,2,\dots,N_{m} \tag{1}\]  
where \(N_{m}=N-(m-1)\tau\), \(Y_{i}\) stands for the reconstructed state space vector, \(m\) is the embedding dimension, \(\tau\) is lag time measured in units of sampling interval.  
Following reconstruction, the correlation integral \(C_{m}(r)\) is defined in the \(m\)-dimensional reconstructed space as the probability of finding a pair of vectors whose distance is not larger than \(r:\)  
\[C_{m}(r)=\frac{2}{N_{m}(N_{m}-1)}\sum_{i,j=1}^{N_{m}}H(r-r_{i,j}),i\
eq j, \tag{2}\]  
Moreover:  
\[C(r)\propto r^{D_{2}}\ r\to 0 \tag{3}\]  
where \(H(x)\) is the Heaviside Step function \([H(x)=1\) for \(x>0\) and \(H(x)=0\) for \(x\leq 0]\) and \(r\) is the distance parameter, \(r_{i,j}\) is the distance between two reconstructed vectors, which is computed using the Euclidean norm:  
\[r_{i,j}=\left\|Y_{i}-Y_{j}\right\|=\left[\sum_{l=0}^{m-1}\left(x_{i+l\tau}-x_{ j+l\tau}\right)\right]^{\frac{1}{2}} \tag{4}\]  
The correlation dimension \(D_{2}\) is defined as:  
\[D_{2}(m)=\lim_{r\to 0}\frac{\ln C_{m}(r)}{\ln r} \tag{5}\]  
Particularly worth mentioning is that the computational precision of correlation dimension is influenced by lag time and embedding, but beyond that, data length and noise levels can also influence it. A detailed discussion can be found in Reference [23].
# Vibration Parameters Identification of Rotating Blades Based on Blade Tip-Timing Sensor Waveforms
## 4 Identification Accuracy Analysis of Waveform Mapping Method
### Identification Accuracy Analysis of Double-Sensors Waveform Mapping Method  
The influence of excitation orders on the average error of the double-sensor waveform matching method with different SNR is shown in Figure 8. It can be found from Figure 8a-e  
Figure 7: Influence of excitation order on the average error of single-sensor waveform identification under different SNR: (**a**) SNR 40 db; (**b**) SNR 50 db; (**c**) SNR 60 db; (**d**) SNR 70 db; (**e**) SNR 80 db; (**f**) SNR 90 db.  
that when the SNR is 20 dB, 30 dB, 40 dB, 50 dB and 60 dB, and the excitation order is \(N_{e}\geq 18\), \(N_{e}\geq 7\), \(N_{e}\geq 6\), \(N_{e}\geq 5\) and \(N_{e}\geq 1\), respectively, the excitation order can be accurately identified by the double-sensor waveform matching method, and the accuracy of the identified initial phase, amplitude and constant offset meet the requirements. The relative error of vibration constant offset identification is the largest, the relative error of initial phase is in the middle and the relative error of vibration amplitude is the smallest. As the SNR becomes smaller, the lower the accuracy of the signal, the smaller the range of excitation order accurately identified. This method can accurately identify all excitation orders when the SNR is 60 db.
# Modeling and Simulation of a Wave Energy Converter _Nwave_
## 3 Modeling of the Device's Dynamics
### Buoy-Counterweight Modeling
\begin{array}{l}f_{ex}\left(t\right)=\frac{1}{2\pi}\int_{-\infty}^{\infty}f _{ex}\left(\omega\right)e^{i\omega t}d\omega,\\ f_{ey}\left(t\right)=\frac{1}{2\pi}\int_{-\infty}^{\infty}f_{ey}\left(\omega \right)e^{i\omega t}d\omega,\\ f_{e\theta}\left(t\right)=\frac{1}{2\pi}\int_{-\infty}^{\infty}f_{e\theta} \left(\omega\right)e^{i\omega t}d\omega.\end{array}  \tag{7}\]  
\(\psi\) is the wave elevation and \(\hat{f}_{e}=\left[f_{ex},f_{ey},\hat{f}_{e\theta}\right]\) and \(f_{e}=\left[f_{ex},f_{ey},f_{e\theta}\right]\) are the summation of the Froude-Krylov force and diffraction force vector (or named the excitation force) in the frequency domain and its kernel function in the time domain, respectively. We set the negative sign in front of \(f_{ex}\) in (6) because the wave progresses to the left, as seen in Figure 1.  
\(F_{r}\) is the radiation force vector and is expressed as follows:  
\[F_{r}=\int_{-\infty}^{t}\left[f_{rx}\left(t-\tau\right)^{T}\ f_{ry}\left(t- \tau\right)^{T}\ f_{r\theta}\left(t-\tau\right)^{T}\right]^{T}\dot{X}\left( \tau\right)d\tau, \tag{8}\]  
where:  
\[\begin{array}{l}f_{rx}\left(t\right)=\frac{2}{\pi}\int_{0}^{\infty}\left\{ \hat{R}_{x}\left(\omega\right)+i\omega\left(\upmu_{x}\left(\omega\right)-\upmu _{x}\left(\infty\right)\right)\right\}\cos\left(\omega t\right)d\omega,\\ f_{ry}\left(t\right)=\fracwhere:  
\[k_{y} =\pi\rho_{w}gR^{2},\] \[k_{\theta} =\frac{\pi}{4}\rho_{w}gR^{4}.\]  
Here, \(\rho_{w}\) is the density of the seawater. \(k_{\theta}\) is the spring constant when the buoy rotates by \(\theta\) of the small displacement in the pitching direction and is obtained as follows:  
\[k_{\theta} =2\rho_{w}g\int_{0}^{R}2r^{2}\sqrt{R^{2}-r^{2}}dr=\frac{\pi}{4} \rho_{w}gR^{4}.\]  
When substituting (1) and (2) into (3), we can obtain the combined dynamics of counterweights and the buoy, expressed as follows:  
\[\left\{M_{b}+HE_{1}\right\}\dot{X}\left(t\right)+F_{r}\left(t\right)+K_{h}X \left(t\right)=F_{ex}\left(t\right)+H\left(E_{2}+E_{3}\right), \tag{11}\]  
where:  
\[E_{1} =\left[ \begin{array}{cc}-m_{1}\cos q_{1}&-m_{1}\sin q_{1}&m_{1} r\sin\left(q_{1}-\theta\right)\\ m_{2}\cos q_{2}&-m_{2}\sin q_{2}&-m_{2}r\sin\left(q_{2}+\theta\right)\end{array}  \right],\] \[E_{2} =\left[ \begin{array}{c}m_{1}g+f_{1}\\ m_{2}g+f_{2}\end{array} \right],\] \[E_{3} =\left[ \begin{array}{c}m_{1}\left\{r\dot{\theta}^{2}\cos\left( q_{1}-\theta\right)+l_{1}q_{1}^{2}\right\}\\ m_{2}\left\{r\dot{\theta}^{2}\cos\left(q_{2}+\theta\right)+l_{2}q_{2}^{2}\right\} \end{array} \right].\]
# Numerical Analysis of a Spiral Tube Damping Busbar to Suppress VFTO in 1000 kV GIS
## 2 The Suppression Mechanism of the New Method  
Several studies have shown that VFTO is generated as a superposition of multiple different reflected electromagnetic waves with complex nonharmonic time dependence and covers a wide frequency range from 100 kHz to 100 MHz [27]. The wavefront steepness, amplitude, and high-frequency components of VFTO can be suppressed by inductance and resistance. Based on this, this research proposes a VFTO suppression method--the spiral tube damping busbar--located before the disconnector switch (DS), as shown in Figure 1b. At the rated frequency, the damping busbar transmits current and voltage waves like a normal busbar, but when VFTO passes through the damping busbar, it will be suppressed. Also, the energy of the travelling waves is consumed by the resistance. When the resistance and inductance of the damping busbar match each other, the biggest wave energy consumption can be obtained and the best VFT damping can be achieved.
## 4 Results and Discussion
### Experiment with Random Test Cases
#### 4.1.4 RFR  
Finally, similar models were built with Random Forest Regression (RFR) for the estimation of glucose level and performances were evaluated using the same metric. RFR models are built with estimator trees/nodes and in this study, the total number of trees/nodes was increased up to 70 for all the models to identify the optimum number of trees required for the prediction with the lowest error. Some sample leaves were also added for the improvements and the total number was set to six. The SEP of RFR models built with different features against the number of estimator tress/nodes can be found in Figure 12. The prediction error for all the RFR models decreased with the increase in the number of trees/nodes. This reduction in SEP was comparatively sharp for the model built with first derivative features particularly for the first 15 trees. The lowest SEP recorded for different models along with the number of trees required is provided in Table 5. Notable in the table is that RFR model built with first derivative features had the lowest SEP of 21.88 mg/dL with requiring 25 trees to estimate. The model built with second derivative characteristic features had a similar prediction error of 22.11 mg/dL, though it required nearly double the number of estimators.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Features** & **SEP (mg/dL)** \\ \hline
1 st Derivative & 18.58 \\
2 nd Derivative & 18.74 \\
2 nd Derivative Characteristics Points & 18.52 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of performances of different SVR models.  
Figure 11: SEP of different Support Vector Regression (SVR) models against the \(\varepsilon\) values.  
Figure 12: SEP of different Random Forest Regression (RFR) models against the number of estimator tress.
## 6 Sensor Network Traffic Measurement  
In order to show the benefits of the proposed system, in this section we compare the traffic measurement provided by a single sensor node that takes images of a 360 \({}^{\circ}\)of view from the vineyard field and transmits them to a central server, in order to analyze the images, with our sensor node that only sends one image (when it founds a bad leaf while going around 360 \({}^{\circ}\)). In order to have enough image quality, the images had a resolution of 640 \(\times\)480 pixels and a frame rate of 30 fps. No audio was transmitted. Figure 18 shows a comparison of two video bit rates (4 Mbps and 512 kbps) with our system, which sent a picture of 640 \(\times\)480 pixels. The camera needed 120 seconds to make a round of 360 \({}^{\circ}\). We can see that there are more bytes sent to the network for the 4 Mbps video stream. There is a  
Figure 17: Four examples of detections in images taken from different distances. In each case, we show the original image in the first column, the final detection mask obtained in the second, and the masked image in the third. **(a)** An example of an image with large leaves. **(b)** and **(c)** Examples of medium leaf size. **(d)** Example of small leaf size.  
mean value of 146,130.64 bytes per second. When the 512 kbps is sent there is a mean value of 74,785.76 bytes per second. In our case, the picture was sent in the 20 th second. There are other packets in the network because of the regular procedure of the WSN. In our case there is a mean value of 4,259.86 bits per second. Now we can see that, in terms of bytes transmitted, there is a decrease of 97.09% from the 4 Mpbs to our system and a decrease of 94.30% from the 512 kbps to our system. Bearing in mind that the most power consumption issue in a sensor to transmit bytes through the wireless interface [53], we can state that our system saves energy.  
Now, in Figure 19, we compare the number of packets sent to the network for the 4 Mbps and the 512 kbps video streams with our system. We can see that there are quite less packets sent to the wireless in our system. Only the forwarded messages and the image sent in the 20 th second can be seen in the network. 4 Mbps video stream is the one that sends more packets.  
These measurements show that our system saves energy because there are less packets and less bytes transmitted to the wireless medium.  
Figure 19: Packets comparison when there is 4 Mbps video stream, 512 kbps video stream and our system.  
Figure 18: Bytes comparison when there is 4 Mbps video stream, 512 kbps video stream and our system.
# An Indoor Collaborative Coefficient-Triangle APIT Localization Algorithm
## 4 Simulation and Analysis of Results
### Positioning Error of the Proposed Localization Algorithm  
In a WSN positioning system, the proportion of anchor nodes has a great influence on the performance of the localization algorithm. The experiments in [25] were conducted as follows:  
In the experiments, assume that the weighting coefficients of the mean value and the standard deviation are \(\alpha=0.5\) and \(\beta=0.5\). The positioning errors of the CCAL algorithm, RSSI algorithm, IAPIT algorithm [26] and APIT algorithm were determined by varying the ratio of the anchor nodes and the communication radius of the unknown nodes.  
Simulations of the CCAL algorithm, RSSI algorithm, IAPIT algorithm, and APIT algorithm were carried out when the communication radius of unknown nodes remained 30 m and the proportion of anchor nodes varied in a wider range. Figure 8 shows the resulting curves of the node positioning errors of the localization algorithms with the increase in the proportion of anchor nodes.  
It is shown in Figure 8 that the CCAL algorithm had the best performance. Generally, the positioning error of CCAL is 15% smaller than that of APIT, 13% smaller than that of the RSSI algorithm, and 8% smaller than that of the IAPIT algorithm. This is because the CCAL algorithm introduces legality testing to the estimated unknown nodes, which avoids the effect of those nodes with large positioning error.  
Figure 8: Positioning error curves with the proportion of anchor nodes varying.  
Figure 7: Curves of the localization coverage rate with various communication radii of unknown nodes.  
Simulation was also carried out when the proportion of anchor nodes remained 20% and the communication radius of unknown nodes varied. The results are shown in Figure 9.  
As shown in Figure 9, the positioning errors of four algorithms were reduced when the communication radius of unknown nodes increased, and the positioning error of the CCAL algorithm was the smallest, i.e., 5% smaller than that of IAPIT, 10% smaller than that of RSSI, and 14% smaller than that of APIT. This is because when the communication radius of unknown nodes increases, the number of neighboring anchor nodes and valid triangles increases, and the positioning error decreases.
## 3 Modeling Framework
### Aerodynamic Corrections via CFD
#### 3.4.2 Thrust Variation Results  
The CFD analysis yielded average thrust variation values relative to the reference condition (free-flight hover), summarized in Table 2.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scenario** & **Constraint Applied** & **Parameter Affected** & **Effect on Energy** \\ \hline S1 & None (ideal conditions) & – & Baseline \\ \hline S2 & Delivery time window & \(v_{h}\uparrow\) & Moderate increase \\ \hline S3 & Aerodynamic disturbance & \(F_{T}\uparrow\) & Significant increase \\ \hline S4 & Early bus rejoin & \(t_{h}\downarrow,v_{h}\uparrow\) & Maximum increase \\ \hline \hline \end{tabular}
\end{table}
Table 1: Overview of the Four Mission Scenarios.  
To simplify integration into the energy model, \"average correction coefficients\" were derived for each flight segment of the delivery mission:  
* **+5.14%** for takeoff and landing phases near static structures (used in phases A-1, 2-B, B-3, and 4-C).
* **-12.55%** for hovering over moving vehicles (used in segments 1-2 and 3-4).
* **-7.00%** for undisturbed horizontal cruise (nominal condition).  
Note that during segments 1-2 and 3-4, the drone is assumed to be affected 20% of the time by moving vehicle wake (scenario 2) and 80% by open-air cruise conditions. The weighted average thrust variation for these segments is thus:  
\[\Delta F_{1-2,3-4}=0.2\cdot(-12.55\%)+0.8\cdot(-7.00\%)=-8.11\% \tag{7}\]
# Secure Video Communication Using Multi-Equation Multi-Key Hybrid Cryptography
## 4 Experimentation
### End-to-End Decryption Delay  
This section has looked at how long it takes for the receiver-side pipeline to process data. The receiver application receives the video chunks that have been encrypted, and it decrypts them in the order that they were received. Later, the chunks are assembled and displayed on a certain device. In this section, the length of time required for this processing cycle has been taken into consideration. Due to the fact that the decryption process is affected by the transmission media, receiver applications are required to wait until they have received the complete chunk before beginning to process it. When compared  
Figure 7: End-to-end encryption delay (Compared with Multi-Key [13]).  
to encryption, the latency could potentially become even longer. The time taken by the proposed method is compared with the method discussed in [13] and the results are shown in Figure 8.
# Multi-Source Data Fusion for Vehicle Maintenance Project Prediction
## 2 Related Work  
Predicting vehicle maintenance projects is a complex endeavor, involving the forecasting of future maintenance needs using historical maintenance records and fundamental vehicle information, which constitutes a quintessential time series prediction task. Accordingly, we will offer a comprehensive description of the principal time series prediction techniques. Time series prediction techniques can be classified into traditional approaches, machine learning-based methods, and deep learning-based techniques.
## 4 Actual Detected Temperature and Numerical Simulation Results
### Finite Element Simulation Results
The thermal flux distribution, displayed in Figure 14d, shows a similar process with the fluid field that the main heat flux is basically along the windings and reaches the highest value in the top area (the total heat exchange along the fins is also very active but it is not obvious when split into each one). The internal heat convection process is almost completed by the circulating oil and it is thus not strange that these two field simulations share a similar distribution. Figure 14: Transient simulation results of (**a**) temperature field (**b**) fluid field (**c**) vector diagram of oil stream and (**d**) thermal flux distribution. The vector diagram of the oil streams is displayed in Figure 15, where different perspectives are presented to aid further understanding. The flow vectors exhibit a same whole-region oil circulation with the aforesaid process. Indeed, the relatively good cooling conditions in the winding top area would have a considerable impact on the hotspot locations, which is usually ignored by the field operation and maintenance staff or the manufacturers. Also, the real location of the winding hotspot tends to appear at around 90% of the winding height rather than the winding top according to our simulation and actual detected data.