esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Measurement Uncertainty  
The experimental results are finally characterized as the average Nusselt number, which is actually a function of nine measured parameters. The Nusselt number is calculated using the following expression:  
\[Nu=\frac{hd_{h}}{k}=\frac{kQ_{c}d_{h}}{kA_{s}\Big{(}t_{f}-t_{wi}\Big{)}}=\frac {\xi d_{h}c_{\text{water}}\rho_{\text{water}}(t_{2}-t_{1})q_{v}}{kA_{s}\Big{(}t _{f}-t_{wi}\Big{)}} \tag{10}\]  
where \(A_{s}\) is the calculated effective heat transfer area for each pinned heat exchanger; \(t_{f}\) and \(t_{wi}\) are the mean temperatures of the fluid and wall on the internal side, respectively.  
Since the measurement errors of different variables are independent of each other, according to the principle of error propagation, the uncertainty of the Nusselt number is:  
\[\sigma_{Nu}=\sqrt{\sum_{i=1}^{9}\Big{(}\frac{\partial f}{\partial x_{i}} \Big{)}^{2}{\sigma_{x_{i}}}^{2}} \tag{11}\]  
where \(\partial f/\partial x_{i}\) is the partial derivative of the function on one of the measured parameters. \(\sigma_{xi}\) is the uncertainty of each measured parameter. For simplicity, the influence of five measurement errors on the Nusselt number were considered, including the inlet and outlet cooling water temperatures \(t_{1}\) and \(t_{2}\), the fluid mean temperature \(t_{f}\), the mean wall temperature \(t_{2w}\) on the external side, and the cooling water flow rate \(q_{v}\). According to the principle of error propagation:  
\[\begin{array}{l}(\frac{\partial f}{\partial x_{i}})^{2}=(\frac{\partial Nu} {\partial t_{v}})^{2}=(\frac{\xi d_{h}c_{\text{water}}(t_{2}-t_{1})}{kA_{s}(t _{f}-t_{2w})})^{2}\\ (\frac{\partial f}{\partial x_{f}})^{2}=(\frac{\partial Nu}{\partial t_{v}})^ {2}=(\frac{\xi d_{h}c_{\text{water}}(t_{2}-t_{1})}{kA_{s}(t_{f}-t_{2w})})^{2} \\ (\frac{\partial f}{\partial x_{i}})^{2}=(\frac{\partial Nu}{\partial t_{f}})^ {2}=(\frac{\partial Nu}{\partial t_{\text{ave}}})^{2}=(\frac{\xi d_{h}c_{ \text{water}}d_{v}(t_{2}-t_{1})}{kA_{s}(t_{f}-t_{2w})^{2}})^{2}\end{array} \tag{12}\]  
After calculating the error propagation, the total uncertainty of the Nusselt number can be obtained, according to Equation (10).
# Aerodynamic Modeling and Performance Analysis of Variable-Speed Coaxial Helicopter
## 2 Establishment of an Aerodynamic Model
### Dynamic Model of Blade Swing  
Taking the following rotor swing as an example, the swing motion equation [21] of the blade can be obtained from the balance of various moments at the swing hinge:  
\[I_{\beta}\bar{\beta}+I_{\beta}\Omega^{2}\beta+M_{C}+M_{R}=M_{T}-M_{S}g \tag{10}\]  
where \(I_{\beta}\) is the moment of inertia of the blade around the swing hinge, \(\beta\) is the swing angle, \(M_{C}\) is the Coriolis moment, \(M_{R}\) is the restraint moment of the swing hinge, \(M_{T}\) is the aerodynamic moment, and \(M_{S}\) is the mass static moment of the rotor around the swing hinge. For rectangular blades, \(I_{\beta}\) can be expressed as:  
\[I_{\beta}=mx^{2} \tag{11}\]  
where \(m\) is the mass of the blade and \(x\) is the distance from the center of gravity of the blade to the rotation axis. For rectangular blades, \(M_{S}\) can be expressed as:  
\[M_{S}=mx \tag{12}\]  
For rotors with swing angle constraints, \(M_{R}\) can be expressed as:  
\[M_{R}=K\beta \tag{13}\]  
where \(K\) is the stiffness coefficient of flapping rubber, in N\(\cdot\)m/rad. The aerodynamic moment \(M_{T}\) can be obtained by integrating the blade element theory. After sorting, the blade flapping motion equation can be obtained:  
\[\begin{bmatrix}\ddot{a_{0}}\\ \ddot{a_{1}}\\ \ddot{b_{1}}\end{bmatrix}+D\begin{bmatrix}\dot{a_{0}}\\ \dot{a_{1}}\\ \dot{b_{1}}\end{bmatrix}+K\begin{bmatrix}a_{0}\\ a_{1}\\ b_{1}\end{bmatrix}=f \tag{14}\]  
where \(f\) can be expressed as:  
\[f=F_{1}\begin{bmatrix}\theta_{0}\\ \theta_{t}\\ A_{1}\\ B_{1}\end{bmatrix}+F_{2}\begin{bmatrix}\omega_{x}\\ \omega_{z}\end{bmatrix}+F_{3}\lambda_{1}+F_{4} \tag{15}\]  
Among them, \(D\), \(K\), \(F_{1}\), \(F_{2}\), \(F_{3}\) and \(F_{4}\) are coefficient matrices and vectors, and their values are related to the swing hinge offset, swing rubber stiffness, incoming flow condition and blade lock number of the rotor. It is worth mentioning that after derivation, \(F_{4}\) is related to various inertia forces and moments of the blade, and attention should be paid to the position of the speed variable; otherwise, the final equation group will have no solution, and its specific expression is:  
\[F_{4}=\begin{bmatrix}-\frac{M_{4}}{I_{\beta}I_{\beta}}g\\ \frac{\gamma}{2}\left(\frac{K_{1}v_{1}+K_{2}\delta_{1}v_{2}}{I2K}\right) \left(\frac{1}{4}-\frac{2}{3}\epsilon+\frac{1}{2}\epsilon^{2}\right)\\ 0\end{bmatrix} \tag{16}\]  
where \(G\) is the acceleration of gravity, and \(\gamma\) is the number of blades.
## 6 Numerical Simulation  
In this paper, the finite element analysis is carried out by using ANSYS [16]. An element (SHELL 99) is selected for the main plate in which this element works with thin and thick plate-shell structures. The element (SHELL 99) has eight nodes with six degrees of freedom at each node; translations in the (x, y and z) axes and rotations about the (x, y and z) axes. This kind of elements used for layered applications for modeling composite plates and shells includes already the effect of transverse shear deformation. For the stiffened plate, the element (SOLSH 190) is used in the simulation, which is having eight nodes connectivity with three degrees of freedom at each node: translations in the nodal (x, y and z) directions. Another three degrees of freedom (rotation) has been added at each node in the nodal (x, y and z) directions. A first order shear deformation theory with the aid of Mindlin-Reissner of shell theory is used by ANSYS software. The global (x) coordinate is directed along the width of the plate, while the global (y) coordinate is directed along the length. The global (z) coordinate corresponds to the thickness direction, which is taken to be outward normal of the plate surface, as shown in Figure 8. For the contact analysis between the main plate and the stiffener, the element (TARGE 170) and the element (CONTA 174) have been used to create the mesh between the target and the contact surfaces. The stiffener represents the target, while the main plate is the source. The mesh generation for un-stiffened plates, stiffened plates with one stiffener and stiffened plates with two stiffeners are illustrated in Figures 10-12. The convergence test is completed using a high number of elements to determine the exact size of the element when the value of bending deflection is settled down, as indicated in Figures 13 and 14.  
Figure 11: Mesh contour for composite laminated plate with one stiffener.  
Figure 10: Mesh contour of composite laminated plate without stiffener.  
Figure 12: Mesh contour for composite laminated plate with two stiffeners.  
Figure 13: Convergence test of bending deflection against number of elements for plate with one and two stiffeners.
## 4 Discussion
If the reinforcement/supports are supposed to be installed at the same time and distance from the excavation face, then the initial displacement for the individual support \"\(i\),\" i.e., \(u_{in,i}\) is equal to \(u_{in}\). The load, \(p_{i}\), which is applied to the generic support, \(i\) (if it has not reached its elastic limit, \(u_{el,i}\)), becomes a function of the radial displacement (\(u-u_{in}\)) and its stiffness, \(k_{i}\), in Equation (13):  
\[p_{i}=k_{i}\times(u-u_{in}) \tag{13}\]  
Generally, when different supports and/or reinforcements are installed at different times or at different distances from the excavation face (\(u_{in,i}\
eq u_{in,i}\), for I \(\
eq\) j), the reaction line of the composite support can assume the form represented by Case 2, in Figure 9 [56]. A good rock mass has greater self-supporting capability, and thus requires less support. Moreover, in a good rock mass, the load transfer mechanism is better, and, therefore, the rock-mass quality has a positive impact on the bond strength between the grout and drilled hole's periphery. The pull-out strength increases, and the displacement decreases, as the rock-mass quality increases. The median pull-out strength (kN) and the pull-out displacement (mm) are 127.6 and 8.545; 148.8 and 8.42; and 159.3 and 6.29, for weathered, soft, and moderate rocks, respectively (Figure 10). The median pull-out strength of the rock bolt and the empirical suggested rock load using Equation (12) indicates that the experimental results are within the range for moderate rocks. In soft and weathered rock masses, the rock-bolt pull-out strength is lower than the empirical suggested rock load (Figure 11). In a water-bearing rock mass, groundwater has an adverse effect on the fully grouted rock bolts during the pull-out test. From four pull-out test results in slight-water-leakage soft rock, the pull-out load-displacement behavior of the fully grouted rock bolt varies irregularly with the leaking amount (Figure 12). The pull-out test results show that, in both cases of the grout materials, the pull-out strength is lower than that in the dry condition. In the case of high-leakage weathered rock, rock bolt was pulled out before yielding occurred with low pull-out load (Figure 13a). In both groundwater-leakage cases, the pull-out load-displacement curve shows no inflection point. Compared to fully grouted rock bolts, the results of the ISR showed that the inflection point of the pull-out load--displacement curve was obvious in the presence of groundwater. The pull-out resistance of the ISR was higher than that of the fully grouted rock bolt (FGR) in slight-leakage conditions. In high-water-leaking weathered rocks,the pull-out loads of the ISR tests were considerable, even with a leaking rate of 1.2\(\sim\)2.85 L/min. The average pull-out resistance of the ISR under a high leaking condition was around 150 kN, which is considerably more than that of the FGR.
# Hybrid Quantum Neural Network Image Anti-Noise Classification Model Combined with Error Mitigation
## 3 Construction of Mixed Variational Quantum Neural Network and Error Mitigation Model
### CAE (Feature Extraction and Dimension Reduction)  
The convolutional autoencoder (CAE), inspired by [PERSON]'s seminal work [39], serves as a paradigm in unsupervised learning neural network models, designed to proficiently capture data representations and extract salient features.  
CAE Architecture and Weight Sharing: In preserving spatial locality, CAE employs weight sharing across all positions in the input, adhering to a structural resemblance with  
Figure 1: (**a**) Classical neural networks typically comprise three layers: an input layer, a hidden layer, and an output layer. Each layer contains multiple neurons, and the connections between neurons have varied weights. (**b**) In contrast, QNN involves three layers: F(x) serves as the coding layer, \(\alpha\)(x) acts as the variable layer, and O functions as the measurement layer.  
traditional autoencoders. The latent representation, denoted as \(l^{m}\), for the \(m\)-th feature map of a single-channel input tensor, is intricately expressed as  
\[h^{m}=\omega(t*W^{m}+b^{m}) \tag{4}\]  
where \(\omega\) represents the activation function, and \(*\) symbolizes 2D convolution. Reconstruction Process in CAE: The reconstruction process within CAE unfolds through a linear combination of fundamental image blocks contingent upon the latent code. The reconstruction equation takes the form  
\[I=\omega(\sum_{m\in H}h^{m}*\widetilde{W}^{m}+c) \tag{5}\]  
where H denotes the set of latent feature maps, \(\widetilde{W}\) embodies a two-dimensional weight-flipping operation, and \(*\) denotes the 2D convolution operation. Cost Function and Optimization in CAE: The imperative cost function guiding CAE's training regimen is the mean square error (MSE), formalized as  
\[E(\theta)=\frac{1}{2n}\sum_{i=1}^{n}{(ti-Ii)^{2}} \tag{6}\]  
To minimize this cost function, the optimization process leverages backpropagation to compute gradients of the error function concerning the parameters. The gradients are ascertained through convolution operations, expressed as  
\[\frac{\partial E(\theta)}{\partial W^{m}}=t*\delta h^{m}+\widetilde{h}^{m}* \delta I \tag{7}\]  
where \(\delta h\) and \(\delta I\) denote the incremental changes in hidden states and reconstruction, respectively.  
Stochastic gradient descent plays a crucial role in optimizing the CAE model by iteratively adjusting weights to improve overall performance. Grayscale images, with their straightforward structure, allow for direct feature extraction. However, for color images, conversion of RGB values to corresponding grayscale values is necessary before applying this algorithm. Figure 2 illustrates an example of multi-channel image feature extraction.  
Figure 2: The image includes convolution automatic encoder for feature extraction and dimensionality reduction, and convolution automatic encoder includes convolution layer (CONV), pooling layer (POOL), and full-connection layer (FC).
# Landslide-Tunnel Interactions and Control Countermeasures under an Orthogonal System
## 2 Evaluation of Landslide Effects on Tunnels  
### Spatial Location of Landslides and Tunnels  
The stability of tunnel structures affected by landslides is influenced by numerous factors, such as the angle of the sliding surface, the size of the landslide range, the relative position of the tunnel and the landslide, and the orientation of the tunnel. Different spatial relationships between the tunnel and the landslide can lead to varying effects on the tunnel, such as stress distribution, deformation, and failure characteristics. In particular, the relative position of the tunnel to the sliding plane determines the deformation pattern, stress properties, and failure mechanisms of the tunnel. Figure 1 shows three different positional relationships between a tunnel and a sliding surface.  
The orthogonal relationship between a tunnel and a landslide can be divided into three geometrical cases: the tunnel is in the landslide, the tunnel intersects with the sliding surface, and the tunnel is located below the sliding surface. Their interaction can be defined as follows: the construction disturbance of the tunnel causes local deformation in the landslide. When slow deformation occurs to a certain extent, it will cause a landslide; in turn, the landslide affects the tunnel, causing cracks and deformations where the two coincide, seriously affecting the safety of the tunnel and the stability of the landslide.
## 3 Methods
### Measuring Sea Ice Motion and Deformation
#### 3.1.2 Maximum Cross-Correlation Approach for Measuring Sea Ice Motion
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Image Pair** & **Time Interval (hh:mm:ss)** \\ \hline
1 & KOMPSAT-2 (14 August 2014)–KOMPSAT-3 (14 August 2014) & 01:57:55 \\
2 & KOMPSAT-3 (14 August 2014)–KOMPSAT-2 (15 August 2014) & 21:02:56 \\
3 & KOMPSAT-2 (15 August 2014)–KOMPSAT-3 (15 August 2014) & 03:35:28 \\
4 & KOMPSAT-2 (14 August 2014)–KOMPSAT-2 (15 August 2014) & 23:00:51 \\
5 & KOMPSAT-3 (14 August 2014)–KOMPSAT-3 (15 August 2014) & 24:38:24 \\
6 & KOMPSAT-2 (14 August 2014)–KOMPSAT-3 (15 August 2014) & 26:36:19 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Combinations of image pair for measuring and validating sea ice motion. during the sea ice motion measurement, image entropy was adopted to statistically measure the texture of the image block, as in Equation (1):  
\[\text{Entropy}=-\Sigma\;\text{p}\times\text{log}_{2}(\text{p}) \tag{1}\]  
where p is the histogram counts for the image in each template window [36].
# Review of Magnetoelectric Effects on Coaxial Fibers of Ferrites and Ferroelectrics
## 3 Nanofiber Synthesis  
There are several techniques, including sol-gel routes [48; 49], electrodeposition [50], template assisted synthesis [51], and electrospinning [39; 40; 41; 42; 43], that are utilized for the synthesis of coaxial fibers. Electrospinning has several advantages over other competing techniques for the synthesis of core shell fibers, e.g., (i) it is a low-cost synthesis technique compared with lithography or template-assisted processes; (ii) fibers of uniform core and shell structures free of any defects can be prepared; (iii) the technique can be easily scaled up for the large-scale synthesis of nano- and microfibers. In this review, we focus on fibers made by electrospinning. The synthesis in general involves the following steps [52; 53]: The first step in the process involves the preparation of the sols for core and shell materials separately with precursors that are soluble in water/alcohol or that are liquid themselves. For ferrite fibers, one generally uses metal acetates or nitrates for the sol. A polymer, usually polyvinylpyrrolidone (PVP), is added to the solutions to make the sol viscous. Second, the sols are loaded onto two separate syring and dispensed with a syringe pump, as in the setup shown schematically in Figure 3. The viscosity of the sols has to be adjusted for optimum pumping rates and to control the fiber dimensions.  
Figure 2: Estimated maximum value of HEVC as a function of the ratio of the radius of PZT core and (**a**) Ni\({}_{2}\)Y- or Co\({}_{2}\)W-type hexagonal ferrite shell and (**b**) Zn\({}_{2}\)W- or Zn\({}_{2}\)Y-type hexagonal ferrite shell [47].  
Finally, the sol fed through a dual chamber stainless steel needle is subjected to an electric field of 1.5-2 kV/cm by applying a DC voltage between the needle and a metal drum used to collect the fibers (Figure 3). As the sols exit the needle tip they are electrically charged, and the repulsive Coulomb force leads to the formation of a Tyler cone and eventually to the formation of fibers of the ceramics that are collected on a rotating metal drum. As-spun fibers are dried at room temperature for 24 h and then annealed at a desired temperature in order to complete the formation of ferrites and ferroelectrics [52; 53].
## 2 Hybrid Framework Description  
In this section, we introduce our proposed framework based on a low-cost foot-mounted inertial/magnetic sensor. A flow chart of the framework is shown in Figure 1. The next four sections describe the different modules of the framework. The AFM, aided by the MDD and the HMC, is leveraged to compute the fused heading error measurement. The MDD is capable of detecting magnetic fields with different qualities, and the HMC is used to recognize straight-line motion. Triggered by the output from the multi-class FSC, the ZUPT algorithm is available in every stance phase. In the still phase, the state lock is active; i.e., the position and heading are locked, and the velocity is set to zero. Simultaneously, ZARU is used to estimate the gyro bias. More details of the operation of the proposed framework are given in Algorithm 1.  
```
0: Inertial and magnetic data
0: Estimated position
1: Initialize error covariance matrix \(\mathbf{P}_{0}\), process noise covariance matrix \(\mathbf{Q}\), measurement noise covariance \(\mathbf{R}\), attitude quaternion (\(\mathbf{q}_{0}\)), and position (\(\mathbf{r}_{0}\)) and velocity (\(\mathbf{v}_{0}\)) vectors, and compute initial gyro bias \(\mathbf{b}_{g}\)[50]
2:repeat
3: Subtract gyro bias from measured angular rate;
4: Magnetic disturbance detection; // see Section 2.2.2
5:if\(ZUPT(k)==2\) // see Section 2.1 then
6:\(\mathbf{r}_{k}=\mathbf{r}_{k-1}\), \(\mathbf{v}_{k}=\mathbf{0}\) and \(\mathbf{q}_{k}=\mathbf{q}_{k-1}\); // state lock
7: Update the gyro bias; // ZARU algorithm
8:\(\mathbf{P}_{k}=\mathbf{P}_{k-1}\); // store the error covariance matrix
9:else
10: Compute navigation equations; // see Section 2.3
11: Compute error state transition matrix \(\mathbf{F}\) and \(\mathbf{G}\); // see Section 2.4.1
12: Predict the error covariance matrix \(\mathbf{P}_{k|k-1}\)= \(\mathbf{F}\mathbf{P}_{k-1|k-1}\mathbf{F}^{T}+\mathbf{G}\mathbf{Q}\mathbf{G}^{T}\);
13:if\(ZUPT(k)==1\)then
14:\(\Delta\mathbf{v}_{k}=\mathbf{0}-\mathbf{v}_{k|k-1}\); // the well-known ZUPT algorithm
15: Compute heading error measurement; // see Section 2.4.2 and Algorithm 2
16: Compute Kalman filter gain \(\mathbf{K}_{k}=\left(\mathbf{P}_{k|k-1}\mathbf{H}^{T}\right)\left(\mathbf{H} \mathbf{P}_{k|k-1}\mathbf{H}^{T}+\mathbf{R}\right)^{-1}\);
17: Compute correction \(\delta\mathbf{x}_{k|k}=\mathbf{K}_{k}\mathbf{x}_{k}\); // see Section 2.4.2
18: Update the error covariance matrix \(\mathbf{P}_{k|k}=\left(\mathbf{I}-\mathbf{K}_{k}\mathbf{H}\right)\mathbf{P}_{ k|k-1}\);
19: Compensate state vector; // see Section 2.4.3
20:endif
21:endif
22:\(k=k+1\);
23:until Power off the system
```  
**Algorithm 1** Operation of our proposed framework.  
Figure 1: Flowchart of our proposed hybrid framework. Heading error measurement updating and the zero-velocity update (ZUPT) algorithm are triggered by the stance-phase signal from the foot-state classifier (FSC). The zero-angular-rate update (ZARU) algorithm and state lock work once the still phase is detected
# Parameter Optimization for Low-Rank Matrix Recovery in Hyperspectral Imaging
## 3 Results  
We analyze how different parameter settings affect the PSNR and computational times. We are able to show that different parameter values and their combinations have an effect on the PSNRs and computational times of the LRMR method. The initial parameter values  
Figure 4: The Pavia University data set displayed for spectral reflectance bands 1, 50, and 103.  
Figure 3: The Pavia Centre data set displayed for spectral reflectance bands 1, 50, and 102.  
are optimized with respect to PSNR and CPU time. The parameter value combinations are studied in detail, and the results are presented visually.  
We study the initial parameter value combinations for three integer-valued parameters--\(r\), \(s\), and \(b\)--and one real-valued parameter \(p\). We apply nonlinear optimization with respect to the real-valued noise estimation parameter \(p\), which results in an improvement in PSNR. The integer parameters are analyzed on a series of test sets. The optimized values are chosen according to their best PSNR performance. For all analyzed settings and resulting combinations, we show CPU times in MATLAB and Python. The computational experiments are performed on a laptop with an Intel(R) Core(TM) i5-8250U CPU @ 1.60 GHz 1.80 GHz processor and 16.0 GB RAM.  
Figure 5 shows the performance of the method for a noise-corrupted waveband of the Indian Pines data set [16] for the parameter settings \(r=7\), \(p=0.15\), \(b=20\), and \(s=8\).
## 2 Influence Factors of Service Performance of LSDM  
### The Pointing Accuracy of Satellites in Space  
Earth observation satellites are capable of imaging and remotely measuring Earth's surface and of tracking and observing aerial and ground targets, as shown in Figure 2. To achieve precise target location observation, satellite antenna panels demand high pointing accuracy. The LSDM serves as the payload platform of the antenna panel. Its assembly quality is ultimately evaluated to ensure that the antenna panels' pointing accuracy meets the service requirements during an in-orbit satellite mission. To guarantee alignment between the antenna panels and satellite body in space, ensuring the pointing accuracy between the normal vector of the antenna panels and the coordinate system of the satellite body during ground assembly is necessary.  
As shown in Figure 3, to quantitatively analyze the pointing angle \(\theta\), the normal vector of the antenna panel \(\overrightarrow{N}\) should be projected onto the X-O-Z and Y-O-Z planes. The resulting angles between the projected vector and the \(Z\)-axis in each plane are, respectively, referred to as the yaw angle \(\alpha\) and the pitch angle \(\beta\). These parameters are critical for ensuring accurate alignment between the antenna panel and satellite body in space. The equivalent model of the projection angles is shown in Figure 3b, and the pointing angle \(\theta\) can be expressed by the yaw angle \(\alpha\) and pitch angle \(\beta\):  
\[\theta=\arccos\frac{1}{\sqrt{\tan^{2}\alpha+\tan^{2}\beta+1}} \tag{1}\]