esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Double Low-Rank and Sparse Decomposition Model
### Optimization
(3) Updating \(L\)  
In order to solve \(L\), the optimal solution can be obtained by Equation (15):  
\[\min_{L}\biggl{(}\frac{1}{2}\biggl{|}\biggl{|}D-S+\frac{Y_{1}}{\mu}-L\biggr{|} \biggl{|}_{F}^{2}+\frac{1}{2}\biggl{|}\biggl{|}J+\frac{Y_{3}}{\mu}-L\biggr{|} \biggl{|}_{F}^{2}+\frac{1}{\mu}||L||_{*}\biggr{)} \tag{15}\]  
It can be rewritten as follows:  
\[\min_{L}\biggl{(}\frac{1}{2}\biggl{|}\biggl{|}\frac{1}{2}\biggl{(}D-S+J+\frac{ Y_{1}+Y_{3}}{\mu}\biggr{)}-L\biggr{|}\biggl{|}_{F}^{2}+\frac{1}{4\mu}||L||_{*}\biggr{)} \tag{16}\]  
Its solution is  
\[L^{*}=U\Psi_{\frac{1}{4\mu}}(\Sigma)V^{T} \tag{17}\]  
where \((U,\Sigma,V)=\text{svd}\left[\frac{1}{2}\Bigl{(}D-S+J+\frac{Y_{1}+Y_{3}}{\mu} \Bigr{)}\right]\), \(\text{svd}(\cdot)\) denotes singular value decomposition operator. (4) Updating \(S\)  
In order to solve \(S\), the optimal solution can be obtained by Equation (18):  
\[\min_{S}\biggl{(}\frac{1}{2}\biggl{|}\biggl{|}D-L+\frac{Y_{1}}{\mu}-S\biggr{|} \biggl{|}_{F}^{2}+\frac{1}{2}||H+\frac{Y_{2}}{\mu}-S||_{F}^{2}+\frac{\alpha} {\mu}||S||_{*}\biggr{)} \tag{18}\]  
It can be rewritten as follows:  
\[\min_{S}\biggl{(}\frac{1}{2}\biggl{|}\biggl{|}\frac{1}{2}\biggl{(}D-L+H+\frac {Y_{1}+Y_{2}}{\mu}\biggr{)}-S\biggr{|}\biggl{|}_{F}^{2}+\frac{\alpha}{4\mu}|| S||_{*}\biggr{)} \tag{19}\]  
Its solution is  
\[S^{*}=U\Psi_{\frac{a}{4\mu}}(\Sigma)V^{T} \tag{20}\]  
where \((U,\Sigma,V)=\text{svd}\left[\frac{1}{2}\Bigl{(}D-L+H+\frac{Y_{1}+Y_{2}}{\mu }\Bigr{)}\right]\). (5) Updating \(Y_{1}\), \(Y_{2}\) and \(Y_{3}\)  
\[ \begin{array}{l}Y_{1}=Y_{1}+\mu(D-L-S)\\ Y_{2}=Y_{2}+\mu(H-S)\\ Y_{3}=Y_{3}+\mu(J-L)\end{array}  \tag{21}\]  
(6) Updating \(\mu\)  
\[\mu=\min(\rho\mu,\mu_{\max}) \tag{22}\]  
where \(0<\rho<1\). ```
Input: Data matrix \(D\in\mathbb{R}^{d\times K}\), parameters \(\alpha>0\), \(\beta>0\), \(\gamma>0\) and \(\epsilon>0\) Output: The optimal solution \(L^{*}\in\mathbb{R}^{d\times K}\) and \(S^{*}\in\mathbb{R}^{d\times K}\)
1: Initializing \(L=S=H=J=0\), \(Y_{1}=Y_{2}=Y_{3}=0\)\(\mu=10^{-1}\), \(\mu_{max}=10^{10}\), \(\rho=1.1\), \(NUM=100\), \(k=1\)  While \(k\leq NUM\) OR \(||D-L-S||_{F}^{2}<\epsilon\), \(||H-S||_{F}^{2}<\epsilon\), \(||J-L||_{F}^{2}<\epsilon\)  2: Updating \(H\) \(H^{*}=\Big{(}S-\frac{Y_{2}}{\mu}\Big{)}\Big{(}I+\frac{2\beta}{\mu}M\Big{)}^{-1}\)  3: Updating \(J\) \(J^{*}=\Psi_{\frac{\gamma}{p}}\Big{(}L-\frac{Y_{3}}{\mu}\Big{)}\)  4: Updating \(L\) \(L^{*}=U\Psi_{\frac{1}{\mu}}(\Sigma)V^{T}\)  5: Updating \(S\) \(S^{*}=U\Psi_{\frac{\epsilon}{\mu}}(\Sigma)V^{T}\)  6: Updating \(Y_{1}\), \(Y_{2}\) and \(Y_{3}\) \(Y_{1}=Y_{1}+\mu(D-L-S)\)  \(Y_{2}=Y_{2}+\mu(H-S)\)  \(Y_{3}=Y_{3}+\mu(J-L)\)  7: Updating \(\mu\) \(\mu=\min(\rho\mu,\;\mu_{\max})\)  8: Iteration \(k=k+1\)  End While
```  
**Algorithm 1** Solving DLRSD via ADM.
# High-Power Broadband Frequency Chirped Intensity-Modulated Single-Frequency 1064-nm Laser
## 2 Application Background of Broadband Chirped Modulation in FDR  
In the FDR method, a stepped frequency modulation is applied to the laser transmitter. The receiver records the magnitude and phase of the return signal at each frequency step, yielding the frequency response of the channel. Range information is retrieved by applying the inverse fast Fourier transform (IFFT). The range resolution is determined by the frequency chirping bandwidth while the unambiguous range is decided by the frequency step or frequency resolution of the modulation.  
Suppose that the total modulation bandwidth is B, and the frequency response of the detected objects and surroundings are acquired at a frequency increment of \(\Delta f\). The unambiguous range and range precision are simply expressed as [13]:  
\[d_{UNAMB}=\frac{v}{4\Delta f}, \tag{1}\]  
and:  
\[\delta d=\frac{v}{4B}, \tag{2}\]  
where \(v\) is the speed of light in the medium. From Equation (1) and Equation (2), one could infer that in order to have a long unambiguous range and high ranging resolution, wideband frequency chirping with a precise frequency resolution is needed for the light source.  
Linear frequency modulated (LFM) signal is used to modulate the laser to obtain chirped intensity-modulated light. The frequency expression of the LFM signal is [14; 15]:  
\[f(t)=f_{0}+\frac{B}{T}t,0\leq t\leq T, \tag{3}\]  
where \(f_{0}\), \(B\), and \(T\) are the initial frequency, bandwidth, and period of chirping in time, respectively.  
The signal in Equation (3) is added at an EOM driver and used to modulate the intensity of the input laser to the EOM; the output from the EOM has an intensity expression as:  
\[I(t)=\frac{A^{2}}{2}\Big{[}1+\cos(f_{0}t+\frac{B}{T}t^{2})\Big{]}\cos^{2}( \omega t+\varphi), \tag{4}\]  
where \(A\), \(\omega\), and \(\varphi\) are the amplitude, frequency, and phase of the input laser, respectively.
## 3 Proposed Key Exchange Protocol
### Protocol Proposal
#### 3.3.2 Level 1: One-Pass SKEM Symmetric Session Key  
In order to establish a level 1 secure channel, the node and the server execute the SKEM scheme in two main steps:  
* Step 5--Key encapsulation: The node device generates a random point \(C\) on the elliptic curve. Then, the encapsulation of the random point \(C\) and the \(ID\)s of the node and the server are computed: \[h=\mathcal{H}_{1}(C,(ID_{N}||ID_{S}))\] (4) The session key is created at the node side using the encapsulation, the node's private key, and the server's public key. The session key is computed as follows: \[K=\mathcal{H}_{2}((t+k_{N}h)K_{S})\] (5) With the session key, the node can encrypt its data and send it to the server. Thanks to the one-way design of SKEM, the node can combine the ciphertext and the materials to generate the same session key into a compound message. Then, it transmits the message to the server.
* Step 6--Key decapsulation: After receiving the information, the server retrieves each segment and starts computing the session key: \[K=\mathcal{H}_{2}(k_{S}(C+hK_{N}))\] (6) After the server decrypts the ciphertext, successful communication is guaranteed. A meaningful message indicates that the communication is successful; otherwise, an adversary may have compromised the node. If this is the case, the server can force an ECQV key pair update or wait until the node's key pair expires.
# Detection and Classification of Bearing Surface Defects Based on Machine Vision
## 3 Materials and Methods  
The bearing surface defect detection and classification algorithm comprise the following five steps, as shown in Figure 1:  
* Perform image preprocessing, filtering, and correction.
* Perform defect detection, position the inspection object, and detect whether it has defects.
* Perform fine segmentation of the defect area. If a defect is detected, the defect area will be precisely segmented, and the detailed features of the defect area will be retained to the greatest extent possible.
* Perform feature selection. According to the sample data and dimensionality reduction goals, use the designed feature selection algorithm to select a feature combination with good classification performance from the feature pool.
* Perform defect classification. Based on the selected features, use pattern recognition technology to identify the type of defect.
# Towards Integrated Digital Twins for Industrial Products: Case Study on an Overhead Crane
## 2 Methods and Materials
### OPC UA Interface of the Crane  
OPC UA is an industrial standard for communication continuously developed by OPC Foundation [30]. It defines information, message, communication, and conformance models to enable interoperability, is platform-independent, and supports several communication protocols and data formats [31]. OPC UA has become a common standard especially among PLC manufacturers and is an important enabler for Industrial Internet applications. It is used mainly inside local factory networks.  
The OPC UA server of the crane allows monitoring its current status variables, such as position and speed. The crane can also be controlled via the interface. Description of the OPC UA interface is currently available in IImatar OIE via sign-up [32]. The server itself is not publicly on the Internet, but in a password protected network in the laboratory hall. Authentication is not currently required to access the OPC UA server, but to control the crane, a specific access code has to be written periodically to a certain node. Modifications to the OPC UA server, such as adding new nodes, are made by manufacturer technicians to ensure safety.  
Figure 2: Overhead crane IImatar at Aalto University Industrial Internet Campus.
# NTPP-MVSNet: Multi-View Stereo Network Based on Neighboring Tangent Plane Propagation
## 5 Conclusions and Future Work  
To address the insufficient accuracy of scene details in multi-view stereo tasks, we proposed NTPP-MVSNet. There are two modules that make NTPP-MVSNet efficient and highly accurate. Firstly, we designed a depth sampling module to make the depth hypotheses closer to the ground truth. The novel depth sampling module takes advantage of neighborhood tangent plane propagation. It guides the NTPP-MVSNet to understand scene information from the geometric structure and obtain more accurate depth predictions. Secondly, we introduced the normal estimation module to receive neighborhood tangent planes. In addition, the normal estimation module plays an important role in completing  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sampling** & **Acc.** & **Comp.** & **Fscore** \\ \hline \([0,0,0]\) & 0.358 & 0.357 & 0.357 \\ \([0,0,4]\) & 0.353 & 0.356 & 0.355 \\ \([0,8,4]\) & **0.337** & 0.356 & **0.346** \\ \hline \hline \end{tabular}
\end{table}
Table 4: In the case of the same depth sampling ratio, different depth sampling combinations are used to gradually strengthen the sampling ratio based on neighborhood tangent plane propagation and the evaluation results on the DTU dataset.  
Figure 14: During the training process, the proportion of pixels the depth prediction of which results in the validation set is within the error range of 2 mm.  
Figure 13: During training, the absolute difference between the depth prediction results of the validation set and the true depth value is averaged within 2 mm of error.  
the mutual optimization of the depth prediction map and the normal estimation map. The procedure of the mutual optimization is as follows: the cost volume of the depth prediction map provides input for the normal estimation and then the normal estimation map provides the geometric structural hints for depth estimation in return.  
Extensive experiments were conducted to examine the effectiveness of our NTPP-MVSNet. The result shows that the F score ranks first on the DTU dataset. The ablation experiments and the visual display of the results proved the high reconstruction accuracy of NTPP-MVSNet for local details, as shown in Figure 10. Future work may focus on the improvement of completeness in low-overlap outdoor areas.  
Not applicable.  
We mainly use DTU data set for multi-view stereo. The data set's official web site is [[http://roboimagedata.compute.dtu.dk](http://roboimagedata.compute.dtu.dk)]([http://roboimagedata.compute.dtu.dk](http://roboimagedata.compute.dtu.dk)).  
The authors declare no conflict of interest.
## 2 Backgrounds
### Filtering Methods  
A filtering method is employed to remove noise from an original signal, and we herein introduce five well-known filtering methods. Let \(f_{t}\) be the value of the feature \(f\) at time \(t\) in the following.  
* Simple moving average (SMA)--SMA is the unweighted average of values over the past time points as follows. \[SMA(f_{t})=\frac{f_{t}+f_{t-1}+\ldots+f_{t-n+1}}{n}\,\] (1) where \(n\) is the number of past time-points.
* Central moving average (CMA)--SMA causes a shift in a trend because it considers only the past samples. On the other hand, CMA is the unweighted average of values over both the past and future time points as follows. \[CMA(f_{t})=\frac{f_{t-n/2}+\ldots+f_{t-1}+f_{t}+f_{t+1}+\ldots+f_{t+n/2}}{n}\,\] (2) where \(n\) is an odd number specifying the number of time points to be averaged.
* Exponential moving average (EMA)--EMA, which is also known as an exponentially weighted moving average (EWMA), is a type of infinite impulse response filter with an exponentially decreasing weighting factor. The EMA of a time-series of the feature \(f\) is recursively calculated as follows. \[EMA(f_{t})=\left\{\begin{array}{ll}f_{t}&if\ t=1\\ \frac{(1-\alpha)\cdot f+\alpha\left(1-\alpha^{t-1}\right)\cdot EMA(f_{t-1})}{ 1-\alpha^{t}}&if\ t>1\end{array}\right.,\] (3) where, given the total number of observations \(N\), \(\alpha=e^{-1/N}\) is a constant factor.
* Exponential smoothing (ES)--Similar to EMA, ES is another weighted recursive combination of signals with a constant weighting factor \(\alpha\) as follows. \[ES(f_{t})=\left\{\begin{array}{ll}f_{t}&if\ t=1\\ (1-\alpha)\cdot f_{t}+\alpha\cdot ES(f_{t-1})&if\ t>1\end{array}\right.\.\] (4)
* Linear Fourier smoothing (LFS)--LFS is based on the Fourier transform, which decomposes a signal into its frequency components. By suppressing the high-frequency components, one can achieve a denoising effect. \[LFS(f)=\mathcal{F}^{-1}\Big{(}\chi_{[-\lambda,\lambda]}\mathcal{F}(f)\Big{)},\] (5) where \(\mathcal{F}(\cdot)\) and \(\mathcal{F}^{-1}(\cdot)\) denote the forward and inverse Fourier transform, respectively, and \(\chi_{A}\) is the characteristic function of the set \(A\) (\(\lambda\) is the cut-off frequency parameter). We used the standard fast Fourier transform algorithm to compute the one-dimensional discrete Fourier transform of a real-valued feature \(f\).
## 5 Discussion: Limitations and Future Works  
The presented approach has proven to be valuable both in the design phase and during discussions with companies, irrespective of their size or sector. It is adept at handling various products/systems, ranging from purely software-based to more mechanical ones, encompassing all the nuances between the two. The roadmap serves as a useful tool for informing the development or digitalization team about the project's status and evolution, its need for innovation, and/or the necessary steps for system digitalization. Furthermore, it has demonstrated its efficacy as a tool for consensus-building and fostering agreement around a plan. Initially drafted at the project's outset, the roadmap is continuously updated throughout development, serving as a blueprint for both the project and the organization championing it.  
Despite its utility, the approach does exhibit certain limitations (outlined in Section 5.1) and will benefit from further developments (introduced in Section 5.2).
## 2 Path Planning
### Pathfinding Using Grids
#### 2.1.2 Irregular Grids  
Irregular grids are not formed from the smallest unit shape unlike the regular grids. On the basis of its pattern, it is classified into waypoints, visibility graphs, and mesh navigation as shown in Figure 4. They also have a number of applications in the fields of pathfinding and robotics. They are of three types, as follows.  
1. Waypoints: Waypoints have a number of applications mainly in robotics as well as pathfinding. As the name suggests, waypoints are navigation guides or markers that direct the Algorithm to move in a particular direction of shortest path.
2. Visibility graphs: In the fields of computational geometry and graph theory, visibility graphs are fundamental structures. They have applications in several other fields and in recent times have been applied to Euclidean distance calculations for shortest paths when obstacles are present [17].
3. Mesh navigation: A mesh can be formed from different shapes, commonly triangles and other polygons. Mesh graphs are somewhat identical to the visibility graphs in terms of looks. However, the complexity of visibility graphs is greater than the mesh graphs. Most of the applications of this graph are present in games [18].  
The different types and its categories of grid along with its smallest unit such as equilateral triangle, square, regular hexagon, cube, navigation marker, graph node, and edge and its applications are detailed in Table 1.  
Figure 4: (a) Top left: waypoints, (b) top right: visibility graph, (c) bottom: navigation mesh.
# Digital Twin Technology-Based Networking Solution in Low Earth Orbit Satellite Constellations
## 5 Networking Protocol Based on Digital Twins
### Construction of DT Platform  
The focus of the research lies in the virtual reconstruction technology of twin systems that are consistent with the tested low Earth orbit (LEO) satellite constellation network in terms of scale, identical network element functionalities, twin application, and lifecycle management. There are two main approaches to the construction of network element  
Figure 3: Twin platform architecture of low-orbit constellation network networking scenario.  
digital twin models. The first approach is based on KVM virtualization technology, which builds a virtualization layer on the physical resource layer and runs multiple KVM virtual machines on top of it. Each virtual machine operates its own independent operating system, providing various mainstream Linux operating systems. The network layer, transport layer, application-layer protocol software, and various deployed upper-layer network business application codes in the real devices do not require porting and can be directly applied, achieving the high-fidelity simulation of various types of network nodes. The KVM virtual machines can realize the functionalities of LEO satellite onboard routing and switching, satellite terminals, and gateway nodes at the satellite-ground station boundary.  
The second approach is based on container-based lightweight virtualization technology, where the process of the operating system serves as the basic unit. It runs a complete operating system on the virtual hardware, but, instead of creating a separate virtual machine, it isolates and further abstracts the resources of the host machine to provide a relatively independent runtime environment. Compared to virtual machines, containers consume fewer resources and have higher resource utilization, faster startup speeds, and more efficient and convenient deployment. Therefore, under the same physical hardware conditions, a significantly larger number of container instances can be virtualized compared to virtual machines. Additionally, the time from creating to starting a container instance is in the millisecond to second range, far superior to the minutes required for virtual machine startup. Furthermore, container technology allows the packaging of target applications for single-address access and image storage, requiring only simple commands for deployment. The comparison between container technology and KVM virtualization technology is shown in Table 1.  
Therefore, the proposed twin platform in this study supports two different approaches to constructing twin network elements, catering to diverse application requirements. For instance, for scenarios demanding large-scale deployment and rapid implementation, the adoption of container-based lightweight virtualization technology for twin network element nodes is recommended. Conversely, for cases with specific demands regarding performance and operating systems, the use of KVM virtualization technology is suggested for the construction of twin network element nodes.
###### Abstract  
Difficulty in clarifying the deformation characteristics of deep rocks under a high water pressure environment is a technical bottleneck restricting the safe operation of large hydropower stations. In order to study the effect of reservoir water level changes on the mechanical behavior of deep limestone, a series of mechanical tests were conducted under different dynamic high water pressure environments using a self-developed hydraulic loading test device. The test results show that the unsaturated limestone always undergoes compressive deformation during the linear increase in external water pressure, and the saturated limestone changes its deformation state from compression to expansion during the linear decrease in external water pressure. The stress-strain curve of limestone shows apparent hysteresis characteristics during the cyclic increase and decrease in external water pressure. Overall, the rock strain rate showed a significant negative correlation with the external water pressure, and the rock deformation modulus showed a certain positive correlation with the external water pressure. During hydraulic loading, saturated rocks had a smaller range of variation in the strain rate and deformation modulus and were more resistant to deformation than unsaturated rocks. Limestone was subjected to both external water pressure and internal pore water pressure in a cyclic cycle, where pore water pressure promotes pore creation and expansion, while external water pressure prevents water from degrading the pore structure. The periodic change of water pressure has a significant influence on rock mechanics and deformation behavior, and the rock mass will undergo elastic deformation, plastic deformation, and even fracture. Further study of this deformation rule can provide a more accurate theoretical basis for the safe operation of water conservancy projects.  
Keywords: limestone; high water pressure; cyclic loading; water rock coupling +
Footnote †: journal: Applied sciences