esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Results and Discussion
### Re-Analysis of Optimized Designs  
Detailed 3D solid models were built and analyzed to validate the structural responses of the optimized ITPSs. Maximum temperatures at TFSs (\(T_{t,\text{max}}\)) and BFSs (\(T_{b,\text{max}}\)) are extracted and plotted in Figure 14. Figure 15 provides the temperature distribution along \(x\)-directions on the bottom surfaces at Time 1 when the temperature of the TFS reaches maximum. The maximum temperature location can be indicated by the corresponding contour plots. It is obvious that in the optimized designs, more heat was absorbed by insulation materials and less heat was conducted to the bottom surface through webs. The maximum BFS temperature was reduced from 416 K to 377 K, 338 K and 351 K in OPT1, OPT-SIZE and OPT-SHAPE, respectively, illustrating that all the optimized designs have better insulation capacity than the initial design.  
The maximum deformations of TFSs are plotted in Figure 16. Trend of deformation approximately agreed with the TFS temperature, indicating that the deformation is mainly controlled by thermal expansion. As shown in the figure, for OPT-SIZE and OPT-SHAPE, the maximum deformation of the TFS was slightly increased by 0.16 mm and 1.2 mm, respectively, which is acceptable considering the overall height of the ITPS. Correspondingly, the maximum thermal stress was reduced from 1.08 GPa to 446.4 MPa and 420.1 MPa, respectively, indicating fewer thermal expansion effects in optimized designs.  
Figure 14: Maximum temperature evolution on (**a**) top surface and (**b**) bottom surface of the initial and optimized designs.  
Figure 13: Buckling mode of (**a**) OPT-SIZE and (**b**) OPT-SHAPE at Time 3.  
Figure 17 presents the comprehensive summary of the thermal and mechanical characteristics of the initial and optimized designs. OPT1 stands for the direct application of 2D optimized configuration in 3D structures. It shows better insulation performance, however, worse buckling resistance capacity. Both 3D optimized designs performed better in the thermal and mechanical responses, indicating that they are superior to the initial design.  
Figure 16: Mechanical responses of the initial and optimized designs.  
Figure 17: Comparison of the thermal and mechanical responses of the initial and optimized designs.  
Figure 15: (a) Temperature along the path on bottom surface. (b) INI, (c) OPT1, (d) OPT-SIZE and (e) OPT-SHAPE. The paths are marked by arrow lines.
## 3 Results and Discussion  
### Powder Distribution and Packing Density  
One of the critical factors for the success of the additive manufacturing process is the homogeneous distribution of the powder bed and the packing density. The additive manufacturing process flow diagram presented in Figure 3 encompasses the stages from the formation of the powder bed to the development of the molten pool. The uniformity of powder distribution directly influences material homogeneity and the quality of the final structure, playing a pivotal role in mechanical performance.  
DEM simulations have shown that the irregular packing density in the powder bed significantly affects thermal behavior. It has been observed that smaller particles settle between larger particles, forming a denser structure, which increases packing density and improves thermal conductivity. The increase in packing density contributes to a more homogeneous energy distribution during laser interaction, resulting in a more balanced melting process. The simulated powder bed structure is shown in Figure 4.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Min** & **Baseline** & **Max** \\ \hline Scanning Speed (mm/s) & 80 & 150 & 300 \\ Laser Power (W) & 50 & 200 & 400 \\ Laser Spot Diameter (\(\upmu\)m) & 40 & 50 & 100 \\ Powder Layer Thickness (\(\upmu\)m) & 50 & 50 & 100 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Input parameters and boundary values defined for HEEDS software.  
Density variations in the powder bed can affect heat absorption during laser interaction and the consistency of the melting process, potentially leading to the formation of microstructural defects in the final structure. Particularly in areas with high density differences, heat transfer occurs at varying rates, resulting in issues such as incomplete melting or excessive melting in certain regions. This situation is a critical factor, especially regarding mechanical strength and material homogeneity, as it directly impacts the structural integrity of the component.
## 5 Experiments
### Implementation Details  
To comprehensively evaluate the algorithm's performance, experiments were conducted to verify the impact of three key factors on registration results: the noise level of graph nodes, the difference in initial translation and rotation angles, and the overlap rate between the graphs to be registered.  
First, a noise-free clean dataset was constructed. Using the aforementioned method, graph structures of simulated buildings were generated, and subgraphs with overlap rates of 20%, 40%, and 60% were set. Subsequently, these graphs were subjected to random rotations and translations. For the initial parameter settings, the random translation range in each direction was set to \([-10,10]\) meters, and the rotation angle range was set to \([-\pi,\pi]\), thereby generating the rotation matrix \(\mathbf{R}\) and translation vector \(\mathbf{T}\). A total of 1000 graphs \(G_{tgt}\) to be registered were generated. Based on the 60% clean data, point cloud data with Gaussian noise were further constructed. Normal distribution noise with a mean of 0 and a standard deviation of 1 was added to the clean data to simulate positional changes of each point in real-world scenarios.  
Our model was run on an NVIDIA GeForce RTX 4090 (NVIDIA, Santa Clara, CA, USA) and implemented within the PyTorch 2.3.1 framework, with 100 training epochs. The Adam optimizer was used with an initial learning rate of 0.001. Training was performed using random sampling, and the dataset was split into training, validation, and test sets in an 8:1:1 ratio. Since conventional point cloud registration techniques are mainly applied in scenarios featuring large-scale data and dense point clouds, and they either do not utilize edge information or rely on image-based point cloud data, we opt for the graph neural network approach for comparison to ensure a fairer benchmarking. We compared our method with several state-of-the-art algorithms, including Graph Convolutional Network (GCN) [21], Graph Attention Network (GAT) [44], and three other learning-based methods: GDC [53], GraphKAN [50], SGC [54], and NIGCN [55]. For the comparison methods, we used the code provided by the authors and trained the models according to the settings specified by the authors. The input and output of the networks were set to be the entire concatenated graph, consistent with our method. All networks were retrained from scratch, as pre-trained models were not available.  
Through these detailed experimental settings, the algorithm's performance can be comprehensively evaluated under different noise levels, initial rotation angles, and overlap rates.
## 2 Drone Clustering Based on the K-Means++ Algorithm
### Selection of Clustering Evaluation Indicators  
To validate the scientificity and effectiveness of the K-Means++ algorithm, this section selects three commonly used evaluation metrics: the Silhouette Coefficient, Sum of Squared Errors (SSE), and Davies-Bouldin Index, to comprehensively assess the clustering results. Below is a detailed description of these evaluation metrics:  
(1) Silhouette Coefficient (Sil): This metric measures the relative distance between samples within each cluster and samples from other clusters. It evaluates the compactness of the samples within their assigned cluster and the degree of separation between clusters by calculating the relative difference between the average distance of each sample to other samples in the same cluster and the average distance to samples in other clusters. The calculation formula is as follows:  
\[\text{Sil}=\frac{b_{i}-a_{i}}{\max(b_{i},a_{i})} \tag{3}\]  
In Equation (3), \(i\) denotes the ith sample; \(a_{i}\) denotes the average distance between sample point i and all other sample points in the same cluster, i.e., intra-cluster dissimilarity; and \(b_{i}\) denotes the average distance between sample point i and all sample points in other clusters, i.e., inter-cluster dissimilarity.  
(2) Sum of Squared Errors (SSE): As one of the most common clustering quality metrics, this indirectly reflects the closeness of the clusters by calculating the sum of squares of the distances between each sample and the cluster center they belong to. The specific formula is as follows:  
\[\text{SSE}=\sum\limits_{i=1}^{k}\sum\limits_{p\in C_{i}}\left|p-m_{i}\right|^{2} \tag{4}\]  
In Equation (4), SSE denotes the sum of squared errors, k denotes the number of clusters, i denotes the cluster number, \(C_{i}\) denotes the set of model performance data samples in cluster i, p denotes the model performance data sample points, and \(m_{i}\) denotes the center of data samples in cluster i. The smaller the sum of squared errors, the closer the data points are to the center of clusters they belong to, and the better the clustering results.  
(3) Davies-Bouldin Index: This index evaluates the degree of separation of clusters by calculating the average distance between each cluster and its most similar cluster, taking into account the closeness within the cluster. A lower Davies-Bouldin Index (close to 0) indicates a better clustering effect. The specific formula for this is as follows:  
\[\text{DBI}=\frac{1}{k}\sum\limits_{i=1}^{k}\max\limits_{j\
eq i}\frac{\overline {S_{i}}+\overline{S_{j}}}{\left\|w_{i}-w_{j}\right\|_{2}} \tag{5}\]where DBI denotes the value of the Davidson-Bourdain index, \(\overline{S_{i}}\) denotes the average distance of all sample element points of the ith category to the cluster center of that category, \(\left\|w_{i}-w_{j}\right\|_{2}\) denotes the distance between the cluster centers of the ith category and the jth category, and \(k\) denotes the number of cluster centers.
# Medium- and Long-Term Load Forecasting for Power Plants Based on Causal Inference and Informer
## 3 Methods
### Load Forecasting Model for Power Plants  
As shown in Figure 2, the external factors were first screened by the MI method to obtain the factors related to load, which was fully described in Section 3.1. Subsequently, the load series with the specified forecast length was obtained using the improved Informer presented in Section 3.2. Then, the causal inference model introduced in Section 3.3 was used: first, a causal diagram was constructed; second, causality was identified by the back door criterion and the front door criterion; and then, causal effects were calculated via different methods. The causal effects were calculated to determine the contribution or inhibition of different external variables to load and thus adjust the prediction results. Historical data were used for the causal effect estimation in the present study. The final predicted load \(L_{n}\) is:  
\[L_{n}=A_{n}\ *\ \frac{1919+\sum_{i=1}^{6}ATE_{i}}{1919} \tag{17}\]  
where \(n\) represents the specific prediction time length; \(A_{n}\) represents the prediction result of the improved Informer model; \(I\) represents the external factor. \(ATE_{i}\) is the causal effect of external variable \(i\) in the forecast period, and 1919 is the historical single-day average value of load. Notably, in a real scenario, the external variables used to calculate the causal effects are predicted by the Informer model, including temperature, rainfall, wind speed, and GDP. Other external variables, such as workday and servicing, can be obtained by inference. To reduce prediction error, external variables other than temperature were designated as binary variables for the rough causal effect calculation.
# Hysteretic Behavior of Steel Reinforced Concrete Columns Based on Damage Analysis
## 4 Determination of Skeleton Curve  
### Simplified Skeleton Curve  
At present, most skeleton curves are obtained by connecting the peak points of the member hysteresis curves. In fact, the members would produce a certain degree of damage under the process of cyclic loading. With the increase of the number of cycles and displacement amplitude, the damage  
Figure 5: Hysteresis curves and skeleton curve of specimens. (**a**) SRC-2; (**b**) SRC-3; (**c**) SRC-4; (**d**) SRC-5; (**e**) SRC-6; (**f**) SRC-7; (**g**) SRC-8.  
accumulation of the members continuously increases. Therefore, it is difficult to determine the skeleton curve by the existing method and truly reflect the degradation of the mechanical properties of the members under an earthquake. A monotonic load-displacement curve can be used as a skeleton curve to better reflect the degradation of the structural members performance caused by cyclic loading and describe the hysteresis characteristics of structural members under an earthquake [56; 57]. Therefore, in this paper, the load-displacement curve under monotonic loading of members was used as the skeleton curve as shown in Figure 6. Based on the results of this test, it can be seen that the SRC frame column slightly cracks before yielding. In addition, the lateral deformation of the member is smaller and the slope of the loading curve changes little. At the same time, the initial stiffness of the skeleton curve of the members is relatively large, there is no obvious inflection point when the specimen yields. The strength after yielding is still greatly improved. Therefore, at the initial stage of loading, the skeleton curves are basically coincident and the peak load is close. After the peak load, although the strength of the member decreases, the slope of the falling part is not large, which indicate that the strength degradation of the members is relatively slow. However, the damage accumulation of the members continually increases under repeated loading, which induces the degradation of the bearing capacity and stiffness, and the falling part of the skeleton curve becomes steeper. The ultimate deformation is reduced. Considering that the main purpose of the elastoplastic seismic response analysis is to study the mechanical behavior of the member after entering the inelastic stage, in order to simplify the calculation, in this paper, the skeleton curve before the yield of the SRC frame column can be simplified by a connection from the coordinate origin to the yield point. Therefore, the skeleton curve of the SRC frame column can be simplified to an ideal trilinear skeleton curve model that is shown in Figure 7. The segment OA is the elastic stage, and the segment AB that has a significant strength hardening section in the skeleton curve after the specimen yielded, is the elastic-plastic stage. In addition, the segment BC is the plastic descent segment.  
Figure 6: Typical monotonic and cyclic experimental response of the steel reinforced concrete (SRC) frame column.  
Figure 7: Simplified skeleton curve.
# C-RAN Traffic Aggregation on Latency-Controlled Ethernet Links
## 3 Traffic Aggregation
### Integrated Hybrid Optical Network in C-RAN  
Figure 1 shows a sample network topology implementing the C-RAN. The BBU serving a RRH can be activated in different hotels for resource optimization, service continuity or energy efficiency, thus possibly requiring dynamic association between RRHs and BBUs. This dynamic association is thought to be managed by a suitable SDN control/management plane. Moreover, traditional base stations (e.g., LTE eNB) may also be present in the same area, requiring connection to the core network. As a consequence, both FH and BH traffic need to be transferred on each optical network segment. A solution to deploy such a scenario can be to assign dedicated wavelength channels to each kind of traffic, either FH or BH, so that FH links can be designed to meet strict delay requirements and BH traffic is statistically multiplexed on separated channels. FH delay requirement comes from the 3 milliseconds budget for round trip time in Hybrid Automatic Repeat Request (HARQ). This budget includes the RRH and BBU processing, which leaves only 100-200 microseconds for fronthaul one-way propagation delay. In addition, CPRI has one-way jitter requirement of few nanoseconds.  
The integrated hybrid multiplexing scheme IHON was firstly proposed to implement statistical multiplexing of the GST (Guaranteed Service Traffic) and SM (Statistical Multiplexed) in Ethernet packet-based nodes [7]. In IHON, a small fixed delay (\(\Delta\)) is added to guaranteed traffic (GST) so that statistically multiplexed (SM) traffic can be inserted in GST gaps, with minimum delay and zero PDV (Figure 2), as it was experimentally proved in [18]. With the aim to minimize the delay of GST traffic, IHON can be extended to allow GST traffic pre-emption on SM traffic and the effectiveness of this mechanism was analyzed in [20].  
Here, the integrated hybrid concept with pre-emption is applied to a network segment of a C-RAN where FH traffic, i.e., CPRI flow encapsulated in Ethernet frames [27], is identified as GST, with zero PDV, while BH traffic deals with pre-emption as SM traffic. During the transmission of a FH frame, incoming BH packets are stored in a buffer until an output channel is free. A scheduler (represented by the block S in Figure 2) senses the input channels to detect FH frames and is in charge of deciding when to start and interrupt the transmission of BH packets on the output channels. IHON eliminates PDV of the FH traffic because the fixed delay \(\Delta\) enables a time-window which gives sufficient time for processing and decision of BH packet preemption. This goes beyond, e.g., the IEEE 802.1 Qbu pre-emption [28] recommended in the IEEE 802.1 CM standard [29] for FH, where FH packets may experience PDV corresponding to the service time of 155 Bytes anyway.  
Figure 2: Integrated Hybrid Node (IHN) multiplexing scheme.
# Plant-Inspired Soft Growing Robots: A Control Approach Using Nonlinear Model Predictive Techniques
## 5 Results and Discussion
### MHE Performance Evaluation  
In the first set of simulation experiments, we evaluated the performance of the proposed MHE towards full state estimation of the vine robot. Measurements of joint-space values \(\mathbf{y}_{m}\) were involved in the estimation process with estimation horizon \(N_{e}=10\) and sample time \(T=0.1\). A sensor noise was added to the measurements with \(\sigma_{s}=0.1\) (m), \(\sigma_{\theta}=10\) deg., and \(\sigma_{\phi}=10\) deg. while uncertainties in the control inputs with \(\sigma_{s}=0.1\) (m/s), \(\sigma_{\theta}=10\) deg./s, and \(\sigma_{\phi}=10\) deg./s were considered. Figure 4 shows the joint-space values \(s_{e},\theta_{e}\) and \(\phi_{e}\) estimated from measurements \(s_{e},\theta_{e}\) and \(\phi_{e}\). Meanwhile, the robot's Cartesian position, \(x_{e}\), \(y_{e}\) and \(z_{e}\) are estimated and compared to the ground-truth data generated beforehand. A satisfactory small Sum of Root Mean Square Errors (SRMSE) is achieved of 74.5 mm where  
\[\text{SRMSE}=\text{RMSE}_{x}+\text{RMSE}_{y}+\text{RMSE}_{z} \tag{12}\]  
and where  
\[\text{RMSE}=\sqrt{\frac{1}{N_{s}}\sum_{i=1}^{N_{s}}(\psi-\psi_{e})^{2}},\quad \psi=x,y\text{ or }z\]  
with \(N_{s}\) samples of the estimated \(\psi_{e}\) and the ground-truth \(\psi\) data.  
Table 1 shows how increasing the estimation horizon values could affect the estimation performance and the mean computation time of the MHE. Particularly, increasing \(N_{e}\) values will increase the mean computation time dramatically. However, surprisingly, there is no significant enhancement achieved in terms of reduced SRMSE. This is due to the initial state estimation at \(t_{k}=N_{e}\) that mainly depends on the unknown initial state \(\mathbf{x}(0)\). It is worth mentioning that increasing the estimation horizon has negative effects when it comes to incorporating the state estimation of MHE with MPC, since the controller has to wait for \(N_{e}\) samples until having a reliable estimation of the unknown state. Otherwise, during the time \(t_{k}<N_{e}\), the MPC will rely on inaccurate estimation, as will be shown shortly.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \(\mathbf{N_{e}}\) & **RMSE (m)** & **Avg. Computational Time (ms)** \\ \hline
6 & 0.1333 & 19.3 \\
8 & 0.0785 & 19.8 \\
10 & 0.0745 & 21.4 \\
15 & 0.0609 & 24.6 \\
20 & 0.0625 & 29.0 \\
40 & 0.0633 & 44.0 \\
100 & 0.0645 & 112.2 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Effect of increasing the estimation horizon \(N_{e}\) on the performance and the average computational time of the MHE.
## 2 Principle
### Phase Recovery Theory
The gradient of the loss concerning the output is:  
\[\frac{\partial\mathcal{L}}{\partial\hat{\mathbf{s}}}=\frac{1}{N}(\hat{\mathbf{ s}}-\mathbf{s}) \tag{14}\]  
The gradient of the output concerning the input of the fully connected layer is:  
\[\frac{\partial\hat{\mathbf{s}}}{\partial\text{flatten}(\mathbf{Y}^{(L)})}= \mathbf{W}_{fc}^{T} \tag{15}\]  
The gradient of the input to the fully connected layer concerning the weight is:  
\[\frac{\partial\text{flatten}(\mathbf{Y}^{(L)})}{\partial\mathbf{W}_{fc}}= \text{flatten}(\mathbf{Y}^{(L)})^{T} \tag{16}\]  
Consolidated using the chain rule:  
\[\frac{\partial\mathcal{L}}{\partial\mathbf{W}_{fc}}=\frac{\partial\mathcal{L }}{\partial\hat{\mathbf{s}}}\cdot\frac{\partial\hat{\mathbf{s}}}{\partial \text{flatten}(\mathbf{Y}^{(L)})}\cdot\frac{\partial\text{flatten}( \mathbf{Y}^{(L)})}{\partial\mathbf{W}_{fc}} \tag{17}\]  
Ultimately, we derive:  
\[\frac{\partial\mathcal{L}}{\partial\mathbf{W}_{fc}}=\frac{1}{N}(\hat{\mathbf{ s}}-\mathbf{s})\cdot\text{flatten}(\mathbf{Y}^{(L)})^{T}+\lambda\cdot\text{ sign}(\mathbf{W}_{fc}) \tag{18}\]  
The gradient of the bias \(\mathbf{b}_{fc}\) is expressed as:  
\[\frac{\partial\mathcal{L}}{\partial\mathbf{b}_{fc}}=\frac{\partial\mathcal{L }}{\partial\hat{\mathbf{s}}}\cdot\frac{\partial\hat{\mathbf{s}}}{\partial \mathbf{b}_{fc}}=\frac{1}{N}(\hat{\mathbf{s}}-\mathbf{s}) \tag{19}\]  
The parameter update formula using the AdamW optimizer, which separates weight decay from gradient computation, is as follows:  
Estimation of gradient momentum and variance:  
\[m_{t}=\beta_{1}m_{t-1}+(1-\beta_{1})g_{t} \tag{20}\]  
\[v_{t}=\beta_{2}v_{t-1}+(1-\beta_{2})g_{t}^{2} \tag{21}\]  
\[\hat{m}_{t}=\frac{m_{t}}{1-\beta_{1}^{t}},\;\delta_{t}=\frac{v_{t}}{1-\beta_{ 2}^{t}} \tag{22}\]  
Here, \(g_{t}\) represents the current gradient, whereas \(\beta_{1}=0.9\) and \(\beta_{2}=0.999\) denote the momentum coefficients. The parameter update including weight decay is expressed as:  
\[\theta_{t}=\theta_{t-1}-\eta\bigg{(}\frac{\hat{m}_{t}}{\sqrt{\hat{\theta}_{t }}+\epsilon}+\lambda\theta_{t-1}\bigg{)} \tag{23}\]  
Here, \(\eta\) denotes the learning rate, \(\lambda\) signifies the weight-decay coefficient, \(\epsilon=10^{-8}\) represents the smoothing term, and \(\theta\) encompasses parameters such as \(\mathbf{K}^{(l)}\), \(\mathbf{W}_{fc}\), and \(\mathbf{b}_{fc}\), among others. Through the optimization of weights via backpropagation and the minimization of the MSE, a comprehensive mapping from the noisy signal to the denoised output post-neural network processing is accomplished. \[f_{CNN}\Bigg{(} \begin{bmatrix}a(n)\\ b(n)\end{bmatrix} ;\mathbf{W}\Bigg{)}= \begin{bmatrix}\cos\hat{\theta}(n)&\sin \hat{\theta}(n)\\ -\sin\hat{\theta}(n)&\cos\hat{\theta}(n)\end{bmatrix}\begin{bmatrix}a(n)\\ b(n)\end{bmatrix} = \begin{bmatrix}\hat{a}(n)\\ \hat{b}(n)\end{bmatrix}  \tag{24}\]The network outputs \(\hat{a}(n)\) and \(\hat{b}(n)\) constitute the reconstructed complex signal \(\hat{y}(n)=\hat{a}(n)+j\hat{b}(n)\).