esa-sceva/satcom-chunk-collection huggingface dataset:
# A Parallel Approach for Multi-GNSS Ultra-Rapid Orbit Determination
## 3 Computation and Comparison
### Impact of Parallel Approach on the Orbit Solution  
Before further analyzing the efficiency and accuracy of the parallel approach, it is necessary to analyze the accuracy of the non-parallel GNSS POD method. The observation data from DOY 182 to 188, 2018 of the above 131 IGS/MGEX stations are used to carry out the multi-GNSS POD. Analysis of the errors in the radial, along and cross directions of the multi-GNSS orbits using the non-parallel method is performed. As a result, the along track direction accuracy is the lowest, followed by the cross track, and the radial is the highest. Except for slightly larger fluctuations in the BDS in the sense of the orbit RMS, the other systems have little change and the accuracy is relatively stable. The accuracy of each system is further analyzed, which is shown in Table 3. It can be seen from the table that the 1D mean RMS (\(1 DRMS=\sqrt{(\sigma_{R}^{2}+\sigma_{A}^{2}+\sigma_{C}^{2})}/3\)) of GPS, GLONASS, Galileo and BDS are 1.3 cm, 2.7 cm, 2.7 cm, and 5.4 cm, respectively, which are at the same accuracy level as reported by international institutions [42]. The results show the correctness of the non-parallel POD processing, which lays the foundation for the proposed parallel POD.  
It is necessary to further analyze the impact of the parallel approach on the covariance matrix and solution of the normal equations, as well as the precision loss of orbit. Based on MPI, the entire 480 epochs are divided into 2 periods. Statistics of the difference between the matrix elements of the parallel method and those of the non-parallel method is shown in Table 4. It can be seen from these figures that the error impact of the parallel approach on the covariance matrix and unknown parameters are approximately \(10^{-13}\) and \(10^{-6}\), respectively.  
Using the same set of data, the normal equation coefficients of the above-mentioned parallel approach and the normal equation coefficients of the non-parallel approach are saved. After the procedures of parameter estimation, orbit update, and result output, the two sets of orbits are obtained. The comparison of the two sets of orbits show that their  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Satellite System** & **R** & **A** & **C** & **RMS** \\ \hline GPS & 1.0 & 1.5 & 1.2 & 1.3 \\ GLONASS & 1.6 & 3.2 & 2.6 & 2.7 \\ Galileo & 2.7 & 2.8 & 2.4 & 2.7 \\ BDS & 5.9 & 5.3 & 4.2 & 5.4 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Accuracy statistics of multi-GNSS orbit using the non-parallel method (cm).  
Figure 2: Distribution of GNSS-tracking stations. Red triangles denote stations used for GNSS precise orbit determination and blue pentagrams denote stations used for GNSS ultra-rapid orbit determination.  
difference is below the millimeter level, which indicates that the precision loss caused by parallel method can be negligible.
## 2 Hanger Bending Damage and Suspended Lateral Bracing
### Suspended Lateral Bracing for Configuration Transformation  
To address the issue of hanger bending during the configuration transformation, this paper proposes an SLB system. By applying tension to the SLB, the lateral displacement of the main cable in the FHC can be controlled, simplifying the hanger tensioning process and making it more similar to that of traditional planar cable suspension bridges. As shown in Figure 3, the SLB system consists of several key components: the main trusses, wire ropes, remote-controlled winches, a vertical tensioning system, and a lateral stabilizing system. The main trusses serve as axial elements that counteract the lateral forces exerted by the main cable, while the winches and wire ropes are used to position the main cable according to design specifications. The combined action of the vertical tensioning system and the lateral stabilizing system ensures that the temporary structure remains stable during construction. Once the wire ropes are tensioned and the main cable reaches the desired position, the winches are locked in place, effectively reducing the risk of hanger buckling during installation.  
The SLB system functions similarly to a spring, offering a flexible restraint for the main cable. This flexibility allows the cable to undergo controlled lateral displacement under sudden loads. After the load is removed, the system automatically returns to its original position, preventing brittle failure at the connection points between the cable and SLB. This dynamic response mechanism significantly enhances the adaptability and stability of the construction process, providing additional fault tolerance during the configuration transformation of the main cable. By employing the SLB system, the construction process becomes more flexible, and the risk of hanger bending due to angle deviation during the configuration transformation is minimized. The system's ability to adapt to dynamic load changes ensures the stability and safety of the bridge during this critical stage.  
Figure 2: Longitudinal bending damage of hanger during configuration transformation.
However, a few studies considered hybrid meta-heuristic approaches, which are used to explore and exploit the solution search space better. Further, the iterative method used in [11] for unit sizing problem was highly computational, which spanned several hours to find an optimal solution. Further, the HOMER software tool used by researchers [26; 27; 28] for techno-economical analysis of HRESs also suffers from some limitations. For instance, the HOMER tool does not take into account multi-objective problems along with its formulation, ranking of HRESs based on levelized cost, and the depth of discharge (DoD) of the battery bank. Therefore, this paper proposes meta-heuristic algorithms with their hybridization to achieve objectives, including good convergence speed, efficiency, and flexibility for the unit sizing problem. The previous work [30] is enhanced, and the contributions are given below. * A model based on HRESs is proposed, where a PV-WT-battery system and its components are formulated and elaborated. * Meta-heuristic algorithms: teaching-learning based optimization (TLBO), enhanced differential evolution (EDE), and salp swarm algorithm (SSA) are firstly used to find the optimal number of HRESs with an objective function to minimize the user's TAC in an SA environment. * Two novel hybrid approaches based on combining (TLBO + EDE and TLBO + SSA) are also proposed for the better exploitation of the search space. These hybrid approaches are called enhanced evolutionary sizing algorithms (EESAs). * The results obtained by EESAs are compared to their ancestor schemes in three different scenarios: PV-WT-battery, PV-battery, and WT-battery systems for a yearly user's load profile. Further, the real solar irradiation and wind speed data are used, which are obtained from Rafsanjan, Iran. * The reliability of HRESs is considered using four maximum allowable LPSP (\(LPSP^{max}\)) values: 0%, 0.5%, 1%, and 3%, which are provided by the user. The TACs at different \(LPSP^{max}\) values are presented and analyzed. The remaining paper is organized as follows. Section 2 describes the system model, and Section 3 states the formulation of HRESs. The proposed algorithms are elaborated in Section 4. Section 5 discusses the simulation results, and finally, the paper is concluded in Section 6.
## 2 Materials and Methods
### Evaluation Strategy  
In this study, the correlation coefficient, the Nash-Sutcliffe efficiency coefficient, and the normalized root mean squared error were used as indicators of predictive power. Correlation coefficients are methods used to analyze the relationship between two variables.  
\[\text{correlation coefficient}\ =\frac{\sum_{i=1}^{n}(x_{i}-\overline{x})(y_{i}- \overline{y})}{\sqrt{\sum_{i=1}^{n}(x_{i}-\overline{x})^{2}}\sqrt{\sum_{i=1}^{ n}(y_{i}-\overline{y})^{2}}}. \tag{8}\]  
In Equation (8), \(x_{i}\) is the observed value, \(\overline{x}\) is its mean, \(y_{i}\) is the predicted value, and \(\overline{y}\) is its mean. That is, x denotes the data from the station, and y denotes the data from the prediction model.  
The Nash-Sutcliffe efficiency coefficient means that the predicted result is poor or inconsistent if the value is negative and can be computed as:  
\[\text{Nash-Sutcliffe efficiency coefficient}=\frac{\sum_{i=1}^{n}(y_{i}- \overline{y})^{2}-\sum_{i=1}^{n}(y_{i}-\overline{y}_{i})^{2}}{\sum_{i=1}^{ n}(y_{i}-\overline{y})^{2}}, \tag{9}\]  
where \(y_{i}\) is the observed value, \(\overline{y}\) is the mean, and \(\overline{y}_{i}\) is the predicted value. A positive value means that using the predicted result will provide better results than using the average of the observations, and a value closer to 1 means an ideal result.  
Furthermore, the normalized root mean squared error is the value obtained by dividing the numerator root mean squared error by the range (maximum-minimum) of the denominator, the actual value. The closer it is to 0, the smaller the degree of error.  
\[\text{Normalized root mean squared error}\ (\%)=\frac{\sqrt{\frac{1}{n}\sum_{i=1}^{n} \left(y_{i}-\hat{y_{i}}\right)^{2}}}{Max(y_{i})-Min\left(y_{i}\right)}\times 100. \tag{10}\]  
In Equation (10), \(y_{i}\) is the observed value, and \(\hat{y}_{i}\) is the predicted value.  
Figure 5: Conceptual diagram of the deep neural network.
# DPS Clustering: New Results
## 4 Results: Third Stage of DPS
### FirstPart: The Theory of \(d\)-Clusters
#### 4.2.1 The Notation
Proof of the inequality \(r(X_{k}(x))\leq\max_{i=1}^{k}d_{i}(x)\). Induction on \(k\), \(1\leq k\leq|X|-2\)  
* \(k=1\): \(X_{1}(x)=\{x_{0},x_{1}\}\) and \(d(x_{0},x_{1})=d_{1}(x)\) according to (14) and (15). * Suppose that \(r(X_{k-1}(x))\leq\max_{i=1}^{k-1}d_{i}(x)\), that is, any two points in \(X_{k-1}(x)\) can be connected by a path with distance transitions \(\leq\max_{i=1}^{k-1}d_{i}(x)\). Let \(x^{*}\) be the point in \(X_{k-1}(x)\), closest to \(x_{k}\). According to (15), \(d_{k}(x)=d(x^{*},x_{k})\). Through \(x^{*}\) any point in \(X_{k-1}(x)\) can be connected to \(x_{k}\) by a path with distance transitions \(\leq\max_{i=1}^{k}d_{i}(x)\). 2. Proof of the inequality \(r(X_{k}(x))\geq\max_{i=1}^{k}d_{i}(x)\): let \(d_{i^{*}}(x)=\max_{i=1}^{k}d_{i}(x)\), then \(d_{i^{*}}(x)=d\left(X_{i^{*}-1}(x),\overline{X_{i^{*}-1}(x)}\right)\), and any path with ends in \(X_{i^{*}-1}(x)\) and \(\overline{X_{i^{*}-1}(x)}\) has at least one jump between them. Therefore, \(r(X_{k}(x))\geq d_{i^{*}}(x)\). For the eigen \(d\)-cluster \(C\) (Definition 7), the proved statement means that the necessary condition is fulfilled  
\[r(C)<e(C). \tag{17}\]  
It is invariant not only from the beginning of the enumeration but also from the enumeration itself, which is obligatory at this point for the definition of \(C\). Therefore, it is natural to check this condition for sufficiency of \(d\)-clustering. **Statement 5**. : _If (17) is satisfied for an eigensubset of \(A\) in \(X\), then \(A\) is a \(d\)-cluster and \(A=C_{|A|-1}(x)\ \forall x\in A\)._  
Proof. : There exists \(r^{1}\): \(r(A)\leq r^{1}<d(A,\bar{A})\) for which the set \(A\) is \(r^{1}\)-connected. Hence, in the enumeration \(X(x)\) of space \(X\) from any point \(x\in A\) the elements from \(\bar{A}\) will appear only at the \(|A|\)-th step. The result of Definition 8, Statement 4 and Statement 5 is a new invariant and more complete definition of a \(d\)-cluster. **Definition 9**. : _Let us call a \(d\)-cluster in \(X\) the subset \(C\) for which there is a true inequation: \(r(C)<d(C,\bar{C})\)._To the eigenclusters \(C\)\((1<|C|<|X|)\) will be added all points \(x\in X\): \(x=C_{0}(x)\), and all space \(X\): \(X=C_{|X|-1}(x)\)\(\forall x\in X\). Thus, the restrictions in Definition 7 on \(k\)\((1\leq k\leq|X|-2)\) are removed:  
* \(x\Leftrightarrow d\)-cluster, since \(0=r(x)<e(x)\)\(\forall x\in X\),
* \(X\Leftrightarrow d\)-cluster, since \(r(X)<e(X)=\infty\): no appearance for \(X\) means that it is at infinity.
# Optimization of Truck-Drone Parcel Delivery Using Metaheuristics
## 1 Introduction
### Solution-Based Metaheuristic Approaches to TSP-D  
Solution-based metaheuristics have been used in previous studies to solve the TSP-D [6; 11; 25] and related FSTSP problems [12; 22; 23; 24]. An initial tour for the simulated annealing algorithm [26] was implemented by [PERSON] [22] using a nearest-neighbor heuristic. To make a move (i.e., selecting a drone node for a sortie), several neighbors were randomly generated, and the roulette-wheels selection method [27] was used to choose a neighbor. [PERSON] and [PERSON] [23] first found the optimal solution for the TSP using the Concorde solver. The initial solution for the FSTSP was then defined, using a heuristic utilizing a greedy approach. This procedure removes a truck customer and assigns it to a drone, effectively partitioning the truck route into sub-routes. The initial solution was optimized using the variable neighborhood search [28]. Seven different neighborhood structures were used and randomly selected, resulting in a change in the original sequence of node visits. Similarly, [PERSON] and [PERSON] [23; 29] used a randomized variable neighborhood descent heuristic with five different neighborhoods. [PERSON] et al. [11] attempted to solve the TSP-D using two heuristics, TSP-LS and GRASP. The aim of this paper was to minimize the total operational cost of the two vehicles. In each iteration, a new giant tour (TSP tour) was generated using three different heuristics: k-nearest neighbors, k-cheapest insertion, and random insertion. A split algorithm built the minimum cost (min-cost) TSP-D solution from the giant tour solution by substituting a truck customer with a drone. After building the min-cost solution, the LS improved the solution using four move operators. The tests conducted in this study showed that the k-nearest neighbors generated a better min-cost TSP, when compared with k-cheapest insertion and random insertion. The quality of solutions obtained with GRASP outperformed those obtained with TSP-LS. However, TSP-LS was faster than GRASP. The proposed GRASP method has been modified by [PERSON] et al. [6], such that the drone can launch from and join the truck not only at a customer node, but also along the route.
## 3 Methodology
### IPTs for Crack Segmentation  
In the present hybrid approach, DO-YOLOv4-IPTs, once the crack region is detected by DO-YOLOv4, the IPTs based on the adaptive thresholding method and connected component analysis will be further used for crack segmentation, as shown in Figure 7. To effectively identify crack pixels for each input pixel, the adaptive thresholding method will assign an adaptive threshold as \(A_{\text{th}}=I_{\text{m}}-C\), in which \(I_{\text{m}}\) is the mean pixel intensity of a square region around the input pixel and \(C\) is a given constant. When the intensity of the input pixel is lower than the threshold, it is classified as the crack pixel (black), and the contrary is classified as the background pixel (white). For example, for the input pixel A with an intensity of 70, as shown in Figure 7, the adaptive threshold is taken as \(A_{\text{th}}=I_{\text{m}}-C=97-5=92\), in which \(I_{\text{m}}=97\) is the mean pixel intensity of a region of \(3\times 3\) pixels around pixel A and \(C=5\) is the given constant. As the intensity of pixel A is smaller than the adaptive threshold, it is identified as a crack pixel. However, for the input pixel B in Figure 7, it can be identified as a background pixel using the same method.  
Figure 5: Bounding boxes for crack detection.  
Figure 6: The definition of an oriented bounding box.  
To further improve the accuracy of crack segmentation, the connected component analysis is conducted to eliminate the falsely classified crack pixels. For illustration, the crack pixels in Figure 8 are first clustered into several connected components, and the respective areas can be calculated based on the number of crack pixels within each component. Then, an area threshold \(AR_{\text{th}}\) can be determined by analyzing the size of each component. The crack pixels within the components that are smaller than the area threshold \(AR_{\text{th}}\) can be regarded as falsely classified crack pixels and thus can be removed, leading to a more accurate segmentation result.
## 3 The Picking Problem  
### Problem Statement  
The research is based on data made available by a German retailer with the layout of one of their stores and real BOPS orders placed online to be picked up at the store. Following the idea of [17; 18], the layout of the store was divided into 15 zones (Figure 1) according to the locations and product categories. Zone 1 contained the entrance and zone 15 contained the exit. Each product is located in a certain zone. By assuming each product in the given zone has an equal probability of being picked, we are able to define the center of zones and calculate the approximated distances \(d_{ij}\) between zone \(i\) and zone \(j\) (\(i\
eq j|i,j\in\{1,2,\ldots,15\}\)). With a walking speed estimated at 0.85 m/s, the approximate travel time between different zones is shown in Table 1.  
A BOPS order is a list of products to be picked by an employee of the store. To complete our simulation analysis in this work, each product has the attributes of volume, mass, density and type of packaging on top of the zone containing it.  
As stated in Section 1, for retailers such as the one under investigation, there is currently no optimization being developed relative to the in-store picking process of BOPS orders. A list of articles is usually presented alphabetically or randomly to the person in charge. After a preliminary review of the list, an experienced employee normally uses the store topology to self-organize a time- and distance-saving path through the store based on their knowledge of the store. In practice, however, pickup of online orders is frequently assigned to part-time workers with marginal experience. In such a case, a simple optimization aiming at minimizing the travel distance to fulfill the orders can be proposed. Extended modeling with impacts of the employees' characteristics on the optimization approach is expected in a future work.  
In the following subsections, we introduce three shortest path-like analyses that focus on different aspects to optimize the picking process.
# Effect of PVA/PVAc Based Polymer Coating on Dust Reduction in Playground
## 4 Conclusions  
This study investigated the effect of PVA coating on the physical properties, permeability, and dust generation of playground soil. The following conclusions can be drawn based on the results.  
Coating the playground soil particles with PVA/PVAc solution reduced the moisture content and slightly increased the specific density. It caused a reduction in the absorption of soil samples, which ultimately reduced the liquid and plastic limits. The coefficient of permeability increased with the increase in coating solution content. Further, coating the soil particles significantly reduced the PM\({}_{10}\) and PM\({}_{2.5}\) generation due to the wind effect, as well as human activity.  
Based on the findings of this study, it can be concluded that coating the soil particles of playgrounds will significantly reduce dust generation. Reduction in dust generation will ultimately reduce threats to the health of children associated with dust ingestion and inhalation. However, an extended observation is required to be carried out to understand dust reduction in real playgrounds.
## 1 Introduction  
The state-dependent Riccati equation (SDRE) method has become more popular due to the possibility of designing more effective nonlinear controllers and providing flexibility through state-dependent weighting matrices, which is well presented in [1]. This method scheme originates from the LQR method [2, 3] and is also similar to the MPC (or its nonlinear version, NMPC) [4, 5, 6]. The main differences between SDRE and those two methods are, for example, unlike the LQR method, the SDRE sets up its control laws at every time-step. The MPC method requires a convex optimization technique, while SDRE and LQR methods utilize optimal control laws for linear systems [7, 8].  
The SDRE control method reformulates the nonlinear dynamics using parameterization to a linear structure with state-dependent coefficient (SDC) matrices, which are essential to solve an algebraic Riccati equation (ARE) and obtain the suboptimal control law. The coefficients of the ARE equation differ in the state space. Thus, at a given point in state space, it is essential to solve an algebraic state-dependent Riccati equation. The nonuniqueness of the state-dependent parameterization (SDP) allows us to obtain extra degrees of freedom, which may help to enhance controller performance. Minimization of the nonlinear performance index gives a quadratic-like structure [9, 10, 11, 12].  
In the last decade, this method has been used in many different areas of research, for example, satellite and spacecraft control and estimation [13, 14], control of servoprenumatic drives [15], control of quadrotor aircraft [16, 17, 18, 19, 20], robotics [21, 22], control of non-affine systems [23], and even in medical sciences for cancer treatment allowing optimization of drug dosing control [24].  
The main disadvantage of this classic SDRE strategy is that Riccati equations are state dependent. Therefore, it is necessary to solve SDRE multiple times during the control process [25, 26]. Nowadays, the solution can be successfully implemented in real control systems due to developments of digital controllers. However, the solution can be found faster, reducing computational effort and introducing linearization of closed-loop form. As a new contribution, the paper presents a possible solution for suboptimal control of nonlinear systems by solving the algebraic Riccati equation only once in the whole control process. Using linearization of the closed-loop system and introducing Moore-Penrose inversion [27], it is possible to modify SDRE into ARE. For the modified SDRE method, it is possible to obtain the same solution as for classic SDRE method. The advantage of the modified case is that there is no need to solve the state-dependent Riccati equation for each state of the control process. This allows us to save space for implementation in real-time control systems and simplifies computations. The specific differences between classical and modified methods are presented in the sections below.
# Residual Life Prediction of SA-CNN-BILSTM Aero-Engine Based on a Multichannel Hybrid Network
## 4 Experimental Validation
### Evaluation Criteria
#### 4.1.2 RMSE  
The prediction of an aero-engine's remaining useful life (RUL) is typically classified as a regression task. The root-mean-square error (RMSE) is a commonly employed evaluation metric in regression problems. The RMSE is utilized to gauge the disparity between the true value and the predicted value. The smaller the RMSE value, the more favorable the prediction performance of the model. Its calculation formula is presented as follows:  
\[RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_{i}-\widetilde{y_{i}})^{2}} \tag{8}\]  
where \(n\) is the total number of test samples, and \(y_{i}\) and \(y_{i}\) are the true and predicted remaining useful life (RUL) values for the \(i\)th test sample data, respectively.