esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Global Positioning System (GPS) L1 Receiver: 2D Pattern vs. 3D Pattern
### Navigation Solution
#### 3.4.1 Least Squares Estimation  
In Table 4 the navigation solution statistics are shown, while Figure 17 illustrates the zoomed navigation solution for the two assumed patterns. Looking at Figure 17, we can see that the performance is quite similar for both cases; however, according to Table 4, using a 2D pattern would result in better navigation performance for the full MTO; on the other hand, looking at the statistics of each evaluated portion using a 3D pattern results generally in better statistics. This is only true because of a few points where the GDOP considerably affects the navigation solution in the case of a 3D pattern. Indeed, as already mentioned in Section 3.2, the number of observations available when using a 3D pattern has a higher standard deviation, leading to a larger number of outages (as well as more peaks in the number of satellites), which causes a very bad relative geometry between the transmitters and the receiver. Indeed, the maximal GDOP for the 2D pattern is \(2.5\times 10^{6}\), while for the 3D pattern it is \(4.7\times 10^{7}\) and the GDOP has more peaks in case of the 3D pattern compared to the 2D one.  
Figure 16: \(\sigma_{DDLL}\), when assuming 3D transmitter patterns.
## 2 Topology Optimization under Single- and Multiple-Loading Conditions  
In this section, we begin by discussing the TO formulation of an optimum design problem under a single-loading condition based on the SIMP approach. This discussion will provide a foundational understanding of how to state TO problems by choosing the objective function and design variables. Subsequently, we extend our discussion to consider multiple load cases. Towards the end of this section, the min-max compliance formulation of TO under multiple-loading conditions is explained. This formulation serves as a critical foundation for the method proposed in this article.
## 1 Introduction
Based on the assumption that only the position and attitude of the quadrotor are known, we devise an ESO to supply estimations of velocity, angular rate states, and the lumped disturbances. (ii) We devise a robust backstepping TTC algorithm to achieve the tracking control task in the presence of lumped disturbances and control input saturation. This contribution is clearly superior to the reduced-order observer based control approaches presented in [30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42], which can only achieve a partial solution of the robust adaptive saturated tracking control problem. To overcome the problem of \"explosion of complexity\", which is generally problematic in integrator backstepping control, dynamic filters (also referred to as linear tracking differentiator [49]) are applied to compute the derivative of virtual control signals. (iii) We use the Lyapunov theory to verify the stability of the closed-loop system and prove that both the ESO estimation errors as well as tracking errors are ultimately bounded, despite the presence of lumped disturbances and control input saturation. The remainder of this paper is organized as follows. Section 2 presents the quadrotor dynamics model and problem formulation. Section 3 contains the design and stability analysis of an ESO. Based on the devised ESO, a robust trajectory backstepping saturated controller is proposed in Section 4. The stability of the closed-loop system is analyzed in Section 5. Numerical simulation results and discussions are provided in Section 6, before ending with overall conclusions in Section 7.
## 3 Methodology
### Evaluation Metrics  
To evaluate model performance on the test set (15% of the data), several statistical metrics are employed: Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), accuracy, Pearson correlation coefficient, and the coefficient of determination (\(R^{2}\)). These metrics are computed by comparing predicted values against ground truth observations and are widely used in the evaluation of time series forecasting models.  
* **RMSE (Root Mean Squared Error)**: Square root of the average of the squared errors: \[RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_{i}-\hat{y}_{i})^{2}},\] where \(y_{i}\) are the actual values and \(\hat{y}_{i}\) are the predicted values.
* **MAE (Mean Absolute Error)**: Average of the absolute errors: \[MAE=\frac{1}{n}\sum_{i=1}^{n}|y_{i}-\hat{y}_{i}|.\]
* **Accuracy**: A measure of model precision; in this case, a prediction is considered correct if the difference between the predicted and actual value is less than 10% of the actual value: \[\text{Accuracy}=\frac{\text{Number of predictions within the 10% threshold}}{\text{Total number of predictions}}.\] The 10% threshold is justified considering that the analyzed ambient noise levels have average values around 60 dB. Thus, a relative error of less than 10% corresponds approximately to an absolute error of less than 6 dB, which is within the acceptable range for urban noise prediction and operational monitoring tasks.
* **Pearson Correlation**: Measures the strength and direction of the linear relationship between two variables: \[r=\frac{\sum_{i=1}^{n}(y_{i}-\bar{y})(\hat{y}_{i}-\bar{y})}{\sqrt{\sum_{i=1}^ {n}(y_{i}-\bar{y})^{2}\sum_{i=1}^{n}(\hat{y}_{i}-\bar{y})^{2}}},\] where \(y_{i}\) represents the actual values, \(\hat{y}_{i}\) represents the predicted values, \(\bar{y}\) is the mean of the actual values, and \(\bar{y}\) is the mean of the predicted values.
# Performance Analysis of BDS-5G Combined Precise Point Positioning
## 2 Methodology
### Observation Model for BDS-5G PPP
#### 2.1.3 Observation Model for BDS-5G PPP  
BDS PPP uses the ionosphere-free combination, and then, the BDS PPP observation model and 5G millimeter wave observation model are normalized to a unified coordinate system. Equations (1)-(3) are coupled to obtain the combined BDS-5G observation model as shown in Equation (4):  
\[\left\{\begin{aligned} P^{(s)}=\rho^{(s)}-c(\delta_{tr} \leavevmode\
obreak\ -\delta_{ls}^{(s)})+\delta_{trop}+\delta_{ tide}+\delta_{rel}+\varepsilon_{Pc}\\ \lambda\Phi^{(s)}=\rho^{(s)}-c(\delta_{tr}\leavevmode\
obreak\ -\delta_{ls}^{(s)})+\lambda N^{(s)}+\delta_{trop}+\delta_{ tide}+\delta_{rel}+\varepsilon_{qc},\\ cT^{(b)}=d^{(b)}-c\cdot\delta_{tb}+\varepsilon_{T}\end{aligned}\right. \tag{4}\]  
where \(P\) and \(\Phi\) are the pseudorange and carrier phase of dual-frequency ionosphere-free combination observations, respectively; \(N=\frac{f_{1}N_{1}-f_{2}N_{2}}{f_{1}-f_{2}}\); \(\lambda=\frac{c}{f_{1}+f_{2}}\); \(\varepsilon_{Pc}\) and \(\varepsilon_{qc}\) are the residuals of iono-free combination.
# A Size-Controlled AFGAN Model for Ship Acoustic Fault Expansion
## 2 GAN for Acoustic Fault Sample Expansion
### AFGAN Network Architecture  
The AFGAN is modelled by employing the DCGAN structure. Unlike a conventional GAN which generates two-dimensional images, the AFGAN generates one-dimensional signals. A schematic diagram of the AFGAN architecture is shown in Figure 1.  
The generator performs signal expansion. Its inputs are the latent representation \(z\) (\(z\in\mathbb{R}^{Q}\)), and its output is the expanded signal \(G(z)\) (\(G(z)\in\mathbb{R}^{p}\)). The generator is designed to be fully convolutional, which makes the model focus only on the time correlation of the input signal. Its input is uniformly distributed noise \(z\), and then its output is reshaped into a four-dimensional tensor. Finally, a single-channel acoustic fault signal \(G(z)\) can be generated through multiple fractional-strided convolution layers. The output layer adopts the Tanh activation function while the other layers adopt the ReLU activation function [20]. For the discriminator, the input signal, i.e., expanded signal \(G(z)\) or the real signal \(x\), is converted to a single-feature map through multiple convolution layers in order to tell whether it comes from real or generated samples. The leaky ReLUn [20] is adopted in the activation function in all the layers.  
An important feature of the AFGAN model is its end-to-end structure. The original signal does not need to be specially processed, such as undergoing feature extraction and can be directly inputted into the AFGAN model to generate expanded samples.
## 2 Sea Surface Model
### Statistical Model  
Results from a field experiment and in situ measurement show that the probability distribution function (PDF) of sea surface slopes can be approximated by a Gaussian distribution [16,26,27,28]:  
\[p(\theta)=\frac{2}{\pi\sigma^{2}}\mathrm{exp}\left[-\frac{\tan^{2}\theta}{ \sigma^{2}}\right]\tan\theta\mathrm{sec}^{2}\,\theta \tag{1}\]  
where \(\theta\) is the isotropic surface slope, and \(\sigma^{2}\) is the total MSS related to the wind speed \(U\).  
The cumulative distribution function (CDF) for \(\theta\) is  
\[P(\theta)=1-\mathrm{exp}\left[-\frac{\tan^{2}\theta}{\sigma^{2}}\right]. \tag{2}\]  
Therefore, the polar angle of the normal to a wave facet can be written as tan\(\theta\) = \(\sqrt{-2\sigma^{2}\mathrm{ln}(\eta)}\), and the isotropic azimuthal angle is \(\varphi\) = 2\(\pi\eta\), where \(\eta\) is uniformly distributed between 0 and 1. The normal vector \(\overrightarrow{n}\) with respect to the normal to the horizontal is a combination of the wave facet slope \(\theta\) and direction \(\left]\varphi\right]\)[17,22,23].  
The wind field above the sea surface influences the distribution of sea surface slopes by impacting the \(\sigma^{2}\) values. [PERSON] and [PERSON] proposed a linear relationship between the MSS and wind speed for the open ocean based on aerial photographs [16]:  
\[\sigma^{2}=0.003+5.12\times 10-3U\pm 0.004 \tag{3}\]  
Furthermore, [PERSON] et al. obtained a nonlinear relationship between the MSS and \(U\) by comparing sea surface backscatter data from Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) with matched-up Advanced Microwave Scanning Radiometer for EOS (AMSR-E) wind speed measurements [29]:  
\[\sigma^{2}=\left\{\begin{array}{ll}0.0146\sqrt{U}\left|\right|\right|&U<7 \;\mathrm{m}\;\mathrm{s}^{-1}\\ 0.003+0.00512U\left|\right|\|&7\;\mathrm{m}\;\mathrm{s}^{-1}\leqslant U<13.3\; \mathrm{m}\;\mathrm{s}^{-1}\\ 0.138\mathrm{log}_{10}U-0.084\left|\right|&U\geqslant 13.3\;\mathrm{m}\; \mathrm{s}^{-1}\end{array}\right. \tag{4}\]For wind speeds from 7 m s\({}^{-1}\) to 13.3 m s\({}^{-1}\), Equation (4) directly follows the formula of Equation (3), whereas a bias is observed at other wind speeds. This discrepancy is due to the sensitivity of the laser to finer capillary wave structures, resulting in higher values from Equation (4) at wind speeds below 7 m s\({}^{-1}\) than those from Equation (3) [29]. Even though Equation (3) is commonly employed [17; 18; 19; 20; 21; 22], Equation (4), derived from LIDAR data, may offer a suitable framework for analyzing laser transmission characteristics [23; 27; 28; 29].
# MBSE Testbed for Rapid, Cost-Effective Prototyping and Evaluation of System Modeling Approaches
## 3 Results
### Logical Architecture of MBSE Testbed
#### 3.3.1 System Modeling and Verification  
The testbed offers both deterministic-modeling and probabilistic-modeling capabilities. In particular, it offers SysML modeling for deterministic systems and partially observable Markov decision process (POMDP) modeling for probabilistic systems. Exemplar models of both types are provided in an online \"starter kit\" to allow users to make a copy before commencing the system modeling activity. Verification in this context pertains to ascertaining model correctness (i.e., model completeness with request to questions that need to be answered, semantic and syntactic consistency, and model traceability to requirements).  
Figure 2: Prototype MBSE testbed logical architecture.
# Application of Bonded-Block Models to Rock Failure Analysis
## 5 Concluding Remarks  
Discrete element models, a class that presently encompasses a wide variety of numerical formulations, have been primarily employed in rock mechanics to study collapse mechanisms induced by rock mass discontinuities. In such cases, rigid or elastic blocks are a common assumption and provide an effective performance. The bonded-block concept, by addressing the possibility of block fracture, enhances the range of applications of these models, namely, for underground excavation problems involving higher stress levels. Another important application lies in the analysis of block systems generated by discrete fracture network algorithms, in which bonded-block models may be used to take into account the possible breakage of rock bridges.  
The present investigation shows that a bonded-block model based on simple mechanical assumptions is able to reproduce fairly complex modes of failure found in underground works in rock. This type of model can be built with a discrete element code based on a standard contact formulation and the use of rigid blocks. Fracture energies can be controlled by incorporating a bilinear softening curve into the contact models.  
In the example presented, polygonal and triangular-block systems were used, both displaying suitable performance. Voronoi polygons provide a natural representation of a rock grain structure. Triangular networks facilitate mechanisms governed by dominant shearing patterns. Further research is required to assess their comparative advantages, in 2D and 3D, for typical underground excavation problems. The selection of the required block size, considering the excavation dimensions and the expected extent of failure regions, also requires more comprehensive studies of validation against field data. Another critical research topic is the development of robust procedures for the calibration of micro-properties in a systematic manner.  
In order to focus on the key bonded-block concepts, the example analyzed was simplified by omitting pre-existing rock mass discontinuities. In practical problems, when rock mass jointing is included, the inner-block mesh is an important tool to allow the breakage of blocks, thus preventing non-realistic safety assessments. In these cases, the type of interior pattern may be less critical, while the calibration of the micro-properties that govern rock matrix fracture remains a central issue.  
This research received no external funding.  
**Institutional Review Board Statement**: Not applicable.  
**Informed Consent Statement**: Not applicable.  
**Data Availability Statement**: The data presented in this study are available on request from the author.  
**Conflicts of Interest**: The author declares no conflict of interest.  
Figure 7: Failure modes for the case of vertical side walls. (**a**) Voronoi block model; (**b**) triangular-block model.
# Underlying Security Transmission Design for Orthogonal Time Frequency Space (OTFS) Modulation
## 5 Security Performance Analysis
### Brutal Force Attacks  
Brutal force attacks are also exhaustive search attacks. In this attack mode, the attacker [PERSON] insists on trying all possible secret keys in the secret key space until the correct secret key is successfully found. In fact, when the key space is large enough, it will cause the exhaustive search to fail, thereby resisting brutal force attacks. In other words, whether an encryption system can resist brutal force attacks depends on the size of the key space. Because our key is extracted based on channel state information, the slightest change in the channel will result in a completely different key. Take the OTFS system with \(N=256\) and \(M=16\) as an example, the size of the IFFT matrix is \(256\ast 256\), so its key space size is \(256\); the size of the FFT matrix is \(16\ast 16\), so its key space size is \(16\)!. Therefore, the total key space of our proposed transmission mechanism is \(10^{578}\). Assuming that the fastest computer, whose calculation speed is \(2.5\times 10^{13}/s\) that, is used to obtain the correct secret key, the illegal eavesdropper [PERSON] will spend \(10^{556}\) years. This will cause the exhaustive search to fail, so the transmission mechanism we propose is sufficient to resist brutal force attacks.
## 3 Calculation Results and Discussion
### Hybrid System Off-Design Performance Evaluation under Variable Operation Parameters
#### 3.3.3 Effect of Variable AS-Ratio on Hybrid System Performance
Figure 14A illustrates the variation of key performance parameters with six AS-cathode from Table 7, perturbed from 0.2 to 0.9. As AS-cathode increases, SOFC power converges to design point demand. Moreover, at lower AS-cathode ratios in Figure 15, the CPOx fuel generation is suboptimal leading to lower SOFC FU, hence lower electric efficiencies in the SOFC (Figure 14A). Higher AS-cathode values enhance stack efficiency by improving working temperature and electrochemical reactions, yielding design point power output. Enhanced SOFC FU at higher AS-cathode ratios approaches the ideal 75%, improving electric efficiency, enabling the SOFC to produce 102 kW, and meeting design point power demand. Evaluation of GT performance parameters from Figure 14B reveals an inverse trend compared to Figure 12B. TSFC increases with higher AS-cathode ratios, from 280 to 312.5 mg/s/N, and this is due to decreasing thrust, necessitating more fuel consumption for less thrust generated--an undesirable outcome. However, the thrust decrease remains within an acceptable range, ranging from 8.7 to 8 kN, a modest reduction given the concurrent improvement in SOFC performance within the same range. Hence, achieving a delicate balance between thrust and electric power generation is crucial, and optimal equilibrium is achieved towards AS-cathode 6, where reformer operation ensures adequate fuel supply for the SOFC without compromising thrust generation. The shaded region represents the design point where optimal performance is achieved. The introduction of a variable AS-combustor induces fluctuations in SOFC power output, ranging from approximately 60 to 120 kW. This range encompasses the required power of about 102 kW at the design point, and a significant jump in SOFC power is noted from AS-combustor 2, which moderately increases for subsequent increases in AS-combustor ratios. Notably, Figure 16A illustrates the variations in the three main performance parameters of the SOFC. Beyond AS-combustor 2, fuel utilization in the SOFC begins to increase, an undesirable outcome. This occurs because, with changes in the AS-ratio, the CPOx reformer yields less fuel than required for optimal SOFC operation, as shown in Figure 17. While the power output remains elevated, surpassing the FU safe margin for continual operation, the heightened fuel utilization poses a considerable risk. The design point performance region lies between AS-combustor 1 and AS-combustor 2, as depicted in Figure 16. The GT performance also improves, at the expense, however, of SOFC stack safe operation, as shown in Figure 16B. As the AS-combustor ratio increases, the TSFC decreases from 315 to 256 mg/s/N means a more efficient conversion of fuel to thrust. The thrust also increases from 7.78 to 8.6 kN. Therefore, under a variable AS-combustor, the shaded region here yields an optimal performance. This correlates to the design point AS-combustor of about 0.15.
## 2 Optimization
### Adaptive Learning Rate Optimizers
#### 2.2.2 Adadelta  
The Adadelta [25] optimization algorithm tries to correct the diminishing learning rate problem in the Adagrad algorithm by accumulating the squared gradients over the fixed-size window instead of using gradients from all previous iterations. Instead of inefficient storing of all previous squared gradients from the current window, Adadelta implements accumulator as exponentially decaying average of squared gradients.  
\[\mathbf{m}_{0} =0,\;\;\mathbf{v}_{\mathbf{0}}=0\;\;\text{(initialize accumulation variables)}\] \[\mathbf{v}_{t} =\beta\mathbf{v}_{\mathbf{t-1}}+(1-\beta)\left(\
abla J(\mathbf{\theta}_{t-1} )\right)^{2}\quad\text{(accumulate squared gradient)} \tag{11}\] \[\Delta\theta_{t} =-\frac{\sqrt{\mathbf{m}_{t-1}+\epsilon}}{\sqrt{\mathbf{v}_{t}+\epsilon}} \circ\
abla J(\mathbf{\theta}_{t-1})\quad\text{(compute update)}\] (12) \[\mathbf{m}_{t} =\beta\mathbf{m}_{t-1}+(1-\beta)(\Delta\theta_{t})^{2}\quad\text{(accumulate squared update)}\] (13) \[\mathbf{\theta}_{t} =\mathbf{\theta}_{t-1}+\Delta\mathbf{\theta}_{t}\quad\text{(apply update)}. \tag{14}\]  
Constant \(\epsilon\) in Equation (12) is added in the denominator to condition it better and in the numerator to ensure that first update \(\Delta\theta_{1}\
eq 0\) and also to ensure progress when update accumulator \(\mathbf{m}\) becomes small. It should be noted that the Adadelta optimization algorithm does not use the learning rate \(\eta\). Instead, the size of an update made to parameter \(i\) in iteration \(t\) is controlled by the \(i\)th component of the vector \(\frac{\sqrt{\mathbf{m}_{t-1}+\epsilon}}{\sqrt{\mathbf{v}_{t}+\epsilon}}\) that can be viewed as the quotient of RMS of updates \(\Delta J(\mathbf{\theta})\) and gradients up to time \(t\), i.e., the update rule (14) can be rewritten as  
\[\mathbf{\theta}_{t}=\mathbf{\theta}_{t-1}-\frac{RMS\big{[}\Delta\mathbf{\theta}\big{]}_{t -1}}{RMS\big{[}\
abla J(\mathbf{\theta})\big{]}_{t}}\circ\
abla J(\mathbf{\theta}_{t -1}). \tag{15}\]
# Rock Mass Structure Classification of Caves Based on the 3D Rock Block Index
###### Abstract  
In large-scale water conservancy and hydropower projects, complex rock structures are considered to be the main factor controlling the stability of hydraulic structures. The classification of rock mass structure plays an important role in the safety of all kinds of large buildings, especially underground engineering buildings. As a quantitative classification index of rock mass, the rock block index is very common in the classification of borehole and dam foundation rock mass structures. However, there are few studies on the classification of underground engineering rock masses. Moreover, their classification criteria have disadvantages in spatial dimension. Therefore, this paper takes the long exploratory cave CPD1 in the water transmission and power generation system of the Qingtian pumped storage power station in Zhejiang Province as the research object and launches a study on the structural classification of the rock mass of a flat cave based on the 3D rock block index. According to the group distribution of joints, the sections are statistically homogeneous. Additionally, the Monte Carlo method is used to carry out random simulations to generate a three-dimensional joint network model. The virtual survey lines are arranged along the center of the shape of the three different orthogonal planes of the 3D joint network model to represent the boreholes, and the RBI values of the virtual survey lines on each orthogonal plane are counted to classify the rock mass structure of the flat cave in a refined manner using the rock block index of the rock mass in 3D. The above method realizes the application of the 3D rock block index in underground engineering and overcomes the limitations of traditional rock mass classification methods in terms of classification index and dimension. The results show that: (1) Three-dimensional joint network simulations built on statistical and probabilistic foundations can visualize the structure of the rock mass and more accurately reflect the structural characteristics of the actual rock mass. (2) Based on the 3D rock block index, the rock mass structure of the long-tunnel CPD1 is classified, from that of a continuous structure to a blocky structure, corresponding to the integrity of the rock mass from complete to relatively complete. The classification results are consistent with the evaluation results of horizontal tunnel seismic wave geophysical exploration. (3) Based on the 3D joint network model, it is reasonable and feasible to use the 3D rock block index as a quantitative evaluation index to determine the structure type of flat cave rock masses. The above method is helpful and significant in the classification of underground engineering rock mass structures.  
rock mass structure; cave; joint network simulation; 3D rock block index +
Footnote †: journal: Applied Sciences