esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Controller Design
### NN-Based Motion Intention Estimation  
Radial basis function neural networks (RBF NNs) are employed for motion intention estimation. The continuous function \(\Phi(W,\hbar)\) can be represented through the usage of an RBFNN as follows [44]:  
\[\Phi(W,\hbar)=W^{T}S(\hbar) \tag{9}\]  
where \(W\) is the adjustable weight vector and \(S(\hbar)\in\Re^{p}\) is the basis function, which is described as  
\[W =\left[\begin{array}{cccc}w_{11}&w_{21}&\cdots&w_{r1}\\ w_{12}&w_{22}&\cdots&w_{r2}\\ \vdots&\vdots&\vdots&\vdots\\ w_{1p}&w_{2p}&\cdots&w_{rp}\end{array}\right]\] \[S(\hbar) =\left[\ell_{1}(\hbar),\ell_{2}(\hbar),...,\ell_{p}(\hbar) \right]^{T}\] \[\ell_{j}(\hbar) =\exp\left(\frac{-(\hbar-\mu_{j})^{T}(\hbar-\mu_{j})}{\eta_{j}^{2 }}\right)\]  
where \(\hbar\in\Omega_{\hbar}\subset R^{m}\) is the input of the NN, \(r\) represents the number of output neurons in the NN, \(p\) is the number of NN nodes, \(\mu_{j}=\left[\mu_{j,1},\mu_{j,1},\ldots,\mu_{j,m}\right]^{T}\) is the center of the receptive field, and \(\eta\) is the width of the Gaussian function.  
Using (9), \(\xi_{H,i}\) and its estimation \(\xi_{H,i}\) are given as  
\[\zeta_{H,i} =\hat{\Theta}_{i}^{T}\delta_{i}(\eta_{i})+\varepsilon_{i}\] \[\xi_{H,i} =\hat{\Theta}_{i}^{T}\delta_{i}(\eta_{i}) \tag{10}\]  
where \((\cdot)_{i}\)\((i=1,2,\ldots,n)\) is the \(i\)th component of \((\cdot)\), \(\eta_{i}=[f_{i}^{T},\zeta_{i}^{T},\xi_{i}^{T}]^{T}\), \(\delta_{i}(\cdot)\) is the radial basis function, and \(\hat{\Theta}_{i}\) and \(\varepsilon_{i}\) denote the estimated weight and the estimation error, respectively.  
We define the cost function as  
\[E_{M,i}=\frac{1}{2}f_{i}^{2} \tag{11}\]  
Figure 1: Control structure.  
From the above analysis, if the interaction force between the patient and the exoskeleton can be minimized, it means that the rehabilitation exoskeleton can track the predetermined position determined by the patient's motion intention. Thus, the adaptive law is selected as  
\[\dot{\Theta}_{i} =-\beta_{i}\frac{\partial E_{M,i}}{\partial\dot{\Theta}_{i}}\] \[=-\beta_{i}\frac{\partial E_{M,i}}{\partial f_{i}}\frac{\partial f _{i}}{\partial\xi_{H,i}}\frac{\partial\xi_{H,i}^{\epsilon}}{\partial\dot{ \Theta}_{i}} \tag{12}\]  
where the partial derivatives \(\frac{\partial E_{M,i}}{\partial f_{i}}\), \(\frac{\partial f_{i}}{\partial\xi_{H,i}}\), and \(\frac{\partial\xi_{H,i}^{\epsilon}}{\partial\dot{\Theta}_{i}}\) are given as  
\[\frac{\partial E_{M,i}}{\partial f_{i}}=f_{i},\frac{\partial f_{i}}{\partial \xi_{H,i}}=\psi_{H,i},\frac{\partial\xi_{H,i}^{\epsilon}}{\partial\dot{\Theta} _{i}}=\delta_{i}(\bar{\eta}_{i}) \tag{13}\]  
Then, (12) is rewritten as  
\[\dot{\Theta}_{i} =-\beta_{i}f_{i}\psi_{H,i}\delta_{i}(\bar{\eta}_{i})\] \[=-\gamma_{i}\beta_{i}\delta_{i}(\bar{\eta}_{i}) \tag{14}\]  
where \(\beta_{i}\) is a positive constant and is absorbed by \(\gamma_{i}\) together with \(\psi_{H,i}\). There is  
\[\dot{\Theta}_{i}=\dot{\Theta}_{i}(0)-\gamma_{i}\int_{0}^{t}\left[f_{i}(w) \delta_{i}(\bar{\eta}_{i}(w))\right]dw \tag{15}\]  
Then, the human motion intention \(\dot{\xi}_{H,i}\) is obtained with (10) and (15).
# A Random Forest-Based Precipitation Detection Algorithm for FY-3C/3D MWTS2 over Oceanic Regions
## 2 Data and Methods
### Precipitation Identification Method Based on the Random Forest Algorithm  
The random forest algorithm is an ensemble learning method based on decision trees. First proposed by [PERSON] [19] in 2001, the random forest algorithm combines the bagging-based ensemble learning algorithm [21] with a random subspace [22], which can naturally model nonlinear decision boundaries and thus effectively solve nonlinear problems. The basic building blocks of the random forest model are decision trees, and the decision trees used in this paper are classification and regression trees (CARTs) [23].  
The random forest model has been demonstrated to effectively simulate strongly nonlinear processes such as precipitation [15]. In comparison with other machine learning or deep learning models, the most distinctive feature of a random forest is its ability to conveniently calculate the sensitivity (or importance) of each input variable via its unique Gini importance index. This facilitates researchers in assessing the plausibility of random forest simulation results in conjunction with prior atmospheric science knowledge, thereby enhancing the interpretability of the developed model.  
The training process of the random forest algorithm used in the model is shown in Figure 4, with the training set samples, including atmospheric and cloud surface parameters (HPF, CLC, UTH, and CTT, denoted as x) retrieved based on FY-2 VISSR infrared and visible-band detection data and the _SI_ calculated from the AMSU-A brightness temperature as the labels for machine learning.  
First, the bootstrap resampling method is used to select m group samples from the total number of samples n (Sample Group 1, Sample Group 2,\(\ldots\), Sample Group \(m\)). Each set of samples is subsequently used to train a CART, and m trained CARTs are obtained, as shown in Figure 4a, which are recorded as h\({}_{i}\) (\(i\) = 1, 2, 3,\(\ldots\), \(m\)). After the test set data are input into the prediction stage, each CART obtains a random forest-simulated _SI_ value (\(RF\_SI_{i}\), \(i\) = 1, 2, 3,\(\ldots\), \(m\), denoted as h\({}_{i}\) (\(i\) = 1, 2, 3,\(\ldots\), \(m\))). Then, the SIs of the \(m\) decision tree simulations are multiplied by the corresponding weights \(w_{i}\), as defined in (10), to obtain the final simulation result (e.g., (9)), where \(H(x)\) is the scatter index \(RF\_SI\).  
Figure 3: Example of the matching process performed for VISSR pixels that satisfy the _dmax_ threshold within a given AMSU-A pixel.  
\[H(x)=\frac{1}{m}\sum_{i=1}^{m}w_{i}h_{i}(x) \tag{9}\]  
\[w_{i}>0,\ \sum_{i=1}^{m}w_{i}=1 \tag{10}\]
# The Application of Augmented Reality in the Automotive Industry: A Systematic Literature Review
## Results
### General Characteristics of 'Other' AR-Based Systems
#### 3.7.2 Development Tools  
The analysis of development tools reveals that 25.87% of the studies have presented systems that use self-developed software. Ten studies (47.62%) have used the AR development tools Vuforia and ARToolkit, while one study declared the use of the OpenCV library. Four articles did not specify the implementation software, or this characteristic is not applicable (Figure 15a). The distribution of development tool per year is presented in Figure 15b. One tendency that can be identified is the increasing number of uses of the Vuforia library in recent years.
# Influence of Fatigue Crack Formation and Propagation on Reliability of Steel Members
## 4 Fatigue Crack Propagation  
In general, the rate of fatigue crack growth is given as the derivation of crack depth \"a\" with respect to number of loading cycles \"N\". It means that it is ratio da/dN. For simplification, the constant range of the nominal stress \(\Delta\sigma\) is considered. Then, for a given crack depth and constant stress range \(\Delta\sigma\) one can plot the values log da/dN in terms of log \(\Delta\mathrm{K}\), where \(\Delta\mathrm{K}\) is the SIF (stress-intensity factor) range  
\[\Delta\mathrm{K}=\mathrm{K_{max}}-\mathrm{K_{min}}=\mathrm{F(a)}\cdot\Delta \sigma.\sqrt{\frac{\mathrm{\pi\cdot a}}{\mathrm{\Phi}}}. \tag{18}\]  
Dependence of log (da/dN) on log \(\Delta\mathrm{K}\) is approximately linear and is expressed by the Paris-Erdogan law  
\[\frac{\mathrm{da}}{\mathrm{dN}}=\mathrm{C}\cdot(\Delta\mathrm{K})^{\mathrm{m}}, \tag{19}\]  
where:  
da/dN is the change in the length of the fatigue crack per load cycles,  
\(\Delta\mathrm{K}\) is the interval (range) of the stress intensity factor (SIF),  
C, m are the material constants,  
N is the number of loading cycles.  
The material constants C and m are empirical constants, which are functions of the material properties and microstructure and are obtained experimentally and also usually depend on environment, fatigue frequency, temperature and mean stress or load ratio, loading mode, stress state, where m is the slope of the curve showing the rate of crack propagation according to the Paris-Erdogan equation in the mean linear region (on a logarithmic scale). The upper limit for C = 6.89:10\({}^{-12}\) MPa\({}^{-3}\cdot\)m\({}^{-1/2}\) (in the case of the use of millimeters 2.18:10\({}^{-13}\) MPa\({}^{-3}\cdot\)mm\({}^{-1/2}\)) is used and m = 3 for structural steels in the case of tensile cracks.  
Paris-Erdogan' law is a crack growth equation that gives the rate of growth of a fatigue crack. The stress intensity factor K characterizes the load around a crack tip and the rate of crack growth is experimentally shown to be a function of the range of stress intensity \(\Delta\mathrm{K}\) seen in a loading cycle. The stress intensity factor, K, is used in fracture mechanics to predict the stress state (\"stress intensity\") near the tip of a crack or notch caused by a remote load or residual stresses [37]. [PERSON] introduced the idea that the rate of crack growth may depend on the stress intensity factor [38] in a year 1961. Then in their 1963 paper [39], [PERSON] and [PERSON] indirectly suggested the equation with the aside remark \"The authors are hesitant but cannot resist the temptation to draw the straight line slope 1:4 through the data\" after reviewing data on a log-log plot of crack growth versus stress intensity range. The Paris equation was then presented with the fixed exponent of 4.
## 4 Results
For Zone 3:
* The main contributions on Dim-1 are those of F5, F6, F9, and F10 (i.e., skewness, kurtosis, ACF, and PACF);
* The most important contributions on Dim-2 are those of F2, F4, F3, and F8 (i.e., maximum, standard deviation, average, and homoskedasticity);
* The main contributions on Dim-1-2 are those of the skewness (F5), average (F3), maximum (F2), and standard deviation (F4);
* The essential contributions on Dim-1-2-3 are those of the standard deviation (F4), maximum (F2), average (F3), and skewness (F5). * Considering the locations, the most important contributions to the dimensions are those of 5 and 4 (on the positive direction of the first one), 3 (on the negative direction of the first one), 6 and 11 (on the positive direction of the second one), and 12, 14, and 9 (on the negative direction of the second one). * The above analysis points to the following ideas. (1) The number of clusters must be rigorously selected and validated. The number of clusters must be chosen after comparing all criteria, given that stability and inner connectivity criteria can indicate as best \(k\) a value that does not concord with the number provided by the majority selection criterion (used by NbClust). (2) The most significant contributions on the first three dimensions are maximum, standard deviation, and average (in this order). ACF and PACF also significantly contribute  
Figure 15: Contributions of the variables to (**a**) the first two and (**b**) the third dimension. The dashed line shows the expected average contribution. The most important contributions are those above the expected value. to the first or second dimensions. The comparison of the cluster obtained by the k-means algorithm on the raw and features series indicates a better classification provided by the last method, which considers the series' similar statistical characteristics. From a practical viewpoint, it points out unusually high emissions and the necessity of tank inspection, which can have significant implications for operational decision-making. Figure 16: Individuals PCA for Zone 1. Figure 17: (**a**) Contributions of the features in Zone 2 on Dim1-Dim5, (**b**) PCA–biplot for Zone 2, (**c**) Contributions of the features in Zone 3 on Dim1-Dim5, (**d**) PCA–biplot for Zone 3. (3) A deeper investigation of the distributions of the series in each cluster might lead to determining similar underlying distributions. For example, based on the Anderson-Darling goodness-of-fit criterion, we found that the most suitable distribution for the series in the first cluster in Zone 1 is Wakeby (Table 6). In contrast, other distributions were fitted for the series in the second cluster. For the cluster with the highest number of elements in Zone 2, the best distributions fitted were Dagun and/or Wakeby.
# Designing Audio Equalization Filters by Deep Neural Networks
## 6 Results
### Remarks  
One concern related to the proposed filter design technique is the computational cost, since the design procedure requires a complete training of the network. However, despite the very large number of iterations set for the experiments, the loss decays exponentially as it is typical of neural networks. As an example, in the Alfa Romeo Giulia 1024-th order CNN experiments, the MSE decays below \(1\cdot 10^{-4}\) after 4200 iterations. It is thus possible to set a desired error threshold and stop the training as soon as it is reached.  
For what concerns the filters, we have concentrated our attention on the frequency response, without considering the phase. The Frequency Deconvolution method provides symmetrical, thus linear, phase frequency responses, while the Steepest Descent algorithm does not. We would expect an arbitrary phase response from the proposed approach, since we do not constrain the phase in any way. However, from all our experiments we observe an almost linear phase response, as seen in Figure 9, where this is compared with a linear phase response, showing a close match. As an example, the mean squared phase error compared against a perfectly linear phase response and averaged over all the filters generated in the 1024 th-order CNN case from Table 2, is 0.8 rad.  
Another important issue to consider is the group delay introduced by the filters. As shown by the results, the most performing ones in terms of frequency response equalization are 1024-th order. This filter length, however, may not be acceptable in some applications due to computational cost and the introduction of a group delay of 513 taps (approximately 1.1 ms at a 44,100 Hz sampling rate). Experimental tests have proven that FIR filters of 512-th order present very good equalization capabilities, inferior by 1 order of magnitude compared to the 1024-th order case, but still largely superior than baseline techniques.
## 4 Experimental Evaluation  
To test the behavior of the algorithms, two severe Rayleigh channel scenarios were considered with 8 and 32 symbol-spaced multipath channels echos (channel taps), respectively, with uncorrelated Rayleigh fading, and were used to evaluate frame-detection probability error and the channel estimator's performance through analysis of the BER of the received signal. The parameters for the TIBWB-OFDM wireless SISO model simulations are defined in Table 1.  
Since it was expected that successful frame synchronization would be dependent on the power of the sent ZC preamble, we also considered three cases where the average power of the transmitted ZC sequence was the same, and 3 or 6 dB higher than the average TIBWB-OFDM data power block. We also evaluated the impact of this feature on the channel estimators' performance.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **TIBWB–OFDM** & **Preamble** \\ \hline Shaping pulse & SRRC & - \\ Roll-off factor & \(\beta\) = 0.5 & - \\ Modulation & QPSK & - \\ OFDM symbols & \(N_{s}\) = 42 & - \\ Root element & - & \(n\) = 34 \\ Sub-block length & \(N\) = 64 & \(N_{ZC}=95\) \\ Block size & \(N_{b}\) = 4032 & \(N_{p}\) = 96 \\ LDPC & (128, 64) & - \\ Bit interleaving & 10 consecutive words & - \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation Parameters.
## 2 The Bridge Project-Level Maintenance Decision Process  
In terms of bridge project-level maintenance decision optimization, this paper aims to explore the optimal maintenance strategy for all elements of a bridge. Based on the actual occurrence of defects in bridges, the decision is made by considering the minimization of maintenance costs as the objective. The maintenance effect matrix, which represents the probability of technical condition transitions for elements after executing maintenance plans, is introduced. A sequential decision optimization model is established for bridge project-level maintenance, and the optimal maintenance plan is obtained using dynamic programming in the sequential decision making process. The decision optimization process is depicted in Figure 1.  
(1) The analysis of actual defect conditions and technical conditions of bridges elements is based on the regular inspection reports of bridges. It involves gathering information on the types and quantities of defects observed in bridge elements, as well as the attributes of these defects. The technical condition level of each element is calculated, and this information serves as the foundation for maintenance decision making, thereby ensuring the practicality of the decisions.  
(2) Based on all the observed defect types, corresponding maintenance plans were determined, where each plan may include multiple repair measures. By considering the cost of measures in the maintenance plans and the distribution of the elements' technical condition levels, the cost of repairing elements with different condition levels is calculated,  
Figure 1: Decision flow chart of bridge project-level maintenance.  
thereby generating a maintenance cost matrix (referred to as the reward matrix). By implementing different maintenance plans for elements with defects, the effects of various maintenance strategies are explored, thus forming a transition probability matrix (known as the maintenance effect matrix, which represents the transition of element conditions before and after maintenance).  
(3) The state distribution of elements, the transition probability matrix for element conditions before and after maintenance, and the maintenance cost matrix are used as inputs to the sequential decision making model. A dynamic programming algorithm is employed to solve the model.
## 3 Background Theory
### Convolutional Neural Network (CNN)
The number of weights for each neuron in the convolutional layer can be found using the following equation:  
\[N_{w}=L_{F}^{2}\times D_{i} \tag{4}\]  
Figure 3: The first layer of the CNN is shown with the 3-dimensional input image (red), filter (yellow), activation map (blue), and five neurons activation (stacked in-depth dimension for the same region of filter convolution (yellow) with the input image) resulting from five filters of the corresponding colors (yellow, green, pink, purple, and brown) [12]. where \(N_{w}\) is the number of weights, \(L_{F}^{2}\) is the filter area, and \(D_{i}\) is the depth of the input layer. The ReLU Layer brings nonlinearity to the linear structure after convolutional layer computations. The ReLU activation function proved to be more efficient than the traditional activation functions [16], to be less prone to decrease the accuracy, and to improve the gradient fall due to which the lower layers of the system perform slow computations. The ReLU function zeroes the negative activations in the input layer with the following function:  
\[f(x)\ =\max(0,x) \tag{5}\]  
The pooling layer is used after the ReLU layer to down-sample the fed input layer, thus having the role of controlling the overfitting and reducing the parameters in the CNN architecture. The downsampled output of the pooling layer could be found using the following equation:  
\[L_{op}=\ \left(L_{ip}-L_{PF}\right)/S+1 \tag{6}\]  
where \(L_{op}\) and \(L_{ip}\) are the length of the square-shaped output and input area, respectively, and \(L_{PF}\) is the pooling filter length. \(L_{PF}\) is chosen to be minimal to avoid too much deterioration of input layer details. The depth, being the third constituent of input and output with the area, remains constant in the volumetric details of the layer. Figure 4 shows the pooling layer structure of the CNN. The fully connected layer is the final layer of the CNN architecture that performs the task of forming the vector of probabilities for the input image, showing how likely the input falls among all classes. It is called fully connected due to the neurons of this layer being fully connected to the activations of the fed input layer. Generally, the fully connected layer is followed by the softmax function that is the unit activation function for the output. It is considered as the generalization of the logistic sigmoidal function for the multiple classes [17; 18]. \[P(C_{r}|x,\theta)\ =\ \frac{P(x,\theta|C_{r})P(C_{r})}{\sum_{j=1}^{S}P(x, \theta|C_{j})P(C_{j})}=\frac{\exp(a_{r}(x,\theta))}{\sum_{j=1}^{S}\exp(a_{j}(x,\theta))} \tag{7}\]  
Figure 2:0 Input layer with several slices has been downsampled after pooling to reduce parameters and avoid overfitting [12]. where \(\sum\limits_{j=1}^{S}P\big{(}C_{j}|x,\theta\big{)}\ =1\), \(0\leq P(C_{r}|x,\theta)\leq 1\) and \(a_{r}=\ln(P(x,\theta|C_{r})P(C_{r}))\), \(P(x,\theta|C_{r})\) are the conditional probabilities of the known sample class r, and \(P(C_{r})\) is the prior probability of the class.
## 4 Discussion
### MyFlex-\(\delta\) vs. Their Own Prosthesis
#### 4.1.2 Sagittal Plane Kinematics  
_Plantarflexion at Toe Strike: Prosthetic Leg vs. Healthy Leg_  
The second section of Table 5 (\"Prosthetic Leg Plantarflexion-Healthy Leg Plantarflexion\") shows how, regardless of the prosthesis used, the plantarflexion with the prosthetic foot is less than that with the healthy foot.  
_Plantarflexion at Toe Strike: MyFlex-\(\delta\) vs. Own Prosthesis_  
According to their feedback, the three participants perceived a lower absorption of the impact between the foot and the ground during the heel strike, while using MyFlex-\(\delta\). Unfortunately, this was probably due to a problem of interference between two components during the plantarflexion (Figure 7). This perception can be confirmed by the diminished plantarflexion at the end of the early stance of the prosthetic leg, while using MyFlex-\(\delta\), compared to the plantarflexion of their own prosthesis. Indeed, observing the results given in the third section of Table 5 (\"Plantarflexion Using MyFlex-\(\delta\)-Plantarflexion Using their Own Prosthesis\"), in particular those concerning the prosthetic leg, Myflex-\(\delta\) gave less plantar flexion than the participant's own prosthesis.  
_Dorsiflexion at Heel-Off: Prosthetic Leg vs. Healthy Leg_  
In the second section (\"Prosthetic Leg Dorsiflexion-Healthy Leg Dorsiflexion\") of Table 6 the differences between the dorsiflexion measured at the prosthetic leg and the dorsiflexion measured at the healthy leg, both for a participant's prosthesis and for MyFlex-\(\delta\), were reported. From the results, it is clear that the dorsiflexion for both prostheses is greater in the prosthetic foot.  
_Dorsiflexion at Heel-Off: MyFlex-\(\delta\) vs. Own Prosthesis_  
As can be seen in the second section of Table 6 (\"Dorsiflexion Using MyFlex-\(\delta\)-Dorsiflexion Using their Own Prosthesis\"), for all three participants, from their own prosthesis to MyFlex-\(\delta\), there was an increase in dorsiflexion with the prosthetic leg, which could be equivalent to the increased elastic energy stored by the elastic elements of the prosthesis.