esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Transition Models For Piezoelectricity
### Basic Models of Linear Piezoelectricity
#### 3.1.1 Hierarchical or Three-Dimensional Models  
For both the cases, when the transverse mechanical and electric fields are polynomially constrained through the thickness of the thin-walled piezoelectric member or the transverse direction is treated in the same way as the longitudinal directions of the three-dimensional piezoelectric member, the same constitutive relations hold.  
In order to present these relations, let us convert the Equation (12) to the form suitable for the variational and finite element formulation of the general piezoelectric problem. This needs inversion of the first Equation (12) and its substitution into the second one. The resultant form reads:  
\[\left\{\begin{array}{rcl}\mathbf{\sigma}&=&\mathbf{D}\mathbf{e}-\mathbf{C}\mathbf{E}\\ \mathbf{d}&=&\mathbf{C}^{T}\mathbf{e}+\mathbf{\gamma}\mathbf{E},\end{array}\right. \tag{16}\]  
where the following definitions of the orthotropic matrix \(\mathbf{C}\) of piezoelectric constants under constant strain and the isotropic matrix \(\mathbf{\gamma}\) of dielectric constants under constant strain were introduced:  
\[\mathbf{\gamma} = \delta-\mathbf{c}^{T}\mathbf{D}\mathbf{c} \tag{17}\] \[\mathbf{C} = -\mathbf{D}\mathbf{c}.\]  
The first of the above definitions gives the following non-zero terms of the matrix \(\mathbf{\gamma}\):  
\[\mathbf{\gamma}=\left[\begin{array}{ccc}\gamma_{11}&0&0\\ 0&\gamma_{22}&0\\ 0&0&\gamma_{33}\end{array}\right]=\left[\begin{array}{ccc}\delta_{11}-c_{6 1}D_{66}c_{61}&0&0\\ 0&\delta_{22}-c_{52}D_{55}c_{52}&0\\ 0&\delta_{33}-c_{13}(D_{11}c_{13}+D_{12}c_{23}+D_{13}c_{33})\\ 0&0&-c_{23}(D_{21}c_{13}+D_{22}c_{23}+D_{23}c_{33})\\ -c_{33}(D_{31}c_{13}+D_{32}c_{23}+D_{33}c_{33})\end{array}\right]. \tag{18}\]  
The second definition leads to the following structure of the matrix \(\mathbf{C}\):  
\[\mathbf{C}=\left[\begin{array}{ccc}0&0&C_{13}\\ 0&0&C_{23}\\ 0&0&C_{33}\\ 0&0&0\\ 0&C_{52}&0\\ C_{61}&0&0\end{array}\right]=-\left[\begin{array}{ccc}0&0&D_{11}c_{13}+D_{12}c_ {23}+D_{13}c_{33}\\ 0&0&D_{21}c_{13}+D_{22}c_{23}+D_{23}c_{33}\\ 0&0&D_{31}c_{13}+D_{32}c_{23}+D_{33}c_{33}\\ 0&0&0\\ 0&D_{55}c_{52}&0\\ D_{66}c_{61}&0&0\end{array}\right]. \tag{19}\]
# Bearing Capacities and Failure Behaviors of F-Type Socket Joint in Rectangular Pipe Jacking Tunnel
## 5 Conclusions  
Based on full-scale experiments and a series of numerical simulations, this paper presents the Bearing Capacities and Failure Behaviors of F-Type Socket Joint in Rectangular Pipe Jacking Tunnel. The failure processes, rotational angle, and bending stiffness of segments were monitored and analyzed in the full-scale tests. The influence law of different foundation stiffness on bearing characteristics of jacking pipe tunnel is clarified. The main research conclusions are as follows.  
1. Under the same loading displacement, the greater the foundation stiffness, the greater the bending moment borne by the joint, and the higher the joint bending capacity. The bending moment of the joint is mainly borne by the steel ring, which will eventually be damaged by bending.
2. The change of joint opening is closely related to the change of joint bending moment; the larger the joint bending moment, the larger the corresponding joint opening. In addition, the larger deformation of the pipe joint itself will lead to a slower  
Figure 21: Relationship of joint rotation angle and moment under the influence of length.  
Figure 22: Relationship of joint rotation angle and moment under the influence of thickness.  
rate of change of the joint opening, resulting in an increase in the slope of the joint bending stiffness.
3. The deformation of the pull-wire displacement gauge at the joint, the concrete strain and the steel collar strain show the same change pattern, which all indicate that the joint tends to be flattened during the bending loading process.
4. The deformation of the steel collar is closely related to the deformation of concrete, and the two are in the same state of stress at the same position. In addition, the top bottom plate of the steel ring will be warped near the socket side, and the degree of warping is most obvious at the axillary corner of the top bottom plate due to stress concentration. When the bottom of the pipe joint is separated from the socket end, the structure is eventually deformed due to the large deformation of the bottom of the pipe joint.
5. Joint bending deformation is influenced by the foundation stiffness of the strata. The larger the foundation stiffness and the harder the strata, the smaller the joint bending deformation; the larger the section size of the pipe joint, the smaller the joint bending deformation; the larger the size of the steel collar, the smaller the joint bending deformation.  
Date analysis, Writing--original draft, Writing--review and editing, Supervision, Y.X.; Experimental operation, Software, Validation, Data curation, Date analysis, Writing--original draft, Z.H.; Resources, Methodology, Supervision, Writing--review and editing, C.Z.; Experimental operation, Software, Validation, Y.P.; Data curation, Date analysis, Writing--original draft, T.L. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China (51868062).  
Not applicable.  
The authors declare no conflict of interest.
## 4 Results and Validations
### Assessment of IGS-RT Orbit and Clock Products
In summary, the quality of real-time products provided by these RT services is different from each other. This may be related to the different processing strategies and different observation streams of real-time precise orbit determination (POD) and precise clock estimation (PCE) adopted by various analysis centers. They are improving their models and strategies for better quality of real-time products.
# Noise Cancellation Method Based on TVF-EMD with Bayesian Parameter Optimization
## 1 Introduction
[28] proposed the parameter-adaptive TVF-EMD feature extraction method, based on improved GOA, to deal with the mechanical fault diagnosis. However, the Genetic algorithm and the swarm intelligence optimization algorithm can be categorized as population optimization algorithms. Population optimization algorithms are not particularly suitable for model hyperparameter tuning because they require a sufficient number of initial sample points and are not particularly efficient for optimization. To accelerate computation, Bayesian hyperparameter optimization based on surrogate algorithms is widely used. The tree-structured Parzen estimator (TPE) is one of the most notable hyperparameter optimization methods [29; 30]. The Parzen-based estimator can naturally handle complex search spaces and can be extended to dozens of variables, with at least a thousand observations [31]. Therefore, selecting a BO algorithm based on a tree-structured Parzen estimator (BO-TPE) is a reasonably effective method for TVF-EMD parameters. In the aforementioned denoising theories, the smoothing method can reduce the signal resolution in time. Indoor CO\({}_{2}\) concentrations in buildings is a typical non-stationary signal. These signal-denoising methods, such as Fourier transform, EMD, ensemble EMD, and noise-assisted MEMD, are not suitable for processing non-stationary signals. The wavelet transform is suitable for dealing with non-stationary, time-varying signals, but there is the problem of difficult wavelet basis selection. The TVF-EMD method can solve the shortcomings of the above methods. Combined with the hyperparameter algorithm, the TVF-EMD method can match the appropriate parameters more quickly to achieve accurate noise reduction of the indoor CO\({}_{2}\) concentration. Considering this background, this study proposed an optimized TVF-EMD method, based on the BO-TPE algorithm, for noise cancellation. First, the correlation coefficient was defined as a comprehensive index for the objective condition of TVF-EMD parameter optimization. In addition, the correlation coefficient was used as the mode selection criterion for the target IMF. Second, an optimization algorithm called BO-TPE was used to search for the optimal combination of TVF-EMD parameters to match the input signal. The effectiveness of the proposed method was suitable for processing the noise of the non-stationary signal, especially large amplitudes, but with dispersed distribution noise signals. The noise reduction results of the CO\({}_{2}\) concentration signals from two different sets of functional building spaces demonstrated that the method was successful in canceling noise and could be effective in CO\({}_{2}\)-monitoring engineering applications.
## 4 Research on the Influence of Track Structure Stiffness Change on Track Deformation
### Analysis of Sensitivity Indexes of Vehicle-Track System Dynamics Response
#### 5.2.2 Vertical Ride Comfort Analysis  
The change of vertical ride comfort coefficient sensitivity indexes with different structural stiffness is shown in Figure 25, which shows that:  
1. The change tendency of the wear coefficient with the stiffness of the track structure are basically same. It is mostly affected by the vertical stiffness under block and increases with the increase in the vertical stiffness under block. Therefore, the larger the vertical stiffness under block, the higher the wear coefficient will be. It will adversely affect the service life of the rail, so the vertical stiffness under block should be set in a reasonable range to extend the rail change cycle;
2. The vertical displacement of the rail is significantly affected by the vertical stiffness of the track structure, while the lateral stiffness has little effect, and it is more affected by the vertical stiffness under block, which decreases with the increase in the vertical stiffness, indicating that a greater vertical stiffness under block is more conducive to maintaining the vertical smoothness of the track.
# Research into Image Point Positioning Compensation of a High-Orbit Thermal Infrared Staring Camera
###### Abstract
[PERSON] [12] studied the in-orbit geometric calibration of the space linear array CCD sensor, established the detection model of the external orientation elements with the help of SPOTS HRS image auxiliary data, and calibrated the space linear array CCD sensor using the self-rectifying bundle adjustment to achieve good calibration accuracy. [PERSON] [13] proposed a simplified line-of-sight vector correction model in the form of a non-pointing angle for in-orbit geometric calibration and carried out relevant experiments with the help of simulation data, proving that the model did not need to solve the satellite earth distance, and with a simplified calculation process, it had stronger applicability. Most of the above research work is aimed at the in-orbit geometric calibration of the low-orbit remote sensing linear array satellites to the ground. At present, there has been little research into the error compensation of high-orbit infrared cameras. For the geosynchronous orbit satellite, the solar illumination is uneven, and the satellite temperature changes dramatically [14], with the variation in laws of its temperature of annual long periodicity and short diurnal periodicity [15]. The infrared camera collects the temperature information of sensitive targets in the geosynchronous orbit, and due to its high-orbit height, the concentrated imaging line of sight, and severe temperature changes, the geometric imaging model needs to be studied [16]. The geosynchronous orbit satellite is affected by the drastic change in temperature, which will cause the relative installation relationship between the star sensor and the early warning camera to change. The change in the installation angle will be directly reflected in the error of attitude measurement. Therefore, we have carried out a detailed study on the influence of temperature on the camera distortion error. In addition, most of the objects observed by this type of satellite show point features, and there is almost no ground control point information in the process of real-time geo metric processing, which brings great difficulties regarding the accuracy of the motion parameter estimation of high-value targets [17]. Therefore, according to the geometric imaging characteristics and the error sources of the high-orbit thermal infrared staring camera, this paper proposes a geometric imaging model based on the two-dimensional pointing angle of temperature change. It can provide effective help to realize the two-dimensional trajectory reconstruction and provide more accurate observation trajectories for target parameter estimation.
## 2 The Model  
An asynchronous stochastic game of \(n\) players is the tuple \([(S_{t},\Sigma_{t}),(u_{it})_{i=1}^{n},A_{t},q_{tr}]_{t}\) and an assignment \(p:\mathbb{N}\rightarrow\{1,\cdots,n\}\)  
**(i)**: \(S_{t}\) is the _State Space_ in period \(t\). It is finite.
**(ii)**: \(A_{t}\) is the action set in period \(t\). It is finite.
**(iii)**: \(u_{it}:S_{t}\times A_{t}\rightarrow\mathbb{R}\), is the single-period payoff function of player \(i\) in period \(t\). It depends on the current state and the current action.
**(iv)**: The assignment \(p:\mathbb{N}\rightarrow\{1,\cdots,n\}\) assigns the _active_ player to each period. That is, in any period \(t\), the player who is active is \(p(t)\) and is the player who chooses an action from the action set \(A_{t}\).  
_Payoffs and Strategies_  
We will focus on a special class of strategies, namely _Markov strategies_.  
**Definition 1**.: \(A\) **Markov strategy**_\(f_{i}\) of a player \(i\) is a sequence \(\{f_{it}\}_{t\in p^{-1}(i)}\) such that \(f_{it}:S_{t}\to A_{t}\). A_ **[PERSON] strategy combination**_\(f=(f_{i})_{i\in\mathbb{N}}\) is a combination of [PERSON] strategies._  
Clearly, _Markov strategies_ restrict players to making their choice of action in each period as a function of only the current state.  
Given a [PERSON] strategy combination \(f=(f_{1},\cdots,f_{n})\),  
\[\sum_{a\in A_{t}}u_{it}(s_{t},f_{p(t)}(s_{t},a))\]gives the expected payoff of player \(i\) given the choice of player \(p(t)\). Let this be denoted by \(u_{it}(s_{t},f_{p(t)})\). Let the future expected payoff of player \(i\) from period \(t+1\) onward, when the [PERSON] strategy combination is \(f=(f_{1},\cdots_{m})\), be denoted by  
\[v_{i(t+1)}(f)(s_{t+1}).\]  
The payoff of a player \(i\) in period \(t\) is then given by  
\[u_{it}(s_{t},a_{t})+\delta\sum_{s_{\omega}\in S}v_{i(t+1)}(f)(s_{\ell})q_{t}(s _{\ell};s_{t},a_{t}). \tag{1}\]  
For player \(p(t)\), the player who chooses in period \(t\), this is  
\[u_{p(t)t}(s_{t},a_{t})+\delta\sum_{s_{\omega}\in S}v_{p(t)(t+1)}(f)(s_{\ell})q _{t}(s_{\ell};s_{t},a_{t})\]  
so that player \(p(t)\) can choose an action in \(A_{t}\) to maximize their payoff simply as a function of the realized state \(s_{t}\in S_{t}\).  
Definition 2: A [PERSON] strategy combination \(f^{*}\) is a Markov perfect equilibrium if for any \(s_{t}\) in any period \(t\)  
\[v_{p(t)}(f^{*})(s_{t})\geq v_{p(t)}(f^{*}_{-p(t)},b_{p(t)})(h_{t-1},s_{t})\]  
for any behavior strategy \(b_{p(t)}\) (not necessarily Markovian) (We note here that when the players use behavior strategies that are more general strategies that can depend on the past history and also allow mixed actions, the expected future payoffs \(v_{p(t)}(b):H_{t-1}\times S_{t}\rightarrow\mathbb{R}\) can be constructed in the same way as the expected payoffs for Markov strategies by looking at the discounted sum of the iterated integrals (see also [PERSON] [31]). Here \(H_{t-1}\) is the set of possible past histories.).  
It is of interest to note that when one considers deviations from the Markov perfect equilibrium strategy, one allows a deviation using a general behavior.
# Post-Fire Vegetation Succession and Surface Energy Fluxes Derived from Remote Sensing
## 4 Discussion
### Uncertainty Analysis  
Boreal forests are subject to fire disturbances, and climate change will increase the frequency of fires. The EVI, LST and LSWI dramatically changed after the fire, and the seasonality aggravated changes in the magnitude. The short growing seasons at high latitudes limit annual tree growth and severe winters control the time of forest succession, so the seasonality primarily controls the land-surface energy fluxes during vegetation regeneration. In this paper, the results confirmed the correlation between the EVI and GPP/NPP from MODIS. The rough data resolution and simple estimation method added considerable uncertainty to the estimation results. Surface energy flow is a more complex process, especially during vegetation regeneration. Therefore, we must improve the data resolution and the accuracy of the model algorithm to estimate the influence of vegetation succession on the carbon flux.
###### Abstract
Considering the convergence speed of the algorithm and the process of the maintenance task, the problem is decomposed into two parts, including multiobjective optimization selective maintenance decision and maintenance scheduling based on maintenance hours. An MSSA heuristic algorithm and the SA algorithm are used to solve the problem. The structure of this paper is as follows: In Section 2, a mathematical model for selective maintenance planning of a fleet is established. In Section 3, a framework for solving the model is proposed, and an MSSA algorithm and an SA algorithm are used to optimize the model. In Section 4, a case is selected to verify the above model and algorithm, and the results are analyzed. Finally, we summarize the content of this paper.
# A Hierarchical Generative Embedding Model for Influence Maximization in Attributed Social Networks
## 4 The Proposed Method
### Learning Procedure
#### 4.2.1 Hierarchical Network Optimization  
First, the similarity of the same community node is captured by optimizing the lower bound of the loss function. Nodes in the same community can be closer in the hidden space, while nodes in different communities will be pushed farther apart. This can be defined as follows:  
\[\mathcal{L}_{hor}=\sum_{l=3}^{T}\sum_{\begin{subarray}{c}i,j,k\in S_{l},\\ fa(v_{l}^{l})=fa(v_{l}^{l})\
eq fa(v_{l}^{l})\end{subarray}}\delta(v_{l}^{l},v_{j}^{l})^{2}+exp^{-\delta(v_{l}^{l},v_{k}^{l})}, \tag{9}\]  
where \(\mathcal{S}_{l}\) is the vertex set of layer \(l\), and \(T\) is the depth of the clustering tree.  
In order to capture the hierarchical vertical relationship, we use the following loss function to achieve the personalized distance ranking in Equation (7), as shown below:  
\[\mathcal{L}_{ver}=\sum_{l=1}^{T-1}\sum_{\begin{subarray}{c}i,j\in S_{l},\\ fa(v_{l}^{l})=fa(v_{l}^{l})\end{subarray}}\delta(v_{l}^{l},fa(v_{l}^{l}))^{2 }-exp^{\delta(v_{l}^{l},fa(v_{l}^{l}))}, \tag{10}\]  
when \(n(v_{i}^{l})<n(v_{j}^{l})\).  
To capture hierarchical affiliation, the HGE model assumes that the mean of the node embedding is subordinated to the Gaussian distribution corresponding to its father vertex. We use maximum likelihood to approximate the embedding of the father node. For an arbitrary vertex \(i\), suppose that vertices \(v_{1}\), \(v_{2}\),..., \(v_{m}\) are children of vertex \(i\) with \(\mathbf{\Phi}_{v_{1}}=\mathcal{N}(\mu_{1},\Sigma_{1})\), \(\mathbf{\Phi}_{v_{i}}=\mathcal{N}(\mu_{i},\Sigma_{i})\),..., \(\mathbf{\Phi}_{v_{m}}=\mathcal{N}(\mu_{m},\Sigma_{m})\). Then, the maximum likelihood function can be defined as follows:  
\[L(\mu,\Sigma)=\prod_{i=1}^{m}f(\mu_{i};\ \mu,\Sigma)\\ =\prod_{i=1}^{m}(2\pi)^{-\frac{n}{2}}|\Sigma|^{-\frac{1}{2}}\exp (-\frac{1}{2}(\mu_{i}-\mu)^{T}\Sigma^{-1}(\mu_{i}-\mu))\\ =(2\pi)^{-\frac{m}{2}}|\Sigma|^{-\frac{m}{2}}\exp(-\frac{1}{2}\sum _{i=1}^{m}(\mu_{i}-\mu)^{T}\Sigma^{-1}(\mu_{i}-\mu)) \tag{11}\]where \(n\) is the dimension of \(\mu\).  
The logarithmic likelihood function is:  
\[\ln L(\mu,\Sigma)=\ln(2\pi)^{-\frac{m}{2}}+\ln|\Sigma|^{-\frac{m}{2}} \\ +\ln\exp(-\frac{1}{2}\sum_{i=1}^{m}(\mu_{i}-\mu)^{T}\Sigma^{-1}(\mu_ {i}-\mu))\\ =C-\frac{m}{2}\ln|\Sigma|-\frac{1}{2}\sum_{i=1}^{m}(\mu_{i}-\mu)^ {T}\Sigma^{-1}(\mu_{i}-\mu)), \tag{12}\]  
where \(C\) is a constant.  
We use the negative logarithmic maximum likelihood as the loss function to capture hierarchical affiliation:  
\[\mathcal{L}_{aff}=-\ln L(\mu,\Sigma) \tag{13}\]  
To sum up, the objective function to capture the hierarchical network structure can be defined as follows:  
\[\mathcal{L}_{hie}=\mathcal{L}_{hor}+\mathcal{L}_{ver}+\lambda_{1}\mathcal{L}_ {aff}, \tag{14}\]  
where \(\lambda_{1}\) is a trade-off parameter to balance the three parts of the loss function \(\mathcal{L}_{hierarchical}\). We can optimize the parameters such that the loss \(\mathcal{L}_{hierarchical}\) is minimized; thus, the three constraints we proposed can be satisfied.
# Trajectory Optimization with Dynamic Drivable Corridor-Based Collision Avoidance
## 3 Collision Avoidance Constraint Formulation
### Preprocessing  
Prior to constructing the DC, a series of preprocessing steps are required. As a common practice, the vehicle is approximated by two discs representing the front and rear parts of the vehicle body [29], as illustrated in Figure 2a. The center positions of the front and rear discs are determined by (7):  
\[\begin{array}{l}x_{\mathrm{f}}(t)=x(t)+\frac{1}{4}(3\mathrm{L}_{\mathrm{W}}+3 \mathrm{L}_{\mathrm{F}}-\mathrm{L}_{\mathrm{R}})\cdot\cos\theta(t),\\ y_{\mathrm{f}}(t)=y(t)+\frac{1}{4}(3\mathrm{L}_{\mathrm{W}}+3\mathrm{L}_{ \mathrm{F}}-\mathrm{L}_{\mathrm{R}})\cdot\sin\theta(t),\\ x_{\mathrm{r}}(t)=x(t)+\frac{1}{4}(\mathrm{L}_{\mathrm{W}}+\mathrm{L}_{ \mathrm{F}}-3\mathrm{L}_{\mathrm{R}})\cdot\cos\theta(t),\\ y_{\mathrm{r}}(t)=y(t)+\frac{1}{4}(\mathrm{L}_{\mathrm{W}}+\mathrm{L}_{ \mathrm{F}}-3\mathrm{L}_{\mathrm{R}})\cdot\sin\theta(t).\end{array} \tag{7}\]  
The radius of the discs is determined by Formula (8):  
\[\mathrm{R}=\frac{1}{2}\sqrt{\left(\frac{\mathrm{L}_{\mathrm{R}}+\mathrm{L}_{ \mathrm{W}}+\mathrm{L}_{\mathrm{F}}}{2}\right)^{2}+(\mathrm{L}_{\mathrm{B}})^ {2}}. \tag{8}\]  
The vehicle body is approximated by two discs. Thus, avoiding collisions means ensuring that neither disc intersects with any obstacles (c.f. Figure 2b). By reducing each disc to its center and expanding the obstacle radius by R in the environment (c.f. Figure 2c), the original condition transforms into ensuring that the centers of the front and rear discs, \(\mathrm{P}_{\mathrm{f}}\) and \(\mathrm{P}_{\mathrm{r}}\) (c.f. Figure 2a,b), do not collide with these expanded obstacles. To achieve this, a separate DC is constructed for each disc center at each discretized time instant.