esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Conclusions
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Cars** & **Window** & **Wall** & **Building** & **Tank** \\ \hline \multirow{3}{*}{EARI} & SSIM = 0.9466 & SSIM = 0.9909 & SSIM = 0.9196 & SSIM = 0.9356 & SSIM = 0.9894 \\  & PSNR = 36.0382 & PSNR = 45.3721 & PSNR = 36.9036 & PSNR = 37.7624 & PSNR = 46.8909 \\  & RMSE = 0.0158 & RMSE = 0.0055 & RMSE = 0.0143 & RMSE = 0.0129 & RMSE = 0.0045 \\ \hline \multirow{3}{*}{NP} & SSIM = 0.9582 & SSIM = 0.9933 & SSIM = 0.9614 & SSIM = 0.9518 & SSIM = 0.9927 \\  & PSNR = 37.4198 & PSNR = 46.3064 & PSNR = 39.6867 & PSNR = 39.1404 & PSNR = 48.1039 \\  & RMSE = 0.01346 & RMSE = 0.0048 & RMSE = 0.0104 & RMSE = 0.0110 & RMSE = 0.0039 \\ \hline \multirow{3}{*}{PCDP} & SSIM = 0.9554 & SSIM = 0.9930 & SSIM = 0.9435 & SSIM = 0.9518 & SSIM = 0.9920 \\  & PSNR = 36.9204 & PSNR = 46.1596 & PSNR = 38.2077 & PSNR = 38.9414 & PSNR = 47.6478 \\  & RMSE = 0.01426 & RMSE = 0.0049 & RMSE = 0.0123 & RMSE = 0.0113 & RMSE = 0.0042 \\ \hline \multirow{3}{*}{MP} & SSIM = 0.9918 & SSIM = 0.9983 & SSIM = 0.9974 & SSIM = 0.9706 & SSIM = 0.9977 \\  & PSNR = 47.1006 & PSNR = 56.4553 & PSNR = 42.0427 & PSNR = 56.1393 \\  & RMSE = 0.0044 & RMSE = 0.0015 & RMSE = 0.0016 & RMSE = 0.0079 & RMSE = 0.0016 \\ \hline \multirow{3}{*}{This Work} & SSIM = 0.9948 & SSIM = 0.9888 & SSIM = 0.9981 & SSIM = 0.9857 & SSIM = 0.9965 \\  & PSNR = 49.6021 & PSNR = 45.8931 & PSNR = 57.6130 & PSNR = 45.9872 & PSNR = 53.0169 \\ \hline \multirow{3}{*}{NP} & SSIM = 0.8284 & SSIM = 0.9419 & SSIM = 0.6942 & SSIM = 0.7590 & SSIM = 0.7227 \\  & PSNR = 29.3589 & PSNR = 30.6841 & PSNR = 24.7070 & PSNR = 27.8181 & PSNR = 28.3058 \\  & RMSE = 0.0340 & RMSE = 0.0292 & RMSE = 0.0582 & RMSE = 0.0407 & RMSE = 0.0384 \\ \hline \multirow{3}{*}{PCDP} & SSIM = 0.8216 & SSIM = 0.9484 & SSIM = 0.6709 & SSIM = 0.7798 & SSIM = 0.7113 \\  & PSNR = 28.9635 & PSNR = 31.2784 & PSNR = 22.9016 & PSNR = 28.0442 & PSNR = 27.7868 \\ \cline{1-1}  & RMSE = 0.0356 & RMSE = 0.0273 & RMSE = 0.0716 & RMSE = 0.0396 & RMSE = 0.0408 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Objective evaluation indexes of S2 results of different algorithms on different test images. **Table A4. **_Cont. \begin{tabular}{c c c c c c} \hline \hline
**Method** & **Cars** & **Window** & **Wall** & **Building** & **Tank** \\ \hline \multirow{4}{*}{PARI} & SSIM = 0.9496 & SSIM = 0.9747 & SSIM = 0.9682 & SSIM = 0.9293 & SSIM = 0.9213 \\  & PSNR = 36.8699 & PSNR = 40.9748 & PSNR = 44.0480 & PSNR = 36.1728 & PSNR = 37.4231 \\  & RMSE = 0.0143 & RMSE = 0.0089 & RMSE = 0.0063 & RMSE = 0.0155 & RMSE = 0.0135 \\ \hline \multirow{4}{*}{This Work} & SSIM = 0.9653 & SSIM = 0.9496 & SSIM = 0.9775 & SSIM = 0.9599 & SSIM = 0.9338 \\  & PSNR = 40.6423 & PSNR = 31.4468 & PSNR = 45.8423 & PSNR = 39.6173 & PSNR = 35.5246 \\  & RMSE = 0.0093 & RMSE = 0.0268 & RMSE = 0.0051 & RMSE = 0.0105 & RMSE = 0.0167 \\ \hline \hline \end{tabular}   
**Table A5. ** Objective evaluation indexes of AP results of different algorithms on different test images.
# Seismic Performance of Ductile Column with Rectangular Hollow Cross-Section in RC Building
## 4 Discussion
### Equivalent Viscous Damping Ratio  
The difference in energy absorption capacity, between solid and hollow sectioned columns, was inspected by comparing their equivalent viscous damping ratios (\(h_{eq}\)).  
Figure 11: Deformation distribution: (**a**) N-series (\(R\) = 4.0%); (**b**) S-series (\(R\) = 2.0%).  
Figure 12 shows the \(h_{eq}\) distributions along with the peak drift angles in all specimens. Herein, \(h_{eq}\) was calculated by using the second cycle loops of the hysteresis curves. The values of \(h_{eq}\) in CM1, CM11, CM2, and CM13 were calculated up to \(R=4.0\%\), whereas that of CM12 was calculated until \(R=1.5\%\), which was the drift angle just before the sudden drop in load-bearing capacity.  
As can be seen in Figure 12, \(h_{eq}\) gradually increased with the increase in drift angles in all specimens. Although slight differences in \(h_{eq}\) values, approximately within \(\pm 1.5\%\), were found between the solid- and hollow-sectioned specimens, their development and tendency were almost the same. CM12 also exhibited the same \(h_{eq}\) values as CM11, until the development of the unexpected failure. From these observations, before the brittle failure, it is confirmed that no degradation in energy absorption capacity occurred even in the cases with hollow cross-sections, which is attributed to equivalent hysteresis loops, failure patterns, and deformation patterns.
# Evaluation of Methods Based on CPTu Testing for Prediction of the Bearing Capacity of CFA Piles
## 2 Materials and Methods
### Cone Penetration Testing and Pile Bearing Capacity Prediction
#### 2.3.1 UniCone Method  
The UniCone method was proposed by [PERSON] and [PERSON] and it underwent several modifications summarized by [PERSON] [10; 58]. The method uses three quantities of CPTu measurement using piezoelectric cone and it provides bearing capacity calculation for various pile types manufactured by different technologies. Modification involves extension of pile load test database from 142 to 330 pile tests.  
The method prefers geometric averaging to obtain filtered and representative values for determining the pile tip bearing capacity using corrected cone tip resistance (Equations (3)-(5)):  
\[q_{e}=q_{t}-u_{2}, \tag{3}\]  
\[q_{Eg}=\sqrt[q_{e,1}\times\;q_{e,2}\;\times\;\ldots\;\times\;q_{e,n}, \tag{4}\]  
\[q_{b}=C_{te}\;\times\;q_{Eg}, \tag{5}\]  
where \(q_{t}\) is the corrected penetration resistance; \(u_{2}\) is the pore pressure; \(C_{te}\) is the correlation coefficient for the pile tip based on pile diameter \(d\) (C\({}_{te}\) = 1.0 if \(d\leq 0.4\) m, \(C_{te}\) = 1/3\(d\) if \(d>0.4\) m); \(q_{Eg}\) is geometric average of effective cone resistance; and \(q_{e,n}\) is effective cone resistance.  
Unit shaft friction\(f_{p}\) is calculated for a particular soil layer (Equation (6)):  
\[f_{p}=C_{se}\;\times\;q_{Eg}, \tag{6}\]where \(C_{\kappa}\) is correlation coefficient based on soil type in classification chart (Figure 5) and \(q_{E}\) is average of values of effective cone resistance.  
Correlation coefficient \(C_{\kappa}\) is selected according to CPT outputs in classification chart in Figure 5 and corresponding zone in Table 1.
# A Simplified Matrix Formulation for Sensitivity Analysis of Hidden Markov Models
## 3 Sensitivity Analysis of Filtering Probability
### Transition Parameter Variation  
In this subsection, the simplified matrix formulation (SMF) for sensitivity of the filtering probability to variation of the transition parameter is proposed. Let us consider the sensitivity functions \(p(x_{v}^{t},\mathbf{y}_{\mathbf{e}}^{1:t})(\theta_{a})\) for a filtering probability and transition parameter \(\theta_{a}=a_{r,s}\). From Equation (6), the recursive filtering probability sensitivity function, it follows that for \(t=1\) we have the constant \(p(x_{v}^{1},\mathbf{y}_{\mathbf{e}}^{1})(\theta_{a})=o_{v,\mathbf{e}^{t}} \cdot\gamma_{v}\), and for \(t>1\),  
\[p(x_{v}^{t},\mathbf{y}_{\mathbf{e}}^{1:t})(\theta_{a})=o_{v,\mathbf{e}^{t}} \cdot\sum_{z=1}^{n}a_{z,v}(\theta_{a})\cdot p(x_{v}^{t-1},\mathbf{y}_{\mathbf{ e}}^{1:t-1})(\theta_{a}) \tag{7}\]  
In the next sub-subsections, the formulation of the proposed method to compute the coefficients of the sensitivity function in Equation (5) is presented in detail. First, the decomposition of the transition matrix into the parts of \(A\) independent of and dependent on \(\theta_{a}\) and the observation matrix representation for the simplified matrix formulation is presented. Then the SMF representation for the sensitivity of the filtering probability to transition parameter variation and its algorithm implementation are discussed.
## 2 Analysis of the State of the Art
### OpenDDR
#### 2.3.5 Ontologies  
There are other alternatives for modeling devices. As occurs with users and context ontologies allow us to give some meaning to the modeled concepts and the collected information. From the reviewed ontologies we remark the SOUPA ontology which, in addition to consider context information, it models many different aspects of static mobile capabilities and characteristics [72]. Another significant ontology is the one presented by [PERSON], [PERSON] and [PERSON] [73] as part of the PIVOn ontology. The Device Model Ontology describes not only the device's capabilities but its relationships with the service and user ontologies, dependencies and other features.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**DDR** & **Advantages** & **Drawbacks** \\ \hline WURFL & Upgradeable to new versions & Errors in data \\  & A hierarchy which allows to infer values & Many empty values \\  & Many capabilities modelled & \\  & Very easy to configure & \\  & Powerful API & \\ \hline OpenDDR & Free to use, even commercially & Limited number of \\  & Growing community & Default values for \\  & & unknown data \\ \hline
51 Degrees.mobi & A Lite version, free to use & Limited number of \\  & & capabilities \\  & even commercially & \\  & Easy to install and use & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Analysed DDRs comparison [71].
# Integration of Production Planning and Scheduling Based on RTN Representation under Uncertainties
## 4 Case Study  
The classical example [40] was used to verify the feasibility and effectiveness of the two-layer integrated model of planning and scheduling in dealing with the uncertain problems of demand and utility based on the RTN representation. The example uses RTN representation to describe the production process, as shown in Figure 5. The three raw materials S1, S2 and S3 produce two products S8 and S9 through a series of endothermic and exothermic reactions, in which the endothermic reaction requires high-pressure steam (HS) and the exothermic reaction requires condensed water (CW). Due to the limitations of the energy system, the average supply of HS and CW is 64 and 69 kg/min, respectively. Heating can be performed on heater J1. Reaction 1 can be performed on reactors J2, J3. Reaction 2 can be performed on reactors J2, J3. Reaction 3 can be performed on reactors J2, J3. Separation can be performed on separator J4. The study involved a total of eight different production processes. Unlimited storage policy is adopted for raw materials and products, and limited storage policy is adopted for intermediate materials [41; 42]. The relevant data of the calculation example are shown in Tables 1-3.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Task (i)** & **Unit (j)** & \(\alpha_{i}\) & \(\beta_{i}\) & \(B_{i}^{\text{min}}\) & \(B_{i}^{\text{max}}\) \\ \hline Heating (i = 1) & Heater & 0.667 & 0.00667 & - & 100 \\ Reaction 1 (i = 2) & Reactor 1 & 1.334 & 0.02664 & - & 50 \\ Reaction 1 (i = 3) & Reactor 2 & 1.334 & 0.01665 & - & 80 \\ Reaction 2 (i = 4) & Reactor 1 & 1.334 & 0.02664 & - & 50 \\ Reaction 2 (i = 5) & Reactor 2 & 1.334 & 0.01665 & - & 80 \\ Reaction 3 (i = 6) & Reactor 1 & 0.667 & 0.01332 & - & 50 \\ Reaction 3 (i = 7) & Reactor 2 & 0.667 & 0.008325 & - & 80 \\ Separation (i = 8) & Separator & 1.3342 & 0.00666 & - & 200 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Task processing time coefficient and capacity data.  
Figure 5: Resource-Task Network diagram.
# Breaking Alert Fatigue: AI-Assisted SIEM Framework for Effective Incident Response
## 2 Background and Related Work
### Feature Engineering
#### 2.3.2 Featureless Approach  
Despite its high performance, the feature engineering process has been criticized for reducing adaptability and being tedious and time consuming [49]. It has been referred to as a pain point in building trained systems, and it requires a high level of computer science expertise [50].  
A recent study [16] proposed a method to correlate and filter data without relying on domain knowledge or feature engineering. Here, the alerts from an IDS are processed as text strings and transformed into numerical representations. These representations are then grouped into representative profiles using clustering methods. The authors presented two implementations of their approach using a long short-term memory recurrent neural network and latent semantic analysis. Although these implementations did not perform as well as existing methods that rely on feature engineering when evaluated using common detection metrics, they demonstrated promise when evaluated using practical metrics for filtering and correlating.
## 4 Case Study  
### Numerical Simulation Results  
The fuzzy set theory-based navigational obstacle risk assessment system that considers both collision and pollution risks was applied to both micro- and macro-level case studies to verify its performance. In the micro-level case study, the collision and pollution risks were evaluated for virtual drifting fishing boats, and a comprehensive risk was inferred using the developed system. In the macro-level case study, the comprehensive risk was inferred by adding a random index based on the collision risk level after calculating the pollution risk index for each location using data on the status of sunken ships from the Korea Maritime Environment Corporation [37].
## 5 Calculation Method for Residual Bearing Capacity  
Based on the Chinese \"Technical specification for concrete-filled steel tube composite column structures\" (CECS188:2005) [33], the axial bearing capacity of the concrete-encased CFST composite columns (\(N_{\text{u}}\)) is regarded as the sum of the bearing capacity of the outer RC and the core CFST column. The formula for calculation of the axial bearing capacity of the concrete-encased CFST short column is as follows:  
Figure 11: Damage evolution curve. (**a**) Influence of \(T\). (**b**) Influence of \(d\) and \(a\). \[N_{\rm u}=0.9\big{(}f_{\rm co}A_{\rm co}+f_{\rm y}A_{\rm ss}\big{)}+f_{\rm cc}A_{ \rm cc}(1+1.8\theta) \tag{5}\]  
\[\theta=f_{\rm a}A_{\rm a}/(f_{\rm cc}A_{\rm cc}) \tag{6}\]  
\[f_{\rm cc}=f_{\rm co}=0.88a_{\rm c1}a_{\rm c2}f_{\rm cu} \tag{7}\]  
where \(\theta\) denotes the confinement index of the core CFST; \(f_{\rm cc}\) and \(f_{\rm co}\) are the compressive strength of concrete inner and outer steel tubes, respectively, which have the same strength value in this test; \(a_{\rm c1}\) and \(a_{\rm c2}\), which are determined according to Chinese code GB 50010-2010, represent the ratio of prismatic strength to cube strength (\(f_{\rm cu}\)) and the brittleness coefficient of concrete, respectively; \(f_{\rm y}\) and \(f_{\rm a}\) are the yield strength of longitudinal reinforcement and steel tube, respectively; \(A_{\rm cc}\) and \(A_{\rm co}\) are the sectional area of concrete inside and outside steel tube, respectively; and \(A_{\rm ss}\) and \(A_{\rm a}\) are the sectional area of longitudinal reinforcement and the steel tube, respectively. Considering only the damage from heating temperature to the residual bearing capacity of the overall specimen, the residual bearing capacity (\(N_{\rm u}(T)\)) of the concrete-encased CFST composite columns subjected to high temperature can be calculated by Equation (8). \[N_{\rm u}(T)=k_{\rm T}N_{\rm u} \tag{8}\]  
where \(k_{\rm T}\) denotes the high temperature influence coefficient of the residual bearing capacity after fire exposure, which is usually related to the heating temperature, section size, and other parameters. It is mainly regarded as the influence function of the heating temperature (\(T\)) and the position coefficient \(\kappa\) (\(\kappa=d/b\), where \(d\), \(b\) are the tube diameter and the section width, respectively) of the steel tube in this paper. Regression analysis of the test results can obtain the expression \(k_{\rm T}\), as follows:  
\[k_{\rm T}=\frac{1}{1+\kappa^{os}(T-20)^{1.8}\times 10^{-5}} \tag{9}\]  
Table 6 shows the theoretically calculated values for \(N_{\rm u\_c}\)(\(T\)) of the residual bearing capacity. As can be seen from Table 6, the average ratio of the calculated values to the test values was 0.976, and the coefficient of variation was 0.067, which shows that the calculated results using the above method are in good agreement with the test results.
## 4 Experiment and Results
### Evaluation Criteria  
Three indicators were used to evaluate the performance of character detection, including F-measure, Precision, and Recall. Precision measured the consistency between the detected area and the marked area of the test data. The larger the value is, the higher the accuracy is. The recall rate was used to measure the ability of the detection algorithm to  
Figure 9: Schematic diagram of training label generation. The meaning of color is the same as that in Figure 5.  
detect all marked areas. The higher the value, the smaller the missed detection. F-measure is the harmonic average of precision and recall rate, and the overall performance was evaluated. Moreover, on this basis, we compared the test results with the label information of the test set to verify.  
The evaluation standard uses the minimum bounding rectangle as the marking and detection area. Facing the inclined character, the detection area \(r_{1}\) and the annotation area \(r_{2}\) are first rotated to be parallel to the coordinate axis, and then the matching degree between the areas is calculated according to Formula (6).  
\[m(r_{1},r_{2})=\frac{A(r_{1}\cap r_{2})}{A(r_{1}\cup r_{2})} \tag{6}\]  
In the formula, \(A(r_{1}\cap r_{2})\) and \(A(r_{1}\cup r_{2})\) represent the area of the intersection and union of regions \(r_{1}\) and \(r_{2}\), respectively. \(m(r_{1},r_{2})\) indicates the matching degree between two regions. If the included angle between the detection area and the marked area is less than \(\pi/8\) and the matching degree is more significant than 0.5, the marked area is considered to be successfully detected. The precision \(p\) and recall \(r\) are shown in Equations (7) and (8):  
\[r=\frac{|TP|}{|T|} \tag{7}\]  
\[p=\frac{|TP|}{|E|} \tag{8}\]  
In the formula, \(|TP|\) represents the number of successfully detected areas, \(|T|\) and \(|E|\) represents the number of detected and marked areas. The F-measure \(f\) is the harmonic average of precision and recall, as shown in Equation (9).  
\[f=\frac{2*p*r}{p+r} \tag{9}\]
## Biomedical Applications
### Anti-Inflammatory Activity  
Inflammation is caused by the release of chemicals from tissues and cells that migrate throughout the organism. Associated inflammatory receptors are prostaglandin (PG), leukotrienes (LT5), histamine, bradykinin, platelet-activating factor (PAF), and interleukin-1 [118]. Ulvan has anti-inflammatoryactivity that has been tested in vitro in several animal species, including mice injected with radicals such as D-Gal (500 mg/kg) [82; 83; 84] and a mouse ear edema model of topical inflammation [85]. Vero cells have been employed to identify the anti-inflammatory effects caused by infection [98].  
The ulvan anti-inflammatory mechanism is related to granuloma in the liver. Administration of sulfated polysaccharides for 24 weeks significantly reduces liver inflammation and necrosis and induces apoptosis. Sulfate polysaccharides increase the volume of liver lobules through mild sinusoid dilatation. The biological effects alter the response, stimulate the immune system via splenocytes and macrophages, and induce the release of anti-inflammatory cytokines that can suppress the growth of cancer cells [83]. Ulvan has the potential to reduce the chronic symptoms of inflammation [119]. Indeed, sulfated polysaccharide effectively reduces pro-inflammatory cytokine production in primary glial cells infected with various Japanese encephalitis virus (JEV) strains [98]. Ulvan can also reduce interferon-gamma (IFN-\(\gamma\)), tumor necrosis factor alpha (TNF-\(\alpha\)), and interleukin 6 (IL-6), and elevates brain-derived neurotrophic factor (BDNF) and choline acetyltransferase (ChAT) levels as part of hippocampal neuronal protection [13; 84]. Mice induced with D-Gal exhibit abnormal liver structure, characterized by hepatocellular necrosis and inflammation. Ulvan (100 mg/kg) attenuates this damage: The mice show partial recovery from tissue damage [82]. Ulvan exhibits vascular anti-inflammatory effects, with bradykinin as the primary target because it does not reduce histamine and serotonin-induced foot edema. Therefore, ulvan acts an on bradykinin pathway in antinociceptive and anti-inflammatory responses [52].
## 3 Controller Design and Stability Analysis
### RBFNN-Based Backstepping Attitude Control Design  
Attitude control using the adaptive RBFNN-based backstepping control method is shown in inner loop of Figure 5. The attitude control of the quadrotor helicopter is controlled by three different inputs (roll, pitch, and yaw). The attitude control in roll, pitch, and yaw have the same design procedure in the proposed control method. For the sake of simplicity, we only take the roll channel as the example design process to describe in this section.  
The roll channel is denoted as  
\[\begin{array}{l}\dot{x}_{1}=x_{2}\\ \dot{x}_{2}=\frac{M_{x}}{I_{x}}+D_{\theta},\end{array} \tag{5}\]  
where \(x_{1}\) is the roll angle and \(x_{2}\) denotes the derivation of \(x_{1}\).  
The external disturbance is denoted, by \(D_{\theta}\), as  
\[D_{\theta}=\Xi_{x}+\varpi_{x}, \tag{6}\]  
where \(\Xi_{x}=\Delta M_{x}/\left(I_{x}+\Delta I_{x}\right)\) denotes the external bounded disturbance and \(\varpi_{x}=-\Delta I_{x}M_{x}/\left[I_{x}(I_{x}+\Delta I_{x})\right]\) is treated as the model uncertainty.  
The tracking error of roll angle is defined as [33]  
\[e_{1}=x_{1d}-x_{1}, \tag{7}\]  
where \(x_{1d}\) is the desired roll angle.  
Then, the derivative of \(e_{1}\) is  
\[\dot{e}_{1}=\dot{x}_{1d}-x_{2}. \tag{8}\]  
The first Lyapunov function is chosen as  
\[V_{1}=\frac{e_{1}^{2}}{2}. \tag{9}\]  
The tracking error of roll angle velocity is defined as  
\[e_{2}=x_{2}-\dot{x}_{1d}-c_{1}, \tag{10}\]  
where the stabilizing function \(c_{1}\) is defined as  
\[c_{1}=\alpha e_{1}, \tag{11}\]  
where \(\alpha\) is a positive constant.  
Thus, the derivative of \(V_{1}\) can be obtained by  
\[\dot{V}_{1}=e_{1}\left(\dot{x}_{1d}-x_{2}\right)=-e_{1}e_{2}-\alpha e_{1}^{2}. \tag{12}\]Then, the derivative of \(e_{2}\) can be represented as  
\[\begin{array}{c}\dot{e}_{2}=\dot{x}_{2}-\ddot{x}_{1d}-\alpha\dot{e}_{1}=\\ \frac{M_{x}}{l_{x}}+D_{\theta}-\ddot{x}_{1d}+\alpha\left(e_{2}+\alpha e_{2}\right).\end{array} \tag{13}\]  
The associate Lyapunov function is denoted as  
\[V_{2}=V_{1}+\frac{1}{2}s^{2}, \tag{14}\]  
and the related sliding surface is designed as  
\[s=ke_{1}+e_{2}, \tag{15}\]  
where \(k\) is a positive constant.  
The derivation of \(V_{2}\) can be obtained by  
\[\begin{array}{c}\dot{V}_{2}=\dot{V}_{1}+s\dot{s}\\ =-e_{1}e_{2}-\alpha e_{1}^{2}+s\left(k\dot{e}_{1}+\dot{e}_{2}\right)\\ =-e_{1}e_{2}-\alpha e_{1}^{2}+s\left[(k-\alpha)\dot{e}_{1}+\frac{M_{x}}{l_{x}}+ D_{\theta}-\ddot{x}_{1d}\right].\end{array} \tag{16}\]