esa-sceva/satcom-chunk-collection huggingface dataset:
# Demodulation Technique Based on Laser Interference for Weak Photo-Acoustic Signals on Water Surface
## Appendix A  
The interference signal we set in the article is:  
\[U(t)=A\cos\{\frac{4\pi}{\lambda}[\sum_{i}A_{i}\cos(\omega_{i}t+\theta_{i})+A_{ s}\cos(\omega_{s}t+\theta_{s})]+\Phi\} \tag{1}\]  
In order to simplify the derivation, we set \(k=2\pi/\lambda\), \(\theta_{i}=0\), \(\theta_{s}=0\), therefore:  
\[U(t)=A\cos\{2k[A_{i}\sin(\omega_{i}t)+A_{s}\sin(\omega_{s}t)]+\[PERSON]\} \tag{2}\]  
We first use the trigonometric function to expand it:  
\[\begin{array}{ll}U(t)&=A\cos\[PERSON]\{\cos[2 kA_{i}\sin(\omega_{i}t)]\cdot\cos [2 kA_{s}\sin(\omega_{s}t)]\}\\ &=-A\cos\[PERSON]\{\sin[2 kA_{i}\sin(\omega_{i}t)]\cdot\sin[2 kA_{s}\sin(\omega_{s}t )]\}\\ &=-A\sin\[PERSON]\{\sin[2 kA_{i}\sin(\omega_{i}t)]\cdot\cos[2 kA_{s}\sin(\omega_{s}t )]\}\\ &=-A\sin\[PERSON]\{\cos[2 kA_{i}\sin(\omega_{i}t)]\cdot\sin[2 kA_{s}\sin(\omega_{s}t )]\}\\ \end{array} \tag{3}\]Combining the expansion formula of Bessel function:  
\[\left\{\begin{array}{l}\cos[x\sin(\omega t)]=J_{0}(x)+2\sum\limits_{k=1}^{ \infty}J_{2k}(x)\cos(2k\omega t)\\ \sin[x\sin(\omega t)]=2\sum\limits_{k=0}^{\infty}J_{2k+1}(x)\sin[(2k+1)\omega t )]\end{array}\right. \tag{10}\]  
The \(J_{k}(x)\) is the first-class Bessel function value of \(k\) order of \(x\):  
\[J_{k}(x)=\sum\limits_{m=0}^{\infty}\frac{(-1)^{m}}{m!\Gamma(m+k+1)}(\frac{x}{ 2})^{2m+k} \tag{11}\]  
We further simplify the interference signal by using the Bessel function. We can clearly see the frequency components and their magnitude of the interference signal:  
\[\begin{array}{ll}U(t)&=AJ_{0}(2 kA_{s})J_{0}(2 kA_{i})\cos\Phi\\ &+2 AJ_{0}(2 kA_{s})\cos\Phi\sum\limits_{m=1}^{\infty}J_{2m}(2 kA_{i})\cos(2m \omega_{i}t)\\ &-2 AJ_{0}(2 kA_{s})\sin\Phi\sum\limits_{m=0}^{\infty}J_{2m+1}(2 kA_{i})\sin[(2 m+1)\omega_{i}t]\\ &+2 AJ_{0}(2 kA_{i})\cos\Phi\sum\limits_{m=1}^{\infty}J_{2n}(2 kA_{s})\cos(2n \omega_{s}t)\\ &-2 AJ_{0}(2 kA_{i})\sin\Phi\sum\limits_{n=0}^{\infty}J_{2n+1}(2 kA_{i})\sin[(2 n+1)\omega_{s}t]\\ &+4A\cos\Phi[\sum\limits_{m=1}^{\infty}[PERSON]_{2m}(2 kA_{s})\cos(2m\omega_{i}t)] \cdot[\sum\limits_{n=1}^{\infty}[PERSON]_{2n}(2 kA_{i})\cos(2n\omega_{s}t)]\\ &-4A\cos\Phi\left\{\sum\limits_{m=0}^{\infty}[PERSON]_{2m+1}(2 kA_{i})\sin[(2m+1) \omega_{i}t]\right\}\cdot\left\{\sum\limits_{n=0}^{\infty}J_{2n+1}(2 kA_{s}) \sin[(2n+1)\omega_{s}t]\right\}\\ &-4A\sin\[PERSON]\left\{\sum\limits_{m=0}^{\infty}J_{2m}(2 kA_{i})\cos(2m\omega_{i} t)\right]\cdot\left\{\sum\limits_{n=0}^{\infty}J_{2n+1}(2 kA_{s})\sin[(2n+1) \omega_{s}t]\right\}\\ &-4A\sin\[PERSON]\left\{\sum\limits_{m=0}^{\infty}J_{2m+1}(2 kA_{i})\sin[(2m+1) \omega_{i}t]\right\}\cdot[\sum\limits_{n=1}^{\infty}J_{2n}(2 kA_{s})\cos(2n \omega_{s}t)]\end{array} \tag{12}\]  
There is no detailed explanation in this paper, but we describe the interference signal with simulation, which is consistent with the theory from the simulation result.
## WT1 Immunohistochemical Expression in Human Embryonal/Fetal and Neoplastic Tissues
### WT1 Expression in Sertoli Cell Tumors  
Sertoli cell tumors are composed of Sertoli cells with rare Leydic cells. They are typically a solid mass with a tan to yellow cut surface. The tumor cells are cuboidal or columnar with pale cytoplasm,  
Figure 4: Ovarian granulosa cell tumor, adult type (**A**). Nuclear WT1 (_N-terminus_) expression in neoplastic cells at low (**B**) and high (**C**) magnification.  
and less frequently, deeply eosinophilic or vacuolated. The nuclei are round-oval in shape and uniform with inconspicuous nucleoli. Atypical and bizarre nuclei are rarely observed. Mitotic activity is variable, but not \(>\) 5/10 HPF. The lesion is well limited by the surrounding ovarian parenchyma.  
The cells are typically arranged in a diffuse or nodular pattern, but they can be observed as a mixture of different patterns (tubules, cord or trabeculae, sheets, pseudo-papillae and more rarely, retiform, islands or spindly patterns). The main differential diagnoses are the Sertoli-Leydig cell tumor, endometriioid carcinoma, carcinoid tumor and female adnex tumor.  
Several studies have investigated the expression of WT1 in Sertoli cell tumors in order to identify new diagnostic markers. [PERSON] et al. [99] suggested including WT1 protein (6F-H2 antibody) in the immunohistochemical panel, together with inhibin, to distinguish Sertoli cell tumors from endometrioid and neuroendocrine tumors. In addition, the authors stated that the diagnostic utility of WT1 in Sertoli cell tumors is similar to inhibin, and better than that of calretinin [99]. Another study evaluated WT1 expression in ovarian stroma and its tumors. The results showed that ovarian stromal cells, ovarian fibroma, cellular fibroma, fibrothecoma and ovarian leiomyoma expressed WT1, whereas non-gynecologic smooth muscle tumors and other spindle cell tumors were usually negative for WT1. These findings suggest that WT1 may be used as an immunohistochemical marker for spindle cell tumors derived from the ovary and uterus, including Sertoli cell tumors (Figure 5). WT1, SF-1 and inhibin are the most informative sex cord-stromal markers to be used for the distinction of non-sex cord-stromal tumors; however, the usefulness of immunohistochemistry for the diagnosis of fibroma/fibrothecoma is limited [100].  
Figure 5: Sertoli cell tumor (**A**). Neoplastic cells showing nuclear WT1 (_N-terminus_) expression (**B**).
## 1 Introduction
DIET, a transformer-based model, efficiently categorizes intents and extracts entities, which is compatible with pre-trained embedding models such as BERT, GloVe, and ConvexRT [8]. However, there is a notable research gap in the application of the RASA framework to the Arabic language, which is characterized by complex syntax and rich morphology, presenting unique challenges for NLP [25; 26; 27]. Tayseer was developed using the DIET architecture with attention-based mechanisms to address these challenges, as shown in Figure 1. The integration of pre-trained models within DIET enables the chatbot to effectively handle intent and entity recognition tasks [28; 29; 30]. Moreover, the system was designed to securely store individual academic backgrounds and dialogue histories in a structured SQL database, facilitating personalized and context-aware responses. An integrated feedback loop leveraging sentiment analysis of student conversational experiences was employed to incrementally improve the system's effectiveness over time. This applied research seeks to contribute to the field by integrating data-driven machine-learning methods with custom knowledge representation within a modular Arabic chatbot framework. The framework was specifically designed to address admission inquiries and frequently asked questions (FAQs) in the context of higher education for technical students. The findings of this study are intended to inform the ongoing development of effective and user-friendly conversational interfaces for the Arabic-speaking student population in line with the identified key features and design principles. The rest of the paper is structured as follows: Section 2 offers a comprehensive overview of pertinent prior research, providing a background for our study. Section 3 presents the methodology and the proposed model. Section 4 presents and discusses the results and highlights the key findings. Finally, Section 5 concludes the paper and offers recommendations for future research.
###### Abstract  
This study investigated the impact of incorporating _Cissus quadrangularis_ (CQ) powder into Yanggaeng, a traditional Korean food, focusing on its functional properties. This study examined the proximate composition, physicochemical characteristics, antioxidant capabilities, sensory attributes, and consumer preferences of Yanggaeng when treated with different levels (CON [0%], CQ2 [2%], CQ4 [4%], and CQ6 [6%]) of CQ powder. Yanggaeng with CQ powder exhibited a significantly reduced pH, and among the CQ additive groups the highest \({}^{\circ}\)Brix value was observed in CQ2. The water holding capacity (WHC) decreased after adding CQ powder. The color properties of Yanggaeng with CQ powder, including \(L^{\star}\), \(a^{\star}\), and \(b^{\star}\), were measured. \(L^{\star}\) values dose-dependently decreased as the amount of CQ powder increased. Conversely, \(a^{\star}\) values increased significantly with CQ powder addition compared with CON, and \(b^{\star}\) values were highest in CQ2. Similarly, the browning index (BI) increased in the CQ powder treatment groups compared with CON. The antioxidative properties of Yanggaeng with CQ powder were evaluated by measuring the total phenolic content (TPC), total flavonoid content (TFC), 1,1-diphenyl-1-picrylhydrazyl (DPPH) and 6-hydroxy-2,5,7,8-tetramethylchroman-2-carboxylic acid (ABTS) radical scavenging activities, and ferric reducing antioxidant power (FRAP). The antioxidant capacity dose-dependently increased with higher levels of CQ powder added. Regarding the texture profile of Yanggaeng, compared with the control group, adding CQ powder caused decreased hardness, gumminess, and chewiness. In consumer preference evaluations, CQ2 showed similarities to CON in all aspects (color, scent, flavor, sweeteness, taste, chewiness, overall acceptance, and purchase intention). Therefore, incorporating CQ powder, a natural and edible antioxidative ingredient, into Yanggaeng may be acceptable to consumers despite significant changes in its physicochemical properties.  
Cissus quadrangularis; Yanggaeng; physicochemical properties; antioxidant capacities; sensory attributes +
Footnote †: journal: Applied Sciences
## 2 Materials and Methods  
### Calcium Sulfate and Phase Change Materials  
Figure 1 illustrates the observations made with a Scanning Electron Microscope of the calcium sulfate and the PCM used in this study. The raw material is a natural plaster, Extha Iberica (cf. Figure 1a), which is a \(\beta\)-calcium sulfate hemihydrate (CaSO\({}_{4}\)-0.5H\({}_{2}\)O, containing 5% CaCO\({}_{3}\) and some traces of SiO\({}_{2}\)) in powder form, with a median particle diameter of 15.5 \(\upmu\)m and a density of 2300 kg\(\cdot\)m\({}^{-3}\). As observed in the literature [22; 23], its heterogeneous microstructure is easily characterized by the acicular morphology of its crystals. For the 3D printing process, cellulose ether, at 2% of the plaster mass, was added as an additive to the plaster. This additive allows us to control the naturally uncontrolled capillary-driven penetration of water into the powder bed [26; 27].  
A commercial micro-encapsulated phase change material 28-S50, supplied by Mikro-Caps (Ljubljana, Slovenia), was used in this work because of its high thermal energy storage capacity and phase change temperature, which occurs within a comfortable temperature range for the building. The MikroCapsPCM28-S50 is made of a paraffin wax and has a spherical membrane of polyurethane, as observed in Figure 1b. As specified in the product data sheet, its phase change temperature is around 23-27 \({}^{\circ}\)C (melting at 27 \({}^{\circ}\)C, crystallization at 23 \({}^{\circ}\)C) and its latent heat is between 140 and 180 \(\cdot\)g\({}^{-1}\). Its apparent density is  
Figure 1: Scanning Electron Microscope photos of (a) hydrated calcium sulfate and (b) MikroCapsPCM28-S50.  
between 880 g\(\cdot\)L\({}^{-1}\) and 950 g\(\cdot\)L\({}^{-1}\) and its equivalent diameter ranges between 1 and 20 \(\upmu\)m (see Table 1).
## 4 Benchmark Databases and Performance Evaluation Metrics
### Evaluation Metrics
#### 4.2.3 Specificity  
It is a measure of the normal traffic that is accurately predicted. The specificity (\(S_{p}\)) is expressed as below:  
\[S_{p}=\frac{T_{N}}{T_{N}+F_{P}} \tag{28}\]  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Dataset** & **Year** & **Publicly** & **Traffic** & **Format** & **Traffic Volume** & **Span** & **Traffic Present** & **Attack Type** \\ \hline NDSeC-1 & 2016 & No & Simulated &.pcap, logs & 3.5 M packets & - & Attack traffic only & Botnet, HTTP flood, SYN flood, UDP flood, SSL proxy, SQL injection, spoofing, exploits \\ \hline DDoS 2016 & 2016 & Yes & Synthetic &.pcap & 2.1 M packets & - & Normal and attack traffic & HTTP flood, Shnurf ICMP flood, UDP flood \\ \hline CICIDS2017 & 2017 & Yes & Simulated &.pcap,.csv & 3.1 M flows & 5 days & Normal and attack traffic & Botnet, LOIC, SQL injection, slowloris, SSH brute force \\ \hline CICIDS2018 & 2018 & Yes & Simulated &.pcap,.csv & 6.89 GB packets & 10 days & Normal and attack traffic & Brute force, botnet, Heartbleed, DoS, DDoS, web attacks, infiltration \\ \hline CICDDoS2019 & 2019 & Yes & Simulated &.pcap,.csv & 13.01 GB packets & 2 days & Normal and attack traffic & PortMap, NetBIDS, MSSQL, UDP, UDP-Lag, SYN, NTP, DNS, SNMP, SSDP, TFTP, Web-DDoS \\ \hline IoTID20 & 2020 & No & Simulated &.csv & - & - & Normal and attack traffic & SYN, UDP, HTTP, ACK floods, Host brute force, port scan \\ \hline UAV-IDS-2020 & 2020 & Yes & Real &.csv & - & - & Normal and attack traffic & GPS spoofing, jamming, DoS \\ \hline \hline \end{tabular}
\end{table}
Table 11: _Cont._
## 4 Deformation Force Monitoring Based on Adaptive Adjustment of Clamping Force
### Optimal Estimation of Deformation Forces Based on the Kalman Filter Algorithm  
In machine learning, it is usually assumed that, while the training data and the test data are independent of each other, they are identically distributed. However, the training data are derived from simulation while the model needs to be applied to real world data. We consider the difference between the simulated data and the real world data as a modeling error. Kalman filtering is an algorithm that uses the system state equation to optimally estimate the state of the system by using the system observations, and it can reduce the measurement noise to restore the true measurement value. The deformation force measurements and the deformation force prediction values are the input to the Kalman filter algorithm. The optimal estimate of the deformation force is calculated  
Figure 3: The structure of deformation force prediction model based on deep autoregressive neural network and Kalman filter.  
according to Equation (21), which is then input to the deep autoregressive neural network to predict the deformation force of the next machining step.  
\[\begin{split}\hat{\mathbf{x}}_{k}&=f\big{(}\hat{x}_{0 }^{\prime}\dots\hat{x}_{k-1}^{\prime}\big{)}\\ \mathbf{P}_{k}&=\mathbf{F}_{\mathbf{k}}\mathbf{P}_{k-1 }^{\prime}\mathbf{F}_{k}^{\prime}+\mathbf{Q}_{k}\\ z_{k}&=h(\hat{\mathbf{x}}_{k})+v\\ \mathbf{R}_{k}&=\mathbf{H}_{k}\mathbf{P}_{k}\mathbf{ H}_{k}^{\mathsf{T}}-\xi_{k}\\ \hat{\mathbf{x}}_{k}^{\prime}&=\hat{\mathbf{x}}_{k}+ \mathbf{K}^{\prime}(\mathbf{z}_{k}-h(\hat{\mathbf{x}}_{k}))\\ \mathbf{K}^{\prime}&=\mathbf{P}_{k}^{-1}\mathbf{ H}_{k}^{\mathsf{T}}\left(\mathbf{H}_{k}\mathbf{P}_{k}^{-1}\mathbf{H}_{k}^{ \mathsf{T}}+\mathbf{R}_{k}\right)^{-1}\\ \mathbf{P}_{k}^{\prime}&=(\mathbf{I}-\mathbf{K}^{ \prime}\mathbf{H}_{k})\mathbf{P}_{k}\end{split} \tag{21}\]  
where \(\hat{\mathbf{x}}_{k}\) is the \(k\)-moment prediction, \(\hat{\mathbf{x}}_{k-1}^{\prime}\) is the previous moment system estimate and \(f\) is the state transfer function; \(\mathbf{P}_{k}\) is the covariance of the current moment extrapolated from the previous moment, \(\mathbf{Q}_{k}\) is the prediction model that brings the covariance noise, \(h\) is observation function, and \(\mathbf{H}_{k}\) is the observation matrix; \(v\) is the observation error; \(z_{k}\) is the observation at the current moment, \(\mathbf{R}_{k}\) is the observation covariance, and \(\mathbf{K}^{\prime}\) is the Kalman gain.
## 2 Materials and Methods
### Vegetation Indices Calculation  
The normalized difference vegetation index (NDVI) and optimized soil-adjusted vegetation index (OSAVI) [37] were calculated by Equations (22) and (23), respectively:  
\[\mathrm{NDVI}=\frac{\mathrm{NIR}-\mathrm{RED}}{\mathrm{NIR}+\mathrm{RED}} \tag{22}\]  
\[\mathrm{OSAVI}=\frac{\mathrm{NIR}-\mathrm{RED}}{\mathrm{NIR}+\mathrm{RED}+0.16} \times 1.16 \tag{23}\]  
where NIR and RED are the surface reflectance values (decimals), for the near-infrared and red bands, provided by a given RS platform (dimensionless).  
The f\({}_{\mathrm{c}}\) model used in the \(\mathrm{TSEB_{\mathrm{ser}}}\) and \(\mathrm{TSEB_{\mathrm{par}}}\) approaches is presented by Equations (24)-(28), as follows [21]:  
\[\mathrm{f_{c,o}}=1-\mathrm{exp}(-0.50\mathrm{LAI}) \tag{24}\]  
\[\mathrm{LAI_{L}}=\mathrm{LAI}/\mathrm{f_{c,o}} \tag{25}\]  
\[\mathrm{f_{s}}=1+\mathrm{f_{c,o}}\times\mathrm{exp}(-0.50\mathrm{LAI_{L}})- \mathrm{f_{c,o}} \tag{26}\]  
\[\mathrm{CF}=-\mathrm{ln}\left(\frac{\mathrm{f_{s}}}{0.50\mathrm{LAI}}\right) \tag{27}\]  
\[\mathrm{f_{c}}=1-\mathrm{exp}(-0.50\times\mathrm{CF}\times\mathrm{LAI}) \tag{28}\]  
where f\({}_{\mathrm{c,o}}\) is the initial f\({}_{\mathrm{c}}\) value before adjustments (dimensionless); \(\mathrm{LAI_{L}}\) is the local LAI (m\({}^{2}\)/m\({}^{2}\)); f\({}_{\mathrm{s}}\) is the soil fractional cover (dimensionless); CF is the vegetation clumping factor (dimensionless).  
The LAI is calculated using the model from [38], an exponential model calibrated for maize and sorghum and indicated by Equation (29) below:  
\[\mathrm{LAI}=0.263\times\mathrm{exp}(3.813\times\mathrm{OSAVI}) \tag{29}\]  
Maize h\({}_{\mathrm{c}}\) was estimated through an exponential model for maize and soybeans and indicated by Equation (30) below [39]:  
\[\mathrm{h_{c}}=(1.86\mathrm{OSAVI}-0.20)\times\left[1+4.82\times 10^{-7}\mathrm{ exp}(17.69\mathrm{OSAVI})\right] \tag{30}\]
## 3 Cooperative Perception Information-Sharing
### Cooperative Perception Information-Sharing Strategy
The mechanism takes advantage of the fact that the transmitting vehicle can request the confirmation of certain or crucial broadcast information and retransmit anomalous broadcasts on a selective basis. The approach lowers data transmission interference and collisions while also increasing data transmission accuracy. Furthermore, many scholars define CPM-sharing strategies according to the value of CPM [88; 89]. [PERSON] et al. [90] proposed deciding whether to send the CPM policy by predicting the importance of the CPM to the receiver. If the detected object information is included in the cooperative perception information, it is transmitted only when the sender evaluates the object to be valuable to the receiver. This method reduces the information transmission rate of low-value objects and realizes the effective control of channel congestion. However, the difficulty is how to obtain an accurate estimate of the information value. This problem was partially solved by [91], who proposed selectively transferring higher-valued data of perceived demand using reinforcement learning. Reference [92] proposed enhancing the timeliness and accuracy of cooperative perception information by improving the freshness of sensing information. [PERSON] et al. [93] defined the coverage of the ROI of the vehicle and the update rate of perceived information. When communication resources are limited, they choose to maximize the perceptual data of the ROI of the shared vehicle. At the same time, based on the premise of ensuring the most appropriate CPM update frequency, the information of interest is selectively transmitted. This can expand the perception range, reduce the information age, and achieve real-time situational awareness of the surrounding environment. With the continuous development of intelligent roadside equipment, the interaction of information between the vehicle and the roadside is equally important to enhance the cooperative perception effect. The RSU is usually located in a fixed location and supports the deployment of edge computing devices, so it can better support the perception data processing capability of autonomous driving. By analyzing the advantages and applications of existing V2I communication systems, [PERSON] et al. [94] pointed out the important role of V2I communication in realizing autonomous driving cooperative perception. [PERSON] et al. [95] proposed a cooperative system utilizing V2I communication. It can combine its perception data with a high-precision map to assist the self-driving vehicle in better understanding the driving environment and provide driving suggestions when the vehicle enters the service range of the roadside equipment. The performance of the proposed cooperative system was tested in two traffic scenarios of road icing and construction, which proved the effectiveness of the cooperative perception of the system. Perceptual information-sharing strategies are summarized in Table 7 according to the type of shared information.
## 4 Fuzzy Fatigue Reliability Assessment of Welded A-Type Frame
### Fuzzy Fatigue Performance Function Considering Multi-Source Uncertainties  
#### 4.5.1 Determination of Random Variables and Fuzzy Variable  
The fuzzy fatigue reliability of welded A-type frame was relative with many factors. In this paper, the random excitation produced the loads, and thus the vertical force at front traction joint \(F_{1}\), the lateral force at right and left steering joint \(F_{2}\) and \(F_{3}\), and the lateral force at front lateral stabilizer joint \(F_{4}\) were considered as the random variables. The A-type frame was welded by different thickness of plates, while this dimension could be changeable as long as the maximum equivalent stress trended to be smaller. Therefore, the thickness of tail plate \(t_{1}\), the thickness of roof plate \(t_{2}\), the thickness of lateral plate \(t_{3}\), and the thickness of base plate \(t_{4}\) were also considered as the random variables. In addition, the material properties of the welded A-type frame were related to the working stress in the elastic and plastic period. Therefore, the elastic parameters, including Young modulus \(E\) and Poisson ratio \(\upsilon\), and the plastic parameters, including cyclic strength coefficient \(K^{\prime}\) and cyclic strain hardening exponent \(n^{\prime}\), were taken as the random variables in virtue of the manual manufacturing process. The quality of weld seam could not be evaluated by a specific value, because it depended on the welding process. Thus, the fatigue strength was considered as the fuzzy variable. The maximum equivalent stress \(S\) was the pivotal parameter to determine the fatigue reliability, and it was considered as the output variable. Subsequently, twelve random variables and one fuzzy variable were defined and are listed in Table 5.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbols** & **Random Variables** & **Mean Values** \\ \hline \(x1\) & Young Modulus \(E\) (MPa) & 201,000 \\ \(x2\) & Poisson ratio \(\upsilon\) & 0.3 \\ \(x3\) & Cyclic strength coefficient \(K^{\prime}\) (MPa) & 860.99 \\ \(x4\) & Cyclic strain hardening exponent \(n^{\prime}\) & 0.1792 \\ \(x5\) & Thickness of tail plate \(t_{1}\) (mm) & 36 \\ \(x6\) & Thickness of roof plate \(t_{2}\) (mm) & 32 \\ \(x7\) & Thickness of lateral plate \(t_{3}\) (mm) & 20 \\ \(x8\) & Thickness of base plate \(t_{4}\) (mm) & 20 \\ \(x9\) & Vertical force at front traction joint \(F_{1}\) (N) & 77,500 \\ \(x10\) & Lateral force at right steering joint \(F_{2}\) (N) & 22,500 \\ \(x11\) & Lateral force at left steering joint \(F_{3}\) (N) & 22,500 \\ \(x12\) & Lateral force at front lateral stabilizer joint \(F_{4}\) (N) & 62,500 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Random variables and their mean values.  
Figure 13: Layout of one strain gauge.