esa-sceva/satcom-chunk-collection huggingface dataset:
# PROFEE: A Probabilistic-Feedback Based Speed Rate Adaption for IEEE 802.11 bc
## 5 Experiments
### Performance of the Three Estimators
As Table 4 shows, it becomes clear why we cannot use all three estimators and why we selected the _silence_ estimator for the first algorithm of the proposed method that searches for a probability that guarantees low estimation error in a short time. It is worth noticing from this table that the estimation obtained after 2000 messages is very similar to the one obtained for 5000 messages, which shows that it is unnecessary to wait for 5000 messages to get an accurate estimate on \(n_{ACK}\) and \(n_{NACK}\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**STAs**} & \multirow{2}{*}{\(\begin{array}{c}p(p_{ACK}\text{ or}\\ p_{NACK})\end{array}\)} & \multirow{2}{*}{**Estimator**} & \multicolumn{2}{c}{\(n_{ACK}\) Error [STAs]} & \multicolumn{2}{c}{\(n_{NACK}\) Error [STAs]} \\ \cline{5-8}  & & & \(2f=2k\) & \(2f=5k\) & \(2f=2k\) & \(2f=5k\) \\ \hline \multirow{5}{*}{n = 10} & \multirow{5}{*}{0.001} & Correct feedback & **0** & **0** & **1** & **0** \\  & & Collisions & 3 & 3 & 7 & 7 \\  & & Slicenes & **0** & **0** & **1** & **0** \\ \cline{2-8}  & & Correct feedback & 510 & 526 & 394 & 392 \\ \cline{2-8}  & & Collisions & 3 & **0** & 3 & 2 \\  & & Slicenes & **0** & **0** & **0** & **1** \\ \cline{2-8}  & & Correct feedback & 17 & 17 & 2 & 2 \\  & & Collisions & **0** & **0** & 3 & 3 \\  & & Slicenes & **0** & **0** & **0** & **0** \\ \hline \multirow{5}{*}{n = 100} & \multirow{5}{*}{0.001} & Correct feedback & **0** & **1** & **9** & 5 \\  & & Collisions & 18 & 18 & 82 & 46 \\ \cline{1-1}  & & Slicenes & **0** & **1** & 12 & **2** \\ \cline{1-1} \cline{2-8}  & & Correct feedback & 267 & 269 & 17 & 17 \\ \cline{1-1}  & & Collisions & **4** & 7 & 20 & 21 \\ \cline{1-1}  & & Slicenes & **1** & **0** & **2** & **0** \\ \cline{1-1} \cline{2-8}  & & Correct feedback & 9 & 9 & 22 & 22 \\ \cline{1-1}  & & Collisions & 7 & 7 & **19** & **19** \\ \cline{1-1}  & & Slicenes & **0** & **0** & 1918 & 1918 \\ \hline \multirow{5}{*}{n = 1000} & \multirow{5}{*}{0.001} & Correct feedback & 8 & 11 & 159 & 159 \\  & & Collisions & 50 & 41 & 215 & 197 \\ \cline{1-1}  & & Slicenes & **1** & **3** & **6** & **9** \\ \cline{1-1} \cline{2-8}  & & Correct feedback & 60 & 60 & 156 & 174 \\ \cline{1-1}  & & Collisions & 57 & 60 & 147 & 163 \\ \cline{1-1}  & & Slicenes & **4** & **3** & **85** & **63** \\ \cline{1-1} \cline{2-8}  & & Correct feedback & 128 & 128 & 841 & 841 \\ \cline{1-1}  & & Collisions & **124** & **124** & **450** & **454** \\ \cline{1-1}  & & Slicenes & 1841 & 1841 & 1159 & 1159 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Absolute error of three estimators after 2 k and 5 k messages for 10, 100, and 1000 STAs, radius = 100 m.
## 3 Results
### Measurements
#### 3.1.2 Broadband Tuner with Filter  
The FSS-ES used a filter technique for the term extended C-band in adding filter-1 with 100 MHz GB and low interference at an 85 m distance, as shown in Figure 12. A similar filter technique with 100 MHz GB exhibited a minimal increased interference with 22 dB, as shown in Figure 13. However, the filter technique for the extended C-band in adding filter-2 with 100 MHz GB showed differences in the shape of interference that reduced the interference by using a different filter technique with 35.7 dB, as shown in Figure 14.  
Figure 11: FSS for 85 m (new C-band 50 MHz GB).  
Figure 10: FSS for 85 m (new C-band 100 MHz GB).  
Table 8 shows the test matrix: direct-facing VSAT and then indirect at 85 m. Extended C-Band-LNB + BPF, C-Band-LNB + BPF, and new C-Band-LNB + BPF, 5G off, then 100 MHz Gard Band (GB), and lastly, 50 MHz GB. The 5G cellular was on idle near VSAT and then performed a full buffer download. And the frequency range was C-Band-LNB: 3625 to 4200 MHz; extended C-Band LNB: 3400 to 4200 MHz; and the new C-Band LNB: 3700 to 4200 MHz (with built-in BPF).
Our experimental results show significant improvements over the cutting-edge methods currently in use, with competitive quantitative metrics for PSNR and SSIM and useful effectiveness in real-world applications. To summarize, our contributions are threefold:  
1. We introduce a synergistic combination of CSPDarknet53 and BiFPN, enhanced with separable convolutional blocks, for robust and efficient feature extraction and multi-scale fusion. 2. The integration of HINet for meticulous image refinement ensures comprehensive occlusion removal, addressing both local and global features effectively. Figure 1: The left side shows a light-field camera system that focuses the scene through a microlens array onto a photosensor. The right side displays the resulting sub-aperture image grid, with u and v indicating angular resolution (different viewpoints) and w and h denoting spatial resolution within each sub-aperture image. Our method is extensively evaluated on diverse datasets, demonstrating significant improvements over state-of-the-art methods and practical effectiveness in real-world applications. This comprehensive approach not only achieves superior quantitative results but also sets a new standard for future research in light-field occlusion removal. The source code will be made available upon publication, facilitating further research and development in this domain.
# Design of an Isolated Bidirectional Symmetric Resonant Converter
## 6 The Measurements and Operating Efficiency Analysis
### Critical Measurements for the Reverse Discharging Mode  
Figure 18 shows the measurement results of \(v_{\text{C}SS}\), \(v_{\text{D}SS}\), and \(i_{\text{D}SS}\) in the cases where the discharging battery voltages are \(V_{\text{B}at}\) = 280 V and \(V_{\text{B}at}\) = 403 V, respectively, and \(V_{\text{DC\_Grid}}\) = 400 V. It is obvious that there appears a reverse current \(i_{\text{D}SS}\) inside the power switch both in Figure 18a,b, which helps remove the energy on the parasitic capacitance and rapidly decline \(v_{\text{D}SS}\) to 0 V, thus achieving ZVS.  
Notably, Figure 19a clearly exhibits the advantage of a symmetric dual resonant converter in that the voltage gain is obviously greater than 1.  
Figure 17: Waveforms of \(v_{DB7}\) and \(i_{DB7}\) with two battery voltages: (**a**) \(V_{Bat}\) = 280 V; (**b**) \(V_{Bat}\) = 403 V.  
Figure 18: Waveforms of \(v_{GSS},\upsilon_{DSS}\), and \(i_{DSS}\) with two discharging battery voltages: (**a**) \(V_{Bat}\) = 280 V; (**b**) \(V_{Bat}\) = 403 V.  
Figure 19 shows the measurement results of \(v_{DB4}\) and \(i_{DB4}\) in the cases where the discharging battery voltages are \(V_{Bat}\) = 280 V and 403 V, respectively, and the DC grid voltage \(V_{DC\_Grid}\) = 400 V. By observing Figure 19a, the diode current \(i_{DB4}\) has fallen to 0 A prior to the cut-off of diode \(D_{B4}\) and thus leads to diode ZCS being successful. It is worth noting that there appears oscillation of \(v_{DB4}\) at the switching instant, which resulted from the resonance of parasitic capacitance and the secondary resonant inductance. Due to the resonant converter working at Region I, Figure 19b shows that the diode current \(i_{DB4}\) has not reached 0 A before diode \(D_{B4}\) turns off and thus fails in ZCS of \(D_{B4}\).
## 2 Methodology
### Detailing Data Reconciliation to a Singular Mathematical Model  
Considering the basic mathematical model, \(m_{1}^{c}=m_{2}^{c}=\cdots=m_{N}^{c}\), which may be useful for applications related to the assessment of conformity of physical-chemical properties, the reconciliation of \(N\) outcomes of the same quantity is performed as follows:  
\[Z^{e}=\begin{bmatrix}m_{1}^{e}\\ m_{2}^{c}\\ \vdots\\ m_{N}^{e}\end{bmatrix}Z^{c}=\begin{bmatrix}m_{1}^{c}=m^{c}\\ m_{2}^{c}=m^{c}\\ \vdots\\ m_{N}^{c}=m^{c}\end{bmatrix}=\begin{bmatrix}m^{c}\\ m^{c}\\ \vdots\\ m^{c}\end{bmatrix}Z^{e}-Z^{c}=\begin{bmatrix}m_{1}^{e}-m^{c}\\ m_{2}^{c}-m^{c}\\ \vdots\\ m_{N}^{e}-m^{c}\end{bmatrix}\]  
If the quantities are not correlated themselves, Equation (11) assumes the following:  
\[F_{ob}=min\left[\begin{bmatrix}m_{1}^{c}-m^{c}\\ m_{2}^{c}-m^{c}\\ \vdots\\ m_{N}^{e}-m^{c}\end{bmatrix}^{T}\begin{bmatrix}\sigma_{1}^{2}&0&\cdots&0\\ 0&\sigma_{2}^{2}&\cdots&0\\ \vdots&\vdots&\ddots&\vdots\\ 0&0&\cdots&\sigma_{N}^{2}\end{bmatrix}^{-1}\begin{bmatrix}m_{1}^{c}-m^{c}\\ m_{2}^{c}-m^{c}\\ \vdots\\ m_{N}^{c}-m^{c}\end{bmatrix}\right] \tag{12}\]  
The inverse of a matrix is a special matrix that \"undoes\" the effects of the original matrix.  
\[F_{ob}=min\left[\begin{bmatrix}m_{1}^{e}-m^{c}&m_{2}^{e}-m^{c}&\cdots&m_{N}^{e }-m^{c}\end{bmatrix}\begin{bmatrix}\
icefrac{{1}}{{\sigma_{1}^{2}}}&0&\cdots&0 \\ 0&\
icefrac{{1}}{{\sigma_{2}^{2}}}&\cdots&0\\ \vdots&\vdots&\ddots&\vdots\\ 0&0&\cdots&\
icefrac{{1}}{{\sigma_{N}^{2}}}\end{bmatrix}\begin{bmatrix}m_{1} ^{c}-m^{c}\\ m_{2}^{c}-m^{c}\\ \vdots\\ m_{N}^{e}-m^{c}\end{bmatrix}\right] \tag{13}\]  
The objective function can be represented as follows:  
\[F_{ob}=min\left[\frac{\left(m_{1}^{e}-m^{c}\right)^{2}}{\sigma_{1}^{2}}+\frac {\left(m_{2}^{e}-m^{c}\right)^{2}}{\sigma_{2}^{2}}+\cdots+\frac{\left(m_{N}^{ e}-m^{c}\right)^{2}}{\sigma_{N}^{2}}\right] \tag{14}\]  
\[\frac{\partial F_{ob}}{\partial m^{c}}=minF_{ob}=\begin{bmatrix}\frac{-2\left( m_{1}^{e}-m^{c}\right)}{\sigma_{1}^{2}}-\\ \frac{2\left(m_{2}^{e}-m^{c}\right)}{\sigma_{2}^{2}}-\cdots\\ -\frac{2\left(m_{N}^{e}-m^{c}\right)}{\sigma_{N}^{2}}\end{bmatrix}=0 \tag{15}\]  
\[m^{c}=\frac{\frac{m_{1}^{c}}{\sigma_{1}^{2}}+\frac{m_{2}^{c}}{\sigma_{2}^{2}}+ \cdots+\frac{m_{N}^{c}}{\sigma_{N}^{2}}}{\frac{1}{\sigma_{1}^{2}}+\frac{1}{ \sigma_{2}^{2}}+\cdots+\frac{1}{\sigma_{N}^{2}}} \tag{16}\]  
\[m^{c}=\frac{\sum\frac{m_{1}^{c}}{\sigma_{1}^{2}}}{\sum\frac{1}{\sigma_{1}^{2}}} \tag{17}\]  
Thereby, the standard uncertainty, based on GUM [30], is as follows:  
\[u_{m^{c}}^{2}=\begin{pmatrix}\frac{\frac{1}{\sigma_{1}^{2}}}{\frac{1}{\sigma_ {1}^{2}}+\frac{1}{\sigma_{2}^{2}}+\cdots+\frac{1}{\sigma_{N}^{2}}}\times u_{m _{1}^{c}}\end{pmatrix}^{2}+\begin{pmatrix}\frac{\frac{1}{\sigma_{2}^{2}}}{\frac{1}{ \sigma_{1}^{2}}+\frac{1}{\sigma_{2}^{2}}+\cdots+\frac{1}{\sigma_{N}^{2}}} \times u_{m_{2}^{c}}\end{pmatrix}^{2}+\cdots \tag{18}\]Equation (18) becomes Equation (19) when \(\sigma_{i}^{2}\) is assumed to be equal to \(u_{m_{i}}^{2}\) for \(i=1,2\), \(\ldots\), \(N\).  
\[u_{m^{c}}=\sqrt{\frac{1}{\sum\frac{1}{\sigma_{i}^{2}}}} \tag{19}\]
## 3 Results
### Comparison with Existing Schemes  
As the existing pricing-based spectrum-sharing schemes have differences in the network model and in utility function, it is difficult to compare them with our scheme. Nonetheless, we compare the performance in terms of trade success probability and fairness. All measures are based on 50 simulation runs. The trade-success probability of the proposed scheme is the probability of finding a unique NBS  
Figure 11: The discontinuous spectrum demand’s influence on licensed user’s utility.  
Figure 12: The existence of several subgame-perfect equilibria.  
before the ultimatum game. Network fairness (_F_) is calculated based on the [PERSON]'s fairness index [28], as follows:  
\[F=\left(\sum_{i=1}^{M}\sum_{j=1}^{N}\bigl{(}D_{j}\times x_{ij}\bigr{)}\right)^{2} \Bigg{/}\left(M\times\sum_{i=1}^{M}\left(\sum_{j=1}^{N}\bigl{(}D_{j}\times x_{ ij}\bigr{)}\right)^{2}\right), \tag{8}\]  
where \(F\) ranges from 0 to 1. To obtain the network fairness, this paper reset the bandwidth to an equal value.  
In Figure 13, we compare the performance of the proposed scheme with three published schemes: The MMS scheme [12], RPSA scheme [20], and DOCR scheme [11], in terms of network fairness. As various SNRs decide different spectrum demands for a licensed user (different demands lead to the differences for each licensed user), an obvious reduction in fairness occurs when the offered load (service request rate, i.e., spectrum demand divided by spectrum supply) is more than 1. Nonetheless, when the offered load is less than 1.5, the proposed scheme has an absolute advantage.  
When compared with the proposed scheme with three schemes: the RBA scheme [17], the RABL scheme [18], and the DASS scheme [19], in terms of the trade success probability, Figure 14 shows that the proposed scheme has the highest probability when the offered load is less than 1. The existence of the ultimatum game, does not mean that the proposed scheme cannot apply to a case where the offered load is greater than 1.  
Figure 14: Trade success probability.  
Figure 13: Network fairness.  
Note that the results shown in Figures 13 and 14 indicate that only the proposed scheme has a non-linear performance. This depends on the rules that spectrum price be directly related to the supply-and-demand relationship, and that unlicensed users buy spectra only when spectrum price leads to a non-negative utility. Different from existing schemes, the proposed scheme allows an unlicensed user to not buy spectra in this period for a positive utility. Therefore, when the offered load is greater than a certain value (almost 1), the rate of unlicensed users choosing to buy spectra will reduce significantly. Of course, it will reduce the trade success probability and fairness more substantially than other schemes. Therefore, as shown in Figures 13 and 14, when other schemes have an approximately linear performance, the proposed scheme cannot be obtained.
# Automatic Detection of Marine Litter: A General Framework to Leverage Synthetic Data
## 2 Materials and Methods
### Case Study on Sentinel-2
#### 2.2.3 Assessment of the Simulation Performance  
Figure 5 shows the output obtained by the simulation for the following inputs with a random jitter (constant across the entire image and all bands). For visibility purposes, only band B01 and B02 are displayed.  
* Shape: rectangle;
* Size: \(30\,\mathrm{m}\times 30\,\mathrm{m}\);
* Type of plastic: wet bottles frame;
* Rotation: 10 deg;
* Fraction of plastic: 1;
* Noise level: 0.01.  
It is easy to identify the bands with the best spatial resolution and the worst ones. Band B01 has a GSD of 60 m, the plastic pixels are barely recognizable on a seawater background without noise and with a noise with \(\sigma=0.01\), the plastic is no longer detectable. This observation also applies for bands B09 and B10. The bands with a GSD of 10 m (B02, B03, B04, and B08) are better suited for plastic detection with a sharp noticeable signal, even in the presence of noise.  
Figure 6 shows the spectral signature of both the plastic simulated with the inputs mentioned above and the plastic collected from an Level 2A S2 image acquired on 11 June 2021 over the Gulf of Gera on the island of Lesvos, Greece. The PLP team deployed a circular target of 28 m diameter made out of HDPE (high-density polyethylene) mesh for the PLP21 [39] and we collected the plastic spectral signature from this target. The fraction of plastic for the simulated image was set to 0.6 to match the fraction of plastic of the HDPE mesh, and the noise was set to 0.01. The reflectance values of the spectral signature are different in the visible range, particularly for B02, B03, B04 and B05. The reasons of these discrepancies could be that the materials are not exactly the same. More particularly, the colors are different: the HDPE mesh is white whereas the bottles frame material are supposedly transparent, explaining the lower reflectance values. All things considered, the results are satisfying and close to in situ measurements. However, as the noise level increases, the discrepancies increase as well and the spectral signature is less recognizable. For a noise with \(\sigma=0.02\), the results are not far from the ones at 0.01, but when it comes to a noise level of 0.1, the results are less satisfying.  
Figure 4: Illustration of the inputs and outputs of the simulation.
## 4 Results and Discussion  
### Performance Statement  
The experiment was conducted from June to July, 2019 in the laboratory environment. On the first day as shown in Figure 8, the prototype was verified at 620 W/m\({}^{2}\) solar radiation and 29 \({}^{\circ}\)C  
Figure 6: (**a**) Experimental setup of the developed hardware model; (**b**) Photovoltaic (PV) panel installation in the vicinity of the laboratory hardware model.  
Figure 7: Integration of MATLAB-dSPACE Code Generation block diagram.  
ambient temperature. The PV supply was sufficient (nearly 10.8 W) on that day to support the 5 W load demand. Since, the battery was contented with the maximum 80% SOC, the storage system resulted in an islanding mode to extend the battery execution lifetime.  
On the second day (540 W/m\({}^{2}\), 27 \({}^{\circ}\)C), 65% SOC containing battery was experimented and BMS changed the battery to charging mode for that day as shown in Figure 9. Because 8.2 W PV supply was adequate to charge the battery together with supporting the load demand. On the third day, the developed system was carried out in 55% SOC, 372 W/m\({}^{2}\) irradiance 23 \({}^{\circ}\)C atmospheric temperature. On this day, the PV supply (3.8 W) was insufficient to support the load demand. Hence, the battery bank was brought to the discharging mode to cover the load as shown in Figure 10. On the fourth day (322 W/m\({}^{2}\), 21 \({}^{\circ}\)C), the BMS was examined with the minimum 40% SOC. As shown in Figure 11, neither the PV supply, nor the battery source was able to deliver the load demand adequately. Hence, the BMS islanded the battery discharging file to maintain the battery life against deeper depth of discharge (DOD). The generated DC voltage is converted into AC voltage waveform as shown in Figure 12. Figure 12a shows the generated AC voltage from which the pure sine wave as shown in Figure 12b, is revealed for a particular period. Figure 12c shows the experimental modified AC signal obtained in the laboratory for the operation of low powered equipment.  
Figure 8: Experimental analysis for Day 1: 620 W/m\({}^{2}\), 29 \({}^{\circ}\)C.  
Figure 9: Experimental analysis for Day 2: 540 W/m\({}^{2}\), 27 \({}^{\circ}\)C.
# Marine Internet for Internetworking in Oceans: A Tutorial
## 4 Communication Systems in Oceans
### Maritime Radio System
To handle this problem, two additional 25-kHz channels have been suggested to support application-specific message communication, and six VHF channels have been used to design a VHF Data Enhanced System (VDES) [39] to provide a maximum rate of 302.2 kbps. Some advanced communication technologies such as Orthogonal Frequency Division Multiplexing (OFDM) and distributed antenna are also used for VDESs. Some results of the VDES channel sounding campaign are reported in [40]. Similarly for on-board communication for maritime operations, six ultra-high frequency (UHF) channels between 450 and 470 MHz are also used with narrower channel spacing [41; 42]. On the other hand, the communication capacity of maritime radio systems is insufficient for many Internet applications. For example, the audio codec bandwidth ranges in 11.8-128 kbps, and that for video is about 250-4000 kbps. Consider network protocol overheads incurred for transport, it requires an additional bandwidth of about 12.5-55.5% the original one for audio with only considering the IP header [43]. All these rates go beyond the capacity of the current maritime radio systems.
# Best Practices Evidenced for Software Development Based on DevOps and Scrum: A Literature Review
## 3 Results
### Quantitative Evidence of Scrum and DevOps Benefits
#### 3.7.2 Software Quality Improvements  
Scrum, as a key Agile framework, promotes continuous delivery, iterative development, and strong collaboration, according to the author of [4]. His findings highlight that Scrum enables teams to maintain steady velocity, improve predictability, and enhance product quality through shorter feedback loops and frequent releases.  
DevOps also contribute significantly to improved software quality. The authors of [93] analyzed over 250 open-source and proprietary projects, finding that CI adoption led to a 12% reduction in defect density and a 15% increase in developer productivity. Reinforcing these findings, the authors of [99] conducted a large-scale empirical study on GitHub projects and found that versioning and CI adoption increased the number of merged pull requests by 22% and reduced pull request resolution time by 18%, leading to better code quality and defect management, pointing to early and continuous feedback to generate deliverable quality.  
Additionally, automated testing practices further enhance software quality according to the authors of [111], who demonstrated that integrating automated testing frameworks improved test execution speed by 35% and increased defect detection rates by 18% compared with manual testing, as demonstrated using automated tests.
## 2 Experimental and Methods
### Fire Analysis
#### 2.2.2 Mesh Resolution  
The calculation accuracy strongly depends on the FDS mesh size. The size of the analysis grid can be determined by the characteristic fire diameter using Equation (1) in the fire plume analysis:  
\[\text{D}^{*}=\left(\frac{\dot{\text{Q}}}{\rho_{\infty}\text{C}_{\text{P}}\text{T }_{\infty}\sqrt{\text{g}}}\right)^{2/5} \tag{1}\]  
where D\({}^{*}\): characteristic fire diameter, \(\dot{\text{Q}}\): total heat release rate (kW), \(\rho_{\infty}\): outside air density (kg/m\({}^{3}\)), C\({}_{\text{P}}\): specific heat (kJ/kg\(\cdot\)K), T\({}_{\infty}\): outside air temperature (K), g: acceleration of gravity (m/s\({}^{2}\)), and \(\delta_{\chi}\): nominal size of a mesh cell.  
The D\({}^{*}\)/\(\delta_{\chi}\) parameter is only valid if the value is between 4 and 16 [24]. The D\({}^{*}\) applied to this analysis is 0.503 m, and in this paper, D\({}^{*}\)/\(\delta_{\chi}\) has a value of 10.06.
## 4 Numerical Procedure and Results
### Computational ElastoPlastic Stress Distribution around the Defect  
In this study, we considered the defect as a crack because it behaves like a notch, and the radius of curvature is too small. For that reason, we utilised the volumetric method. The distribution of the elastoplastic circumferential stress ahead of the defect is illustrated in Figure 5. The curve has a maximal value of \(\sigma_{\text{max}}~{}=~{}43,236\) MPa at \(X_{\text{max}}=0.09\) mm. The results are close to the work of [41], who carried out the simulation by the finite element method under CASTEM Software, obtaining \(\sigma_{\text{max}}=435.49\) MPa at \(X_{\text{max}}=0.087\) mm.  
The equation below presents the polynomial fit of the opening stress distribution:  
\[\sigma_{yy}(x)~{}=~{}\sum_{i=0}^{n}a_{i}x^{i} \tag{10}\]  
The polynomial fit approximation distribution of \(\sigma_{yy}\) and the gradient of this distribution are given in Figure 6. Moreover, we used relation (1) to compute the distribution of the relative stress gradient \(\chi\) ahead the defect. From Figure 6, we can extract the effective value \(X_{eff}~{}=~{}0.17\) mm, which correlates to the minimum of the relative stress gradient \(\chi\). Using equation (2) will allow us to determine the effective stress \(\sigma_{eff}~{}=~{}311\) MPa. The volumetric technique enables the estimation of the stress intensity factor as follows:  
\[K=~{}311\sqrt{2\pi\times 0.17}=~{}10.164\text{ MPa}\sqrt{m} \tag{11}\]  
Figure 5: The distribution of the elastoplastic circumferential stress ahead of the defect: (**a**) Result of the simulation by the XFEM technique; (**b**) the curve of \(\sigma_{yy}\).